Daily observed rainfall data from 34 rain gauges over Kyushu island were used as reference data to validate the GSMaP_MVK estimation. The rain gauge data were obtained from AMEDAS (Automated Meteorological Data Acquisition System) developed by the Japan Meteorological Agency (JMA) during 2005 to 2007 through the rainy season, from May to July. The distribution of the rainfall stations was shown in Figure 1. The total observation data were obtained by multiplying the total day (92 days × 3 years) and the number of rain gauge data (34 points). Due to some lack of in-situ data, the total of observational data was 9276. The data are available online at the JMA website (http://www.data.jma.go.jp).

GSMaP was initiated by the Japan Science and Technology Agency (JST) in 2002 and has been promoted by the Japan Aerospace Exploration Agency (JAXA) Precipitation Measuring Mission (PMM) science team since 2007 to produce a global precipitation product with high temporal and spatial resolution [23] . Moreover, the data set produced by GSMaP product can be downloaded from their website:

http://sharaku.eorc.jaxa.jp/GSMaP_crest/html/data.html. The standard version of the GSMaP data sets includes GSMaP_TMI (retrieved from TRMM/TMI algorithm), GSMaP_MWR (retrieved from six space borne microwave radiometers), GSMaP_ MWR+ (retrieved from six space borne microwave radiometers with AMSU-B product), GSMaP_MVK (retrieved from MWR GEO IR combined algorithm), GSMaP_ MVK+ (retrieved from MWR GEO IR combined algorithm with AMSU-B product) and other rainfall estimates from passive microwave radiometer [24] .

The GSMaP rainfall product used here for comparison with reference gauge data set is GSMaP_MVK product version 5. This product is the combination of low earth orbit multi satellite microwave radiometer data and infrared radiometer (IR) on geostationary (Geo) orbit. The available microwave sensors are SSM/I (Special Sensor Microwave/Imager), TMI (TRMM Microwave Imager), and AMSR-E (Advanced Microwave Scanning Radiometer for EOS). Whereas, the IR data sets used in the current version of the system are from the CPC (Climate Prediction Centre). The algorithm to regain surface precipitation rate based on the Aonashi, et al. (1996) was conducted in this product. The brightness temperature at microwave frequencies as the main input of GSMaP_MVK system was converted into precipitation data [23] . The combination technique to produce 0.1˚ in latitude and longitude and 1 hour resolution with the domain covering 60˚N to 60˚S was obtained using a morphing technique based on an infrared cloud moving vector and Kalman Filter technique (Ushio, et al., 2009). GSMaP_MVK version 5 is available from March 2000 until December 2010. Thus the history of rainfall data which caused flood in Kyushu Island can be obtained. The rain rate daily data of GSMaP_MVK from May to July in 2005 to 2007 were downloaded and then converted into accumulated daily rainfall of GSMaP_MVK. GSMaP_MVK was processed by using Open GRADS software and one-pixel average of precipitation data was calculated based on the rain gauge data position. Detail about GSMaP MVK was shown in Table 1.

The data coverage of this study was three years (2005 to 2007) in the rainy seasons. It was selected based on the annual flood occurrence in the study area. The main validation was for daily satellite rainfall product. As shown in Figure 1, the validation region has very complex terrain. Thus validation data from the whole island may not give the whole picture. Therefore, validation of the daily satellite products was conducted separately for the elevation (highland and lowland part of Kyushu), location (west and east of Kyushu) and heavy rainfall to investigate the performance of the product over different climatic regimes. Lowland was defined where the elevation was under 500 m and highland was defined where the elevation was above 500 m [16] The west and east Kyushu were defined by dividing the prefectures according to the wind direction. In addition, heavy rain was defined as daily rainfall exceeding the 95th percentile (rain_P95) for all stations and all categories [25] . Point by point analysis and spatial average analysis were conducted to compare gauge data and satellite data. [26] and [27] also applied this method.

