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Journal of Hydrology
journal homepage:www.elsevier.com/locate/jhydrol
Research papers
Space-time variogram for daily rainfall estimates using rain gauges and
satellite data in mountainous tropical Island of Bali, Indonesia (Preliminary
Study)
Novi Rahmawati
⁎Department of Water Resources, Faculty of Geo-information Science and Earth Observation (ITC), University of Twente, Enschede, the Netherlands
A R T I C L E I N F O
This manuscript was handled by Emmanouil Anagnostou, Editor-in-Chief, with the assistance of Kuo-Lin Hsu, Associate Editor
Keywords:
Blended daily rainfall estimates CMORPH
Space–time variogram Bali Island
A B S T R A C T
High spatio-temporal variability of daily rainfall in Bali Island can create the absence of structure in the daily variogram in certain days. This research proposes a new technique applying space–time variogram for 3-suc-cessive daily rainfall to detect structure in variogram estimation by merging rain gauges and satellite data applying ordinary kriging (OK), regression kriging with CMORPH (CM), regression kriging with TRMM (TR), and blended monthly rainfall (MONT) to obtain daily blended gridded rainfall estimates. Original retrieval of CMORPH (CM_OR) and TRMM (TR_OR) also used as control points to assess the proposed method. Uncertainty and sensitivity analysis including cross validation were carried out to validate the proposed method.
The result shows that a new technique, adapted from CMORPH specific character, can be applied to detect the existence of structure in variogram. Blended gridded daily rainfall estimates of CM has highest probability detection of rainy events, while OK the lowest. Generally, the four interpolation methods (OK, CM, MONT, TR) have low accuracy at leeward and in a coastal area. All of them have almost similar performance indicated by no clear distinction of RMSE value from cross validation. CM, MONT, and TR have a good sensitivity with maximum and minimum temperature, indicating that satellite data can improve the gridded rainfall estimates. However, it is required an improvement of daily gridded rainfall estimates since there are large RMSE values and low coefficient correlation in certain days because of strong and erratic behavior of rainy events in a mountainous tropical island of Bali.
1. Introduction 1.1. Background
As the rainiest places in the world, mountainous tropical island is characterized by highly variable of daily precipitation (Cronin et al., 2015). The presence of sea border, mountain range, and prevailing winds enhances the complexity of convective circulation system in this island leading to complex rainfall structure in space and time (Qian, 2008; Sato et al., 2009; Yokoi et al., 2017). Kriging is one of common methods to investigate rainfall structure in space–time which is able to include linearity correlation with some parameters, i.e. environmental condition of the island (Kyriakidis et al., 2001; Seo et al., 2015; Vajda and Venäläinen, 2003), satellite data (Li and Shao, 2010; Velasco-Forero et al., 2009), and extended to space–time domain (Spadavecchia and Williams, 2009). One of kriging approach implementing a linear relationship between rainfall and these parameters is regression kriging
(Hengl et al., 2007).
In regression kriging, rain gauge data is as the source of primary variable and satellite data as an additional or secondary variable. Both data sources were merged to obtain distributed blended daily rainfall estimates (Velasco-Forero et al., 2009). This merged technique takes advantages of the strength of both data sources. Satellite data can provide a spatial structure of rainfall in ungauged sites (Gebregiorgis and Hossain, 2013; Woldemeskel et al., 2013) because of time series data availability and area coverage irrespective of terrain or climate (Grimes, 2008). Rain gauge data provides true value in corresponding gauge location (Ebert et al., 2007).
The selection of satellite data to be merged with rain gauge data in a certain area depends on the performance of satellite data, the spatio-temporal resolution of satellite data, the algorithm of satellite data, geographic location and environmental condition of the study area. CMORPH (The Climate Prediction Center Morphing Method) coarser resolution (CMORPH25), ~ 27 km2grid size, is the best performance in
https://doi.org/10.1016/j.jhydrol.2020.125177
Received 28 February 2018; Received in revised form 15 February 2019; Accepted 9 June 2020
⁎Address: Delanggu Baru, RT.01/10, Delanggu, Klaten, Jawa Tengah 57471, Indonesia.
E-mail address:n.rahmawati@utwente.nl.
Journal of Hydrology 590 (2020) 125177
Available online 09 July 2020
0022-1694/ © 2021 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Bali Island (Rahmawati and Lubczynski, 2018). However, CMORPH finer spatial resolution (CMORPH8), ~ 8 km2grid size, was selected to
blend with rain gauge data because this finer spatial resolution can provide more detail rainfall information in limited rain gauges net-works (Clarke and Buarque, 2013) in Bali Island. Moreover, Blended monthly rainfall estimates from CMORPH8 and rain gauge is also merged with daily rain gauge data to regionalize geographic and en-vironmental condition of daily rainfall. TRMM TMPA (Tropical Rainfall Measuring Mission Multi-Satellite Precipitation Analysis) 3B42 was used to obtain distributed blended daily rainfall estimates because it had lowest hits bias in estimating rainfall in Bali Island (Rahmawati and Lubczynski, 2018).
