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  • View in gallery

    The vertical line in the center denotes time t = 0, and the area to the left denotes the training area where a large number of forecast experiments are carried out by the multianalysis–multimodel system. During the training period, the observed fields provide statistics that are then passed on to the area on the right, where t > 0. Here the multianalysis–multimodel forecasts along with the aforementioned statistics provide the superensemble forecasts

  • View in gallery

    An example of superensemble methodology at a single site. (top) Training period rainfall for 3 multianalysis forecasts—the ensemble mean (thin lines), observed rain (dark, thick line), and the superensemble forecast (thick line). (bottom) Rain predicted by 3 multianalyses, the ensemble mean, the superensemble, and the observed rain, all in units of mm day−1. The acronyms FER, OLS, and TMI represent the multianalysis components of Ferraro, Olson, and TMI+SSM/I forecasts, respectively

  • View in gallery

    The correlation of forecast rain against observed estimates, from Treadon (1996), plotted as a function of forecast days. The results from the operational forecasts from NCEP and from two versions of physical initialization are shown here. These results were obtained using NCEP operational model at the resolution T62 from several experiments

  • View in gallery

    Observed (TRMM-2A12 + SSM/I-GPROF) and physically initialized rain for 14 Jun 2000. Units: mm day−1

  • View in gallery

    Days 1, 2, and 3 of forecast rain (mm day−1) for 6 June 2000 from the superensemble forecast is compared with the observed rainfall estimate from the TMI-2A12 and SSM/I-GPROF algorithm

  • View in gallery

    The observed rainfall estimate from the TMI-2A12 and SSM/I-GPROF algorithm for 6 Jun 2000 is compared with the day 3 forecasts from the 11 member models of the multimodel–multianalysis system studied here

  • View in gallery

    Skill of rainfall forecasts (rmse) over the global belt between 50°S and 50°N for days 1, 2, and 3 of forecasts. Dotted lines denote multimodel skills. The heavy, dashed line denotes skill of the ensemble mean, and the thin, solid line denotes skill of the individual model's bias-removed ensemble mean, and the thick, black line denotes the superensemble. The first 75 days denote a training period, whereas the last 15 days are the forecast days

  • View in gallery

    Forecast skill (based on correlation of observed rainfall estimates from TRMM-2A12 and the SSM/I-GPROF) and the superensemble for day 1, day 2, and day 3 forecasts during Mar and Apr 2000

  • View in gallery

    Rmse of precipitation forecasts over different domains. The results for 6 member models, the ensemble mean, and the superensemble are displayed for 6 regions

  • View in gallery

    Percentage improvement (based on correlation) of the superensemble forecasts over the ensemble mean, the best, and the poorest models

  • View in gallery

    Histograms showing percent improvement (based on correlation) of the superensemble forecast over the ensemble mean, the best model, and the worst model for the global belt, 50°S–50°N

  • View in gallery

    Rmse skill is plotted as a function of the number of training days over North America. The skill is for 3-day forecasts made after the training on several successive forecast days during Apr 2000

  • View in gallery

    (a) Day 1, (b) day 2, and (c) day 3 forecasts's rmse skill using a poor analysis of initial rain as the training rainfall is shown. The skill of that superensemble is the top curve with the largest rmse. The skill of the multianalysis–multimodel superensemble based on TRMM-2A12 and the SSM/I-GPROF is the bottom curve with the highest skill. The remaining curves denote the skills of selected member models and that of the ensemble mean

  • View in gallery

    Day 1 superensemble forecast of rain (mm day−1) for representative points over 6 different regions are compared to the observed estimates derived from different rain-rate algorithms from TMI + SSM/I, Ferraro, Olson, GEO, and Turk forecasts. These are averaged for the entire month of April 2000

  • View in gallery

    A Hovmöller diagram of daily precipitation (mm day−1) on day 3 of forecasts during the Mozambique floods. Ordinate shows days (bottom to top); abscissa denotes longitude. The three panels denote (left) observed rain (from TRMM-2A12 plus SSM/I GPROF); (middle) superensemble forecasts; (right) best operational model

  • View in gallery

    (a)–(d) Track forecasts for Hurricane Floyd on different start dates. Heavy black line denotes official best track. The red line adjacent to it is the superensemble forecast. The others are for some of the member multimodels. (e) Observed 5-day rainfall over North Carolina from Hurricane Floyd during 12–17 Sep 1999. (f)–(k) Observed, day 2, and day 3 superensemble-based precipitation forecasts during the passage of Hurricane Floyd are shown. Two start dates of forecasts are illustrated here

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Real-Time Multianalysis–Multimodel Superensemble Forecasts of Precipitation Using TRMM and SSM/I Products

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  • * Department of Meteorology, The Florida State University, Tallahassee, Florida
  • | + Department of Atmospheric Sciences, Colorado State University, Fort Collins, Colorado
  • | # NASA Goddard Space Flight Center, Greenbelt, Maryland
  • | @ NASA Headquarters, Washington, D.C.
  • | 5 Joint Center for Earth Systems Technology, University of Maryland, Baltimore County, Baltimore, Maryland
  • | * *Marine Meteorology Division, Naval Research Laboratory, Monterey, California
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Abstract

This paper addresses real-time precipitation forecasts from a multianalysis–multimodel superensemble. The methodology for the construction of the superensemble forecasts follows previous recent publications on this topic. This study includes forecasts from multimodels of a number of global operational centers. A multianalysis component based on the Florida State University (FSU) global spectral model that utilizes TRMM and SSM/I datasets and a number of rain-rate algorithms is also included. The difference in the analysis arises from the use of these rain rates within physical initialization that produces distinct differences among these components in the divergence, heating, moisture, and rain-rate descriptions. A total of 11 models, of which 5 represent global operational models and 6 represent multianalysis forecasts from the FSU model initialized by different rain-rate algorithms, are included in the multianalysis–multimodel system studied here. In this paper, “multimodel” refers to different models whose forecasts are being assimilated for the construction of the superensemble. “Multianalysis” refers to different initial analysis contributing to forecasts from the same model. The term superensemble is being used here to denote the bias-corrected forecasts based on the products derived from the multimodel and the multianalysis. The training period is covered by nearly 120 forecast experiments prior to 1 January 2000 for each of the multimodels. These are all 3-day forecasts. The statistical bias of the models is determined from multiple linear regression of these forecasts against a “best” rainfall analysis field that is based on TRMM and SSM/I datasets and using the rain-rate algorithms recently developed at NASA Goddard Space Flight Center. This paper discusses the results of real-time rainfall forecasts based on this system. The main results of this study are that the multianalysis–multimodel superensemble has a much higher skill than the participating member models. The skill of this system is higher than those of the ensemble mean that assigns a weight of 1.0 to all including the poorer models and the ensemble mean of bias-removed individual models. The selective weights for the entire multianalysis–multimodel superensemble forecast system make it superior to individual models and the above mean representations. The skill of precipitation forecasts is addressed in several ways. The skill of the superensemble-based rain rates is shown to be higher than the following: (a) individual model's skills with and without physical initialization, (b) skill of the ensemble mean, and (c) skill of the ensemble mean of individually bias-removed models.

The equitable-threat scores at many thresholds of rain are also examined for the various models and noted that for days 1–3 of forecasts, the superensemble-based forecasts do have the highest skills. The training phase is a major component of the superensemble. Issues on optimizing the number of training days is addressed by examining training with days of high forecast skill versus training with low forecast skill, and training with the best available rain-rate datasets versus those from poor representations of rain. Finally the usefulness of superensemble forecasts of rain for providing possible guidance for flood events such as the one over Mozambique during February 2000 is shown.

