Sampling errors for satellite‐derived tropical rainfall: Monte Carlo study using a space‐time stochastic model

Evaluation of satellite and simulated rainfall products for hydrological applications in the Notwane catchment, Botswana

ABSTRACTApplication of the Tropical Rainfall Measuring Mission (TRMM) can be an efficient method for precipitation measurement in Bangladesh. The TRMM was a joint US−Japan space programme used to measure tropical rainfall with spatial and temporal distribution. This study analyses the reliability of TRMM data by comparing them with the rain gauge data of Bangladesh Meteorological Department at 35 different locations. The comparison is made for the data from 1998 to 2010. Extensive analyses were performed on the basis of different temporal scales (daily, monthly, seasonal and yearly). Both datasets were compared for average, peak and total values. The correlation co‐efficient and bias of TRMM rainfall data with respect to rain gauge values were also determined. However, the rainfall products are also compared at the two most extreme elevation stations to observe the influence of station topography (if any). Results show that TRMM rainfall data closely match with rain gauge data for average values on an annual basis, and the correlation co‐efficient is found to be greater than 0.90. However, significant deviation is found for daily peak rainfall values. Again, a seasonal comparison shows that the TRMM data outputs match with station data except during the dry season. The rainfall data at the highest and lowest elevations show that the TRMM data follow a similar trend to the station data but they underestimate the value to some extent, especially during the wet season. Finally, it is inferred that the TRMM data are reliable in estimating the average rainfall in Bangladesh for hydrological analyses of watersheds.

Four years of outgoing longwave radiation (OLR) and rainfall data from the Tropical Rainfall Measuring Mission (TRMM) are investigated to find the dominant large-scale wave modes in the Tropics. By using space– time cross-section analysis and spectral analysis, the longitudinal and latitudinal behaviors of the overall waves and the dominant waves are observed. Despite the noisy nature of precipitation data and the limited sampling by the TRMM satellite, pronounced peaks are found for Kelvin waves, n = 1 equatorial Rossby waves (ER), and mixed Rossby–gravity waves (MRG). Madden–Julian oscillation (MJO) and tropical depression (TD)-type disturbances are also detected. The seasonal evolution of these waves is investigated. An appendix includes a study of sampling and aliasing errors due to the peculiar space–time sampling pattern of TRMM. It is shown that the waves detected in this study are not artifacts of these sampling features. The results presented here are compared with previous studies. Consistency with their results gives confidence in the TRMM data for wave studies. The results from this study can be utilized for modeling and testing theories. Also, it may be useful for the future users of the TRMM data to understand the nature of the TRMM satellite sampling.

Evaluation of the Tropical Rainfall Measuring Mission (TRMM) satellite observations is conducted through a comprehensive ground validation (GV) program. Since the launch of TRMM in late 1997, standardized instantaneous and monthly rainfall products are routinely generated using quality-controlled ground-based radar data adjusted to the gauge accumulations from four primary sites. As part of the NASA TRMM GV program, effort is being made to evaluate these GV products. This paper describes the product evaluation effort for the Melbourne, Florida, site. This effort allows us to evaluate the radar rainfall estimates, to improve the algorithms in order to develop better GV products for comparison with the satellite products, and to recognize the major limiting factors in evaluating the estimates that reflect current limitations in radar rainfall estimation. Lessons learned and suggested improvements from this 8-yr mission are summarized in the context of improving planning for future precipitation missions, for example, the Global Precipitation Measurement (GPM).