Bali Island is a mountainous tropical island which has high spatial and temporal variability of daily rainfall (Rahmawati and Lubczynski, 2018). Highly variable of rainfall in Bali Island is because of the mixture effect of land-sea breeze and topography, concavity of land, windward-leeward monsoon mean flows and gravity wave (Kikuchi and Wang, 2008). These conditions resulting in daily complex convective circula-tion system that is responsible for the absence of structure of daily variogram in certain days. Highly variable of precipitation amount at coast to coastline, coastal to inland areas, windward to leeward sides which depends on the conditions (Ogino et al., 2016; Smith et al., 2012) leading to the absence of the structure in daily variogram. However, the possible existence of structure in the variogram can be detected with an appropriate method (Finkelstein, 1984). Therefore, the aim of this
research is to propose a new technique applying space–time variogram for 3-successive daily rainfall in a day where the absence of structure in the daily variogram estimation was found at limited rain gauge net-works.
The proposed method applied 3-successive daily rainfall (e.g. not 2 or 4 days) to build space–time variogram to detect possible existence of variogram structure. It is related to the behavior of CMORPH8 which mostly have difficulty in detecting 3 days successive rainfalls in Bali Island. At least 40–60% of miss rainfall events performed by CMORPH8 is from the inability to detect these 3 days successive rainy events. Each of 35 daily ground rainfall estimates was compared with the corre-sponding of CMORPH8 pixel within period 1 October 2003–30 September 2006 (Rahmawati and Lubczynski, 2018) to find this be-havior. CMORPH25 and TRMM 3B42 were also been compared with daily ground rainfall estimates, however, the specific behavior can clearly be detected in CMORPH8. Since this paper used the finer spatial scale of CMORPH8 not the coarse spatial scale of CMORPH25 to detect possible existence of variogram structure, therefore, from this point forward CMORPH8 is called CMORPH.
In order to obtain distributed gridded daily rainfall estimates, the specific purposes of this research are as follows: (1) daily blended rainfall estimates with space–time variogram of 3-days successive daily rainfall, and (2)validation of daily blended rainfall estimates using space–time variogram of 3-successive daily rainfall with uncertainty analysis, and sensitivity analysis.
Fig. 1. Bali Island map with the grid of CMORPH, 0.0727 deg and TRMM, 0.25 deg, reflecting pixels of CMORPH and TRMM, and network of rain gauges to be used
to obtain distributed gridded daily rainfall estimates; 45 daily gauge data (red circle) for daily interpolation blended CMORPH-rain gauge, 5 additional monthly gauges (yellow circle) for monthly blended CMORPH-rain gauge. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
1.2. Study area description
The Indonesian Bali Island is a mountainous tropical island that has various altitudes ranging from 0 to 3,028 m a.s.l. Bali Island mostly has undulating-rolling topography, ~66% of the area, with slope ranging from 3 to 14%. This island has a latitudinal mountain range of Gunung Agung that separates Bali into two watershed divides, northern and southern, which has different rainfall characteristics. The northern has an average annual rainfall of 1761.3 mm, while the southern 2024.5 mm.
2. Methods
2.1. Data and materials
The 3-years data (1,097 days) from 1 October 2003 to 30 September 2006 of daily rainfall from 45 rain gauge stations (Fig. 1) obtained from Research Center for Water Resources (locally known PUSAIR) and from Indonesian Agency for Meteorology, Climatology, and Geophysics (lo-cally known BMKG) was used to detect a days where there is the ab-sence of variogram structure on daily basis. Daily variogram estimation was built for 1,097 days from 45 rain gauges to obtain gridded rainfall estimates over Bali Island. From the total number of 1,097 sample days, it was detected that there are 398 number of days that no possible existence of structure in the daily variogram. The possible existence of structure in the variogram for 398 days is carried out applying space–time variogram of 3 successive daily rainfall. Four interpolation methods were performed to obtain gridded rainfall estimates for these 398 days. These interpolation methods consisted of ordinary kriging (OK), regression kriging with CMORPH as an additional variable (CM), regression kriging with blended monthly CMORPH as an additional variable (MONT), and regression kriging with TRMM as an additional variable (TR). Then, the original of CMORPH (CM_OR) and TRMM (TR_OR) retrievals was also compared with gridded blended rainfall estimates as control points. CM_OR and TR_OR were not assessed in cross validation and sensitivity analysis.
