1. Introduction
Despite its crucial importance in many meteorological, hydrological, and water resources management applications, accurate measurements of regional and global precipitation remain a challenging task. In particular, precipitation variations of fine spatial and temporal scales are not well observed over most of the globe, although they represent a substantial portion of the overall variability and play an important role in hydrological cycle and land–atmosphere interactions (Dai et al. 1999, 2007; Tian et al. 2007; Hong et al. 2007).
While precipitation products based on observations from individual platforms and instruments (gauge, radar, satellites, etc.) have been widely utilized in a variety of operational and research applications, integrating information from multiple satellite sensors as well as ground observations (gauges and radars) further improves the quality and resolution of precipitation analysis (Adler et al. 1994; Huffman et al. 1997; Xie and Arkin 1996, 1997; Sapiano et al. 2008). Substantial progress has been made in the past decade to generate precipitation estimates at high spatial and temporal resolutions through combined use of infrared (IR) and passive microwave (PMW) observations from multiple satellites. Two categories of techniques have been developed to combine the precipitation and/or cloud information from individual satellite PMW and IR observations. The first category includes the Precipitation Estimation from Remote Sensing Information using Artificial Neural Network (PERSIANN; Hsu et al. 1997), the Naval Research Laboratory (NRL) blended satellite precipitation estimates (Turk et al. 2003), and the Tropical Rainfall Measurement Mission (TRMM) Multisatellite Precipitation Analysis (TMPA; Huffman et al. 2007, 2009). A temporally changing and regionally dependent empirical relationship between precipitation intensity and cloud-top temperature is defined using collocated IR and PMW data, assuming that PMW estimates represent the “truth” of instantaneous precipitation rates at the ground. This relationship is then applied to estimate precipitation over the globe from the high-resolution IR data observed from geostationary (GEO) platforms. In some of the algorithms, the IR-based precipitation estimates are further merged with PMW estimates from low-Earth-orbit (LEO) satellites, wherever available, to form the final satellite-based precipitation products. Key to this category of techniques is the IR–precipitation relationship, established through a sophisticated artificial neural network system in the PERSIANN (Hsu et al. 1997) and through matching the probability density function (PDF) of IR against that of the PMW precipitation estimates in the NRL (Turk et al. 2003) and TMPA (Huffman et al. 2003, 2007). While utility of the GEO–IR data ensures the production of high-resolution precipitation estimates over a quasi-global domain, lack of direct physical linkage between the precipitation and cloud-top temperature results in substantial error in the IR-based precipitation estimates and thereby the final PMW–IR merged analyses. Currently, the official TRMM (Simpson et al. 1988; Kummerow et al. 2000) takes the 3-hourly precipitation analysis generated by the TMPA algorithm (3B42) as its official level 3 product. For convenience purposes, here we call the techniques of this category “Euler approach” to reflect their common feature that only the PMW and IR observations available locally inside the target grid box are used directly in the definition of analysis.
In the second category of techniques, called “Lagrangian approach,” estimates of instantaneous rain rates from the PMW observations from LEO are propagated and interpolated in the combined time–space domain through the use of the precipitating cloud system advection vectors (CSAVs) computed from consecutive IR images from the GEO platforms (Joyce et al. 2004; Ushio et al. 2009). PMW estimates are propagated along the advection vectors from the time of observation to that of the target analysis. Since the IR observations are not used directly to estimate precipitation, the error inherent in the IR estimates (especially when PMW observations are available around the target analysis time) is excluded as a potential contaminate of the merged analysis. Recently, Behrangi et al. (2010) proposed a conceptual model to construct high-resolution precipitation analysis by propagating PMW estimates along motion vectors defined by cloud tracking with consideration of intensity changes during the propagation.
The Lagrangian approach of propagating and morphing high-resolution satellite precipitation estimates was first adopted by Joyce et al. (2004) in the development of their Climate Prediction Center (CPC) morphing technique (CMORPH). The success of CMORPH inspired other agencies such as Japan Aerospace Exploration Agency (JAXA) with their Global Satellite Mapping of Precipitation (GSMaP) algorithm to follow CMORPH’s methodology of using PMW rainfall in a Lagrangian framework with IR-derived vectors as the method of propagation (Ushio et al. 2009). Recent evaluation results showed superior performance of CMORPH and GSMaP compared to other high-resolution satellite precipitation products derived using an Euler approach (Xie et al. 2007; Ebert et al. 2007; Shen et al. 2009). The high temporal and spatial resolution global precipitation estimates that are created by these algorithms are applied in a wide variety of research and operational applications.