Corresponding author address: Dr. T. N. Krishnamurti, Department of Meteorology, The Florida State University, Tallahassee, FL 32306-4520. Email: tnk@io.met.fsu.edu

Abstract

This paper addresses real-time precipitation forecasts from a multianalysis–multimodel superensemble. The methodology for the construction of the superensemble forecasts follows previous recent publications on this topic. This study includes forecasts from multimodels of a number of global operational centers. A multianalysis component based on the Florida State University (FSU) global spectral model that utilizes TRMM and SSM/I datasets and a number of rain-rate algorithms is also included. The difference in the analysis arises from the use of these rain rates within physical initialization that produces distinct differences among these components in the divergence, heating, moisture, and rain-rate descriptions. A total of 11 models, of which 5 represent global operational models and 6 represent multianalysis forecasts from the FSU model initialized by different rain-rate algorithms, are included in the multianalysis–multimodel system studied here. In this paper, “multimodel” refers to different models whose forecasts are being assimilated for the construction of the superensemble. “Multianalysis” refers to different initial analysis contributing to forecasts from the same model. The term superensemble is being used here to denote the bias-corrected forecasts based on the products derived from the multimodel and the multianalysis. The training period is covered by nearly 120 forecast experiments prior to 1 January 2000 for each of the multimodels. These are all 3-day forecasts. The statistical bias of the models is determined from multiple linear regression of these forecasts against a “best” rainfall analysis field that is based on TRMM and SSM/I datasets and using the rain-rate algorithms recently developed at NASA Goddard Space Flight Center. This paper discusses the results of real-time rainfall forecasts based on this system. The main results of this study are that the multianalysis–multimodel superensemble has a much higher skill than the participating member models. The skill of this system is higher than those of the ensemble mean that assigns a weight of 1.0 to all including the poorer models and the ensemble mean of bias-removed individual models. The selective weights for the entire multianalysis–multimodel superensemble forecast system make it superior to individual models and the above mean representations. The skill of precipitation forecasts is addressed in several ways. The skill of the superensemble-based rain rates is shown to be higher than the following: (a) individual model's skills with and without physical initialization, (b) skill of the ensemble mean, and (c) skill of the ensemble mean of individually bias-removed models.

The equitable-threat scores at many thresholds of rain are also examined for the various models and noted that for days 1–3 of forecasts, the superensemble-based forecasts do have the highest skills. The training phase is a major component of the superensemble. Issues on optimizing the number of training days is addressed by examining training with days of high forecast skill versus training with low forecast skill, and training with the best available rain-rate datasets versus those from poor representations of rain. Finally the usefulness of superensemble forecasts of rain for providing possible guidance for flood events such as the one over Mozambique during February 2000 is shown.

Corresponding author address: Dr. T. N. Krishnamurti, Department of Meteorology, The Florida State University, Tallahassee, FL 32306-4520. Email: tnk@io.met.fsu.edu

1. Introduction

This paper is built on two concepts, physical initialization (Krishnamurti et al. 1991; Puri and Miller 1990; Treadon 1996, 1997; Kasahara et al. 1994; Marécal and Mahfouf 2000; Hou et al. 2000) and multianalysis–multimodel superensemble forecasts (Krishnamurti et al. 1999, 2000a,b). This study is different from our previous papers, in that we combine here several multianalysis models with the results from several operational models. A list of acronyms is provided in Table 1. The size of the overall ensemble (11) is much larger than our previous studies. Furthermore, this modeling study exploits precipitation estimates from TRMM (Kummerow et al. 2000) for the real-time prediction of precipitation. In order to improve precipitation forecast skills, we address the following: (a) Improved global rainfall estimates, such as those provided by TRMM and DMSP satellites. For this purpose, several current rain-rate algorithms that translate microwave radiances from the satellites into rainfall estimates were compared in the context of global numerical weather prediction. (b) Physical initialization, where these rain rate estimates were assimilated by the models. (c) Rainfall forecasts from several current operational models. These provide the current operational skills of rainfall forecasts. (d) Multianalysis–multimodel superensemble. This includes a training and a forecast phase from many experiments. Figure 1 provides an outline of this procedure. Here we take some 120 3-day forecasts made by global modelers. Given roughly 120 such recent past global forecasts and the best estimate of the respective observed fields, a simple linear multiple regression is computed to determine the statistical weights (see appendix B). Some 106 such weights describe the model biases at each geographical location, each vertical level, each variable, and for each of the participating member models. These statistics are next used to construct the superensemble forecasts. It has been shown by Krishnamurti et al. (1999, 2000a,b) that this is a very powerful method. The superensemble invariably performs somewhat better than all multimodels that participate in this exercise.

Many results on tropical numerical weather prediction have emerged from these studies. The superensemble has a higher forecast skill compared to that of the ensemble mean. That difference arises because the ensemble mean assigns a weight of 1.0 to all participating models and does not correct the bias of the models based on their past behavior. This results in the inclusion of some of the poorer models as well, thus the skill of the ensemble mean is degraded. The superensemble is selective in assigning weights and the past history of performance of models has a major role compared to that of current forecasts by the multimodels. The superensemble also performs better than the ensemble mean of “bias removed” individual models.

In this study the rainfall estimates are derived from the microwave images of NASA's TRMM and the U.S. Air Force's four DMSP satellites. A total of five satellites provided coverage over the global belt between roughly 60°S to 60°N. The footprint of the TRMM and the DMSP's SSM/I images averages to around 35 km. It was possible to obtain between three and four rainfall estimates per day at roughly this resolution over the entire belt. Rainfall estimates are obtained from a variety of rain-rate algorithms. Given the microwave imager's datasets, we next made use of these algorithms to obtain rain rates. These are then subjected to physical initialization that passes the rain rate to the model during its assimilation cycle. This is carried out via a number of reverse physical parameterization algorithms that permit the model to assimilate a nearly identical rain rate (Krishnamurti et al. 1991). These different rain-rate initializations provided multianalysis forecasts for this study. The assimilated states differ in their initial descriptions of rainfall, divergence, heating rates, moisture, and surface pressure tendencies. In addition to these, we make use of the multimodels from a number of weather services that provide real time global forecast datasets to us. These include the NCEP, BMRC, JMA, NOGAPS, and RPN models. Thus, in all, we include 11 models (of which 6 are multianalysis and 5 are multimodels) in our multianalysis–multimodel system. The procedure for the superensemble training and forecasts were discussed in Krishnamurti et al. (2000b). Section 2 provides a description of datasets and lists of participating multianalysis–multimodel components are given in section 3. A brief review of physical initialization is given in section 4. Section 5 provides a description of the various rain-rate algorithms used in this study. Section 6 of this paper discusses the results of real-time forecasts of precipitation. Conclusions are summarized in section 7. It should be noted that this global real-time system does include forecasts for all of the variables.

a. What is a precipitation superensemble?

This is best illustrated from the examination of rainfall forecasts at a single site. In Fig. 2, we show the 3-day forecasts from the multianalysis (from a sample of just three models). Here the period, 1 August–30 September 1999, is shown. The site chosen is located at 5°N and 125°E (or the grid point closest to it). The top panel shows the predicted rainfall (thin lines) and the observed rainfall (24-h totals in mm day−1) using heavy dark lines. Using a multiple regression approach, we can calculate the multiregression coefficient for the multimodel forecast rainfall totals against the observed rainfall. That, for the training period between 1 August and 30 September 1999, is shown in the top panel by the next thickest line. Using these coefficients, one can make a 3-day forecast for the next day (i.e., 1 Oct 1999). These are shown in the lower panel. The member model forecasts of rain for day 3 of the forecasts lie between 9.5 and 13.4 mm day−1. The observed rain was 21.0 mm day−1. The superensemble forecast based on these model forecasts and the training period coefficients comes to roughly 19.3 mm day−1. This major improvement in rainfall forecasts is reflected in the global applications illustrated in this paper.