30-minutes CMORPH was aggregated into daily basis and resampled into 1 km2 grid size. CMORPH gridded rainfall is generated every
30 min at 0.0727 × 0.0727 degrees lat/lon (Fig. 1) as a merged product of Infra-Red (IR) and Passive Micro-Wave (PMW) images using La-grangian interpolation to morph PMW datasets (Janowiak et al., 2005; Joyce et al., 2010). It is available at global coverage at 60 N-60S.
Total 50 rain gauges with monthly data at the same period from 1 October 2003 to 30 September 2006 were used to define monthly blended ground rainfall estimates with CMORPH rainfall estimates. Five additional rain gauge stations with monthly data (Fig. 1) were available for interpolation. The 30-minutes CMORPH is aggregated into monthly basis and resampled into 1 km2grid size to be blended with
monthly gauge rainfall estimates.
TRMM 3B42 (TRMM) is a product of TRMM 2A25 precipitation radar with infrared precipitation estimates. The monthly total from TRMM was used to calibrate infrared precipitation estimates from three hours temporal resolution of Geostationary Operational Environmental System (Ward et al., 2011). TRMM has a temporal resolution of 3 h and a spatial resolution of 0.25⁰ (Huffman et al., 2010). The TRMM data covers over tropics between 30⁰ N and 30⁰S (Ward et al., 2011).
The dataset for validation includes measurement from 2 in-dependent rain gauges for which one of them has missing data. These gauges are: a) Ngurah Rai, with complete 3-years data period, b)Tiying Gading, with missing data of 31 days within period 1 October-31 December 2003. The maximum and minimum daily temperature from climatology station of Ngurah Rai also used to assess sensitivity analysis with the volume of gridded blended rainfall estimates in Bali Island.
2.2. Methodology
It is necessary to find an appropriate method to obtain the possible existence of variogram structure to generate gridded rainfall estimates for advances application and many purposes in water resources related studies in Bali Island. In total 398 days from 1,097 days (1 October 2003 to 30 September 2006) was identified no possible existence of spatial structure in the daily variogram. The absence of spatial structure in the daily variogram within a period of 1,097 days was detected ap-plying variogram estimation with three cutoff and width scenarios. The three scenarios of cutoff and width were: a) 58,500 m and 5,000 m; b) 60,000 m and 4,500 m; c) 60,000 m and 4,200 m. These 3 scenarios of cutoff and width were used to acquire a sufficient number of points pairs in every distance class minimum 30 (Journel and Huijbregts, 1978). Spherical and exponential models were used to fit variogram estimation.
Space-time variogram from 3 successive daily rainfall was estimated to build possible existence of spatial structure in variogram for each 398 days. Regression kriging with CMORPH as an additional variable (CM), regression kriging with blended monthly CMORPH as an addi-tional variable (MONT), and regression kriging with TRMM as an ad-ditional variable (TR) was applied to obtained gridded blended rainfall estimates. Daily rainfall interpolation applying ordinary kriging (OK) was also performed as an additional sensitivity test when there are no additional variables in blended rainfall estimates (Kebaili Bargaoui and Chebbi, 2009). The formula for ordinary kriging is illustrated as in Equation(1), while the formula for regression kriging is expressed as in Equations (2) and (3) (Feki et al., 2012; Hengl et al., 2007; Moral, 2010). The formula of space–time variogram estimation is expressed in Equation(4)modifying fromSterk and Stein (1997). The data from 3 successive days of rainfall was combined only not standardized as in Equation (4) in Sterk and Stein (1997). The example of this new modified method is shown inFig. 2.
= = z x( ) z x( ) i n i i 0 1 (1)
where z(x0) is rainfall prediction at location x0, rainfall sample data at
location xi, x2, …, xn, weight λi depends on spatial autocorrelation
structure of the variables. This weight is selected a minimized predic-tion error variance.
= +
ZRK( )x m x( ) r x( ) (2)
where ZRK(x) is daily rainfall at point prediction of x ,m (x) is the trend
that is fitted using linier regression at point prediction of x and the r(x) is the residuals at point prediction of x that is estimated using ordinary kriging. Therefore, for the n sample points the prediction of ZRK(x) is:
= + = = ZRK( )x j c v x. ( ) w x r x( ). ( ) p j j i n i i 0 1 (3) = v x0( ) 1
where the coefficients of estimated trend model is cj, the jth
pre-dictor at location × is vj(x), the number of predictors is p, the weights
determined by solving the ordinary kriging system of the regression residuals is r(xj). = = = + n h z z 1 2 ( ) t ( ) T i n h it i h t 1 1 ( ) , 2 t (4) where is variogram for a days where there is no spatial structure of rainfall, zitand zi+h,tis the ith pair of standardized rainfall observations
at time t, separated by vector h, of which they are nt(h). The total
number of pairs of points for each vector h is equal to n(h). t is 1th day successive daily rainfall and T is 3rd day of successive daily rainfall, i is different spatial locations of the observations.