While CMORPH consistently presents excellent performance in estimating the spatial distribution and temporal variations of precipitation over most of the global regions and for all seasons, shortcomings exists in the current version CMORPH and its high-resolution precipitation products. Further improvements are needed for the CMORPH technique to better meet the requirements of both science and societal communities.
First, the current CMORPH technique does not take full advantage of precipitation information from PMW observations and other sources. In the process of propagating the PMW precipitation estimates, only data from one scan closest to the target analysis time from each of the forward and backward directions are included; IR-based precipitation estimates are not used at all to adjust the rainfall estimate. Despite their relatively poor accuracy, IR-based estimates may provide useful information when no PMW estimates are available around the target analysis time. The weights used to define the final analysis from the propagated PMW estimates are approximated as inversely proportional to the length of the propagation time without consideration of the instrument dependency, temporal propagation direction, surface type, season, latitude, or the nonlinear nature of the estimation error. In addition, the intensity of the precipitation is assumed unchanged over the duration of both the forward and backward propagation of the PMW estimates.
The objective of this work is to develop a prototype model of the Kalman filter (KF)-based CMORPH that is capable of producing high-resolution global precipitation analysis with improved accuracy through the incorporation of additional IR-based information and through the integration of all PMW- and IR-based information available using more precise weights. Section 2 of this paper describes the current CMORPH algorithm and individual datasets used as inputs to the merging process, sections 3 and 4 present the development of the prototype model of KF-based CMORPH over the conterminous United States (CONUS) and its implementation over the globe, and a summary and discussion is provided in section 5.
2. Input data to the CMORPH processing system
a. A brief description of the current CMORPH algorithm
CMORPH derives high-resolution (8 × 8 km2) half-hourly precipitation analyses over a quasi-global domain (60°S–60°N) through the integration of PMW estimates from all available LEO satellites in a Lagrangian framework. First, advection vectors of precipitating systems over the globe are determined by computing spatially lagged correlation between consecutive IR images observed by GEO satellites. The CSAVs are then further refined as a proxy to rainfall propagation through adjustments determined from comparison studies against radar rainfall motion. Precipitating cloud systems detected from PMW satellite observations are then propagated along the advection vectors from the orbit observation time to the target analysis time under the assumption that precipitation intensity remains the same over the period. This propagation is performed in both forward and backward directions in time. The final precipitation analysis is defined as the weighted mean of the propagated PMW estimates with the weights inversely proportional to the length of propagation.
b. PMW precipitation estimates
Previously the only source of the information used by CMORPH to define global high-resolution precipitation analyses was the level 2 instantaneous rain-rate products retrieved from PMW observations of LEO satellites (Ferraro 1997; Ferraro et al. 2000; Kummerow et al. 2001). At the time of this writing, PMW precipitation estimates from up to nine LEO satellites are available and utilized as inputs to the CMORPH processing system. The most recent Goddard profiling algorithm (GPROF; Kummerow et al. 1996; Olson et al. 1999) is used to derive rainfall from PMW imagers. The technique used to retrieve precipitation from the PMW Advanced Microwave Sounding Unit (AMSU)/Microwave Humidity Sounder (MHS) is the latest National Environmental Satellite, Data, and Information Service (NESDIS) algorithm (Vila et al. 2007), which reduces the error associated with the over- or underestimation of rainfall over nadir–limb beam positions of the cross-track scanners observed in the previous version of the algorithm. Fairly well spaced in orbit time, observations from these platforms combined provide critical information in defining precipitation analysis around the diurnal cycle.
A series of innovative preprocessing procedures are developed and implemented to prepare the PMW precipitation estimates to be used in the morphing process. First, level 2 PMW estimates of instantaneous rain rates generated at individual retrievals [or field of view (FOV)] are mapped onto a global grid of 0.0727° latitude–longitude (8 × 8 km2, at equator). Multiple 8-km grid boxes covered by a single satellite retrieval are assigned with the same rain-rate value to ensure the spatial completeness and representativeness of the resulting 8-km gridded fields of PMW estimates.
