scholarly journals Multiscale assessment of TRMM (3B42 V7) and GPM (IMERG V5) satellite precipitation products over a Mediterranean mountainous watershed with sparse rain gauges in the Moroccan High Atlas (case study of Zat basin)

2021 ◽  
Author(s):  
Myriam Benkirane ◽  
Nour-Eddine Laftouhi ◽  
Said Khabba ◽  
Bouabid El Mansouri
Keyword(s):  
Probability Of Detection ◽  
Satellite Precipitation ◽  
Critical Success ◽  
Precipitation Measurement ◽  
Catchment Areas ◽  
Mountainous Watershed ◽  
Short Time ◽  
Global Precipitation ◽  
Trmm 3B42 ◽  
Precipitation Events

Abstract. The performance of Tropical Precipitation Measurement Mission (TRMM) and its successor, Global Precipitation Measurement (GPM), has provided hydrologists with a source of critical precipitation data for hydrological applications in basins where ground-based observations of precipitation are sparse, or spatially undistributed. The very high temporal and spatial resolution satellite precipitation products have therefore become a reliable alternative that researchers are increasingly using in various hydro-meteorological and hydro-climatological applications. This study aims to evaluate statistically and hydrologically the TRMM (3B42 V7) and GPM (IMERG V5) satellite precipitations products (SPPs), at multiple temporal scales from 2010 to 2017, in a mountainous watershed characterized by the Mediterranean climate. The results show that TRMM (3B42 V7) and GPM (IMERG V5) satellite precipitation products have a significant capacity for detecting precipitation at different time steps. However, the statistical analysis of SPPs against ground observation shows good results for both statistical metrics and contingency statistics with notable values (CC > 0.8), and representative values relatively close to 0 for the probability of detection (POD), critical success index (CSI), and false alarm ratio (FAR). Moreover, the sorting of the events implemented on the hydrological model was performed seasonally, at daily time steps. The calibrated episodes showed very good results with Nash values ranging from 53.2 % to 95.5 %. Nevertheless, the (IMERG V5) product detects more efficiently precipitation events at short time steps (daily), while (3B42 V7) has a strong ability to detect precipitation events at large time steps (monthly and yearly). Furthermore, the modeling results illustrate that both satellite precipitation products tend to underestimate precipitation during wet seasons and overestimate them during dry seasons, while they have a better spatial distribution of precipitation measurements performance, which shows the importance of their use for basin modeling and potentially for flood forecasting in Mediterranean catchment areas.

scholarly journals Systematical Evaluation of GPM IMERG and TRMM 3B42V7 Precipitation Products in the Huang-Huai-Hai Plain, China

2019 ◽  
Vol 11 (6) ◽  
pp. 697 ◽  
Author(s):  
Fenglin Xu ◽  
Bin Guo ◽  
Bei Ye ◽  
Qia Ye ◽  
Huining Chen ◽  
...  
Keyword(s):  
Tropical Rainfall Measuring Mission ◽  
Accurate Estimation ◽  
Detection Capability ◽  
Satellite Precipitation ◽  
Precipitation Measurement ◽  
Daily Precipitation Data ◽  
Precipitation Estimates ◽  
Global Precipitation Measurement ◽  
Global Precipitation ◽  
Precipitation Events

