High resolution numerical weather prediction over the

High resolution numerical weather predictionover the Indian subcontinent

T S V Vijaya Kumar1,2,∗ and T N Krishnamurti1

1Department of Meteorology, Florida State University,Tallahassee, Fl 32306-4520, USA.2Present address: Environmental Modeling Center, National Centers for Environmental Prediction, Camp

Springs, Maryland, USA.∗e-mail: [email protected]

In this study, the Florida State University Global Spectral Model (FSUGSM), in association witha high-resolution nested regional spectral model (FSUNRSM), is used for short-range weatherforecasts over the Indian domain. Three-day forecasts for each day of August 1998 were performedusing different versions of the FSUGSM and FSUNRSM and were compared with the observed fields(analysis) obtained from the European Center for Medium Range Weather Forecasts (ECMWF).The impact of physical initialization (a procedure that assimilates observed rain rates into themodel atmosphere through a set of reverse algorithms) on rainfall forecasts was examined in detail.A very high nowcasting skill for precipitation is obtained through the use of high-resolution physicalinitialization applied at the regional model level. Higher skills in wind and precipitation forecastsover the Indian summer monsoon region are achieved using this version of the regional model withphysical initialization.

A relatively new concept, called the ‘multimodel/multianalysis superensemble’ is described inthis paper and is applied for the wind and precipitation forecasts over the Indian subcontinent.Large improvement in forecast skills of wind at 850 hPa level over the Indian subcontinent isshown possible through the use of the multimodel superensemble. The multianalysis superensembleapproach that uses the latest satellite data from the Tropical Rainfall Measuring Mission (TRMM)and the Defense Meteorological Satellite Program (DMSP) has shown significant improvement inthe skills of precipitation forecasts over the Indian monsoon region.

1. Introduction

Numerical weather prediction (NWP) is one ofthe challenging tasks in meteorology and has beensubjected to extensive research in the last fewdecades. Current developments in NWP includethe utilization of very high-resolution global andregional models, new methods for discretization ofthe dynamical equations, inclusion of more sophis-ticated physical processes, ensemble forecasting,and coupled ocean–atmosphere–land models. Inaddition, these models are used to understand thenonlinear dynamics of the atmosphere and theinternal structure and evolution of storms (e.g.,

hurricanes, squall lines, mesoscale convective com-plexes, and snowstorms) in a better way. Progressin tropical weather prediction has been hinderedfor a long time by lack of data over the vast oceanicregions and inadequate understanding of the phys-ical processes of weather patterns as compared tothe extra-tropics.

The recent inclusion of space-borne remotelysensed data collection systems and application ofnew techniques in data assimilation provided animpetus to NWP studies, since it is possible tohave a better description of the initial state ofthe atmosphere utilizing this data. Another majorcontribution for improving skills of the numerical

Keywords. Numerical weather prediction; spectral modeling; physical initialization; high resolution regional models; mul-timodel superensemble forecasts.

J. Earth Syst. Sci. 115, No. 5, October 2006, pp. 529–555© Printed in India. 529

530 T S V Vijaya Kumar and T N Krishnamurti

model forecasts came from the use of ensembleforecasting methods, where different model fore-casts are statistically combined to give a betterprediction. In the last two decades, weather fore-casts have become much more skillful and reliable.For example, in the mid-latitudes, today’s 3-dayforecasts are about as accurate as the one-day fore-casts used to be twenty years ago. The improve-ment in skill over the last 40 years of NWP isdue to increased power of supercomputers, allowingmuch finer horizontal resolution and fewer approx-imations in the operational atmospheric models;improved representation of small-scale physicalprocesses (clouds, precipitation, turbulent trans-fers of heat, moisture, momentum and radiation)within the models; use of more accurate meth-ods of data assimilation; increased availability ofdata, especially satellite and aircraft data over theoceans and the southern hemisphere; and sophis-ticated statistical ensemble methods that removethe model biases and improve the accuracy of theforecasts.

In a series of remarkable papers, Lorenz (1963,1965, 1968) made the fundamental discovery thateven with perfect models and perfect observations,the chaotic nature of the atmosphere would imposea finite limit of about two weeks to the predictabil-ity of the weather. Because the skill of the fore-casts decreases with time, Epstein (1969) and Leith(1974) suggested that instead of performing deter-ministic forecasts, stochastic forecasts providing anestimate of the skill of the prediction should bemade. The only computationally feasible approachto achieve this goal is found to be through ensem-ble forecasting (Kalnay 2002).

Though tropical NWP has gained importancein recent times, the progress is slow; the fore-casts over the monsoon domain are usually poorafter about a 24-h period and sometimes unre-alistic on day-2 and day-3. Particularly over theIndian domain, the forecasting skill of operationalNWP models is quite inapt. Statistical methodsof long range forecasts of monsoon rainfall dom-inated the numerical forecasts in India and offi-cially the India Meteorological Department (IMD)uses a set of statistical models (Thapliyal andKulshrestha 1992; Thapliyal 1997; Rajeevan et al2004) for sub-seasonal to seasonal forecasts dur-ing the summer monsoon period from June to Sep-tember. On short to medium range, the NationalCentre for Medium Range Weather Forecasting(NCMRWF) uses a spectral model at T80 reso-lution and issues operational real time forecasts.(A list of acronyms is provided in table 1.) IMDuses a Quasi Lagrangian Model (QLM) and a Lim-ited Area Model (LAM) on a daily basis to providenumerical forecasts for the Indian region. How-ever, the forecast skill of these models is very

Table 1. List of Acronyms.

Acronym Full form

BMRC Bureau of Meteorology Research Center

Cal/Val Calibration/Validation

CMC Canadian Meteorological Center

DMSP Defense Meteorological Satellite Program

DSS Data Storage Section

ECMWF European Centre for Medium Range

Weather Forecasts

FSUGSM Florida State University Global

Spectral Model

FSUNRSM Florida State University Nested Regional

Spectral Model

GPROF Goddard Profiling (algorithm)

IMD India Meteorological Department

JMA Japan Meteorological Agency

NASA National Aeronautics and

Space Administration

NCAR National Centers for

Atmospheric Research

NCEP National Centers for Environmental

Prediction

NCMRWF National Centre for Medium Range

Weather Forecasting

NESDIS National Environmental Satellite, Data,

and Information System

NOAA National Oceanic and Atmospheric

Administration

NRL Naval Research Laboratory

NWP Numerical Weather Prediction

OLR Outgoing Longwave Radiation

PI Physical Initialization

RMSE Root Mean Square Error

RPN Recherche Prevision Numerique

SST Sea Surface Temperature

SSM/I Special Sensor Microwave/Imager

TMI TRMM Microwave Imager

TRMM Tropical Rainfall Measuring Mission

UKMO United Kingdom Meteorological Office

UTC Universal Time Constant

less, particularly for important variables like rain-fall (Roy Bhowmik et al 2001; Rama Rao et al2005). Hence, there is a dire necessity for effortsto improve performance of the numerical modelsin short-range NWP on a real-time basis for theIndian region. The FSU global and regional modelsFSUGSM and FSUNRSM have shown significantperformance in simulating the features of the globaltropics, especially of Indian summer monsoon andtropical cyclones (Krishnamurti et al 1984, 1995,1998; Cocke 1998; Williford et al 1998, etc.). Hav-ing observed the merits of these two models, thispaper aims to examine the skills of these modelsin a detailed way and explore the possibility ofusing these models for efficient weather forecastsover the Indian sub-continent. The motivation for

High resolution numerical weather prediction over the Indian subcontinent 531

this study came from the fact that the forecast-ing skills of FSUGSM and FSUNRSM improvedwith increase in the model horizontal resolution,optimization of model parameters and incorpo-ration of physical initialization of observed rainrates.

