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  • View in gallery

    NCEP wind flow (vectors) and isotachs (shaded units are m s−1), for the monsoon precipitation event shown corresponding to (a) end of physical initialization, day 0 (0000 UTC 25 Jun 2005) and (b) day-2 forecast (0000 UTC 27 Jun 2005).

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    Snapshot of Hurricane Frances from NOAA AVHRR at 1905 UTC 31 Aug 2004.

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    Schematics of rain-rate physical initialization (every model time step).

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    Rainfall (mm day−1) at day 0 (0000 UTC 25 Jun 2005) corresponding to (a) TRMM, (b) experiment with physical initialization (PINIT), (c) control experiment without physical initialization (CTRL), (d) equitable threat scores for CTRL and PINIT experiments, (e) 700-hPa relative humidity (%) for CTRL, and (f) 700-hPa relative humidity (%) for PINIT.

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    Rainfall (mm day−1) at day 1 (0000 UTC 26 Jun 2005) corresponding to (a) TRMM, (b) experiment with physical initialization (PINIT), (c) control experiment without physical initialization (CTRL), and (d) equitable threat scores for CTRL and PINIT experiments.

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    Rainfall (mm day−1) at day 2 (0000 UTC 27 Jun 2005) corresponding to (a) TRMM, (b) experiment with physical initialization (PINIT), (c) control experiment without physical initialization (CTRL), and (d) equitable threat scores for CTRL and PINIT experiments.

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    Time series of the parameters at grid point 17.89°N, 92.5°E for the monsoon precipitation prediction experiment for the period 0000 UTC 24–27 Jun 2005 with (a) specific humidity (g kg−1) at 850 hPa, (b) vertical velocity (m s−1) at 850 hPa, (c) minimum sea level pressure (hPa), (d) divergence (×10−3 s−1) at 850 hPa, and (e) rainfall (mm day−1). The vertical line at 0000 UTC 25 Jun 2005 indicates the end of the physical initialization.

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    (a) Frequency distribution of rain rates from TRMM estimates and experiments with/without physical initialization. (b) Normalized rain rates (with respect to means for the class intervals) for the experiments with/without physical initialization.

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    Life cycle of a cloud cluster (identified as A) during the monsoon precipitation event shown at every 3-h interval starting from 0009 UTC 26 to 0000 UTC 27 Jun 2005. (left) TRMM observations; (middle) physical initialization (PINIT); and (right) Control (CTRL) experiment.

  • View in gallery

    Rainfall (mm day−1) at day 0 (0000 UTC 25 Jun 2005) corresponding to (a) experiment with physical initialization (PINIT), (b) control experiment without physical initialization (CTRL), and (c) equitable threat scores for CTRL and PINIT experiments. These results are from Kain–Fritsch cumulus scheme.

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    (a) Track positions and (b) minimum sea level pressure (hPa) of Hurricane Frances 0000 UTC 26 to 0000 UTC 29 Aug 2004. OBS, PINIT, and CTRL (from 0000 UTC 27 Jun) denote official estimates, physical initialization, and control experiments, respectively.

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    Rainfall (mm day−1) at day 0 (0000 UTC 27 Jun 2005) corresponding to (a) TRMM, (b) experiment with physical initialization (PINIT), (c) control experiment without physical initialization (CTRL), and (d) equitable threat scores for CTRL and PINIT experiments.

  • View in gallery

    Rainfall (mm day−1) at day 2 (0000 UTC 29 Jun 2005) corresponding to (a) TRMM, (b) experiment with physical initialization (PINIT), (c) control experiment without physical initialization (CTRL), and (d) equitable threat scores for CTRL and PINIT experiments.

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    Time series of the parameters at grid point 16°N, 49°W for the Hurricane Frances experiment for the period 0000 UTC 26–29 Aug 2004: (a) rainfall (mm day−1), (b) specific humidity (g kg−1) at 850 hPa, (c) vertical velocity (m s−1) at 850 hPa, and (d) divergence (×10−3 s−1) at 850 hPa. The vertical line at 0000 UTC 27 Aug 2004 indicates the end of the physical initialization.

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    (a) Hurricane Wilma IR satellite imagery at 0745 UTC 20 Oct 2005, and 6-h forecast of rainfall (mm) IC 0000 UTC 20 Oct 2005 from (b) physical initialization experiment (PINIT), and (c) control experiment (CTRL) with horizontal resolution of 5 km.

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Mesoscale Moisture Initialization for Monsoon and Hurricane Forecasts

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  • 1 Department of Meteorology, The Florida State University, Tallahassee, Florida
  • | 2 Department of Meteorology and Oceanography, Andhra University, Visakhapatanam, India
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Abstract

This paper addresses physical initialization of precipitation rates for a mesoscale numerical weather prediction model. This entails a slight modification of the vertical profile of the humidity variable that provides a close match between the satellite and model-based rain rates. This is based on the premise that the rain rate from a cumulus parameterization scheme such as the Arakawa–Schubert scheme is most sensitive to the vertical profiles of moist static stability. It is possible to adjust the vertical profile of moisture by a small linear perturbation by making it wetter (or drier) in the lower levels and the opposite at levels immediately above. This can provide a change in the moist static stability in order to achieve the desired rain rate. The procedure is invoked in a preforecast period between hours −24 and 0 following Krishnamurti et al. The present study is the authors’ first attempt to bring in this feature in a mesoscale model. They first noted that the procedure does indeed provide a much closer match between the satellite estimate of initial rain and that from the physical initialization for a mesoscale model. They have examined the impacts of this procedure for the initialization and short-range forecasts of a monsoon rainfall event and a hurricane. In both of these examples it became possible to improve the forecasts of rains compared with those from control runs that did not include the initialization of rains. Among these two examples, the results for the monsoon forecasts that deployed a uniform resolution of 25 km and the Grell and Devenyi scheme over the entire domain had the largest positive impact. The hurricane forecasts example also show improvement over the control run but with less impact, which may be due to heavy rains from explicit clouds in the nonhydrostatic model. Here the results did convey a strong positive impact from the use of the physical initialization; however, forecasts of very heavy rains carry smaller equitable threat scores. These require development of a more robust precipitation initialization procedure.