Accurate estimation of high-resolution satellite precipitation products like Global Precipitation Measurement (GPM) and Tropical Rainfall Measuring Mission (TRMM) is critical for hydrological and meteorological research, providing a benchmark for the continued development and future improvement of these products. This study aims to comprehensively evaluate the Integrated Multi-Satellite Retrievals for GPM (IMERG) and TRMM 3B42V7 products at multiple temporal scales from 1 January 2015 to 31 December 2017 over the Huang-Huai-Hai Plain in China, using daily precipitation data from 59 meteorological stations. Three commonly used statistical metrics (CC, RB, and RMSE) are adopted to quantitatively verify the accuracy of two satellite precipitation products. The assessment also takes into account the precipitation detection capability (POD, FAR, CSI, and ACC) and frequency of different precipitation intensities. The results show that the IMERG and 3B42V7 present strong correlation with meteorological stations observations at annual and monthly scales (CC > 0.90), whereas moderate at the daily scale (CC = 0.76 and 0.69 for IMERG and 3B42V7, respectively). The spatial variability of the annual and seasonal precipitation is well captured by these two satellite products. And spatial patterns of precipitation gradually decrease from south to north over the Huang-Huai-Hai Plain. Both IMERG and 3B42V7 products overestimate precipitation compared with the station observations, of which 3B42V7 has a lower degree of overestimation. Relative to the IMERG, annual precipitation estimates from 3B42V7 show lower RMSE (118.96 mm and 142.67 mm, respectively), but opposite at the daily, monthly, and seasonal scales. IMERG has a better precipitation detection capability than 3B42V7 (POD = 0.83 and 0.67, respectively), especially when detecting trace and solid precipitation. The two precipitation products tend to overestimate moderate (2–10 mm/d) and heavy (10–50 mm/d) precipitation events, but underestimate violent (>50 mm/d) precipitation events. The IMERG is not found capable to detecting precipitation events of different frequencies more precisely. In general, the accuracy of IMERG is better than 3B42V7 product in the Huang-Huai-Hai Plain. The IMERG satellite precipitation product with higher temporal and spatial resolutions can be regarded a reliable data sources in studying hydrological and climatic research.

scholarly journals Performance Assessment of GSMaP and GPM IMERG Products during Typhoon Mangkhut

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 134
Author(s):  
Xiaoyu Li ◽  
Sheng Chen ◽  
Zhenqing Liang ◽  
Chaoying Huang ◽  
Zhi Li ◽  
...  
Keyword(s):  
Mean Squared Error ◽  
Southern China ◽  
Eastern China ◽  
Mainland China ◽  
Rain Gauge ◽  
Probability Of Detection ◽  
Critical Success ◽  
Rainfall Occurrence ◽  
Precipitation Measurement ◽  
Global Precipitation

This paper evaluated the latest version 6.0 Global Satellite Mapping of Precipitation (GSMaP) and version 6.0 Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG) products during 2018 Typhoon Mangkhut in China. The reference data is the rain gauge datasets from Gauge-Calibrated Climate Prediction Centre (CPC) Morphing Technique (CMORPHGC). The products for comparison include the GSMaP near-real-time, Microwave-IR merged, and gauge-calibrated (GSMaP_NRT, GSMaP_MVK, and GSMaP_Gauge) and the IMERG Early, Final, and Final gauge-calibrated (IMERG_ERUncal, IMERG_FRUncal, and IMERG_FRCal) products. The results show that (1) both GSMaP_Gauge and IMERG_FRCal considerably reduced the bias of their satellite-only products. GSMaP_Gauge outperforms IMERG_FRCal with higher Correlation Coefficient (CC) values of about 0.85, 0.78, and 0.50; lower Fractional Standard Error (FSE) values of about 18.00, 18.85, and 29.30; and Root-Mean-Squared Error (RMSE) values of about 12.12, 33.35, and 32.99 mm in the rainfall centers over mainland China, southern China, and eastern China, respectively. (2) GSMaP products perform better than IMERG products, with higher Probability of Detection (POD) and Critical Success Index (CSI) and lower False Alarm Ratio (FAR) in detecting rainfall occurrence, especially for high rainfall rates. (3) For area-mean rainfall, IMERG performs worse than GSMaP in the rainfall centers over mainland China and southern China but shows better performance in the rainfall center over eastern China. GSMaP_Gauge and IMERG_FRCal perform well in the three regions with a high CC (0.79 vs. 0.94, 0.81 vs. 0.96, and 0.95 vs. 0.97) and a low RMSE (0.04 vs. 0.06, 0.40 vs. 0.59, and 0.19 vs. 0.34 mm). These useful findings will help algorithm developers and data users to better understand the performance of GSMaP and IMERG products during typhoon precipitation events.

scholarly journals Assessment of GPM-Era Satellite Products’ (IMERG and GSMaP) Ability to Detect Precipitation Extremes over Mountainous Country Nepal

