The study demonstrates that the temporal downscaling of rain gauge–measured precipitation with satellite-based precipitation estimates enhances the accuracy of hydrological simulations, especially for flood duration. Multiple regression analysis was examined to predict which hydrometeorological parameters have a significant influence on accuracy. The approach was examined at the Hương River basin in Vietnam (1520 km2), which is a mountainous region subject to heavy rainfall. The multisensor algorithm Global Satellite Mapping of Precipitation, version Moving Vector with Kalman (MVK; GSMaP_MVK; Psat), was employed to downscale the daily gauge precipitation measurements into 6-h time steps. Discharge in the rainy season in 2006–09 was simulated by a distributed hydrological model with 6-h time steps with four precipitation datasets: 6-h gauge (Pcontrol), daily uniform gauge (Puni), Psat, and the downscaled satellite product (Pds). Flood simulation with Pds performed better than that with Puni in 14 out of the 18 flood events, being close to the results with Pcontrol (median Nash–Sutcliffe efficiencies of 0.776, 0.261, and 0.710, respectively). Multiple regression analysis showed that the effectiveness of the downscaling method was significantly related to the bias and random errors of the satellite product. In conclusion, satellite-based precipitation measurements have potential for temporal downscaling of discharge simulations from daily to subdaily resolutions in moderate-sized watersheds that lack subdaily rainfall records, and the degree of simulation improvement can be estimated by statistical analysis. The suggested method can be broadly applied to watersheds where the daily precipitation is measured and when satellite-based precipitation measurements are available.
Flood simulation should be performed with spatial and temporal resolutions that are as high as possible, especially for a mountainous or small watershed that has a quick hydrological response (Wang et al. 2009; Waichler and Wigmosta 2003). High-resolution simulations can greatly contribute to river management. Historical records permit one to prepare “flooding” maps to analyze flood characteristics and to evaluate catastrophic flood disasters. However, it may be difficult in developing countries to obtain the input flood-causing data required. The number of rain gauges may not be enough to cover a target area, and the frequency of measurements may be insufficient to capture an intensive event such as a short storm. The temporal resolution of rainfall data available for practical applications is often lower than that required for hydrological models (Aronica et al. 2005). This may be because obtaining records with a high resolution using rain gauges is too expensive because of the number of rain gauges required in comparison to discharge measurement in watersheds. In most cases, precipitation records accessible in developing countries or in historical archives are on a daily basis (Beuchat et al. 2011; Segond et al. 2006), especially from areas that are geographically difficult to get to such as hilly mountainous terrain. Hourly or subdaily rainfall data may only be available for recent years or for a few gauges (Choi et al. 2008). Therefore for flood simulation on a finer temporal scale, the coarse daily temporal resolution of these rainfall measurements needs to be downscaled.
To solve this issue, satellite-based precipitation measurement and downscaling methods have been broadly implemented. Satellite-based precipitation measurement has greatly contributed to hydrology since the Tropical Rainfall Measuring Mission (TRMM; Simpson et al. 1988) was launched in 1997. The combination of satellite precipitation products with a hydrological model has great potential to estimate flood events (Schultz 1996) because the sensors on satellites can capture the heterogeneity of precipitation patterns with high temporal (e.g., TRMM 3 h) and spatial resolutions (0.25° × 0.25°) currently. Several satellite products were compared to each other by directly using them as inputs to the hydrological simulation (Behrangi et al. 2011; Bitew et al. 2012). However, the bias and random errors of the products must be considered because the rainfall retrieval algorithms are based on some assumptions, such as hydrometeor profiling for rainfall and a lookup table for determining the intensity (Berg et al. 2006). Most of the products tend to underestimate strong and local precipitation intensity (Jobard et al. 2011); however, satellite-based rainfall estimations provide a good representation of rainfall patterns on a large scale (Collischonn et al. 2008). Hence, the adjustments of these biases and errors have often been discussed for basin (Tobin and Bennett 2010) and regional scales (Boushaki et al. 2009; Tian et al. 2010b). Current statistical schemes that consider these errors were briefly summarized by Li and Shao (2010). However, there is no research that clarifies under which conditions hydrological simulations will perform sufficiently well if using satellite-based precipitation measurements containing such errors.