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

Abstract

This paper addresses physical initialization of precipitation rates for a mesoscale numerical weather prediction model. This entails a slight modification of the vertical profile of the humidity variable that provides a close match between the satellite and model-based rain rates. This is based on the premise that the rain rate from a cumulus parameterization scheme such as the Arakawa–Schubert scheme is most sensitive to the vertical profiles of moist static stability. It is possible to adjust the vertical profile of moisture by a small linear perturbation by making it wetter (or drier) in the lower levels and the opposite at levels immediately above. This can provide a change in the moist static stability in order to achieve the desired rain rate. The procedure is invoked in a preforecast period between hours −24 and 0 following Krishnamurti et al. The present study is the authors’ first attempt to bring in this feature in a mesoscale model. They first noted that the procedure does indeed provide a much closer match between the satellite estimate of initial rain and that from the physical initialization for a mesoscale model. They have examined the impacts of this procedure for the initialization and short-range forecasts of a monsoon rainfall event and a hurricane. In both of these examples it became possible to improve the forecasts of rains compared with those from control runs that did not include the initialization of rains. Among these two examples, the results for the monsoon forecasts that deployed a uniform resolution of 25 km and the Grell and Devenyi scheme over the entire domain had the largest positive impact. The hurricane forecasts example also show improvement over the control run but with less impact, which may be due to heavy rains from explicit clouds in the nonhydrostatic model. Here the results did convey a strong positive impact from the use of the physical initialization; however, forecasts of very heavy rains carry smaller equitable threat scores. These require development of a more robust precipitation initialization procedure.

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

1. Introduction

In recent years rain-rate initialization, also termed physical initialization (Krishnamurti et al. 1988), has been introduced in several large-scale operational models (e.g., ECMWF, JMA, BMRC, and NCEP/EMC). A list of acronyms and symbols are presented in Table 1. Krishnamurti et al. (1988, 1991) first proposed this concept for the improvement of short-range numerical weather prediction over the Tropics. This was followed by a number of studies (Krishnamurti et al. 1993, 1995) in which further refinements of physical initialization were addressed. Treadon (1996) used Geostationary Operational Environmental Satellite (GOES) precipitation index (GPI) rain rates (rainfall estimates based on TRMM and SSM/I microwave radiances) within a 3DVAR for the NMC (NCEP) operational global model and noted a measurable positive impact in forecasts. Marécal and Mahfouf (2002) utilized a similar procedure for the ECMWF operational model and demonstrated a positive impact for precipitation forecasts. Their procedure first assimilates observed surface rain rates to modify the model temperature and humidity profiles through 1DVAR, and then the total column water vapor from 1DVAR is assimilated through 4DVAR. Hou et al. (2004) utilized a one-dimensional variational data assimilation of precipitable water and precipitation rates from TRMM satellite-based estimates and showed forecast improvements for the rain rates. Their study uses the assimilation of observed precipitation through the temperature and moisture tendencies as control variables. Similar analysis has been provided by JMA and BMRC in published (Davidson and Weber 2000) and unrefereed reports (Tada 2002; Tauchi et al. 2003). The inclusion of initial rains, based on Newtonian relaxation or using variational data assimilation, has only seen limited application for very high resolution mesoscale models (Ishikawa 2002; Koizumi et al. 2005; Macpherson 2001; Jones and Macpherson 1997).

From the experience gained in physical initialization with large-scale models (Krishnamurti et al. 1991, 1993, 2001), it is possible to formulate a simplified version of rain-rate initialization for mesoscale models. That is the goal of this paper. We hope to see the extent to which the observed estimates of rain rate from satellites can be incorporated within a mesoscale model. We also wish to ask how far into the future we can demonstrate a positive impact on the forecast skills. In our study we illustrate two short-range forecasts covering examples of a summer monsoon event and a hurricane passage over the Atlantic Ocean. This covers two diverse atmospheric circulations: (i) rainfall related to monsoon circulation extending over a wide spread region where a large coverage of nimbostratus was noted and (ii) rainfall associated with hurricane that is heavy and concentrated over a small region of few hundred kilometers of radius arising from tall cumulus clouds and their anvils. These were chosen to study the impact of the rain-rate initialization for two different atmospheric phenomena.

We also wish to explore whether such an initialization can carry the life cycle of a mesoconvective element (size of the order of few hundred kilometers). The notion of tracing mesoconvective precipitating elements in short-range numerical weather prediction was previously carried out by Krishnamurti et al. (1998). In that study, a global model at a high resolution of T255 (spectral triangular truncation with 255 waves, transform grid separation of 45 km) was used to study transient mesoconvective systems in the monsoon environment at 15°N over the monsoon belt. Thus mesoconvective precipitation elements of scales ≈300 km were resolved by only six or seven grid points. Even at that resolution, subsequent to a complete physical initialization following Krishnamurti et al. (1991), it was possible to follow the life cycle of the passage of these mesoconvective precipitating elements over a domain of the summer monsoon. Several such elements were individually followed and their passages were traced, and that history was compared with high-resolution satellite imagery. That study suggested strongly that a tracing of mesoconvective elements should be possible in mesoscale models. In this study, we have also examined the prediction of the life cycle of a mesoscale cloud cluster in the summer monsoon region, with and without the rain-rate initialization, using the NCAR WRF model to emphasize the impacts of rain-rate initialization.

2. The WRF model

The NCAR WRF Euler mass coordinate model (Skamarock et al. 2005) is used for carrying out these experiments. The WRF model is designed to be highly modular, and a single source code, which can be configured for both research and operational applications. The model has transportable, flexible, state-of-the-art physics and dynamics options and is efficient in a massively parallel computing environment (accommodating vector environments as well) and provides portable performance on diverse computing architectures. The model equations are integrated using terrain-following mass vertical coordinate. The prognostic variable includes horizontal wind velocity components (u and v), vertical wind velocity (w), perturbation potential temperature, perturbation geopotential, and perturbation surface pressure of dry air, and optionally, turbulent kinetic energy and any number of scalars such as water vapor mixing ratio, rain/snow mixing ratio, and cloud water/ice mixing ratio. The WRF model used for this study was initialized from NCAR-archived FNL analyses (1° resolution) datasets using an advanced version of the WRF standard initialization package (WRFSI). Table 2 illustrates the WRF model configuration (dynamics, physics, and resolution) used for the present study.