In final form 30 May 2007 © 2007 American Meteorological Society he global hydrological cycle is central to Earth’s climate system, with rainfall and the physics of precipitation formation acting as the key links in the cycle. Two-thirds of global rainfall occurs in the Tropics with the associated latent heat (LH) release accounting for three-fourths of the total heat energy available to Earth’s atmosphere. In addition, freshwater provided by tropical rainfall and its variability exerts a large impact upon the structure and motion of the upper-ocean layer. The four-dimensional distribution of precipitation in the tropical atmosphere has been observed by the Tropical Rainfall Measuring Mission (TRMM) satellite since its launch in November 1997. TRMM’s passive microwave radiometer [TRMM Microwave Imager (TMI)] and precipitation radar (PR) are the primary instruments providing these data. In the last decade, standard LH products from TRMM measurements have become valuable resources for scientific research and applications. Such products enable new insights on and investigations of the complexities of convective life cycles, the diabatic heating controls and feedbacks of mesosynoptic circulations and their forecasts, the relationship of patterns of tropical LH to the global circulation and climate, and strategies for improving cloud parameterizations in environmental prediction models. The Fourth TRMM Latent Heating Workshop was convened to exchange scientific information and experience concerning the retrieval, validation, and application of satellite-derived LH products. In addition, the 26 participants met to examine and discuss the results of a comprehensive LH algorithm intercomparison–validation project; define an initial set of standard LH products; discuss validation issues, particularly the use of diagnostic analysis as the primary validation approach; deliberate further scientific requirements and applications issues related to standardized TRMM LH products; and identify future data products and validation procedures that will be required for the upcoming Global Precipitation Measurement (GPM) Mission. THE FOURTH TRMM LATENT HEATING WORKSHOP

Tropical Rainfall Measuring Mission (TRMM) rainfall products ((precipitation radar (PR) 2A25 and 3B42 or TMPA)) and hourly rainfall data in Hong Kong from January 1, 1998 to December 31, 2007 were used to examine the spatial and temporal rainfall structure and their relation in Hong Kong. The hourly gauge data show a spatial decorrelation distance of about 28 km. There are large inter-annual variability of satellite and gauge rain rate distributions and their relations; however, there are consistent differences in the rain rate distribution between gauge and TRMM products. Analyses of rainy pixels between gauge and PR show small biases, decreasing root mean square error, mean absolute error for increasing grid sizes. The correlation coefficients between TRMM PR and hourly gauges data improved from 0.16, 0.34, to 0.52 for 0.1, 0.2 and 0.4 degree gridded rain rates, in that order. For TMPA 3-hourly 0.5 degree rainfall rates, the correlation coefficient is 0.35, with large inter-annual variations.

A method of combining satellite estimates of rainfall into gridded monthly averages suitable for climatological studies is examined. Weighted averages of the satellite estimates are derived that minimize the mean squared error of the grid-box averages. A spectral model with nonlocal, scaling, diffusive behavior at small distances, tuned to tropical Atlantic (GATE) statistics, is developed to study the optimal weighting method. Using it, the effect of optimal weighting for averaging data similar to what will be provided by the Tropical Rainfall Measuring Mission (TRMM) satellite is examined. The improvement in the accuracy of the averages is found to be small except for higher-latitude grid boxes near the edges of the satellite coverage. The averages of data from a combination of TRMM and a polar orbiting instrument such as SSM/I, however, are substantially improved using the method. A simple formula for estimating sampling error for each grid box is proposed, requiring only the local rain rate an...

The Tropical Rainfall Measuring Mission (TRMM) was extended by the boost to a higher altitude in August, 2001 to gain further benefits in operational weather forecasting and climate research. To establish the credibility of TRMM data, it is necessary to analyze the impacts of orbit boost on TRMM rainfall data retrieval. In this study, the orbital boost's effects are investigated in the spectral domain by comparison with other data sets not affected by boost. The TRMM boost introduces spurious spectral biases differences between pre‐ and post‐boost periods and the independent sampling error study is used to ascertain them. The boost effects are usually exposed as small‐scale, high‐frequency wave signals in TRMM infrared radiation (IR) and microwave imager (TMI) data sets, whereas the spurious spectral differences between the two periods are not as clear in TRMM precipitation radar (PR) data due to the small sampling.