The space–time variogram estimation and interpolation were per-formed in R-software applying gstat package (Pebesma and Heuvelink,
2016; Pebesma and Wesseling, 1998). Space-time variogram can im-prove the reliability of prediction by incorporating space–time corre-lation (Varouchakis and Hristopulos, 2017) that provide probability framework for data analysis and prediction based on the joint spatial and temporal dependencies between observations (Zeng et al., 2014). Principal component analysis (PCA) is also applied in R-software to set daily CMORPH, monthly blended rain gauge-CMORPH, and TRMM as an independent variable in interpolation. PCA is a linear method to reduce the dimensionality of the data by transforming the initial vari-ables into new varivari-ables, i.e. the so-called principal components, while capturing the maximum information present in the data set and mini-mizing errors between the initial variables with new variables. PCA maps the original n dimensions (variables) of the data matrix X onto a new orthogonal space, so that a new data orientation follows the di-rection of the largest variance in the data. PCA produces a visualization of the 2D relationship between variables and illustrates a group of subjects with similar characteristics (Demšar et al., 2013; Emmanuel et al., 2012).
The performance of daily gridded blended rainfall estimates was evaluated applying uncertainty analysis, cross validation and sensitivity analysis. The validation scheme applying cross validation and sensi-tivity analysis is separated into the rainy and dry season. Rainy season is from October-March, while April-September dry season.
The uncertainty was carried out for each of the 45 rain gauges (Fig. 1), which used for interpolation, were compared with corre-sponding pixels of daily blended rainfall estimates applying probability of detection for rain (PODrain = Equation(5)) and false alarm ratio
(FAR, Equation(6)) followingTang et al. (2010)as shown in matrix in Table 1. POD and FAR can evaluate the ability of a blended model to detect rainfall and the nature of the error (Cohen Liechti et al., 2012; Ebert et al., 2007). Also, POD-rain can be used to detect the accuracy in estimating rainy events and to show the highest level of reliability and precision compared to other common metrics in categorical statistics, while FAR is to detect the probable frequency in estimating rainfall. Both of them has the highest accuracy to detect transfer error in in-terpolation (Tang and Hossain, 2009, 2011). The optimal value of POD is 1, while FAR 0 (Duan et al., 2016). There is no separation analysis
between rainy and dry season to evaluate gridded blended rainfall es-timates with this validation scheme.
= + POD rain N N N A A B (5) = + FAR N N N B B A (6)
Cross-validating the blended rainfall datasets was performed to evaluate the quality of rainfall estimates applying space–time vario-gram of 3-successive daily rainfall. Cross validation is also called a leave-one-site-out procedure which is a technique to remove one rain gauge and re-estimate rainfall at removed rain gauge station at the remaining rain gauges. In this method, one rain gauge is disregarded from the dataset and other available rain gauges are used for rainfall estimation for each time step (Diodato, 2005; Rabiei and Haberlandt, 2015; Schuurmans et al., 2007). Cross validation statistics of daily mean error (ME, Equation (7)) and daily root mean square error (RMSE, Equation(8)) from the difference between estimated value Z and the observed value z1 (Diodato, 2005), xiis the location at i or at station i,
then n is the number of observation (45 rain gauges), is as below. ME and RMSE in cross validation statistics are the common method to check the quality of interpolation. The analysis was carried out in rainy and dry season separately.
= = ME n Z x z x 1 ( ( ) 1( )) i n i i 1 (7) = = RMSE n Z x z x 1 ( ( ) 1( )) i n i i 1 2 (8) Next, the validation of daily gridded rainfall estimates is by com-paring each of the 2 independent rain gauges (Fig. 1) with corre-sponding pixels of daily blended rainfall estimates applying ME (mean error, Equation(9)), RMSE (root mean square error, Equation(10)), and CC (coefficient correlation, Equation(11)) as follows. The analysis was carried out in rainy and dry season separately.
= = ME N Rm Rg 1 ( i N i i 1 (9) = = N Rm Rg RMSE 1 ( ) i N i i 1 2 (10) = = = = CC Rg Rg Rm Rm Rg Rg Rm Rm (( )( )) ( ) ( ) i N i i i i i N i i i N i i 1 1 2 1 2 (11)
where Rmiis rainfall value based on blended rainfall estimation in day t Fig. 2. Space-time variogram from 3-days
suc-cessive rainfall within period 19–21 March 2006 to define spatial structure of variogram and grided rainfall estimates on 20 March 2006 ap-plying ordinary kriging (OK), regression kriging with CMORPH as additional variable (CM) and blended monthly CMORPH-rain gauge (MONT). Nuggets parameter for OK, CM, MONT and TR are 19.1; 0; 28.3; and 37.5 respectively; Partial sills for OK, CM, MONT, and TR are 253, 253, 244.8, and 232.8 respectively. Then Range for OK, CM, MONT, and TR are 7034 m; 6150 m; 7343 m; and 7366 m respectively.
