9.0 Overview

The chapter first describes the challenges of tropical weather forecasting. Then, we examine types of observations and weather analysis techniques used by tropical forecasters. The last three sections focus on numerical weather prediction including: the fundamentals, comparisons of statistical and dynamical models, ensemble techniques, cumulus convection, tropical cyclone prediction, and forecast verification and validation. The Australian-Indonesian monsoon focus section applies various analysis and forecasting techniques. Finally, tropical cyclone forecasters describe their forecast routine.

Focus Areas

Quiz and Survey

Take a quiz and email your results to your instructor.

After completing this chapter, please submit a User Survey.

9.0 Overview »
Learning Objectives

At the end of this chapter, you should be able to:

• Discuss the unique challenges of weather forecasting in the tropics
• Describe types and methods of accessing weather observations in the tropics including: Point (surface and upper air), Radar (few ground-based, TRMM PR), geostationary satellites (clouds, surface, soundings), low earth orbiting satellites (precipitation, winds, water vapor, pollutants, lightning), GPS satellite soundings
• Discuss the advantages and weaknesses of different types of observations
• Describe sources of observation error
• Perform synoptic-scale analysis using streamlines, velocity potential, satellite images
• Identify major tropical features such as the ITCZ, Monsoon trough, and TUTTs
• Interpret radar and satellite imagery for mesoscale analysis and nowcasting
• Understand the conservation principles and associated equations
• Describe at least one method of data assimilation
• List sources of numerical model errors
• Describe characteristics of dynamical models
• Describe characteristics of statistical/inductive models
• Describe characteristics of dynamical-statistical models
• Explain what constitutes an ensemble forecast
• Describe strength and weaknesses of tools used to interpret ensemble forecasts
• Compare the relative advantages and disadvantages of these different types of models
• Explain the rationale for cumulus parameterization schemes
• Describe at least two types of commonly used cumulus parameterization schemes
• Describe the general characteristic of and rationale for cloud resolving models
• List factors that control tropical cyclone motion and intensity
• Provide a basic description of at least one statistical model used for tropical cyclone prediction
• Provide a basic description of at least two dynamical models used for tropical cyclone prediction
• Understand the basics of how ensemble techniques are applied to tropical cyclone prediction
• Describe techniques used to verify and validate tropical weather forecasts
• Discuss their advantages and inadequacies

9.1 Challenges of Tropical Weather Forecasting

Tropical weather is difficult to forecast. Midlatitude weather is dominated by synoptic systems moving in the westerlies, which formed the basis for the weather analysis methods developed in the 19th and 20th centuries. In the midlatitudes, baroclinic instability results from air masses with contrasting temperature and density. There, energy is concentrated in extratropical cyclones that can be tracked fairly easily. By comparison, the tropics have a relatively homogeneous air mass and fairly uniform distribution of surface temperature and pressure. Therefore, local and mesoscale effects are more dominant than synoptic influences, except for tropical cyclones. For example, surface temperature and pressure can change quickly with convection and sea breezes.

Numerical weather prediction (NWP) has been the key to rapid improvements in weather prediction in the midlatitudes but its benefits are yet to be fully exploited in the tropics. NWP presents its own challenges such as the need for parameterizations, difficulties with convective processes, and systematic errors¹ related to the assimilation of sparse and heterogeneous data.

Tropical weather forecasting cannot rely on midlatitude synoptic weather models or even climatology to meet these forecasting challenges. While midlatitude cyclones have readily observed pressure signatures, locating the pressure signature of many tropical weather systems can be difficult. Here we explore analysis tools and forecast methods appropriate to the unique complexity of tropical weather systems.

9.2 Observations »
9.2.1 The Global Observation System »
9.2.1.1 Point Observations

Upper-air stations are expected to report at least twice per day (usually 0000 and 1200 UTC) but many tropical stations only report once per day. Radiosonde wind measurements are calculated by following the instrument remotely and computing velocities from its displacement at fixed time intervals.

Instruments deployed for research field campaigns sometimes supplement routine weather observations and global data assimilation. For example, since 1997 the National Center for Atmospheric Research (NCAR) GPS Dropsonde system has provided high resolution vertical profiles of the atmosphere in support of operational weather forecasting and research. The first author was present when a dropsonde released from the NASA ER-2 aircraft during the 4th Convection and Moisture Experiment (CAMEX-4), provided the first stratosphere to surface profile of the eye of a tropical cyclone (Hurricane Erin 2001). The addition of dropwindsonde data has significantly improved tropical cyclone track forecasts—by 12-15% for the 12-48 h forecasts (Fig. 9.3).⁶

NCAR GPS Dropsonde, http://www.eol.ucar.edu/instrumentation/sounding/dropsonde

9.2 Observations »
9.2.1 The Global Observation System »
9.2.1.2 Remote Sensing: Area-averaged Observations

Satellite

Satellite remote sensing is the main source of routine tropical weather observations. Geostationary satellites plus polar and research satellites in low earth orbit (LEO) cover the global tropics (compare the coverage in Figs. 9.1 and 9.4), much of which is ocean.

Geostationary satellites offer wide spatial coverage and high temporal coverage (every 15-30 minutes) which makes them suitable for tracking weather phenomena, estimating winds from cloud driftestimating winds from cloud drift, nowcasting high impact weather, and data assimilation into NWP models. The next generation of geostationary satellites will have sensors currently available only on LEO, e.g., the geostationary lightning mapper on the GOES-R satellites will provide routine lightning observationslightning observations for weather analysis and forecasting.

LEO satellites offer high spatial resolution and are better suited for active instruments and microwave sensors. These satellites observe precipitation, winds, water vapor, lightning, and air quality. However, they have low temporal resolution and need a constellation to ensure a reasonable temporal sampling. Currently, significant gaps in coverage occur between LEO satellite swaths across the tropics (Fig. 9.4). The planned Joint Polar Satellite System (JPSS, formerly NPOESS) and Global Precipitation Measurement (GPM) mission, in combination with the European MetOp satellite, will dramatically improve coverage and the number of observations (Chapter 2, Focus 2Chapter 2, Focus 2).

Another critical tropical data void that satellites fill is atmospheric sounding. In addition to soundings from geostationary and LEOsoundings from geostationary and LEO satellites temperature and humidity profiles are derived from the occultation of signals from GPS satellitestemperature and humidity profiles are derived from the occultation of signals from GPS satellites. Real-time soundings from the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) are available from http://www.cosmic.ucar.edu/.

Radar

9.2 Observations »
9.2.1 The Global Observation System »
Box 9-1 Weather Observations

9.2 Observations »
9.2.1 The Global Observation System »
9.2.1.3 Observation Error

Observations serve to characterize the state of the atmosphere as accurately as possible. The defining characteristics of an observation network are the variables being measured, the instrument errors, and the spatial and temporal distribution of measurements. Errors in observations can be caused by poorly calibrated instruments,¹⁴ instrument siting,¹⁴ and human observer error.¹⁵ Observation error can be categorized as:

Rain gauges: Are They Really Ground Truth?, http://www.meted.ucar.edu/qpf/rgauge/

9.2 Observations »
9.2.1 The Global Observation System »
9.2.1.4 Status of Current and Future Observing Systems

Current surface and upper air observing systems are monitored twice per year by the WMO World Weather Watch (WWW). In some regions, such as tropical Africa, the numbers of observations have decreased during recent decades. Figure 9.5 shows the trend and geographic distribution of how frequently stations are reporting observations. Most of the stations in the tropics have a less than 50% rate of reporting and many are “dead” stations (Fig. 9.5b). Efforts are underway to reverse that trend in some regions. For example, through the African Monsoon Multidisciplinary Analysis (AMMA) program, operational agencies in Africa and AMMA scientists have been reactivating silent stations, renovating others, and installing new stations in West Africa.⁵

WMO Global Observing System, http://www.wmo.int/web/www/OSY/GOS.html
European Center for Medium-range Weather Forecast (ECMWF) data coverage maps,
http://www.ecmwf.int/products/forecasts/d/charts/monitoring/coverage/dcover

9.3 Weather Analysis

In order to forecast the weather, the forecaster needs to analyze the current weather. The primary tool of weather analysis is the weather map, on which all available data, needed to accurately depict the state of the atmosphere, are plotted. The scale of the weather phenomena being forecasted determines how frequent or dense the observations need to be. For example, short-term weather forecasts require very frequent observations over a small area while planetary-scale, long-range forecasts require a much less dense and less frequent network of observations. In recent decades, weather observation plotting has become an automated computer task but the manual method is still used in some tropical forecast centers.

In the next several subsections, we will examine a variety of tools commonly used for tropical weather analysis, from flow pattern analysis to remote sensing products, and finally, computer applications that help forecasters to synthesize observations and numerical model forecasts.

9.3 Weather Analysis »
9.3.1 Analysis Tools »
9.3.1.1 Velocity Potential and Stream Function

In general, the tropical wind field provides more information about synoptic conditions than the pressure or geopotential height field. According to Helmholtz’s theorem, the wind velocity can be separated into two components:

                                                                 (1)

The rotational wind, , has all of the vorticity and no divergence and has all of the divergence and no vorticity. Vorticity, a measure of the local rotation of the flow, is calculated as the cross product of the vector windVorticity, a measure of the local rotation of the flow, is calculated as the cross product of the vector wind and has units of inverse seconds (s^-1). Divergence measures the spreading out of the flow (also with units of s^-1). Figure 9.7 illustrates the differences between the rotational and divergent components of the wind velocity. The two components can be further broken down into variables that are useful for tropical weather analysis, the stream function, , and velocity potential, χ:

           Rotational wind,                            (2)
            Divergent wind,                              (3)

Rotational winds are parallel to the stream function contours and their speeds are proportional to the stream function gradient. Divergent winds flow out low velocity potential and their speed is proportional to the gradient of velocity potential (Fig. 9.7b,c). Velocity potential and stream function are defined at the equator which makes them useful for model initialization in the tropics.

Because the velocity potential is proportional to divergence, it can be used to track regions of upper-level divergence where convection is enhanced (Fig. 9.8). Divergence from deep convection drives tropical circulations.

Anomalies or deviations from the mean velocity potential are much more useful than actual values for distinguishing the regions of deep convection or suppression. Figure 9.8 illustrates the correspondence between 200 hPa velocity potential anomalies and deep convection identified by enhanced satellite IR imagery. In this example, the ITCZ can be identified as the broken band of convection extending from Central Africa west to the central Pacific. A broad area of deep convection is apparent over the Western Pacific.

Pacific Streamline Analysis Plots, http://www.prh.noaa.gov/cphc/pages/analyses.php
MJO indices, http://www.cpc.ncep.noaa.gov/products/precip/CWlink/MJO/index.primjo.html
Use of streamfunction and vorticity to objectively diagnose tropical waves,
http://www.atmos.albany.edu/student/gareth/diagnostics.html
NOAA/NWS Tropical Prediction Center Analysis Tools,
http://www.nhc.noaa.gov/analysis_tools.shtml
Tropical Analysis Charts, http://nomads.ncdc.noaa.gov/ncep/NCEP

9.3 Weather Analysis »
9.3.1 Analysis Tools »
9.3.1.2 Kinematic Analysis: Streamlines and Isotachs

Kinematic analysis creates a continuous representation of the wind field from observations of the horizontal wind velocity. Although the stream function is a better variable than isobars for low latitude weather analysis, it is not the best representation of the air flow. Streamlines and isotachs provide more details of the horizontal flow at a given level than isobars (Fig. 9.9a, d, and e). Streamlines are lines that represent the flow tangential to the instantaneous wind direction. Forecasters use streamline analysis to identify many features. Figure 9.9d shows examples of the following features:

In Figure 9.9 (a,b), both the streamline analysis and the isobaric analysis identify the tropical cyclone over the South China Sea, the ridge across Australia, and a cyclone over the northeast Pacific. However, only the streamline analysis (Fig.9.9b) shows the South Pacific Convergence Zone, including the cyclonic circulations of the cloud clusters. Confluence into the ITCZ on the eastern edge of the domain is also evident in the streamline analysis.

The plots in Fig. 9.9 are generated by an automated analysis system. However, the methods used to create the plots can make mistakes because of lack of data or bad data points.

Can you identify a significant cyclonic feature that the automated analysis missed?

Feedback:

The automated analysis did not identify Tropical Storm Kujira (Fig. 9.10). However, the storm is present in the Unified Surface Analysis created by forecasters at the U.S. National Weather Service, Ocean Prediction Center, and Tropical Prediction Center. This example highlights the importance of the human forecasters, who synthesize all of the information and improve on the automated system, which in this case does not account for the satellite data.

Fig. 9.10. Streamline analysis by an automatic objective technique (left) and the Unified Surface Analysis, an enhanced product created by NWS forecasters (right).

NOAA/NWS Unified Surface Analysis, http://www.opc.ncep.noaa.gov/UA.shtml

It is clear that the sparsely distributed station observations are insufficient to resolve all of the weather features, and therefore need to be supplemented by satellite products. Upper level streamline/isotach analysis is enhanced by the addition of satellite water vapor images (Fig. 9.11). The radiosonde observations resolve the jet stream speed and horizontal structure over Australia but do not fully resolve outflow from the two tropical cyclones.

NOAA/NWS Unified Surface Analysis, http://www.opc.ncep.noaa.gov/UA.shtml

9.3 Weather Analysis »
9.3.1 Analysis Tools »
9.3.1.3 Satellite Imagery

The sharp edge of the cold frontal clouds, extending northeast to southwest across the Atlantic, is evident in the visible images. The eastward flow at the upper levels is associated with the subtropical jet stream which has wind speeds greater than 40 m s^-1; as derived from cloud motion vectors (Fig. 9.12, right). Wind velocity in the lower troposphere is derived from visible images of clouds (Fig. 9.12, left).

Animation of IR, visible and water vapor images.

Moisture fields derived from satellite microwave measurements are especially critical for tracking synoptic features over the tropical oceans while combinations of LEO microwave and geostationary measurements provide precipitation estimates. The latter is especially critical because of the dearth of routine radar coverage. Figure 9.14a shows how satellite-derived total precipitable water (TPW) is combined with global model analysis to aid in forecasting tropical cyclogenesis in the Indian Ocean. Animations of TPW are useful for tracking the movement of tropical waves. Precipitation accumulations are estimated by blending measurements from TRMM Precipitation Radar, microwave, and geostationary IR (Fig. 9.14b).

Given the importance of satellite images to tropical weather analysis and forecasting, continuing education of tropical forecasters is necessary. Internet and other digital technologies are being exploited to enhance training in satellite interpretation for the tropics and elsewhere. For example, forecasters in the Caribbean, Central America, and South America have virtual monthly weather briefings, which use satellite images, animations, and allow participants to communicate using audio, text, and screen annotations.