This study also includes forecasts from multi-models of a number of global operational centersthat are combined through a sophisticated sta-tistical tool known as the ‘superensemble’, devel-oped by Krishnamurti et al (1999, 2000a, 2000b,2001). This method differs from the conventionalensemble mean where all member model fore-casts are given equal weight. Superensemble col-lectively removes the bias of individual membermodels at every grid point, at every vertical leveland at each time of forecast. Different weightsare assigned to each member model at everygrid point for each variable based on the model’spast performance examined in a training phase ofthe superensemble. A multianalysis superensem-ble component is included in this study, whichis based on the FSUGSM that utilizes TRMMand SSM/I data sets and a number of rain ratealgorithms. The difference in the analysis arisesfrom the use of these rain rates within physi-cal initialization that produces distinct differencesamong these components in the divergence, heat-ing, moisture, and rain rate descriptions. A totalof 12 models, of which 7 represent global opera-tional models and 5 represent multianalysis fore-casts from FSU model initialized by different rainrate algorithms, are included in the multianaly-sis/multimodel superensemble system studiedhere.

There were three major goals of this study. Thefirst of these was to show that the forecasts madetherefrom using a regional spectral model carry ahigher skill compared to global models at compar-atively lower resolution. The second was to obtaina very high nowcasting skill of rainfall using a high-resolution regional spectral model, while the thirdgoal was to demonstrate the performance of thesuperensemble methodology for short-range windand precipitation forecasts.

The salient features of the FSUGSM andFSUNRSM are given in section 2. The experimen-tal setup and some important results from thesemodels are presented in section 3. Section 4 dealswith the high resolution physical initializationwithin the FSUNRSM along with explicit speci-fication of soil temperatures. Section 5 describesthe data, experimental setup and results obtainedusing the multimodel/multianalysis superensem-ble method, and a detailed summary, conclu-sions and scope for future work are provided insection 6.

2. FSU global and regionalspectral models

2.1 Florida State University GlobalSpectral Model

The Florida State University Global SpectralModel (FSUGSM) is one of the state-of-the-artNWP models with special emphasis on tropicalweather prediction. This model owes its origin tothe Canadian spectral model RPN, Daley et al(1976), and has been used in various configurationsto study a wide range of atmospheric phenomena.Typical configuration changes, such as spatial res-olution, choice of parameterization schemes, lengthof model integration, etc. involve simple modifica-tions to initial model parameters without changingthe model code. A detailed documentation of theFSUGSM was given in Krishnamurti et al (1991)and Kumar (2000).

The resolution of the FSUGSM, both in thehorizontal and vertical, can be varied to accommo-date various research purposes. The model integra-tion utilizes semi-implicit time differencing schemewith Asselin (1972) time filter. The vertical dif-ferential terms in the model equations are solvedby applying finite-difference methods, while thehorizontal differential terms are determined spec-trally. All variables in the vertical are solvedby using a centered differencing approach, excepthumidity which is handled by an upstream dif-ferencing scheme. The FSUGSM uses a standardapproach for atmospheric spectral models, wherelinear terms in time tendencies are computed inthe spectral space and non-linear terms are com-puted in the physical space on a Guassian grid (ortransform grid). The FSUGSM has a wide rangeof physical processes to choose for specific objec-tives of research. Salient features of the FSUGSMare given in Appendix 1.

2.2 Florida State University nested regionalspectral model

On account of their definite advantages over thegrid point models, global spectral models are beingused by most of the operational NWP centers forshort and medium range weather forecasts. Theaccuracy of the numerical forecasts by these mod-els (both spectral and grid-point) increases as themodel resolution is increased, since at a higherresolution, these models are able to capture finerscales that are necessary to define and forecastsmaller, regional scale weather systems. For a veryhigh-resolution forecast over some specified limitedarea over the globe, using a very high-resolutionlimited area model in conjunction with a relatively


low-resolution global model is computationallymore advantageous than increasing the resolutionof the global model. Until recently, most of the lim-ited area models used grid-point or finite differencemethods. However, these models exhibit problemssuch as phase and biased errors and non-linearinstability (Roache 1976; Baer 2000). Computingspace derivatives with high-order accuracy alsodoes not resolve these problems. Besides, economi-cal time integration methods, such as semi-implicitschemes, are not very convenient to implementin a grid-point model. To overcome these problemsand exploit the advantages of spectral methods,a number of limited area spectral models havebeen developed for operational use at NCEP andECMWF (Tatsumi 1986; Hoyer 1987; Juang andKanamitsu 1994).

The nested regional spectral model developedat FSU (FSUNRSM) was first used in Atlantichurricane prediction studies (Cocke 1998) and hasundergone considerable enhancement since then.FSUNRSM uses a perturbation method similar tothat used at NCEP and ECMWF but largely dif-fers from these models, particularly in the areasof map projection, boundary relaxation procedure,finite differencing schemes, etc. The FSUNRSMwas designed to be compatible with the FSUGSM.These models have the same vertical σ coor-dinate system, horizontal diffusion, Asselin timefilter, semi-implicit time integration and physi-cal parameterization schemes. The regional modelsolution is the sum of the global model solutionplus the perturbations. These perturbations arespectrally represented by bi-periodic trigonomet-ric series and are relaxed at the lateral bound-aries so that the regional fields approach the globalmodel solution. Only the perturbations are rep-resented by the trigonometric functions, not theregional fields themselves. This enables a naturalmeans to incorporate the lateral boundary condi-tion. Depending on the variable, the perturbationssatisfy a zero or mirror boundary condition. Oneadvantage of the perturbation technique is that theglobal model predicts the large-scale flow whereasthe finer-to-intermediate scales are predicted bythe regional model. In most other regional mod-els, the large scale flow is passed into the regionaldomain through a narrow blending or relaxationzone, typically a few grid points in width, at the lat-eral boundaries. The perturbation method incorpo-rates the large-scale flow throughout the regionaldomain.

The global model is run first, and the global out-put fields are then spectrally transformed to theregional grid at every 3 hours. The use of a spec-tral transformation eliminates the need for hor-izontal interpolation, thus reducing error. These

transformed global fields are then linearly inter-polated in time to the time steps of the regionalmodel. The perturbation time tendencies at ini-tial time of the regional model integration areset to zero. At each time step, the perturbationsare added to the global fields to obtain the fullregional fields, and the nonlinear dynamical andphysical tendencies are computed. The perturba-tion time tendencies are obtained by subtractingthe regional time tendencies from the global timetendencies (which were obtained by an inversesemi-implicit algorithm). Currently, only one-waynesting is done; the regional solution does not feedback into the global model.

The FSUNRSM uses a Mercator projection inthe horizontal. The advantage of using the Merca-tor type projection lies in the fact that it incor-porates a means of compatibility between theFSUGSM and the FSUNRSM, thus allowing boththe global and the regional models to use the samelongitudinal co-ordinate. This convenience resultsin a reduction of computational time, as the globalvariables and derivatives can be easily transformedto the regional grid via a fast Fourier-Legendretransform. FSUNRSM has slip wall lateral bound-ary conditions with respect to perturbations, i.e.,there can be perturbation wind flow along theboundary but not across the boundary. Accord-ingly, no advection of perturbations of scalar fieldslike temperature, pressure and moisture is allowedacross the boundaries. The mathematical formula-tion and detailed description of the FSUNRSM aregiven in Kumar (2000).

