View of Mapping of Design Rainfall at Multiple Return Periods Using Spatial Interpolation in Abab Sub-Watershed, Blitar Regency

(1)

Jurnal Teknik Pengairan: Journal of Water Resources Engineering, 2023, 14(1) pp. 38-52 https://jurnalpengairan.ub.ac.id/ | p-ISSN : 2086-1761 | e-ISSN : 2477-6068

____________________________________________________________________________________

Mapping of Design Rainfall at Multiple Return Periods Using Spatial Interpolation in Abab Sub-Watershed, Blitar Regency

Ageng Galih Fans Muhammad Fiqri^1*), Donny Harisuseno¹, Jadfan Sidqi Fidari¹

1Department of Water Resources Engineering, Faculty of Engineering, Brawijaya University, Malang 65145, Indonesia

Article info: Research Article

DOI :

10.21776/ub.pengairan.2023.014.01.04

Keywords:

Design rainfall; isohyet map; return period; SMADA Distrib 2.13.

Article history:

Received: 02-11-2022 Accepted: 19-05-2023

*)Correspondence e-mail:

[email protected]

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Abstract

The main occupation of residents who live in Abab Sub-Watershed, Blitar Regency, is as farmers in agriculture and plantations.

Agriculture and plantations need rain data that have been calculated to maximize the yields to be obtained. Hydrometeorological disasters, specifically floods, often occur at this location. Therefore, research is needed on calculating design rainfall, outlined in easy-to- understand isohyet maps. The research aims to assist the planning of water structures or other hydrological research without having to recalculate or retest data from the beginning. This study's utilized return periods were 2, 5, 10, and 25 years, plotted as isohyet maps.

Before calculating the design rainfall, the rainfall data had to be tested first. Calculation of design rainfall used SMADA Distrib 2.13 application and was tested with the distribution suitability test. The results of the distribution suitability test showed that Log Normal is appropriate to be used. The results of plotting the design rainfall on an isohyet map using the IDW, Kriging, and Spline methods showed that the IDW and Spline maps are smoother and not as broken as Kriging. Next, a comparative analysis of RMSE and NSE was carried out. For return periods of 2, 5, 10, and 25 years, IDW has the smallest RMSE mean value of 0.016 and the highest NSE average value of 0.9999.

Cite this as: Fiqri, A, G, F, M., Harisuseno, D., Fidari, J, S. (2023). Mapping of Design Rainfall at Multiple Return Periods Using Spatial Interpolation in Abab Sub-Watershed, Blitar Regency. Jurnal Teknik Pengairan: Journal of Water Resources Engineering, 14(1), page. 38-52. https://doi.org/10.21776/ub.pengairan.2023.014.01.04.

1. Introduction

In the past several years, Blitar Regency and its surrounding areas have experienced flooding, from minor occurrences in March 2022 with a water surface height of 30 cm to major incidents in February 2020 with a water surface height of 1.5 m. The Abab sub-watershed, which mostly lies in Blitar Regency, relies on agriculture and plantations as the primary field of work and is thus in great need of rainfall and rainfall data. The Regional Disaster Management Agency (BPBD) of the Blitar Regency website stated that floods have often occurred almost every year, caused by torrential rains[1]. The floods that occurred have caused many losses, both small and large. Major losses have been recorded in broken bridges and inundated fields, causing crop losses. The planning of water structures certainly needs hydrological data, which in this case concerns rainfall data. The existing rainfall data cannot be immediately used; it is necessary to conduct a quite extensive process of analysis and testing on the hydrological data. After going through several stages of analysis and testing, only then can the data be used in the calculations to plan water structures.

In Indonesia, rainfall stations or posts only take rainfall data from a single point (the point rainfall). Therefore, the rainfall data comprising point rainfall cannot illustrate the amount of rainfall for a certain region or area expanse. As such, it is necessary to use a method to transform that point rainfall of a single point into regional rainfall [2]. One of the most accurate methods to transform that point rainfall of a single point into regional rainfall is the isohyet method. The isohyet method is the most detailed method for calculating mean rainfall intensity for a certain stretch of a region. In

(2)

39 Fiqri, Harisuseno, Fidari: Mapping of Design Rainfall of Various Return Periods for Abab Sub-Watershed research on rainfall distribution in the Jangkok watershed of Lombok Island, which compared several methods of rainfall distribution (arithmetic, Thiessen polygons, and isohyet), the result was that the isohyet method was the method that had the greatest calculation accuracy in the calculation of the mean regional rainfall [3].