Temporal downscaling schemes of daily rain gauge data offer a primary solution to the resolution problem. The concepts of disaggregation have considerable advantages because they can increase the resolutions of hydrological processes (Koutsoyiannis 2003). Approaches for disaggregation often derive from stochastics (Lanza et al. 2001), statistics (Onof et al. 2000; Beuchat et al. 2011), and heuristics (Langella et al. 2010). The notable advantage of these methods is its applicability not only to archived data but also for future prediction products such as short-term forecasting and general climate models (Trigo and Palutikof 2001). The common drawback is that the accuracy of the disaggregation techniques may become poor if only few or no historical records exist at the locations of interest (Koutsoyiannis 2003). Furthermore, these stochastic methods sometimes miss extreme events that are hard to predict from the long-term flooding tendency.
The change in simulation response of hydrological models due to the resolution of precipitation data must be considered (Salathé 2003). The spatial resolution of inputs significantly influences the accuracy of hydrological simulation (Yang et al. 2001). Therefore, many spatial interpolation methods have been developed for rainfall data (Cho et al. 2009; Tetzlaff and Uhlenbrook 2005). However, the effect of temporal changes of precipitation intensity on the model response has not been deeply explored. The effect of a temporal resolution of precipitation of less than 1 day on the accuracy of discharge simulation was recently demonstrated by Littlewood and Croke (2008) and Wang et al. (2009). The former group studied a small catchment (10.6 km2) in Wales with the time step ranging from hourly to daily; and the latter group examined a small domain (0.21 km2) in Japan with a time step ranging from 10-min intervals to 1 day. Both cases asserted the advantages of using precipitation data with higher temporal resolutions within daily time steps. However, this concept needs to be further examined over much larger watersheds. Moreover, little research has been conducted aimed at downscaling rain gauge precipitation from daily to subdaily resolution using satellite data in order to enhance discharge simulation on a basin scale in comparison to regional and global scales (Boushaki et al. 2009). For temporal downscaling of rain gauge data from basins with a sparsity of rain gauges, we assume the following: 1) regional measurements with high temporal resolution such as subdaily rain gauge and radar measurements are unavailable, and 2) the “statistically unexpected” heavy rainfall must be properly captured.
The aim of our study is to examine the effect of temporal downscaling once-a-day rain gauge precipitation measurements to a subdaily resolution using a global satellite–based rainfall product on hydrological simulation of a moderate-sized steep watershed. This objective is achieved in four steps. First, the accuracy of the satellite precipitation product is evaluated in comparison with the subdaily rain gauge–measured precipitation within a basin scale at subdaily resolution. Second, the daily rain gauge data are downscaled to subdaily using the satellite product and compared with subdaily gauge measurements to evaluate the validity of the downscaling scheme. Third, a flood simulation on the study area is conducted with four precipitation datasets: subdaily rain gauge, daily rain gauge, satellite-based precipitation, and the downscaled satellite precipitation product. Finally, performance and multiple linear regression analyses are conducted to evaluate quantitatively the conditions under which hydrometeorological condition the downscale approach using satellite data significantly enhances the discharge simulation.
2. Study area
The Hương River basin, capturing the heaviest precipitation in Vietnam during the monsoon season from September to November, is located in Thừa Thiên-Huế Province of central Vietnam between 16° and 17°N and 107° and 108°E. The total catchment area is 2830 km2, the topography varies from 1 to 1708 m MSL, and the mean basin slope is 28.5%. The terrain of the region is classified as hilly mountainous terrain. The Hương River has three main tributaries, the Tả Trach, the Huu Trạch, and the Bo. We targeted two subbasins, as shown in Fig. 1: the Tả Trach basin (drainage area 729 km2 and stream length 51 km) and the Huu Trạch basin (691 km2 and 70 km, respectively). The total catchment area including their confluence is 1520 km2. The confluence of the tributaries causes floods and damages to the downstream city of Hué. Floods with threat water levels occur 3.5 times per year statistically (NCAP 2008). The flood control point, Kim Long station, was chosen as the outlet of the study area. The outlet and the lower inundation area are affected by tides in dry season with salty water intrusion, but this effect is negligible in flood simulation.
