Short- to medium-range superensemble precipitation forecasts using satellite products: 1. Deterministic forecasting

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. D8, 8383, doi: /2001jd001510, 2003 Short- to medium-range superensemble precipitation forecasts using satellite products: 1. Deterministic forecasting D. W. Shin and T. N. Krishnamurti Department of Meteorology, Florida State University, Tallahassee, Florida, USA Received 14 November 2001; revised 14 May 2002; accepted 20 May 2002; published 18 March [1] As a comprehensive extension of the previous multimodel/multianalysis superensemble (SE) studies of rainfall forecasts, the benefits and prospects of the SE precipitation forecasts are explored using satellite products. Three different precipitation ensemble configurations are first established from a great number of numerical experiments. These configurations are multianalysis (MA), multicumulus-scheme (MC), and multimodel (MM) configurations. A set of MA ensemble comes from the use of several different satellite-derived rain rates through the physical initialization procedure within the Florida State University Global Spectral Model (FSUGSM) system. Six different state-of-the art cumulus parameterization schemes are incorporated into the FSUGSM in order to introduce the MC ensemble configuration. The MM configuration is composed of an FSU control forecast and those provided by five operational numerical weather prediction centers. In addition to the original technique, a possible deterministic SE enhancement technique (regression dynamic linear model) is then proposed and applied to the above three configurations of ensemble members as well as all of them together. The impact of a higher resolution family of models on the performance of SE forecasts is extensively investigated by repeating the above procedure with T170 resolution precipitation forecasts. Results show that short- to medium-range SE forecasts are generally superior in skill to various conventional forecasts. A notably improved (20%) quantitative precipitation forecast is exhibited by the newly proposed SE technique. The MM configuration proved to be the most effective ensemble prediction system. Although a higher-resolution SE forecast requires a large amount of computing time, it turns out that the impact is significant not only in skill scores but also in resolving mesoscale-based convective disturbances. INDEX TERMS: 3354 Meteorology and Atmospheric Dynamics: Precipitation (1854); 3337 Meteorology and Atmospheric Dynamics: Numerical modeling and data assimilation; 3360 Meteorology and Atmospheric Dynamics: Remote sensing; 3374 Meteorology and Atmospheric Dynamics: Tropical meteorology; KEYWORDS: precipitation forecasting, superensemble, TRMM, ensemble forecasting Citation: Shin, D. W., and T. N. Krishnamurti, Short- to medium-range superensemble precipitation forecasts using satellite products: 1. Deterministic forecasting, J. Geophys. Res., 108(D8), 8383, doi: /2001jd001510, Introduction [2] Satellite weather observing technologies have made it possible to better observe and understand important (severe) weather phenomena occurring all over our globe, the Earth, and hence to protect human beings from impending natural hazards. The weather satellite has become an indispensable tool for many purposes. One of the most critical weather systems to be watched and understood is the tropical convective rain system. A long-term accumulation of precise information on the rainfall systems will increase our understanding of various fields of atmospheric sciences, such as the hydrological cycle, the global energy budget, and global circulations. As a major step towards the Copyright 2003 by the American Geophysical Union /03/2001JD surveillance of tropical rainfall systems, the Tropical Rainfall Measuring Mission (TRMM) satellite has been providing accurate observational measures of spatiotemporal coverage and intensities of precipitation over the global tropics since its successful launch on 27 November TRMM was designed to monitor tropical and subtropical precipitation and to estimate its associated latent heating using a precipitation radar (PR) and the TRMM Microwave Imager (TMI) instruments [Kummerow et al., 2000]. [3] Precipitation forecasting, which is commonly regarded as our Achilles heel in numerical weather prediction (NWP), is the main topic in the present study. The current short- to medium-range prediction skill of precipitation almost always exhibits the lowest scores among the predicted meteorological variables in most of the current operational centers. It is beyond reproach to say that NWP models do not have any useful skills (in terms of CIP 8-1