Standard validation statistics are used to evaluate the GSMaP_MVK product to the rain gauge data. Qualitative and quantitative validations were conducted as follows. Qualitative method is to measure the correspondence between the value of the estimates and the observations. To quantify the correspondence value, the following five statistical indices were used [28] , the relative bias (B), the mean error (E), the Nash- Sutcliffe (C_NS), the Root Mean Square Error (RMSE) and the correlation coefficient (r). These indices are given by following Equations.

where, n is the total number of the rain gauge data or GSMaP data; S_i is the satellite estimates and G_i is the rain gauge observation values.

The other validation statistics is the quantitative method which based on the contingency tables shown in Table 2. The rainfall threshold used for rain/non rain discrimination is 0 mm/day.

In Table 2, A, B, C, and D represent “hit”, “false alarm”, “miss” and “correct negative”. “Hit” represents correctly estimated rain events, “miss” describes when rain is not estimated but actual rain occurs, “false alarm” represents when rain is estimated but actually rain doesn’t occur, and “correct negative” represents correctly estimated no- rain events. Using the results shown in Table 2, Probability of Detection (POD), False Alarm Ratio (FAR), and Heidke Skill Score (HSS) statistics parameters are calculated by following Equations.

where, POD explains how good the GSMaP estimates are in detecting the occurrence of rainfall. FAR shows how often the GSMaP detects rainfall when rain gauge measurement is zero. Furthermore, HSS measures the rainfall detection accuracy of the satellite estimates relative to matches resulting from random chance.

Comparison between GSMaP_MVK data with ground station measurement showed large differences during heavy rainfall as shown in the following sections. Therefore, the previous researchers obtained bias correction equations to achieve the best result. To accommodate for finding the relative bias varied with daily rainfall, a power function was applied to derive bias corrected rainfall (P*) [29] as follows:

where P is GSMaP_MVK, P₀ is the reference daily rainfall (1 mm/day), a (mm) is the constant and b is the power function. The linear regression analysis was previously applied to obtain the values of a (1.41 mm/day) and b (0.15) where all the data were transformed into logarithmic. This analysis is as a reference test for correction only for heavy rainfall section because this correction method has not been applied to the heavy rainfall case.

According to the previous research, GSMaP_MVK had underestimated the rain gauge data. Therefore, a bias correction equation was applied to achieve a closer fit between daily GSMaP_MVK and rain gauge data. GAM was applied because it has been widely adopted as an effective model and it has smoothing functions to analyze many complex time series data [17] . GAM have been widely employed in other disciplines to model the health impacts of air pollution or long term variability in biota spatial density, but rarely applied in hydrology [30] [31] .

GAM was created by R version 3.0.2 software, using the gam function of the mgcv package [17] , with the rain gauge data as response variables and GSMaP data as predictor variables. GAM model in the form of an Equation (10) was applied:

where g is the link function (identity link), µ is the expected value of the rain gauge data, α₀ is the model constant and f₁ is a smoothing function of the X (which corresponds to the daily GSMaP_MVK data) [17] . The α₀ was calculated according to the total average of AMEDAS data (i.e., 12.4 mm/day). In addition, when the GSMaP_MVK value is zero, the expected value of rain gauge data is equal to 2.16 mm/day.

The Gaussian distribution is generally used in GAM, but we did not use the Gaussian distribution because the distribution of the rain gauge data was asymmetric. The rain gauge data could be predicted using the predict.gam function in the mgcv package using similar covariates as were used to build the model.

This study first compared daily rain gauge data (AMEDAS) with GSMaP_MVK data. Figure 2 shows the scatter plot of AMEDAS data versus daily GSMaP_MVK data, the total data number and the mean values are also indicated in the plot. The validation statistics of GSMaP_MVK are listed in Table 3. In general, rainfall from GSMaP_MVK was lower than rainfall from rain gauge data: the average rainfall from rain gauge data was 12.39 mm/day, whereas the average rainfall from GSMaP_MVK was 6.59 mm/day. GSMaP_MVK data in the study area have a strong correspondence with rain gauge data

(r = 0. 74), with the bias value was −46.78%. Moreover, the variance magnitude of individual errors can be described by calculating the values of E and RMSE (i.e., −5.8 mm/day and 22.82 mm/day, respectively). The greater difference between them, the greater the variance in the individual errors in the sample.

