Simulating the regional water balance through hydrological model based on TRMM satellite rainfall data

the foreseeable future, however, it is necessary to evaluate the products before further implication. The objective of this paper is to provide assessments of: (a) the Tropical Rainfall Measuring Mission (TRMM) rainfall product using gauge data, (b) the TRMM rainfall as forcing data for hydrological simulation, and (c) the role of satellite data in calculating water balance and water management. TRMM rainfall data show reason10


Introduction
Precipitation is widely accepted as a fundamental component of the global water cycle and in a sense governs the renewable water resources that affect economic, ecological and agricultural development.The spatial and temporal resolutions of precipitation data are mutually influenced, and both have significant impacts on determining surface hydrology (Masih et al., 2011;Michaelides et al., 2009;Xu et al., 2013).As hydrological models are abstract and simplified representations of natural hydrological processes, those models well founded in physical theory and empirically justified by past performance.However, those models will fail to produce accurate hydrograph predictions if the precisions of inputting precipitation data are not high enough.In general, precipitation gauges provide the primary means of estimating precipitation at a point, and calculated regional precipitation by interpolation methods such as Kriging, Thiessen polygons and Trend surface analysis.It is commonly believed that the areas of high rain gauge density can provide more reliable estimates at an unsampled location than that of low rain gauge density (Chappell et al., 2013).However, in some places the ground-based observations are usually sparse or unevenly distributed due to economic or terrain limitation.Furthermore, rain gauge observations are usually not available in real time in many regions.
The estimation of the spatial distribution of rainfall can be improved with the inclusion of ancillary data such as radar, satellite and topography.Moreno et al. (2012) revealed that radar and multisensor quantitative precipitation estimates lead to improving hydrologic model performance compared to simulations driven with rain gauge data only.Hunink et al. (2014) found that blending satellite rainfall products with altitude and vegetation index would continuously improve quantification the spatial distribution of precipitation.In addition, high resolution satellite rainfall estimates was used in quite a lot of studies as a source of data for hydrological application and water resources planning (Masih et al., 2011;Ud din et al., 2008;Wilk et al., 2006;Yan and Gebremichael, 2009;Zhang et al., 2009).As a result, satellite rainfall estimates open novel avenues for forecasting in regions with limited access and sparse observations (Moreno et al., 2012).
Since the launch of the Tropical Rainfall Measuring Mission (TRMM; Kummerow, 1998) in 1997, the first precipitation radar sensor stared to be operated in space.The availability of active precipitation detection from space has laid the groundwork for spaceborne estimations from radar and radar + radiometer (Michaelides et al., 2009).However, the absolute accuracy of satellite rainfall products is questionable (Tian and Peters-Lidard, 2010), and needs a thorough validation before it can be used extensively.
Recently, many studies evaluated the performance of satellite rainfall products over different regions in the world (Dinku et al., 2008;Hu et al., 2013;Jiang et al., 2010 et al., 2012;Ochoa et al., 2014;Shen et al., 2010;Stampoulis and Anagnostou, 2012;Worqlul et al., 2014).The results of these studies indicated that the quality of satellite rainfall products varies with season, region, and elevation.Basically, the TRMM 3B42 product performs reasonably well over most regions in depicting the overall rainfall spatial patterns with only small biases compared to the gauge data.But the TRMM 3B42 generally underestimates rainfall over higher elevations, especially during the cold season.However, fewer studies compare TRMM rainfall data and rain gauge data at catchment scale, and fewer evaluation of hydrological processes using TRMM rainfall data in simulation and water balance analysis in catchments scale, which will provide useful information for hydrology research and water management.
This study is aimed at: (1) evaluate the accuracy of TRMM rainfall product by using a hydrologic model to calculate runoff and compare to measured runoff, (2) evaluate the suitability of TRMM rainfall product used for simulating regional water balance.
Section 2 of this paper provides a brief introduction of the focus region of this study, along with a brief discussion on the rain gauge and TRMM rainfall data.Section 3 first presents the performance of TRMM rainfall to the rain gauge data, then processes the hydrological simulation driven by two types of rainfall, and finally describes the water balance of the watershed.