2.3 Physical initialization

Physical initialization (Krishnamurti et al 1984,1991) is a powerful tool, which primarily assim-ilates satellite derived observed rainfall distrib-utions along with calculated surface fluxes ofmoisture to produce a physically consistent andmore realistic spin-up of the initial state. Thisis accomplished through a number of reversephysical algorithms within the assimilation mode.Physical initialization is invoked 24 h prior tothe initial forecast start time. By using a New-tonian relaxation process, certain forecast vari-ables are relaxed until they converge to that of theobserved, satellite derived or computed known vari-ables. Thus the initial fields of mass divergence,moisture sink, surface pressure, vertical distribu-tion of the humidity variable and surface fluxes ofmoisture as proposed by the model are modified tobe in agreement with the observed rain rates, sur-face fluxes and the OLR. The observed rain ratesare derived from DMSP SSM/I datasets. Thesedatasets have a lot of gaps in the global coverage of


rainfall distribution, and are hence filled with therain rates obtained from the geo-stationary satel-lite based OLR fields. The total field is a mergedSSM/I – OLR product. The process of physical ini-tialization incorporates a reverse cumulus parame-terization scheme, a reverse similarity algorithm,an OLR matching algorithm and Newtonian relax-ation of the model variables. The brief procedureof the PI is as follows:

Step 1: Diagnostic calculations of the surfacefluxes, and humidity analysis consistent with thesurface fluxes, rainfall rates and the net OLR. Thisstep is done through a set of reverse physical algo-rithms. The first part uses a reverse similarity the-ory to compute the surface evaporative fluxes fromthe sum of the apparent moisture sink (Q2, Yanaiet al 1973) and the observed rain rates. The sur-face sensible heat fluxes are obtained from theknowledge of the apparent heat source (Q1, Yanaiet al 1973) and the net radiative heating. Afterthe assimilation procedure, the resulting surfacefluxes tend to exhibit consistency with the observedrain rates. In order to solve for the potential tem-perature and the moisture variable (assumed tobe unknowns) at the top of the constant fluxlayer, the Yanai fluxes of sensible heat and latentheat are used as input to the similarity theory(Businger et al 1971). The second part is obtainedthrough a reverse cumulus parameterization algo-rithm which reanalyzes the vertical distribution ofspecific humidity such that the rainfall implied bythe cumulus parameterization algorithm (modifiedKuo scheme, Krishnamurti et al 1983) matches thegiven observed rainfall rates. Since the observedrain rates are known quantities, the specific humid-ity in the vertical can be obtained through aniterative procedure. The humidity measurementsfrom conventional radiosonde above 500 hPa sur-face are generally quite unreliable and hence thehumidity distribution is restructured using an OLRmatching algorithm between the model calculatedOLR and the satellite based observations througha local structure function for the moisture variable.More details on the computational aspects of thesereverse algorithms are described in Kumar (2000),Krishnamurti et al (1991) and Shin (2001).Step 2: Incorporation of these computed fluxes,observed (estimated) rain rates and observedclouds during the pre-integration phase, wherethe diagnostically computed fluxes (from Yanai’sformulation) (first part of step 1), ‘observed’rain rates and ‘observed’ clouds (through OLRmatching algorithm) are incorporated into the pre-integration phase of the model, wherein an addi-tional term is added to the model’s dynamicaland thermodynamical equations. The additional

term defines a Newtonian Nudging that relaxesmodel-forecast values to certain observed esti-mates. This is the crucial step in the physical ini-tialization procedure. Here the vorticity, divergenceand pressure tendency equations are subjected tothe relaxation, where the spectral equations takethe form

∂Aml

∂t= F m

l (A, t) + N(A, t) • (A0ml − Am

l ).

Here N represents the relaxation coefficient, A0ml

a specified future value to which the Newtonianrelaxation is aimed at, and F m

l (A, t) the forcingterm of the equations of variable A. (l,m are zonaland meridional wave numbers.) Solving the aboveequation iteratively, the variable Am

l attains a solu-tion that falls between the model derived value andthe observed value during this relaxation. If therelaxation coefficient (N) is too large, the modelstate will not be in primitive equation balance, andif N is too small, there will be little impact on theevolution of the model state during this assimila-tion. The relaxation coefficients employed in ourstudy are 1×10−4 s−1 for vorticity and surface pres-sure, and 5 × 10−5 s−1 for divergence. There is norelaxation for humidity variable; it is reanalyzedusing the reverse algorithms and OLR matching.

3. NWP experiments from FSUGSMand FSUNRSM

The capability of FSUGSM and FSUNRSM inpredicting the monsoon weather over the Indiansubcontinent for the month of August 1998 isexamined in detail in this section. The FSUGSMwas run with two different horizontal resolutions,T42 and T126, corresponding to approximately2.8 degrees and 0.94 degrees latitude/longitude(Guassian grid) near the equator respectively. Thevertical resolution is fixed for both T42 and T126at 11 levels for the moisture variables and 14levels for the remaining variables. These levelsare unevenly spaced (staggered) between 10 and1000 hPa. The model is capable of increased ver-tical resolution to as many as 29 levels. The cur-rent version of FSU model is run at T126L29, butrequires more time (almost double) to completea 3-day forecast. The results, when interpolatedto the standard pressure levels, did not show anymarked differences. Keeping in view of the compu-tational resources and operational feasibility, it wasthought initially to use 14 levels in the vertical andtwo different horizontal resolutions for the globalmodel (T42 and T126). Three-day global forecastswere made for each day of August and the out-put was stored at every 6-h interval. The initial


data sets and surface parameters had a resolutionof approximately 1.125 degrees (T106) and weretaken from the ECMWF operational analysis at1200 GMT of every day. These data sets were inter-polated to the respective global model resolutionsand were used to initialize the models. These samedata sets were also used subsequently for the fore-cast verification. The initial spectral start files foreach of these model runs consist of all basic vari-ables (u, v, w, z, T and q) for all 14 levels (exceptfor moisture where only 11 levels were used). Thesurface parameters like SST, orography, ice cover,land category and other boundary conditions wereacquired from the NCAR DSS and were trans-formed to the Gaussian grid of required resolution.The SSTs were fixed at the initial start time ofany 3-day forecast. The topography was specifiedusing US Navy’s high-resolution orographic datasets. The FSUNRSM was also run at two differenthorizontal resolutions – 1 degree and half-degree.While the regional fields at 1 degree resolution wereinterpolated from the T42 experiments, regionalfields at the half-degree resolution were taken fromthe T126 experiments.

The geographical domain covered by the regionalmodel is approximately the same as the domainof study, i.e., 0–30◦N, 60–120◦E. For computationalfeasibility in spectral space, currently the follow-ing conditions are necessary to set the regionaldomain: 2 × (nlonr − 1) must be equal to 2p×3q × 5r, p > 0, q ≥ 0, r ≥ 0; same is true for nlatr.nlonr and nlatr correspond to the number of longi-tude points and latitude points respectively, p, q, rare integers. Also, the regional domain cannotcross the Greenwich meridian. To satisfy the aboveconditions, regional model for 1-degree resolutioncontains 65×33 points in the east–west and north–south directions, with a starting longitude of 60◦Eand equator as the starting latitude, extending thedomain to 125◦E and 33◦N. The half-degree res-olution is represented by 129 points in the east–west and 65 points in the north–south with thesame starting longitude and latitude. For present-ing the results, we have chosen a uniform area com-prising the region between equator and 30◦N and60◦E–120◦E.