Local dry/wet conditions are of great concern in regional water resource and floods/droughts disaster risk management. Satellite-based precipitation products have greatly improved their accuracy and applicability and are expected to offer an alternative to ground rain gauges data. This paper investigated the capability of Tropical Rainfall Measuring Mission (TRMM) rainfall data for monitoring the temporal and spatial variation of dry/wet conditions in Poyang Lake basin during 1998–2010, and validated its reliability with rain gauges data from 14 national meteorological stations in the basin. The results show that: (1) the daily TRMM rainfall data does not describe the occurrence and contribution rates of precipitation accurately, but monthly TRMM data have a good linear relationship with rain gauges rainfall data; (2) both the Z index and Standardized Precipitation Index (SPI) based on monthly TRMM rainfall data oscillate around zero and show a consistent interannual variability as compared with rain gauges data; (3) the spatial pattern of moisture status, either in dry months or wet months, based on both the Z index and SPI using TRMM data, agree with the observed rainfall. In conclusion, the monthly TRMM rainfall data can be used for monitoring the variation and spatial distribution of dry/wet conditions in Poyang Lake basin.

Precipitation is a vital component of the hydrologic cycle, and successful hydrological modeling largely depends on the quality of precipitation input. Gridded precipitation datasets are gaining popularity as a convenient alternative for hydrological modeling. However, many of the gridded precipitation data have not been adequately assessed across a range of conditions. This study compared three gridded precipitation datasets, Tropical Rainfall Measuring Mission (TRMM), Climate Forecast System Reanalysis (CFSR), and Parameter-elevation Relationships on Independent Slopes Model (PRISM). This study used the conventional gauge observation as reference data and evaluated the suitability of the three sources of gridded rainfall data to drive rainfall-runoff simulations. The Soil and Water Assessment Tool (SWAT) and Artificial Neural Network (ANN) were used to create daily streamflow simulations in the Leon Creek Watershed (LCW) in San Antonio, Texas, with the TRMM, CFSR, PRISM, and gauge rainfall data used as inputs. A direct comparison of the gridded data sources showed that the TRMM data underestimates the volume of rainfall, while PRISM data most closely matches the volume of rainfall when compared to the gauge rainfall observations. The hydrological simulation results showed that the PRISM and TRMM rainfall data driven models had preferable results to the CFSR and gauge driven models, in terms of both graphical comparison and goodness-of-fit indicator values. Additionally, no significant discrepancy was found between SWAT and ANN simulation results when the same precipitation data source was used, while SWAT and ANN simulation results varied in an identical pattern when different precipitation data sources were applied.