a. Geomorphology data preparation
The geographic data gathered to support modeling are gridded maps of elevation, soil type, vegetation index, and land use. The Shuttle Radar Topography Mission (SRTM), which is a digital elevation model (DEM) with a 90-m resolution, was used to determine the topography of the basin. The SRTM is an international project spearheaded by the National Geospatial-Intelligence Agency and the National Aeronautics and Space Administration (NASA). The soil type map representing several parameters such as hydraulic conductivity and porosity was collected from the global soil type map of the Food and Agriculture Organization (FAO) Harmonized World Soil Database, version 1.2 (FAO et al. 2009). The vector data were converted to three categories of soil type of raster with a 1000-m grid size (Fig. 2a). The dominant soil type is acrisol with coverage of 95% and the entire region is composed of silt (Table 1). The downstream area around Hué city is dominated by low hydraulic conductivity while the conductivity in the subbasin of Tả Trach is relatively high. The leaf area index (LAI), with a spatial resolution of 1000 m and a temporal resolution of 8 days, was used for the calculation of evapotranspiration from vegetation. It is derived from bands 1 and 2 of the Moderate Resolution Imaging Spectroradiometer (MODIS) on board NASA’s Terra satellite (ORNL DAAC 2011). The land use type was classified using a map provided by the Vietnamese National Centre for Hydro-Meteorological Forecasting. The 1000-m land use data showed six categories for the region (Fig. 2b). The target area is dominantly composed of evergreen broadleaf trees (56%) and evergreen shrubs (20%). The remaining parts are deciduous broadleaf trees (8.7%), tall grass (8.4%), cropland (5.2%), and bare soil with shrubs (1.3%).
b. Precipitation datasets
The rain gauges and the satellite-based precipitation estimates are spatially distributed as shown in Fig. 1. Rainfall amounts are observed by the seven gauges surrounding the basin. The available temporal resolutions are 6 h and daily. The mean values of the annual and monthly precipitations from September to November in 2006–09 are summarized in Table 2. The precipitation amount in the rainy season is nearly 75% of the annual precipitation (2487 of 3329 mm). The heaviest rainfall occurred in October with a mean of 1093 mm. The rain gauge precipitation data was spatially interpolated by inverse distance weight (IDW), which is relatively fast and easy to compute and frequently used in hydrology (Lu and Wong 2008). Besides the ground network, we also gathered the Global Satellite Mapping of Precipitation, version Moving Vector with Kalman (MVK; GSMaP_MVK), which estimates hourly quasi-global precipitation patterns with a grid spacing of 0.1° latitude–longitude. The following various sensor algorithms are merged to retrieve rainfall rates: passive microwave radiometers of TRMM/TRMM Microwave Imager (TMI), Aqua/Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E), Advanced Earth Observing Satellite-II (ADEOS-II)/Advanced Microwave Scanning Radiometer (AMSR), Defense Meteorological Satellite Program (DMSP)/Special Sensor Microwave Imager (SSM/I), and infrared brightness temperature provided by National Centers for Environmental Prediction (NCEP)/Climate Prediction Center (CPC). The version MVK is reanalyzed using bias retrieval from the near-real-time product (version NRT). GSMaP project activities are promoted by the Japan Aerospace Exploration Agency (JAXA) Precipitation Measuring Mission Science Team (Okamoto et al. 2005). All datasets were handled with Geographic Resources Analysis Support System (GRASS) GIS, version 6.4.2 (GRASS Development Team 2012).
Four precipitation datasets with 6-h temporal resolution were prepared for the hydrological simulation: Pcontrol, Puni, Psat, and Pds. The quantity Pcontrol is the 6-h rain gauge precipitation previously, which is a control dataset to evaluate the validity of a temporal downscale approach. The quantity Puni is obtained by dividing the daily cumulative amount (Pday) by four (Puni = Pday/4). The quantity Psat is the GSMaP_MVK, which is an amount accumulated from 1 to 6 h. The quantity Pds is the 6-h precipitation downscaled from the daily cumulative amount by Psat:
where i distinguishes time step in a day with a temporal resolution of 6 h (e.g., time step i = 1 represents 0100–0600 LT; local time is UTC + 7 h).
Note that the temporal change of the basin mean precipitation amount estimated by Psat is used for downscaling. We assume that Pcontrol represents the most reliable estimation of precipitation on the basin. Therefore, how much the downscaled precipitation Pds resembles the Pcontrol is the issue in this study. To evaluate the significance, we intentionally set the daily uniform value Puni, which is to be compared with Pds.