Virtual Monthly Weather Briefing Focus Group of the Americas and the Caribbean,
http://rammb.cira.colostate.edu/training/rmtc/focusgroup.asp
WMO-CGMS Virtual Laboratory for Education and Training In Satellite Meteorology
http://www.wmo-sat.info/vlab/
Report on Centers of Excellence in Satellite Training,
http://www.wmo-sat.info/vlab/regional-focus-groups/

Archives of scatterometer wind vectors, http://manati.orbit.nesdis.noaa.gov/quikscat/
http://manati.orbit.nesdis.noaa.gov/cgi-bin/quikscat_amb_glo.pl
Real-time 3-hourly tropical rainfall analysis,
http://precip.gsfc.nasa.gov/rain_pages/3hrly.html

9.3 Weather Analysis »
9.3.1 Analysis Tools »
9.3.1.4 Radar Imagery

Operational weather radars in the US NWS scan in: (i) Clear Air Mode that is, typically, more sensitive, detects bugs, dust and is useful for identifying boundaries such as gust fronts; (ii) Precipitation Mode that detects precipitation and storm structure but is less sensitive.

Reflectivity

The most frequently used radar images are base and composite reflectivity, which show the location, intensity, and type of precipitation (e.g., Fig. 9.15). The Plan Position Indicator (PPI) radar display is used to analyze the horizontal structure of convective weather systems. Radar observations help refine the placement of frontal boundaries and gust fronts. The latter is often only evident when radars scan in clear air mode. Animations of radar images are valuable for short-term forecasting or nowcasting of severe weather and flash floods. For example, on 6 May 2001, areas in western Puerto Rico experienced flash floods that killed two people and caused damage worth $146 million.²⁰ While the visible satellite image, in Fig. 9.15, shows widespread cloudiness associated with the trough, the radar reflectivity image shows the detailed structure of the precipitation. Within the large precipitation band are several heavy precipitation cells, with the heaviest concentrated over the southwestern part of the island. Animation of the radar image shows hours of heavy precipitation over that region where convection was enhanced by orographic uplift along the “Cordillera Central” (inset map, Fig. 9.15).

Animation of the radar images

The PPI reflectivity scans capture the distribution of convective and stratiform precipitation in a tropical squall line passing over Niger, West Africa (Fig. 9.16a). The propagation velocity of various features, such as the convective line or the gust front, can be estimated.

Vertical scan or Range Height Indicator (RHI) display is another useful tool for analysis and forecasting. The RHI images show strong reflectivity in the convective updrafts, up to 13 km (Fig. 9.16b). The convective downdrafts and updrafts, at the leading edge of the squall line, are of special interest to aviation forecasters who issue severe turbulence warnings. Later in the lifecycle of the squall line, the convective line decays but stratiform precipitation continues. The bright band of strong reflectivity just below 5 km is associated with melting ice particles.

Forecasters can glean more information about mesoscale and convective scale phenomena from Doppler radar wind velocity images. Using the case of Hurricane Rita near landfall, we can understand how to interpret velocity images (Fig. 9.18). The green areas indicate movement toward the radar and red areas indicate movement away from the radar. The yellow arrows show the general counter-clockwise motion around the eye. Remember that the radar beam is angled upward which means that farther observations are at higher altitude. For instance, in the image of Rita, numbers 1 to 3 indicate winds at increasing distance and altitude.

Doppler velocity is very useful for the identification of mesocyclones and tornadoes (Fig. 9.19). The signature is a velocity couplet indicating the mesocyclone circulation (indicated by the white arrow in Fig. 9.19b). The reflectivity signature is referred to as a “hook” echo because of its shape (white arrow in Fig. 9.19a). Fig. 9.19c is an example of a hook echo observed over Australia. In the cross-section of Figure 9.19d, the weak echo region bounded by high reflectivity indicates a strong updraft.

The Doppler velocity can also be used to derive an averaged wind profile. A Velocity Azimuth Display (VAD) wind profile is a time-height display of wind velocity (Fig. 9.20). It is derived from a volumetric sample of backscatter from dust, insects, and cloud droplets. The VAD wind profile is used to diagnose vertical wind shear, the depth of the boundary layer, and boundaries such as fronts, dry lines or sea breezes.

Precipitation

On a daily basis, a large community of users is interested in knowing when, where, how much, and what type of precipitation to expect. For example, quantitative precipitation estimates and forecasts are needed to manage agriculture, water resources, and renewable energy. Radar data provide high resolution spatial and temporal information on rainfall (Fig. 9.21) distribution which is useful for forecasting normal precipitation as well as high impact hydrometeorological events such as flash floods.

Animation of reflectivity

Animation of rainfall total estimates

Precipitation is derived from relating a reflectivity factor, Z, to the number and size of raindrops per cubic meter (a measure of rainfall rate, R).

where Z is the reflectivity factor, D is the drop diameter, and N(D) is the number of drops of given diameter per cubic meter. “Z-R” relationships make assumptions about the drop size distribution of hydrometeors encountered by the radar beam. Different Z-R relationships are used for different atmospheric conditions. For example, a “convective” Z-R relationship is used with warm moist air and high concentrations of large droplets. Errors in radar-derived precipitation result from:

Polarimetric radar can improve the accuracy of precipitation when compared to standard Z-R methods because they differentiate between echoes from hydrometeors and non-hydrometeors and improve classification of hydrometeor types.^21,22 Learn more about radar precipitation estimates in COMET Module, Precipitation Estimates, Part I: Measurement, http://www.meted.ucar.edu/hydro/precip_est/part1_measurement/

NWS Doppler Radar Tutorial,
http://www.srh.noaa.gov/srh/jetstream/doppler/doppler_intro.htm
Dual Polarization Radar Training,
http://www.wdtb.noaa.gov/modules/dualpol/

9.3 Weather Analysis »
9.3.1 Analysis Tools »
9.3.1.5 Thermodynamic Diagram: Radiosonde Analysis

Radiosondes are released at 0000 and 1200 UTC each day and provide a vertical profile or "sounding" of the atmosphere. Vertical profiles are also provided by aircraft and satellite measurements. Thermodynamic diagrams (e.g., Skew-Temperature-LogPressure diagram, Fig. 9.22) help forecasters to determine the relative humidity, stability, vertical wind shear, severe weather, and flash flood potential of the atmosphere in the vicinity of the sounding. For instance, the sounding in Fig. 9.22a shows a deep layer of saturated and near saturated air up to 500 hPa, unstable temperature profile, weak mid-level shear, all of indicators of heavy rainfall. Additional factors in enhanced upward motion are strong mid-upper level shear associated with an upper-level trough and divergence; warm, moist easterly flow towards high terrain enhances orographic precipitation. Not surprising, this profile, with deep layer of moisture, near moist adiabatic temperature in the lower troposphere, and vertical wind shear to sustain long-lived convection and heavy precipitation, was associated flash floods in Puerto Rico.

Most forecast centers have programs to calculate and display key forecast parameters from thermodynamic diagrams. Critical information from the thermodynamic profiles includes:

9.3 Weather Analysis »
9.3.1 Analysis Tools »
9.3.1.6 Vertical Cross Sections

Upper air data, usually from radiosondes, provides information about the vertical structure of weather systems. Cross-sections through various layers provide information about where the air is rising or sinking, moist and dry layers, and the vertical extent of surface or upper tropospheric fronts. Using the Puerto Rico floods of 6 January 1992 as an example, we see an influx of air with high equivalent potential temperature (θ_e) at 850 hPa, one indicator of high flood potential (Fig. 9.23). A cross-section through the layer of high θ_e air reveals other ingredients for the deep convection and heavy rainfall over Puerto Rico: A deep layer of high specific humidity and rising motion.

9.3 Weather Analysis »
9.3.1 Analysis Tools »
9.3.1.7 Trajectories

Trajectory analysis is used to monitor and forecast dispersion and deposition of pollutants such as volcanic ash, dust, smoke, and other aerosols. Air parcel trajectories are calculated by integrating data from discrete points in space and time (x,y,z,t) into a continuous function. Air pollution dispersal models have been adapted for various applications and regions. Most dispersion models ingest gridded NWP model output to calculate transport and diffusion of pollutant plumes. Backward trajectories are useful for determining the source region of pollutants in the forecast region of interest. Forward trajectories show where pollutants from a source region will travel.

The HYbrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) is run by US National Weather Service, the Australian Bureau of Meteorology, and the Volcanic Ash Advisory Centers (VAAC). HYSPLIT trajectory maps typically show plan and vertical views of the air parcels paths (Fig 9.25); these can also be projected onto Google Earth (Fig. 9.25b). The position of the air parcel for a user-defined period is marked along the trajectory. HYSPLIT applies to gases and particles that have limited chemical reactivity and with neutrally buoyant releases. Like other dispersion models, HYSPLIT inherits errors from the underlying NWP model. HYSPLIT also has problems with flow and dispersion through complex terrain on scales not resolved by the meteorological model (HYSPLIT Applications for Emergency Decision Support, http://www.meted.ucar.edu/training_module.php?id=773).

NOAA ARL/READY, http://www.arl.noaa.gov/ready.php
NOAA Smoke Forecasts, http://www.arl.noaa.gov/smoke.php
Ocean Prediction Center, Volcanic Ash, http://www.opc.ncep.noaa.gov/volcano/

9.3 Weather Analysis »
9.3.1 Analysis Tools »
9.3.1.8 Marine Analysis

Marine forecasters predict the state of the ocean and other open waters such as large lakes. Of primary concern are waves: their steepness, height, velocity, period or wavelength, shoaling (where long waves become steep in shallow water), and degree of confusion (when different waves are present). For marine forecasts, we need to analyze:

• Winds
  Wind stress is the primary driver of waves, so accurate marine wi0nd analysis and forecast are critical to marine forecasts. The wind stress, τ, varies as the square of the wind, τ = ρ_a C_D U², where ρ_a is the density of air, C_D is the drag coefficient, (a measure of the roughness of the ocean surface determined empirically), U is the wind speed. Swells are waves that have moved out of its wind generation source region and are usually less steep than the original wave.

• Wave Speed and Wavelength
  Wave speed depends on wavelength. For deep water waves, the longer the wavelength, the faster the wave speeds. Wave speeds slow as water becomes shallower and the waves become steeper. Note that wave group velocity (not individual wave speed) must be used to estimate the time it takes for waves/swell to arrive at a given location.

• Wave Height and Wave Energy
  As wave height doubles, wave energy quadruples. This relationship is very significant in forecasting wave height. Forecasts of wave heights must be kept within a narrow range as inaccuracies in height are multiplied dramatically for wave energy and the potential for destruction.

Forecasters focus on forecasting "significant wave height" or “combined seas” and "peak wave period" while bearing in mind that a spectrum of waves make up the total sea state. Trained observers report wave heights that most often correlate with the mean height of the highest one third of the waves passing a point. Another useful operational concept is “Maximum Combined Seas”, the maximum height likely to occur when one or more wave groups pass a location simultaneously. The Maximum Combined Seas can be much greater than the height of any individual wave or swell, especially if there are multiple swells and/or wave groups with similar periods. Such situations can create waves with dramatic heights, so called rogue waves.

Observations of the sea state are obtained from buoys (Fig. 9.26) and from satellite sensors (Fig. 9.13a, 9.13b, 9.13c). The current network of ocean observations is shown in Figs. 9.1c and 9.4d. Observations are analyzed and combined with guidance from wave models to produce forecasts such as wave heights (Fig. 9.27).

• Temperature, Salinity and Currents
  Observations over the ocean suffer from sparseness and measurement errors. Ocean circulation models combine these observations with physics to create analyses for diagnosing temperature, salinity, currents, and sea height (Fig. 9.28).

A set of interactive wind and wave forecasting tools are available from COMET at http://www.meted.ucar.edu/marine/widgets/. You can learn more about wind and wave forecasting in the COMET distance learning course on wind and wave forecasting at http://www.meted.ucar.edu/dl_courses/Wind_Wave_Fcsting/.

National Data Buoy Center (NDBC), http://www.ndbc.noaa.gov/
NCEP Marine Forecasts,
http://mag.ncep.noaa.gov/NCOMAGWEB/appcontroller
NOAA/NWS/NCEP Ocean Prediction Center, http://www.opc.ncep.noaa.gov/

9.3 Weather Analysis »
9.3.1 Analysis Tools »
9.3.1.9 Synthesis

Modern digital tools allow forecasters to overlay a variety of data and zoom to assess the weather at various scales. In the following sections, we explore each scale in turn. Even in the modern era, manual skills are still useful to synthesize the information and to make adjustments where the automated techniques fail to capture critical features. Figure 9.29 shows two examples of operational display and analysis systems. The first one shows the overlay of radar, satellite, surface observations, and lightning flashes on a map of towns and highways. The radar reflectivity allows the forecaster to see the intensity and structure of the thunderstorm cells. The widespread cloudiness is shown by the grayscale visible satellite image. Station plots (peach) and lightning (green) show weather at specific locations. In the second example, from Synergie, colored symbols illustrate circulation features, weather systems, and boundaries to provide a synthesized picture of the weather.

US National Weather Service, AWIPS, http://www.srh.noaa.gov/mob/?n=awips
NOAA/NWS Aviation Weather Analysis, http://aviationweather.gov/

Examples of synthesized tropical weather analysis

African Centre of Meteorological Application for Development (ACMAD),
http://www.acmad.ne/en/homepage.htm
Unified Surface Analysis, http://www.opc.ncep.noaa.gov/Loops/#Unified_Surface_Analysis_Products
Tropical Analysis Charts, http://nomads.ncdc.noaa.gov/ncep/NCEP (choose from list)
South African Weather Service, http://www.weathersa.co.za/

NCEP International Desk Non-operational Products (may not be current or available on a routine basis)
http://www.hpc.ncep.noaa.gov/international/intl2.shtml#charts
http://www.hpc.ncep.noaa.gov/discussions/fxca20.html
http://www.hpc.ncep.noaa.gov/discussions/fxsa20.html
http://www.hpc.ncep.noaa.gov/international/scs/Columbia4.html

9.3 Weather Analysis »
9.3.2 Global-scale Circulations:Top of the Forecast Funnel

Now that we have identified various analysis tools, we are ready to start tropical weather analysis. Using the principle of the forecast funnel(from the large-scale to the small-scale), forecasters should be first aware of the climatology and the planetary circulations that affect their region.

One of the most important features of the tropical atmosphere is the equatorial trough, the region of minimum surface pressure. The northeast and southeast trade winds converge into this low pressure, hence its other name, the InterTropical Convergence Zone (ITCZ). The ITCZ is usually identified as a belt of thunderstorms around the global tropics but it is not continuous and the cloud systems within it change every day (for example, see Fig. 9.8). The equatorial trough, convergence zones, and other surface circulations migrate through the year in response to surface heating (Fig. 9.30).

As illustrated in Fig. 9.30 (bottom panel), the trade winds converge north of the equator over the eastern Pacific. The convergence zone is known there as the Near Equatorial Trade Wind Convergence (NETWC). For Asia and Australia, the maximum heating and low pressure are in continental regions far from the equator. There the trough is part of the monsoon system and referred to as the Monsoon Trough. Flow into the monsoon trough is predominantly westerly (in contrast to easterlies elsewhere in the tropics). Flanking the equatorial trough are the subtropical highs and ridges, regions of subsidence.