The prognostic output fields emanated fromthese model experiments are sea level pressure,accumulated precipitation, relative humidity, zonaland meridional components of wind, temperature,dew point temperature and geopotential height.The model output was interpolated to standardpressure levels (from sigma to p) using sophisti-cated vertical interpolation programs. Skills of theforecasts were measured for different parametersusing RMS errors and spatial correlation coeffi-cients. All the output fields from T42 experiments

Table 2. Selected list of experiments using different versionsof FSU Global Spectral Model and FSU Nested Regional Spec-tral Model.

Experiment Description

GT42 FSUGSM at a resolution T42(2.8125 degrees latitude/longitude onGaussian grid) in the horizontal withdefault model parameters.

GT126 FSUGSM at a resolution T126(0.9375 degrees latitude/longitude onGaussian grid) in the horizontal withdefault model parameters.

GT126PI GT126 with physical initialization.

R1T42PI Same as R1T42 but initial base fields aretaken from the output of a separateGT42NEW experiment using physicalinitialization from day-1 to day 0.

R5T126PI Same as R5T126 but initial basefields are taken from GT126PI.

PIR5T126PI A separate experiment with R5T126PIwhere physical initialization is applieddirectly at the regional model level.

were linearly interpolated to a 1-degree lat./lon.resolution while output fields from T126 experi-ments were brought on to a uniform half-degree res-olution. Based on the relative performance of eachof the experiments conducted, only a total of fivesets of experiments (from both low and high res-olution categories) were chosen among the globaland regional models and results from these experi-ments are presented in this section. Details of theseselected experiments are provided in table 2. ThePI experiments use the physical initialization pro-cedure illustrated in section 2.3.

3.1 The summer monsoon during August 1998

The region of southeast Asia, particularly theIndian subcontinent and its adjoining oceanicregion, experiences a characteristic seasonality ofwinds and precipitation, termed as the monsoon.The sequence of events that trigger the monsooncirculation are formation of heat low over north-west India preceding the transport of moistureinto the land mass convergence of heat, profoundcumulus convection and enhancement of diabaticheating and precipitation events. The onset of sum-mer monsoon takes place towards the end of Mayand the monsoon prevails till the end of Septem-ber. During 1998, the southwest monsoon set inover Kerala and south Tamilnadu on 2 June. Afteradvancement towards most parts of the Indian sub-continent, the monsoon experienced a break situ-ation during July 14–26 and regained its strengthafterwards. The axis of the monsoon trough wasnorth of its normal position on most of the days ofAugust 1998. The monsoon was active or vigorous


Figure 1. Mean RMS errors of zonal wind (u), meridional wind (v) and total magnitude of wind |V |(m s−1) at 850 hPa (toppanels) and 200 hPa (bottom panels) over the Indian monsoon domain for the month of August 1998. Details of experimentslisted in the legend are provided in table 2.

in peninsular India during this month, with rainfallexceeding the normal in 13 meteorological subdi-visions while 15 subdivisions received normal rain-fall and the remaining 7 subdivisions experienceddeficit rainfall (IMD, 1999). The pressure anom-alies were positive over most parts of the country.Two weak low-pressure systems formed during thismonth, it is being one among very few occasions inAugust when no depression formed over the Indianseas throughout the month.

3.2 Wind forecasts

The mean RMS error of the zonal, meridional andtotal wind at 850 hPa and 200 hPa is presentedin figure 1. This diagram gives an indication ofthe superior performance of the high resolutionregional model (R5T126PI) over all other ver-sions of the model. The global model with PI(GT126PI) also has shown better skill but it isthe regional model that outperformed all othermodels, by having least RMS error for all compo-nents of the wind for both 850 hPa and 200 hPa

levels. It is also evident from these histograms thatthe high-resolution numerical experiments usingPI have shown major improvements over the low-resolution global/regional models. The impact ofresolution on improving the wind forecasts is bet-ter seen in this figure where the mean RMS errorsof wind forecasts from R5T126PI (high resolu-tion regional model) are much lower than theGT42 (low resolution global model). This is notsurprising, since increase in resolution in general,enhances the forecast skill. However, comparedto the GT126 model outputs at approximately1 degree resolution, results from the regional modelexperiments at 1 degree resolution (RT42PI) haveshown superior performance, indicating the advan-tage of the use of regional models over the globalmodels, apart from the impact of physical ini-tialization. Though the order of magnitude oferror was increased with the increase in the fore-cast period, the errors from the regional modelwere much less. About 40% of improvement wasachieved using high-resolution regional model for


Figure 2. Streamlines and isotachs at 850 hPa for 1, 2 and 3-day forecasts from GT42 and R5T126PI, valid on August 7,8 and 9, 1998. Observed fields (ECMWF analysis) for corresponding days are shown in the top panel. Wind speeds (m s−1)are shown shaded. (X-axis from 60◦E to 110◦E, Y-axis from equator to 30◦N.)

zonal wind forecasts on day-1, and about 25%on day-3. Approximately 30% improvement wasnoticed in the skill for wind forecasts at 850 hPa.More or less similar improvement was noticed for200 hPa wind forecasts as well.

The streamlines and isotachs at both 850 and200 hPa levels on a typical monsoon day are pre-sented in figures 2 and 3 respectively, for obser-vations, GT42 and R5T126PI. In these diagramsa sequence of three-day forecast starting from 23to 25 August 1998 is presented. Shaded regionrepresents the magnitude of the wind speed inms−1. The monsoon circulation at 850 hPa, char-acterized by strong Somali jet near 10◦N and65◦E, the southwesterly flow across the Indian

subcontinent, an elongated monsoon trough alongthe Indo-Gangetic region, a trough along the eastcoast of India and typical anticyclonic flow overthe Arabian Sea were well represented by theR5T126PI experiment in its day-1 forecast ascompared to other experiments. The control fore-casts from GT42 (and even GT126, not shownhere) without physical initialization could notcapture any of these features. The wind speedswere better predicted by the R5T126PI. GT126PIalso had shown some similarity with observedfeatures (not shown here) but the R5T126PI out-performed its global counterpart. Similar improve-ment by R5T126PI could be observed even inday-2 and day-3 forecasts. By day-3, forecasts from


Figure 3. Same as figure 2, but for 200 hPa streamlines and isotachs.

all other experiments including regional model at1-degree resolution largely degraded except theR5T126PI. The 200 hPa wind forecasts demon-strated in figure 3 also reveal similar improvementsby R5T126PI compared to other model exper-iments. The Tibetan High, strong anticycloniccirculation over northern India and strong east-erly jet stream were well captured by R5T126PIcompared to other versions of the model. How-ever, since at the time of designing the domainfor the regional model, only the Indian landmasswas considered keeping in of the computationalrestrictions and domain size parameters (nlonr andnlatr), and entire Tibetan plateau was not cov-ered by the regional model domain. Even on day-3, the forecasts given by R5T126PI were strikinglyclose to the observed, indicating the fact that the

regional models have better short-range predictionskills compared to global models. These resultsclearly demonstrate the improvement in forecastskill obtained by increased resolution as well as theimpact of physical initialization.

3.3 Precipitation forecasts

Though practically it is not possible to predict pre-cipitation rates with high accuracy, any improve-ment in its prediction is considered a significantachievement, particularly for the Indian regionwhere its economy depends on the rainfall activityand its predictability. In figure 4, the rainfall pre-dictive skill over the Indian subcontinent is shownthrough the correlation coefficients. The three pan-els show correlation coefficients for forecast days


Figure 4. Time series of absolute correlation of observed and predicted rainfall over the Indian domain for the month ofAugust 1998. Details of experiments listed in the legend are provided in table 2.