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 254
Author(s):  
Bikash Nepal ◽  
Dibas Shrestha ◽  
Shankar Sharma ◽  
Mandira Singh Shrestha ◽  
Deepak Aryal ◽  
...  
Keyword(s):  
Extreme Precipitation ◽  
Daily Precipitation ◽  
Precipitation Amount ◽  
Probability Of Detection ◽  
Precipitation Extremes ◽  
Extreme Precipitation Events ◽  
Precipitation Measurement ◽  
Global Precipitation Measurement ◽  
Global Precipitation ◽  
Precipitation Events

The reliability of satellite precipitation products is important in climatic and hydro-meteorological studies, which is especially true in mountainous regions because of the lack of observations in these areas. Two recent satellite rainfall estimates (SREs) from Global Precipitation Measurement (GPM)-era—Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG-V06) and gauge calibrated Global Satellite Mapping of Precipitation (GSMaP-V07) are evaluated for their spatiotemporal accuracy and ability to capture extreme precipitation events using 279 gauge stations from southern slope of central Himalaya, Nepal, between 2014 and 2019. The overall result suggests that both SREs can capture the spatiotemporal precipitation variability, although they both underestimated the observed precipitation amount. Between the two, the IMERG product shows a more consistent performance with a higher correlation coefficient (0.52) and smaller bias (−2.49 mm/day) than the GSMaP product. It is worth mentioning that the monthly gauge-calibrated IMERG product yields better detection capability (higher probability of detection (POD) values) of daily precipitation events than the daily gauge calibrated GSMaP product; however, they both show similar performance in terms of false alarm ratio (FAR) and critical success index (CSI). Assessment based on extreme precipitation indices revealed that the IMERG product outperforms GSMaP in capturing daily precipitation extremes (RX1Day and RX5Day). In contrast, the GSMaP product tends to be more consistent in capturing the duration and threshold-based precipitation extremes (consecutive dry days (CDD), consecutive wet days (CWD), number of heavy precipitation days (R10mm), and number of extreme precipitation days (R25mm)). Therefore, it is suggested that the IMERG product can be a good alternative for monitoring daily extremes; meanwhile, GSMaP could be a better option for duration-based extremes in the mountainous region.

Understanding performance of GPROF precipitation retrievals over the Netherlands in relation to precipitation characteristics as derived from ground-based dual-polarization radars

2021 ◽  
Author(s):  
Linda Bogerd ◽  
Hidde Leijnse ◽  
Aart Overeem ◽  
Remko Uijlenhoet
Keyword(s):  
The Netherlands ◽  
Background Radiation ◽  
A Priori ◽  
Dual Frequency ◽  
Dual Polarization ◽  
Ground Clutter ◽  
Precipitation Measurement ◽  
Precipitation Estimates ◽  
Global Precipitation ◽  
Precipitation Events

<p>The Global Precipitation Measurement mission (GPM) is one of the recent efforts to provide satellite-based global precipitation estimates. The GPM Profiling Algorithm (GPROF) converts microwave radiation measured by passive microwave (PMW) sensors onboard constellation satellites into precipitation. Over land, precipitation estimates are obtained from high frequency PMW-channels that measure the radiance scattered by ice particles in rain clouds. However, due to the limited scattering related to shallow and light precipitation, it is challenging to distinguish these signals from background radiation that is naturally emitted from the Earth’s surface.</p><p>Increased understanding of the physical processes during precipitation events can be used to improve PMW-based precipitation retrievals. This study couples overpasses of GPM radiometers over the Netherlands to two dual-polarization radars from the Royal Netherlands Meteorological Institute (KNMI). The Netherlands is an ideal setting for this study due to the availability of high-quality ground-based measurements, the frequent occurrence of shallow events, the absence of ground-clutter related to mountains, and the varying background emission related to its coastal location.</p><p>The coupling of overpasses with ground-based precipitation radars provides the opportunity to relate GPROFs performance to physical characteristics of precipitation events, such as the vertical reflectivity profile and dual-polarization information on the melting layer. Furthermore, simultaneous radiometer estimates and space-based reflectivity profiles from the dual-frequency precipitation radar (DPR) onboard the GPM core satellite are coupled to the ground-based reflectivity profiles for selected case studies. Because the a-priori database implemented in the GPROF algorithm is based on observations from the DPR, the comparison of the reflectivity profiles further unravels discrepancies between GPROF and ground-based estimates.</p>

scholarly journals How Well Can IMERG Products Capture Typhoon Extreme Precipitation Events over Southern China?