3. Data

a. Initial model data

The datasets for the initial state and time-varying boundary conditions for the two numerical experiments, one for the Indian summer monsoon precipitation forecasts and the other for the Atlantic Hurricane Frances, were obtained from the NCEP FNL analyses for the respective model domains. These datasets are the Global Final (FNL) Analyses available from NCEP–NCAR at 1° grid at every 6 h. The analyses consists of surface pressure, sea level pressure, geopotential height, temperature, sea surface temperature, soil values, ice cover, relative humidity, zonal and meridional winds, and other parameters at 26 mandatory pressure levels from 1000 to 10 hPa and at boundary. The model topography at the 25-km resolution for the domain regions were obtained and interpolated from the USGS topography data at 10′ resolution. For the experiment of the Indian summer monsoon rainfall prediction, the initial conditions were derived for 0000 UTC 24 June 2005 with the time-varying lateral boundary conditions and sea surface temperatures derived at every 6-h interval during the period 0000 UTC 24–0000 UTC 27 June 2005 from NCEP FNL analyses. For the experiments on the prediction of Hurricane Frances over the Atlantic Ocean, the initial conditions were derived for 0000 UTC 26 August 2004 with time-varying lateral boundary conditions and sea surface temperatures at intervals of every 6 h during the period 0000 UTC 26–0000 UTC 29 August 2004 from NCEP FNL analyses.

b. Rainfall datasets

For the purpose of rain-rate initialization and comparison of model rainfall, TRMM rainfall datasets were collected for the 3-day period for both of these experiments. The precipitation datasets (i.e., NASA TRMM/3B42) were obtained from NASA GSFC, which provides gridded 3-hourly rain-rate estimates at a horizontal resolution of 0.25° × 0.25° in global belt extending from 50°S to 50°N. This precipitation estimate (3B42) is a blended product obtained from a number of satellite sensors (TRMM, SSMI, AMSR, and AMSU). The 3B42 precipitation estimates are produced broadly in four stages: 1) the microwave precipitation estimates are calibrated and combined (Kummerow et al. 1996), 2) infrared precipitation estimates are created using the calibrated microwave precipitation, 3) the microwave and IR estimates are combined (Huffman et al. 2003), and 4) rescaling to monthly data is applied. Each precipitation field is best interpreted as the precipitation rate effective at the observation time. The TRMM rainfall data available at 3-h intervals are interpolated for every 1-min interval, the time step of the WRF model, for the first 24-h period of the experiments for the purpose of rain-rate physical initialization.

4. Synoptic description of the atmospheric circulation for the two experiments

A brief description of the synoptic conditions for the individual 3-day periods of the two prediction experiments performed for this study is provided here.

a. Synoptic description of monsoon circulation (0000 UTC 24–0000 UTC 27 June 2005)

It is well known that the monsoon rainfall has a large spatial variability and that the rainfall during any day of the monsoon season (i.e., June to September), is a function of the synoptic situation of the atmospheric circulation. The synoptic situation pertains to the period 24–27 June 2005. During this 3-day period, two persistent weather systems contributed to the observed rainfall. One of these was a Bay of Bengal disturbance near 20°N that moved northwestward during a 3-day period. The other feature relates to strong moist westerly winds along the west coast of India that contributed to strong orographic precipitation (Fig. 1). During the 24-h period ending 0300 UTC 25 June 2005, a sea level pressure trough was present with its axis extending from northwest India toward southeast to east central Bay of Bengal. An offshore trough at sea level with cyclonic circulations extending up to the 500-hPa level over along the west coast was also present. These systems produced heavy rains over western India and over the east-central India extending zonally toward north Bay of Bengal. During the 24-h period from 0300 UTC 25 June to 0300 UTC 26 June, the offshore trough was persistent along the west coast to southwest coast. A cyclonic circulation extending up to midtropospheric levels lies over northwest Bay of Bengal and over central parts of India. During the next 24-h period (i.e., from 0300 UTC 26 June to 0300 UTC 27 June 2005), the midtropospheric cyclonic circulation moved over to the east-central Indian region and offshore over the west coast persisted giving widespread rain over provinces of western and central India. The description corresponds to an active phase of monsoon.

b. Synoptic description of Hurricane Frances

Hurricane Frances was a classic Cape Verde tropical cyclone, with guidance initiated by the National Hurricane Center (NHC) on 24 August 2004 when the storm was well out into the Atlantic Ocean. Frances created significant damage in the Bahamas as a major hurricane (category 3), lingering for some time in the waters between the Bahamas and south Florida before finally making landfall as a category 2 storm on the night of 5 September near Sewall’s Point/Hutchinson Island, a sparsely populated barrier island in Martin County. As it approached the Bahamas and Florida, Frances exhibited a tremendous storm envelope (Fig. 2), and in general the population was well prepared to evacuate as ordered. Frances devastated several inland Florida counties, including Orange and Polk, dealing a tremendous blow to residents and the citrus industry. At least 35 deaths have been attributed to Frances and $10 billion in total damage has been estimated for this storm. Frances emerged in the northeast Gulf of Mexico for a short time, making landfall as a tropical storm near St. Marks, Florida, and causing some damage in the Big Bend area east of Tallahassee, Florida. Frances produced over 100 tornadoes in Florida and along the eastern seaboard. For more information about the storm, refer to the National Hurricane Center Web site (http://www.nhc.noaa.gov/2004frances.shtml?).

5. Design of the numerical experiments

Two numerical experiments were designed to study the impact of rain-rate physical initialization: one includes the rain-rate initialization algorithm and the other is carried out without the initialization. The experiment without initialization is referred to as the control experiment and the experiment with initialization is here referred to as the physical initialization experiment. The WRF model, described in section 2, has been suitably adapted for the two experiments. The model is designed to have a single domain with 25-km horizontal resolution. The regions covered by the model domains are given in Table 2. At this resolution, the time step for the model integration is taken as 1 min. The WRF model design including the options chosen for the various physical processes are mentioned in Table 2. The initial conditions and the time-varying boundary values at every 6-h interval are obtained from the NCAR FNL at 111.1-km (approx) resolution. These data include the sea surface temperatures along with all the required meteorological variables. TRMM rainfall data (3B42) are available at 25-km resolution at 3-h intervals. The data were collected and interpolated at every 1-min interval for the purpose of rain-rate initialization. In the sensitivity experiment, the WRF is integrated for a total period of 72 h, of which rain-rate initialization is implemented for the first 24-h period and a forecast/simulation run is carried out thereafter to hour 48. During the first 24-h period, the process of rain-rate initialization, described in section 6, was implemented for each time step (i.e., 1-min interval at every grid point of the domain). This process in effect alters the humidity profile from the surface up to roughly 500 hPa in order to obtain a closer match among the TRMM estimates of rainfall and those from the model. The control experiment was integrated continuously for 48 h (i.e., up to 0000 UTC 27 June). A similar rationale was followed for the hurricane experiment.