Calculations for the isohyet map may use three methods, which are Inverse Distance Weighted (IDW), Kriging, and Spline. These three methods have advantages and disadvantages, resulting in differing interpolation results. [4] in research comparing rainfall interpolation methods in East Java, IDW interpolation had the smallest error. Meanwhile, [5] Another study comparing interpolation methods for data on solar energy potential in South Jakarta concluded that the Spline method had more precise results. Further, [6] stated that the Kriging method was more accurate in the research regarding the comparison of accuracy for interpolation methods for the mapping of groundwater- surface in Sleman Regency.

This research aims to plot the mean rainfall using the isohyet method as a map that can be easily read and understood to aid in planning water structures. The calculation for the isohyet method used three methods: Inverse Distance Weighted (IDW), Kriging, and Spline, for which the most appropriate method for calculating the planned rainfall is to be determined. Creating an isohyet map can provide input as a reference for research on water resources and/or the planning of water structures to lighten the workload.

2. Materials and Methods

2.1. Materials 2.1.1. Study Location

This research is located on the Abab sub-watershed as seen at Figure 1, which covers several regions such as Blitar Regency, Tulungagung Regency, Kediri Regency, and the City of Blitar in East Java. The Abab sub-watershed geographically located within 111° 55' 00" – 112° 18' 00" East Longitude and 7°50' 00" – 8° 13' 00" South Latitude. The Abab sub-watershed, which lies at an elevation greater than 100 m above sea level, belongs to the area of the Abab watershed, is 26 km wide, and has a watershed area of 536.46 km². This region is generally used as an agricultural region for growing crops such as sugarcane, rice paddies, tobacco, pineapple, and other vegetables. In addition, the Abab sub-watershed possesses 22 rain stations that are spread out in the region.

The region of Abab sub-watershed sufficiently varied elevation, with an average elevation of 243 meters above sea level. The southern part of the Abab sub-watershed is made up of rocky hills, while the northern part is of fertile land due to the still-active Mount Kelud and the evenness of river flows in the area. The annual rainfall of the Abab sub-watershed has a mean of 1,478.8 mm, with the highest being 2,618.2 mm and the lowest being 1,024.7 mm per year. The area of the Abab sub-watershed is composed of 19.96% land for wet fields, 35.34% plantations, and 26.85% houses and their yards, with the rest being used for pastures or meadows, fish farming, forests, ponds, and other purposes.

2.1.2. Research Data

Before conducting this research, the data that would be used in the research were first collected, which comprised:

1. Map of the Abab sub-watershed 2. Regional map of Blitar Regency 3. Coordinates of rain stations

4. Daily rainfall data from 22 rain stations for 20 years (2002-2021) 2.2. Method

The isohyet map of design rainfall of various return periods will assist the calculations for planning water structures or research on water resources. Before calculating design rainfall, the rainfall data was first tested. The tests involved consistency testing, absence of trends testing, stationary testing, persistence testing, and outlier testing.

(3)

40 Fiqri, Harisuseno, Fidari: Mapping of Design Rainfall of Various Return Periods for Abab Sub-Watershed

Figure 1. Location Map of the Abab Sub-Watershed and Rain Stations

2.3. Method

The isohyet map of design rainfall of various return periods will assist the calculations for planning water structures or research on water resources. Before calculating design rainfall, the rainfall data was first tested. The tests involved consistency testing, absence of trends testing, stationary testing, persistence testing, and outlier testing.

This study's design rainfall was calculated using the Log Normal, Gumbel, and Log Pearson III methods, for which the most suitable utilized method was then determined. The SMADA Distrib 2.13 application was used to calculate the design rainfall. The determination of the most suitable utilized method used goodness of fit testing.