c. Distributed hydrological model
A physically based distributed hydrological model (DHM) was applied to the target basin to simulate the discharge at the outlet with the four precipitation datasets. The DHM employed is the geomorphology-based hydrological model (GBHM; developed by Yang et al. 2002; see Fig. 3 and appendix for details). Hydrological processes such as precipitation, canopy interception, evapotranspiration, infiltration, percolation, and groundwater flow are simulated. The discharge is computed with the kinematic wave equation. The computational grid size was set to 500 m and the unit time step was set to 6 h in order to include the heterogeneity of the precipitation pattern, land use, and soil type inside the basin. The accumulated time steps start at 0100 LT 1 September and continue to the end of November. Parameter calibration was conducted by the University of Arizona Shuffled Complex Evolution (SCE-UA) method by using the Pcontrol precipitation data in 2006 (Duan et al. 1993; Fig. 4). The initial conditions of the soil moisture, the groundwater level, and the discharge were obtained by spinning up the model 3 months ahead of 1 September (June–August). We confirmed that the selected spinup time was satisfactory for flood discharge simulation in this research. The initial soil moisture value, which was set to 0.25 in June, was adopted from the satellite-based soil moisture estimation provided by the Soil Moisture Climate Change Initiative of the European Space Agency (Naeimi et al. 2009). The simulated discharge was compared to the observed discharge at the outlet of the watershed.
The parameters of soil and land use were optimized in the feasible value ranges for the purpose of maximizing the value of Nash–Sutcliffe efficiency (NSE) with Pcontrol (Table 3). The saturated hydraulic conductivity at the top soil layer and the surface roughness for calculating overland flow used have high values [162 mm h−1 and 0.21 (unitless), respectively]. The anisotropy ratio of the surface soil layer was also set to a high value (17.8). These high values might imply the existence of a litter biomat, in which flow can be assumed to follow Darcy’s law for a soil surface with very high conductivity (Sidle and Hirano 2007). In the forested areas of Vietnam, high conductivity was often reported [e.g., the value 10–290 mm h−1 for forests in Vietnam was observed by Ziegler et al. (2004)]. Hence, the values of the optimized parameters used are reasonable. Although the parameters could be more finely calibrated with a longer running period [e.g., 3–5 yr recommended by Gan et al. (1997)], a previous study (Saavedra V. et al. 2009) demonstrated enough simulation accuracy of a 1-yr calibration. The performance indicators of the calibration—correlation coefficient R, mean bias (BIAS), root-mean-square error (RMSE), and NSE—were 0.97, 3.7%, 130 m3 s−1, and 0.927, respectively. The validation period was set to September–November in the following 3 yr from 2007 to 2009.
The model calibrated by Pcontrol can be assumed to represent the most feasible hydrological parameter set for the basin in this research. The validity of the downscale scheme is tested by comparing Pcontrol with Psat, Puni, and Pds as illustrated in Fig. 5. Each discharge simulation result is represented by an amount Q with its corresponding subscript—control, sat, uni, and ds. In general, calibration for each precipitation product enhances the individual performance for the discharge simulation by making the best use of its data characteristics. However in contrast, we aim to evaluate the intrinsic performances of these datasets from a statistical point of view. Therefore, the conditions for the model— values of the hydrological parameters, time resolution, and initial condition—were fixed to the calibration based on Pcontrol.
d. Performance statistics
The basin average values for Psat and Pcontrol were compared in order to evaluate the precipitation detection ability of the GSMaP_MVK. Linear regressions was conducted in each year to show the gradient, intercept, and R2 with the explanatory variable of Pcontrol. The probability of detection (POD), the false alarm ratio (FAR), and the critical success index (CSI) were also calculated for each month (September–November) with a minimum threshold of 0.1 mm h−1. The best performance of the satellite product provides values of POD, FAR, and CSI of 1, 0, and 1, respectively. The equations are expressed by
where hit is the number of rainfall events that both the satellite and the rain gauge detect, miss indicates that the satellite shows no rain but the rain gauge actually measures precipitation, and false counts the events that the satellite shows as rain and no rain is detected by the rain gauge.
2) Discharge simulation
For the evaluation of the discharge simulations of Qcontrol, Qsat, Quni, and Qds, a set of performance indicators was also used. The correlation coefficient R, the mean bias, the RMSE, and the NSE were computed for total durations in each year and for individual flood events:
where t is the computational time step, n is the total number of the simulation time step, Q(t) is discharge (m3 s−1) at time step t, the subscripts s and o mean the discharge simulated and observed, and the bar over Q indicates the average value over n.
e. Multiple regression analysis for NSE
Multiple linear regression analysis is finally applied for evaluating the simulation with the different precipitation datasets in terms of the NSE value. We aim to detect under which conditions 1) the performance of the discharge simulation is high during flood events, 2) the assumption of uniform distribution of precipitation (Puni) degrades the simulation, and 3) the downscale approach (Qds) is close to the control simulation (Qcontrol). The equation, given k explanatory variables (x) and n observations, is described as
where y is the response variable, the a values are the estimated parameters for the regression equation line, and ε is the model deviation. Here, y was set to the NSE of Qcontrol, Quni, Qds, and the difference between NSE of Qcontrol and Qds (ΔNSE). The smaller ΔNSE is, the better the downscaling effect performs.