6. Physical initialization for mesoscale models

a. Summary of previous work based on global model

This refers to rain-rate initialization that was described in a series of papers by Krishnamurti et al. (1991, 1993, 1995). A major application was presented in Krishnamurti et al. (2001) where it was shown that consistently we could improve the nowcasting of precipitation with correlations greater than 0.9 between observed (satellite based) estimates and the model rain rates. These results pertain to large-scale models that utilized horizontal grid resolutions of the order of 70 km. This large-scale physical initialization carried four steps: (i) During a preforecast stage (i.e., hour −24 to 0), we bring in the observed estimates of precipitation. This rainfall is interpolated to each time step of a forecast model. A reverse cumulus parameterization algorithm is next used that restructures the vertical profile of moisture consistent with the satellite-based rainfall estimate. Such a reverse algorithm was possible for certain cumulus parameterization schemes such as a modified Kuo’s scheme based on Krishnamurti et al. (1980, 1983). The restructuring of the vertical profile of moisture covered the region between the cloud base at the 900-hPa level and a cloud top near the top of the troposphere (Krishnamurti et al. 1991). (ii) The moisture profile in the surface layer was also modified consistent with these observed rainfall estimates and the apparent moisture sink following Yanai et al. (1973). Here we used what was called a reverse surface similarity algorithm (Krishnamurti et al. 1991). (iii) Above the middle troposphere, where the moisture analysis was unreliable, satellite-based estimates of the outgoing longwave radiation were used to restructure the upper-tropospheric moisture such that the implied clouds and the model-based OLR matched those from the satellite closely. This required the solution of a minimization of these OLR differences using a Newton–Raphson method. These three aforementioned components of physical initialization are carried out at each time step of the preintegration phase (i.e., hour −24 to 0) of forecast. The moisture profile at the end of this exercise provides more reasonable precipitation rates, surface fluxes, and the OLR. (iv) To make this procedure an integral part of the model initialization, it was necessary to perform a Newtonian relaxation (i.e., nudging) where some of the dependant variables were nudged strongly compared to others. At the end of this relaxation the temperature and rotational wind are kept close to the analysis at hour 0 (stronger relaxation toward observation) whereas fields such as moisture, vertical motion, heating, and surface pressure tendencies were weakly relaxed to permit their adjustments (i.e., spinup toward the improved observed rainfall estimates).

b. Application to mesoscale models

The aforementioned complete procedure has not been tried for mesoscale models. In this study we illustrate the impacts of rain-rate initialization for examples of hurricane and monsoon forecasts from the WRF model. Our use of the WRF model deployed the Grell and Devenyi (2002) version of the cumulus parameterization scheme for the subgrid-scale precipitation and an explicit cloud scheme for grid-resolvable precipitation. The Grell and Devenyi scheme for the cumulus parameterization in WRF is based on the simple type of Arakawa–Schubert scheme as proposed by Grell (1993) in which the scheme is run as an ensemble with different variants of the closure and changes in the sensitivity parameters. Four different types of closure (i.e., removal of convective available potential energy) (Kain and Fritsch 1993); moisture convergence (Krishnamurti et al. 1983); quasi equilibrium (Arakawa and Schubert 1974); and low-level vertical velocity (Brown 1979) were adopted in combination with changes in parameters such as entrainment, cloud radius, precipitation efficiency, and others. The scheme produces about 144 ensembles and the ensemble mean is passed on to the dynamical part of the numerical model. Our method of rain-rate initialization for mesoscale models that utilize Arakawa–Schubert-type cumulus parameterization is described as follows.

The precipitation rate in the Arakawa–Schubert scheme is most sensitive to the vertical distribution of moist static stability [i.e., −Cp(T/θ)(∂θe/∂p) or −(∂/∂p)(gz + CpT + Lqs)]. Here Cp is specific heat constant at a constant pressure, g is acceleration due to gravity, z is geopotential height, qs is the saturation specific humidity, T is temperature, and L is latent heat of vaporization. The initial humidity data (and its vertical distribution) on the mesoscale (i.e., at horizontal resolutions of the order of 25 km) carry a high degree of uncertainty. It is possible to calibrate the vertical distribution of the specific humidity slightly in order to arrive at a close match between the modeled rain and that from the observations. This procedure does not require one to work on the inner details of a cumulus parameterization scheme. Figure 3 illustrates the schematics of physical initialization with cumulus parameterization where the input fields generate a one-time-step predicted rain.

Our method of implementing the rain-rate initialization in the present study is as follows. We assume an error ε (which varies linearly along the vertical) for the relative humidity (RH). Thus we denote a corrected relative humidity by the Eq. (1),
i1520-0493-135-7-2716-e1
The linear variation of ε along the vertical coordinate is expressed by
i1520-0493-135-7-2716-eq1
We provide several assigned values for this correction at the σ = 1 surface. These range in values from −20% to +20% for the surface relative humidity. We furthermore assume that this correction is zero at a sigma level that partitions the precipitable water equally above and below that σ level. All of these vertical linear correction profiles pass through this zero correction at this σ level. Thus the prevailing relative humidity is made drier (or wetter) below that level and the opposite correction is applied above that level from a choice of these linear correction profiles of different positive and negative slope angles a. This addition (or subtraction) of moisture renders the moist static stability more unstable (or less unstable) compared to what was initially present. The choice of these linear profiles of correction provides different moisture profiles to the cumulus parameterization algorithm. Each of these possibilities provides a different rainfall rate because of the extreme sensitivity of the precipitation rate to the cumulus convection scheme. It then becomes a simple exercise to find an optimal linear profile for these corrections ε(σ) that provides the closest match between the model rain and the observed rainfall (interpolated to that grid point using a bilinear interpolation at that time step). This entire exercise is repeated for each time step of the physical initialization (i.e., between t = −24 h and hour 0) for each grid location separately. During this preintegration physical initialization phase, the imposed rain provides a spinup for the model variables such as heating, precipitation, divergence, and the surface pressure tendencies. In our earlier study on physical initialization (Krishnamurti et al. 1991), we had explicitly invoked a condition for the conservation of moisture; that is, ∫qp remains invariant before and after the physical initialization. This feature is not explicitly invoked in the present study where linear perturbations based on relative humidity were involved. We recognize that it may be preferable to carry out this procedure using the constraints of moisture conservation in the future. The current state of initialization for mesoscale model includes 3DVAR and 4DVAR (Zou and Xiao 2000) that however does not directly make use of observed precipitation estimates within the variational assimilation. For large-scale models Hou et al. (2004) and Marécal and Mahfouf (2002) have added the difference between the model and the observed rain estimates within the cost function (J). Such a procedure is currently needed for the mesoscale models. The Newtonian relaxation (based on nudging) of this study is being viewed as a first step for the incorporation of the observed rain rates in a mesoscale model.

c. Spinup during and after physical initialization in a mesoscale model

In large-scale models when one performs normal-mode initialization (Daley 1991), or physical initialization (Krishnamurti et al. 1991), the fields exhibit noise prior to the initialization and become monotonically varying subsequent to the initialization. This largely suppresses the gravity-inertio oscillations as the model arrives at a quasi- balanced state subsequent to the initialization. We have tested the spinup issue for the NCAR WRF model in the context of the rain-rate initialization.