After the design rainfall with return periods of 2, 5, 10, and 25 years were obtained, this was followed by plotting them as an isohyet map. The utilized method for creating the isohyet map was spatial interpolation with IDW, Kriging, and Spline. Finally, RMSE and NSE comparison analyses were performed to find the best and most appropriate spatial interpolation method for the Abab sub- watershed area.

The following are the stages in the research that were conducted.

1. Testing of Rainfall Data

The obtained rainfall data cannot be used immediately for hydrologic analysis. Before conducting the analysis, the rainfall data needed to be tested first. The data were tested to determine the data quality, which would later be used.

a. Filling in missing rainfall data with the Normal Ratio Method.

The Normal Ratio Method has the requirement that rain stations that are missing data are to possess its rata-rata mean annual rainfall, although aided by data on mean annual rainfall and data from surrounding rain stations [6].

b. Consistency Testing with Double Mass Curve.

Consistency testing of the data is an activity of testing to find out changes in the environment or even changes in measurement methods [6].

c. Absence of Trends Testing with Rank Correlation by the Spearman, Mann-Whitney, and Cox-Stuart Methods.

The absence of trend testing aims to determine trends or variations in the rainfall data.

d. Stationary Testing with T-Test and F-Test.

Stationary testing aims to test the mean stability and variances of time-series data.

(4)

e. Persistence Testing.

Persistence testing aims to determine whether or not the tested data came from free or random sampling. It means that free data are not time-dependent, and random data possess the same opportunity to be selected.

f. Outlier Testing.

Outlier testing was performed to evaluate whether the maximum and minimum data from the data series were appropriate to be used or not.

2. Calculating the Design Rainfall

The objective of frequency analysis is to calculate estimates of variance values with certain recurrences [7]. Calculations for frequency analysis with the Log Normal, Gumbel, and Log Pearson III methods used the SMADA Distrib 2.13 application. Then, the goodness of fit testing was performed to find the appropriate method of frequency analysis for the Abab sub- watershed. There are two calculation methods for parameter testing: the Chi-Squared and Kolmogorov-Smirnov tests. The Chi-Squared test was used for vertical goodness of fit testing, while the Kolmogorov-Smirnov test was used for horizontal goodness of fit testing.

3. Plotting the Isohyet Map

The isohyet method involves lines that connect points with the same rainfall height. Rainfall for a region within two of these isohyet lines in this method is considered even and the same as the mean value of the two isohyet lines [8]. The utilized methods of spatial interpolation were IDW, Kriging, and Spline. IDW calculations involve pure interpolation from station distances, Kriging considers factors that affect estimation accuracy, while Spline results in appropriate interpolated values through sample points [9].

4. Performing Comparison Analysis

Comparison analysis was performed to find the best method among IDW, Kriging, and Spline. The utilized comparison methods were Root-Mean-Square Error (RMSE) and Nash- Sutcliffe Efficiency (NSE). The formula for RMSE is shown as Equation 1, and the formula for NSE is shown as Equation 2.

RMSE =

√

^∑^𝑛^𝑖=1^(𝑥^𝑖^−y^𝑖⁾²

𝑛

(1)

Remarks:

𝑥_𝑖 = observed values on the field

y_𝑖 = resulting values from interpolation calculations n = number of data

NSE = 1 − ^∑ ^(𝑥^𝑖^−y^𝑖⁾

𝑛 2 𝑖=1

∑^𝑛_𝑖=1(𝑥_𝑖−𝑥_̅𝑖)²

(2) Remarks:

𝑥_𝑖 = observed values on the field

y_𝑖 = resulting values from interpolation calculations 𝑥̅_𝑖 = mean of field-observed values

n = number of data

2.3.1. SMADA Distrib 2.13 Application

The Stormwater Management and Design Aid (SMADA) application is an application to assist in the calculation and analysis of stormwater systems. Distribution analysis with the SMADA application may be carried out by using the DISTRIB 2.13 (Statistical Distribution Analysis) module.