2. Datasets used

This study makes use of a number of datasets:

  1. Daily ECMWF operational analysis. This analysis is based on four-dimensional data assimilation that includes a variety of datasets. Some 350 000 observations in total arrive on a 24-hr interval that are presently being handled by the ECMWF. These include roughly 50 000 upper air stations roughly 35 000 commercial aircraft wind reports, roughly 35 000 land and marine surface stations, roughly 25 000 cloud-and water vapor–tracked winds from geostationary satellites, roughly 120 000 TOVS radiances from NOAA satellites, and roughly 35 000 AMSU data products.

  2. We augment the ECMWF analysis by performing physical initialization. Here we currently use microwave radiance datasets from five satellites. These include the NASA TRMM satellite that provides microwave datasets over the tropical latitudes, Kummerow et al. (1998). Furthermore, we include microwave datasets from the polar-orbiting DMSP satellites of the U.S. Air Force. These are the current F11, F13, F14, and F15 satellites. The microwave datasets derived from these satellites are identified as SSM/I products.

  3. In addition to the above datasets, we also use tabulations of current 10-day averaged sea surface temperatures from NCEP.

  4. Other time invariant data sets include topography and surface albedo derived from the files of U.S. Navy and NASA-Goddard respectively.

3. List of participating models

The following is a list of multimodels that are used in the present study: (a) NCEP Aviation model, (b) BMRC, (c) NOGAPS, (d) JMA, and (e) RPN. The reader is referred to the official documentation of the relevant operational centers for descriptions of the models.

The following is a list of the multianalysis components of this study, all of these make use of the FSU model for forecasts: (a) FSU Global Spectral Model, (see Appendix A); (b) physical initialization using Ferraro (1997) and Ferraro et al. (1998) algorithm and SSM/I rain rates; (c) physical initialization using the Olson et al. (1990) algorithm and SSM/I rain rates; (d) blended geostationary and microwave rain-rate (GEO) algorithm (Turk et al. 2001), (e) combined TRMM, SSM/I and geostationary satellite-based algorithm (Turk et al. 2001); and (f) combined TRMM (2A12) and SSM/I (GPROF) algorithm (Kummerow et al. 2000).

4. Physical initialization

An important element of the multianalysis component is the physical initialization (Krishnamurti et al. 1991). Given these different initial rain rates from the different satellite-based algorithms, the use of physical initialization within the data assimilation produces sufficiently different analyses. This enables us to tag these as distinct members of a multianalysis superensemble. The analysis differences arise from the differences in the prescribed rain rates. This results in differences in the mass and moisture convergence fields, vertical distribution of heating, vertical distribution of specific humidity, and the surface pressure tendencies.

Physical initialization passes the observed interpolated rainfall rates, every time step and at every rain location via a number of reverse algorithms. The following components of physical initialization are used in this study:

  1. The reverse surface similarity makes use of the vertically integrated equations for the apparent moisture sink, following Yanai et al. (1973), i.e.,
    2êp̂.
    The total precipitation, p̂, is provided by the TRMM and SSM/I estimates from the various rain rate algorithms. 2 is determined during the data assimilation phase. This field (called the apparent moisture sink) evolves with the prescribed rain-rate inputs. Thus, the reverse similarity provides an evolving field of evaporation ê consistent with the imposed rain rates. The final step in this component of the analysis is to derive the moisture field of the constant flux layer that is consistent with ê using the reverse surface similarity algorithm (Krishnamurti et al. 1991). That moisture data is assimilated by the model to assure that the forward model's constant flux layer is consistent with the observed rain rates.
  2. OLR matching is another component of physical initialization. This is a simple procedure that forces the model-based OLR field toward those of the satellite observation. It is based on the premise that moisture observation (and the analysis of moisture) is deficient above the 500-hPa level. Over that region a simple structure function for the specific humidity, which is an exponential decay function of the type aebp where a and b are constants and p is the pressure level, utilizes the moisture analysis at the 500-hPa surface to determine one of these constants, and the other constant is determined by requiring that the difference between the model and the satellite-based OLR is vanishingly small (i.e., ≈10 W m−2). This procedure improves the structure of the upper tropospheric moisture distribution somewhat. The moisture distributions are nudged towards these values during the data assimilation.

  3. The reverse cumulus parameterization algorithms have been developed for FSU's modified Kuo scheme (Krishnamurti et al. 1991), and also for the Arakawa–Schubert scheme (Treadon 1996). The Kuo scheme described in Krishnamurti et al. (1991) is used in the present study. Given rainfall distribution derived from SSM/I and/or TRMM datasets and rain-rate algorithms, the reverse algorithms (within the data assimilation and physical initialization) augments the humidity, heating, divergence, and surface pressure tendencies consistent with the imposed precipitation rates and the nudged large-scale fields of vorticity and divergence.

The nowcasting skill of physical initialization has been known to be very high. This is often expressed as a correlation of the imposed precipitation rate and the precipitation rate at the initial time of the model. These are invariably around 0.9 from the use of the reverse cumulus parameterization schemes of FSU and NCEP (Krishnamurti et al. 1994; Treadon 1996). Figure 3, from the study of Treadon, illustrates the forecast skill of the NCEP model for days 0, 1, 2, 3, and 4 of forecasts (based on the use of the reverse Arakawa–Schubert scheme). These forecasts show a major improvement from the physical initialization over the operational skill for days 0 and 1 of forecasts and only a marginal improvement is noted thereafter. Various attempts were made to further improve beyond these skills by implementing various parameter estimation techniques for the entire global spectral model (Shin and Krishnamurti 1999). None of these efforts provided any major improvements beyond those seen in Fig. 3. This present paper shows an avenue for improving the skills beyond those seen from running a single model with physical initialization.

The robustness of physical initialization is best seen from a comparison of the “observed” rain (based on current TRMM algorithms, described in section 5, TRMM-2A12 + SSM/I-GPROF) with the physically initialized rain. Figure 4 shows a recent example of rainfall total (from 1200 UTC 13 June to 1200 UTC 14 June 2000) from our real-time files. The top panel describes the observed rain, whereas the bottom panel is from the model. The correlation between these panels is 0.95. This illustration deserves a careful look. The more reddish colors denote rainfall totals above 40 mm day−1. A large number of small pockets of heavy rain, in excess of 40 mm day−1, have been very successfully captured in size and location by the physical initialization. It is that robustness (in detail) of physical initialization that provides a consistent nowcasting skill of around 0.90 or higher each day in our real-time forecasts. This is being accomplished for each member of the multianalysis component; as a consequence, this skill gets passed on to the superensemble whose nowcasting skill also reaches very high values for its initial state.

5. Rain-rate algorithms

The TRMM microwave instrument TMI is a nine-channel radiometer. Eight of these are dual-polarization channels measuring radiances in both horizontal and vertical polarizations at 10.7, 19.4, 37, and 85.5 GHz. There is an additional channel at 21.3 GHz, which only provides measurements in the vertical polarization. This radiometer receives passive microwave radiation from atmospheric oxygen and water vapor, liquid and ice-phase hydrometeors in clouds, and the Earth's surface. The different channels have responses through different depths of the atmosphere. Thus, a combination of these channels yields information regarding cloud and precipitation vertical structure. Ground validation is a major component for rainfall retrievals for the microwave radiance datasets (Kummerow et al. 2000).