2 CIP 8-2 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION verification statistics, such as root mean square error, correlation, etc., with respect to the observed) at all in medium-range (3 to 6 days) rainfall predictions. [4] There have been abundant efforts to remedy this low rainfall forecast skill in the NWP society during the last several decades. Two main approaches were, as pointed out by Shin and Krishnamurti [1999], the enhancement of model initial conditions and the advancement of cumulus parameterizations. In the initial condition approach, many researchers have been working on a challenging issue, how to effectively incorporate satellite-based rain estimates into a numerical model in order to improve model initial states (especially for hydrological fields) and hence weather forecasts. Several methods have been utilized in this area. Among them are two promising approaches - physical initialization (PI) and four-dimensional variational (4DVAR) data assimilation. PI, first proposed by Krishnamurti et al. [1984], assimilates satellite-based measures of rain rates into an atmospheric forecast model through a number of reverse physical algorithms as well as Newtonian Relaxation [Krishnamurti et al., 1991]. With its sound mathematical background in minimizing the distance between model-predicted and observed rainfall, the 4DVAR method has also become popular in assimilating rainfall as well as other variables [e.g., Zou and Kuo, 1996]. Recently, Hou et al. [2001] have also shown the improvement of short-range forecasts of precipitation as well as other important variables in their global data assimilation system using rainfall and total precipitable water information derived from TMI and Special Sensor Microwave/Imager (SSM/I) instruments. [5] Considerable effort has also been made in the precipitation-related physics packages [e.g., Krishnamurti et al., 1983; Emanuel and Raymond, 1993]. There exist numbers of different cumulus parameterization schemes in the operational numerical models. Most of them basically stem from two main categories: Kuo and Arakawa-Schubert (AS) types. Numerical modelers have no objection to the following statement: a good representation of convective schemes plays a crucial role in the reliable predictions of rainfall as well as the heating and moistening. [6] In addition to the above approaches, ensemble forecasting systems have been shown to help one recognize the effects of initial condition uncertainties, thus helping to yield better short-range predictions with their ensemble statistics [e.g., Palmer et al., 1992; Toth and Kalnay, 1993, 1997; Zhang and Krishnamurti, 1997; Stensrud et al., 1999]. [7] It has not, however, been possible to make any significant improvements for the rainfall prediction from the aforementioned approaches. The numerous studies dedicated to this topic demonstrated the complexity involved in properly producing a rainfall forecast. Only skillful nowcastings and one day rainfall forecasts were achieved from the inclusion of PI. The correlations were on the order of 0.9 and 0.5, respectively. The skill of forecasts beyond one day did not exhibit an appreciable advantage from the inclusion of PI [Krishnamurti et al., 1993]. It appeared that an entirely different approach is warranted for improving the short- to medium-range rainfall forecasts. The first major breakthrough in precipitation forecasts emerged from the development of a multianalysis superensemble [Krishnamurti et al., 2000]. They used a multiple regression technique to determine optimal weights for the ensemble members during a training period and passed these statistics to the forecast period in order to assist making a superensemble (SE) forecast. The SE forecast is an optimal ensemble forecast produced by combining individual forecasts from a group of models. In their paper, they showed that the SE days 1, 2, and 3 forecasts of precipitation are generally superior to various conventional forecasts. The global average improvement of the SE was 35% over the ensemble mean. Following the same notion for the construction of SE forecasts, a useful precipitation forecast guidance has successfully been made from the real time multimodel/multianalysis SE for up to three days [Krishnamurti et al., 2001]. [8] As a comprehensive extension of the previous multimodel/multianalysis SE studies of precipitation forecasts, several features of the SE forecast will be reviewed and elaborated in this study. This work is different from the previous study in the following areas. A new SE technique will be introduced and compared to the original one in deterministic precipitation forecasts. A probabilistic SE approach will be analyzed in a companion paper [Shin and Krishnamurti, 2003]. Cumulus parameterization and high-resolution issues will also be covered. The overall goal of this research is to demonstrate and improve short- to medium-range precipitation predictability using SE approaches within the context of a quasioperational environment. [9] The paper has the following structure. The methodology employed is outlined in section 2. After describing ensemble configurations in section 3, superensemble techniques are presented in section 4. Section 5 is devoted to results from deterministic forecasts. Finally, the summary and conclusions are presented in section Methodology [10] The first step of SE precipitation forecasts is to build extensive ensemble data sets, which are essential components in developing SE statistics during the training period. These data are composed of ensemble members of predicted rainfall and their corresponding observations. The observed rainfall estimates are retrieved from satellite products. The algorithm used is the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) 2A12 rainfall algorithm [Kummerow et al., 1996, 2000] that is supplemented by the National Oceanic and Atmospheric Administration/National Environmental Satellite, Data, and Information Service Special Sensor Microwave/ Imager (NOAA/NESDIS SSM/I) algorithm [Ferraro and Marks, 1995] outside 35 S and 35 N. [11] One of the most important issues to be considered is how to design an optimal set of ensemble members. In this study, ensemble members of rainfall forecasts (days 1 to 6) will be obtained from three different categories of numerical experiments with T126 resolution models. Those experiments include multianalysis (MA), multicumulus-scheme (MC), and multimodel (MM) forecasts. The MA ensemble configuration of precipitation forecasts will be constructed from intensive numerical experiments which assimilate several different satellite-based rain rates into model initial states through the physical initialization procedure. Next,