To remove the systematic differences between PMW estimates derived from observations of different instruments using different algorithms, PMW estimates from the TRMM Microwave Imager (TMI) are selected as the reference standard and those from all other platforms are calibrated against the TMI estimates through matching the rain-rate PDF. The TMI estimates are chosen as the normalization standard because of the finer spatial resolution and emission detection (over ocean) of the imaging sensors along with the dynamic ability of the TRMM satellite to underfly all polar orbiting satellites, allowing precise temporal and spatial matching of the respective estimates. Data pairs of collocated TMI and target PMW estimates observed within 30 min or closer are collected from the mapped 8 × 8 km2 grid fields for a 10-day period up to the target date. Accumulated PDF tables are then constructed and utilized to adjust the target PMW estimates. The PDF tables are created for the land and oceanic regions separately and for each 10° latitude band, using collocated data pairs over a wide domain of 30° in latitudes centering at the target band. Since the TMI PMW estimates are available only from 40°S to 40°N, calibration for PMW estimates from other satellites beyond the 40° parallels is performed against the PMW estimates from the Advanced Microwave Scanning Radiometer (AMSR). A preliminary examination showed very close agreements in rain-rate PDF between the AMSR and TMI over tropics and subtropics. PMW estimates from the future PMM core satellite are expected to provide an improved calibration standard especially over extratropics. Figure 1 illustrates an example of the PDFs for the PMW instantaneous rain rates from the TMI (green), original (blue), and calibrated (red) AMSU estimates for June–August 2005. The PDF of the calibrated AMSU estimates matches much better with that of the TMI than the original AMSU.
While the procedures described above work effectively for the calibration of PMW estimates from most LEO satellites, an additional calibration must be applied for oceanic precipitation estimates derived from the PMW observations of AMSU/MHS aboard National Oceanic and Atmospheric Administration (NOAA) polar orbiting platforms and the Meteorological Operational Satellite (MetOp). Because of the limitations of the PMW sensors, the AMSU/MHS is unable to detect some of the light precipitation over water, resulting in a PDF of substantially reduced raining frequency (Vila et al. 2007). Performing no correction for cases of zero rainfall, the PDF matching procedure described in the last paragraph would generate corrected AMSU precipitation estimates with negative bias in overall magnitude compared to the TMI estimates. To solve this problem, a recursive filter is developed and applied to revise the correction table slightly until the bias between the resulting adjusted AMSU and TMI estimates is negligible.
c. Cloud system advection vectors
Key to the CMORPH technique is the propagation of PMW observations of instantaneous rain rates in the combined time–space domain along the CSAVs. Following Smith and Phillips (1972) and Purdom and Dills (1994), the CSAVs are derived by computing the displacements of cloud systems detected from full-resolution (4 × 4 km2) GEO–IR images in 30-min intervals. Spatially lagged correlation is calculated for the brightness temperature (Tb) arrays on two consecutive GEO–IR images and the displacement with the highest correlation is used to define the CSAV. Assuming the CSAVs do not present substantial variations on small spatial scales, definition of the CSAVs is performed on a 2.5° latitude–longitude grid over the globe from 60°S to 60°N using the GEO–IR data over a 5° latitude × 5° longitude domain centering at the target grid point.
Early versions of CMORPH used CSAVs directly to propagate PMW-derived precipitation. However, it was soon determined that the west–east and south–north advection rates were too fast in the North Hemisphere midlatitudes (Joyce et al. 2004). To correct this, a speed adjustment procedure was developed. First, rainfall system advection vectors were computed by spatially lagging hourly U.S. Next Generation Weather Radar (NEXRAD) stage II (Klazura and Imy 1993) radar rainfall (mapped to the same 8 × 8 km2 grid) in the exact same dimensions and manner CSAVs are computed from IR. The frequency distribution of CSAV and radar rainfall advection rates indicated that north–south rates are quite similar but that west–east CSAV speeds were about 3–4 times as fast compared to the radar-derived vectors, and south–north rates were twice as fast (Joyce et al. 2004, their Fig. 7). These systematic differences are consistent with several case studies that show the tendency of IR features to quickly stream to the northeast on the east side of long-wave troughs, with the actual rainfall also moving in this direction but at a slower rate. The CSAVs computed from the IR images over midlatitudes are adjusted accordingly based on the comparison results. For consistency with the Northern Hemisphere, the meridional adjustment is applied to vectors of the opposite sign in the Southern Hemisphere. The incorporation of this adjustment procedure into the CMORPH processing has resulted in improved propagation of precipitation features.
d. IR-based precipitation estimates
In the first-generation CMORPH algorithm (Joyce et al. 2004), the GEO–IR data are utilized only to compute the CSAVs for propagating the PMW instantaneous precipitation estimates toward the targeted analysis time. In developing the KF-based CMORPH, precipitation estimates derived from GEO–IR observations will also be incorporated to improve the quantitative accuracy of the integrated precipitation analysis when PMW observations are not available over an extended period of time. To this end, a new technique is developed to estimate precipitation from the full-resolution global GEO–IR data of Janowiak et al. (2001) by matching the PDF of Tbs from GEO–IR observations to that of the PMW instantaneous rain rates.
