Evaluation of bias-adjusted satellite precipitation estimations for extreme flood events in Langat river basin, Malaysia

Even though satellite precipitation products have received an increasing amount of attention in hydrology and meteorology, their estimations are prone to bias. This study investigates the three approaches of bias correction, i.e., linear scaling (LS), local intensity scaling (LOCI) and power transformation (PT), on the three advanced satellite precipitation products (SPPs), i.e., CMORPH, TRMM and PERSIANN over the Langat river basin, Malaysia by focusing on five selected extreme floods due to northeast monsoon season. Results found the LS scheme was able to match the mean precipitation of every SPP but does not correct standard deviation (SD) or coefficient of variation (CV) of the estimations regardless of extreme floods selected. For LOCI scheme, only TRMM and CMORPH estimations in certain floods have showed some improvement in their results. This might be due to the rainfall threshold set in correcting process. PT scheme was found to be the best method as it improved most of the statistical performances as well as the rainfall distribution of the floods. Sensitivity of the parameters used in the bias correction is also investigated. PT scheme is found to be least sensitive in correcting the daily SPPs compared to the other two schemes. However, careful consideration should be given for correcting the CMORPH and PERSIANN estimations. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). doi: 10.2166/nh.2019.071 s://iwaponline.com/hr/article-pdf/51/1/105/649604/nh0510105.pdf Eugene Zhen Xiang Soo Wan Zurina Wan Jaafar (corresponding author) Sai Hin Lai Faridah Othman Ahmed Elshafie Hazlina Salehan Othman Hadi Department of Civil Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia E-mail: wzurina@um.edu.my Sai Hin Lai School of Hydraulic Engineering, Changsha University of Science and Technology (CSUST), Changsha, Hunan Province 410004, P. R. China Tanvir Islam Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA Prashant Srivastava Hydrological Sciences, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

However, it is difficult to determine the amount of rain that falls across the world as the temporal and spatial distribution of rainfall is not even (Gu et al. ).
Rain gauges are the most common tools to provide a direct measurement of precipitation reaching the ground, but they cannot be representative of extensive areas and may contain significant bias arising from coarse spatial resolution, location, wind and mechanical errors (Strangeways ). Precipitation can also be estimated using weather radar due to its continuous spatial coverage (Habib et al. ). However, weather radar has difficulties with hardware calibration (Yilmaz et al. ). If the distance between the target area and the radar increases, the precipitation can be undetected, or the rate can be underes- Satellite precipitation products (SPPs) have been emerging as one of the most important precipitation data sources in hydrology, climatology and meteorology studies for the last few decades. These products have been successfully applied in studying the precipitation patterns at global scale as well as regional scale. These remotely sensed data have several advantages over the traditional measurements, including higher spatial resolution and uninterrupted coverage and hence are beneficial over ungauged catchments, especially mountainous and oceanic regions (Collischonn et (Kubota et al. ), and so on. These satellite precipitation products have provided quasi-global high-temporal ( 3 hours) and spatial ( 0.25 ) resolution precipitation maps.
Although SPPs have been widely used in various meteorological models, these satellite estimations are still imperfect and prone to systematic and random errors associated with observations, sampling and retrieval algorithms. The models could augment or suppress rainfall biases to the streamflow based on the response mode of the model (Segond et al. ; Habib et al. ; Fang et al. ). In Asia, the performance of the SPPs varies from country to country. For instance, CMORPH showed poorer performances compared to TRMM 3B42 Version 6 over Indonesia (Vernimmen et al. ) and Philippines (Jamandre & Narisma ). In contrast, Shen et al. () showed that CMORPH performed better for spatial and temporal patterns of precipitation over China compared to TRMM.
These findings are also supported by Shige et al. () who reported that the accuracy of the satellite estimations varies for different regions or countries as well as topo- Evaluation). In their study, they assessed the accuracy and spatial variations of each SPP by region and found that the SPPs performed better in the NEM than in the SWM. Also, the SPPs' performance was the best in the region receiving higher annual precipitation such as eastern and southern In the present study, the performance of SPPs on five extreme flood events due to NEM specifically during the month of December to January are of the main concern of this study. These two months were chosen due to the history of peak flood events that happened annually. As for the river basin, Langat river basin was chosen as flooding is common in this area when it coincides with localized rainfall.
Although climatology adjustments or calibrations have been adopted on the algorithm of these selected SPPs, the rainfall estimations are still imperfect and their performance varies from region to region, as well as season to season.
Thus, three BC schemes, which are linear scaling (LS), local intensity scaling (LOCI) and power transformation (PT) methods, were employed in this study to assess the capability of three advanced SPPs (i.e., CMORPH, TRMM 3B42 Version 7(V7) and PERSIANN) in improving SPPs' accuracy based on Malaysia's weather system after performing bias correction. Suitability of the bias correction methods on specific SPPs could vary regionally due to spatial and temporal heterogeneity of rainfall that might affect the performance of SPPs in capturing rainfall. It is noticeable that several bias correction methods are available, but this study aimed at evaluating these three widely used schemes in order to investigate characteristics of corrected SPPs' data during extreme events.