3 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION CIP 8-3 six different state-of-the art cumulus parameterization schemes are selected from several numerical models and adopted into the Florida State University Global Spectral Model (FSUGSM). These rainfall forecasts form the MC ensemble configuration. The MM configuration is composed of precipitation forecasts provided by five operational numerical weather prediction (NWP) models as well as an FSU control forecast. The provided ensemble precipitation data will be processed and interpolated into the same format as that of FSUGSM to maintain uniformity. [12] After building the above ensemble data sets composed of MA, MC, and MM forecasts, SE techniques will be proposed and applied to the above three configurations of ensemble members as well as all of them together. The original SE technique uses a regular multiple regression method in order to obtain regression coefficients for each ensemble forecast at each grid point for each day of the forecast. A newly proposed SE enhancement technique is the regression dynamic linear model (DLM) approach. [13] SE forecasts at a higher resolution would require a large amount of computer resources. For improving precipitation forecasts, however, this may be necessary in order to resolve the mesoconvective disturbances as long as computational capacities allow. The impact of a higher-resolution family of models on the performance of the SE forecasts will be extensively examined by repeating the above procedure with T170 resolution precipitation forecasts. [14] To quantify the skill of the forecasts, forecast maps will be compared to satellite-based observed maps at the associated verification times. The results of SE forecasts will be analyzed with many verification measures for precipitation, and compared to conventional regular and bias-corrected ensemble mean forecasts. These verification statistics provide a broad picture of the ability of SE in precipitation forecasts. 3. Ensemble Members [15] A SE forecast requires a large database, which is an essential component for computing SE statistics during the training period. In this study, ensemble members of precipitation forecasts are constructed from three different categories of numerical experiments. [16] The usual perfect-model approach to ensemble forecasting is designed to take account of the effect of analysis uncertainties on the forecast evolution. A set of small perturbations to the initial condition is generated and an integration of the model is made from each perturbed analysis. The perturbed initial analyses are chosen to be consistent with the expected uncertainties in the initial condition. A multianalysis (MA) ensemble configuration is constructed in this study to consider partially this aspect of initial condition uncertainties in the ensemble prediction system. [17] Meanwhile, model uncertainty in an ensemble forecast system has also been importantly considered in several recent studies [e.g., Houtekamer et al., 1996; Buizza et al., 1999]. The possible affect of model error during the precipitation forecast is included by employing different cumulus parameterizations in the FSUGSM. This gives birth to the multicumulus-scheme (MC) ensemble configuration. [18] A multimodel (MM) ensemble configuration is also constructed by forecasts from several different operational NWP models as well as a FSU control in order to assess its impact on the SE forecasts Multianalysis Forecasts [19] Satellite-based rainfall retrieval has become one of the more cutting-edge research topics within the discipline of satellite meteorology. The MA ensemble comes from the use of those satellite retrieved rain rates through the physical initialization (PI) procedure [Krishnamurti et al., 2000]. [20] PI assimilates any type of observed measures of rain rates (e.g., land or satellite-based rain rates) into an atmospheric forecast model using reverse physical algorithms within the assimilation mode. This process ends up perturbing the divergence field, the moisture profile, the heating field and the surface pressure tendencies [Krishnamurti et al., 1991]. Therefore, the PIs with different rain rates form a set of ensemble members, those forecasts are all made by different initial conditions. All of these initial analyses make use of the FSUGSM for forecasts that ultimately provide input data to the so-called MA SE forecast. [21] The following is a list of MA components that are used in the present study: (1) CONTROL: This component is based on the precipitation forecast from the FSUGSM without the PI. In other words, no rain rates are assimilated into the initial analysis; it is only subjected to a nonlinear normal mode initialization [Kitade, 1983]. (2) FERRARO: This ensemble member makes use of the NOAA/NESDIS SSM/I algorithm [Ferraro and Marks, 1995] for the PI. (3) OLSON: The PI is carried out using the rain rate algorithm of W. S. Olson et al. (Recommended algorithms for the retrieval of rainfall rates in the tropics using SSM/I (DMSP- F8), unpublished manuscript, 1990). (4) SSMI/TMI: This uses one of the satellite-derived rain rates by F. J. Turk et al. (Blending coincident SSM/I, TRMM and infrared geostationary satellite data for an operational rainfall analysis, part I, Technique description, submitted to Weather and Forecasting, 2001) (hereinafter referred to as Turk et al., submitted manuscript, 2001). This provides the fourth component of the MA forecast. (5) TURK: The rain rate based on a blended geostationary infrared (IR) and microwave rain rate algorithm (Turk et al., submitted manuscript, 2001) is assimilated into the model initial conditions to generate one more precipitation forecast component. (6) TMI2A12: The last PI run utilizes the TRMM 2A12 rain rate supplemented by the NOAA/NESDIS SSM/I rain rate [Kummerow et al., 1996, 2000]. [22] The brief descriptions of the above different satellitebased rain rate algorithms are given by Krishnamurti et al. [2001] and a companion paper [Shin and Krishnamurti, 2003] Multicumulus-Scheme Forecasts [23] A considerable number of schemes have been proposed to parameterize the effects of cumulus convection in large-scale NWP models. The treatment of cumulus convection ranges from adjustment type schemes to different versions of mass flux schemes. In this study, six different cumulus parameterization schemes are incorporated into the FSUGSM in order to introduce a new set of ensemble members.