Furthermore, the consistency of GSMaP_MVK to measure the rainfall amount can be described through C_NS index. The C_NS index of the study area was 0.46 (46%), it means that GSMaP_MVK has the consistency to measure the rainfall amount about 46%. POD of GSMaP_MVK are close to 81% and FAR is generally small (18%). The HSS statistic shows that the GSMaP_MVK estimates have reasonably good skills in detecting the occurrence of rainfall (67%).

A comparison of long term means of daily rainfall measured by GSMaP_MVK and rain gauge data for a three-year period was shown in Figure 3. Figure 3 indicated that the pattern of daily means was similar and had a very strong correspondence to rain gauge data (r = 0.9), but GSMaP_MVK data were underestimated, with the bias, mean error and RMSE were −46.75%, −5.78 mm/day and 9.02 mm/day, respectively. In addition, GSMaP_MVK had high consistency with the C_Ns value of 0.53. In general, GS- MaP_MVK product had underestimated. This will be partly because the current algorithm of microwave radiometer did not include the topographical effect and the brightness temperature from microwave radiometer had directly underestimate relation with precipitation [23] . Consequently, GSMaP_MVK data correction was needed to reduce bias, error and RMSE and to increase C_Ns and correlation coefficient. In this study, GAM approach was applied for bias correction.

The main topographic feature of Kyushu is land is the large mountain ranges which located in the center of the island and the plain regions that cover the eastern and western

part of the island. The elevation of mountainous region can exceed 1700 m while the eastern and western parts are below 500 m. In this study, we first divided the validation and correction based on the elevation because it has significant influence on the rainfall climatological pattern [16] . The eastern and western plain region receives about 2071 mm of annual rainfall while in the mountainous region receives about 3321 mm of annual rainfall. It is said that in the highland region rainfall amount is higher than in the lowland region. In addition, heavy rain is strongly influenced by topography [25] . In other words, heavy rainfall often occurs in the mountainous site.

To assess the orographic effects, the validation of GSMaP_MVK in the highland and lowland region was conducted in this section. Table 4 compares the validation and correction result of GSMaP_MVK in the highland and lowland regions. In the highland the bias, error, RMSE, and C_NS were −56.18%, −8.69 mm/day, 29.5 mm/day and 0.4, while in the lowland they were −41.27%, −4.58 mm/day, 26.3 mm/day and 0.5, respectively. These results showed that the performance of satellite product was superior over the lowland, with lower bias, error and RMSE and better consistency measurement for rainfall estimates. In contrast, the performance of satellite product was seriously underestimated and had lower consistency measurement for rainfall estimates over the highland. This will be partly because the current algorithm of microwave radiometer does not include the topographical effect. This result should be noted that topography obviously influences the accuracy of the satellite product. Moreover, detection probability and HSS also gave the same result that is POD and HSS were higher in the lowland (82 % and 68 %) than in the highland (78% and 65%) while FAR was lower in the lowland (15%) than in the highland (19%) as shown in Table 4.

GSMaP_MVK data have underestimated both in the lowland and highland therefore, the correction was conducted. In this study, GAM was conducted for bias correction. The results showed that the bias, error and RMSE in the highland region decreased significantly and the C_NS value increased. However, GAM did not give the significant impact for the lowland area. It should be noted that GAM only worked in the highland region. It was said that GAM tends to overestimate for forecasting [32] . As a result, GAM only be able to solve the underestimate value when the bias percentage is large. In addition, high bias percentage was found when the amount of rainfall was more than 100 mm/day as shown in Figure 4.

As explained before, the mountain region of Kyushu island is located in the central of the island from north to south and it will affect the rainfall pattern over the region. Therefore, to assess the region effect, validation of GSMaP_MVK in the eastern part and the western part was conducted. The western part locates in the Kumamoto, Saga and Fukuoka Prefectures while the eastern part locates in Kagoshima and Miyazaki. Moreover, Kumamoto, Kagoshima and Miyazaki were hit by flash flood in July 2006 and 2007.