There are six distribution methods: the Normal Method, the Log Normal Method, the 3 Parameter Log Normal Method, the Log Pearson Type III Method, Log Pearson Type III Method, and Gumbel Method. In this study, the calculation methods of Log Normal, Gumbel, and Log Pearson III were used.

2.3.2. Inverse Distance Weighted (IDW)

The Inverse Distance Weighted (IDW) method is a simple interpolation method considering surrounding points (NCGIA 1997). This method assumes that if the point distance is close to the

(5)

42 Fiqri, Harisuseno, Fidari: Mapping of Design Rainfall of Various Return Periods for Abab Sub-Watershed sample point, the chance of the value approaching the sample point becomes greater. The Inverse Distance Weighted method uses the mean of sample data. Thus the interpolated value cannot be larger than the maximum value of the sample data or smaller than the sample data. Therefore, it cannot evaluate from the top of a hill or the deepest bottom of a valley. Furthermore, the utilized data samples must be close together so that the interpolated data results have good values. The possibility that the results are not appropriate may occur if the samples are uneven and the distance between samples is relatively too great.

𝑢(𝑥) =

∑

^𝑤^𝑖^(𝑥)𝑢^𝑖

∑^𝑛_𝑗=0𝑤_𝑗(𝑥)

𝑛𝑖=0

(3)

𝑤_𝑖(𝑥) = ¹

𝑑(𝑥 , 𝑥_𝑖)^𝑝 (4)

Remarks:

ui = u (xi), for i = 0, 1, 2, …, n wi = weight factor of point i x = point to be interpolated xi = known data sample point d = distance between point x and xi

n = number of points

p = power (positive real number) 2.3.3. Kriging

This method assumes that distances and orientations among data samples demonstrate important spatial correlation in interpolation calculation (ESRI 1996). The Kriging method is an interpolation estimation method that resembles IDW, which uses a linear combination of weight to estimate values among data samples. Kriging considers factors that affect accuracy, such as the number of data samples, the position of data samples, the distance between data samples and points to be estimated, the spatial continuity of involved variables, and others. Kriging can calculate the highest and lowest value variances that are not attached to the values of the data sample. Meanwhile, a shortcoming of this method is that there are many ways of constructing it, and thus it requires many assumptions that are hard to fulfill. The Kriging method assumes that data has a normal distribution, while the mean data on the field are not distributed as such.

Z^* =

∑

^𝑛_𝑖=0

𝑤

_𝑖

𝑧

_𝑖 (5)

Remarks:

Z^*= point to be interpolated

zi = measured point at observation location i wi = weight value for location i

2.3.4. Spline

The Spline method results in appropriate surface modeling through sample points. The Spline method uses an interpolation method that estimates values using a mathematical functional formula to minimize all surface curves, resulting in a smoother appearance of all surfaces passing through the input points. This method possesses an advantage in its ability to produce calculation results with sufficiently good accuracy of surfaces, even if there is little of the utilized data. The Spline method is ideal for creating surfaces such as earth contours, groundwater-surface height, or air pollution concentration. However, the method is not ideal to be used when there are significant differences in value at very close distances, as a drawback of the Spline method is that the method cannot perform maximally when very close sample points possess very large value differences. It is because the method uses slope calculations that change based on the distance to estimate surface form.

𝑆(𝑥, 𝑦) = 𝑇(𝑥, 𝑦) + ∑^𝑛_𝑗=1λ_𝑗𝑅(𝑟_𝑗) (6)

(6)

Remarks: j = 1, 2, …, n; n = number of points; λ_𝑗 = coefficient determined from the linear equation system; 𝑟_𝑗 = distance from the point (𝑥, 𝑦) to the j^th point; 𝑆(𝑥, 𝑦) represents the polynomial cubic function; 𝑇(𝑥, 𝑦) and 𝑅(𝑟) are interpreted differently according to the selection method.

3. Results and Discussion

The return periods used in this study were return periods of 2, 5, 10, and 25 years. The selection of the return periods was based on the design return periods often used by projects listed in the Department of Public Works (1987). They were plotted into isohyet maps after calculating the planned rainfall for various return periods.