Study area
The Tiaoxi watershed with an area of 5900 km 2 is situated in eastern China, which is a part of southern catchment of Taihu Lake (Fig. 1).It is located at 119  S1 and S2.

TRMM data
TRMM provides global precipitation estimates from a wide variety of meteorological satellites (Huffman et al., 2010).Indeed, the TRMM estimates are available in the form of two products: a near real-time version (3B42RT) (about 6 h after real time) covering the global latitude belt from 60  TRMM Microwave Imager (TMI), to calibrate precipitation estimates derived from available Low Earth Orbit (LEO) microwave (MW) radiometers.The 3B42RT then merges all of the estimates at 3 h intervals, and the gaps in the analyses are filled using Geostationary Earth Orbit (GEO) infrared (IR) data regionally calibrated based on the merged MW product.The 3B42 adjusts the monthly accumulations of the 3 h fields from 3B42RT based on a monthly gauge analysis, including the Global Precipitation Climatology Project (GPCP) (Arkin and Xie, 1994) 1 • × 1 • monthly rain gauge analysis and the Climate Assessment and Monitoring System (CAMS) 0.5 • × 0.5 • monthly rain gauge analysis (Shanhu Jiang, Liliang Ren, Yang Hong, Bin Yong, Xiaoli Yang, Fei Yuan, 2012).The daily satellite rainfall data employed in the current work are computed by aggregating 3 h temporal resolution data over 24 h for TRMM-3B42 product.

Hydrological model
The Soil and Water Assessment Tool (SWAT) is a well-established, semi-distributed, eco-hydrologic model operating on daily, monthly or yearly time step.Main model components consist of weather, hydrology, soil temperature, plant growth, nutrients, pesticides, land management, bacteria and pathogens (Arnold and Fohrer, 2005;Arnold et al., 2012;Boorman, 2003;Hattermann et al., 2006;Manguerra and Engel, 1998).
Delineating watershed into subbasins and hydrologic response units (HRUs) needs three basic files: a digital elevation model (DEM), a land use and land cover (LULC) map, and a soil map.Topography was represented by a 30 m × 30 m elevation raster.Daily time-series of measured precipitation, air temperature, evaporation capacity and relative humidity were obtained from the six meteorological stations (Huzhou, Anji, Deqing, Changxing, Yuhang, and Linan).
In order to evaluate the quality of TRMM daily precipitation, correlation coefficient (CC), mean bias error (MBE), root mean square error (RMSE) and normalized root mean square error (NRMSE) are calculated.As the root mean square error is an inappropriate measure for mean error and can be easily misinterpreted (Willmott and Matsuura, 2005), in this study, NRMSE and CC are mainly used to evaluate the accuracy of TRMM daily precipitation.For the NRMSE, the simulation is considered excellent if NRMSE < 10 %, good if 10-20 %, fair if 20-30 %, poor > 30 % (Jamieson et al., 1991;Signoretto and Plas, 2011).

Correlation coefficient
CC = cov(P est , P obs ) where P est and P obs are respectively the gauge and satellite time series of rainfall data for a single position/pixel, cov (X , Y ) is the empirical covariance between X and Y variables, and σ(X ) is the empirical SD of X .

Mean bias error
Where P i obs and P i est are respectively the precipitation value provided by gauge data and the precipitation estimation provided by a satellite product for a single position/pixel, at the i th time step with n being the number of considered time steps.

Categorical indexes
For the evaluation of the correspondence between the estimated and observed occurrence of rain events, several categorical verification statistics are also used in this study: probability of detection (POD), false alarm ratio (FAR) and critical success index (CSI).POD measures the fraction of observed events that were correctly diagnosed and is also called the hit rate.FAR provides the ratio of false alarm to total satellite-estimated events.CSI gives the overall fraction of events correctly diagnosed by the TRMM.Perfect values for these scores are POD = 1, FAR = 0, and CSI = 1.