7. Results

The results from two numerical experiments utilizing the WRF model on the impact of rain-rate physical initialization are presented in this section. The results of the monsoon rainfall initialization and prediction experiment are described followed by the experiment for Hurricane Frances.

a. Monsoon precipitation forecasts

In Figs. 4a–f, 5 and 6a–d we present results of monsoon precipitation forecasts. The start date of this forecast was 0000 UTC 25 June 2005. The physical initialization covered the preceding 24 h. In Fig. 4, we show the results for the nowcasting of rain (mm day−1). These are 24-h rainfall totals for the period of the physical initialization (i.e., 0000 UTC 24–0000 UTC 25 June). Figure 4a illustrates the observed estimates for this 24-h rain (based on TRMM). The scales of precipitation intensities range from 5 to ∼100 mm day−1. At this initial period, heavy rain was occurring over the northeastern Bay of Bengal, central India, and the Gujarat coastal area of western India. Rainfall in excess of 20 mm day−1 over the eastern Bay of Bengal, offshore from the Myanmar coast, was another prominent feature in these initial observed rains. Figures 4b and 4c illustrate, respectively, the results for the initial rains from the physical initialization and the experiment that does not include the rain-rate initialization (Control). Visual comparison of panels (a) and (b), and (a) and (c), shows clearly that the control run overestimates the rains over the Bay of Bengal and fails to portray the initial rains over central India. Figure 4c, for the control run, is the accumulated rainfall between hours −24 to 0 (i.e., 0000 UTC 25 June). Figure 4b carries a past history for an entire day (i.e., 0000 UTC 24–0000 UTC 25 June) during the period of the physical initialization. This closer match between the observed rain and the physically initialized rain can be assessed quantitatively from the estimation of equitable threat scores (see the appendix). Here we have used thresholds of rainfall totals in excess of 2, 5, 10, 20, 30, 60, and 75 mm day−1 along the abscissa; the ordinate carries the equitable threat scores. These are shown in Fig. 4d. It is clear from these scores for the initial state that a sizable improvement is seen from the initialization of rain rates. This skill is largest for the total rains in excess of 2 mm day−1. The impact of physical initialization is less for the very heavy rains. Over this monsoon domain, physical initialization would not produce the very heavy initial rains that are largely being described by the explicit physics. The physical initialization is designed for the parameterized component of the convection. The lower skills for the heavier rains are comparable for both experiments and show that we are not handling the initialization of very heavy rains, which are dependent on individual cloud growth. The initial moisture distributions (relative humidity) at the 700-hPa level for the control and the physically initialized experiments are shown in Figs. 4e and 4f, respectively. Basically, what we note here is an enhancement of moisture over regions of respective heavy rain for these two experiments. Overall the physically initialized experiment seems to carry somewhat more moisture at the 700-hPa level.

The forecasts for days 1 and 2 (i.e., valid on 0000 UTC 26 June and 0000 UTC 27 June 2005), respectively, are illustrated in Figs. 5 and 6. Here again we show four panels that illustrate the observed 24-h total rains, the forecasts from the physically initialized experiment, those from the control run, and the equitable threat scores for these two days. As we proceed further in time for these forecasts, the forecast skill, as expected, for rainfall forecasts decreases with increasing time. For the physically initialized forecast, the equitable threat scores for total rain (in excess of 2 mm day−1) started around 0.52, drop to around 0.25 by day 1, and to around 0.18 by day 2 of forecast. However, we do see some marked improvement of these forecasts over those of the control at every stage and for all thresholds of the equitable threat scores. The scores for mesoscale models, especially for heavy rain situations, also tend to suffer from the double penalty syndrome (Cartwright and Krishnamurti 2007). Small phase errors in the propagation of monsoon disturbances can affect the skills drastically. It is also clear that for heavy rains, with thresholds in excess of 30 mm day−1, the skills drop off drastically. The observed synoptic situation called for rains to diminish somewhat over the Bay of Bengal during these two days. The control experiment conveyed much heavier rains initially and for day 2 of forecasts. Offshore over the Gujarat coast of northwestern India, rains persisted between days 0 and 1 in the observations. The control run carried heavy offshore rains for the entire two-day period. The physically initialized experiment conveyed better results in this regard. A spread of rain over interior central India was noted in the observations especially for days 0 and 1. The physically initialized experiment carried these features that were conspicuously absent in the control run. The day-1 forecasts indicate marked improvement in the physical initialization run to simulate the transient rains over east and central India, which the control run could not predict. Similarly in the day-2 forecasts, rains over east-central India and the absence of rains over south Bay of Bengal were well predicted in the physical initialization run whereas the control run fails in both these aspects. Rainfall was excessive over the Bay of Bengal for the control run. Overall we note a positive impact from the physical initialization that improves the nowcasting of rain and also carries that advantage into the two-day forecasts.

b. Monsoon rainfall spinup

Here we shall illustrate the time history of the precipitation spinup at several grid locations covering the physical initialization phase and the postinitialization forecast period. Figure 7 illustrates a typical spinup of specific humidity [at the 850-hPa level (g kg−1)], the vertical velocity [W (m s−1)], the sea level pressure (hPa), the horizontal divergence [at the 850-hPa level (×10−3 s−1)], and the precipitation (mm day−1). These show that there are somewhat different time evolutions for the control and the physically initialized experiments. These results pertain to an average over nine points around a grid point located at 17.89°N, 92.25°E (i.e., over Bay of Bengal). The precipitation spinup shown in the bottom panel also includes the results from the physically initialized run, the control experiment, as well as the observed rainfall estimates (from TRMM). The observed rainfall estimates were small in general and those are clearly better represented by the physically initialized experiment. The control run appears to carry some very large spurious rains at 0000 UTC 26 June 2005. That spurious feature was not present in the physically initialized run. The spinup of the other variables cannot be compared against reliable observations since such are not available over the Bay of Bengal. However, we note that the other variables show some differences for these two experiments (i.e., the control and the physically initialized run). In general, the control run appears to exhibit large gravity-inertio oscillations in these time plots. Overall we find that the spinup histories are quite complex in mesoscale models when they are examined in some detail at single locations. The physical initialization appears to do somewhat better than the control run, which was evident from an area-averaged correlation coefficient (CC), shown in top left of the precipitation panel between the observed and the model rains (CC is 0.39 for the physical initialization experiment, and has a value of −0.24 for the control run). This is the correlation coefficient for the nine-point average at the grid point in the monsoon domain and covering the 48-h forecast time period for both physical initializations as well the control run.

c. Frequency distribution of observed and predicted rainfall

Figures 8a and 8b illustrate how well the rain-rate initialization procedure worked for the monsoon example. Here we show the frequencies and normalized means over certain class intervals from a selected sample of the grid points (80 × 80) over the physical initialization period. In this histogram, we compare the observed rainfall estimates, those from physical initialization and the control experiment (which does not initialize the rain rates). These figures illustrate that the physical initialization moves the model rainfall toward observations for all of the intervals. The frequencies associated with the physical initialized experiment are more (less) than the observed estimates at intervals less (greater) than 6 mm h−1 whereas the control simulation mostly underestimates with rainfall rates close to zero. This is supported from the illustration in Fig. 8b where rain rates normalized to their means are presented. The histograms correspond to the ratio of the average model rain to the average for the observations for each of chosen class intervals. A value of 1.0 denotes the best agreement and the degree of deviation shows the deficiency. Here we note the values are in the range of 0.8 to 1.1 for the physical initialization estimates whereas the noninitialized experiment shows large variations over the range 0 to 1.2. Figures 8a and 8b clearly show a strong positive impact for physical initialization or the nowcasting of rain.