The SSM/I instrument, on board several DMSP satellites (F11, F13, F14, and F15) is also a passive microwave radiometer with channels at four frequencies: 19.35, 22.235, 37.0, and 85.5 GHz. Of these, the 22.235 GHz channel senses only in the vertical polarization, while the other channels are dual-polarized (vertical as well as horizontal). Currently, there are four DMSP satellites that provide these radiometer datasets. The following rain-rate algorithms are being incorporated in our definitions of initial rain using physical initialization for the multianalysis component:

  1. Control experiment (hereafter referred to as Control forecast). We have deliberately included a control experiment within this family of models. This does not include physical initialization, thus this model does not know the initial observed rain rates. This is similar to what is done with several operational models. This generally provides a lower skill among members for the superensemble.

  2. Ferraro and Marks (1995) algorithm (hereafter referred to as Ferraro forecast). This is also called the NOAA–NESDIS SSM/I algorithm. This includes scattering emission aspects in its design. A number of global radar datasets for Japan, the United States, and United Kingdom from as many as 22 sites were used to obtain surface rain estimates. Landscape was distinguished among categories such as bare land, land with vegetation cover, permanent ice, water, water with possible sea ice, and coastal areas. The algorithm makes use of vertically polarized radiances at 19, 22, 37, and 85 GHz and the horizontally polarized radiances at 19 GHz. The land–ocean differentiation is included in the design of this algorithm. Snow, deserts, and arid soils are separately included in the design. The emissions from sea ice are excluded in the calculations of scattering-based rain rates. The emission algorithm is based on the retrieval of cloud liquid water from the 19 and 37 GHz channels. Hakkarinen and Adler (1988) have emphasized the role of land-based precipitation systems for the scattering part of this algorithm. Thus, different directories are used for land and ocean.

  3. Olson (1990) SSM/I algorithm (hereafter referred to as Olson forecast). This is a statistical regression–based algorithm that utilizes the brightness temperatures from the SSM/I. These were regressed against surface radar–based estimates of rain rates as described in Berg et al. (1998). The algorithm makes use of the SSM/I data at the following six channels: 19V, 22V, 37V, 37H, 85H, and 85V. The original statistics were largely based on rain rates less than 6 mm h−1; the algorithm tends to underestimate the heavy rain events. This algorithm makes a clear distinction between land and ocean where separate statistical regressions were deployed.

  4. Turk et al. (2001) blended geostationary + microwave rain-rate algorithm (hereafter referred to as GEO forecast). Turk et al. (2001) developed an algorithm that estimates rain rates using a blend of geostationary satellite-based IR radiance data and microwave radiance data. These data provide 3-hourly rain rates from rapid scan geostationary satellite datasets where IR brightness data is calibrated to provide rain rates using a look-up table that utilizes a 15 class interval. This is especially designed to provide a smooth transition from one pixel to the other through multihour rain accumulation, which is computed using an explicit time integration using successive images. The use of IR datasets using OLR-based algorithms have been studied by Adler and Negri (1998), Adler et al. (1993, 1994), and Xie and Arkin (1998).

  5. Turk et al. (2001) combined algorithm for the retrieval of rain rates from microwave radiance datasets from the SSM/I and the TRMM database and geostationary infrared radiances (hereafter referred to as Turk forecast). S. W. Miller et al. (2001, manuscript submitted to J. Remote Sensing) have also addressed a combined microwave–infrared rain-rate algorithm. Basically, this scheme utilizes microwave-adjusted geostationary satellite–based rain rates in real time. Given the large number of SSM/I (F11, F13, F14, and F15) as well as the TRMM microwave imagers, it was possible to collect a large database of temporally and spatially coincident geostationary IR pixels. A relationship was next developed by Turk et al. (2001) to relate the IR brightness temperatures to the SSM/I-based rain, which is determined using the Ferraro NOAA–NESDIS algorithm (Ferraro 1997; Ferraro et al. 1998). The TRMM-based rain rates are computed following the Kummerow et al. (2000) 2A12 algorithm. The TMI data for the TRMM rain are sampled over a fine resolution (7 km along track and 4 km across track). The geostationary satellite data is spatially averaged to meet this resolution. The high temporal resolution (hourly) of the geostationary satellite data makes it possible to increase the temporal and spatial resolution of the final product from the use of these two systems. Thus it becomes possible to obtain 6-hourly rainfall rates at a high spatial resolution of ½° latitude–longitude global grid (between 60°S and 60°N). This is one of several rainfall datasets we have used in the present study.

  6. Kummerow et al. (1996) and Kummerow et al. (2000) GPROF SSM/I algorithm. The SSM/I version of the GPROF algorithm makes use of vertically polarized radiances at the 19, 22, and 37 GHz and the horizontally polarized radiances at 19, 37, and 85 GHz channels. It examines the microwave radiation from various hydrometeor categories, including precipitating and nonprecipitating clouds in liquid and frozen states. The landscape is subdivided into several categories, such as land, permanent ice, water, and coastal regions. Radiative transfer calculations are used to establish the physical relationship between precipitation and upwelling microwave radiances. An Eddington solution is used to calculate the upwelling radiances at the various sensor frequencies (Kummerow et al. 2000). Convective system simulations from the NASA-Goddard cumulus ensemble model developed by Tao and Simpson (1993) and the University of Wisconsin nonhydrostatic modeling system (Tripoli 1992) provide candidate solution profiles of precipitation for the algorithm. Weights for the different model-generated precipitation profiles are assigned using the probability density functions derived using Bayes theorem: the greater the radiative consistency between a given model profile and the radiometer observation, the greater the profile weight. Therefore, the resulting precipitation profile (and its associated surface rain rate) is a weighted average of all of the model-simulated profiles.

  7. Kummerow et al. (2000) 2A12 algorithm (hereafter referred to as TMI+SSM/I forecast). This is the aforementioned GPROF algorithm applied to the TMI data from TRMM. The algorithm makes use of the 21.3-GHz (vertically polarized) and the 10.7-GHz channels specific to TMI, in addition to the 19.35- 37- and 85.5-GHz channels common to both instruments. Further details can be found in Kummerow et al. (2000).

6. Results from real-time precipitation forecasts

We have examined several issues related to the evaluation of the rainfall forecasts. These range from skills of precipitation forecasts, sensitivity of forecasts to the selection of the training database, bias corrections, prediction of flood and heavy rainfall events, and the current limitations for this approach.

An example of a precipitation forecast from our recent real-time forecasts is shown in Figs. 5a–d. These are forecasts of 24-hourly precipitation at the end of days 1, 2, and 3 of the forecasts, all valid for 6 June 2000. The top left panel shows the observed precipitation field based on TRMM-2A12 plus SSM/I-GPROF. The correlations of the forecast precipitation against the observed fields are indicated at the top of Figs. 5b–d. These are 0.82, 0.65, and 0.61 for days 1, 2, and 3 of the forecasts. These reflect a major improvement compared to what we had seen from the single model runs. The superensemble exhibits some spread of light rain (i.e., spread of rain <10 mm day−1) that comes from the construction of the superensemble using the spread of rain from the 11 models.

The 12 panels of Fig. 6 illustrate the day 3 rainfall valid on 6 June 2000. Here the observed rain is shown on the top left panel. The left panels show the multimodel rainfall distributions and the right panels show those from the multianalysis components of the forecasts. The right panels are based on the forecasts from the FSU model at the resolution T126 using different rain-rate algorithms in their descriptions of the initial rain. The FSU model's rainfall intensity is, in general, larger than the operational models, and its location and phase errors are generally smaller. Overall, this is the type of multianalysis–multimodel rainfall distributions that we use to construct the superensemble forecasts.

a. Rmse skill scores

The root-mean-square errors (rmse) in precipitation forecasts over a global belt, 50°S–50°N, covering a forecast period from 1 April to 15 April 2000 is shown in Fig. 7. The training period for these forecasts included the preceding 75 days. The thick black line denotes the rmse for the multianalysis–multimodel superensemble. The dotted lines show the skills for the selected individual member models, whose skills were high. We have removed in this illustration a display for the bad model's rmse. The thin, solid line shows results for the ensemble mean, with bias removal for individual models. Overall, these results over the global belt show great promise for the 3-day forecasts of precipitation. It should be pointed out that these results are fairly robust and we see the same skills in the day to day real-time runs.