The best parameter combination was calculated by minimizing the sum of the squares of the vertical deviations from a line to the data point. Then, the best-fitting model was selected by minimizing Akaike’s information criteria (AIC). All combinations of the explanatory variables were examined. We omitted variables that are highly correlated with each other in order to avoid multicolinearity (|R| > 0.7). The significance of the chosen variables was evaluated by their p values. The explanatory variables are listed in Table 4. Data analysis was performed with R software, version 2.15.1 (R Development Core Team 2013).
4. Results and discussion
a. Precipitation analysis
1) Rain gauge and GSMaP_MVK
The overall scores of POD, FAR, and CSI during the target periods were 0.62, 0.14, and 0.56, respectively (Table 5). Sapiano and Arkin (2009) reported a similar value of POD and higher value of FAR for other 3-h satellite products on a global scale. The relatively low score of FAR in our study may be attributed to high and frequent rainfall during the target season. The monthly evaluation showed wide ranges of POD (0.43–0.90), FAR (0.03–0.36), and CSI (0.38–0.83). The PODs and CSIs tend to be high in September and low in November. This seasonal effect of GSMaP, high in the warm season and low in the cold season has been found to be one of its general characteristics (Tian et al. 2010a). The lowest CSIs were found in November in all the target periods. Overall, the MVK product showed an acceptable ability to detect precipitation events with a low false alarm frequency at 6-h temporal resolutions.
Linear regression for the basin mean precipitation amount of the rain gauges and the MVK was also examined at daily and 6-h resolutions in the target periods (Fig. 6). The gradients of the regressions for both these temporal resolutions showed similar values. The MVK intensity estimates are three times less than the rain gauge estimates (0.37 for daily and 0.36 for 6 h). The R2 of daily resolution was higher than that of 6-h resolution (0.58 and 0.52). The gradient and R2 of 6-h resolution in each year showed various ranges (Table 6). MVK estimates in 2008 and 2009 were closer to the rain gauge observations than in 2006 and 2007.
2) Precipitation datasets: Pcontrol, Puni, and Pds
Linear regression analysis was also conducted for the three precipitation datasets for each year: Pcontrol, Puni, and Pds. The quantity Pcontrol was considered a reference, and Pds and Puni were compared in order to check the effects of the downscaling method (Figs. 7a–d). During all the target periods, gradients and intercepts of the linear regression of Pds were much closer to 1:1 line than those of Puni, as shown in Fig. 7. This indicates that the downscaling from daily to 6 h with MVK can follow the temporal patterns of precipitation intensity. The gradients of Puni were lower than 1.0 for the durations, which means that using a daily uniform distribution loses the variability of the intensity present in a given day. Furthermore, the intercepts of Puni were higher than those of Pds. This is because Puni assumed a uniform precipitation intensity over a day even if there were a no rain interval detected by Pcontrol. By contrast, the R2 values of Puni were higher than those of Pds, except in 2008. From the viewpoint of discharge simulation, the accuracy of temporal flow variability can be strongly related to R2; and that of peak amounts tend to rely on the gradient. Among them, which is the one more critical for basin flood simulation can be further argued with multiple linear regression.
b. Discharge simulation
1) Performance of simulation with four precipitation datasets
Discharge was simulated with the four precipitation datasets: Pcontrol in 2007–09 for validation and Puni, Pds, and Psat in 2006–09. The parameter sets of the model were consistent with the calibration conducted by Pcontrol (Table 3) for all the precipitation products in order to compare the different hydrological responses directly by multiple regression analysis, though individual calibration may enhance the accuracy for each product (Bitew and Gebremichael 2011). The average values of R, RMSE, and NSE of Qcontrol were 0.966, 203, and 0.922, respectively. The variable Qds (0.955, 208, and 0.903) was slightly worse than Qcontrol but surpassed Quni (0.948, 223, and 0.884) and Qsat (0.76, 596, and 0.257), as shown in Table 7. In addition, Qds performed better than Quni from 2006 to 2008 in terms of R, RMSE, and NSE. This indicates that using downscaling from daily to subdaily resolution with the satellite product provides more accurate flood simulation than using daily rain gauge precipitation data alone. Generally, Qsat showed the worst performance because GSMaP_MVK has a strong negative bias for the estimation of precipitation intensity and weak precipitation is only stored in the soil layer. The correlation coefficient R and NSE of Quni and Qds were lower than Qcontrol, and conversely, their RMSEs were higher in every target year.