REVIEW ON BIAS CORRECTION
Bias correction is a model output statistics approach that seeks to use information from biased model outputs (Chen et al. a). The correction usually identifies possible differences between the observed and simulated climate variables, which provide the basis for correcting both control and scenario model runs with a transformation algorithm. However, BC of precipitation is more challenging compared to other climate variables such as temperature due to the fact of spatial/temporal heterogeneity and zero inflation.
In recent years, numerous studies to improve SPPs' estimations by BC have been done, varying with location, season, topography, climatology and so on (Boushaki et al. Saber & Yilmaz ). Table 1 shows an overview of some BC methods used to correct precipitation data.
The LS scheme corrects the average precipitation value based on the differences between the rain gauge data and satellite data. However, this method does not correct the  precipitation is corrected using a scaling factor. However, the output of this method is limited because, as with LS, the standard deviation and variance are not corrected and all events are adjusted using the same correction factor.
The PT method is a nonlinear correction in an exponential form that combines the correction of the coefficient of variation (CV) with LS. This scheme corrects the mean and variance of the temporal series of estimated precipitation the reduction of biases in rainfall simulated by regional climate models (RCMs). While assessing hydrological response to climate change, Teutschbein & Seibert () reported that all BC methods improved RCM outputs (rainfall and temperature) and distribution mapping method was found to be superior for hydrological simulation but the corrections employed monthly factors.

SCOPE OF STUDY
Description of study area and selected flood events   these five extreme flood events due to NEM specifically during the months of December and January. Table 2 shows the details and general statistics of the five selected flood events. The inter-correlation of the rain gauge observations between these events is tabulated in Table 3. It can be noticed that the rainfall patterns of the selected events were slightly different to each other even though they are for the same monsoon (NEM) and months. Figure 3 exhibits the frequency distribution of daily precipitation in different intensities to each flood event for Langat river basin. It is noticed that Events 2 and 4 are drier compared to the other events whereby more than 50% of the events are no-rain (0 mm/day). As for light rainfall (0-1 and 1-5 mm/day), this type of rainfall occurred for less than 20% of every period, whereas heavy rainfall (20-30 and >30 mm/day) occurred for about 3-8% of the event period.

Data acquisition
This study attempts to evaluate the satellite estimations (before and after BC) with reference to the ground observations during five extreme flood events due to NEM specifically during the months of December and January.
For ground observations, daily rainfall data collected at 28 operating rain gauge stations in Langat river basin were analysed. All data were collected from the Department of Drainage and Irrigation (DID), Malaysia. Table 4

METHODOLOGY
The satellite rainfall estimate was compared to gauged rainfall observation based on the selected events as stated in Table 2. The bias in every satellite estimate was assessed and corrected using the three schemes, i.e., LS, LOCI and PT methods. After being corrected, the improved satellite estimations were compared and analysed again with reference to the gauged rainfall observation. Extended analysis on the parameters of the methods applied was done. Figure 4 shows the overall procedure of this study.  A more detailed description of the selected methods is presented below.

Linear scaling (LS)
The LS method aims to perfectly match the monthly mean of corrected estimations with that of observed ones (Lenderink et al. ). This method operates with monthly correction values based on the differences between observed and estimated data. The daily satellite precipitation amounts, P are transformed into PÃ by multiplying with the monthly scaling factor, s, as shown in Equation (1): The scaling factor is the ratio of the true mean to the mean of biased estimates (Anagnostou et al. ). In this case, this study assumed the rain gauge measurement as the true observation and the satellite estimations (TRMM 3B42 V7, CMORPH and PERSIANN) are the biased estimation, as shown by Equation (2): where S and G represents satellite/gridded and gauge pre-  Table 3.

Local intensity scaling (LOCI)
The LOCI method (Schmidli et al. ) corrects the wetday frequencies and intensities and can effectively improve the raw data which have too many drizzle days (days with little precipitation). It normally involves two steps: first, a wet-day threshold for the mth month P thres,m is determined from the raw precipitation series to ensure that the threshold exceedance matches the wet-day frequency of the observation; second, a scaling factor c ¼ (μ(P obs,m,d jP obs,m,d > 0)=μ(P raw,m,d jP raw,m,d 〉P thres,m )) is calculated and used to ensure that the mean of the corrected precipitation is equal to that of the observed precipitation: Similar to the LS scheme, the scaling factor was calculated and applied separately for every selected event.