Probability of detection
Where t is a threshold value, and I(a|b) is an indicator function indicating the number of occurrences where conditions a and b are respected.
The threshold value for categorical indexes t is fixed equal to 1.0 mm/24 h, according to Ebert et al. (2007).POD indicates the rainfall occurrences correctly detected by the considered estimation product.It is given by the ratio between the number of occurrences registered by both the reference and test data set and the occurrence registered only by the reference data set.POD is equal to 1 if the analyzed data set can represent all occurrences and 0 if no occurrences are detected.

Hydrological model performance indexes
This study adopted two commonly used statistical criteria, the Nash-Sutcliffe Coefficient of Efficiency (NSCE) and the relative bias ratio, to evaluate the hydrological model performance (Meng et al., 2014).NSCE and BIAS are defined as: Where, Q i , o is the observed discharge of the i th day; Q o is the average value of the observed discharge for the whole time; Q i , s is the simulated discharge of the i th day.BIAS assesses the systematic errors of the simulated discharge, and NSCE is an indicator of model fit between the simulated and observed discharge.The highest skill level corresponds to NSCE = 1 and BIAS = 0 %.In addition, the determination coefficient (R 2 ) is used to measure the ability and reliability of the model in simulating the observed discharge.

Comparison of TRMM rainfall with rain gauges data
Table 1 shows the statistics based on two types of rainfall datasets.Areal average rainfall is 2.9-5.0 mm d for TRMM data in the same period.
Figure 4 shows the intensity distribution of daily rainfall and their contributions to the total rainfall as a function of rain rate in different years.It indicated that non-rainy days have the largest occurrence, and the second largest class was 0 < rainfall ≤ 3 mm, occurring about 20-30 % of the total days in gauges.Besides, the statistics for TRMM rainfall were different from gauge rainfall, the largest class was also non-rainy days, occurring about 65-75 % of total days, and the second largest class is 0 < rainfall ≤ 3 mm, occurring about 5-10 % of total days.That is to say more non-rainy days record in TRMM data and more days of light rain class (0 < rainfall ≤ 3 mm) in gauge data.
That is because the TRMM data has a lower skill in correctly specifying moderate and light rain rates on short time intervals (Michaelides et al., 2009), much light rainfall in some days are regarded as non-rainy in TRMM data.The sum of the first two classes, non-rainy and light rain classes, gives the similar percentage (80 %) for both TRMM data and gauge data.It can be calculated that although the occurrences of light rain (0 < rainfall ≤ 3 mm) are as high as 10-30 % of the total days, the contribution to the total rainfall amount is only about 1 % in both rainfall data.
It is important to point that although the high rainfall ranges occurs only about 1.1 % (maximal 2.4 % in 1999) of the total days, it plays a significant role in rainfall amount.The high rainfall class (> 50 mm) contributes to 16.3 % in average values (maximal 34.0 % in 1999) of the total rainfall for rain gauge data and 22.8 % (maximal 34.4 % in 1999) for TRMM data.For the class of 3-10 mm, both the occurrences and contribution rate of TRMM rainfall are smaller than those by gauge data, but the differences are small in every year.And in the range of 10-25 mm, the contribution rates are nearly equivalent between these two datasets.It is noted that TRMM data shows reasonable performances at annual scales.So it reproduces the surface observation-based histogram of precipitation.
The correlation coefficient (CC), probability of detection (POD), false alarm ratio (FAR), critical success index (CSI), and normalized root mean square error (NRMSE) are displayed at the different time aggregation.
Figure 5  In order to further evaluate the relationships between the two data sets, the scatter plots of monthly TRMM rainfall against rain gauges rainfall data is shown in Fig. 6.The comparison was made for the five national meteorological stations and the areal average data of the nearest TRMM pixel.The results indicate very good linear relationship between the two rainfall datasets, with the determination coefficient (R 2 ) ranging from 0.79 to 0.90.The slope of the regression line ranges between 0.83 for Huzhou and 1.00 for Changxing, and 0.90 for areal average dataset.These values again indicate that the TRMM satellite tends to underestimate the monthly rainfall in this area.In general, the TRMM satellite is able to well capture the rainfall characterization well in comparison with the rainfall measurement from traditional rain gauges in different locations of the Tiaoxi watershed, although the systemic errors are also noted at monthly time step.