Two quasi-permanent and extensive convergence zones lead to tropical-temperate interactions: the South Pacific Convergence Zone (SPCZ)²⁴ and the South Atlantic Convergence Zone (SACZ).^25,26,27,28 The SPCZ and SACZ are oriented northwest to southeast from the tropics to the subtropics. They are broad features with precipitation extending more than 30° longitude (Fig. 9.31).

9.3 Weather Analysis »
9.3.3 Intra-seasonal Analysis for Tropical Weather Forecasting

The relationship of MJO phase and tropical cyclone genesis is valuable for tropical forecasting. MJO indices used as predictors of the probability of tropical cyclone formation increased forecast skill out to about three weeks for the south Indian and Pacific Ocean basins.³³

Equatorial Waves

Equatorial Rossby waves are identifiable as cyclonic vortex twins in the Northern and Southern Hemispheres at 850 hPa (e.g., Fig. 9.33, Fig. 5.17, Fig. 8.21). Equatorial waves sometimes form in succession, e.g., in Fig. 9.33e,f. The large-scale pattern can also transition from Mixed Rossby to equatorial Rossby wave (Fig. 9.33a,b) and vice versa within a couple of days.

MRG waves are evident as anti-symmetric circulations about the equator, an anticyclonic circulation in one hemisphere and a cyclonic circulation in the opposite hemisphere (e.g., Fig. 9.33a, 9.34, Fig. 5.18, Fig. 8.22). Strong cross-equatorial flow between the high and the low at 850 hPa is another marker of MRG waves (Fig. 9.34c).

MJO real-time analysis, http://www.cpc.ncep.noaa.gov/products/precip/CWlink/MJO/mjo.shtml
MJO real-time discussion archive, http://www.cpc.noaa.gov/products/precip/CWlink/MJO/ARCHIVE/
MJO indices, http://www.cpc.ncep.noaa.gov/products/precip/CWlink/MJO/index.primjo.html
Real-time analysis and forecast of equatorial waves, Chapter 4: Table 4.2Chapter 4: Table 4.2

9.3 Weather Analysis »
9.3.4 Synoptic-scale Analysis

Unified Surface Analysis, http://www.opc.ncep.noaa.gov/Loops/#Unified_Surface_Analysis_Products
NCEP Model Analyses, Regional and Global, http://mag.ncep.noaa.gov/NCOMAGWEB/appcontroller
NOAA/NWS Facsimile Weather Maps, http://weather.noaa.gov/pub/fax/Areadme_first.html
Tropical Analysis Charts, http://nomads.ncdc.noaa.gov/ncep/NCEP
Regional and Global Analysis, Australia Bureau of Meteorology,
http://www.bom.gov.au/nmoc/MSLP.shtml

NCEP International Desk Non-operational Products (may not be current or available on a routine basis)
http://www.hpc.ncep.noaa.gov/international/intl2.shtml#charts
http://www.hpc.ncep.noaa.gov/discussions/fxca20.html
http://www.hpc.ncep.noaa.gov/discussions/fxsa20.html
http://www.hpc.ncep.noaa.gov/international/scs/Columbia4.html

9.3 Weather Analysis »
9.3.4 Synoptic-scale Analysis »
9.3.4.1 Common Tropical Synoptic-scale Systems

While not as varied or as strong as midlatitude synoptic weather systems, synoptic weather systems are common to many parts of the tropics. For example, the tropical north Pacific is affected by cold fronts and subtropical low pressure systems during the boreal winter, tropical upper tropospheric troughs (TUTTs),^35,36 and tropical cyclones and their precursors (Fig. 9.35). Similar systems affect weather in the tropical Atlantic and south Pacific. The Indian subcontinent and Indian Ocean are affected by monsoon low pressure systems, also referred to as monsoon depressions.^37,38 Southern Africa experiences dramatic inflow of tropical moisture and heavy rainfall with the passage of tropical-temperate troughs (TTT). ³⁹

TUTTs

TUTTS are semi-permanent summertime features of the Atlantic and Pacific Oceans. Streamline analysis of the 200 hPa winds is a useful tool for identifying TUTTs (Figs. 9.35c and 9.36). Divergence downwind of the TUTT enhances rising motion, low-level convergence, and precipitation (Fig. 9.35c). TUTTs contribute to tropical cyclogenesis where the upper trough location relative to low-level circulation reduces the vertical wind shear. Occasionally, a TUTT will become warm-cored and develop into a tropical cyclone. Learn more about TUTTs in the COMET module, Topics in Tropical Meteorology, http://www.meted.ucar.edu/tropical/met_topics/.

Subtropical Cyclones

These cold-core subtropical cyclones form from the tail-end of midlatitude cyclones during the boreal winter. Over the north central Pacific, they can linger and meander for a more than a week (and, occasionally, weeks).^41,42 Typical weather is overcast skies, heavy rains and flooding, severe thunderstorms, and strong winds. Subtropical cyclones over the north Pacific are known as Kona lows because of their association with rainfall over Hawaii.

The typical synoptic pattern of a Kona Low is shown in Fig. 9.37; the analysis tools are surface isotherms, sea level isobars, and enhanced satellite IR temperatures. A trough extends equatorward from the low during its early to intensifying stages. Most of the precipitation is on the downstream side of the low pressure center. During the intensifying and mature stages, clouds and precipitation form a comma shape around the surface low. A high strengthens to the north and east of the low. As the cyclone reaches its dissipation stage, the flow around the low becomes more zonal.

Monsoon Depressions

Monsoon depressions are synoptic-scale low pressure systems that are prevalent over the Indian subcontinent and surrounding waters during the summer monsoon.^37,38 They last for 3–6 days and typically move west-northwestward at 2–6 m s^-1.³⁸ They tilt southwestward with height. Compare the streamline analyses of the surface low location, the 500 hPa cyclone, and 300 hPa trough in Fig. 9.38.⁴³ The heaviest rainfall is usually west of the surface low and the cloud pattern at maturity can resemble weak tropical cyclones (Fig. 9.38d). Many monsoon depressions form from the regeneration of residual low pressure systems that move west from the West Pacific and South China Sea.⁴⁴ The term monsoon depression has also referred to similar systems that form during the Australian-Indonesian monsoon.

Australian Bureau of Meteorology, Regional and Global Analysis,
http://www.bom.gov.au/nmoc/MSLP.shtml
Indian Meteorological Department, http://www.imd.ernet.in/main_new.htm
Indonesian Meteorological and Geophysical Agency, http://www.bmg.go.id/
Malaysian Meteorological Department,http://www.met.gov.my/?lang=english
Pakistan Meteorological Department, http://www.pakmet.com.pk/
Singapore Meteorological Service, http://app2.nea.gov.sg/3hnowcast.aspx

Tropical Temperate Troughs

Tropical-temperate troughs (TTT)³⁹ are troughs that connect westerlies with tropical disturbances and brings heavy rainfall to southern Africa. TTTs are summer time phenomena that are somewhat analogous to the semi-permanent SPCZ in the South Pacific and SACZ in the South Atlantic (Fig. 9.31). Generally, a channel of warm, moist air and associated deep convection extends from the NW to the SE as illustrated in Fig. 9.39. One of the signatures of the TTT is strong inflow of tropical moisture by a low-level jet at 850 hPa as seen over along the southern African coast in Fig. 9.39.

Cold fronts

Cold fronts that extend into the tropics do not have a strong temperature gradient; therefore the primary methods used to locate fronts are wind velocity shifts and humidity gradients. Typical winds in advance of the front are from the equatorward side of the front and the air is relatively humid compared with stronger winds and lower humidity on the poleward side. In the Fig. 9.40 example, winds are from the E to SE ahead of the front, and from the NW behind. Kingston, Jamaica is behind the front with dew point at 18°C, while southeast of the front the dewpoint is 24°C although both locations have the same temperature.

How often are tropical regions affected by cold fronts? The number varies by region. For the Dominican Republic, in the northern Caribbean, 15-20% of their winter days are affected by frontal passage; fronts are the primary synoptic weather systems that cause heavy precipitation and thunderstorms during winter.⁴⁵ The frequency of cold fronts is modulated by interannual oscillations and decadal oscillations. For example, during El Niño winters, strong cold fronts and floods are more frequent across the Caribbean and Central America.^46,47 Forecasters should be aware of the climatology of fronts for their region.

Sometimes a surface trough (dashed line in Fig. 9.40) develops in advance of the front and can bring heavy rainfall. These pre-frontal troughs are usually identified from the surface or gradient level wind field; with winds from the equator on the east side of the trough.

Tropical cyclones and tropical easterly waves

NOAA/NWS Tropical Prediction Center Analysis Tools, http://www.nhc.noaa.gov/analysis_tools.shtml
Unified Surface Analysis, http://www.opc.ncep.noaa.gov/Loops/#Unified_Surface_Analysis_Products
Regional and Global Analysis, Australian Bureau of Meteorology,
http://www.bom.gov.au/nmoc/MSLP.shtml

9.3 Weather Analysis »
9.3.4 Synoptic-scale Analysis »
Box 9-2 Operational Procedure for Synoptic Weather Analysis

While specific analysis tasks may be automated or manual, the following procedure is common to most forecast centers. Weather analysis has been enhanced by the ability to animate, zoom, create cross sections, do rapid combinations of different fields, and to create derived products. Manual methods yield some of that information by overlaying each weather field on a transparent chart on a light table or by analyzing each field with a different colored pencil on the same map.

Climatology and Planetary-scale Circulations

1. Forecasters should be aware of monthly climatology for their area.
2. Examine the current ENSO and MJO assessment and forecast. See if local area is in a favorable location for decrease or increase in precipitation due to passage of the MJO.

Surface and Gradient Level charts

1. Plot all current observations on weather map (a few hours may be plotted to supplement current observations, e.g., Fig. 9B2.1).
2. Examine satellite images (mainly IR, visible), animate geostationary images for previous 12-24 hrs.
3. Identify boundaries such as fronts or the ITCZ with the appropriate symbols.
4. Strive for consistency and continuity with the previous forecast; make incremental adjustments.
5. Analyze pressure field (1-2 hPa interval for the tropics, except for tropical cyclones where larger intervals are necessary).
6. Animate pressure analysis for synoptic hours from previous day (for continuity/trends).
7. Refine current pressure analysis and boundary positions based on supplemental data such as winds or precipitation from LEO satellite images received within past 3 hrs.
8. Analyze streamlines and isotachs based on point and satellite observations.
9. Overlay streamlines on satellite images and animate to refine analysis.
10. Where available, overlay analyzed divergence/convergence contours.

Fig. 9B2.1. (a) Few observations at 0600 UTC and (b) supplemental observations added over an 18-hour period. Different shades indicate the age of the observations.

Upper-Level charts

1. Plot all current observations on your weather map.
2. Examine satellite images (water vapor, enhanced IR, visible), animate geostationary images for previous 12-24 hrs (every hour).
3. Analyze geopotential height field (10 dam interval for the tropics, except for tropical cyclone where larger intervals are necessary).
4. Analyze streamlines and isotachs based on point and satellite observations.
5. Overlay streamlines on water-vapor satellite images and animate to refine analysis of synoptic features.
6. For 250 and 200 hPa, overlay divergence/convergence on streamline analysis.
7. For 850 hPa, analyze the equivalent potential temperature to help identify heavy rainfall and severe weather potential.

NCEP International Desk Non-operational Products (may not be current or available on a routine basis)
http://www.hpc.ncep.noaa.gov/international/intl2.shtml#charts
http://www.hpc.ncep.noaa.gov/discussions/fxca20.html
http://www.hpc.ncep.noaa.gov/discussions/fxsa20.html
http://www.hpc.ncep.noaa.gov/international/scs/Columbia4.html

9.3 Weather Analysis »
9.3.5 Mesoscale and Convective-scale Analysis

As mentioned at the start of this chapter, tropical weather is dominated by local and mesoscale effects rather than by synoptic influences (except for tropical cyclones and even there the core and rainbands are mesoscale features). Summer and winter weather systems over the Caribbean are used to demonstrate some mesoscale analysis and nowcasting techniques such as satellite analysis, radar interpretation, and surface meteograms.

9.3 Weather Analysis »
9.3.5 Mesoscale and Convective-scale Analysis »
9.3.5.1 Satellite-based Mesoscale Analysis

Mesoscale analysis begins with diagnosis of the synoptic regime. First, we look at a winter weather case that included a cold front and pre-frontal trough (shown in Fig. 9.40). We know that these systems usually bring rain to a large area. But how will the rainfall intensity vary within that large area? How will rainfall evolve at the mesoscale?

Enhanced satellite IR images are used to identify mesoscale convective systems (MCSs). First, we identify the most intense convection from the coldest cloud tops, the white areas in Fig. 9.41. Next, we examine the shape and evolution of the convective features. Between 0000 and 1800 UTC on 5 January, the cloud tops are becoming colder. In addition, many more cold clusters are forming and moving southward over the northeastern Caribbean islands. After 1800 UTC, the area of cold cloud decreases but the convection increases in intensity, changes shape, and expands westward. By 0200 UTC 6 Jan, the coldest clouds are aligned in an east-west pattern with an apex formation to the west. An apex point formation in the enhanced IR image indicates back-building (new cells forming upstream of the old cells). When new cells form and track over the same location as the old cells, the result is saturated ground, increased runoff, and flash floods. The ensuing flash flood was one of the worst recorded in Puerto Rico (23 deaths and 88 million US dollars in damage).²³

The synoptic diagnosis shows support for MCS formation over Puerto Rico; the surface trough and approaching cold front (Fig. 9.40), the inflow of high θ_e air at 850 hPa (Fig. 9.23a), and a deep layer of moisture and uplift (Fig. 9.23b). The satellite IR imagery provides the mesoscale details that indicate the flash flood potential. Given the significant impact of these kinds of large MCSs, it is easy to see why it is critical to identify their satellite signature.

 Why should tropical weather forecasters be alert to small mesoscale and convective-scale systems?

To help answer that question, we will now explore summer weather events over the Caribbean. We will use a case identified by Kathy-Ann Caesar of the Caribbean Institute for Meteorology and Hydrology.

With synoptic-scale features such as Tropical Storm Gustav over the east central Caribbean and an associated trough over the eastern Caribbean, and the ITCZ (Fig. 9.42a), it is tempting to ignore other, smaller weather systems (Fig. 9.42b,c).

Rain bands move from south to north across the islands following the flow into Gustav. However, Gustav's rain bands are not the only source of precipitation on 25 August. Confluence along the ITCZ and inflow into Gustav (Fig.9.43) leads to the formation of an intense mesoscale convective system (MCS, Fig. 9.42b) over Venezuela and Trinidad and Tobago. As we move down to smaller spatial scales (Fig. 9.42c), we notice narrow bands of clouds to the east of the MCS. How do these cloud bands fit into the precipitation picture on this day?