Shabalova et al. () and Leander & Buishand ()
advocated the PT method because it uses an exponential form to further adjust the standard deviation of precipitation series, P, as shown in Equation (4): To implement this method, there are two scaling factors to be calculated, a and b. The b factor is calculated iteratively so that the coefficient of variation (CV) of the satellite daily precipitation time series matches that of the gauged precipitation time series. Next, the a factor is calculated, such that the mean of the transformed precipitation values matches that of the gauged precipitation.
Finally, these two scaling factors are applied to each uncorrected daily satellite observation corresponding to that month to generate the corrected daily time series.

Evaluation of raw satellite estimates
Before performing the BC schemes, the accuracy of the three selected satellite products (TRMM, CMORPH and PERSIANN) at Langat river basin were first examined for all events.

Performance evaluation of bias-corrected SPPs
Rainfall pattern and distribution Figure 5 shows the direct comparison of the daily and accumulated rainfall data of every raw and bias-corrected dataset over every study period at Langat river basin to give a first impression of the data characterization. It is found that LS-corrected rainfall estimates predict the overall gauged rainfall reasonably well but as for LOCI, this method was less effective for the PERSIANN estimations as it exacerbates the overall rainfall over the basin by 40-85% overestimation. Nevertheless, this method seemed suitable in certain events for TRMM and CMORPH estimations.
This might be due to the rainfall threshold that we set (1 mm) to ensure that the threshold exceedance matches the wet-day frequency of the observation. In our opinion, sensitivity analysis based on the rainfall threshold is recommended as every region has different geographical conditions and the rainfall will never be equally distributed.
Thus, the rainfall threshold might vary from region to For satellite estimations, T -TRMM, C -CMORPH and P -PERSIANN. region. For PT-corrected rainfall estimates, it is noted that this scheme is much better compared to LOCI. As shown by the result, the difference in total rainfall compared to the accumulated gauge observations was less than 20%, except for PERSIANN estimations corrected by the PT scheme in Event 4 whereby the corrected estimation overestimated the total rainfall over the basin by 31%.
Next, the distribution of the data was evaluated based on the quantile-quantile plots (QQ plots) as shown by Figure 6, and accompanied by

Statistical performance
In the scope of the study section, we described the methods of the BC employed to fit the mean, SD and CV for the precipitation data. Figure 7 shows several scatter plots for the fitting statistics of all events, which implies the observed statistics are plotted versus those of the uncorrected and corrected satellite data. The detailed statistical performances are shown in Table 8. Based on the scatter plots ( Figure 7) and statistical performances (Table 8), it is observed that the LS scheme matches the mean precipitation of every satellite estimation, but it does not correct the biases in SD and CV. When applying a higher degree of BC scheme, such as LOCI and PT schemes, a significant improvement in the SD and CV were noted as the data points in the scatter plots are almost matched to the gauged observations. PT exhibits greater improvement compared to LOCI. These results are considered as good, as the method of BC schemes applied for this study was only intended to correct the aforementioned statistical parameters.

Variation and sensitivity of parameters
Based on the statistical analysis, the determined parameters or bias factors (s for LS scheme, c for LOCI scheme as well as a and b for PT scheme) greatly affected the corrected daily precipitation value of the extreme flood. However, statistical analysis does not provide a true answer for the study as hydrological events are subjected to great variability and uncertainties. Thus, it is important to evaluate the sensitivity of these parameters based on the selected events of this study. Moreover, it is also important to assess whether these parameters can be applied in a similar event of different time period (Terink et al. ). Figure 8 shows the boxplots for every parameter applied throughout the five selected events, with the small circles representing the To address the uncertainty concerning the determined parameters of every scheme, bootstrapping (Tian et al. ) was performed for every parameter of the selected BC scheme. Based on the parameters obtained, 1,000 random samples were generated and the sampling distribution was visualized using histograms to observe the skewness of the samples. This bootstrapping procedure was repeated for every parameter and every satellite estimation. Figure 9 shows one of the histograms for resampled parameter s (bias factor of LS scheme) for January's TRMM estimations. The mean of the original and resampled parameters as well as the 95% confidence intervals are shown in Table 9. These results can be a reference for correcting the near-real-time data for further use.
Based on the results, it is noted that the uncertainty range of every parameter applied for the month of December is larger compared to that for the month of January.
Thus, careful consideration should be given when improving the satellite rainfall estimations. By comparing the BC scheme, the difference between the original and the resampled mean for parameter a and b of the PT scheme is much smaller compared to s for the LS scheme and c

CONCLUSION AND RECOMMENDATIONS
Satellite precipitation has provided an alternative for precipitation measurement due to its large-scale approach.   in the present study, we set 1 mm as the rainfall threshold  crucial assumption, is that the bias correction factors retrieved by any such methods must necessarily be considered valid for the future, assuming a temporal stationarity and thus introducing another, yet often neglected source of uncertainty. This may help the hydrologists to understand the efficiency and application of bias correction on satellite estimation data in rainfall-runoff modelling to predict the river discharge in this catchment, which may be useful to our water resources management.