4 CIP 8-4 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION [24] The following is a list of cumulus convection schemes employed in the present study. For brevity, the details of these cumulus convection schemes are not depicted in this study. (1) FSU (Kuo-type [Krishnamurti et al., 1983]); (2) NCEP/SAS (National Center for Environmental Prediction/ Simplified Arakawa-Schubert [Pan and Wu, 1994]); (3) GSFC/RAS (Goddard Space Flight Center/Relaxed Arakawa-Schubert [Moorthi and Suarez, 1992]); (4) NRL/RAS (Naval Research Laboratory/Relaxed Arakawa-Schubert [Rosmond, 1992]); (5) NCAR/ZM (National Center for Atmospheric Research [Zhang and McFarlane, 1995]); (6) EMANUEL [Emanuel and Živković-Rothman, 1999] Multimodel Forecasts [25] An ensemble set of precipitation forecasts is provided by five operational NWP models in addition to an FSUGSM. The following is a list of participant centers and corresponding models: (1) BMRC/GASP (Bureau of Meteorology Research Centre/Global Assimilation and Spectral Prognosis or Global AnalysiS and Prediction); (2) JMA/ GSM (Japan Meteorological Agency/Global Spectral Model); (3) NRL/NOGAPS (Naval Research Laboratory/ Navy Operational Global Atmospheric Prediction System); (4) RPN/GEM (Recherche en Prévision Numérique/Global Environmental Multiscale model); (5) NCEP/AVN/MRF (National Center for Environmental Prediction/Aviation Medium-Range Forecast global model); (6) FSUGSM (Florida State University Global Spectral Model). [26] These models have different horizontal resolutions with a variety of model physics, data sources, and forecast abilities. In order to maintain uniformity, these models are interpolated to T126 (0.94 ) and T170 (0.70 ) resolutions. All models in this experiment are global models based on the Navier Stokes equation. Within each model, provisions are made for the treatment of snow and ice cover, orography and the parameterization of physical processes. 4. Superensemble Techniques [27] The SE concept is a technique developed by Krishnamurti et al. [1999] that produces a single forecast derived from a set of ensemble forecasts. It is a method of combining individual forecasts from a group of models to produce an optimal ensemble forecast. It differs from a simple ensemble mean forecast in that different models are weighed by sets of regression coefficients obtained during a training period prior to the forecast mode. A simple ensemble mean is equivalent to a SE of models that have the same history of reliability. [28] The general procedure for designing the SE forecast is outlined in Figure 1. First, a training phase and a forecast phase are defined. A large number of precipitation forecasts are available from the MA, MC, and MM configurations during both phases. The observed, or the analysis, is available only for the training phase. A simple averaging procedure that is used to obtain the regular ensemble mean is usually contaminated by the poorly forecasted members, as every member in this method is given an equal weight. Therefore, it is essential to focus on the ensembles that use forecasts and their past behavior with respect to the observations in determining how much weight has to be given to each of the members. A use of the statistical multiple regression method in the model forecasts, with respect to the observed fields, provides useful statistics (regression coefficients for each model forecast at each grid point for each day of the forecast) during the training phase. In the forecast phase, the forecasts together with the aforementioned statistics enable the construction of a SE forecast into the future. It was empirically found that the training period must be at least five times longer than the forecast period in order to have a stable SE forecast. [29] Two SE techniques are depicted in this section. These will be applied to the three configurations (MA, MC, and MM) of ensemble members as well as their combination (ALL) for the SE precipitation forecasts Regular Multiple Regression [30] A SE prediction can be created by the following equation at a fixed grid point. St ðþ¼oþ XN i¼1 a i F i ðþ F t i where S(t) is a SE prediction for day t, O a time mean of the observed state for the training period, a i a weight for model i, i the model index, N the number of models, F i a time mean of the prediction by model i for the training period, and F i (t) a prediction by model i. [31] In the regular multiple regression method, the weights a i are computed at each grid point by minimizing the following function: ð1þ t train J ¼ X ðst ðþ Ot Þ 2 ð2þ t¼0 where O(t) denotes a observed state, t time, and t-train the length of the training period. [32] In most of the applications of SE method, the Gauss- Jordan elimination algorithm can be efficiently used in order to minimize the above function J. However, there are singular value problems in this algorithm especially for the application to precipitation forecasts because of many zero rain events. This problem can satisfactorily be solved by an algorithm, known as singular value decomposition (SVD). Instead of using the Gauss-Jordan elimination algorithm, the SVD is, therefore, the method of choice for solving the equation (2) in this study. Further details on the SVD are given by Press et al. [1989]. Hereafter, this approach of superensemble technique will be called SEO (superensemble technique with the Original method) Regression DLM [33] The Kalman filter (KF) is a recursive solution to the general problem of trying to estimate the state x of a discrete-time controlled process with a measurement z, allowing for control input, process noise and measurement noise. In the discipline of meteorology, the KF has been mainly used for the data assimilation field [e.g., Burgers et al., 1998; Hamill and Snyder, 2000; Houtekamer and Mitchell, 2001]. The main advantages of the KF are that it recursively conditions the current estimate on all past measurements, adapting to the differences between the

5 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION CIP 8-5 Figure 1. The vertical dotted line denotes time t = 0; the area to the left denotes the training phase where a large number of forecast experiments are carried out. During this period, the available observed fields provide statistical relationships, which are then passed on to the area t > 0 (on the right). Here the multi-forecasts along with the above statistics provide the superensemble forecasts. model and the measurement, and the possibility to predict processes governed by non-linear relationships. Another advantage of the KF is that it is adaptive, so when the numerical model changes, the filter will change as well. NWP models do change from time to time. [34] A dynamic linear model (DLM) can be written as, xtþ ð 1Þ ¼ At ðþxt ðþþwt ðþ; zt ðþ¼ht ðþxt ðþþvt ðþ; where x(t) is a state vector and z(t) is a measurement of time t. Equations (3) and (4) are commonly referred to as the state (or system) equation and the output (or observation) equation, respectively. The random variables w(t) and v(t) represent the process and measurement noise, respectively. They are assumed to be independent (of each other), white, and with normal probability distributions, p(w) N[0, Q(t)] and p(v) N[0, R(t)]. A(t) is called a transition matrix and H(t) an output matrix. ð3þ ð4þ [35] In the practical application of the KF to the regression DLM, equation (3) can be rewritten as xtþ ð 1Þ ¼ IxðÞþ t wt ðþ; Here, A(t), in equation (3), is assumed to be an identity matrix (I ). For the present study, z(t) can be regarded as an observed rainfall and H(t) as the model predicted rainfalls (F i (t)). Here, subscript i denotes the model index. So, equation (4) can be expressed as zt ðþ¼ XN q i ðþf t i ðþþ t vt ðþ: i¼1 Here, q i (t)isthei-th dynamic coefficient for time step t. This implies that x(t) =[q 1 q 2 q 3... q N ] T in equation (5). [36] The solution of the regression DLM can be obtained by the KF algorithm. A simple, closed-form Bayesian analysis of the DLM with unknown, constant covariance R is available if a particular structure is imposed on the Q(t) ð5þ ð6þ