Precipitation plays a crucial role to the global water and energy cycle that governs the weather, climate, and ecological systems. Thorough understanding and accurate forecasting of precipitation is essential to the affairs of humans. The Tropical Rainfall Measuring Mission (TRMM), launched in 1997, is a joint space mission between NASA and the Japan Aerospace Exploration Agency (JAXA) designed to monitor and study tropical rainfall. The Precipitation Radar (PR) on board the TRMM satellite is the first space borne instrument, capable of providing high-resolution vertical profile of precipitation on a global scale. TRMM-PR operates at a single frequency of Ku- (13.6 GHz) band. The microphysical retrieval algorithms for TRMM-PR rely on the surface-reference technique (SRT) to estimate path attenuation and correct the measured Ku-band reflectivity. With the attenuation-corrected reflectivities, a modified Hitschfeld-Bordan method [1] is then used to retrieve limited drop size distribution (DSD) information, and the rainfall rate [2]. One disadvantage of single-frequency space borne radar such as TRMM-PR is that it is not easy to retrieve the DSD parameters completely. Therefore, k-Z and Z-R relationships, with their inherent assumptions, are used to estimate rainfall rate which is not sufficient to capture the variability of precipitation and has large uncertainty. Global Precipitation Measurement (GPM) mission is poised to be the next generation observations from space after the TRMM mission. GPM is a science mission with integrated applications goals for advancing the knowledge of the global water/energy cycle variability as well as improving weather, climate, and hydrological prediction capabilities through more accurate and frequent measurements of global precipitation. The GPM core satellite will be equipped with a dual-frequency precipitation radar (DPR) operating at Ku- (13.6 GHz) and Ka- (35.5 GHz) band [3]. Taking two independent sets of observation, DPR on aboard the GPM is expected to improve our knowledge of precipitation processes relative to the single-frequency (Ku- band) radar used in TRMM by providing greater dynamic range, more detailed information on microphysics. Two parameters of DSDs can be retrieved from dual-frequency observations and better accuracies in rainfall estimation can be achieved. Theoretically, rainfall rate is a function of rain drop size distribution and rain drop terminal velocity, R=0.67π∗10−3∫ v(D)D3N(D)dD. The most critical component in rainfall rate estimation is the time-space variation of drop size distribution. Le and Chandrasekar (2014) [4] developed a hybrid method to retrieve drop size distribution parameters for GPM-DPR. The hybrid method is a profile-based optimization algorithm with the philosophy to combine the attributes of forward method and linear constraints of DSDs in rain. Two of the gamma distribution parameters [5], Do and Nw, at surface are optimized when the deviation between estimates and observations are minimized. The hybrid method can be used to estimate DSDs at each space and temporal resolution of GPM-DPR observation. In this paper, rainfall rate is calculated using DSDs retrieved through the hybrid method [4] based on assumptions of particle terminal velocity. Data collected by GPM-DPR is capability to cover ±65° latitude of the earth with every 2–4 hours. Thus, a global rainfall map can be generated. In polarimetric radar system, rainfall rate can be estimated through dual-polarized radar parameter such as Zdr [6][7]. Zdr is called differential reflectivity and it is a function of particle characteristics itself. Similar of Zdr to the dual-polarization radar retrieval, there is a parameter called dual-frequency ratio (DFR) that plays an important role in the dual-frequency radar retrievals. DFR is defined as the difference of the radar reflectivity at two frequencies in decibels which carries information of single particle characteristics. In this study, we investigate potential relation between rainfall rate, reflectivity at Ku- band and DFR using theoretical simulation [8] and curve fitting. Figure 1 shows a scattergram of rainfall rate estimation from R(Zh, DFR) versus true rainfall rate. Both Zku and DFR are in linear form in this equation. This provides a direct estimation of rainfall rate without prior knowledge of drop size distribution. Since both reflectivity and dual frequency ratio are intrinsic values, attenuation correction is needed before rain rate can be estimated through R(Zh, DFR) equation. The hybrid method [4] described in previous paragraph could be one of the algorithms to perform attenuation correction. The global rainfall map generated through R(Zh, DFR) approach will be cross-compared with DSD approach described in the previous paragraph, as well as other approaches such as attenuation based rainfall rate. The comprehensive analysis of the three techniques are presented.

Discrepancies between Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and Precipitation Radar (PR) oceanic rainfall retrievals are prevalent between El Niño and La Niña conditions with TMI exhibiting systematic shifts in precipitation. To investigate the causality of this relationship, this paper focuses on the evolution of precipitation organization between El Niño and La Niña and their impacts on TRMM precipitation. The results indicate that discrepancies are related to shifts from isolated deep convection during La Niña toward organized precipitation during El Niño with the largest variability occurring in the Pacific basins. During El Niño, organized systems are more frequent, have increased areal coverage of stratiform rainfall, and penetrate deeper into the troposphere compared to La Niña. The increased stratiform raining fraction leads to larger increases in TMI rain rates than PR rain rate retrievals. Reanalysis and water vapor data from the Atmospheric Infrared Sounder (AIRS) indicate that organized systems are aided by midtropospheric moisture increases accompanied by increased convective frequency. During La Niña, tropical rainfall is dominated by isolated deep convection due to drier midtropospheric conditions and strong mid- and upper-level zonal wind shear. To examine tropical rainfall–sea surface temperature relations, regime-based bias corrections derived using ground validation (GV) measurements are applied to the TRMM rain estimates. The robust connection with GV-derived biases and oceanic precipitation leads to a reduction in TMI-PR regional differences and tropics-wide precipitation anomalies. The improved agreement between PR and TMI estimates yields positive responses of precipitation to tropical SSTs of 10% °C−1 and 17% °C−1, respectively, consistent with 15% °C−1 from the Global Precipitation Climatology Project (GPCP).