2019 ◽  
Vol 11 (1) ◽  
pp. 70 ◽  
Author(s):  
Chaoying Huang ◽  
Junjun Hu ◽  
Sheng Chen ◽  
Asi Zhang ◽  
Zhenqing Liang ◽  
...  
Keyword(s):  
Extreme Precipitation ◽  
Southern China ◽  
Correlation Coefficients ◽  
Heavy Precipitation ◽  
Spatiotemporal Variability ◽  
Bias Analysis ◽  
Extreme Precipitation Events ◽  
Precipitation Measurement ◽  
Global Precipitation ◽  
Precipitation Events

This study assesses the performance of the latest version 05B (V5B) Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (GPM) (IMERG) Early and Final Runs over southern China during six extremely heavy precipitation events brought by six powerful typhoons from 2016 to 2017. Observations from a dense network composed of 2449 rain gauges are used as reference to quantify the performance in terms of spatiotemporal variability, probability distribution of precipitation rates, contingency scores, and bias analysis. The results show that: (1) both IMERG with gauge calibration (IMERG_Cal) and without gauge correction (IMERG_Uncal) generally capture the spatial patterns of storm-accumulated precipitation with moderate to high correlation coefficients (CCs) of 0.57–0.87, and relative bias (RB) varying from −17.21% to 30.58%; (2) IMERG_Uncal and IMERG_Cal capture well the area-average hourly series of precipitation over rainfall centers with high CCs ranging from 0.78 to 0.94; (3) IMERG_Cal tends to underestimate precipitation especially the rainfall over the rainfall centers when compared to IMERG_Uncal. The IMERG Final Run shows promising potentials in typhoon-related extreme precipitation storm applications. This study is expected to give useful feedbacks about the latest V5B Final Run IMERG product to both algorithm developers and the scientific end users, providing a better understanding of how well the V5B IMERG products capture the typhoon extreme precipitation events over southern China.

scholarly journals Assessment of IMERG-V06 Precipitation Product over Different Hydro-Climatic Regimes in the Tianshan Mountains, North-Western China

2019 ◽  
Vol 11 (19) ◽  
pp. 2314 ◽  
Author(s):  
Anjum ◽  
Ahmad ◽  
Ding ◽  
Shangguan ◽  
Zaman ◽  
...  
Keyword(s):  
Tropical Rainfall Measuring Mission ◽  
Tianshan Mountains ◽  
Western China ◽  
Spatiotemporal Variability ◽  
Eastern Region ◽  
Monthly Precipitation ◽  
Precipitation Measurement ◽  
Global Precipitation Measurement ◽  
Global Precipitation ◽  
Precipitation Events

This study presents an assessment of the version-6 (V06) of the Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG) product from June 2014 to December 2017 over different hydro-climatic regimes in the Tianshan Mountains. The performance of IMERG-V06 was compared with IMERG-V05 and the Tropical Rainfall Measuring Mission (TRMM) 3B42V7 precipitation products. The precipitation products were assessed against gauge-based daily and monthly precipitation observations over the entire spatial domain and five hydro-climatologically distinct sub-regions. Results showed that: (1) The spatiotemporal variability of average daily precipitation over the study domain was well represented by all products. (2) All products showed better correlations with the monthly gauge-based observations than the daily data. Compared to 3B42V7, both IMERG products presented a better agreement with gauge-based observations. (3) The estimation skills of all precipitation products showed significant spatial variations. Overall performance of all precipitation products was better in the Eastern region compared to the Middle and Western regions. (4) Satellite products were able to detect tiny precipitation events, but they were uncertain in capturing light and moderate precipitation events. (5) No significant improvements in the precipitation estimation skill of IMERG-V06 were found as compared to IMERG-V05. We deduce that the IMERG-V06 precipitation detection capability could not outperform the efficiency of IMERG-V05. This comparative evaluation of the research products of Global Precipitation Measurement (GPM) and TRMM products in the Tianshan Mountains is useful for data users and algorithm developers.

scholarly journals Validation of rainfall data estimated by GPM satellite on Southern Amazon region