Animation of IR and visible images of MCS, gust fronts, and convective cells

Figure 9.44 shows the merging of an eastward moving thunderstorm gust front and southeasterly cloud bands over the eastern Caribbean. With a strong mesoscale system over the southern Caribbean during the morning (Fig. 9.42b, Fig. 9.44a), the formation of a strong gust front is not surprising. This gust front remained well defined over a long distance—indicating that the downdrafts generated by the MCS were relatively cool. In fact, Piarco Airport in Trinidad experienced a 3°C drop in temperature with the onset of moderate rain and thunderstorms (Fig. 9.45). For forecasters in the neighboring islands, frequent high-resolution, geostationary satellite images are the only available means of tracking the narrow cloud bands associated with gust fronts over the ocean.

These thunderstorm outflow boundaries are different from cloud lines that form along synoptic shear lines over tropical oceans. The latter often form perpendicular to an abrupt change in the horizontal wind, last for several days, and move with the synoptic flow. Gust front duration is on the order of hours and their pattern will match flow emanating from existing thunderstorms.

9.3 Weather Analysis »
9.3.5 Mesoscale and Convective-scale Analysis »
9.3.5.2 Radar-based Mesoscale and Convective-scale Analysis

Fig. 9.46. Radar reflectivity of convection over Puerto Rico and vicinity, 6 May 2001.
Animation of the radar reflectivity images

Radars enhance forecasters’ ability to monitor and forecast mesoscale and convective-scale phenomena. We will use the Puerto Rico floods of 6 May 2001 (Fig. 9.36) to illustrate. Synoptically, a TUTT produces a broad precipitation band. But, the mesoscale structure and intensity of the precipitation is varied (Fig. 9.46). Radar analysis shows the impact of the island on the precipitation band. As the large precipitation band moves closer to Puerto Rico, the heavy precipitation line breaks into smaller multi-cellular structures. The northern part becomes weaker and more stratiform. By 1700 UTC, the line has two bow echoes along the west coast, critical features to monitor because they can produce swaths of damaging, straight-line surface winds. The most intense cells are concentrated over the southwest. From 1800 to 2200 UTC, the heaviest precipitation is oriented almost west to east with new cells forming to the west and moving along a similar track as older cells. After 2300 UTC, the intense cells are again aligned along a SW-NE line. Other interesting features, revealed by the radar, are lines of new cells forming in advance of the main band of precipitation, indicating uplift along thunderstorm outflow boundaries. An example can be seen at 2303 UTC. Animation of the radar images also shows bands of precipitation to the north of the island oriented from SE to NW and moving towards the northeast.

9.4 Numerical Weather Prediction in the Tropics »
9.4.1 Fundamentals of Numerical Models

Numerical prediction models are ubiquitous in modern weather forecasting. The theoretical basis for numerical weather prediction (NWP)⁴⁸ is dynamical meteorology, which provides the equations that describe the evolution of the atmosphere. Dynamic forecasting predicts the future state of the circulation using numerical approximations of the dynamic equations.

The first attempt at NWP was made by British scientist, L.F. Richardson, who, in 1922, described a procedure for approximating the equations of motion as algebraic difference equations that could be computed for a finite set of grid points. An initial state would be extrapolated forward over a short period to give future estimate. Richardson’s experiment failed to make a decent forecast, in part because of Lamb waves (acoustic waves), dominating the solution. Using the complete equations can create problems, so that filtering the equations (while less accurate in an absolute sense) keeps the meteorologically significant solutions. Richardson estimated that a team of 64,000 people would be needed for a global system of numerical forecasts. His vision has since been realized by high-speed digital computers and a myriad of NWP models categorized by:

9.4 Numerical Weather Prediction in the Tropics »
9.4.1 Fundamentals of Numerical Models »
9.4.1.1 Basic Conservation Principles and Equations

NWP models represent the behavior of the atmosphere that is described by the primitive equations or governing equations:

Two kinds of atmospheric motion and time scales can be defined in the primitive equations:

Usually, for the atmosphere, the advective time scale is more than one day while the inertial time scale is a few hours, τ₂ » τ₁. Inertial-gravity waves have time scales < τ₁, and speeds well in excess of V_H. Advective motions are of primary meteorological significance, especially for the synoptic-scale, except near and above the tropopause where inertial-gravity waves have a significant role. Also, in the tropics f is small; therefore the time scale of inertial-gravity waves is close to other motions and is not as easy to separate. Nevertheless, for the most part, inertial-gravity waves are a minor component of the flow, the noise that is undesirable in numerical prediction models. Learn more about the primitive equations in the COMET module, Model Fundamentals, http://www.meted.ucar.edu/nwp/model_fundamentals/.

9.4 Numerical Weather Prediction in the Tropics »
9.4.1 Fundamentals of Numerical Models »
9.4.1.2 Grid Point Models

All models begin with a system of coupled differential equations. Consider a simple example of a two-dimensional advection equation

                        (11)

where q is any continuous scalar variable, such as temperature, U is constant, t is time, x, and y are distance and the three are continuous.

To solve for q numerically, we consider t, x, and y as discrete dimensions. A continuous field can then be represented by model grid points (e.g., Fig. 9.47).

The advection equation can be approximated by a finite difference equation, the simplest form of discretization. The analytic solution is approximated by a Taylor series. The centered difference form of the equation involves points at equal distances on either side of the forecast point:

               (12)

The predicted value of q at time, t+∆t, is

               (13)

Figure 9.48 illustrates the conceptual form of the equation,

               (14)

Models also use forward and backward difference techniques to calculate the predicted value. Given current and historical values of the variable, q, we can calculate its future values. By repeating the process with continual addition of new data for a prescribed period, we obtain a numerical forecast.

If the difference equations are not stable, if parts of the numerical solution are unbounded, then the numerical solutions will grow exponentially. The stability of a centered difference numerical scheme can be measured by the Courant-Friedrichs-Levy (CFL) criterion,

                     (15)

where c is the speed of the fastest wave in the system. To avoid computational instability, a decrease in the time step requires a decrease in the grid spacing so that the variables are advected less than one grid length per time step. Other forms of finite differencing techniques may require stricter criteria.

9.4 Numerical Weather Prediction in the Tropics »
9.4.1 Fundamentals of Numerical Models »
9.4.1.3 Spectral Models

Spectral models represent the atmospheric spatial variability as a finite series of sine and cosine waves of differing wavelengths. Model resolution is a function of the number of waves that are used to represent variability in the model. Several types of wave orientation are possible in spectral models. The wave length of the smallest number in a spectral model is represented as

The T170 configuration is commonly used in operational models because its resolution in the zonal and meridional directions is almost the same around the globe. Although horizontal gradients are calculated exactly from the wave solution, grids are still used for non-linear and physical calculations. Spectral models are the primary models at operational forecast centers such as ECMWF and NCEP, while grid point models are used for smaller, regional models.

9.4 Numerical Weather Prediction in the Tropics »
9.4.1 Fundamentals of Numerical Models »
9.4.1.4 Vertical Coordinate

Some models use pressure as the vertical coordinate because the primitive equations are simpler on pressure surfaces. The disadvantage is that some pressure surfaces will be below ground. A terrain following or sigma (σ) coordinate avoids those problems and allows representation of high resolution above complex terrain. Sigma ranges from 0 to 1 and is defined as,

                      (16)

where p_s is the ground level pressure and p is the variable pressure. Other models use isentropic surfaces, equal potential temperature surfaces, along which potential vorticity is conserved. The advantage is that synoptic-scale vertical motion can be easily diagnosed on isentropic surfaces but they intersect the surface and they are poor representations of the boundary layer, especially during the daytime. They are better at resolving frontal boundaries and the tropopause.

Many current models use a hybrid sigma-pressure coordinate, with sigma coordinates near the surface and pressure coordinates near the top.⁴⁹ Sigma-isentropic hybrid coordinate systems are formulated similarly. Most models have variable vertical resolution with highest resolution usually in the boundary layer. This is especially important for pollutant dispersion models where vertical mixing and wind shear in the boundary layer are critical. Learn more about model vertical coordinates from the COMET Module, Impact of Model Structure and Dynamics.

9.4 Numerical Weather Prediction in the Tropics »
9.4.1 Fundamentals of Numerical Models »
9.4.1.5 Model Forecast System

A conceptual diagram of a model forecast system is presented in Fig. 9.49. Operational models are typically run at six hourly synoptic intervals (0000, 0600, 1200, 1800 UTC).

Initialization and Data Assimilation

Forecast model

The type of model, computational capacity, and application dictates the choice of numerical formulation, dynamics, physical approximations, and data assimilation procedure. For operational models, efficiency is balanced with accuracy in order to produce timely forecasts. Global model forecasts are provided from 6 hours to 14 days in advance. However, the skill rapidly decreases beyond seven days for synoptic-scale variables such as the 500 hPa geopotential height in midlatitudes. For clouds and precipitation, the skill is considerably less.⁵⁰

Post processing

After the model run is completed, post processing tools are used by the forecaster to derive specific variables of interest such as 500 hPa geopotential height, amount or type of precipitation. The forecaster adjusts the model predictions based on his or her knowledge of the regional climatology, model biases, and recent weather in order to create forecasts for specific user communities. For example, model analysis is combined with observations to diagnose zones of confluence and severe weather over southern Africa (Fig. 9.50) and, consequently, model forecasts are used to identify zones of severe weather and heavy rainfall for the following day (Fig. 9.51).

Verification

Limited Area Models

Limited area models or regional models nested within global models are run operationally and for research. A list of commonly-used regional models is provided in Table 9.1. Regional models are being applied to aviation, agriculture planning, military operations, response to hazardous chemical release, and hydrometeorology, to name a few. While regional models provide high resolution, they are bounded by the lateral boundary conditions from the global models. Those lateral boundary conditions are sources of error, e.g., errors can be created by the numerical techniques used to interface the two different model scales.⁵¹ High resolution models will depict more realistic features but those features are highly likely to be inaccurate in position and timing.

9.4 Numerical Weather Prediction in the Tropics »
9.4.2 Data Assimilation

The aim of data assimilation is to optimize the accuracy of the forecast by blending observations with short range forecasts, also termed the background field. Many observation systems provide data continuously and data assimilation is a way to incorporate those data received between analysis times. The difference between the observation and the background field is called the observation increment or innovation. Data assimilation analyzes the observation increments and creates a grid of “corrections” to the previous short-range forecast (or background field).

Critical information for data assimilation is the background error covariance, which is the covariance of background error at different points. So, if the model error at one place is usually associated with error at another place, then a correction at the first location implies that the second location also needs correction. A key concept of data assimilation is that weights given to the background and observations are inversely proportional to their error variances; information with smaller error variance (which therefore has smaller expected error) receives larger weight. The combined corrections and short-range forecast form the initial conditions for the next forecast cycle (Fig. 9.52).

Data assimilation procedures are quite complex because observations have different spatial resolution, temporal resolution, and accuracy. The quality of observations varies across observation platform, time of day (e.g., LEO satellite data swaths, radiosonde reports) and weather (e.g., rain contamination of scatterometer-derived winds).

Observation increments are weighted according to perceived accuracy and validity. The weighting given to different pieces of information is based on their error covariance. Data assimilation is complicated by the need for well-behaved computational models for the required error covariances and for good estimates of those covariances. Observation error could be large if the instrument is not very accurate or if the observation network resolution differs from the model resolution. Isolated data in a region of sparse data presents problems for data assimilation as there is nothing to corroborate the observation increment. Errors are also introduced via radiative transfer approximations for satellite radiance assimilation. The flow regime will also affect the quality of the first guess field; error variances will increase in regions of rapid change and decrease in slowly evolving, zonal flow or calm regions. If the first guess field is assumed to be good, then little correction is needed and even perfect observations will show little impact.

In four-dimensional data assimilation (FDDA), new information can be introduced through (i) periodic reanalysis, (ii) gradual insertion (also called dynamic relaxation or nudging), (iii) more advanced mathematical techniques, such as variational four dimensional data assimilation (4DVAR). Variational data assimilation methods include the:

Data assimilation is a growing area of weather forecasting as an increasing volume of and variety of data are being incorporated into forecast models. For example, the WRF-Chem model fully integrates both meteorology and chemistry. WRF-Chem explicitly models atmospheric flow and aerosol chemistry and has chemical data assimilation as an experimental option. Only a tiny percentage of available data is currently assimilated into operational models (Fig. 9.6); many are removed prior to using because of redundancy, gross error, or computational expense. Efforts to increase the amount of data assimilated are warranted because satellite data assimilation has improved NWP model performance.^11,60,61 For example, ground-based GPS precipitable water vapor, COSMIC GPS refractivity, and standard meteorological observations over the Caribbean have been assimilated into tropical storm forecasts. Explore more in the COMET module, Understanding Data Assimilation: How Models Create Their Initial Conditions, http://www.meted.ucar.edu/nwp/model_dataassimilation/.

GPS-derived moisture and TC forecasts, http://www.cosmic.ucar.edu/~iwabuchi/caribbean/index.html

9.4 Numerical Weather Prediction in the Tropics »
9.4.3 Sources of Model Forecast Errors »
9.4.3.1 Initial Conditions

The model initial analysis combines a variety of observations (while accounting for differing resolution and accuracy) and the first guess field of the model, which must be consistent with the model resolution and physics. Errors are introduced when observations are sparse and/or infrequent. The initial state may not be realistic because of errors in the observations themselves (e.g., instrument error or lack of representativeness) which are then transmitted to the objective analysis and data assimilation. Errors are also introduced in interpolating the first guess field to the observation location (the model is forecasting a gridded volume while observations may be at a point).

Forecasters can find out what data are in a particular model run by overlaying satellite images, analysis, and raw data. Then they can see inconsistencies caused by data sparseness, wind perturbations from gust fronts, or features too small or fast-moving for the model to predict. Forecasters should become aware of situations in which the assimilation system is more likely to fail and to pay attention to evolving weather in the observations.

9.4 Numerical Weather Prediction in the Tropics »
9.4.3 Sources of Model Forecast Errors »
9.4.3.2 Boundary Conditions

Surface conditions are critical because the model is tuned to respond to surface moisture, land cover, and temperature. The gradients of these values force mesoscale responses, e.g., soil moisture gradients influence where convection develops. Thus errors in the soil moisture will cause errors in the forecast. Furthermore, an unrepresentative surface will affect the surface albedo and subsequent radiation processes.

Regional models are nested within global models, which usually have coarser resolution. The quality of the forecast is potentially degraded because of the differences in horizontal, vertical, and temporal resolution. In addition, errors in the global model forecast can propagate into regional models and contaminate the regional forecast. These errors can be reduced by avoiding strong forcing at the edge of the boundary because the resulting large gradients are not treated realistically, e.g., avoid putting boundaries in complex topography or regions of strong surface temperature gradients. Make a buffer zone between the nested domain and the coarse domain boundary. Interactive nesting, with two-way rather than one-way nesting, should reduce the formation of spurious gradients near the boundaries.⁵¹

It is important to remember that poor initial conditions can outweigh the benefits of high resolution. Forecasters should check the highest-resolution forecast against later coarse resolution forecasts for the same valid time. If conditions are changing rapidly within the forecast cycles, the larger-scale forcing and boundary conditions may have changed and the coarse-resolution forecast could be better.