Figure 5. Same as figure 4 except for RMS error of precipitation in mm.day−1.


Figure 6. Mean RMS error (mm · day−1) and mean correlation of precipitation for August 1998. Details of experimentslisted in the legend are provided in table 2.

1, 2 and 3. The line with the symbol ‘∗’ (thatstayed almost on the top of all other lines in eachpanel) corresponds to the results from R5T126PI.The correlation coefficients for GT126PI are shownthrough the line with ‘♦’ symbol. These resultsshow a marked skill at day-1 for the physicallyinitialized experiments, which were substantiallyhigher than the skill from the control runs. Theskill was measured through the absolute correlationof the 24-h rainfall totals at the transformed gridsquares between 5–30◦N and 65–120◦E. R5T126PIhad shown significant skill throughout the periodof study on all days of forecast. The time series ofRMS errors of rain rates is shown in figure 6. Herealso the R5T126PI had least errors, followed byGT126PI. The superior performance of R5T126PIis a result of both high resolution (0.5 degreelat./lon.) and utilization of physical initialization.On day-1 forecast, R5T126PI had an RMS errorof about 5 mm/day, which was increased to about7 mm/day on day 2 and to about 12 mm/day onday-3 while the control experiment went to theother extremes, starting from about 12 mm/dayof RMS error on day-1 to about 25 mm/day onday-3, which has no practical utility. The improve-ment in precipitation forecast skills by the regionalmodel with physical initialization is a major resultachieved in this study. The mean RMS errors andcorrelation coefficients of precipitation forecastsfrom all experiments are summarized in figure 6.The R5T126PI outperformed all other models at

each forecast range. A very high correlation ofabout 0.8 on day-1 forecast was achieved throughthese experiments.

A sequence of 3-day forecast of 24-h accumu-lated precipitation (mm.day−1) over the Indianmonsoon domain is demonstrated in figure 7(a, b,c). These figures show the rainfall forecasts validon August 7, 8 and 9, 1998. The correspondingobserved rainfall obtained from SSM/I+OLR datasets is shown in the top left panel of each diagram.The high spatial correlation of rainfall predicted byR5T126PI (figure 6) is evident in these diagramsas compared to the low-resolution global model(GT42). All other experiments, including GT126PIhave greatly distorted the rainfall patterns in theirpredictions with lot of spread, whereas R5T126PIcould reproduce most of the observed precipitationfeatures, even on day-3 of forecast. In particular,the regional model captured the heavy rainfall inthe northern parts of Bay of Bengal region withreasonable accuracy on all the three days.

4. High-resolution physical initializationwithin the regional spectral model

In short-range weather prediction over the mon-soon domain, it is important to have the appropri-ate physics to handle the broad scale features ofprecipitation. Although the physics of the modelincludes a cumulus parameterization scheme capa-ble of capturing the magnitude of condensation


Figure 7(a). Day-1 precipitation forecast (mm.day−1) valid on August 7, 1998. Observed precipitation is shown in the topleft panel. (X-axis from 60◦E to 110◦E, Y-axis from equator to 30◦N.) Details of experiments listed at the top of each panelare provided in table 2.

heating, the forecast deteriorates rapidly, probablydue to improper assimilation of rain rates. Physicalinitialization procedure assimilates observed rain

rates in to the model atmosphere and improvesthe forecasting capabilities of the model (sec-tion 3). However, the high resolution of global


Figure 7(b). Same as figure 7(a) but for day-2 forecast valid on August 8, 1998.

model (T126) is still not sufficient to examinethe meso-convective features of monsoon rainfall.The resolution of SSM/I microwave channels variesfrom roughly 30 to 60 km. Physical initialization atthis high resolution (about 50 km) is required to

nearly reproduce the ‘observed’ rain rates over thetransform grid squares. The stronger divergenceand heating fields evolve locally through this pro-cedure, thereby improving both the precipitationforecasts and wind forecasts. Though R5T126PI


Figure 7(c). Same as figure 7(a) but for day-3 forecast valid on August 9, 1998.

takes into account the physically initialized basefields obtained from GT126PI, it still lacks somevital information required at its resolution. It isimportant to redesign the physical initializationprocedure so that it can be applied directly at theregional model level to avoid loss of information

through interpolation from global to regional grid.In a detailed study by Krishnamurti et al (1998),experiments carried out at the resolution of T255(corresponding to about 50 km near the equator)were performed with a detailed physical initial-ization that described the initial distribution of


convective elements quite reasonably. The com-putational difficulties in using a high resolutionglobal model like T255 make it practically notviable for operational use. However, it is possible toimprove the tropical precipitation forecasts up to3 days by invoking physical initialization within ahigh resolution regional spectral model. In order toachieve this, temperature of the bottom slab of theatmosphere (soil temperature) is also prescribedduring the physical initialization procedure. Thiswas required since heat and moisture fluxes fromthe surface modify the state of the boundary layer,the mixing processes and the convective processes,which have relation to the overall circulation fea-tures. The ground flux (heat flux into the ground)is a small but very significant component of thesurface energy budget. This flux is also related tothe surface skin temperature. Since this flux is notmeasured directly, it needs to be parameterized fornumerical models. The FSUGSM contains a PBLparameterization scheme based on the similaritytheory (Businger et al 1971), which implicitly pre-scribes the ground temperature in calculating thesurface fluxes. In order to improve this formulation,the soil temperature was prescribed into the modelatmosphere based on the Force-Restore method(Stull 1988). The procedure for physical initializa-tion, including the incorporation of soil tempera-ture, at a high resolution, for the FSU modelingsystem is described below:

Step 1: Physical initialization of the global modelwith observed SSM/I and OLR merged rain ratesand soil temperature during pre-integration phase.The ECMWF’s observed (analyzed) soil temper-ature was also used along with the observed rainrates and OLR fields in this new physical initial-ization procedure.Step 2: The global model fields were interpolatedto the regional grid akin to the procedure explainedin section 2.2.Step 3: The regional model was physically ini-tialized (separately) using the observed SSM/Iand OLR merged rain rates and soil temperature(interpolated to the regional model resolution) forthat particular domain during the pre-integrationphase. This creates the physically initialized fieldsfor the regional model at a high resolution. Thenudging coefficients used for the regional modelwere slightly different from the global physicalinitialization procedure. Here the relaxation coef-ficients were 6 × 10−4s−1 for vorticity and sur-face pressure, and 1 × 10−4s−1 for divergence. Theincrease in these values compared to the globalmodel allows the iteration procedure to convergerapidly, approximately in 5–6 scans.

The global model and the regional model werethen integrated for 72 hours starting with the

Figure 8. Day-0 regional precipitation fields (mm.day−1) ofFSUNRSM at 0.5 degree resolution, obtained through phys-ical initialization at regional model level, valid on August 19,1998. Top panel shows the observed estimates for the sameday.

initial states obtained from the physical initializa-tion procedure described above. Using this proce-dure, one set of experiments was performed with astart date of August 18, 1998. Figure 8 illustratesthe initial rainfall from the regional physical ini-tialization. The top panel shows the observed esti-mates of rainfall while the bottom panel shows theinitialized rainfall estimates assimilated throughphysical initialization procedure applied separatelyfor the regional model. A very high nowcasting skillof above 0.95 was realized through this procedure.This is much higher than the correlation betweenobserved and initialized estimates of rain ratesachieved by the global model through the sameprocedure. An example of a 3-day forecast of pre-cipitation over the tropics from the regional modelwith physical initialization (Reg + PI + TSOIL)is presented in figure 9. A comparison of thisforecast with satellite based estimates of precip-itation (observed) provided in the extreme leftpanels and with other models, namely the controlexperiment (here GT126), and T126 with new


Figure 9. Day-1 to Day-3 forecasts of precipitation (mm.day−1) valid on 20, 21 and 22, August 1998. PI+TSOIL representsthe new physical initialization scheme that includes prescription of soil temperature. Observed precipitation is shown in theleft panel valid for each day of forecast. Control is the G126 experiment.