Table 1
Contingency table.
Contingency table Rain gauge (Rg)
Rainy No Rainy
Daily blended rainfall estimates (Rm) Rainy NA (Hits) NB (Miss)
at station i (mm·day−1), Rg
iis rainfall value based on rain gauge
ob-servation in day t at station i (mm·day−1). N is total number of
ob-servation (1 gauge). The optimal value of ME and RMSE is 0, while CC 1.
The sensitivity analysis was carried out for testing the daily gridded blended rainfall estimates corresponding to the volume of rainfall as the input for an integrated hydrological model. Ordinary kriging was used to check the changes in volume using the additional variable of CM, MONT, and TR. The formula to calculate volume is in Equation(12), while sensitivity analysis formula is varying on input volume because of varying additional variable modified fromLee and Chung (2007). This volume was compared with maximum and minimum temperatures from the gauge that was not used for interpolation to check the sensi-tivity of interpolation method. Temperature can be used to test the performance of gridded blended rainfall estimates (Lee and Chung, 2007) and rainfall sensitivity (Polson et al., 2016). Minimum and maximum temperature were selected to test the sensitivity of gridded rainfall estimates because the daily temperature has a close relationship with daily rainfall (Berg et al., 2015; Rehfeld and Laepple, 2016). Rainfall and temperature have a negative correlation in daily time scale in the tropics (Williams et al., 2012). Moreover, changes in temperature effects total column water vapor, moisture, clouds, and total rainfall (Lauer et al., 2013; Strauch et al., 2015).
=
Vt Pm xat (12)
where Vtis the volume of rainfall in day t (m3·day−1), Pm tis merged
rainfall estimates in day t (mm·day−1), and a is the area (mm2) 3. Result and discussion
The absence of rainfall structure in the daily variogram usually occurs in a day before or after heavy rainfall in Bali Island. This heavy rainfall probably can be related to Madden-Jullian Oscillation (MJO). MJO influences deep convection and heavy rainfall in Maritime Continent (Kanamori et al., 2018) including in Bali and Borneo Islands especially in rainy season (Hidayat and Kizu, 2010). MJO especially has a stronger effect for a diurnal cycle in the coastal region compared to the inner region in Borneo (Ichikawa and Yasunari, 2006). Differences of rainfall peak migration from the coastline into inner region result in highly variable of daily rainfall in space and time (Mori et al., 2004) which probably leading to the absence of rainfall structure in daily variogram.
In total 398 days is no possible existence of structure in the daily variogram from the total number of sample days 1097 within the period of 1 October 2003 to 30 September 2006. The analysis of these 398 days could be separated into the rainy and dry season. The rainy season consisted of rainy season 1 (1 October 2003–31 March 2004), rainy season 2 (1 October 2004–31 March 2005) and rainy season 3 (1 October 2005–31 March 2006). The number of absence in variogram structure in rainy season 1, 2 and 3 respectively 65 days, 53 days and 50 days. The dry season consisted of dry season 1 (1 April-30 September 2004), dry season 2 (1 April-30 September 2005) and dry season 3 (1 April-30 September 2006) with the number of absence in variogram structure respectively 61 days, 71 days and 98 days.
3.1. Uncertainty analysis
Fig. 3presents the probability of detection (POD) of rainy events between OK, CM, CM_OR, MONT, TR and TR_OR against 45 rain gauges within 398 days in Bali Island. The distribution of OK POD is quite similar at coastal, inner and mountainous areas, indicating that OK has a comparable probability to detect rainy events in any part of the study area. The value of POD is mostly low which more than 50% of POD value is ≤ 0.5. Additionally, OK is mostly not capable to detect greater than 70% precipitation events indicating OK has the lowest level of reliability and precision in detecting rainy events. In contrast with OK,
CM has a larger probability to detect rainy events. The POD of CM is mostly between 0.5 and 0.7., only 15% is ≤ 0.5, and 17% is ≤ 0.7. CM also significantly shows improvement in estimating rainfall when it compared with CM_OR. At least 22% of low POD values, ≤ 0.5, de-creases in CM when CM_OR was blended with rain gauge data. CM is also more capable to detect 70% precipitation events than CM_OR. This detection ability approximately increases 75% from the total of the sample observation. The distribution of CM POD illustrated it has a good performance at inner and mountainous areas than at coastal areas. There is no improvement in POD value of ≤ 0.5 in coastal areas when CM compared to CM_OR. The coastal POD values also can be lower than 0.5. CM is not a good performance at coastal areas because PMW sen-sors of CMORPH mask out emission signal from coastline areas in case the emission signal comes from the land (Janowiak et al., 2005) so CMORPH estimates rainfall based on where the emission of the signal originates from (land or sea). CM also performs better in rainfall esti-mation than MONT, especially at the mountainous area. Similar case with TR, CM has better accuracy than TR. However, MONT and TR POD values show improvement than CM_OR and TR_OR, reflecting higher accuracy of rainfall estimates to blend rain gauge with satellite data.