6 CIP 8-6 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION Table 1. Available Ensemble Configurations for T126 Precipitation Forecasts Ensemble Configuration Number of Members Forecast Days MA 6 x x x MC 6 x x x x x x MM 6 x x x x x ALL 16 x x x and on the initial prior for x(0). This structure enables a conjugate sequential updating procedure for R, in addition to that for x(t). In this study, we will allow R to vary according to an inverse gamma distribution. This is effectively the same as letting the noise have a T-distribution rather than a Gaussian distribution. Further details on the regression DLM are given by West and Harrison [1997]. This approach of superensemble technique will further be referred to as SEK (superensemble technique with the Kalman filter) in this study. 5. Numerical Experiments and Results [37] A great number of numerical experiments are conducted in order to construct ensemble data sets of precipitation forecasts. These data sets are essential components in developing the SE statistics. Four configurations of ensemble members are organized from the precipitation forecasts as detailed in section 3. Those are MA, MC, MM, and ALL configurations. The experiment time period is from April 1 to August 15, This period is intentionally chosen to exhibit the predictability of summer time precipitation, which is notorious for its difficulty in prediction. Three to six day precipitation forecasts are made from the above ensemble members everyday. [38] Two deterministic SE techniques (regular multiple regression (SEO) and regression DLM (SEK)) are then applied to each ensemble configuration. The results are analyzed with several verification measures for precipitation, such as the root mean square error (RMSE), the correlation coefficient, and the equitable threat score (ETS), and they are compared to those of conventional regular ensemble mean (RE) and individually bias-corrected ensemble mean (BCE) forecasts Results From T126 Forecasts [39] SE precipitation forecasts using a group of T126 resolution models have been implemented in the FSU quasioperational center since its first release of forecast on August, The resolution of T126 is still employed in the current real time global SE rainfall forecast system. [40] Numerical experiments conducted for the T126 ensemble configurations are summarized in Table 1. Ensemble members of MA and MM configurations are operationally provided by the FSU real time SE forecast system. That is why the MA rainfall forecasts are only available for up to day 3. Some of MM members provide numerical forecasts only up to day 5. Those of MC configuration are separately obtained from numerical integrations in no connection with the real time forecast. ALL configuration is the sum of MA, MC, and MM configurations. Because of a common member between configurations, only 16 members exist for the ALL configuration. If there is any missing on the ensemble configurations for any forecast days, those configurations are considered to be unavailable for those days. Just as the MA forecasts are only available for up to day 3, so is the ALL configuration. [41] In general, the FSU MA precipitation forecasts show a widespread rainfall distribution compared to the MC and MM forecasts. The intensity is usually greater than the operational models. Excluding day 1 forecasts, slightly higher prediction skills are due to MC or MM configurations. Large variability exists for the rainfall totals from member to member. Since the main purpose of the present study is to construct the best deterministic forecast using SE approaches, individual skills will not be inter-compared. [42] Regular ensemble mean (RE) and individually biascorrected ensemble mean (BCE) precipitation forecasts can, respectively, be defined as RE ¼ 1 N X N i¼1 F i ; and BCE ¼ O þ XN i¼1 1 N F i F i ; where N is the number of models, F i a precipitation prediction by model i, O a time mean of the observed state, and F i a time mean of the prediction by model i. It must be noted here that the SE prediction equation (equation (1)) is equivalent to that of the BCE forecast if the weights of each model, a i, are assumed to be equally reliable, i.e., a i =1/N. It should be mentioned that the averaging of several rain forecasts has the effect of increasing the rain area, reducing the mean rain intensity, and improving location of the rain maxima, which show the benefit of a consensus (i.e., ensemble mean) forecast. [43] Figures 2 and 3 display respectively 15-day averaged (August 1 to 15, 2000) RMSEs and spatial correlation coefficients of T126 precipitation forecasts for MA (panel a), MC (panel b), MM (panel c), and ALL (panel d) ensemble configurations over the global tropics, 45 Sto 45 N. The forecast skills of RE, SEO, BCE, and SEK are compared with different bars. All forms of skill are computed after applying 2.5 area-averaging to ensure consistency in comparison. The training period includes the preceding 4 months (April 1 to July 31). [44] The RMSEs of MA SEO and SEK are quite better than those of RE and BCE for all days 1 to 3 (Figure 2a). Figure 3a shows the associated skills in terms of the spatial correlation coefficient. The highest correlation is consistently obtained by SEK forecasts for days 1, 2, and 3. [45] Forecast skills for T126 MC, MM, and ALL ensemble configurations are shown in Figures 2 and 3 in panels b, c, and d in terms of RMSE and correlation coefficient. While the MC configuration includes skills up to day 6, the MM configuration shows forecast skills up to day 5. Owing to MA components, precipitation forecast skills are shown only up to day 3 in the ALL configuration which used 16 members to construct the RE, BCE, and SE forecasts. [46] The best verification scores are almost always obtained by the SEK forecasts in the all configurations. Although there are not significant skill differences between SEO and SEK in terms of RMSE for the MC configuration for days 3 to 6 rainfall forecasts, there are distinct improve-