The entries in the illustrations of this manuscript include the rms errors for the member models, the ensemble mean (of the bias removed individual models) and the superensemble. There is some noticeable improvement in the skill for the superensemble over the ensemble mean. This arises from the fact that the poorer models are assigned weights of 1.0 over the entire globe, whereas the superensemble is more selective regionally (and vertically, for each variable and for each model). Its weights are fractionally positive or negative, based on the member models's past performance.

The bias correction is based on the regression technique where it is possible to examine the bias of a simple model with a simple regression of the type
yiaxib.

We can also look at the correlation of the observed rain (24-hourly totals ending on days 0, 1, 2, and 3 of the forecasts) derived from the TRMM-2A12 plus the SSM/I-GPROF-based rainfall against the global gridded forecasts of the superensemble-based rains. Those are shown in Fig. 8 for the months of March and April 2000. The global forecast correlation skills for days 0, 1, 2, and 3 lie roughly around 0.9, 0.8, 0.62, and 0.55 for these months. These are higher skills compared to what were seen for a single model shown in Fig. 3.

b. Equitable threat scores

This is a standard skill score that is being used by various weather services to evaluate their precipitation forecasts. It is frequently used to assess skill of rainfall forecasts above certain predefined thresholds of intensity of rain.

The equitable threat score is defined by the expression EQTS = (AAr)/(A + B + CAr), where Ar denotes the expected number of correct forecasts above the selected threshold. A contingency table partitions the precipitation forecasts into four mutually exclusive and collectively exhaustive categories: A denotes the number of locations with both the forecast and verification greater than the preassigned threshold; B denotes the number of locations which are at or above the threshold and verify at or below “false alarms;” C denotes the number of locations which are forecast below, but are verified at or above the threshold, that is, “misses;” and D denotes cases where both the forecasts and the verification are below the threshold.

The variable Ar denotes the expected number of correct forecasts above the threshold for a random forecast, that is, where the yes/no's for the forecasts are independent of the yes/no's for the verification, and is defined by Ar = (A + B)(A + C)/(A + B + C + D). The bias is defined by the rates of the number of “yes forecasts” divided by the number of “yes observed”, that is, bias = (A + B)/(A + C). In this paper, we have selected the following thresholds: >0.2, >10, >25, >50, and >75 (units mm day−1). We have calculated these equitable threat scores for the multianalysis and for the multimodel products for the following domains: the global belt (i.e., between 50°S and 50°N), North and South America, Africa, Asia, and Australia. Table 2 illustrates the results of the threat scores for eight participating members of the real-time multianalysis–multimodel system. The threat scores are evaluated covering the precipitation rate intervals greater than 0.2, 10.0, 25.0, 50.0, and 75.0 mm day−1. The size of the individual domains is identified within the table. The bias values for the member models, ensemble mean and superensemble, were found to be comparable (not shown).

What we see here are the following: the threat scores for the superensemble for all rainfall intervals are the highest compared to the member models and the ensemble mean rainfall. We have also shown the threat scores for the Eta Model in the last column over North America. The forecasts for the member models and superensemble are all for April 2000. This covers a 30-day period. The Eta Model's equitable threat scores for April over different years (shown by the Eta entry) are shown with their highest scores included. Here again, the superensemble threat scores are higher than those for the Eta. The superensemble was cast at the resolution T126 (i.e., roughly 90 km horizontal resolution) whereas the operational Eta Model had a resolution of 32 km. Considering those differences in resolution, the performance of the superensemble (for these experiments) appears impressive.

Although the improvement in the equitable threat scores appears quite large, it should still be regarded as modest. Heavy rain events in excess of 75 mm day−1 are not handled very well by any of the models. The superensemble also underestimates the precipitation by roughly a factor of 2. We have examined such cases in some detail and it is clear that much further improvement is needed from the member models in order to improve the superensemble-based precipitation forecasts. This may require higher resolution modeling for the member models with improved physics and initialization of rain.

c. Regional skills

The precipitation forecast skills were also evaluated regionally (Fig. 9). The following regional domains were examined: (a) a global belt between 50°S and 50°N; (b) North America between 120°W and 65°W, and 20°N and 50°N; (c) South America between 110°W and 10°W, and 50°S and 15°N; (d) Africa between 20°W and 55°E, and 35°S and 40°N; (e) Asia between 50°E and 120°E, and 15°S and 45°N; and (f) Australia between 110°E and 160°E, and 40°S to the equator.

Forecast skills (rmse) for day 3 of forecasts for the multimodels (thin dotted lines), new ensemble mean [of bias-corrected individual member models (thin solid lines)], and the superensemble (heavy line) are shown in Fig. 9. Out of the 11 member models, we have only displayed the results for the 6 best models (based on rmse); however, the new ensemble mean and the superensemble are constructed from the entire family of 11 models. Also shown are results for a training period of 75 days (from a total of 120 days) and 15 days of forecasts. The abscissa covers all the 3-day forecasts made since 1 April 2000.

The results clearly show that the superensemble skills hold regionally in every part of the globe studied for each day of forecast. The superensemble forecasts are clearly superior to those of the member models and the ensemble mean. Somewhat higher skills for the superensemble are noted over the Asian belt compared to the best model. In terms of rmse, the highest skills are noted over North America. These are clearly features related to the overall data coverage that affects member model performance and then is passed on to the superensemble.

d. Percent improvement of rainfall forecasts from the superensemble

We compared two recent months (January and February 2000) of global rainfall forecasts (between 50°S and 50°N) from the multianalysis–multimodel superensemble to the following: (a) ensemble mean forecasts, (b) the best operational model (assessed from the correlation of daily rainfall during the two months), and (c) the poorest operational model (assessed again from the correlation of daily rainfall during the two months).

The results for day 3 of forecasts for rain (total rain between 48 and 72 h) are shown in Figs. 10a–c. The color bar shows the percent improvement of the superensemble over the respective models. It is apparent that improvements well over 100% over the poorest model by the superensemble were evident over this part of the global belt. The improvements over the best operational model are also quite substantial; a preponderance of yellow, green, and red colors implies improvement well over 40% to even 100% over the global belt. The new ensemble mean (of the bias-removed individual models) assigns a weight of 1.0 to all models including the poorest model in its averaging. Thus, it is clear that the superensemble (with selective weights) improves considerably over that in the global belt. Overall, these results are quite impressive considering that there are no negative values, that is, the superensemble improves over every region. We have deliberately shown results for slightly different periods to illustrate the robustness of the proposed method. The percent improvements of rainfall forecasts over the bias-removed ensemble mean and the best and the worst models are quite substantial. This is computed from the correlation of forecast model rain against the best rainfall estimates (i.e., TMM-2A12 + SSM/I-GPROF). Given the correlations of these respective models, the improvement of the superensemble over these other models can be simply expressed as a percentage; these are shown in Fig. 11. These improvements over the bias-removed ensemble mean, the best, and the worst models for day 3 of forecasts are around 48, 68, and 79% respectively. The training contributes a lot to these improvements, mostly as incremental improvements over the bias-removed ensemble mean.

e. How many training days are needed for improving precipitation forecasts?