In general, the gridded rainfall estimates of CM performs the best in detecting rainy events, while OK the worst. The satellite data improves rainfall estimation resulting in better performance the gridded rainfall estimates of CM, TR, and MONT compared to OK. The four interpola-tion performs relatively similar with POD ≤ 0.5, which mostly occurs in the coastal area. There is a possibility that the life cycle of diurnal precipitation from the coast, coastline, to landward at coastal areas had large variation (Kikuchi and Wang, 2008). This condition cannot be predicted by all four interpolation methods, therefore, the POD values are low. Moreover, rapid growth phase of intense precipitation from the seaside of coastal to landside of coastal due to the different shifting time of rainfall event and rainfall amount at a different location of the island resulting in an error of rainfall estimation (Saito et al., 2001).
Fig. 4 shows false alarm ratio (FAR) between OK, CM, CM_OR, MONT, TR, and TR_OR against 45 rain gauges within 398 days in Bali Island. There is a clear evident that satellite data can improve the ac-curacy of gridded rainfall estimates. The acac-curacy of blended CM and TR is larger compared to satellite data only, CM_OR and TR_OR. The FAR values of CM and TR decrease compared to CM_OR and TR_OR. CM_OR also performs better than rain gauge data only, OK, to obtain gridded rainfall estimates. The performance of interpolation methods can be clearly ranked as follows: CM > TR > MONT > OK. Then, the value of FAR between satellite data and rain gauge data is as fol-lows: TR_OR > OK > CM_OR, reflecting that CM_OR best perfor-mance.
The spatial distribution of FAR shows the rainfall estimates have better performance at windward than at leeward. The number of FAR values is comparable for ≥ 0.6 at windward and leeward sides, al-though the number of observation is larger at windward than leeward. The improved performance of blended models, i.e. CM, MONT and TR, are lower at the leeward than at windward sides when they are com-pared to rainfall estimates from the gauge data only and satellite data only, i.e. CM_OR, OK, and TR_OR. It is related to the difficulty of the algorithm to detect rainfall at leeward location because extensive rain frequently does not occur. The occurrence of this extensive rain de-pends on stabilization of convection, forced descent and wave breaking, while at windward heavy rainfall will occur as the slope increase (Kirshbaum and Smith, 2009).
The cross validation ME and RMSE boxplot made for OK, CM, MONT, and TR are presented inFigs. 5 and 6in a rainy and dry season, respectively.Fig. 5shows that all four interpolation methods under-estimate rainfall in both rainy and dry season. The differences perfor-mance of all of the four gridded rainfall estimates is not significantly clear, except in rainy season 3 and dry season 1. The superiority per-formance among all four methods does not show obviously. The four interpolation methods underestimate precipitation with an average ME
value ranging from −0.06 to −0.08 mm·day−1in rainy season, while
−0.05 to −0.07 mm·day−1 in dry season. The tendencies of
estimation by all of the interpolation method because of under-estimation of strong rainy events.
The general trend evident ofFig. 6is that, using root mean square error as validation measure, there are no significant differences
performance observed across various interpolation method. It is related to CM generally performs better than OK, TR and MONT in the mag-nitude of 1–2 mm·day−1. The RMSE distribution is mostly below
20 mm·day−1 which is much lower than average daily rainfall,
~48 mm·day−1, within this period in Bali Island.
The validation of four interpolation methods, i.e. OK, CM, MONT,
Fig. 3. Spatially distributed of daily probability of detection (POD) between 45 rain gauges and four interpolation methods, OK, CM, MONT, and TR within 398 days
applying space–time variogram of 3 successive daily rainfall. Original retrieval of CM and TR, CM_OR and TR_OR, also used as control analysis. The diameter of circle is proportional to POD which violet is ≤ 0.5, pink is 0.5 < POD < 0.7 and blue is ≥ 0.7. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Spatially distributed of daily false alarm ratio (FAR) between 45 rain gauges and four interpolation methods, OK, CM, MONT, and TR within 398 days
applying space–time variogram of 3 successive daily rainfall. Original retrieval of CM and TR, CM_OR and TR_OR, also used as control analysis. The diameter of circle is proportional to POD which violet is ≤ 0.5, pink is 0.5 < POD < 0.7 and blue is ≥ 0.7. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
and TR, including satellite data only, i.e. CM_OR and TR_OR, applying ME is presented inFig. 7for 2 rain gauges separately in a rainy and dry season. During most of the period, there is an underestimation in rainfall values from all interpolation methods and all satellite data products in rainy and dry season. The maximum daily rainfall is 120 mm in both stations in rainy season, while the maximum daily rainfall can be captured by CM_OR, TR_OR and OK is 102, 102 and 99.2 mm respectively, resulting in an underestimation of rainfall in most of the period of simulation. OK shows close performance to CM and MONT but with underestimation of peak rainy events and over-estimation of low rain-rate in rainy and dry seasons, although OK and CM perform better than MONT. TR outperforms OK, CM and MONT, mirroring from the pattern observed in orange lines of ME. With respect to CM_OR and TR_OR, CM and TR significantly improve the accuracy estimation of precipitation. The magnitude of underestimation and overestimation for CM_OR and TR_OR decrease in CM and TR. The large value of ME in CM_OR can be dropped significantly in CM which means the finer resolution of CM_OR performs better than courser resolution of TR_OR to be blended with ground rainfall estimates.