Figure 9. (Continued)

physical initialization (Glob + PI + TSOIL), indi-cates that this new experiment captures most ofthe precipitation features noted in the observedestimates on each day of the forecast. The impact

of physical initialization on precipitation forecastsfor the regional model is found to be much highercompared to that of the global model. Particu-larly, the rainfall that occurred over the southeast


Figure 10. Correlation of precipitation estimates overthe Indian monsoon domain for 3-day forecasts from(a) control (GT126), (b) GT126 with physical initializa-tion (global+PI), (c) GT126 with new PI that assimilatessoil temperature (global + PI + TSOIL) and (d) regionalmodel with new PI that assimilates soil temperature(regional + PI + TSOIL).

Indian region and across the Western Ghats wasreasonably captured by the regional model. Fig-ure 10 illustrates the correlation of the observedand the 24-hourly rainfall totals (mm.day−1) fordays 1, 2 and 3 of forecasts. It is apparent fromthese statistics that a much higher forecast skill ofprecipitation is realized from the use of physicalinitialization within the high resolution regionalspectral model. Both the global models (GT126PIand GT126PI +TSOIL) exhibit a high correlationof about 0.6 for day-1 forecasts whereas a cor-relation of about 0.7 is obtained by the regionalmodel with physical initialization that includessoil moisture initialization.

5. Multimodel/multianalysissuperensemble forecasts

The process of integrating several model fore-casts using statistical techniques (ensemble aver-aging) to reduce the forecast errors is found to bevery useful, particularly in the context of short-to-medium range weather prediction. Since theimprovement in model physics is inhibited bysparse observational network, many operationalforecasting centers round the globe have startedusing ensemble forecasting methods to improvethe skills of their forecasts. The success of super-ensemble methodology (Krishnamurti et al 1999,2000a, 2000b, 2001) in providing superior weatherand climate forecasts has opened gates for a newera of numerical weather forecasting. Unlike the

Figure 11. A schematic diagram of superensemble approachfor multimodel forecasts.

ensemble methodology where different model fore-casts are combined uniformly to minimize the fore-cast errors, superensemble removes the biases ofits model members collectively at every grid point,for each variable at each level. Superensemble isdeveloped by using a number of forecasts from avariety of NWP models. Along with the bench-mark observed (analysis) fields, these forecasts areused to derive simple statistics on the past behav-ior of the models. These statistics, combined withmultimodel forecasts, enable the construction of asuperensemble. The skill of this multimodel sta-tistical superensemble appears to far exceed thoseof the conventional ensemble averages and of themember models. The procedure used for designingthe superensemble forecasts is outlined in figure 11.This defines a control (training) phase and a fore-cast phase. The multimodel forecasts are availableduring both phases. The observed fields (analysis)are available only for the control phase. A simplemultiple linear regression of the model forecasts(anomaly fields) with respect to the observed fields,provide the useful statistics, which are deployedduring the forecast phase. The creation of a mul-timodel superensemble prediction at a given gridpoint is described through the formula:

S = O +n∑

i=1

ai(Fi − Fi)

where S is the superensemble prediction, O thetime mean of ‘observed’ state, ‘ai’ is weight for


Figure 12. Mean RMS error of 850 hPa total wind |V |(ms−1) over the Indian domain August 1998, from multimodels,ensemble mean (EM) and superensemble (SENS), for day-1, day-2 and day-3 forecasts.

model ‘i’, i is the model index, N is the number ofmodels used in constructing the superensemble, Fi

is the time mean of prediction by model ‘i’ and Fi

is the actual prediction by model ‘i’. The weights‘ai’ are computed at each grid point by minimizingthe function G =

∑t-traint (St − Ot)2. Here ‘O’ is

the observed state at time ‘t’ and ‘t-train’ is lengthof the training period.

5.1 850 hPa wind forecasts frommultimodel superensemble

In this study, seven NWP models were used toconstruct the superensemble forecasts: BMRC,ECMWF, UKMO, JMA, NRL, NCEP and CMC.These models have differing horizontal resolutionsand a wide variety of physical parameterizationschemes (Kumar 2000). In order to maintainuniformity, the model derived 850 hPa wind fore-casts were interpolated on to a 2.5 degree lati-tude/longitude grid. In total, the 7 models, eachmaking 92 3-day forecasts with a start time at12 UTC for each day starting from June 1, 1998were used in constructing the superensemble fore-casts. 61 days during June and July were treatedas the control (training) period and the remaining31 3-day forecasts for the month of August 1998were used in the forecast phase. The 850 hPa windsobtained from the experiments with FSUGSM andFSUNRSM during August 1998 were also used herefor comparison with multimodels, ensemble meanand the superensemble.

The mean rms error statistics for total wind(ms−1) over the Indian monsoon region at 850 hPa

for August 1998 corresponding to day-1, day-2 andday-3 of forecasts are shown in figure 12. Thesuperensemble was found to outperform variousmodels by roughly 20% to 45% at each forecastrange. A typical improvement of skill scores as highas 100% by the superensemble can be seen whencompared to one of the poorer models (here JMA).

In figure 13, the streamlines and isotachs at850 hPa for a typical day-3 forecast valid on August22, 1998 from the superensemble, best model (hereECMWF) and poor model (here JMA) are shownalong with the observed (analysis) winds valid forthat day. The improvements of the superensemble(shown in figure 13b) arise from a closer agree-ment of both wind direction and wind speed withrespect to the analysis field over the monsoondomain. The southwesterlies were somewhat over-estimated by the ECMWF forecast (figure 13c) andthe overall patterns of wind circulation were dis-placed, whereas the superensemble could predictthe observed features reasonably well. The fore-casts from JMA (figure 13d) were totally distorted,both in terms of wind direction and speed. Thiskind of performance of superensemble on a day-3 forecast can be considered as one of the majorbreakthroughs in the field of NWP.

5.2 Rainfall forecasts frommultianalysis superensemble

The method of multianalysis superensemble forprecipitation forecasts, originally developed byKrishnamurti et al (1999, 2001) utilizes a sim-ilar approach described in section 5.1. Here,


Figure 13. 850 hPa streamlines and isotachs for day-3 forecast valid on August 22, 1998. Magnitude of wind (m s−1) isshaded. (a) Observed, (b) superensemble, (c) best model (here ECMWF) and (d) poor model (here JMA). (X-axis from60◦E to 110◦E, Y-axis from 0◦–30◦N.)

combination of physical initialization based dataassimilation of observed rainfall rates is used togenerate a superensemble for precipitation fore-casts. The process of physical initialization tendsto have limitations beyond 24 h forecast, as it hasbeen noted that the correlation of rain rates rapidlydecreases from 24 h to 72 h of forecast. Inspired bythe success of multimodel superensemble approachfor NWP, the method of multianalysis superensem-ble was designed for use in precipitation fore-casts over the tropics. This method is similar tothe multimodel superensemble forecasting shown

in figure 11, except that instead of multimod-els, different versions of a single model (here theFSUGSM T126) were used with physical initializa-tion of observed rain rates derived from differentrain rate algorithms listed in table 3. Descriptionof these algorithms is provided in Krishnamurtiet al (2001) and Kumar (2000). The basic rain ratedata sets were derived from the TRMM satellitesand the SSM/I data from U.S. Air Force DMSPsatellites. A total of 155 precipitation forecastsfrom 5 different versions of FSUGSM were con-ducted using these rain rate algorithms, of which


Table 3. The rain rate algorithms used in the multianalysis superensemble.