First, combined PMW precipitation estimates (MWCOMB) are defined in a 30-min interval on the 8 × 8 km2 global grid system by averaging the calibrated PMW rain rates from individual LEO satellites. Meanwhile, global arrays of IRTb are created on the same time–space resolution by utilizing the full-resolution (4 km–30 min) GEO–IR data of Janowiak et al. (2001). Collocated pairs of the IRTb and MWCOMB rainfall data are then collected and used to create PDFs. An estimation of 30-min precipitation over an 8 × 8 km2 grid box is assigned by matching the cumulated PDF of the IRTb with that of the MWCOMB rain rates. To ensure statistical stability and temporal–spatial continuity for the estimation of global precipitation, the PDF tables are constructed for each 30-min time step and for each 5° × 5° latitude–longitude grid box using collocated data pairs collected over a 15° × 15° latitude–longitude region centered at the target 5° latitude–longitude grid box and covering a 9.5-hr time window centered at the target estimation time. The short time window is used to capture the current location in the diurnal cycle. Estimation procedures are performed separately for land and ocean to account for the differences in the IRTb–precipitation relationship. Called IR rainfall frequency (IRFREQ), precipitation estimates generated by this technique are capable of capturing the spatial distribution and temporal variations of precipitation with reasonable quality over tropical and subtropical regions during warm seasons (Fig. 2). A comprehensive evaluation of several IR-based precipitation algorithms revealed superior performance of the IRFREQ precipitation estimates compared to other IR-based products (R. Kuligowski 2009, personal communication).
3. Development of the prototype KF-based CMORPH over CONUS
a. Conceptual model of the KF-CMORPH
Utilized widely in the atmospheric and oceanic data assimilation community, the Kalman filter is an efficient and effective recursive data processing algorithm to estimate the state of a linear system from a series of observations with different error characteristics. In general, a Kalman filtering process consists of two sequential steps: a “forecast step” that creates the “forecast” of the final analysis as well as the error variance for the forecast, followed by an “analysis step” that modifies the forecast with the observations (Kalnay 2003).
The forecast error, as defined in Eq. (2), should be composed of two portions: i) propagation of the error in the input PMW estimates composed mainly of the level 2 PMW retrieval error, and ii) KF-CMORPH model error arising in the process of defining the forecast from the PMW estimates caused by, among many other factors, inaccurate estimation of the propagation vectors and unrealistic assumption of unchanged precipitating systems (pattern and intensity) over the period of propagation. In the development of this conceptual model, however, the error for the forecast is simplified as a function of the propagation time and defined separately for PMW estimates of different sensor types (section 3b). It is critically important that future work will quantify the error in the PMW estimates, its propagation in the processing, and the error caused by various imperfect assumptions and estimations in the integration process to further improve the quantitative accuracy of the combined satellite precipitation estimates.
Our final goal is to construct a KF-based system to produce high-resolution pole-to-pole global precipitation analysis through integration of information from satellite IR, PMW observations, numerical model simulations, and other available sources. As a first step, we have developed a prototype model of the KF-based CMORPH to combine precipitation estimates derived from PMW and IR observations over a global domain from 60°S to 60°N. The IR-based estimates are included only when no PMW data are available within a window of 90 min centered at the target analysis time.
b. Development of the prototype model over CONUS
Key to the development of the KF-CMORPH is the definition of error structure for the propagated PMW- and IR-based estimates as a function of instrument type, propagation time and temporal direction, location, and season. A preliminary test is first performed to define the error through comparison of the IRFREQ and the PMW estimates propagated through various lengths of time against the stage-II radar observations (Klazura and Imy 1993) over CONUS for summer 2007. Estimation error is expressed here as the correlation between the satellite estimates and the stage-II radar data. Correlation for the PMW estimates degrades sharply as they are propagated from their observation time (Fig. 3). The magnitude and the degradation rate of the correlation, however, differ for different instruments, indicating the importance of defining the error separately for estimates from different platforms. During this summertime study over land, the IR-based precipitation estimates outperform the PMW estimates when the propagation time is longer than 90 min or so, suggesting potential improvements in the final analysis through the inclusion of IR estimates to fill in PMW observation gaps.