All four interpolation methods have a tendency to underestimate rainfall estimates because the algorithms have difficulty to detect heavy rain-rate that do not occur at the same time in any part of the island. Rainfall is suppressed over the island the morning, but strong convec-tion develops in offshores, dropping much rain, which is the opposite in the evening where over the island dropping much rain (Ichikawa and Yasunari, 2006) resulting in all interpolation methods underestimates rainy events (Sato et al., 2009). It is clearly presented in coastal area gauge station, Ngurah Rai, and inner region gauge station, Tiying Gading. The peak of underestimation occurs differently within the time period of simulation in both stations.
The validation of the proposed methods applying RMSE is presented
inFig. 8for 2 rain gauges separately in a rainy and dry season. The RMSE graph shows that the four interpolation methods are quite similar to each other. In each gauge, the RMSE of OK, CM, TR, and MONT is mostly overlapping each other emphasizing small value differences of RMSE in the range of 0.1–0.4 mm·day−1. The similarity performance of
these four interpolation methods also can be identified from the large of RMSE values in certain days which can be in transition, wettest or driest months. It is likely because the highly variable rainfall in these days at coastal, at inner and mountainous areas could not be predicted cor-rectly resulting in large RMSE value.
The performance of four interpolation methods at individual gauges, Ngurah Rai and Tiying Gading stations, shows large RMSE in certain days in the rainy and dry season. At Ngurah Rai, the coastal station, the large RMSEs occur on the wettest month of January in rainy season, while in dry season no specific month. At Tiying Gading station, the inner station, there is no specific indication in which months of certain days have large RMSE. It is probably a lot of factor influence rainfall events at inner than at coastal area such as land-sea breeze from the south and the breeze from mountain range in the north, concavity of the land-sea (Kikuchi and Wang, 2008), therefore, a lot of extensive rain could not be predicted in a specific day at inner area.
Scatterplots of daily coefficient correlation for all gridded rainfall estimates againt 2 rain gauge data are shown inFig. 9in rainy and dry season separately (1st row is Ngurah Rai, 2nd row is Tiying Gading). CM and OK capture such patterns with a higher coefficient correlation compared to others. However, CM performs better than OK because OK has a lower coefficient correlation of 0.01 and 0.05. The largest coef-ficient correlation value of 0.8 is observed in the dry season. It is be-cause rainfall in Indonesia is most predictable during dry season which is related to the lack of spatial coherence due to low-latitude convective dynamics and non-balanced flow regime in rainy season (Haylock and
Fig. 5. Boxplot cross validation of daily mean error (ME) between 45 rain gauges and four interpolation methods, OK, CM, MONT, TR within 398 days applying
Fig. 6. Boxplot cross validation of daily root mean square error (RMSE) between 45 rain gauges and four interpolation methods, OK, CM, MONT, TR within 398 days
applying space–time variogram of 3 successive daily rainfall in rainy and dry season separately.
Fig. 7. Graph of daily mean error (ME) between 2 independent rain gauges, first row is Ngurah rai and Tiying gading is second row respectively, and three
interpolation methods, OK, CM, MONT, TR within 398 days applying space–time variogram of 3 successive daily rainfall. Rainy1 is rainy season1, dry1 is dry season 1, etc.
McBride, 2001). In addition,Fig. 9 shows that the lowest coefficient correlation value of 0.0 is observed for TR. It can be seen that there is a poor agreement between gridded rainfall estimates and rain gauge data with very low coefficient correlation in the certain time period in rainy and dry season. It is because one-two days erratic rainy events with rain-rate 40–100 mm·day−1in transition season are measured by rain
gauge, while gridded rainfall estimates only predict 3–5 mm·day−1,
resulting in a low coefficient correlation of rainfall estimates in Bali Island. It is in agreement withSanchez-Moreno et al. (2014)that states
a single strong rainy event can control daily rainfall in the time of si-mulation, leading to a very low correlation coefficient. It is also in agreement withPrasetia et al. (2013)that a daily rainfall has a coef-ficient correlation value of 0.16–0.58 for a local pattern because local effects are dominating rainfall (Haylock and McBride, 2001), while 0.07–0.52 for an equatorial pattern in Indonesia (Prasetia et al., 2013). It can be noticed also fromFig. 9, the CC values of CM and TR are lower compared to CM_OR and TR_OR at certain time only. It is because the additional information from gauge data give a false rain-rate
Fig. 8. Graph of daily root mean square error (RMSE) between 2 independent rain gauges, first row is Ngurah rai and Tiying gading is second row respectively, and
three interpolation methods, OK, CM, MONT, TR within 398 days applying space–time variogram of 3 successive daily rainfall. Rainy1 is rainy season1, dry1 is dry season 1, etc.