7 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION CIP 8-7 Figure 2. T day mean (August 1 to 15, 2000) RMSEs over the global belt between 45 S and 45 N for (a) MA, (b) MC, (c) MM, and (d) ALL ensemble configurations of precipitation forecasts. ments in terms of correlation coefficient. This fact is also applied to the MM configuration. The correlation coefficients of BCE forecasts indicate that they have slightly better or equivalent skills compared to the SEO forecast for days 1 to 6 in the MC configuration. [47] For the MM configuration, there are almost no skill differences among RE, BCE, SEO, and SEK in terms of RMSE for days 2 to 5. This might cause one to be confused into thinking that not much improvement can be obtained by the SE approaches in the MM configuration. However, other verification measures (e.g., correlation coefficient) clearly show their superiority over the conventional ensemble forecasts. [48] RMSEs in T126 ALL precipitation forecasts over a global belt, starting period from August 1 to August 15 are shown in Figure 4. The training period for these forecasts includes the preceding 4 months, whose skills are not shown in this figure. The dotted lines denote skills for the individual ensemble member models. Each model clearly shows varying abilities to predict the rainfall. The thin solid lines denote results of the RE forecast. The heavy dashed lines indicate BCE forecasts. Whereas the thick solid line denotes the RMSE for the SEO, the thick gray line denotes the RMSE for the SEK. The skills of SEK are quite better than those of RE, BCE, SEO, and individual members for all days 1 to 3. The significant improvement of SEK skills over the other techniques is more conspicuous in terms of the correlation coefficient (Figure 5). [49] The scores in panel d in Figures 2 and 3 summarize respectively the RMSE (Figure 4) and the correlation coefficient (Figure 5) for various precipitation forecasts constructed from all ensemble members (16 members). While BCE and SEO skills are comparable to each other for all days 1 to 3, SEK skills outperform others. The SEK verification scores are slightly better than or almost equivalent to those of the MM configuration in terms of both

8 CIP 8-8 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION Figure 3. measures. This implies that most of the useful information for SE forecasts comes from the MM configuration. In other words, higher weights are assigned to MM members than other members. However, other configurations can not be Same as Figure 2 but for the correlation coefficient. ignored since some members of them have their own merits regarding the final SE forecasts. [50] It was clearly shown in the above that the best precipitation forecasts are achieved by the SEK method Figure 4. T126 ALL RMSEs over the global belt between 45 S and 45 N for (a) day 1, (b) day 2, and (c) day 3 of precipitation forecasts. The abscissa denotes forecast starting dates.

9 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION CIP 8-9 Figure 5. Same as Figure 4 but for the correlation coefficient. for most of the configurations and forecast days. The skills of MM and ALL configurations are better than those of MA and MC. The impact of the SE techniques on precipitation forecasts are more apparent in MA configuration, compared to others. However, most of the useful information for SE precipitation forecasts comes from the MM configuration, which consistently shows better skills than the others. [51] Since each verification score has its strength and weakness, forecast skills can not be easily judged by one or two skill measures. Here, two more verification statistics are applied to the precipitation forecasts verified before by the RMSE and the correlation coefficient. These commonly used categorical measures are the equitable threat score (ETS) and the bias score (BS). Definitions of these are given by Du et al. [1997]. In fact, the ETS has been the most popular verification measure of the quantitative precipitation forecast (QPF) because it seems to be an adequate estimate for overall precipitation forecast skill. This quantity scores the forecast purely on its ability to predict rain existence. The higher the value, the better the forecast model skill is for a particular threshold. The score can vary from a small negative number to 1.0, where 1.0 represents a perfect forecast. Meanwhile, the BS measures the ratio of forecast to observed frequency. The BS does not comment at all on the skill of a model forecast in terms of the placement of precipitation, but does give an indication if a model is consistently over or under-predicting the areas of precipitation. The best forecast is generally the one that remains near the 1.0 line. [52] Figures 6 and 7 show the ETS and the BS (>5 mm d 1 threshold) respectively inspected for 15-day mean precipitation forecasts for MA, MC, MM, and ALL ensemble configurations over the global tropics. The ETS diagram proves also that the SEK is the most effective technique for precipitation forecasts. Unlike that of RMSE or correlation coefficient, the score of SEO surpasses that of BCE in the ALL configuration. It implies that both SE approaches have their superiorities to the simple bias correction forecast with improved ensemble members (such as, MM). Their superiorities are much more evident in the BS diagram (Figure 7). While the scores of RE and BCE show unrealistically large rain extent, those of both SEO and SEK forecasts remain near the 1.0 line. As the forecast lead time increases, the SEK forecasts seem to be slightly under-forecasting of precipitation in the MA and MC configuration. On the other hand, slightly over-forecasting areas are maintained in MM and ALL configurations, but closest to the 1.0 line. Here, it is clear that compared to the SEO and SEK, the BCE can not efficiently remove the bias areas. [53] As an illustration, day 1 predicted rainfalls (mm d 1 ) for August 16, 2000 from the BCE, SEO, and SEK using all members are compared to the observed TMI2A12 rainfall estimate in Figure 8. All of them look similar, but the pattern and intensity of the SEK forecasts are the closest to those of the observed rainfall. The correlation coefficient is 0.78 for the SEK. Figure 9 shows day 3 rainfall maps of T126 forecasts. These figures provide a means of visually analyzing forecast maps for veracity. Overall, predictability of precipitation tends to slowly degrade with forecast lead times. RMSEs (correlation coefficients) of the SEK forecast are 3.7 (0.78) and 4.6 (0.63) for day 1 and day 3, respectively. These scores are much better than those of conventional forecasts (e.g., RE and BCE) as well as the SEO. Utilizing the correlation coefficient as a verification measure, the skill scores of SEK in this case are approximately 33% and 16% with respect to the SEO for days 1 and 3, respectively. [54] The main sources of the largest forecast errors are due to Typhoon Ewiniar over the western Pacific and Hurricane Alberto over the central Atlantic in this case. Missed locations of such salient rain features in the numerical predictions corrupt rainfall forecast skills. While tropical cyclone Ewiniar was a category 1 typhoon with 965 hpa central pressure and 75 knots maximum wind, Alberto was a category 3 hurricane with 950 hpa minimum sea-level pressure and 110 knots maximum wind. During the forecast period (model initial days; August 1 to 15, 2000) of the present study, there have been several tropical cyclones over the various locales, which partially produce a bad effect on our rainfall forecast skills. Moreover, tropical cyclones seem to have a strong influence upon superensemble statistics obtained during the training period (April 1 to July 31, 2000). Precipitation forecasts related to tropical cyclones are planning to be investigated at length in a future study. [55] A close cross-examination on individual ensemble forecast maps (not shown) reveals that if none of the ensemble members predicted a rain event, neither did the SE forecast. The SE forecast modulates intensities of predicted rainfalls close to the observed at each grid point Impacts of Higher-Resolution (T170) Forecasts [56] In the T126 forecast, it has been successfully proven that the skill and accuracy of the deterministic SE precip-