9.4 Numerical Weather Prediction in the Tropics »
9.4.3 Sources of Model Forecast Errors »
9.4.3.3 Physical Approximations or Parameterization

The model cannot represent all processes and features that occur within a grid box. Some processes may not be understood well enough to be represented numerically or the data are not available at the scale of interest. The phenomena may be too small or too complex to be resolved numerically. Parameterization is one method of adding the net influence of those processes to the model. It is, arguably, one of the most difficult and controversial area of atmospheric modeling.

Physical processes such as water phase changes, radiation, and turbulence in the boundary layer are usually parameterized and referred to as the “physics” of the model. In most models, each process is parameterized separately. However, the model evolves according to their combined effect. It is difficult to diagnose model error associated with each separately. An error in one parameterization may be nurtured by another parameterization and their effect may be compounded at different model resolutions. For example, the vertical distribution of temperature and water vapor content are affected by how convection is coupled to the surface processes. Errors in predicting or diagnosing the presence of clouds produce large errors in short- and longwave radiation calculations. The shapes of cloud particles, whose growth is prescribed by a particular microphysical scheme, also affect radiation fluxes.

Model performance and organization of precipitating systems are sensitive to the microphysics, which control grid-scale clouds and precipitation, through latent heat release distribution and radiative feedbacks.

Turbulence and friction in the boundary layer are sensitive to the prescribed roughness length, which may introduce errors in the forecast winds, vertical wind shear, and consequently to the fluxes of heat, moisture that are transported upward. Errors in emulating surface processes are caused by incorrect surface energy and/or water balances in the model. Certain assumptions, such as the profile of diffusion rate in the PBL, may introduce errors. Learn more about physical assumptions in the COMET module, Influence of Model Physics on NWP Forecasts, http://www.meted.ucar.edu/nwp/model_physics/index.htm.

9.4 Numerical Weather Prediction in the Tropics »
9.4.3 Sources of Model Forecast Errors »
9.4.3.4 Numerical Approximations

Finite difference techniques in grid point models produce truncation errors because they approximate a continuous derivative and higher order derivatives are truncated. Also when equations are integrated over long periods, small-scale noise grows. The error can be reduced by reducing the integration time step.

The shape of the grid also affects the accuracy of the model. The traditional latitude-longitude grids creates problems because the shape of the grid cells becomes more distorted at higher latitudes (Fig. 9.53a), and the discrete approximations become more difficult to implement on multi-processor computer systems. Hexagonal grids have the advantage that cells have nearly equal size and discrete approximations are relatively easy to implement but high-order discretization is difficult. Hexagonal grids and cubed spheres (Fig. 9.53b,c) are being tested for implementation in the next generation of weather prediction models. The computational domain is another source of error. Some grid point models are more difficult to implement on parallel processing systems.

The ability of a model to represent particular phenomena is a function of the size and speed of the features relative to the number of grid points that are needed to sample those features. Grid point models do a poor job of handling waves that are only a few grid points across. Truncation errors occur in spectral models because they only have information for waves that they resolve; smaller scale wave information is not included. Errors occur in spectral models when transformations are made between spectral and grid point physics calculations. In addition, the damping mechanisms used to reduce spurious oscillation during model initialization could adversely affect meteorologically significant motions.

9.4 Numerical Weather Prediction in the Tropics »
9.4.3 Sources of Model Forecast Errors »
9.4.3.5 Intrinsic Predictability

Predictability is intrinsically limited because of the chaotic nature of the atmosphere. Numerous scales of motion exist in the atmosphere and energy transfers among them. Energy from scales smaller than the resolution of the observations is not in numerical models. Therefore, the real atmosphere and the model atmosphere are different. Over time, the numerical forecast and the real atmosphere will diverge (Fig. 9.54). Any error in the initial condition or in the model will cause a loss of predictability.⁶² Even small differences in initial conditions can lead to large errors in a long range forecast. This intrinsic error grows faster at smaller scales than larger scales, which means that small scale weather phenomena are less well forecasted. Predictability limits of small scale phenomena may be as short as 75 minutes for a 20-km wavelength.^62,63 Note that chaotic does not mean random but rather we can define a system with a range of possible states (the climate in our case) and predict the evolution of that system with some accuracy for a short period.

COMET Module, Ten Common NWP Misconceptions, http://www.meted.ucar.edu/norlat/tencom/index.htm

9.4 Numerical Weather Prediction in the Tropics »
9.4.4 Dynamical and Statistical Models

9.4 Numerical Weather Prediction in the Tropics »
9.4.5 Ensemble Prediction Systems

A single numerical model produces a specific or deterministic forecast from a specific model configuration (grid spacing, initial conditions, physics, etc.) with its systematic errors. It is possible to measure forecast sensitivity to uncertainty in the model configuration, such as the initial conditions, by perturbing the initial conditions in an NWP model. An ensemble of predictions can then be used to predict uncertainty in the forecast.^{68,69,70,71,72} Thus, the imperfect nature of initial conditions and NWP models can be used strategically in an ensemble prediction system (EPS) to:

Ensembles help to distinguish between weather situations with high or low predictability by tracking how uncertainty in the initial condition will evolve.⁷³ Ensemble means can be better estimates of the expected value of weather variables than a single deterministic forecast. The ensemble spread and higher moments of the forecast probability distribution allows comparison of timing and strength of the perturbations of the ensemble members.

Single-model ensembles have multiple members from the same model and starting time, but using slightly different initial conditions, thereby accounting for the uncertainties in the initial states of the model. Combinations of different models are called multi-model ensembles. For an ensemble forecast to be completed at the same time as an operational deterministic model forecast, the ensemble model usually has lower horizontal resolution. An in-exhaustive list of advantages and weaknesses of ensemble prediction systems is provided in the COMET module, Ensemble Forecasting Explained, http://www.meted.ucar.edu/nwp/pcu1/ensemble/1_1_1.htm.

Regional Ensembles

The NCEP Short-range Ensemble forecast (SREF)^74,75 system is the first operational, real-time regional ensemble forecast system. Its ensemble members include one of three dynamical models (Eta model, Regional Spectral Model, WRF), different physical parameterizations (deep convection, boundary layer, radiation, …), one of two different analysis systems, different horizontal and vertical resolution, and perturbations that are bred to sample flow-dependent initial condition error.

9.4 Numerical Weather Prediction in the Tropics »
9.4.5 Ensemble Prediction Systems »
9.4.5.1 Ensemble Output

Different kinds of plots are used to interpret ensemble forecasts. The most common are:

• Spaghetti plots
  Plots of contours with each member appear similar to strands of spaghetti, except color-coded for ease of readability. The choice of variables and levels to plot depends on the forecast application, e.g., the freezing level is a critical parameter for aviation. Fig. 9.55a shows the spaghetti plot for the 1012 hPa isobar from NCEP Global Ensemble Forecast System (GEFS). Over the continent, the ensemble members are in very good agreement while over the eastern Pacific, the forecasts are farther apart. For this case, the ensemble forecasts were relatively close to the analysis (Fig. 9.55b).
  
  These plots provide a quick measure of uncertainty (through differences in distance and amplitude among the contours) but are an incomplete picture of the forecast probability distribution. Small differences where the gradient is large can be significant, while large difference where the flow is zonal is of less consequence.

• Ensemble Means and Spread
  The mean is the simple average of all ensemble members. The spread is the standard deviation. More spread means more uncertainty in the forecasts. Fig. 9.56 illustrates the interpretation of the mean and spread plots.

A real case is shown in Fig. 9.57, in which the biggest spread in 850 hPa temperature is found over the South Atlantic Ocean and very little spread over the continent except for northeastern Brazil. The analysis confirms the more skillful forecast over the continental interior, while over the south Atlantic and northeast Brazil, the analysis is very different from the ensemble mean.

The advantage of the ensemble mean and spread is that a lot of information is summarized in one graph. But, we need to consider that the ensemble mean may not be the best forecast. If clusters of similar forecast outcomes exist, the mean may lie between the clusters.

• Probability of Exceedance Plots
  These plots show the probability of the forecast value exceeding a meaningful threshold and are used to identify the probability of extreme events.

• Plume diagram
  These are time series of ensemble forecasts from a grid box showing the time evolution of a forecast variable. For example, a plume diagram could show the ensemble forecasts of SST anomaly for the Niño 3.4 region (Fig. 5.51) or the forecast drop in temperature during a cold frontal passage.

• Ensemble Soundings
  Each ensemble member profile and ensemble mean is plotted on a thermodynamic diagram with specific color code.

• Box and Whiskers Diagrams
  These show the range of error as a time series (e.g., Fig. 9.58).

EPS forecasts are verified by comparing forecast probability distributions and other statistics of the EPS to the frequency of observations over time. Therefore a large set of ensemble forecasts, often over an entire season, is needed to obtain stable results. TIGGE, the THORPEX Interactive Grand Global Ensemble (THORPEX: THe Observing system Research and Predictability EXperiment), was established to archive and compare large numbers of operational EPS output.⁷⁶

Roots of Ensemble Forecasting,
http://journals.ametsoc.org/perlserv/?request=get-abstract&doi=10.1175%2FMWR2949.1
NCEP Ensemble Training,
http://www.hpc.ncep.noaa.gov/ensembletraining/

9.4 Numerical Weather Prediction in the Tropics »
9.4.5 Ensemble Prediction Systems »
9.4.5.2 Ensemble Data Assimilation

For ensemble modeling systems, a commonly used data assimilation technique is Ensemble Kalman Filter (EnKF).^77,78 EnKF uses ensembles to determine the error statistics associated with the first guess field of the model. Unlike 3DVAR (Section 9.4.2), for which error statistics are isotropic and stationary, ensemble-based error statistics have flow dependence and can adjust to the unique flow of the day. The ensemble transform Kalman filter (ETKF) is a specific form of the EnKF that has the advantage of being fast, suitable for generating ensemble initial conditions, and updating perturbations of the initial conditions. However, it does not represent sampling error efficiently.⁷⁹ The ETKF has been used to select flight tracks and target deployment of dropwindsondes for tropical cyclone surveillance.⁸⁰ Data assimilation by variational, ensemble, and hybrid techniques have relative merits and weaknesses for operational forecasting.^81,59 Hybrid variational and EnKF data assimilation systems are being tested to better handle data that involves highly non-linear processes such as clouds and precipitation. For instance, the WRF hybrid system⁸² combines ensemble covariances and 3DVAR covariances, both climatological and flow-dependent estimate of the background error statistics.

You can learn more about ensemble forecasting in the COMET module, Ensemble Forecasting Explained, http://www.meted.ucar.edu/nwp/pcu1/ensemble/)

NCEP Ensemble Training, http://www.hpc.ncep.noaa.gov/ensembletraining/

9.4 Numerical Weather Prediction in the Tropics »
9.4.6 Cumulus Convection in NWP

Cumulus convection is ubiquitous in the tropics and latent heat transport in cumulus convection is the primary method of transferring energy from the surface to the atmosphere. Therefore, cumulus convection needs to be represented in numerical models of tropical weather. As illustrated Fig. 9.59, cumulus convection occurs at several scales, which means that it is impossible to predict individual clouds. Therefore, numerical models create parameters to account for the effect of cumulus convection within a given grid box.

Cumulus parameterization schemes try to account for many processes, including the vertical transports of heat, moisture, and momentum by convective updrafts and downdrafts; some of these processes are illustrated in Fig. 9.59b.

A summary of approaches to cumulus parameterization in mesoscale models⁸³ is presented in Table 9.2. Models with sufficiently small grid spacing to resolve mesoscale circulations (less than 5 km grid spacing in the midlatitudes) can be run without cumulus parameterization. Instead precipitation is produced using explicit microphysics at each grid point. With the traditional approach, grid-scale precipitation is produced by cumulus parameterization, the implicit method. Other models use a hybrid of the two approaches.

Below are characteristics of three convective parameterization schemes often used for tropical weather prediction (conceptual models of two of them are shown in Fig. 9.60). For a more complete list and detailed description of current convective parameterization schemes, see the COMET module, http://www.meted.ucar.edu/nwp/model_precipandclouds/.

With advances in computer power, very high resolution models are now being run operationally. While models do not predict individual clouds, models with grid spacing of less than 5 km can resolve mesoscale cloud features.^90,91,92 However, while convection permitting 2-km grid models produce detailed convective activity, they had little forecast skill on the scales where those details appear.⁵⁰ Therefore it may not be worth the computational cost to implement operational models with such high resolution.

Cloud resolving models (CRMs) were developed as one method of modeling the complex interactions among cloud microphysics, cloud dynamics, radiation processes, and surface processes in tropical cumulus. CRMs explicitly resolve the dynamical circulations that directly couple these various physical processes. They were first applied to modeling convection in climate models.⁹³ In recent years, computational advances have facilitated “superparameterization”, a process that combines conventional cumulus parameterization on a coarse grid with detailed cloud-resolving modeling on a finer grid. The effects of moist convection are expressed through explicit turbulent fluxes.

How Models Produce Precipitation and Clouds,
http://www.meted.ucar.edu/nwp/model_precipandclouds/print.htm#page_3.0.0

NOAA Geophysical Fluid Dynamics Laboratory, Mesoscale Dynamics,
http://www.gfdl.noaa.gov/visualizations-mesoscale-dynamics
Cumulus parameterization on the mesoscale,
http://www.bom.gov.au/bmrc/basic/wksp15/Dare.pdf
Ten Common NWP Misconceptions,
http://www.meted.ucar.edu/norlat/tencom/index.htm

9.5 Tropical Cyclone Prediction

Accurate forecasts of tropical cyclone (TC) evolution rely first on having an effective conceptual model that incorporates the key physics of this evolution. These physics must be accounted for in NWP models used by forecasters. Because all forecast models have some weaknesses, we need effective ways of evaluating model forecasts to identify their good and bad points. With this knowledge, forecasters can integrate all of the possible futures given by the different models and produce the most skillful forecast. We will explore each of these facets here.

9.5 Tropical Cyclone Prediction »
9.5.1 Factors that Influence Motion and Intensity »
9.5.1.1 Factors Contributing to Tropical Cyclone Motion

Tropical cyclone motion is predominantly governed by the steering flow of its environment. The steering flow is the net effect of the winds from all of the other weather systems that affect the tropical cyclone. Since tropical cyclones extend through many kilometers, with the most intense of them reaching up to the tropopause, we must consider the winds through this whole layer when calculating the steering flow.

If steering were all that was important, we could think of a tropical cyclone like a cork in a river and things would be simple. But a tropical cyclone is much more complicated: it is comprised of hundreds of thunderstorms, all growing and dying constantly, and held together by the storm’s wind field. The structure of the tropical cyclone means that other factors affect its motion.

Since the β-gyres rely only on the tropical cyclone and the Earth’s vorticity (Coriolis), the tropical cyclone will move due to the β-gyres, even if there is no steering flow. Typically, propagation due to the β‑gyres adds 2–5 m s^-1 to the speed and is directed poleward and westward of the storm. Therefore, a storm at 20°N would propagate towards the northwest, while a storm at 20°S would propagate to the southwest. Using vector addition, we calculate tropical cyclone motion due to steering flow and propagation due to the β-gyres (Fig. 9.61).