Satellite based rainfall estimation techniques have emerged as a potential alternative to ground based rainfall measurements. The Tropical Rainfall Measuring Mission (TRMM) precipitation, in particular, has been used in various climate and hydrology based studies around the world. While having wide possibilities, TRMM rainfall estimates are found to be inconsistent with the ground based rainfall measurements at various locations such as the southwest coast and Himalayan region of India, northeast parts of USA, Lake Victoria in Africa, La Plata basin in South America, etc. In this study, the applicability of TRMM estimates is evaluated over the Upper Ganga Basin (Himalayan catchment) by comparing against gauge-based India Meteorological Department (IMD) gridded precipitation records. Apart from temporal evaluation, the ability of TRMM in capturing spatial distribution is also examined using three statistical parameters namely correlation coefficient (r), mean absolute error (MAE) and relative bias (RBIAS). In the results, the dual nature of bias is evident in TRMM precipitation with rainfall magnitude falling in the range from 100 to 370 mm representing positive bias, whereas, rainfall magnitude above 400 mm, approximately, representing negative bias. The Quantile Mapping (QM) approach has been used to correct the TRMM dataset from these biases. The raw TRMM precipitation is found to be fairly correlated with IMD rainfall for post-monsoon and winter season with R2 values of 0.65 and 0.57, respectively. The R2 value of 0.41 is obtained for the monsoon season, whereas least correlation is found for the pre-monsoon season with an R2 value of 0.24. Moreover, spatial distribution of rainfall during post-monsoon and winter season is captured adequately; however, the limited efficiency of TRMM is reflected for pre-monsoon and monsoon season. Bias correction has satisfactorily enhanced the spatial distribution of rainfall obtained from TRMM for almost all the seasons except for monsoon. Overall, the corrected TRMM precipitation dataset can be used for various climate analyses and hydrological water balance based studies in the Himalayan river basins.

The limitations of good rainfall data due to constraints on direct measurements can be overcome by using satellite data or reanalysis data. The use of this data must, of course, go through a validation process first. This research aims to evaluate daily data from the Tropical Rainfall Measurement Mission (TRMM) version 3B42RT (TRMM_3B42RT) and European Center for Medium-Range Weather Forecasts (ECMWF) Reanalysis 5 (ERA5) data against data collected from 17 rain gauges in the Sumatra region South. Evaluation is carried out based on the Correlation Coefficient (CC), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Bias Error (MBE) values between the data. In addition, the estimation capabilities of TRMM_3B42RT and ERA5 were evaluated based on the Probability of Detection (POD), False Alarm Ratio (FAR), and Critical Success Index (CSI) values. The results show a very high correlation between TRMM_3B42RT and ERA5 with rain gauge data, especially in terms of monthly data. These values (monthly data) for TRMM_3B42RT and ERA5 data are 0.3-0.9 and 0.2-0.9, respectively. The RMSE values of TRMM_3B42RT and ERA5 data in monthly analysis are 75-250mm/month and 100-180mm/month, respectively. The forecasting performance of TRMM_3B42RT and ERA5 shows good results, especially for moderate rainfall in daily data and heavy rainfall in monthly data. The results of this analysis show tha the monthly data TRMM_3B42RT is more in line with the station data and can be used in further research.

Data for the investigation of Clouds and the Earth's Radiant Energy System (CERES) began with the launch of the CERES instrument on the Tropical Rainfall Measuring Mission (TRMM) and continues with two CERES instrument on the EOS Terra satellite. The new instruments will sample regions poleward of the surface viewable from TRMM, and will thus place CERES in a position to contribute global observations of reflected sunlight and emitted terrestrial fluxes, beyond what could be observed from the TRMM equatorial orbit. During the initial observations from Terra, the new CERES instruments have undergone the same kind of initial checkout as the instruments on TRMM, as well as more detailed intercomparisons between the three CERES instruments now in orbit. Beyond the classic measurements of fluxes at the top of the Earth's atmosphere, CERES will also produce new observations that combine radiances from sister instruments on TRMM and Terra, namely VIRS and MODIS, to produce much more reliable retrievals of cloud properties that will provide new insights into the cloud-radiative feedback that remains one of the largest uncertainties in our understanding of the Earth's climate.