Table 5 shows the validation and correction result of GSMaP_MVK in the eastern part and the western part of the region. In the eastern part the bias, error, RMSE, and C_NS were −40.1%, −4.95 mm/day 21.37 mm/day and 0.52 while in the western part they were −55.07%, −7 mm/day, 24.73 mm/day and 0.4. These results indicated that the performance of satellite product was better over the eastern part, with lower bias, error and RMSE and better consistency measurement for rainfall estimates. It was strongly influenced by the location of the mountain area which affected local wind directions, then influenced the rainfall pattern. The wind direction in the study area moves from west to east. The water vapor as a main source of precipitation was not distributed perfectly in the region because the mountain is located in the central area as a barrier for cloud distribution. As a result, the rainfall pattern will be different.

However, the result showed that both in the western part and the eastern part of Kyushu, GSMaP_MVK data has underestimated. Thus, a correction was necessary. The results showed that the bias, error and RMSE in the western part of the region decreased significantly and the C_NS value increased. However, GAM did not give the significant impact for the eastern part of the region. It should be noted that GAM only worked in the western part of the region. The same statement can be concluded that, GAM can greatly correct the GSMaP_MVK data if the bias percentage is large (i.e., more than 55%). In contrast, the correlation coefficient did not change significantly among eastern part, western part, before and after correction. Additionally, detection probability, FAR and HSS also did not give the different result between the eastern part (81%, 18% and 68%) and western part (81%, 18% and 67%).

Heavy rainfall is one of the important factors which trigger the occurrence of flash floods. Thus, predicting the amount of heavy rainfall by satellite precipitation, which close to rain gauge data is necessary. Here, heavy rain is defined as daily rainfall exceeding the 95th percentile (rain_P95) for all stations and all categories [25] . In addition, extreme rain is described as daily rainfall exceeding the 99th percentile (rain_P99) for all stations and all categories [25] . According to the definition, the heavy rains ranged equal and more than 66 mm/day (n = 465) and the extreme rainfalls ranged equal and more than 146 mm/day (n = 95). According to [16] and [11] stated that GSMaP_MVK had serious underestimation when heavy rainfall occurred. Thus, validation and correction of GSMaP_MVK during heavy rainfall is a challenge.

Table 6 describes the validation and correction result of GSMaP_MVK during heavy rainfall. During heavy rainfall, the bias, error, RMSE and C_NS of uncorrected GSMaP_ MVK are −59.5%, −70.3 mm/day, 90.6 mm/day and −0.98. Validation of uncorrected GSMaP_MVK results showed that the performance of satellite products was a serious underestimate because the bias was the highest compare from other categories. This is probably because sudden increase in rain rate did not reflect the IR brightness temperature in this time scale (Ushio et al., 2009). In this section, GAM and power function [29] for bias correction were applied. We did both correction method and then compared. After GSMaP_MVK was corrected by power function, the bias, error, RMSE and C_NS were −63.2%, −63.1 mm/day, 85.6 mm/day and −0.77 while by GAM the yare −8.8%, −10.44 mm/day, 55.44 mm/day and 0.26, respectively. After correction, the bias, error and RMSE values decreased dramatically and the C_NS values increased of both correction methods. However, the GAM correction method gave the most significant result to reduce the error index. Moreover, when the values of C_NS is positive, the correcting of GSMaP_MVK indicates that almost accurate (i.e. C_NS = 0 means the models are accurate while C_NS one means the models are perfectly accurate) [33] .

Because GAM approach gave the best result, Figure 5 only compare AMEDAS, GSMaP_MVK and corrected GSMaP_MVK by GAM. Figure 5(A) shows the heavy rainfall graphic from those components. It described that the underestimate of GSMaP_MVK could be reduced almost in all points. Figure 5(B) shows the extreme rainfalls, which caused flooding in the Miyazaki, Kagoshima and Kumamoto in 2006 and in Kumamoto in 2007. In the extreme rainfalls the bias of GSMaP_MVK is very large. On the other hand, the GAM can reduce the bias of GSMaP_MVK.