d. The life cycle of a single cloud cluster

With the model output of rainfall rates from a mesoscale high-resolution model, it is possible to see the life cycle of a mesoscale precipitating element whose dimensions are around 100 km. The growth and decay of one such cluster is illustrated in Fig. 9. Here we show rainfall rates at 3-hourly intervals from TRMM datasets, those from the corresponding forecasts from the physically initialized run, and from the control run (which did not include the rain-rate initialization). The life cycle of the cloud cluster, started at hour 33 of the forecast, which correspond to 0900 UTC 26 June 2005, and located near 21°N, 85°E was followed in time in this illustration. This cluster (following TRMM) was quasi-stationary, stationary for the first 6 h, and thereafter moved to roughly 81.5°E and amplified to become a major cluster before it dissipated by 0000 UTC on 27 June. This cluster formed and dissipated by 21 h after its formation. The forecasts based on physical initialization exhibited a remarkable success in predicting this life cycle of the precipitating element. The control run appeared to have lost this cluster by 6 h. Although the effects of physical initialization may not be very large by day 2 of forecasts, it appears to carry information on clusters during days 1 and 2 of forecasts when they are either captured by the physical initialization at the start of the forecast run, or they are simulated in the early part of the forecast run after such a rain-rate initialization has been carried out.

e. Results from Kain–Fritsch cumulus scheme

The question can be raised as to how this proposed rain initialized method works for a different cumulus parameterization scheme. The modified Kuo’s scheme was the one that was addressed in our first paper (Krishnamurti et al. 1991). In this paper we have discussed the results obtained from the Grell and Devenyi (2002) scheme after invoking rain-rate initialization methodology. We have also successfully adapted this methodology for other cumulus parameterization algorithms that are part of the WRF model. In Fig. 10 we illustrate another application for the Kain and Fritsch (1993) cumulus parameterization scheme. The enhancement of skills from the physical initialization over that of the control was not as large we had noted for the Grell and Devenyi (2002) scheme. In Figs. 10a–c, we show the day-0 precipitation for physical initialized experiment (Fig. 10a), the control run (Fig. 10b), and the equitable threat scores (Fig. 10c). We do note a consistent improvement for the nowcasting skill of precipitation at thresholds.

f. A hurricane example (Hurricane Frances: 0000 UTC 27–0000 UTC 29 August 2004)

The day-2 forecasts of track and intensity (minimum sea level pressure) are illustrated in Figs. 11a and 11b. In these illustrations we show the observed (best track and intensity) and the forecasts for the physically initialized and the control run. As before, the control run was performed for 48 h from day 0 (i.e., 0000 UTC 27 August 2004). Clearly we see a superior performance for the hurricane forecast when the rain-rate initialization was included. The observed estimates of the minimum sea level pressure show a steady decrease of pressure with a minimum of 960 hPa on day 2 (i.e., at 0000 UTC 29 August 2004). This is consistent with the development seen from satellite imagery and the TRMM-based rainfall fields, which show organization of the storm convection during the 3-day period. The control run shows minimum sea level pressure at around 1010 hPa throughout the 3-day period whereas the physically initialized experiment carries a value close to 980 hPa by day 2. It appears from a comparison, given these best observed and model estimates of minimum sea level pressure, that the physical-initialization-based forecast clearly carries a positive impact. A similar comparison of the track (Fig. 11a) also shows improvement of the track for the physically initialized experiment. For Hurricane Frances we noted an increase in the initial position error from the PINIT experiment. The possible reason for this could be explained as follows; physical initialization improves the convective rain and the related motion field around the storm cluster during the preintegration phase between hours −24 to 0, as the convection improves and the lower-tropospheric motion adjusts to that convection; often the center thus derived can be off located compared to observations. This center for physical initialization is consistent with the organized convection around that center and the resulting dynamics. Even if the center is off located after physical initialization, the overall consistency of the fields ends up providing a better track forecast compared to that of the control.

In Figs. 12 and 13, we present the results of precipitation forecasts with and without the use of rain-rate initialization for the Hurricane Frances forecasts. The day 0 (initial state after the completion of physical initialization) precipitation field is shown in Figs. 12a–d. Here we present the precipitation totals between hours −24 and 0 from the (a) observed estimates, (b) physically initialized experiment (PINIT), (c) the experiment that does not include rain-rate initialization (control), and (d) the equitable threat scores for precipitation from these respective experiments. This was the stage when Hurricane Frances was a tropical storm with a minimum pressure close to 1010 hPa well out over the Atlantic ocean near 15°N, 44°W. The initial observed rainfall rates ranged as high as 50 to 100 mm day−1 (Fig. 12). When we compare the initial rains from the runs with and without physical initialization (Figs. 12b and 12c, respectively), it is clearly evident that the rain-rate initialization carried a far better distribution of these initial rains for Hurricane Frances. The control experiment without initialization carries a more widespread rain clearly showing less of an agreement with the observed estimates. This major improvement of the initial rain is better described in Fig. 12d, where the equitable threat scores of the rain-rate initialization are displayed. Here the abscissa denotes the rainfall thresholds (i.e., rain in excess of 0.2 mm day−1, 2 mm day−1, and so on to the heavy rains in excess of 70 mm day−1). The ordinate provides the equitable threat scores. The two vertical bars show the scores for the rain-rate initialization (left bar) and for without the initialization (the right bar). It is possible to capture most of the rains at all thresholds at an equitable threat score of 0.3 or higher when physical initialization is invoked. The control experiment carries a much lower skill for all thresholds and fails for thresholds in excess of 50 and 70 mm day−1. The day-2 forecasts, displaying four similar panels, are presented in Figs. 13a–d. The observed rain rates have clearly increased as Frances moves near 17°N and 52°W by 0000 UTC 29 August 2004. The maximum rains are in excess of 100 mm day−1 (Fig. 13a). These rains were clearly better described and carried through day 2 of the forecast when the physical initialization was included (Fig. 13b). The control run carried somewhat more widespread and weaker rains. Overall the day-2 rainfall forecasts were better described with the rain-rate initialization and were clearly reflected by the equitable threat scores (Fig. 13d). These scores have dropped in magnitude by day 2 of forecasts. This may be due to large variations in the horizontal distribution of rainfall intensities in the vicinity of hurricane core region. Such a drop of equitable threat scores for precipitation forecasts has been noted for mesoscale forecasts (Cartwright and Krishnamurti 2007). The double penalty issue arising for the phase errors makes these drops in scores somewhat more drastic for mesoscale forecasts. Overall, we do see a clear impact from the use of the rain-rate initialization through day 2 of forecasts.