Since the β-gyres result from advection of varying background vorticity, if the environment of the tropical cyclone has relative vorticity gradients of similar magnitude to β, we need to include these in calculating the storm propagation. However, because the relative vorticity due to other weather systems could have gradients in any direction, the direction of propagation is not known ahead of time.

Other factors affect the motion of a tropical cyclone: tropical cyclone structure and intensity, as well as the vertical shear of the environmental winds and the presence of other weather systems. The tropical cyclone structure governs the size and strength of the β-gyres, so the propagation of two tropical cyclones at the same latitude, but with different structures, will be different.

The intensity of the tropical cyclone is linked to the vertical extent of the storm. Stronger tropical cyclones have more vigorous thunderstorm activity and are generally taller than weaker tropical cyclones. This means that we need to calculate the steering flow through a deeper layer for a strong tropical cyclone than a weak one (Fig. 9.62).

The vertical wind shear can change motion since the average wind through the depth of the tropical cyclone is the steering flow. It can also affect the motion in another way; if the wind shear is too strong, the tropical cyclone will weaken and its structure will change.

Clearly the environmental factors affecting motion are linked with each other and with the intensity of the TC. Next we will look briefly at the factors affecting intensity.

9.5 Tropical Cyclone Prediction »
9.5.1 Factors that Influence Motion and Intensity »
9.5.1.2 Factors Affecting Tropical Cyclone Intensity Change

The environment of the storm (vertical wind shear, ocean temperatures, relative humidity, other weather systems) and its own current structure and intensity affects its future intensity. The key to a storm maintaining its current intensity or intensifying further is the maintenance of the deep convection surrounding its core.

In summary, intensity forecasting is a much more complicated problem than track, and indeed it depends strongly on the track (if the TC is forecast in the wrong location, it will experience a different environment). TC intensity depends critically on wind, temperature and moisture patterns in the core of the storm and in the near environment. These are often very challenging to measure and assimilate into models. Intensity change is also governed by internal processes, such as eyewall replacement cycles, that are poorly understood. Intensity change is a multi-scale problem that involves complex interactions between thunderstorms in the TC core and the TC environment, as well as air-sea interactions.

Motion and intensity are not the only important factors needed to forecast the societal impacts of the passage of a tropical cyclone. If we do not know the structure of the wind field – where the strongest winds are and how far out the dangerous winds extend – we are not able to give much guidance to the population. Figure 9.65 shows the dramatic difference in size between Hurricanes Floyd (1999) and Andrew (1992). For example, you might be terrified at the thought that a storm with 40 m s^-1 peak winds is headed your way; you may even think of evacuating. However, if you knew that the storm was small enough that you would only experience 10 m s^-1 winds – a stiff breeze – you could relax. Conversely, if you knew that this was a really large storm and your house was likely to experience hurricane force winds, you might evacuate to a safe place.

Now that we have the basics of TC evolution, it is time to look at a variety of forecast techniques and methods for deciding which techniques provides the best forecast in a given situation (Spoiler alert: no single technique is the best all of the time)!

9.5 Tropical Cyclone Prediction »
9.5.2 Dynamical Forecast Models Applied to TCs

Simplified Dynamical Track Models: Beta and Advection Models (BAMD, BAMM, BAMS)

These “Beta and Advection Models” (BAM) are simple trajectory models that only consider steering and the β-effect on TC motion. In these models, the TC cannot change nor have any impact on its environment.

The three-dimensional wind forecast from a more complex model is averaged in the vertical to create a two-dimensional wind field, the steering flow of the TC. The distinction between BAMD, BAMM, and BAMS is the depth of the layer over which the steering flow is calculated: Deep, Medium, or Shallow. This is the only way that variations in the vertical are incorporated into the BAM motion forecast. The choice of steering layer depends on the intensity of the TC being forecast (see schematic in Fig. 9.64).

One advantage of the BAM models is their speed. As of 2008, the BAM models run almost instantaneously and so the forecaster can create many forecasts of TC motion, varying the depth of the steering layer and the location of the TC (which can be in doubt, especially for weak systems with indeterminate eye structure). Thus, the forecaster can see how sensitive the forecast could be to these factors and get a sense of the potential for track errors in this situation (Fig. 9.66). Of course, these insights are limited by the lack of consideration of TC evolution and of vertical structure effects.

Global Dynamical (Track and Intensity) Models: ECMWF, GFS, UKMET, NOGAPS

The more complicated, three dimensional dynamical models come in two flavors: Global and Regional. Rather than the single layer of the BAM models, these can include 25-90 layers in the vertical!

Here we briefly review the models available to forecasters at the National Hurricane Center (NHC) in Miami; the main ones used are listed in Table 9.3. Most of these dynamical models are available to all forecast centers. One exception is that the regional (limited area) models will necessarily vary from one region to another. A list of operational limited area models and their applicable regions is given in Table 9.4.

Regional Dynamical (Track and Intensity) Models: GFDL, GFDN, HWRF

To achieve the highest possible resolution with the available computer capacity, limited area models typically have multiple layers: a number of finer “nests” exist inside the largest limited area grid. In this way, the model can simulate the atmosphere far from the storm with coarser resolution then increase the resolution near the TC, and increase even more near the TC core. Operational versions of both the GFDL and HWRF models have 9.5 km (6 mile) resolution of their innermost nest; approaching the resolution needed to simulate a realistic eyewall.

Higher resolution means the regional models can potentially do a better job of handling interactions between the tropical cyclone and the environment, which can result in better track and intensity forecasts (e.g., Fig. 9.67, for Hurricane Katrina 2005) at short time range.

Regional models now have fine enough resolution to begin to simulate the hurricane core (Fig. 9.68), and are capable of predicting rapid changes in intensity. Unfortunately, they do not do so reliably! Presently the dynamical regional model skill is approaching that of the statistical models for intensity. One limiting factor in dynamical forecasts of intensity is the lack of necessary measurements of wind, temperature, and moisture throughout the core and near environment to initialize the models properly. Without these observations, the initial conditions of the model are imperfect, leading to imperfect intensity forecasts.

In summary, multi-level regional and global dynamical models are the most skillful models for TC track forecasting. Among these models, the GFDL and GFS have provided the best overall guidance in recent years, but the performance of each model varies significantly from year to year and storm to storm. While it is possible to beat the models from time to time, model performance for track forecasts has improved significantly over the years, and they are very difficult to beat on a consistent basis. Dynamical models cannot as yet out-perform statistical models for intensity forecasting. While neither dynamical nor statistical models can capture rapid intensity changes reliably, dynamical models (in particular, the coupled GFDL model) have shown better, if intermittent, skill.

Technical Summary of NHC Track and Intensity models,
http://www.nhc.noaa.gov/modelsummary.shtml
How Mesoscale (Limited Area) Models Work,
http://www.meted.ucar.edu/mesoprim/models/index.htm
Hurricane intensity forecast improvements through high resolution models,
http://www.dtcenter.org/plots/hrh_test/HIRES_HFS_Test_Plan.pdf
Features of Current Operational Dynamical Forecast Models
http://www.meted.ucar.edu/nwp/pcu2/index.htm
GFDL Hurricane Visualizations,
http://www.gfdl.noaa.gov/visualizations-hurricanes

9.5 Tropical Cyclone Prediction »
9.5.3 Statistical Forecast Models

Statistical forecast models are based on historical relationships linking a forecast product of interest (motion or intensity) with the behavior of past storms using storm-specific information (i.e., storm location, time of year, current motion, intensity, and environment). The most important thing to remember about statistical models is that they forecast the typical TC behavior in similar situations and do not have skill in forecasting outlier situations such as rapid intensification or sharp track changes. We will now review the statistically-based track and intensity models used at NHC.

Statistical Track Models: CLIPER (Climatology-Persistence)

This is the only statistical model used in forecasting TC track. Since it relies purely on the climatology derived from past storms and on continuing the current TC track, CLIPER knows nothing about the current state of the atmosphere; it simply replicates the typical track for TC in this location, at this time of year, that begin moving in a similar direction. For this reason, CLIPER should not be used as a forecast. However, CLIPER does have one practical application: it is used as a skill baseline to evaluate more complex models. If a track model is not more accurate than CLIPER, it is deemed unusable. After all, if you cannot beat a simple “tomorrow’s track is the average of other TC tracks that were here today” you are in trouble!

Statistical Intensity Models

We have already determined that intensity forecasting is challenging and dynamical models do not yet show reliable skill in forecasting TC intensity—the most skillful intensity forecast models are statistical models. Statistical models merely predict the average behavior of a storm in a given situation. So, our best performing intensity models tell us only what is normal behavior in a particular state. This makes it extremely difficult to forecast unusual or extreme changes in intensity such as occurred with Hurricane Wilma (2005) and illustrated in Fig. 9.69. Statistical intensity forecast models used at the NHC are described below and listed in Table 9.5.

Statistical Hurricane Intensity Prediction Scheme (SHIPS)

SHIPS is a statistical-dynamical intensity model whose forecasts are based on statistical relationships between TC behavior and predictors obtained from dynamical model forecasts.⁹⁸ SHIPS also includes predictors from satellite data such as the strength and symmetry of convection as measured from IR satellite imagery and the heat content of the upper ocean determined from satellite altimetry observations. Since it includes information about the current state of the atmosphere in addition to climatology and persistence, SHIPS average intensity errors are typically 10%-15% less than the SHIFOR5 errors (See Table 9.5 below).

SHIPS uses multiple linear regression to combine information from the predictors into an intensity forecast. The set of open ocean tropical cyclones from 1982 to the present were used to develop SHIPS; the regression equations are re-derived each year to include TCs from the previous year. This means that the weighting (and so the importance to the forecast) of the predictors can change from year to year. The predictors for SHIPS include:

The most statistically significant predictors to a skillful intensity forecast are (as of 2008):

SHIPS has historically outperformed most of the dynamical models, including the GFS which provides the dynamical predictors to SHIPS!

Including information from dynamical models into statistical models can provide increased skill over tropical cyclone forecasts based on current information only. What impact might other approaches, such as ensemble techniques have on tropical cyclone forecasts? We will examine those methods next.

9.5 Tropical Cyclone Prediction »
9.5.4 Application of Ensemble and Consensus Forecast Techniques

9.5 Tropical Cyclone Prediction »
9.5.4 Application of Ensemble and Consensus Forecast Techniques »
9.5.4.1 Single Model Ensemble Forecasts

Single-model ensembles are from the same model and starting time, but using slightly different initial conditions. The idea is to maximize the spread of the forecasts at a chosen forecast lead time to ensure that the forecast includes the actual (later observed) TC evolution. However, the ensemble runs often have coarser resolution than the deterministic version of the model. This resolution change can introduce differences in the forecast that are not directly related to changes in the initial conditions.

Here is a summary of ensemble forecast systems often used for TC forecasting:

U.S. National Weather Service Global Ensemble Forecast System (GEFS)

The GEFS is based on the GFS model and consists of a low-resolution (~ 100 km horizontal grid spacing with 28 vertical levels) control run of the GFS, and 20 ensemble members at the same resolution. GEFS produces forecasts out to 16 days, four times per day. TC vortex relocation is applied to the initial conditions of each ensemble member so that the initial TC location is the same in the initial states of all ensemble members.

Meteorological Service of Canada, Canadian Ensemble Forecast System (CEFS)

The ECMWF Ensemble Prediction System (ECMWF EPS)

The ECMWF EPS has approximately 40 km equivalent horizontal resolution and 62 vertical levels. Its 51 member ensemble, 25 “singular vectors”,⁹⁹ are developed to generate initial conditions for 50 perturbed forecasts; the deterministic control forecast is the remaining member. These “singular vectors” are measures of forecast differences that will grow most rapidly over time.¹⁰⁰ The EPS determines the structure of the initial condition uncertainty tied to these rapidly growing vectors. To include effects of diabatic processes in the region of a TC, moist “tropical” singular vectors¹⁰¹ were introduced into the ECMWF EPS in 2002. Tropical singular vectors are computed in target areas centered on a tropical cyclone of at least tropical storm strength.

Japanese Meteorological Agency Typhoon Ensemble Model (JMA TEM)

The purpose of the Typhoon Ensemble Model is skillful track forecasting. It is a global model with approximately 60 km horizontal grid spacing and 60 levels in the vertical; five day forecasts are run four times per day. The ensemble consists of 11 members. Perturbations are derived using the singular vector approach, which is applied to JMA global model analyses to give the 11 ensemble member initial conditions.

9.5 Tropical Cyclone Prediction »
9.5.4 Application of Ensemble and Consensus Forecast Techniques »
9.5.4.2 Multi-Model Ensembles: Consensus Forecasts

The simplest way to form a consensus forecast is to average the output from all model, e.g., one computes the mean of all of the model’s predicted latitudes and longitudes of the TC center at some forecast time. At the NHC, the most commonly-used consensus forecasts are GUNA, CONU, and FSSE, which are described below. Consensus forecasts are typically more accurate (on average) than the predictions from their individual models.

Of course, the consensus approach does not always work, particularly if the model scenarios are completely different. For example, the loops executed by Hurricane Ophelia (2005) off the Florida, Georgia and South Carolina coasts (Fig. 9.71) were not well simulated by most of the models (Fig. 9.69). During the model forecast time Ophelia made a loop off the east coast of Florida.¹⁰⁴ The forecast period spanned the time of a subsequent loop off the Georgia and South Carolina coasts on 11-12 September.

Consensus models available at NHC:

Even if the forecasters do not make a formal selection of models to use in a consensus forecast, automated “corrected consensus” models produce both track and intensity forecasts. A corrected consensus forecast uses past performance of the member models to reach an optimal combination (subset) and/or to correct the biases of these models to derive the most skillful forecast possible. Specific constituents of each consensus model are available from the NHC.⁹⁷

Consensus TC Intensity Models: An example

ICON: Decay-SHIPS, GFDI, HWRF, LGEM

ICON was introduced in 2008. It is an intensity consensus forecast computed as the equally weighted average of the Decay-SHIPS, GHMI (adjusted GFDI forecast), HWRF and LGEM intensity output. It has the advantage of including two statistical and two dynamical models, which brings an additional degree of independence to the forecast approach.

Consensus TC Track Models: Examples

GUNA, CGUN: GHMI, EGRI, NGPI and GFSI

The GUNA track consensus forecast is an average of four models: GHMI, EGRI, NGPI and GFSI.^a All four member models must be available and all models receive equal weight. CGUN is GUNA corrected for the individual model biases. The model bias corrections are derived statistically using parameters known at the start of the forecast, such as model spread, initial intensity, location, etc.

TVCN, TVCC: GFDI, GFNI, NGPI, UKMI, GFSI, HWFI, EMXI

TVCN is the uniformly weighted average of the guidance from seven models but only a subset (at least two) is required to produce a forecast. Its members are evaluated each year and may vary from year to year. TVCC is the bias corrected version of TVCN.