2019 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Luiz Octavio Fabricio dos Santos ◽  
Carlos Alexandre Santos Querino ◽  
Juliane Kayse Albuquerque da Silva Querino ◽  
Altemar Lopes Pedreira Junior ◽  
Aryanne Resende de Melo Moura ◽  
...  
Keyword(s):  
Pearson Correlation ◽  
Absolute Error ◽  
High Rate ◽  
Satellite Precipitation ◽  
Precipitation Measurement ◽  
Surface Data ◽  
Precipitation Estimates ◽  
Amazonas State ◽  
Global Precipitation Measurement ◽  
Global Precipitation

Rainfall is a meteorological variable of great importance for hydric balance and for weather studies. Rainfall estimation, carried out by satellites, has increased the climatological dataset related to precipitation. However, the accuracy of these data is questionable. This paper aimed to validate the estimates done by the Global Precipitation Measurement (GPM) satellite for the mesoregion of Southern Amazonas State, Brazil. The surface data were collected by the National Water Agency – ANA and National Institute of Meteorology – INMET, and is available at both institutions’ websites. The satellite precipitation data were accessed directly from the NASA webpage. Statistical analysis of Pearson correlation was used, as well as the Willmott’s “d” index and errors from the MAE (Mean Absolute Error) and RMSE (Root Mean Square Error). The GPM satellite satisfactorily estimated the precipitation, once it had correlations above 73% and high Willmott coefficients (between 0.86 and 0.97). The MAE and RMSE showed values that varied from 36.50 mm to 72.49 mm and 13.81 mm to 71.76 mm, respectively. Seasonal rain variations are represented accordingly. In some cases, either an underestimation or an overestimation of the rain data was observed. In the yearly totals, a high rate of similarity between the estimated and measured values was observed. We concluded that the GPM-based multi-satellite precipitation estimates can be used, even though they are not 100% reliable. However, adjustments in calibration for the region are necessary and recommended.

scholarly journals Seasonal Effect on Spatial and Temporal Consistency of the New GPM-Based IMERG-v5 and GSMaP-v7 Satellite Precipitation Estimates in Brazil’s Central Plateau Region

Water ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 668 ◽  
Author(s):  
Leandro Salles ◽  
Frédéric Satgé ◽  
Henrique Roig ◽  
Tati Almeida ◽  
Diogo Olivetti ◽  
...  
Keyword(s):  
Daily Basis ◽  
Seasonal Effect ◽  
Temporal Consistency ◽  
Time Step ◽  
Central Plateau ◽  
Satellite Precipitation ◽  
Precipitation Measurement ◽  
Precipitation Estimates ◽  
Global Precipitation Measurement ◽  
Global Precipitation

This study assesses the performance of the new Global Precipitation Measurement (GPM)-based satellite precipitation estimates (SPEs) datasets in the Brazilian Central Plateau and compares it with the previous Tropical Rainfall Measurement Mission (TRMM)-era datasets. To do so, the Integrated Multi-satellitE Retrievals for GPM (IMERG)-v5 and the Global Satellite Mapping of Precipitation (GSMaP)-v7 were evaluated at their original 0.1° spatial resolution and for a 0.25° grid for comparison with TRMM Multi-satellite Precipitation Analysis (TMPA). The assessment was made on an annual, monthly, and daily basis for both wet and dry seasons. Overall, IMERG presents the best annual and monthly results. In both time steps, IMERG’s precipitation estimations present bias with lower magnitudes and smaller root-mean-square error. However, GSMaP performs slightly better for the daily time step based on categorical and quantitative statistical analysis. Both IMERG and GSMaP estimates are seasonally influenced, with the highest difficulty in estimating precipitation occurring during the dry season. Additionally, the study indicates that GPM-based SPEs products are capable of continuing TRMM-based precipitation monitoring with similar or even better accuracy than obtained previously with the widely used TMPA product.

scholarly journals Satellite-based high-resolution mapping of rainfall over southern Africa