Using these error statistics, a prototype model KF-CMORPH is developed to construct high-resolution precipitation estimates over CONUS. The IR-based precipitation estimates are included as part of the inputs to the KF-based CMORPH when no PMW observations are available within a window of 90 min.
c. Evaluation of the prototype KF-CMORPH model over CONUS
To assess the performance of the KF-CMORPH analyses relative to the original CMORPH analyses, we compared both analyses with estimates of precipitation from radar over CONUS during July–August 2009. The radar data used for this comparison is the surface rain-rate estimation at 1-km/5-min resolution over CONUS generated by the National Mosaic and Quantitative Precipitation Estimation (QPE) system (NMQ/Q2; Zhang et al. 2009) developed at the NOAA National Severe Storms Laboratory (NSSL) and the University of Oklahoma. The NMQ/Q2 system combines information from all ground-based radars constituting the NEXRAD network and calibrates the radar rain rates with gauge observations. The Q2 radar rainfall data at its original resolution are integrated to define mean rain rates at a space–time scale of 0.25° latitude–longitude and 30 min to compare against the CMORPH satellite estimates over CONUS.
Correlation of daily Q2 radar rainfall with the original and Kalman filter CMORPH with input PMW estimates from various LEO satellite configurations. Comparisons were made for daily 0.25° latitude–longitude rainfall over the CONUS for a two-month period from 1 Jul to 31 Aug 2009.
Names and equatorial crossing times (ECT, local time) used in the synthetic experiments for CMORPH with different LEO satellite configurations.
Both the number and the configuration of the LEO satellites are sensitive to the performance of satellite precipitation estimates derived through the integration of individual PMW estimates through a Lagrangian approach. As shown in Table 1 and Fig. 4, while correlation for both the original and KF-CMORPH improves with increased number of LEO–PMW satellites, correlation differences for precipitation estimates based on four- and seven-satellite configurations are very small. A careful examination (results not shown) revealed that this “level off” in performance is caused primarily by the orbit patterns for the seven-satellite configuration, which contains a “hole” between 19:30 and 01:30 local time in sampling the diurnal cycle (Table 1). By optimizing diurnal sampling, the skill of the four-satellite configuration offsets the addition of PMW satellites in a poorly designed seven-satellite configuration. Turk et al. (2010) performed a similar experiment and found that performance for precipitation estimates based on an Euler approach will degrade when all cross-track sounders or the morning local time crossing satellites were removed. While it is not the central topic of this work to examine the sensitivity of integrated precipitation estimates to the availability, quality, and configuration of input PMW and IR satellite observations, future work is planned to address this critically important issue to get a better understanding of how the integration algorithm should be designed for the estimation of precipitation for periods observed with fewer satellites.
A set of synthetic experiments are designed and implemented to further understand the performance of the KF-CMORPH in generating integrated precipitation estimates from various LEO–PMW configurations. To this end, high-resolution precipitation estimates over CONUS are generated for the two-month period in 2009 using the original and the KF-based CMORPH algorithms with input PMW observations from only one, two, four, and seven satellites selected from the all nine available platforms (Table 2). The selection of the satellite configuration is to mimic the PMW instrument availability over the entire time span from 1987 to the present.
With fewer PMW observations available as inputs, pattern correlation for the original CMORPH degrades sharply from 0.717 for the nine-satellite configuration to 0.469 for the one-satellite simulation (Table 1). The correlation for the original CMORPH is especially low for the half-hourly local time slots precisely between two consecutive LEO orbit times (Figs. 5b–e). The pattern correlation for the original CMORPH degrades linearly with the propagation time and falls down to ~0.1 for estimates defined by propagating PMW by more than 5.0 h (Fig. 6, top).
The KF-CMORPH shows much less degradation in correlation with PMW observations from a reduced number of platforms (Table 1, Figs. 4b–e), thanks to the contribution from the IR-based precipitation estimates. The daily 0.25° pattern correlation, computed using all data for the two-month period and over all grid boxes over CONUS, is 0.725 and 0.653, respectively, for the KF-CMORPH with the nine- and one-satellite configurations (Table 1). Thirty-minute 0.25° pattern correlation for KF-CMORPH decreases initially as the propagation time extends and then becomes stabilized at ~0.45 for propagation time of 1.5 h and longer (Fig. 6, bottom), a substantial improvement upon that for the original CMORPH.