2) Flood simulation analysis
The total number of flood events was 18 during the target periods (three in 2006, six in 2007, five in 2008, and four in 2009). For each flood event, an ID was assigned sequentially for further discussion. Time steps, observed discharge, NSE performance evaluation of the three simulations, initial soil moisture, measured precipitation, and evaluation indicators for the satellite are summarized in Table 8. The bold font of the NSE value emphasizes that Qds performed better than Quni during a flood event. Median values of NSEs calculated for the simulations Qcontrol, Quni, and Qds were 0.776, 0.261, and 0.710, respectively. In addition, in 14 out of 18 cases, the NSE of Qds was higher than that of Quni. For the other four cases, the NSE of Qds was slightly lower than that of Quni, with very high Qcontrol NSE (>0.90). Mean, median, quartile, and outliers of NSEs of Qcontrol, Quni, and Qds were compared with a box-and-whisker plot to see the variability of the accuracy of the flood simulations (Fig. 8). Overall, the scores of the NSEs of Qds were slightly worse than that of Qcontrol, but they showed significantly high performance.
A comparison of the NSE of Quni and Qds with that of the control simulation Qcontrol is plotted in Fig. 9. The lower the NSE of Qcontrol is, the larger the positive effect of the downscale method will be, as shown by the vertical gap between the two regression lines. By comparing Table 8 with Table 7, the effectiveness of the downscaling approach in the flood simulation is more emphasized than that in the 3-month evaluation in terms of NSE.
Multiple regression analysis was conducted to describe NSEs of Qcontrol, Quni, Qds, and the difference between NSEs of Qcontrol and Qds [ΔNSE = NSE(Qds) − NSE(Quni)]. As explanatory variables, the number of sequential flood events (npeak), total time steps during flood event (ttotal), initial soil moisture (iniθ), logarithm of mean precipitation (meanP) to base 10 (), and the coefficient of variables of the precipitation (CVP) were selected for explaining the NSE of Qcontrol and Quni. Mean soil moisture during flood (meanθ) and standard deviation of the precipitation (SDP) were eliminated from the analysis to avoid multicollinearity. The variables for the discharge (meanQ, SDQ, CVQ, and peakQ), none of which were inputs for the model, were not taken into account. In addition, the satellite performance indicators (POD and FAR) and the gradient (grad), intercept (intcpt), and R2 of the linear regressions were introduced to describe NSE(Qds) and ΔNSE. POD was not used because of its high correlation with CSI. According to the AIC criteria, the best fittings with nonstandardized partial coefficients for the set of NSEs were selected:
All results were statistically significant (p < 0.01) and the adjusted R2 values were 0.51, 0.55, and 0.75, respectively. The results also showed that simulation accuracy (NSE) tends to be high in accordance with strong precipitation intensity expressed by in Eqs. (10)–(12). Therefore, the GBHM we used can be specialized for large flood events. Equation (10) indicates that the model with Pcontrol becomes accurate when both the initial soil moisture (p < 0.05) and the mean precipitation amount (p < 0.01) are high. The duration, number of peaks, and degree of fluctuation of the precipitation pattern may not affect the simulation significantly. This result supports the importance of simulating the sequence for the soil moisture. Equation (11) explained by (p < 0.01) and CVP (p < 0.01) indicates that the performance of the model with Puni is degraded if the temporal pattern of precipitation fluctuates strongly, though the p value is relatively high (<0.1). This is a feasible implication because Puni is uniformly distributed precipitation that has lost its subdaily temporal change. Equation (12) showed that Qds was related to the linear regression of Pcontrol and Psat (both grad and intcpt have p < 0.05), in addition to initial soil moisture (p < 0.01) and mean precipitation intensity (p < 0.01), which similarly influenced Qcontrol. Because grad is 1 and intcpt is 0 in an ideal case, the negative influence of high intercept on discharge simulation is reasonable. The lower the gradient is, the higher is the NSE value estimated. This implication may be related to large errors in the satellite estimation; the overestimation of precipitation intensity by the satellite (high gradient in the linear regression) may worsen the effect of this method. We found that the NSE of Qds tended to be high if the gradient was close to 0.36 (Table 8); this value was similar to that calculated from the long-term analysis in Fig. 6b. We interpreted that excessive deviation from the gradient value degrades the effectiveness of the downscaling approach, whether it is over- or underestimation. The overestimation may happen because the satellite sometimes cannot follow the subdaily temporal pattern.