Algorithm Brief details Reference

Control No physical initializationGPROF Uses SSM/I data Kummerow et al (1996)OLSON Cal/Val Algorithm. Uses SSM/I data Olson et al (1990)

Berg et al (1998)

FERRARO NOAA NESDIS Algorithm. Uses SSM/I data. Ferraro and Marks (1995)2A12 Uses NASA TRMM TMI data Kummerow et al (2000)TMI 2A12 + SSM/I GPROF Combination of TMI and SSM/I data is used. Kummerow et al (2000)

150 were used for the control (training) phaseand 5 for the forecast phase. The control exper-iment did not include any physical initializationand had the lowest skill among all experiments.A relationship between the multianalysis forecastsand the best observed estimates of daily rain ratewas determined through multiple regression basedstatistical weights that vary in space. During theforecast period, the statistics obtained in the con-trol period were applied to the multianalysis fore-casts to obtain the superensemble forecasts. Theforecasted rain rates for day-1, day-2 and day-3were then compared with the multianalysis mem-ber model forecasts and best observed estimates.The multianalysis superensemble forecasts werefound to be superior to that of the other mod-els. These forecasts also demonstrated the largeimpact of TRMM data sets on prediction of tropi-cal rainfall. Forecast skill from the proposed super-ensemble approach improved enormously when theTRMM/SSMI based rain rates were used as abenchmark for the definition of the superensemblestatistics and for the forecast verification.

The mean RMS error of precipitation(mm.day−1) on day-3 of the forecast (for the periodfrom August 1 to 5, 1998) is shown in figure 14.The superensemble had minimum errors comparedto other members of the multianalysis and also theFSUGSM and FSUNRSM experiments describedin earlier sections. RMS error from the super-ensemble stayed close to about 5mm.day−1 whileother members of the superensemble had errorsranging from 7 to 10mm.day−1. An example of aday-3 forecast of precipitation (mm.day−1) validon August 4, 1998 is shown in figure 15. Herethe top left panel shows the observed fields fromTRMM-2A12 + DMSP-SSM/I data sets. Forecastsfrom different versions of the FSU model (listedin table 3) are displayed along with the super-ensemble (SUPER), FSUGSM (GT126PI) andFSUNRSM (R5T126PI). The best model amongthe multianalysis members here is the one thatused TRMM + SSM/I data sets for physical ini-tialization. Invariably, forecasts from the super-ensemble exhibited the highest skill here, having a

close match with the observed patterns of rainfallover the Indian region. All other members had dif-ficulties in carving out the precipitation patternsacross this region, with a huge spread of heavyprecipitation along the central and northern partsof India.

The results shown here are typical of super-ensemble, which are being noted in almost all thedays of forecast. The major question that arises ishow the superensemble pushes the skill to supe-rior levels when the skill of the member mod-els is much less. More than 40% improvementsimply comes from the relationship of the fore-casts from multianalysis members forecasts and theobserved fields during the training period. It wasalso noted that the superensemble performs bet-ter than simple ensemble mean of the forecasts,Krishnamurti et al (1999). The superensemble pro-cedure evidently removes the local rainfall bias ofthe forecasts arising from the use of different rainrate algorithms. The collective bias removal givessuperior results compared to the removal of thebias of the individual members (and averaging suchresults). The feasibility of real time precipitationforecasts using a multianalysis superensemble hasemerged from these experiments, and at present,real time 5-day global precipitation forecasts areproduced on a daily basis at FSU and are postedon the website (http://lexxy.met.fsu.edu/rtnwp).

6. Summary and conclusions

The primary goal of this study was to improve theskills of the numerical weather prediction over theIndian subcontinent. This has been accomplishedthrough the use of a high-resolution nested regionalspectral model with physical initialization. Currentcomputing resources tend to limit the resolution ofglobal models, justifying the use of high-resolutionregional models in studying complex weather pat-terns like monsoon and tropical storms. The nestedregional spectral model developed by Cocke (1998)was used in this study to assess the impact ofresolution and physical initialization of observed


Figure 14. RMS errors of rain rates (mm.day−1) over the Indian region for day-3 forecast (start dates ranging from August1 to 5, 1998). Control is GT126. GPROF, Olson, Ferraro, TRMM and TRMM + SSM/I are multianalysis components ofFSUGSM with PI.

rain rates on short-range weather prediction overthe Indian subcontinent. The compatibility of thisregional spectral model with the FSU global spec-tral model makes it more convenient for opera-tional real time forecast initiative. The forecastskills of the regional spectral model with physicalinitialization of observed rain rates during the pre-integration phase were superior to the skills of boththe low-resolution global/regional models and thecontrol experiments without physical initialization.The regional spectral model at 0.5 degree resolu-tion has shown a higher skill for short-range (up to3 days) forecasts during the monsoon season overthe Indian subcontinent. The wind forecasts andprecipitation rates predicted by the regional modelwere found to be more accurate and had a closermatch to the observed fields.

From all the experiments described in this study,FSUNRSM was found to provide vast improve-ment over the FSUGSM. The greatest increase inperformance occurred during day-1 forecast anddecreased rapidly by the day-3 forecast. Improve-ment of the skills beyond day-1 forecast werefound possible through the use of physical ini-tialization where observed measures of rain ratesobtained from satellite data sets were assimilateddirectly at the regional spectral model level in thepre-integration phase, along with assimilation ofsoil temperature analysis. A high correlation of0.95 was achieved for nowcasting of precipitationthrough this procedure. The correlation of rainrates for days 1, 2 and 3 of forecasts were foundto be of the order of 0.7, 0.6 and 0.55 respec-tively and these correlations were much highercompared to experiments from all other versions

of the FSU spectral model. Physical initializationappears to be a powerful tool for short-rangeforecasting of tropical precipitation. This proce-dure enhances the definition of mesoscale diver-gence, vorticity, vertical motion, convective heatingand the surface pressure tendencies (Krishnamurtiet al 1991), thereby increasing the forecast skill oftropical precipitation. Physical initialization alsoprovides consistency among the model precipita-tion, evaporation, convergence of moisture flux andlocal changes in the precipitable water through aset of reverse physical algorithms and Newtonianrelaxation (nudging) procedure. FSU model has ageneral tendency of overestimation of precipitation(a typical nature of modified Kuo scheme for cumu-lus parameterization). Though the ‘bull’s eye’ pat-tern is noticed in the results, it is not certain atthis time to attribute this to PI procedure alone.More careful evaluation of PI will be presented in afuture publication where we used T255L29 versionof FSU model and TRMM rain rates for PI.

The notion of superensemble, whose skills appearto far exceed those of conventional ensemble meanand member models, is based on the collectivebias removal of member models at every gridlocation for each variable. Seven different oper-ational global models were chosen in this studyto construct the multimodel superensemble thatincludes a training and a forecast phase. The 3-dayforecasts of 850 hPa zonal and meridional windsfor the months of June, July and August 1998from all member models were used along withthe observed (analysis) fields from ECMWF. The61-day data from June and July were used inthe training (control) phase to derive independent


Figure 15. An example of day-3 forecast of precipitation (mm.day−1) valid on August 4, 1998 for the Indian monsoonregion. Observed estimates shown in the upper left panel are from TRMM and SSM/I. Different panels show forecasts frommultianalysis members, superensemble, FSUGSM and FSUNRSM. (X-axis from 60◦E to 120◦E, Y-axis from 0◦–30◦N.)