Hydrological processes simulation
To evaluate the runoff predictions by using the two rainfall datasets, experiment based on the SWAT model were conducted with input from by gauge rainfall and TRMM rainfall across the Tiaoxi watershed.SWAT contains parameters that need to be determined by using calibration.However, calibrated values are affected by correlations among parameters and observed data.For avoiding the effect of two dataset in calibration, the Nash-Sutcliffe efficiency index is used as the objective function, to evaluate hydrologic processes in two scenarios.The first scenario, the daily rain gauge rainfall was used to drive the model and optimize the parameter values, and then the daily TRMM rainfall was used to run the model with same parameter values, and the simulated runoffs in the two model runs were compared to each other.In the second scenario, the daily TRMM rainfall was used to drive the SWAT model and to optimize the parameter values, and then the rain gauge rainfall was used to drive the model.The result of parameters' optimization is shown in Table 2.
Table 3 shows the results of evaluation criteria of model performance.The model using conventional rain gauge data produced an overall good fit for hydrological processes in the first scenario.The relative runoff depth errors were lower than 2 %.In addition, the relatively high values of R 2 (from 0.93 to 0.94) showed that the model described the variation of the observed streamflow well.Therefore, based on the presented results, the model was believed to be robust and provided a sound basis for testing the precision and applicability of TRMM rainfall.However, skill from the SWAT model by using the TRMM rainfall data is relatively lower.The E ns values are not higher than 0.68 and the R 2 ranges from 0.75 to 0.84.In the second scenario, Table 3 shows that the TRMM rainfall-based model calibration had a slightly improved result with E ns ranging between 0.51 and 0.70 and also increased R 2 .
Figure 7 further compares the observed and simulated monthly runoff hydrographs from 1 January 2000 to 31 December 2008 based on TRMM rainfall estimate and rain gauges with their own optimal parameter values.It can be observed that the simulated streamflow hydrographs driven by rain gauge data exhibit a closer agreement with the observations than the model simulation using TRMM rainfall.Although extreme flow peaks tended to be underestimated in the model simulation with the TRMM rainfall, the results indicate that the TRMM rainfall data are still feasible for monthly stream flow simulation in this study area, According to Arnold et al. (2012), models are considered be very reliable if the monthly Nash-Sutcliffe efficiency index (NSE) is greater than 0.75.TRMM rainfall data has potential to be an alternative data source for the datapoor or ungauged basins, particularly in developing countries or remote locations.

Water balance
In addition to the comparison of streamflow hydrographs, water balance result is another important indicator for testing the validity of rainfall data (Xu et al., 2013).We examined the differences of water balance components from monthly streamflow simulations using rain gauges and TRMM rainfall.According to the above modeling results, comparison of the averaged water balance components from 2000 to 2008 is shown in Table 4.The model shows that the water balance partitions the precipitation into evaporation, transpiration, surface runoff and groundwater recharge (includes base flow).In the rain gauge driven calculation, 49.0 % of precipitation were exhausted through evaporation and transpiration, while the rate is 50.2 % in TRMM rainfall data case.The groundwater recharge is 17.2 and 14.8 % respectively in gauge rainfall and TRMM rainfall case.Groundwater recharge is a large component and determines the amount of base flow.Although the volume of precipitation has a little difference (1268.0 and 1322.8 mm yr −1 ), the estimated groundwater recharges are very similar (217.9 and 193.8 mm).In the case of total runoff, more precipitation is distributed into runoff in gauge rainfall case (527.1 mm) than in TRMM rainfall case (507.8 mm).In fact, this difference is mainly due to base flow estimation difference, which is 356.3 mm for gauge rainfall case, and 312.9 mm for TRMM rainfall case while the differences of runoff volume are small (170.8 and 194.9 mm).