The PDF of the rainfall intensity generated by the original and KF-based CMORPH is virtually identical for estimates defined with propagation time within 30 min and it is very close to that of the IR-based estimates (Fig. 7a). All of the three satellite-based products (the two versions of CMORPH and the IRFREQ), however, exhibit overestimation for events of precipitation (>25 mm h−1) compared to the radar observations from Q2 (Fig. 7a) because of the systematic error in the level 2 PMW retrievals. The frequency for heavy precipitation estimates generated by the original CMORPH drops significantly over grid boxes where analysis is defined by propagation of PMW over an extended period of time (Fig. 7, black lines). The PDF for the KF-CMORPH, meanwhile, is relatively stable for precipitation estimates over grid boxes with different propagation times (Fig. 7, green lines), thanks to the incorporation of IR-based estimates that retain the original PMW rainfall rate distribution (Fig. 7, red lines).
Compared to the original CMORPH, the KF-CMORPH described in this paper exhibits substantial improvements and much more stable performance in integrating high-resolution precipitation estimates with limited sampling from the PMW observations. This shows clearly the potential strength of the KF-CMORPH in constructing high-resolution precipitation estimates for the entire TRMM Global Precipitation Mission (GPM) era with relatively stable performance.
4. Global implementation of KF-CMORPH
a. Development of a prototype system for generating global precipitation analyses
This conceptual KF-CMORPH developed using the CONUS data is implemented for constructing the precipitation estimates over the global domain from 60°S to 60°N. Error statistics for PMW- and IR-based precipitation estimates are defined for individual instruments as a function of region and season through comparisons with the concurrent PMW estimates from the TRMM TMI. Error functions for the TMI are taken to be the same as those for the AMSR for Earth Observing System (EOS) (AMSR-E), based on an early comparison against the stage-II radar observations over CONUS. Over land, the error functions are computed for each 10° latitude band using data collected over a 30°-wide latitude band centered on the target band. No zonal differences in the error are considered because of the limited sampling of the data. Over ocean, the error functions are defined for each 20° × 20° latitude–longitude box using data over a 40° × 40° latitude–longitude region centered on the target box. Over both land and ocean, the error functions are calculated for each month using data over a five-month period centered on the target month to account for the seasonal variations. The comparisons against stage II were done once, while those against TMI are updated monthly.
As shown in Fig. 8, evolution of estimation error, shown as correlation with the TMI estimates for the Special Sensor Microwave Imager (SSM/I) and AMSR-E estimates over the propagation period, presents strong regional variations because of differences in the time scales of the target precipitation systems. In particular, error for PMW estimates exhibit distinct contrasts over land and ocean, implying the importance of defining the error separately for land and ocean.
Utilizing the error statistics defined for the propagated PMW and the IR-based precipitation estimates, a prototype KF-based CMORPH algorithm system has been developed at NOAA/CPC to produce high-resolution precipitation analysis parallel with the original version of CMORPH. Figure 9 illustrates the evolution of a rapid developing precipitating system over CONUS as depicted by the original CMORPH (left), the IR-based IRFREQ (second from left), the KF-CMORPH (third from left) and the stage-II radar estimates (right). PMW observations were scanned over the target region at the first and last half-hourly time slots. The original CMORPH, interpolating precipitation estimates from the two PMW orbits, therefore missed the peak of the precipitation event around 21:30 UTC (fifth row from top) as observed by the radar and the IRFREQ. Incorporating IR-based precipitation estimates in 30-min intervals enables the KF-CMORPH to capture the rapid development of the system, improving the overall performance of the new technology.
b. Quantitative examination of the global KF-CMORPH
The same synthetic tests are performed for the original and KF-based CMORPH using PMW estimates from different LEO satellite configurations shown in Table 2. “Ground truth” for precipitation of high space–time resolution, such as the Q2 radar estimates, is not available over most global regions for quantitative assessments of the resulting CMORPH estimates. Therefore, we accumulated the original and KF-based CMORPH to daily precipitation averaged over a grid box of 0.25° latitude–longitude and compared them with both the NOAA/CPC unified global daily gauge analysis (Xie et al. 2010) over land and the in situ measurements made by siphon gauges installed on moored buoys of the Tropical Atmosphere and Ocean (TAO) project (McPhaden et al. 1998) over tropical oceans.