Fig. 9. Graph of correlation coefficient (CC) between 2 independent rain gauges, first row is Ngurah rai and Tiying gading is second row respectively, and three
interpolation methods, OK, CM, MONT, TR within 398 days applying space–time variogram of 3 successive daily rainfall. Rainy1 is rainy season1, dry1 is dry season 1, etc.
estimation to the blended model. It is because the spatial distribution of daily rainfall varies at the leeward, windward, coastal line, coastal areas, an inner region, and mountain area. It depends on a lot of factors such as mountain width (Kirshbaum and Smith, 2009) and distance from the sea (Sato et al., 2009).
3.2. Sensitivity analysis
The sensitivity of interpolation CM, MONT, and TR against the minimum and maximum temperatures applying space–time variogram from 3 successive daily rainfall is displayed inFig. 10. Three of them have sensitivity with maximum and minimum temperatures, reflecting that the three interpolation methods are a good performance to detect the possible existence of variogram structure. It also can be concluded that additional information of rainfall from satellite data can improve the performance of gridded rainfall estimates. All three methods are more sensitive to maximum temperature than the minimum tempera-ture in both rainy and dry season. Generally, gridded rainfall estimates have a negative correlation with temperature, for instance, higher rainfall is associated with lower temperature. In term of the sensitivity of gridded rainfall estimates against temperature, CM performs the best, followed by MONT and TR. CM, MONT and TR also show a good agreement in dry season compared to rainy season because there is possibility rainfall in dry season is more convective in nature.
4. Conclusion
The absence of structure in daily variogram can be built applying space–time variogram from 3 successive daily rainfall. All four inter-polation methods have a weakness to estimate strong rainy events. Among the other interpolation methods, CM has the best consistency in estimating rainfall, achieving the best performance in most of the as-sessment metrics. Several points can be concluded as follows: a) CM perform better than OK, indicating that gridded daily rainfall estimates in this island require additional information such as satellite data to improve rainfall estimates, b) CM performs better than TR, reflecting that high spatio-temporal variability of daily rainfall requires finer spatial resolution, c) OK mostly performs better than CM_OR and TR_OR, while CM_OR and TR_OR performs better than OK in certain
time, indicating that gridded rainfall estimates should take into account both rain gauge data and satellite data.
Further research to improve gridded daily rainfall estimates should be performed in Bali Island for estimating rainfall input for hydrological modeling since spatial variability of rainfall influences in the accuracy of streamflow prediction (Nguyen et al., 2018). The improvement of gridded daily rainfall estimates can be obtained from wind factor and distance from the sea since four interpolation methods have low ac-curacy in the leeward and coastal area. The spatial stratification of interpolation at coastal area, inner and mountainous areas probably also can improve gridded daily rainfall estimates (Beek et al., 1992). However, limited rain gauge networks in each spatial stratification can be an obstacle to detect the existence of structure in variogram on daily basis. It is also recommended to evaluate gridded daily rainfall esti-mates with both spatial stratification of the study area and space–time variogram from 3 successive daily rainfall to solve the absence of structure in daily variogram due to highly variable of spatio-temporal rainfall in Bali. It is also recommended to improve gridded daily rainfall estimates to finer scale rain gauge data to analyze erratic and strong rainy events because of the diurnal cycle of precipitation in the mountainous tropical island of Bali.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influ-ence the work reported in this paper.
Acknowledgement
The authors would like to thank Indonesia Endowment Fund for Education (LPDP) to finance this research. Special thanks also to Maciek W. Lubczynski and Z. Su for an interesting discussion about rainfall to-pics. Moreover, the author would like to thank the Master Program on Watershed and Coastal Management and Planning (MPPDAS), Faculty of Geography, Gadjah Mada University for the help during fieldwork and all institutions (such as PUSAIR and BMKG) for the data collection. The author gratefully acknowledges the comments from the anonymous re-viewers that have helped to improve this manuscript.
Fig. 10. Daily maximum and minimum temperature (in ⁰C)against daily rainfall volume (in 106m3·day−1) from two interpolation methods CM, MONT and TR,
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