g. Hurricane spinup

A typical example of the spinup for Hurricane Frances (Fig. 14) illustrates the impact of physical initialization. Here we present the spinup for the precipitation, specific humidity at the 850-hPa level, the vertical velocity, and the horizontal divergence at the 850-hPa level. These results pertain to an average over nine points centered around a grid point located at 16°N, 49°W over the tropical Atlantic Ocean. Overall, we see that the physical initialization shows a reasonable agreement with the observed rains; the control rain appears to carry two separate pulses of heavy rain on 27 and 28 June. The intensity and duration of heavy rains on 27 June was reasonably reproduced in the physical initialized experiment. There are some marked differences in the time histories for the other variables such as humidity, vertical motion, and horizontal divergence. The control run clearly seem to carry some large pulses of upward motion, which were not reflected in the physically initialized run. The correlation between the observed and the model rain (both nine-point averaged for the selected grid point and computed for the entire time history of the 2-day forecast) was around 0.76 for the physically initialized experiment. That value for the control run was around 0.55. Overall it appears that the rain-rate initialization can improve the performance of a very high resolution mesoscale model. The high correlation indicates that the model could predict the time variation of rainfall reasonably well. The low equitable threat score value implies deficiencies in the skills of the prediction for the horizontal distribution.

An example for Hurricane Wilma of 2005 when it was a category-4 storm (at 0600 UTC 20 October 2005) is illustrated in Figs. 15a–c. Here we show the hurricane’s inner clouds (Fig. 15a shows the IR imagery), around the eyewall, rainbands, and the eye. The physically initialized rains (Fig. 15b) carry most of these feature nicely whereas the control run (Fig. 15c) fails to describe such details.

8. Summary and conclusions

Rain-rate initialization is a necessary element for numerical weather prediction. The rain-rate physical initialization procedure described in section 6 is noted to have more of an impact on the monsoon rainfall prediction compared to that for hurricane experiment. In the design and implementation of this procedure, a number of additional experiments were conducted to study the model sensitivity to the number of vertical profiles of the relative humidity, and the correction factor for the surface humidity and the thickness of the vertical layer over which corrections were made. The RH correction factor here is the degree of perturbation that was introduced to the RH at the surface. The number of vertical profiles that were selected here depends on the interval of perturbation introduced for the RH at the surface level. For example, with a ΔRH = 1% 20 intervals were used. The vertical layer over which an initial relative humidity perturbation (a linear profile) was determined by finding a vertical distance (from the surface level) over which one-half of the total precipitation resides. At that level the linear perturbation of the relative humidity is set to zero. By assigning different surface values of the perturbations, a straight line connects these values of the zero value (from the perturbation) at that upper level and beyond. A number of experiments, with combinations of RH perturbations, its increments, and the designation of top level for adjustment were used to explore the sensitivity for the nowcasting of rain. The perturbation in RH is transformed into the specific humidity field of the model and at each time step the cumulus parameterization scheme was run using each of the profiles that provided rainfall estimates corresponding to each of these perturbations to optimize the best profile. It was confirmed that the cumulus parameterization is indeed very sensitive to perturbations of the vertical profile of specific humidity. Since both the control and physical initialization runs use the same cumulus scheme (i.e., Grell–Devenyi) in this study, the improvements in the model rain-rate estimates are attributable to the impact of the physical initialization. This procedure was tested with four different cumulus schemes available with WRF, which are relaxed Arakawa–Schubert, Kain–Fritsch, Betts–Miller–Janjic, and Grell–Devenyi. Although among these the Grell–Devenyi scheme provided the best response for the specific humidity perturbations, the results from other cumulus schemes were also promising. We have discussed one such example from the Kain and Fritsch (1993) scheme in our results section (Fig. 10).

Further experiments are being carried out to incorporate the physical initialization for addressing the explicit clouds. It is also noted, in the hurricane prediction experiments, to bring in significant horizontal variations in the intensity of rainfall in the inner core region, where the induced specific humidity perturbations along the vertical do not seem to exhibit the desired sensitivity to moisture perturbations. This preliminary study has explored only one of the components of physical initialization (Krishnamurti et al. 1991, 1993). Further work is needed to include the other components, such as reverse similarity to incorporate the apparent moisture sink consistent with the observed rains. We need to also include moisture profiling in the upper troposphere toward improving a match between the observed and the model OLR. These were integral parts of a more complete physical initialization of our previous papers.

In panels (a)–(c) of Figs. 4 and 5 we illustrated the nature of this problem. If one takes a control run for a mesoscale model (WRF in this illustration) the initial monsoon rainfall appears to be dislocated by a large margin. The observed rains (based on TRMM estimates) are shown in Figs. 5 and 6a; the results for the control run are shown in Figs. 5 and 6c; and those from the physical initialization are presented in Figs. 5 and 6b. It is clear from this presentation that uninitialized rain has large errors; those can be reduced from the deployment of physical initialization. The present paper elaborates on this issue from the two examples of mesoscale forecasts: one for a summer monsoon event and the other for Hurricane Frances of 2004. We show that a perceptible improvement of rainfall at time 0 and even through day 2 of forecasts are met as seen from a probabilistic skill metric (i.e., the equitable threat score). That clearly shows the advantage of the physical initialization for both the monsoon and the hurricane examples presented here. We also show that this procedure enables us to follow the life cycle of mesoscale convective precipitating elements for almost 21 h. This present study utilized one of the three parts of the original proposal on physical initialization (Krishnamurti et al. 1991). A complete physical initialization presented in that earlier paper carried a reverse cumulus parameterization algorithm, a reverse surface similarity, and a matching of the model and the satellite-based OLR. The present study is limited to the convective algorithm. It may be possible to include these other features in future studies. It was noted in our previous studies (Krishnamurti et al. 2001) that nowcasting skills for precipitation provide correlation levels higher than 0.9 (between the TRMM-based rains and those from model-based physical initialization). This suggests that further improvements, beyond those of the present paper, may be possible in future studies. In the specific examples we have presented here, we showed a marked improvement in day-2 rainfall forecasts of the monsoon over the land areas that were not handled properly by the control experiment. In the example of Hurricane Frances, the improvement in the forecasts of the intensity from the inclusion of physical initialization was clearly seen.