The results describing the number of training days for 3-day rainfall forecast skills over North America are shown in Fig. 12. We show the skills from 60 to 150 days of training. It is apparent that there is a slow increase of skill as the number of days of training is increased. We believe that this is a function of the type of rain-producing disturbances that prevail in a given region. Over regions with a high degree of quasi-stationary disturbances, such as the ITCZ, a lesser number of training days (≈60 days) were sufficient to acquire a high skill for precipitation forecasts (Krishnamurti et al. 2000b). On the other hand, where there was an abundance of transient disturbances, such as over the monsoon region, a large number of training days is needed.

f. Training with an arbitrary model's GDAS rainfall datasets

The improved results for the superensemble forecasts, shown earlier, came from using “best” rainfall estimates during the training phase. Best rainfall is here defined by the TRMM-and SSM/I-based estimates. One can ask the question, “What happens if the training were done using a lower quality rainfall estimate?” Forecast verification must still be done with respect to the best rainfall estimates, that is, the TRMM-2A12-and the SSM/I-GPROF-based estimates. Fig. 13a–c illustrates the result of the rmse (based on 60 days of training and 5 days of forecasts) starting January 2000. These are averaged over the global belt from 50°S to 50°N. The thick black lines show the results for the multimodel–multianalysis superensemble. Those errors are the smallest compared to the bias-removed ensemble mean (thin solid lines) and the selected member models (dotted lines). The long dashed lines with the largest errors are the results of superensemble forecasts where the training was deliberately carried out using the initial rain (GDAS rain) of a poor model. That resulted in the largest errors in the forecasts for days 1, 2, and 3. It should be noted that these skills depend strongly on the benchmark rain rates that are used for training and forecast verification. We believe that TRMM-2A12-and SSM/I-GPROF-based rain rates are one of the better products currently available for this purpose.

g. Relative performance among the rain-rate algorithms

Ground validation experiments provide excellent datasets for the calibration of rain-rate algorithms. These datasets are also most useful for testing the validity of rain-rate algorithms. When one compares numerical weather prediction analyses with these algorithm products, the model's particular features also play an important role in assessing how well such algorithm-based rain rates fare with respect to the model's results. Model physics, resolution, and dynamics always determine an equilibrium rainfall intensity state to which the forecast models spin up. Those rainfall intensities have more to do with the design of the numerical weather prediction models and less to do with the design of rainfall algorithms. Some of these individual model biases can be reduced by taking the multimodel superensemble approach, which compensates for the growth or decay in the spin up of rain rates from different models. Within the superensemble forecast strategy, we invoke a vast training period during which the model biases, with respect to a particular preassigned best rain-rate algorithm, are evaluated. That so-called best rain-rate descriptor was selected as the TRMM-2A12 plus the SSM/I-GPROF algorithms following Kummerow et al. (1998). That choice was dictated by a consensus from the TRMM science team of NASA. Given that as a built-in feature for our training, the first-day forecasts (after the training) reflect the spun up values of the rain rates from the superensemble (Fig. 14). These rain rates are compared to the “observed” rain rate estimates from six different rain-rate algorithms. The six vertical bars show, respectively, (a) the one-day forecast rain from the superensemble forecasts, (b) the observed rainfall estimate from the TMI-2A12 and SSM/I GPROF algorithm (TMI+SSM/I), (c) the observed rainfall estimate from the Ferraro et al. (1998) algorithms (Ferraro), (d) the observed rainfall estimate from Olson et al. (1990) algorithm (Olson), (e) the observed rainfall estimates from the geostationary satellite-based algorithm GEO of Turk et al. (2001), and (f) the observed rainfall estimates from the combined TRMM, SSM/I and the geostationary satellite–based Turk algorithms (Turk et al. 2001).

The results shown in Fig. 14 are averages for the entire month of April 2000. These results are shown for representative points over six selected domains: India, southeastern United States, Australia, China, western Pacific Ocean, and Africa. In all of these cases, we note that the superensemble forecasts for day 1 closely matches the observed rainfall estimates from TRMM–2A12 and the SSM/I-GPROF algorithms. The superensemble forecasts do not match the other algorithms as closely. That has, of course, a lot to do with the choice of the TRMM-2A12 plus SSM/I-GPROF for our training. This is an important factor that determines the improved precipitation forecasts we report in this paper.

h. Mozambique floods

It is of considerable interest to ask whether the superensemble forecasts of rainfall can provide any useful guidance for floods. Mostly the heavy rains that resulted in the recent Mozambique floods during February and March of the year 2000 resulted from heavy rains over Mozambique and Zimbabwe. The headwaters of the Limpopo River over Zimbabwe experienced the heaviest rainfall, which resulted in the cresting of the river over southern Mozambique where the flooding was most severe. These floods washed away roads, railways, houses, hutments, crops, and cattle. Hundreds of lives were lost and thousands were left homeless.

These floods resulted from an active ITCZ that prevailed around 5°S during most of the period. The moist trade wind easterlies of the southern Indian Ocean periodically extended north and west of Madagascar. Rain-producing disturbances prevailed on the cyclonic shear side of this wind belt. Westerly winds developed to the north of this cyclonic belt near 10°S and aided in the maintenance of the rain areas as far south as 15°S. There were two tropical cyclones that formed during this period. Tropical Storm Eline, over the central Indian Ocean, moved westward across Madagascar entering the Mozambique Channel around 18 February. On 22 February, Eline made landfall over the central Mozambique coast near the town of Beira with a wind force of 71.5 m s−1 (139 kt, or 160 mph). It caused great destruction in its southern sector and torrential rains resulted in the worst flooding. In the beginning of March 2000, another cyclone (Gloria) formed over the central Indian Ocean and moved westward. Although it weakened before reaching the Mozambique coast, its remnants caused further rainfall and flooding as it moved inland.

Forecasts of rain from this study were projected on Hovmöller diagrams (longitude vs time) and are shown in Fig. 15. Here, we show the daily rainfall for the belt 10°–15°S covering the longitudes 24°–45°E for the entire month of February (dates are plotted from bottom to top). The three panels show the observed estimates (left), those based on the superensemble forecasts (for day 3 of forecasts) valid on the dates of the observed rains of the left panel from the multimodel superensemble (center), and those predicted for day 3 of forecasts from the best operational model for this region, (right). The best model is determined from the rmse of rainfall for each model. The units of rainfall are in mm day−1. It is clear that the multimodel superensemble shows the 3-day forecasts of heavy rains associated with the Mozambique floods very well. Given the higher rainfall forecast skills from the superensemble, it appears that useful guidance of heavy rain events resulting in floods may be possible from this approach.