Conclusions
The paper compares TRMM rainfall retrievals with rain gauge data and evaluates the TRMM rainfall as forcing data for hydrological applications and water balance analysis at the Tiaoxi catchment, China.
The results show that the differences of areal average rainfall calculated from two rainfall sources are small within an acceptable extent, but differences of the maximal daily and maximal 5 day rainfalls are large.So that the daily TRMM rainfall data are better at determining rain occurrences and mean values than at determining the rainfall extremes.Furthermore, the simulation of monthly hydrological processes shows that the SWAT model using both two types of data produces an overall good fit, but the statistical results indicate that the TRMM rainfall data are not suited for daily streamflow simulation in this area.The comparison of water balance components calculated by two types of rainfall shows that both data sources could describe the volume value of runoff and its compositions, which is very useful for watershed management.
The TRMM data as an example of the satellite-based rainfall products have great potential for applications in hydrological simulation and water balance calculations at monthly or seasonal time steps.However, several shortcomings, such as the TRMM overestimates or underestimates in some years and areas cannot detect the extreme rainfall precisely, reducing the accuracy of streamflow simulation at short time steps and other applications including flood forecasting.
It is necessary to further develop algorithms of satellite-based rainfall estimation with combining different retrieval strategies in term of reaching better space-time resolutions and alleviating some of the deficiencies of single-sensor methods (Michaelides et al., 2009).And the extensive efforts of satellite based products evaluations are required in different climatic areas using different sensors and retrieval methods (Li et al., 2012).Moreover, as satellite-based rainfall data cover a great part of the world, we recommend an evaluation with global historical rainfall record (Matos et al., 2013).So that hydrologists and engineers could apply current generation satellite-based rainfall products for various purposes.
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ; Li 2499 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | • × 0.25 • spatial resolutions.The 3B42RT uses the TRMM Combined Instrument (TCI) dataset, which includes the TRMM precipitation radar (PR) and 2501 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Discussion
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Paper | Discussion Paper | Discussion Paper | Discussion Paper | and 3.1-5.2mm d −1 for TRMM data in 1999-2008, respectively.While the difference is small, areal average rainfall based on TRMM is higher than that based on rain gauge data in most years except 2006 and 2008.A comparison of rainfall SDs calculated from the two data sets shows a greater difference than areal average rainfall.Maxim daily rainfall from rain gauge data is 56.
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | shows the results of analyses at different time resolutions from one day to one month.Precipitation maps have been first temporally aggregated to the time resolution before evaluation analyses.Then, spatially averaged analyses for each time resolution were derived.A constant threshold value equal to 1.0 mm/24 h has been used to compute values.The values of indices on the daily scale, as CC = 0.57, POD = 0.60, and CSI = 0.46, are smaller than on the monthly scale, as CC = 0.87, POD = 0.94, and CSI = 0.92, in addition the indices of FAR and NRMSE are decreased from 0.34 and 265 to 0.02 and 40 with the increase of temporal resolution.The results underline that statistical indices describe an improvement of performances as time aggregation increases.And TRMM provides reasonable performance at monthly scales.2507 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

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Figure 3 .Figure 4 .
Figure 3.The soil type map of study area.
Where FAR indicates the amount of rainfall occurrences detected by the considered estimation product when the reference data set is not indicating rainfall.It is equal to 0 if estimates do not reproduce any false occurrence and 1 if all registered occurrences do not correspond to observed data.Where CSI indicates the overall fraction of events that are correctly captured by the TRMM data.CSI is equal to 1 if the analyzed data can represent all occurrences and the estimates do not reproduce any false occurrence.

Table 1 .
Comparison of statistical indexes between areal averaged TRMM rainfall and rain gauges rainfall.

Table 2 .
Sensitivity analysis results for hydrologic parameters.