Table 4. Correlation of precipitation forecasts from different experiments.

Forecast experiment Day 0 Day 1 Day 2 Day 3

Without physical initialization (Control – GT126) 0.35 0.40 0.35 0.30With physical initialization (Global Model – GT126PI) 0.87 0.58 0.42 0.35With high-resolution physical initialization 0.95 0.71 0.62 0.55

(Regional Model – PIR5T126PI)Multianalysis superensemble 0.93 0.73 0.65 0.58

sets of regression coefficients for all grid pointsat each forecast range. Using these coefficientsin the forecast phase (here August 1998), thisnew approach succeeded in achieving remarkableimprovements in the forecasting skills. The multi-model superensemble method greatly enhanced theskills of wind forecasts at 850 hPa over the mon-soon domain and it outperformed all other mem-ber models, including the conventional ensemblemean where all member models are given uniformweight irrespective of their past performance. RMSerrors of superensemble forecasts for 850 hPa windsover the Indian region were reduced by about 20%compared to the best model. The multianalysissuperensemble method provided a new approachto produce more reliable rainfall forecasts overthe Indian subcontinent. Each of the multianaly-sis components come from the use of the FSUglobal spectral model physically initialized usingrain rate estimates retrieved from different algo-rithms for the TRMM/TMI and SSM/I data sets.A major improvement in the skills of rainfall fore-casts is obtained through this method. The essen-tial nature of precipitation over the tropics wasmeso-convective in character, and the loss of accu-racy of the larger scale models was sufficient tooffset any positive impacts from simple changesin the initialization procedures. The multianalysissuperensemble proposed here looks at past rain-fall observations derived from the TRMM and theDMSP satellites’ microwave instruments. Inclusionof the detailed past rainfall data sets is a uniquefeature of this superensemble. The forecasts fromthe multianalysis data project the past relationship(between model forecasts and the observed rain)into the future, thereby providing a very high skillfor short-range rainfall forecasts.

The results presented in this paper mainly dealwith five types of experiments based on

(a) global model (and its resolution);(b) physical initialization for the global model

(combined with varying resolution);(c) regional model (based on physically initialized

global model data sets);(d) physical initialization for the regional model;

and(e) superensemble.

The skills of the short-range forecasts increasefrom (a) to (e). This is summarized through thecorrelation of the observed and predicted rainfallskills over the Indian monsoon domain from day-1 through day-3 from different experiments con-ducted in this study (table 4). The results obtainedfrom these different experiments provided a greatinsight into the numerical weather prediction capa-bilities over the Indian subcontinent. The high-resolution regional model with physical initializa-tion has shown promising results in this endeavor.More experiments are needed with this regionalmodel to further enhance its forecasting capabil-ities. The prescription of soil moisture throughforce-restore method needs better formulation andpresently some work is going on in this direc-tion. The multimodel/multianalysis superensem-ble approach is also another area where vastimprovements are taking place. The Guass-Jordanmethod of elimination applied in the construc-tion of covariance matrices in the multiple linearregression procedure is found to be sensitive tothe singular values. Different methods like Singu-lar Value Decomposition (SVD), Kalman Filter,EOF, an area of future work would be to explorethe usefulness of Singular Value Decomposition(SVD), Z-transforms, Empirical Orthogonal Func-tions (EOFs) and cyclostationary EOFs are beingused to remove the ill conditioning of the covari-ance matrices (Yun et al 2003). Many other mod-ifications like optimizing the number of trainingdays and the number of multimodels requiredin the training phase of the superensemble arealso being carried out at present and the perfor-mance of superensemble is being tested for tropi-cal cyclone forecasts (Kumar et al 2002; Willifordet al 2002) and flood forecasts apart from seasonalclimate forecasts and real-time numerical weatherprediction.

Acknowledgements

The research reported here was funded by NASAgrant Nos. NAG5-9662 and NAG8-1537; NSF grantNos. ATM-9910526 and ATM-0108741 and FSURFCOE. We acknowledge the constructive commentsof the reviewers and from the editor in improvingthe quality of this manuscript.


Appendix 1: The Florida State UniversityGlobal Spectral Model (FSUGSM)

• Independent variables: λ, θ, σ, t.• Dependent variables: vorticity, divergence, tem-

perature and moisture variable (dew pointdepression).

• Model variables are staggered in the verticalusing Charney–Phillips vertical discretization –vorticity, divergence, wind and geopotentialare located at layer interface while tempera-tures, specific humidity and vertical velocity areassigned at the center of the layer. The verticalgrid has higher resolution in stratosphere and inplanetary boundary layer.

• Time integration scheme: the divergence equa-tion, thermodynamic equation and pressure ten-dency equation are integrated implicitly whilefor vorticity equation and moisture continu-ity equation explicit time integration scheme isused. The tendencies of the physical processesare integrated using a forward time integrationscheme.

• Space differing scheme: Spectral in the horizon-tal; centered differences in the vertical for allvariables except moisture which is handled by anupstream differencing scheme.

• Surface topography is based on envelope orogra-phy (Wallace et al 1983).

• Parameterization of physical processes:

– Deep convection: based on modifiedKuo cumulus parameterization scheme(Krishnamurti et al 1983; Krishnamurti andBedi 1988; Kuo 1965, 1974), where the moist-ening and mesoscale convergence parametersare obtained from 700 hPa vorticity and meanvertical velocity averaged over cloud depththrough a regression relation.

– Shallow convection (Tiedke 1984).– Dry convective adjustment.– Large-scale condensation (Kanamitsu 1975).

The scheme accounts for evaporation of fallingprecipitation.

– Surface fluxes of heat, moisture and momen-tum are calculated using similarity theory (Bu-singer et al 1971). For low speeds (≤ 5m s−1)moisture fluxes are calculated following Bel-jaars and Miller (1990).

– Vertical distribution of fluxes in the freeatmosphere is based on stability (Richardsonnumber) dependent exchange coefficient (Louis1979).

– 4th order horizontal diffusion (Kanamitsu et al1983).

– Vertical diffusion based on the K-theory forrepresentation of energy sinks in the model(Louis 1979).

– Long and shortwave radiative fluxes based ona band model (Harshvardan and Corsetti 1984;Lacis and Hansen 1974).

– Diurnal solar cycle.– Parameterization of low, medium and high

clouds for radiative transfer calculation isbased on threshold relative humidity. Fractionarea of various cloud distribution configura-tions in the vertical is based on random overlapconsideration.

– Surface temperatures: Prescribed over theoceans, while over the land a surface energybalance coupled to the similarity theory deter-mines the surface temperature including itsdiurnal cycle (Krishnamurti et al 1991).

• Initialization: The initialization of the model isachieved in two stages:

– Nonlinear normal mode initialization (Kitade1983), wherein the tendencies of first 5 modeswith phase speed exceeding about 30m s−1

are damped during the initialization. The slowmoving higher modes are allowed to adjustfreely.

– Physical initialization wherein moisture field,heat sources and sinks and divergence fields areinitialized consistent with observed OLR andrain rates (Krishnamurti et al 1991).

Further details of the model including its math-ematical formulation, description of the physi-cal parameterizations and their application inFSUGSM are provided in detail in Kumar (2000).

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High resolution numerical weather prediction over the