i. Precipitation forecasts during the landfall of hurricane Floyd

Another interesting example of flooding occurred during the landfall of Hurricane Floyd over North Carolina during 1999. Floyd originated as an African wave on 2 September 1999. The wave moved westward and became a tropical storm east of the Leeward Islands on 8 September. It acquired hurricane force winds east northeast of the Leeward Islands on 10 September. The major land encounter was over the Bahamas, where it had acquired category 4 hurricane force winds, on 13 September. Thereafter, it moved somewhat parallel to the coast offshore with somewhat diminished intensity. As a category 2 storm, Floyd made landfall near Cape Fear, North Carolina, on 16 September. The major flooding event occurred on 16 and 17 September. It was of considerable interest to see how the heavy rains during the landfall of Floyd were handled by the superensemble forecasts. Figures 16a–h illustrate the forecasts from Hurricane Floyd. Panels (a)–(d) show track forecasts for start dates, 11, 12, 13, and 14 September 1999 (1200 UTC), respectively. The observed tracks are shown by the heavy dark line. The track adjacent to it is the forecast from the superensemble, whereas the other tracks are from some of the other member models. The forecasts from several of the member models called for landfall of this storm over Florida, Georgia, and South Carolina. In that sense, the superensemble forecast was somewhat more realistic since it called for a landfall over southern coastal North Carolina. That was the region of heavy floods, as is shown in panel (e). This region of heavy rain flooding was mapped by the National Weather Services from the rain gauge observations. Precipitation forecasts from the multianalysis–multimodel superensemble are shown in panels (g)–(k). Panels (g) and (h) are days 2 and 3 of forecasts valid on 16 September 1999. The corresponding TRMM-2A12 plus SSM/I-GPROF-based observed rain valid on this data is shown in panel (f). Panels (i), (j), and (k) show the observed and forecast fields valid on 17 September 1999. Overall, the superensemble forecasts of rain were superior to those of the member models. It appears from these rainfall calculations that some useful guidance during flooding episodes may be possible from the use of the multianalysis–multimodel superensemble. We have, however, noted that, in general, the superensemble underestimates 24-hourly rainfall totals in excess of 75 mm day−1 by as much as a factor of 2. Correcting this underestimation likely requires higher resolution multimodels with further improvements (in progress).

7. Concluding remarks

We have shown here that large-scale precipitation forecasts (especially over the Tropics) can be improved by the multianalysis–multimodel superensemble approach. This approach includes an extensive period (based on past forecasts) where the biases of the participating models and the analysis used are collected in the form of statistical coefficients. Those statistics are then used in the future forecasts to correct the biases of the forecasts. Some of the best available rainfall estimates (i.e., the combined TRMM–SSM/I algorithm) were used as the benchmark training datasets that contributed to a major improvement of the real-time forecasts using the superensemble approach. We also show that training with a poor rainfall dataset degrades the forecasts considerably.

Physical initialization utilizes a reverse algorithm for improving rainfall forecasting skill. Forecasts made with a physically initialized initial state have much higher nowcasting skill for rainfall forecasts for day 1, and somewhat higher skill for days 2 and 3, when compared to operational model forecasts that do not deploy this procedure. This procedure requires observed rain-rate estimates according to which the physical initialization is addressed. The observed rain rates from the satellite-based microwave products (TMI, SSM/I) rely heavily on the rain-rate algorithm that is used. The individual algorithms appear to show differences in the 3-day forecasts even though all other aspects of the model and initial datasets were apparently kept the same. Those differences arise largely from differences in heating, divergence, moisture, and pressure tendencies. Thus, differences in the initial rainfall provided a tag for the different versions of the multianalysis component of the superensemble. The multimodel components of the superensemble include the operational rainfall forecasts. In this paper, we have shown that the short range (1–3-day) precipitation forecast skills from the multianalysis–multimodel superensemble are higher than those of the (a) member models included in this exercise, (b) straightforward ensemble mean of the member models, and (c) bias-removed ensemble mean of the member models.

The multimodel forecasts are usually not bias-corrected when they are received. Given a model's bias for days 1, 2, and 3 of forecasts, we can correct the biases of the individual models by simply adjusting the forecast mean values to corresponding observed mean values for the past history of forecasts. Another approach to the bias correction of individual models is to perform a regression of past forecast variables of the single model against observed models. That linear regression provides a bias correction, which is somewhat different from the adjustment of the mean. We have, in effect, examined the precipitation forecasts from (a) the multimodels, (b) ensemble mean of simple bias corrected individual models, (c) ensemble mean of regression-based corrected individual models, and (d) superensemble proposed in this study.

We find that the precipitation forecast skill successively improves as we move from (a) through (d). We do not present the results for the ensemble mean of bias-corrected individual models. Those were illustrated in Krishnamurti et al (2000a). Basically we noted that the superensemble performs better than the bias-corrected ensemble mean of member models because assigning a weight of 1.0 to a poor model (after bias correction) does not make it comparable to the best model (after bias correction). The superensemble assigns fractional or even negative weights and is very selective. The removal of bias of poorer models does not appear to bring them up to the levels of the best models, and assigning an equal weight to such models for the construction of the ensemble mean does not bring it to the level of the proposed superensemble. The latter benefits from the geographically selective weights based on past performance. We have also addressed the issues of extreme rain events (intensity greater than 75 mm day−1), such as those that occurred over the global Tropics in April and May 2000, during the landfall and flooding that occurred from Hurricane Floyd of 1999 and the Mozambique floods during February 2000. We show that useful forecast guidance may be available from the multianalysis–multimodel superensemble for up to 3 days. The success of this study is attributed largely to the rainfall estimates from TRMM, SSM/I products, and the rain-rate algorithms that were developed in this context.

The global average improvement of the predicted rainfall by the superensemble of about 35% over the bias-removed ensemble mean (see Fig. 10a) came about from assigning a score of 0 for the ensemble mean and a score of 100 for the best forecast. The ensemble mean is a product of the multimodel forecasts, whereas the superensemble includes past behavior of the model forecasts as well. If the bias correction is made to each model and a weight of 1.0 (uniformly over the globe) is assigned to each model thereafter, then we find that this ensemble mean has a somewhat lower skill compared to the proposed superensemble. That difference arises from the fact that the latter assigns selective weights to different models (at any grid location). We found that poorer models, after a simple bias removal, do not perform as well as the best model (after its bias removal). The selective weights [some 73 728 (384 × 192 lat/lon) times the number of member models for the precipitation forecasts] appear to provide an edge for the superensemble over an ensemble mean (as is noted in Figs. 10 and 11).

The results shown in this paper demonstrate a modest improvement over earlier work as is evident from Table 2. Although the improvement in the equitable threat scores appear quite large, they should still be regarded as modest. Clearly further work is needed to improve the mesoscale modeling of precipitation.

Further improvements in precipitation forecasts may be possible from an extension of the proposed methodology:

  1. Use of mesoscale multianalysis–multimodels for the construction of the superensemble, that is, use of a higher-resolution family of models.

  2. Further improvements in the remote sensing of rain rates from improved algorithms and ground validation research. A follow-on mission (Global Precipitation Mission) after TRMM is expected in the next five years. This mission will carry a constellation of satellites that would provide a much improved sampling of rainfall. This is expected to provide 3-h sampling of rainfall estimates. A considerable reduction of errors is thus expected.

  3. Further improvements in the cumulus parameterization procedures among the member models. Use of explicit schemes and developing compatibility between the model-based microphysical parameterization and the satellite-based estimates of hydrometeor components.

  4. Further improvements in the data assimilation methodologies for the multimodels where the precipitation components are directly assimilated, for example, Treadon (1996), Hou et al. (2000), Tsuyuki (1996a,b; 1997). Most of these studies have relied upon coarser resolution models. Further improvements should be possible with the use of variational data assimilation of rain rates using mesoscale models.

It would be desirable to address the issue of ensemble spread, probabilistic forecast, and probability density function (pdf). The results of the superensemble forecasts often reside well outside the results of the member models and are quite different, by their nature, from an ensemble mean. Thus, an ensemble spread of member models, although very useful for discussing the properties of the ensemble mean, is not that simply related to the superensemble. The mathematical formulation of the pdf of the superensemble, for the precipitation forecasts, will be addressed in a separate paper in the future.

The overall message of this study is that multianalysis–multimodel performs better than a single model. The percent improvement of the 3-day forecast rainfall distributions over the current best model is quite large, between 40 and 120% over most areas. Thus, it would seem that this procedure could be useful for operational weather prediction.

Acknowledgments

The research reported here was funded by NASA TRMM Grant NAG5-4729 and NAG5-9662, NSF Grant ATM-9710336 and ATM-9910526, and NOAA Grant NA86GP0031 and NA77WA0571.