The CPC unified global daily gauge analysis is defined by interpolating quality controlled gauge reports from over 16 000 stations over the globe using the optimal interpolation (OI) algorithm of Gandin (1965). Effects of orographic influences to the precipitation are considered in the definition of the gridded analysis (Xie et al. 2007). The analysis is originally created on a 0.125° latitude–longitude grid and integrated to a 0.25° latitude–longitude grid box mean for the verifications of CMORPH satellite estimates in this study. The TAO buoy measurements of daily rainfall used here are those observed at 40 moored buoys over equatorial Pacific Ocean (http://www.pmel.noaa.gov/tao/disdel/disdel.html). Since all of the TOA buoys with in situ measurements are positioned at locations of even latitude–longitude (e.g., 8°N, 120°E), mean daily precipitation over four 0.25° latitude–longitude grid boxes cornering at the buoy location is computed for the CMORPH estimates and compared against the buoy measurements. Although differences exist between the area mean precipitation over a 0.5° latitude–longitude grid box targeted by the satellite estimates and the “point” value measured at the buoy location, averaging over a daily period reduces the discrepancies caused by the differences in the spatial representativeness of the two datasets. Same as in the CONUS experiments, examinations are conducted for the two-month period from 1 July to 31 August 2009.
The KF-based CMORPH exhibits superior performance over the original CMORPH in estimating precipitation over both land and ocean and for estimates using PMW observations from all five LEO satellite configurations (Table 3, Fig. 10). Pattern correlation for the precipitation estimates over the global land (equatorial Pacific) based on the original CMORPH degrades sharply from 0.618 (0.596) when PMW observations from all nine satellites are included to 0.428 (0.437) when inputs are available from only one LEO satellite. Performance of the KF-CMORPH, meanwhile, is much more robust, with much smaller decreases in the pattern correlation [0.556 (0.579) for only one LEO satellite] because of the inclusion of the IR precipitation estimates. The two versions of the CMORPH present biases of relatively close magnitude caused by the biases in the PMW estimates used as primarily inputs to the integration algorithms.
(top) Correlation and (bottom) bias (%) between the CMORPH daily 0.25° precipitation estimates and gauge observations for July and August 2009.
To further examine the performance of the original and KF-CMORPH, we analyzed the results from the global synthetic experiment using four LEO satellites. To this end, we compared the precipitation estimates derived by the CMORPH algorithms from the four selected LEO satellites with MWCOMB constructed from the five withdrawn LEO satellites. Since the PMW estimates from the nine LEO satellites are all calibrated against the same reference as described in section 2b, comparisons against the MWCOMB based on the withdrawn satellites’ estimates provide performance metrics for the CMORPH integration algorithms, separating the influence of the error (especially the bias) inherent in the input PMW estimates to more clearly isolate the examination to the integration process performance.
As expected, the KF-CMORPH shows consistently superior performance compared to the original CMORPH (Figs. 11 and 12). Pattern correlation for precipitation estimates constructed by the original CMORPH decreases linearly with the propagation time for the PMW observations. Correlation for estimates of 30-min mean precipitation at a grid box of 0.25° latitude–longitude is as high as ~0.8 when the PMW observations are available within the 30-min window. It degrades down to less than 0.3 when defined by propagating an instantaneous PMW observation 5 h apart using the original CMORPH algorithm. With the KF-CMORPH, the pattern correlation decreases only slightly for the same propagation length, from ~0.8 to ~0.65, thanks to the integration of IR-based precipitation estimates.
The KF-CMORPH also exhibits stronger capability in generating precipitation estimates with much better fidelity in the PDF of precipitation intensity compared to the original CMORPH (Fig. 12). PDF is identical for precipitation estimates derived from the two versions of CMORPH algorithms with propagation time less than 45 min, a reflection that no IR-based estimates are included in the KF-CMORPH when PMW observations are available nearby. The PDF for the CMORPH estimates with propagation time of 0 min (PMW observations available within the 30-min target analysis window) is very close to that for the withdrawn MWCOMB (Fig. 12a). The small differences in the PDF at low rain rates are attributable to the fact that four of the five withdrawn LEO satellites in this synthetic experiment carry sounder-based PMW instruments that are relatively poor at detecting weak precipitation, especially over midlatitude oceans. Morphing the propagated PMW estimates reduces(increases) the PDF for heavy (light) precipitation, even when the propagation is less than 30 min (Fig. 12b). The PDF aliases degrade quickly with the propagation time for precipitation estimates defined with the original CMORPH. The KF-CMORPH, however, generates precipitation analysis with PDF close to that for the withdrawn MWCOMB estimates for propagation time of various lengths (Fig. 12c).