2017 ◽  
Vol 10 (6) ◽  
pp. 2009-2019 ◽  
Author(s):  
Hanna Meyer ◽  
Johannes Drönner ◽  
Thomas Nauss
Keyword(s):  
Southern Africa ◽  
Ground Truth ◽  
Skill Score ◽  
Probability Of Detection ◽  
Rainfall Events ◽  
Precipitation Measurement ◽  
Hourly Rainfall ◽  
Model Probability ◽  
Spatio Temporal ◽  
Global Precipitation

Abstract. A spatially explicit mapping of rainfall is necessary for southern Africa for eco-climatological studies or nowcasting but accurate estimates are still a challenging task. This study presents a method to estimate hourly rainfall based on data from the Meteosat Second Generation (MSG) Spinning Enhanced Visible and Infrared Imager (SEVIRI). Rainfall measurements from about 350 weather stations from 2010–2014 served as ground truth for calibration and validation. SEVIRI and weather station data were used to train neural networks that allowed the estimation of rainfall area and rainfall quantities over all times of the day. The results revealed that 60 % of recorded rainfall events were correctly classified by the model (probability of detection, POD). However, the false alarm ratio (FAR) was high (0.80), leading to a Heidke skill score (HSS) of 0.18. Estimated hourly rainfall quantities were estimated with an average hourly correlation of ρ = 0. 33 and a root mean square error (RMSE) of 0.72. The correlation increased with temporal aggregation to 0.52 (daily), 0.67 (weekly) and 0.71 (monthly). The main weakness was the overestimation of rainfall events. The model results were compared to the Integrated Multi-satellitE Retrievals for GPM (IMERG) of the Global Precipitation Measurement (GPM) mission. Despite being a comparably simple approach, the presented MSG-based rainfall retrieval outperformed GPM IMERG in terms of rainfall area detection: GPM IMERG had a considerably lower POD. The HSS was not significantly different compared to the MSG-based retrieval due to a lower FAR of GPM IMERG. There were no further significant differences between the MSG-based retrieval and GPM IMERG in terms of correlation with the observed rainfall quantities. The MSG-based retrieval, however, provides rainfall in a higher spatial resolution. Though estimating rainfall from satellite data remains challenging, especially at high temporal resolutions, this study showed promising results towards improved spatio-temporal estimates of rainfall over southern Africa.

scholarly journals Conditional Generative Adversarial Networks (cGANs) for Near Real-Time Precipitation Estimation from Multispectral GOES-16 Satellite Imageries—PERSIANN-cGAN

2019 ◽  
Vol 11 (19) ◽  
pp. 2193 ◽  
Author(s):  
Negin Hayatbini ◽  
Bailey Kong ◽  
Kuo-lin Hsu ◽  
Phu Nguyen ◽  
Soroosh Sorooshian ◽  
...  
Keyword(s):  
Mean Squared Error ◽  
Probability Of Detection ◽  
Generative Adversarial Networks ◽  
Generative Adversarial Network ◽  
Convolutional Network ◽  
Critical Success ◽  
Adversarial Network ◽  
Precipitation Estimation ◽  
Precipitation Estimates ◽  
Global Precipitation

In this paper, we present a state-of-the-art precipitation estimation framework which leverages advances in satellite remote sensing as well as Deep Learning (DL). The framework takes advantage of the improvements in spatial, spectral and temporal resolutions of the Advanced Baseline Imager (ABI) onboard the GOES-16 platform along with elevation information to improve the precipitation estimates. The procedure begins by first deriving a Rain/No Rain (R/NR) binary mask through classification of the pixels and then applying regression to estimate the amount of rainfall for rainy pixels. A Fully Convolutional Network is used as a regressor to predict precipitation estimates. The network is trained using the non-saturating conditional Generative Adversarial Network (cGAN) and Mean Squared Error (MSE) loss terms to generate results that better learn the complex distribution of precipitation in the observed data. Common verification metrics such as Probability Of Detection (POD), False Alarm Ratio (FAR), Critical Success Index (CSI), Bias, Correlation and MSE are used to evaluate the accuracy of both R/NR classification and real-valued precipitation estimates. Statistics and visualizations of the evaluation measures show improvements in the precipitation retrieval accuracy in the proposed framework compared to the baseline models trained using conventional MSE loss terms. This framework is proposed as an augmentation for PERSIANN-CCS (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Network- Cloud Classification System) algorithm for estimating global precipitation.

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