We wish to also acknowledge the modeling groups from ECMWF, NCEP, BMRC, JMA, NRL (NOGAPS), and RPN for providing the global datasets. This work could not have been completed without the assistance of the TRMM/TSDIS data centers, especially the support from Erich Stocker and Tony Stocker. We also wish to thank the U.S. Air Force Global Weather Center at Omaha, Nebraska, and the Naval Laboratory in Monterey, California, for the SSM/I datasets.

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APPENDIX A

Outline of the FSU Global Spectral Model

The global model used in this study is identical to that used in Krishnamurti et al. (1991). The following is an outline of the global model:

  • Independent variables: (x, y, σ, t).

  • Dependent variables: vorticity, divergence, surface pressure, vertical velocity, temperature, and humidity.

  • Horizontal resolution: Triangular 126 waves.

  • Vertical resolution: 14 layers between roughly 10 and 1000 mb.

  • Semi-implicit time differencing scheme.

  • Envelope orography (Wallace et al. 1983).

  • Centered differences in the vertical for all variables except humidity, which is handled by an upstream differencing scheme.

  • Fourth-order horizontal diffusion (Kanamitsu et al. 1983).

  • Kuo-type cumulus parameterization (Krishnamurti et al. 1983a).

  • Shallow convection (Tiedke 1984).

  • Dry convective adjustment.

  • Large-scale condensation (Kanamitsu 1975).

  • Surface fluxes via similarity theory (Businger et al. 1971).

  • Vertical distribution of fluxes utilizing diffusive formulation where the exchange coefficients are functions of the Richardson number (Louis 1979).

  • Longwave and shortwave radiative fluxes based on a band model (Harshvardan and Corsetti 1984; Lacis and Hansen 1974).

  • Diurnal cycle.

  • Parameterization of low, middle, and high clouds based on threshold-relative humidity for radiative transfer calculations.

  • Surface energy balance coupled to the similarity theory (Krishnamurti et al. 1991).

  • Nonlinear normal mode initialization—5 vertical modes (Kitade 1983).

  • Physical initialization (Krishnamurti et al. 1991).

APPENDIX B

Creation of a Superensemble Prediction at a Given Grid Point

i1520-0493-129-12-2861-eqb1
where S = superensemble prediction, O = time mean of observed state, ai = weight for model i, i = model index, N = number of models, Fi = time mean of prediction by model i, and Fi = prediction by model i. The weights ai are computed at each grid point by minimizing the following function:
i1520-0493-129-12-2861-eqb2
where O = observed state, t = time, and t−train = length of training period.

Fig. 1.
Fig. 1.

The vertical line in the center denotes time t = 0, and the area to the left denotes the training area where a large number of forecast experiments are carried out by the multianalysis–multimodel system. During the training period, the observed fields provide statistics that are then passed on to the area on the right, where t > 0. Here the multianalysis–multimodel forecasts along with the aforementioned statistics provide the superensemble forecasts

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 2.
Fig. 2.

An example of superensemble methodology at a single site. (top) Training period rainfall for 3 multianalysis forecasts—the ensemble mean (thin lines), observed rain (dark, thick line), and the superensemble forecast (thick line). (bottom) Rain predicted by 3 multianalyses, the ensemble mean, the superensemble, and the observed rain, all in units of mm day−1. The acronyms FER, OLS, and TMI represent the multianalysis components of Ferraro, Olson, and TMI+SSM/I forecasts, respectively

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 3.
Fig. 3.

The correlation of forecast rain against observed estimates, from Treadon (1996), plotted as a function of forecast days. The results from the operational forecasts from NCEP and from two versions of physical initialization are shown here. These results were obtained using NCEP operational model at the resolution T62 from several experiments

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 4.
Fig. 4.

Observed (TRMM-2A12 + SSM/I-GPROF) and physically initialized rain for 14 Jun 2000. Units: mm day−1

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 5.
Fig. 5.

Days 1, 2, and 3 of forecast rain (mm day−1) for 6 June 2000 from the superensemble forecast is compared with the observed rainfall estimate from the TMI-2A12 and SSM/I-GPROF algorithm

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 6.
Fig. 6.

The observed rainfall estimate from the TMI-2A12 and SSM/I-GPROF algorithm for 6 Jun 2000 is compared with the day 3 forecasts from the 11 member models of the multimodel–multianalysis system studied here

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 7.
Fig. 7.

Skill of rainfall forecasts (rmse) over the global belt between 50°S and 50°N for days 1, 2, and 3 of forecasts. Dotted lines denote multimodel skills. The heavy, dashed line denotes skill of the ensemble mean, and the thin, solid line denotes skill of the individual model's bias-removed ensemble mean, and the thick, black line denotes the superensemble. The first 75 days denote a training period, whereas the last 15 days are the forecast days

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 8.
Fig. 8.

Forecast skill (based on correlation of observed rainfall estimates from TRMM-2A12 and the SSM/I-GPROF) and the superensemble for day 1, day 2, and day 3 forecasts during Mar and Apr 2000

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 9.
Fig. 9.

Rmse of precipitation forecasts over different domains. The results for 6 member models, the ensemble mean, and the superensemble are displayed for 6 regions

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 10.
Fig. 10.

Percentage improvement (based on correlation) of the superensemble forecasts over the ensemble mean, the best, and the poorest models

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 11.
Fig. 11.

Histograms showing percent improvement (based on correlation) of the superensemble forecast over the ensemble mean, the best model, and the worst model for the global belt, 50°S–50°N

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 12.
Fig. 12.

Rmse skill is plotted as a function of the number of training days over North America. The skill is for 3-day forecasts made after the training on several successive forecast days during Apr 2000

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 13.
Fig. 13.

(a) Day 1, (b) day 2, and (c) day 3 forecasts's rmse skill using a poor analysis of initial rain as the training rainfall is shown. The skill of that superensemble is the top curve with the largest rmse. The skill of the multianalysis–multimodel superensemble based on TRMM-2A12 and the SSM/I-GPROF is the bottom curve with the highest skill. The remaining curves denote the skills of selected member models and that of the ensemble mean

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 14.
Fig. 14.

Day 1 superensemble forecast of rain (mm day−1) for representative points over 6 different regions are compared to the observed estimates derived from different rain-rate algorithms from TMI + SSM/I, Ferraro, Olson, GEO, and Turk forecasts. These are averaged for the entire month of April 2000

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 15.
Fig. 15.

A Hovmöller diagram of daily precipitation (mm day−1) on day 3 of forecasts during the Mozambique floods. Ordinate shows days (bottom to top); abscissa denotes longitude. The three panels denote (left) observed rain (from TRMM-2A12 plus SSM/I GPROF); (middle) superensemble forecasts; (right) best operational model

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Fig. 16.
Fig. 16.

(a)–(d) Track forecasts for Hurricane Floyd on different start dates. Heavy black line denotes official best track. The red line adjacent to it is the superensemble forecast. The others are for some of the member multimodels. (e) Observed 5-day rainfall over North Carolina from Hurricane Floyd during 12–17 Sep 1999. (f)–(k) Observed, day 2, and day 3 superensemble-based precipitation forecasts during the passage of Hurricane Floyd are shown. Two start dates of forecasts are illustrated here

Citation: Monthly Weather Review 129, 12; 10.1175/1520-0493(2001)129<2861:RTMMSF>2.0.CO;2

Table 1.

List of acronyms

Table 1.
Table 2.

Precipitation equitable threat scores for Apr 2000. The threat score for the respective member models over the indicated domain are displayed for the entire month of Apr 2000. The Eta Model's threat scores for Apr of several years (with the highest scores) are shown in the last column for the North American region

Table 2.
Save