The difference between Qcontrol and Qds was also significantly explained (p < 0.05 and the adjusted R2 = 0.49):
Equation (13) indicates how the downscaling of daily rain gauge data with the GSMaP_MVK can yield results that closely resemble Pcontrol in terms of the flood simulation. It can be interpreted that the downscale performance is excellent if ΔNSE is close to 0. The positive value of ΔNSE indicates that the performance of Qds is lower than that of Qcontrol. From Eq. (13) it was assumed that the downscaling method can be successful if: the mean precipitation is low (p < 0.01), the satellite product underestimates precipitation intensity (grad, p < 0.1), the intercept is high (p < 0.05), and the satellite precipitation correlates highly to the rain gauge measurement value (R2, p < 0.05). The analysis showed no significance of the meteorological performance indicators (CSI and FAR). Therefore, it may be preferred to evaluate satellite-based precipitation estimation with regression analysis, which can include the degree of the error of the intensity in addition to the conventional meteorological indicators for using the product for hydrological application.
3) Representative flood simulations
We visualized three representative flood events (IDs 6, 17, and 14) showing the effect of the downscaling in order to compare the temporal patterns of discharge, estimated mean soil moisture, and precipitation (Figs. 10a–c). The amounts of the peak discharges Quni were generally underestimated. This may be due to the nonlinearity of the runoff generation mechanisms (Marani et al. 1997). The event ID 6 showed the largest difference of the NSE values Quni (−1.166) and Qds (0.590; Fig. 10a). This flood was quick because of the short duration and high intensity of the precipitation. The quantity Pds captured the strong timing, though it could not detect weak precipitation before and after the peak duration. The quantity Quni showed a delayed peak. Event ID 17 had four flood peaks showing the high fluctuation of the discharge for 8 days (Fig. 10b). The quantity Qds also clearly represented the short, strong precipitation three times. In comparison, Quni combined the last two flood peaks and the peak discharge was low. Furthermore, the pattern of the soil moisture estimated with Pds was similar to that with Pcontrol. This may contribute to simulation of the flood discharge with an acceptable accuracy. However, event ID 14 showed that the method significantly degrades the simulation accuracy (NSE became 0.994–0.789; Fig. 10c). The main reason is assumed to be that the temporal pattern of the precipitation was smooth and continuous despite the large errors of Pds.
We demonstrated the effect of a method of temporal downscaling of daily rain gauge precipitation with a global satellite precipitation product on hydrological simulation and compared the results with the controlled simulation. This research quantitatively showed the advantage for flood simulations with high temporal resolution on a middle-sized steep basin of applying subdaily satellite-based precipitation values to downscale daily rain gauge measurements. The applicability of the subdaily downscaling concept at the basin scale ha been further expanded. The enhanced satellite precipitation product could capture the temporal patterns of strong intensity and provide data at 6-h resolutions similar to that of 6-h rain gauge measurements. Though the satellite algorithm generally underestimated the rainfall intensity, it can be utilized to capture the temporal pattern. The method can be broadly applied to watersheds where subdaily discharge and daily precipitation records can be obtained in combination with any kind of satellite precipitation products. In such cases, a hydrological model should be calibrated with the downscaled precipitation product. In addition, once the model is calibrated with subdaily precipitation data collected in recent years, the method can use historical daily precipitation archives for downscaling in discharge simulations.
While the downscaling method we applied is simple, we proposed that uncertainty inside the complexity of hydrological models could be quantitatively analyzed with the multivariate statistical approach. Analysis of the uncertainty is often neglected in hydrological model evaluation because of the complexity of the parameter combinations (Benke et al. 2008). However, we tried to explain why the accuracy and the effectiveness of this method changes depending on flood events and which parameters critically influence the simulation by using multiple regression analysis. We introduced statistical analysis to shed light on the complicated uncertainties in hydrology. One important factor for flood simulation is the initial condition of the soil moisture before flooding. The soil moisture significantly affects hydrological simulation (Zehe et al. 2005). The importance of soil moisture estimation was also reported by Brocca et al. (2009, 2010). The discharge prediction can be further improved by assimilating remotely sensed soil moisture (Pauwels et al. 2001; Srivastava et al. 2013). Another finding is that the effectiveness of using a satellite precipitation product for subdaily downscaling can be estimated by a performance indicator such as R2. Therefore, we suggest evaluating several satellite products beforehand if possible, since the accuracies may depend on the target location. Although we examined the statistical analysis of the temporal pattern, the same approach can be applied to evaluate the spatial variability of satellite-based precipitation. By accounting for the nonlinearity of the hydrological processes for evaluating the model performance, the statistical approach may be more effective for detecting model uncertainty.