Consensus TC Track and Intensity Models: An example

Florida State University Super Ensemble: FSSE

The Florida State University Super Ensemble (FSSE) is a weighted multi-model consensus that uses the previous official NHC forecast and the dynamical model members from the other consensus models. Individual model biases are based on the past performance of each member model using a training database made up of approximately 75 sets of past forecasts from each model. The FSSE assigns different weights to each member model. These weights are determined using linear multiple regression during the 75 forecast set training phase. FSSE is somewhat different from other models used at NHC because it is constantly learning from the past performance of its constituent models.

One limitation of the FSSE occurs when the past performance of the member models does not accurately represent their present performance. For example, if major changes were made to a member model between successive hurricane seasons the FSSE may under- or over-estimate the skill of that model. Thus, the FSSE technique is most accurate when no major changes are made to any of the member models between the training phase and operational forecast phase.

Prediction of Track Error: Goerss Prediction of Consensus Track Error (GPCE)

The GPCE provides a measure of the uncertainty in the consensus track forecast¹⁰⁵ that is better than the standard approach based on forecast skill for previous storms.¹⁰⁵

How does GPCE do it? Intuitively, you might expect a large spread in the model forecasts could lead to large forecast uncertainty and potentially large track errors. Also, differences at the initial forecast time also point to uncertainties that could affect the forecast. Following this logic, Goerss produced this predicted consensus error product which depends on a combination of:

Using these predictors and actual TC behavior for the 2002-2006 seasons, stepwise linear regression models were found to predict the consensus TC track forecast error for each combination of forecast length and consensus mode (Fig. 9.73).

The regression models were then used to determine the radii of circular areas drawn around the consensus model forecast positions within which the verifying TC position was expected to be approximately 75% of the time.

The regression line between the GCPE calculated 120-hour forecast error and the error in the 120 h consensus track forecast is plotted in Figure 9.74. To be sure that the consensus track error is smaller than the GCPE predicted forecast error at least 75% of the time, the regression line is adjusted upwards so that it no longer intersects at the origin. As a result, this adjusted regression gives you 75% “confidence circles” around consensus forecast.

So how did this work? For the 2007 Atlantic season, the circles displayed by GPCE (Fig. 9.75) contained the verifying TC position 72%, 71%, 76%, and 83%, of the time at 24 h, 48 h, 72 h, 96 h, and 120 h, respectively (Fig. 9.76). Therefore if you took notice of the circle, not just the lines, you would have been ready for the storm at least 71% of the time.

How well do the consensus track models perform?

We see that the multi-model consensus forecasts have greater skill overall than either the single GFS model ensemble average (AEMI) or any of the individual models (Fig. 9.77). However, the weighted consensus forecasts (FSSE) do not substantially improve on the simple unweighted average consensus forecasts (GUNA and CONU).

Improving forecast skill requires that we assess our understanding of the underlying physics, how effectively that understanding is translated into the forecast, and the success of new methods. For example, pure extrapolation of the current track forward in time is not a skillful method, but may be all that is available in a data void area. These topics are addressed in the next section using tropical cyclone forecasts as examples.

Example of the creation of a TC ensemble from ECMWF,
http://www.ecmwf.int/research/predictability/projects/IC_pert/tropical_SV/index.html

9.6 Forecast Verification and Validation

To use model guidance effectively when producing a forecast, it is necessary to identify when and why “good models can go bad.”

Are you convinced that the models aren’t perfect? Okay. But to get the best possible forecast we need to decide which model is bestor at least among the best. So we verify the forecast (make sure that the model produces the right results when we know the answer) and validate (assess the forecast accuracy after the event) the utility of the model. Sometimes a model will be skillful in one situation—say a slow intensification or a straight moving track—and will perform poorly in another case—for instance, rapid intensification or recurvature. Knowing these subtleties is important for developing skillful forecasts.

9.6 Forecast Verification and Validation »
9.6.1 Traditional Approaches and New Methods for TC Forecast Verification

There are two aspects to the verification of TC forecasts:

Traditionally the operational forecast verifications have been limited to track and intensity forecasts. Simple difference errors exist between the forecast and observations for chosen lead times and are summarized both by storm and by season (e.g., Fig. 9.78). This gives a visual summary of forecast errors over time. The information is also given in Table 9.6.

Table 9.6 shows that for the period 1990-1991 through 2007-2008, model analysis TC location errors reduced from near 50 km to about 30 km and 48 hour track forecast errors were reduced by 60%. Skill varies from season to season, possibly due to seasons in which TC motion was less predictable and/or changes in forecast products or observing systems.

More complex methods of forecast verification are generally reserved for the forecast models. These methods have been evolving quickly. In the last decade or so, model TC forecast verification has expanded beyond track, intensity and rainfall distributions (using spatially distributed, multi-category or entity-based verification methods) to more involved techniques that provide quantitative information on the model skill.

The availability of ensemble forecasts facilitates the need and opportunity for statistically-based verification measures. A few new approaches are discussed next.

NHC model verifications
http://www.nhc.noaa.gov/verification/verify6.shtml
Example NHC advisories for the 2011 hurricane season
http://www.nhc.noaa.gov/archive/2011/index.shtml
Example Australian BOM TC reports
http://www.bom.gov.au/cyclone/history/index.shtml

9.6 Forecast Verification and Validation »
9.6.2 General Methods for Forecast Verification

Many types of TC forecasts exist, including likelihood of genesis, track and intensity evolution, wind and rain swaths, and watches and warnings; these forecast products are presented in a variety of ways (Table 9.7) and for different domains (Table 9.8). Because of the range of forecast products, each type is evaluated using different verification methods.^{106,107,108,109} These methods have been developed by international working groups of the WMO World Weather Research Program and World Climate Research Program.¹¹⁰

9.6 Forecast Verification and Validation »
9.6.2 General Methods for Forecast Verification »
9.6.2.1 Visual or "Eyeball" Forecast Verification

The quickest way to assess the skill of a forecast in rough terms is to “eyeball” it. One look at the rainfall forecasts below (Fig. 9.79) gives you a sense of the relative skill of the two forecasts for the rainfall distribution of Hurricane Fran (1996). For this case, the GFDL model is more skillful than R-CLIPER.

While visual verification is a great place to start, for a quick reality check, this method is inadequate alone since it is: (i) time consuming, (ii) susceptible to interpretation biases of the observer, and (iii) not a quantitative measure of skill. Without additional quantitative measures of verification, it is hard to determine the relative merits of any forecast procedure over a large set of cases.

9.6 Forecast Verification and Validation »
9.6.2 General Methods for Forecast Verification »
9.6.2.2 Dichotomous (yes/no) Forecast Verification

Dichotomous forecasts provide a clear “yes” or “no” answer to the question “Will this event happen?” Examples of dichotomous forecasts are TC genesis and landfall forecasts. A storm either forms or it does not, it makes landfall or it does not. There are four possible combinations of observations (yes or no) and forecasts (yes or no) for each forecast (Table 9.9). These form the joint distribution of the forecast problem.

The frequency of occurrence of each of these outcomes is easily summarized in a contingency table (Table 9.10), a useful way to see the types of errors being made.

A perfect forecast system produces only hits and correct negatives, no misses or false alarms.

9.6 Forecast Verification and Validation »
9.6.2 General Methods for Forecast Verification »
9.6.2.3 Multi-category Forecast Verification

Multi-category forecasts are dichotomous forecasts with more than two choices. Instead of a yes/no decision, you decide the category to which each observation and forecast belongs.

Intensity forecasts are examples of multi-category forecasts: the total number of time periods when the set of TCs are (a) tropical storms, (b) hurricanes and (c) major hurricanes can be compared between observations and forecasts. This makes a three-category system, the easiest multi-category system for our example!

Verification of multi-category forecasts starts with a contingency table comparing the frequency of forecasts and observations in the various categories. Examples of multi-category forecasts could include TC category, rainfall intensity ranges (e.g., rainfall rate range by mm day^-1), or storm frequency (e.g., active, neutral and inactive season).

Table 9.11 is a multi-category contingency table for a fictional set of TC intensity forecasts. Numbers represent the count of all named storm times for which the intensity category was observed/forecast.

For a perfect forecast, the only cells containing non-zero values would lie along the diagonal from top left to bottom right. The off-diagonal cells tell us about the specific nature of the forecast errors. The last row and rightmost column of the table show whether the forecast produces the correct distribution of category frequencies. For example, in Table 9.11, major hurricanes are forecasted much more frequently than observed.

The information contained in Table 9.11 is represented graphically in Fig. 9.80. Each set of three bars correspond to the forecast category frequencies that verified as the observed TC category listed along the horizontal axis. For example, the first three bars were all observed to be major hurricanes, but for this set of TC only 180 major hurricanes were forecast, with 50 being forecast only as hurricanes and the remaining 20 as TS.

The advantage of the multi-category approach is that the nature of the forecast errors is more readily diagnosed. The disadvantage is that, by retaining more information, it is harder to condense the results into a single number. However, any multi-category forecast verification can be converted to a series of dichotomous verifications by defining “Yes” to be “in this category” and “No” to be "not in this category.” In our example this could correspond to “Is the (observed/forecast) storm a major hurricane or not?”

9.6 Forecast Verification and Validation »
9.6.2 General Methods for Forecast Verification »
9.6.2.4 Verification of Forecasts of Spatially Distributed Information

Much more information exists in the Hurricane Fran (1996) precipitation forecast example (Fig. 9.79) than we could get from a purely visual inspection, yet by reducing these images to a single number, or even a few numbers, much useful information is lost. While we certainly care about whether or not it will rain, we also care about the rain rate, the area and distribution of heavy rain and its location. Hence, errors in this example might derive from (i) rain rate being too weak or strong, (ii) the rain area being too small or large or incorrectly distributed, or (iii) speed of storm motion. We can reduce the first two questions (whether and how hard) to dichotomous or multi‑category tests but the spatial extent and location of the rain are not so readily reduced.

For our rainfall forecast example, one method of spatial verification is entity-based verification¹¹⁴ (Fig. 9.81). This verification method addresses the questions: “What is the location error of the (spatially distributed) forecast?” and “How does the total error break down into components due to incorrect location, volume, and fine scale structure?”

This object-oriented method verifies the properties of spatial forecasts of entities, where an entity is anything that can be defined by a closed contour. Examples of entities are contiguous rain or cloud areas, low pressure centers, and wind maxima. For each entity in the forecast and the observations, object-oriented verification decomposes the total error into the location error, as well as errors in area, mean and maximum intensity, and spatial pattern using pattern matching techniques.

Once observed and forecast entities have been identified, multi-category verification methods can also be applied. For example, each entity can be classified as a “hit", “miss” etc., according to the closeness of the forecast and observed location, and/or the agreement between the observed and forecast maximum intensity.

By invoking multiple thresholds a deterministic forecast system can be evaluated across a range of possible decision thresholds. These might be intensity thresholds or even spatial offsets (e.g., forecast event within 10 km, 20 km, 30 km, etc. of the verifying location). This multi-threshold approach enables a fairer comparison against ensemble prediction systems or other probabilistic forecasts.

Let us return to the Hurricane Fran (1996) precipitation forecast example (Fig. 9.79). Instead of thinking about the rainfall distribution with respect to the storm, we can ask instead, “How much rainfall will State College, PA, receive from Hurricane Fran?” Now we have fixed the location of the rainfall being verified to a point. Note that we still want to know the sources of the forecast error. But now we are interested in how these errors affect a location or region, not the weather system itself. Another method of validating spatially distributed data is to seek the answer to the question,

“What are the spatial scales at which the forecast resembles the observations?”

This can be answered by decomposing a spatially-distributed field (e.g., rainfall, wind speeds) by threshold values, then testing for these threshold values at locations with verifying information. Calculation of a skill score at each location based on the threshold value agreement gives a spatially distributed quantitative measure of skill. A commonly used skill score for spatially distributed forecasts is the Brier Skill Score.^b

The most severe test is a point-by-point skill verification, but, if the skill score is calculated over increasingly larger areas, the test is less onerous and the score should improve.

The Fractions Skill Score (FSS)¹¹⁵ an alternative score, is evaluated for areas of increasing size. It ranges between 0 (complete mismatch) and 1 (perfect match). If either there are no events forecast and some occur, or some occur and none are forecast, FSS is always zero.

As the size of the areas used to compute the fractions gets larger, the score will asymptote to a value that depends on the ratio between the forecast and observed frequencies of the event. The closer the asymptotic value is to 1, the smaller the forecast bias. The score is most sensitive to rare events (or for small areas), which may be particularly useful in identifying mismatches between observations and model forecasts of TC wind fields.

9.6 Forecast Verification and Validation »
9.6.2 General Methods for Forecast Verification »
9.6.2.5 Methods for Probabilistic Forecasts

A probabilistic forecast gives a probability, p, of an event occurring, where p is either expressed as a fractional probability (0 ≤ p ≤ 1) or a percentage likelihood (0 ≤ p ≤ 100%).
An accurate probability forecast system has:

In addition to the Brier skill score and other similar scores that compare forecast and observed values of chosen variables, another class of skill score is valuable. These are ranked probability scores that provide information on the skill of the forecast in predicting the category that the verifying observation fell into. Example categories you might consider are TC intensities or rain rates.

Ranked Probability Score, RPS

The ranked probability score, RPS, for a set of probabilistic forecasts of category membership is calculated as,

                                         (18)

where M is the number of forecast categories, p_k is the predicted probability of an event occurring in category k, and o_k is a binary indicator of which category the event occurred in [o_k = 0 for false alarm in that category and o_k = 1 for correct forecast]. Let us consider an example to illustrate the RPS.

Ranked Probability Skill Score (RPSS) measures the relative improvement of the forecast over climatology. One advantage of the RPSS is that it takes the climatological distribution of events between categories into account. Other reference forecasts, such as climatology and persistence, CLIPER, could also be used, but verification of frequencies among categories would then be with respect to these references, not to observed climatology.

Many other measures of the effectiveness of probabilistic forecasts exist. Our discussion is meant to give a flavor of the possible approaches.

9.6 Forecast Verification and Validation »
9.6.2 General Methods for Forecast Verification »
9.6.2.6 Methods for Verification of Ensemble Forecasts

As we discussed in Section 9.4.5Section 9.4.5, ensembles consist of many versions of a single dynamical model or many different dynamical models. The ensemble forecast captures the uncertainty in the forecast and provides a range of outcomes.

Many methods for evaluating probability forecasts can also be implemented for evaluating ensemble forecasts, where the spread of the ensemble members indicates probability. However, since ensembles provide information on the range of possible outcomes given the particular initial conditions, other measures of skill can also be applied to ensembles. We review just a few. You are encouraged to explore further using the cited references and resource links.