10 CIP 8-10 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION Figure 6. Same as Figure 2 but for the ETS (>5 mm d 1 ). itation forecast exceeded not only that of the individual models, but also that of the simple ensemble mean or biascorrected ensemble mean forecast. [57] The impact of a higher-resolution family of models on the performance of the SE forecasts is extensively examined here by repeating the procedures of T126 resolution precipitation forecasts. SE forecasts at a higher resolution would require a large amount of computer resources. For improving precipitation forecasts, however, this may be necessary in order to resolve the mesoconvective disturbances as long as computational capacities allow. Numerical experiments done for T170 ensemble configurations are summarized in Table 2. All experiments for constructing these configurations are separately carried out with help of a newly installed FSU parallel version of supercomputer called Terragold. Ensemble members of the MM configuration are operationally provided by the FSU real time SE forecast system and simply interpolated into the T170 resolution. For these high resolution experiments, medium-range forecasts (up to day 6) are made also with the MA ensemble configuration. With the extended forecasts, ALL ensemble forecasts can also be made up to day 5. [58] Mesoscale convective systems are well resolved by T170 forecasts, compared to T126 forecasts. More strongly localized convective systems are well reproduced by the MA and MC precipitation forecast components. Since the forecasts from the MM ensemble configuration are simply interpolated into the T170 resolution, it is hard to find any improvements in resolving mesoscale convective disturbances. The higher-resolution impacts on SE precipitation forecasts explored in this study are coming from the MA and MC forecasts not from the MM configuration. [59] For the MA and MC configurations, individual member skills of T170 forecasts turn out to be better than those of T126 s, so do the RE, BCE, SEO, and SEK.

11 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION CIP 8-11 Figure 7. Same as Figure 2 but for the bias score (>5 mm d 1 ). RMSEs of T170 MA SEO and SEK are quite better than those of the BCE, RE, and individual members up to day 6. The highest correlation is consistently obtained by the SEK forecasts for days 1, 2, and 3. But for days 4 to 6, SEO and SEK skills are equally likely. The MC configuration also produces nearly similar results as the T126 case. [60] In terms of RMSE and correlation coefficient, precipitation forecast skills of RE, BCE, SEO, and SEK as well as individual forecasts for T170 ALL ensemble configurations are shown in Figures 10 and 11. The 2.5 area averaged skills shown here are computed over a global belt, 45 S to 45 N, covering a forecast period from August 1 to August 15 in order to ensure consistency in comparison with those of the low-resolution forecast. Owing to MM components, precipitation forecast skills are shown only up to day 5. The same training period as that of the T126 case is used (April 1 to July 31) to develop the SE forecasts. While BCE and SEO skills are comparable to each other for all days 1 to 5, SEK skills are always better than the other forecast skills. [61] Day 3 predicted rainfall maps, all valid on August 16, 2000, from the BCE, SEO, and SEK using all members are compared with the microwave-based observed rainfall estimate in Figure 12. Likewise the T126 case, BCE, SEO, and SEK forecasts all look similar, but the SEK forecast is found to be the closest to the observed rainfall in terms of skill scores as well as the pattern and intensity of rainfall. Much more organized rainfall systems are well-predicted from this high-resolution version of the SE forecasts. The high-resolution family of forecasts also show better skills than those of low resolution (Figure 9). As mentioned in the T126 case, the main sources of forecast errors are tropical cyclone systems not well predicted in NWP models. Although the higher skills are mainly coming from

12 CIP 8-12 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION Figure 8. The observed TMI2A12 rainfall estimate for August 16, 2000 is compared with day 1 T126 precipitation forecasts from (b) the BCE, (c) the SEO, and (d) the SEK in the ALL configuration. the MM ensemble configuration, the reason for improvement of SE precipitation forecasts is due to the improvement of forecast skills in the higher-resolution MA and MC forecasts. [62] In order to make an end of this section, days 1 to 5 predicted rainfall maps from the T170 SEK forecasts are compared to the observed rainfall estimate in Figure 13. These are 24 hourly precipitation forecasts at the end of

13 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION CIP 8-13 Figure 9. Same as Figure 8 but for day 3. days 1 to 5, all valid for August 16, The top left panel presents the observed precipitation field based on satellite microwave instruments. RMSEs and correlation coefficients of the predicted precipitation against the observed field are indicated at the top right corner of each panel. The accuracy of forecast continues to slowly deteriorate as forecast lead time increases. However, even at the 5 day point, the scores are still indicating reasonable skill. The correlation coeffi-