The validated method is compatible with other approaches such as the statistical and probabilistic downscaling methods. We recommend utilizing this weighting method in parallel with other approaches in order to enhance the performance of hydrological models. In addition, it is worth examining this scheme with shorter time steps such as 3 h or with near-real-time satellites. We expect that the utilization of satellite-based precipitation measurements will be further enhanced for real-time flood management for basins with sparse rain gauge networks such as in developing countries.
This study received support from the Japan Society for the Promotion of Science (JSPS) Asia Core program and the Japan Science and Technology Agency (JST) Core Research Evolutional Science Technology (CREST) project. This work was also supported by the 7th Precipitation Measuring Mission (PMM) Science Team under the auspices of the Japan Aerospace Exploration Agency (JAXA) and partially JSPS Core-to-Core Program, B. Asia-Africa Science Platforms. We thank Dr. Wade T. Crow for editing and processing the entire revision; the National Centre for Hydro-Meteorological Forecasting of Vietnam for guiding us in the field and sharing the observation data; and Dr. Y. Iwasaki, Dr. M. Fujii, and Ms. R. Sakazume for their help during this study.
Geomorphology-Based Hydrological Model
The model simplifies geomorphologic properties based on width and area functions (Herath et al. 1999) in order to reduce the computational time, which is of critical importance for flash flood estimation. The catchment was divided into subbasins using the Pfafstetter coding scheme (Verdin and Verdin 1999) and then into flow intervals according to equal flow distance from the outlet of each subbasin. A pair of symmetric hillslope elements is located along the stream segments. The pair of hillslopes is assumed to have the same topographical spatial variability inside the flow interval. The hillslope is a fundamental computational unit providing lateral inflow to the stream. It is represented by rectangular inclined planes. The impervious bedrock is assumed to be parallel to the surface. The length is calculated by dividing the area by the total length of the streams. The hillslope module simulates hydrological processes by solving governing equations: canopy interception, evapotranspiration, infiltration, percolation, and groundwater flow and its exchange with the river. The simulation sequence is performed at each flow interval, and then the volume of the water is gathered at the outlet along the direction of the streamline.
The total amount of evapotranspiration from canopy, vegetation, and soil surface is modeled by Sellers et al. (1996). The seasonal pattern of evapotranspiration is related to LAI. Potential evapotranspiration Ep (mm h−1) is calibrated. The hydraulic conductivity of the soil layer is assumed to decrease exponentially with increasing soil depth: , where k(z) and are hydraulic conductivity (mm h−1) at depth z (m) and at the top soil layer and f is the constant decay factor (Robinson and Sivapalan 1996). The soil layer depth was set to 1.5 m and was divided into 10 sublayers, with the thickness Δz as 0.15 m. At the aquifer layer with the depth of 7.5 m, the hydraulic conductivity (mm h−1) is constant.
The exchange flow among vertical adjacent sublayers of the soil is described by the one- dimensional Richards equation:
where t is time; , , and are volumetric water content, residual water content, and saturated water content, respectively; is hydraulic conductivity (m s−1) calculated with van Genuchten’s (1980) equation with the estimated parameters α and n; is capillary suction (meters); and is the evapotranspiration (meters).
The subsurface flow (m3 s−1 m−1) at each sublayer is calculated if the water content exceeds the field capacity :
where anik(z) is the anisotropy ratio of the hydraulic conductivity decreasing exponentially as well as k(z) and is the surface slope at the computational grid (in meters). Flow in the saturated zone is calculated by solving Darcy’s law with the hydraulic conductivity at the aquifer layer . The total water storage of the layer is expressed by the volumetric water content . The Horton overland flow is calculated with Manning’s equation with roughness coefficient and available water storage on the surface :
The river routine module simulates discharge by the kinematic wave scheme:
where x is the distance of the river section (meters), Q is the discharge, A is the area cross section (m3 m−1), is the total amount of lateral inflow from the hillslope, is the riverbed slope, is the roughness coefficient of the river network, and p is the wetting perimeter of the river section (meters).