• Rank histogram The rank histogram is a quantitative, multi-category method of verification that is represented visually (e.g., Fig. 9.82). It measures how well the ensemble spread of the forecast represents the true variability (uncertainty) of the observations. It is also known as a “Talagrand diagram”.^116,117

In an ensemble with perfect spread, an observation is equally likely to fall between any pair of ensemble members since each ensemble member represents an equally likely scenario. Therefore, we can evaluate the success of the ensemble spread by looking at the shape of the rank histogram. If the histogram is:

Verifying forecasts of rare and/or extreme events

Since we are interested in verification for ensemble forecasts of TC, we will briefly review two methods for verifying ensemble forecasts of rare and extreme events.

• Deterministic limit
  The deterministic limit¹¹⁸ is the forecast lead time at which the number of misses plus false alarms in the ensemble forecast set equals the number of hits for a chosen weather system. It measures the forecast lead time for which the forecast is more likely to be correct than incorrect (Fig. 9.83). While this may not sound too exciting, it could help the forecaster to decide how much weight to give that forecast and, possibly, to decide to switch from deterministic to probabilistic guidance.

One example of the use of a deterministic limit would be the statement that “The deterministic limit for forecasts of TC intensity by the XXX model is 24 hours.”

• Extreme Dependency Score
  The Extreme Dependency Score (EDS) measures the reliability of a model to forecast a specific weather system, such as a TC. The EDS¹¹⁹ is a measure of the forecast skill for observed rare events. It ranges between -1 and 1, where a perfect score is EDS=1.

WRF Model Evaluation Tools (MET),
http://www.dtcenter.org/met/users/index.php
Survey of common meteorology model verification methods,
http://cawcr.gov.au/bmrc/wefor/staff/eee/verif/Stanski_et_al/Stanski_et_al.html
Forecast accuracy and verification scores,
http://www.eumetcal.org.uk/euromet/courses/english/navig/beginn.htm
Statistical challenges for verification of forecasts of weather extremes,
http://cawcr.gov.au/bmrc/wefor/staff/eee/verif/Casati/statxtr.htm
How do I know whether one model is better than another?
http://cawcr.gov.au/bmrc/wefor/staff/eee/verif/CIdiff/FAQ-CIdiff.html

9.6 Forecast Verification and Validation »
9.6.3 Summary: Advantages and Inadequacies of Current TC Forecast Models

Based on results from the current verification methods, we can make some general comments on the skill of the current generation of forecast models.

While it is possible for the human forecaster to show skill over the operational forecast models from time to time, model performance has improved significantly over the years, and they are now very difficult to beat on a consistent basis, at least for track forecasts.

Intensity forecasting is much more complex than track forecasting. For a start, intensity forecasts rely in some measure on the track forecasts (e.g., to get interactions with other weather systems and SST information). Further, intensity depends on details of the TC core structure, such as the distribution of deep convection, and other internal storm processes. Thus, dynamical forecast models still have little skill in predicting TC intensity change.

Statistical models for TC intensity are beginning to provide useful guidance, although since they are built using historical storm information, their skill is restricted to “typical” TC intensity evolution. Events such as rapid intensity change are not well forecast in either statistical or dynamical models. Current statistical models of rapid intensity change are based on a very small set of storms, which limits the range of possible intensity changes that underlie the statistical model.

Consensus forecast systems offer hope for improvements in forecast accuracy. Ensemble prediction systems are beginning to address the problem of TC forecasting directly^101,120 by targeting TC when the ensemble perturbations are developed,⁸⁰ rather than developing the perturbations as part of a larger forecasting problem. These offer hope of improved forecasts, not only of TC track and intensity, but on wind and rainfall distributions and storm structure evolution. Forecasting of extratropically transitioning TC¹²¹ (ET, Section 8.5ET, Section 8.5) and the influence of these ET systems on the midlatitude flow^122,123 is also a critical problem being studied using these targeted model ensembles.

Focus 1: The Australian-Indonesian Monsoon »
9F1.1 Overview of the North Australian Monsoon

by Dr. Mick Pope of the Australian Bureau of Meteorology (BoM)

The monsoon refers to the tropical and subtropical seasonal reversals in the atmospheric circulation and associated precipitation,¹²⁴ leading to two distinct phases, “wet” and “dry” (Fig. 9F1.1).¹²⁵ The changes in the atmospheric circulations arise from reversals in temperature gradients between continental regions and the adjacent oceans. In many cases this is accompanied by the seasonal migration of the Hadley cell and associated monsoon trough or ITCZ. However, in the case of the American monsoons (Fig.9F1.1, left panels), no seasonal reversal of the winds has been identified.¹²⁵ Equatorial regions have two rainy seasons and the trade wind flow collects moisture over the warm tropical oceans. In locations like Australia and India, one rainy season occurs when the cross equatorial flow turns westerly (Fig. 9F1.1, right panels). The corresponding trade wind easterlies are dry and characterized by a low-level inversion which caps deep convection.

This focus section will examine the Australian-Indonesian monsoon as a case study of monsoon dynamics, with a particular focus on the differences between the various intraseasonal phases.

Focus 1: The Australian-Indonesian Monsoon »
9F1.1 Overview of the North Australian Monsoon »
9F1.1.1 The Seasonal Cycle

Like the Indian monsoon,¹²⁶ the Australian-Indonesian monsoon undergoes intraseasonal variation consisting of active and break phases, characterized by widespread and isolated precipitation respectively (Fig.9F1.2).

The NAM forms part of the global monsoon driven by the Hadley Cell. Up motion occurs in the hot towers due to condensational heating, resulting in lower pressures near the surface in the tropics and hence a cross equatorial pressure gradient with the winter hemisphere mid-latitudes. The column heating in the hot tower also produces a much stronger reverse pressure gradient in the upper troposphere which drives the upper return flow into the winter hemisphere.¹²⁷ Modeling studies show that the response to the tropospheric heating is stronger when the heating is off the equator.¹²⁸ Superimposed on this is the land-sea thermal contrast that develops during Austral Spring.¹²⁵ A heat low develops over the Pilbara region, often resulting in shallow westerly flow over northern Australia, which moistens and pre-conditions the environment for deep convection (Fig.9F1.3). The period during which this pre-conditioning and isolated shallow convection occurs is known as the buildup. There is also a forcing due to the seasonal migration of the warmest sea surface temperatures.¹²⁹

Animation of MSLP and 900 hPa vorticity for 1 December 2005 -28 April 2006

A significant amount of rainfall occurs outside of the period of westerly winds. What weather systems would be responsible for this? We will answer this question in a later section.

The seasonal cycle can also be considered in terms of the CAPE—a proxy for the strength of convective updrafts. The most energetic updrafts occur on average during November to January. Figure 9F1.4 shows the month values of CAPE, Convective Inhibition (CIN) and number of zero CAPE days for the 2300 UTC Darwin sounding. The amount of CAPE almost doubles during the late dry season (September through November), with a rapid decrease in the number of zero CAPE days. The increase in the CIN during this period is likely an artifact of the large number of zero CAPE days during September and October. Zero CAPE days reach a minimum at the peak of the monsoon during February, although this is not the time of maximum mean monthly CAPE.

Global circulation with wind vectors, http://www.meted.ucar.edu/mesoprim/coastaljets/mslpwinds.htm

Weekly tropical variability note, http://www.bom.gov.au/climate/tropnote/tropnote.shtml

Focus 1: The Australian-Indonesian Monsoon »
9F1.2 Regimes of the North Australian Monsoon »
9F1.2.1 TWP-ICE

The NAM undergoes significant intraseasonal variability. Figure 9F1.5 shows the area average rain accumulation for January and February 2006 from the Tropical Warm Pool – International Cloud Experiment (TWP-ICE).¹³¹ The active period of the monsoon was marked by deep zonal westerly winds over Darwin and, during 23-26 January, an intense mesoscale convective system (MCS) produced an area averaged rainfall rate of approximately 45 mm day^-1. The period starting February 6th is referred to as a break monsoon with deep tropospheric easterly winds, which produced an area averaged rainfall rate of approximately 8 mm day^-1.

The NAM is characterized by active and break periods.^132,133,134 During periods when the MJO is active (which it is not during all summers) there is a strong synchronization between the active-break cycle and the MJO.^135,136 Likewise, the greatest probabilities of rainfall in the highest quintile are observed during the active MJO phase. Other influences on the monsoon at Darwin include upper troughs¹³⁷ and equatorially-trapped Rossby wavesequatorially-trapped Rossby waves.¹³⁸

The unusual phenomenon observed during TWP-ICE was the suppressed period of relatively small rainfall, together with the three days of clear conditions over Darwin with no rainfall. We now consider these three monsoon regimes in more detail.

Focus 1: The Australian-Indonesian Monsoon »
9F1.2 Regimes of the North Australian Monsoon »
9F1.2.2 The active monsoon

Animation of enhanced IR images of the active monsoon period

The active monsoon is associated with widespread, deep tropical convection, indicated by cold clouds in the IR image (Fig. 9F1.6a); although some cold clouds may be cirrus as IR cannot distinguish between precipitating convection and cold cirrus (Chapter 2, Section 2.5.2Chapter 2, Section 2.5.2). The associated synoptic pattern is a deep low over the Kimberley, directing west to northwesterly winds over northwest Australia and surrounding waters. The Monsoon Trough (MT) is indicated by the east-west oriented cyclonic vorticity maximum. Equatorward of the MT, the flow is converging into the low, resulting in the observed cloudiness and vertical motion profile (Fig. 9F1.6a,c). The sounding shows a typical active monsoon profile with a small dewpoint depression through the depth of the troposphere and a lapse rate close to moist adiabatic. The CAPE is typically small during the active monsoon. The wind profile is westerly to approximately 400 hPa with easterly winds above that. Drosdowsky (1984)¹³⁹ defined the active monsoon in terms of the wind profile, with mean westerly zonal winds to 500 hPa and mean easterly zonal winds above 300 hPa.

Focus 1: The Australian-Indonesian Monsoon »
9F1.2 Regimes of the North Australian Monsoon »
9F1.2.3 The Break Monsoon

In contrast to the active monsoon, clouds are more isolated during the break periods (Fig. 9F1.7), often coastal, due to triggering on the sea breeze, and westward propagating. The MSLP/vorticity plot shows that the MT is to the north of Darwin, extending from the Arafura Sea into the Coral Sea. A region of cyclonic vorticity lies along the west coast of Australia extending into a heat low.

What differences do you observe between the trace (sounding) for the break monsoon period (shown below in 9F1.7c) ) and the active monsoon? (Type your answer in box.)

Fig. 9F1.7. (a) An IR satellite image for 0230 UTC or 1700 LST, (b) Bureau of Meteorology model analysis of MSLP and 900 hPa vorticity at 0000 UTC 7 Feb 2006, and (c) Darwin 2300 UTC sounding for a break phase of the monsoon on 6 Feb 2006. (d) Sample radar images of break phase convection.

Animation of enhanced IR images of the active monsoon period

Feedback:

The main features of the sounding are easterlies through most of the troposphere compared to the westerlies of the active monsoon. The shallow westerlies near the surface are a result of the heat low. The zig-zag pattern in the dewpoint profile indicate dry air in mid-levels, referred to as dry slots.

Where on the satellite image, in Fig. 9F1.7, do you expect the sea-breeze front to be found over northern Australia? (Type your answer in box.)

Feedback:

Where on the satellite image do you expect the sea-breeze front to be found?

Fig. 9F1.8. (a) An IR satellite image and (b) radar reflectivity image (right) for a break monsoon period. (c) Radar reflectivity images showing before and (d) after westward propagating convection encounters the sea breeze.

Animation of radar reflectivity showing deep convection triggered by sea breeze.

Convection usually occurs at the leading edge of the sea-breeze front,¹⁴⁰ where the warm and moist inland air of the prevailing flow is lifted to its level of free convection. The orientation of the prevailing flow determines the preferred locations of convective development (Fig. 9F1.8). Convective rolls are also generated inland. The air mass coastward of the sea-breeze front is indicated by the cloud free region along the coast. On the radar image, the sea-breeze front is indicated by the line of convection parallel to the coast. Convection along the Coburg peninsula is indicative of the convergence of sea breezes (Fig. 9F1.8b).

The sea-breeze front also interacts with existing convection. In Fig. 9F1.8c, the sea-breeze front is seen as a light blue line oriented from Humpty Doo (HDoo) to Finnis Range (Finn). A thunderstorm propagates in from the southeast. Once the storm reaches the sea-breeze front, the outflow interacts with the sea breeze to initiate fresh convection, in this case, a squall line propagating to the northwest.

Focus 1: The Australian-Indonesian Monsoon »
9F1.2 Regimes of the North Australian Monsoon »
9F1.2.4 Comparison Between the Active and Break Periods

The break period has a strong diurnal signal, with a peak at 1400 LST. The timing of this peak is location dependent. It depends on the day to day synoptic forcing, sea-breeze cycle, and occurrence of earlier convection which may suppress the environment. The active period has a relatively flat diurnal cycle, with a weaker diurnal maximum at 1600 LST, compared to the break, and a morning peak at 0700 LST. The relatively flat diurnal cycle is consistent with the maritime nature of the air mass.

Another way to illustrate the diurnal cycle is to compare the mean reflectivity versus height (Fig. 9F1.10). The active monsoon has a very weak diurnal cycle with maximum values at 0930 and 1530 LST. The break period has a flat diurnal cycle except for the pronounced afternoon peak at 1530 LST when the mean reflectivity increases by 10 dBZ over most of the depth of the troposphere. The buildup profile is typical of the early wet season, when the surface moisture is still increasing. The echoes are not as deep as the break period or as large for a given height, indicating weaker updrafts. This is due to the entrainment of drier environmental air in the boundary layer. The gradual increase in reflectivity during the diurnal cycle is consistent with the mechanism by which multiple plumes moisten the atmosphere and allow larger rain droplets to form.

 What differences will the amount of convection make to the thermodynamics of the active and break regions and vice versa?

Active or break environments occur relative to the monsoon trough, as shown in Fig. 9F1.11. In the southeasterly stream poleward of the monsoon trough at O, dry air advection results in the dry slots observed in the dewpoint profile. Equatorward of the monsoon trough at X, moist maritime air is lifted in the convergent region to produce a deep moist profile. The animation of Fig. 9F1.11 illustrates that, as the monsoon trough migrates poleward, winds shift from easterly to northeasterly with southeasterly flow in the upper troposphere to deep monsoon westerly with easterly flow aloft. Tropospheric moisture increases with the change in trajectories and synoptic forcing.

Fig. 9F1.11. Schematic of active and break environments relative to the monsoon trough. Cross section, seen in the animation referenced below, adapted from McBride and Frank 1999.¹⁴²

Animation of environment during active and break periods.

Snapshot of active and break environments animation (Fig. 9F1.11).

The cross section (shown by rolling over X in animation of Fig. 9F1.11) illustrates the difference in CAPE and lapse rate between the active and break period environments. Latent heat release in the mid to upper troposphere warms the environment while evaporation of precipitation cools the lower troposphere, stabilizing the lapse rate. Spreading near surface cold pools reduce the CAPE by bringing down cooler and drier air from aloft. During break periods, shortwave heating of the surface and longwave cooling of the atmosphere destabilize the troposphere and allow CAPE to recover.