Overall we feel that physical initialization (a rain-rate initialization) has an important place for mesoscale models. The FSU procedure for rain-rate initialization utilizes a Newtonian relaxation rather than its direct inclusion within a 3DVAR or 4DVAR. That is another strong avenue for the future pursuits for rain-rate initialization within mesoscale models.

There are still some further issues in this regard that need clarification. Use of raw radiances is a preferred mode for variational data assimilation. ECMWF has recently incorporated an assimilation of brightness temperatures from TRMM and SSM/I datasets for the indirect inclusion of rain rates. NCEP/EMC has been using 3DVAR for the assimilation of total precipitable water derived from the scattering temperatures of TRMM and SSM/I. From a quick look at these real-time products, we noted that if the TRMM-based rain rates from 3B42 were used as a benchmark, then the initial skills of these products from ECMWF and EMC are in fact much lower than what can be obtained using Newtonian relaxation method to an FSU global model. The thrust toward direct use of radiances (i.e., scattering temperatures) for rainfall initialization within mesoscale data assimilation is expected to be an important area of future research. The promise of mesoscale physical initialization deserves to be explored further.

Acknowledgments

This work was supported by NASA TCSP Grant NNG05GH81GNSF, NASA PMM Grant NAGS-13583, and NSF Grant ATM-0419618. The computations were carried out on supercomputing facility at School of Computational Sciences and Information Technology, Florida State University.

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APPENDIX

Equitable Threat Score

The equitable threat score (ETS) indicates the degree of skill to forecast an event. It may be defined as a measure of the correctly predicted events against the observations in a defined range, adjusted for hits with a random chance. ETS is often used in the verification of rainfall in NWP models because its “equitability” allows scores to be compared more fairly across different ranges. ETS could vary between 0 and 1, with a perfect forecast to be scored as 1.0, and a completely deficient forecast as 0. ETS is computed using
i1520-0493-135-7-2716-eqa1
where N = number of grid points, F = area where event is forecasted, O = area where event is observed, and H = hit area, or overlap of areas F and O.

Fig. 1.
Fig. 1.

NCEP wind flow (vectors) and isotachs (shaded units are m s−1), for the monsoon precipitation event shown corresponding to (a) end of physical initialization, day 0 (0000 UTC 25 Jun 2005) and (b) day-2 forecast (0000 UTC 27 Jun 2005).

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 2.
Fig. 2.

Snapshot of Hurricane Frances from NOAA AVHRR at 1905 UTC 31 Aug 2004.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 3.
Fig. 3.

Schematics of rain-rate physical initialization (every model time step).

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 4.
Fig. 4.

Rainfall (mm day−1) at day 0 (0000 UTC 25 Jun 2005) corresponding to (a) TRMM, (b) experiment with physical initialization (PINIT), (c) control experiment without physical initialization (CTRL), (d) equitable threat scores for CTRL and PINIT experiments, (e) 700-hPa relative humidity (%) for CTRL, and (f) 700-hPa relative humidity (%) for PINIT.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 5.
Fig. 5.

Rainfall (mm day−1) at day 1 (0000 UTC 26 Jun 2005) corresponding to (a) TRMM, (b) experiment with physical initialization (PINIT), (c) control experiment without physical initialization (CTRL), and (d) equitable threat scores for CTRL and PINIT experiments.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 6.
Fig. 6.

Rainfall (mm day−1) at day 2 (0000 UTC 27 Jun 2005) corresponding to (a) TRMM, (b) experiment with physical initialization (PINIT), (c) control experiment without physical initialization (CTRL), and (d) equitable threat scores for CTRL and PINIT experiments.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 7.
Fig. 7.

Time series of the parameters at grid point 17.89°N, 92.5°E for the monsoon precipitation prediction experiment for the period 0000 UTC 24–27 Jun 2005 with (a) specific humidity (g kg−1) at 850 hPa, (b) vertical velocity (m s−1) at 850 hPa, (c) minimum sea level pressure (hPa), (d) divergence (×10−3 s−1) at 850 hPa, and (e) rainfall (mm day−1). The vertical line at 0000 UTC 25 Jun 2005 indicates the end of the physical initialization.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 8.
Fig. 8.

(a) Frequency distribution of rain rates from TRMM estimates and experiments with/without physical initialization. (b) Normalized rain rates (with respect to means for the class intervals) for the experiments with/without physical initialization.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 9.
Fig. 9.

Life cycle of a cloud cluster (identified as A) during the monsoon precipitation event shown at every 3-h interval starting from 0009 UTC 26 to 0000 UTC 27 Jun 2005. (left) TRMM observations; (middle) physical initialization (PINIT); and (right) Control (CTRL) experiment.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 10.
Fig. 10.

Rainfall (mm day−1) at day 0 (0000 UTC 25 Jun 2005) corresponding to (a) experiment with physical initialization (PINIT), (b) control experiment without physical initialization (CTRL), and (c) equitable threat scores for CTRL and PINIT experiments. These results are from Kain–Fritsch cumulus scheme.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 11.
Fig. 11.

(a) Track positions and (b) minimum sea level pressure (hPa) of Hurricane Frances 0000 UTC 26 to 0000 UTC 29 Aug 2004. OBS, PINIT, and CTRL (from 0000 UTC 27 Jun) denote official estimates, physical initialization, and control experiments, respectively.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 12.
Fig. 12.

Rainfall (mm day−1) at day 0 (0000 UTC 27 Jun 2005) corresponding to (a) TRMM, (b) experiment with physical initialization (PINIT), (c) control experiment without physical initialization (CTRL), and (d) equitable threat scores for CTRL and PINIT experiments.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 13.
Fig. 13.

Rainfall (mm day−1) at day 2 (0000 UTC 29 Jun 2005) corresponding to (a) TRMM, (b) experiment with physical initialization (PINIT), (c) control experiment without physical initialization (CTRL), and (d) equitable threat scores for CTRL and PINIT experiments.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 14.
Fig. 14.

Time series of the parameters at grid point 16°N, 49°W for the Hurricane Frances experiment for the period 0000 UTC 26–29 Aug 2004: (a) rainfall (mm day−1), (b) specific humidity (g kg−1) at 850 hPa, (c) vertical velocity (m s−1) at 850 hPa, and (d) divergence (×10−3 s−1) at 850 hPa. The vertical line at 0000 UTC 27 Aug 2004 indicates the end of the physical initialization.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Fig. 15.
Fig. 15.

(a) Hurricane Wilma IR satellite imagery at 0745 UTC 20 Oct 2005, and 6-h forecast of rainfall (mm) IC 0000 UTC 20 Oct 2005 from (b) physical initialization experiment (PINIT), and (c) control experiment (CTRL) with horizontal resolution of 5 km.

Citation: Monthly Weather Review 135, 7; 10.1175/MWR3417.1

Table 1.

List of acronyms.

Table 1.
Table 2.

WRF model configuration.

Table 2.
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