Degree of agreements in precipitation patterns examined in sections 3 and 4 is measured mainly using pattern correlation as defined in Eq. (5). We did not perform a significance test for each of the correlation coefficients and the correlation differences shown in the tables and figures. However, a brief estimation using the methods described in the appendix of Xie and Arkin (1995) revealed that most correlation coefficients shown there and any correlation difference of 0.01 or larger is statistically significant at a level of 95% or higher because of the massive number of cases involved in the calculations (e.g., >600 000 cases in calculating each statistic in Table 1). Taking together the statistical significance of the correlation and the consistent trends of variation patterns in the statistics, it is clear that all conclusions we made are based on a solid physical foundation.
5. Summary
A new algorithm has been developed for CMORPH. The Kalman filter technique is adopted to integrate the PMW precipitation estimates from LEO satellites and IR observations from GEO platforms.
The KF-CMORPH derives the precipitation analysis at a grid box of 8 × 8 km2 in three steps. First, PMW estimates of instantaneous rain rates closest to the target analysis time in both the forward and backward directions are propagated from their observation times to the analysis time using the CSAVs computed from the GEO–IR images. The forecast of the precipitation analysis is then defined by averaging the forward- and backward-propagated PMW estimates with weights inversely proportional to their error variance. The IR-based precipitation estimates are incorporated if the gap between the two PMW observations is longer than 90 min.
The CSAVs used to propagate the PMW estimates are calculated by computing the pattern correlation between spatially lagged GEO–IRTb arrays from two consecutive images. The spatial displacement with the highest correlation is used to define the CSAVs. The IR-based precipitation estimates used in this study are defined by matching the PDF of GEO–IRTb with that of the instantaneous PMW estimates.
Major differences between the KF-CMORPH and the original CMORPH include i) the inclusion of the IR-based precipitation estimates to fill in the gaps when PMW observations are not available nearby and ii) the improved error definition for the PMW and IR precipitation estimates as a function of instrument type, surface type, and length of and temporal direction of propagation time, region, and season.
Validation tests showed substantial improvements of the KF-CMORPH against the original version in both the pattern correlation and fidelity of the precipitation intensity PDF. In general, performance of the original CMORPH degrades sharply with poor pattern correlation and substantially elevated (damped) frequency for light (strong) precipitation when PMW precipitation estimates are available from fewer LEO satellites. The KF-CMORPH is capable of producing high-resolution precipitation analysis with much more stable performance with various levels of availability for the PMW observations.
Further improvements and enhancements are desirable for the KF-based CMORPH described in this paper. In particular, error for the individual input PMW and IR precipitation estimates and the propagation of the error along the model integration process need to be accurately quantified. This requires a comprehensive examination of the error in the level 2 PMW precipitation retrievals as well as that generated in the process of propagating precipitating systems. The results of this error analysis will not only lead to improved error definition and thereby the final precipitation analysis, it will also provide insights to how the integration algorithm should be refined to reduce the generation and propagation of errors. While this paper describes an algorithm to construct high-resolution precipitation estimates through the integration of information from individual sources, success of such integration techniques is built upon the production of the input level 2 PMW and IR precipitation estimates with improved quality and refined error quantification.
A prototype system has been developed at NOAA/CPC to construct 30-min precipitation estimates on an 8 × 8 km2 grid over the globe from 60°S to 60°N by integrating PMW estimates from LEO satellites and IR observations from GEO platforms through the KF-CMORPH algorithm described in this paper. Further work is under way to extend the analysis domain to cover the entire globe from pole to pole and to remove the bias in the integrated satellite estimates through comparison against gauge observations.
Acknowledgments
The authors thank S.-H. Yoo and Y. Yarosh for their technical support to part of the study described in this paper. They are grateful to M. Sapiano who kindly provided the SSM/I-based level 2 data used in the synthetic experiments for July–August 2009. Comments from P. A. Arkin, J. Janowiak, R. Ferraro, G. Huffman, W. Shi, M. Chen, and anonymous reviewers were invaluable for improvements to the manuscript. This work is supported by NOAA/Climate Prediction Center (CPC), NOAA/Climate Program Office (CPO), NOAA/National Climatic Data Center (NCDC), and NOAA/USWRP Hydrometeorology Testbed (HMT) as part of NOAA’s contribution to the NASA Precipitation Measurement Mission (PMM) and GEWEX Global Precipitation Climatology Project (GPCP).
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