14 CIP 8-14 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION Table 2. Same as Table 1 but for T170 Forecasts Ensemble Configuration Number of Members Forecast Days MA 6 x x x x x x MC 6 x x x x x x MM 6 x x x x x ALL 16 x x x x x cient of day 5 SEK precipitation forecast is higher than 0.5, showing its capability of making skillful rainfall forecast in the medium-range. This figure exemplifies a key accomplishment in QPF using a SE approach, compared to what we have seen previously from the conventional forecasts. 6. Concluding Remarks [63] This study has extensively evaluated short- to medium-range quasi-operational ensemble rainfall forecasts (up to 6 days) over the global tropics through use of satellite measurements (e.g., TRMM and SSM/I) in a deterministic sense. Several facets of SE precipitation forecasting have been reviewed and analyzed in the present paper. [64] Multianalysis (MA), multicumulus-scheme (MC), and multimodel (MM) ensemble configurations were first devised and generated from a huge number of numerical experiments for precipitation forecasts during the period of April, 1 to August, 15, The MA ensemble members were prepared from the use of five different rain rate algorithms (FERRARO, OLSON, SSMI/TMI, TURK, and TMI2A12) through the physical initialization procedure in addition to a control forecast. In order to introduce the MC ensemble configuration, six different state-of-the art cumulus parameterization schemes were incorporated into the FSUGSM in this study. Those were Kuo-type (FSU), NCEP/SAS, GSFC/RAS, NRL/RAS, NCAR/ZM, and Emanuel schemes. The MM configuration was a set of independent NWP model precipitation forecasts from five operational centers in addition to an FSU control forecast. Those operational centers were BMRC, JMA, NRL, RPN, and NCEP. [65] Next, we reviewed the original deterministic SE technique and proposed a new technique. The original superensemble technique (SEO) uses a regular multiple regression method in order to obtain regression coefficients for each ensemble forecast at each grid point for each day of the forecast. The newly proposed SE enhancement technique was the regression DLM (SEK) approach. These two deterministic SE techniques were applied to the three configurations (MA, MC, and MM) of ensemble members as well as all together (called ALL configuration). [66] A higher-resolution family of models was extensively examined by repeating the above procedure with T170 resolution precipitation forecasts in order to resolve the mesoconvective disturbances better and investigate the impact of them on the SE forecasts. [67] Based upon the results from the experiments carried out in this study, the following conclusions can be drawn: 1. Deterministic SE precipitation forecasts of days 1 to 6 exhibit generally superior forecast results to various conventional forecasts, such as individual model, regular ensemble mean (RE), and individually bias-corrected ensemble (BCE) mean forecasts. The success of the SE concept is owing to its selective nature in the construction of an optimal combination of available forecast products by eliminating spurious information contained in some models. In other words, the better the forecast performances are, the higher the weights, for each ensemble forecast at each grid point for each day of the forecast. Figure 10. Same as Figure 4 but for T170.

15 SHIN AND KRISHNAMURTI: DETERMINISTIC SUPERENSEMBLE PRECIPITATION CIP 8-15 Figure 11. Same as Figure 10 but for the correlation coefficient. 2. The regression DLM (SEK) exhibits a much better deterministic precipitation forecast. It outperforms the SEO as well as conventional ones (RE and BCE). 3. Although SE forecasts at a higher resolution require a large amount of computer resources, it turned out that the impact is significant not only in skill scores, but also in resolving mesoconvective disturbances. 4. The MC configuration, constructed by forecasts of different cumulus parameterization schemes incorporated into the FSUGSM, provided a better ensemble set than the MA configuration. 5. Whereas the most promising role of the SE techniques was found in the MA configuration, the best success with the SE forecasts was found with the MM configuration, surpassing both the MA and the MC configurations. 6. Most of the useful information for SE forecasts in the ALL configuration originated from the MM ensemble members. In other words, higher weights were assigned to MM members relative to the other members. However, other configurations could not be ignored since some members have adequate merits on the final SE precipitation forecasts. 7. If none of the ensemble members predicted a rain event, neither did the SE forecast. The SE forecasts mainly modulate intensities of predicted rainfall close to the observed at each grid point. This is why we should develop a better NWP model in order to give a better component to the SE forecast system. It became apparent that significant improvement of member models is needed for an increase in the skill of the SE. [68] Consideration of the above conclusions suggests the following areas for future research: 1. The SE techniques proposed here must be applied to the other important meteorological variables such as sea level pressure, 850 and 200 hpa wind fields, and 500 hpa height in order to better assess short- to medium-term weather forecasting. 2. Several other statistical techniques, such as the r 2 (spectral) approach and the Z-transformation, should be tested as well to examine their suitability to the SE precipitation forecasts. 3. Since differences due to use of different satellite-based rain rates do not necessarily represent the uncertainties in the initial analysis, multianalysis SE forecasts should be evaluated with use of other common ensemble prediction systems (e.g., breeding or singular vector method). 4. A more robust cumulus parameterization must be developed in order to introduce an improved member for the SE forecast system. 5. The impact of much higher resolution global models such as T255 on the SE forecast should be investigated as long as computational capacities allow. 6. In order to make a better precipitation assimilation and forecast system, time resolution of observation and prediction must be increased to 3-h intervals. This will be realized in the near future ( time frame) by the help of the Global Precipitation Measurement (GPM) mission. GPM is a follow-up of TRMM and plans to expand the scope of rainfall measurement through use of a satellite constellation. 7. Comparisons have to be made between performances of warm season SE and cool season SE forecasts. [69] The characteristics of probabilistic precipitation forecasts from the MA, MC, MM, and ALL ensemble configurations will be investigated in a companion paper [Shin and Krishnamurti, 2003]. We will also extensively explore the impact of the SE approach on probabilistic precipitation forecasts.