3.1. Calculation of Design Rainfall

The rainfall data were first tested before performing calculations for the design rainfall. The performed tests were for consistency, absence of trends, stationary quality, persistence, and outliers.

For the results, it was found that corrections were needed for several rain stations when tested for consistency with Double Mass Curve. The absence of three-step trend testing showed no trends in all rain stations with α = 5%. For stationary testing, all data from rain stations were found to have stable values of variance and means with α = 5%. Next, for persistence testing, all data from rain stations showed no dependence with α = 5%. Finally, the outlier test showed that there were eight rain stations whose data were found to exceed the threshold, and thus the excessive data were discarded. The annual data that after tested are shown at Table 1, Table 2, and Table 3.

Table 1. Annual Rainfall Data After Testing, Birowo-Kaulon

Year

Annual Rainfall Data (mm)

Birowo Bondogerit Garum Gogolatar Judeg Kademangan Kaliputih Kaulon

2002 1702 1359 2205 1965 1791 1369 2115 1783

2003 1519 1621 2126 2212 2090 1672 2698 1685

2004 1934 2185 2578 2127 2226 1828 1452 1725

2005 1781 2080 2097 2187 1826 2081 2322 1618

2006 1478 3221 2031 2087 1398 1738 2297 1717

2007 1841 2230 2418 2639 1754 2227 2700 2273

2008 1793 1472 1966 1885 1269 1539 1955 1351

2009 1316 1587 1700 1562 1265 1371 1826 1472

2010 3105 2906 1550 3484 1995 3256 4079 3430

2011 1629 1474 1508 2350 1153 1981 2178 1752

2012 1950 1440 1717 2015 1282 1658 2137 1785

2013 1268 1759 1843 1590 1079 1634 2053 1327

2014 1756 1526 1837 1925 1155 1433 2072 1496

2015 1457 1342 2134 1907 1115 1666 2452 1665

2016 2420 2523 3030 3183 2431 2647 3934 3009

2017 1857 851 2210 2132 1842 1607 2360 1966

2018 1644 1591 1959 1863 1432 1252 2048 1582

2019 1104 1313 1581 1510 1145 1008 1784 1333

2020 2180 3249 2145 2495 2064 1083 2585 2204

2021 2593 2450 2509 2946 2089 1444 3085 2265

(7)

Table 2. Annual Rainfall Data After Testing, Kepanjenlor-Slemanan

Year

Annual Rainfall Data (mm)

Kepanjenlor Kesamben Klampok Lodoyo Mangunan Ngrendeng Slemanan

2002 1440 2075 1480 1513 2195 2255 1199

2003 1590 1856 1811 1489 1963 2251 1739

2004 2087 2219 1641 2212 2110 1772 1851

2005 1779 1758 1690 1693 2120 1690 1926

2006 1827 1861 1434 1140 2034 1918 2545

2007 1906 2375 2149 1743 2056 2114 2133

2008 1564 2137 1426 1304 1976 2200 2208

2009 1636 1278 1428 1353 1589 1436 1917

2010 2934 3354 2753 2745 4081 3032 4182

2011 1810 2036 1711 1409 2022 1915 1726

2012 1659 2470 1721 1913 2014 2310 1884

2013 1830 1411 1366 955 1691 1439 1550

2014 1479 1433 1391 1155 1726 1472 1324

2015 1463 2005 1455 1373 1964 2034 1907

2016 3838 3280 2746 2268 3248 3347 2587

2017 2273 2207 1657 2157 2535 2304 2256

2018 2167 1662 1681 1776 1888 1860 1688

2019 1634 1344 1642 1600 1528 1643 1506

2020 2854 2237 1848 2450 2805 2165 2312

2021 2937 2490 1904 2504 2654 2004 2496

Table 3. Annual Rainfall Data After Testing, Srengat-Bantaran

Year Annual Rainfall Data (mm)

Srengat Sumberingin Talun Wlingi Wonodadi Kalimanis Bantaran

2002 1835 1855 2034 2547 1672 2209 1727

2003 1454 1888 2497 1912 1255 2137 1691

2004 1535 1952 2297 2563 1196 2338 1832

2005 1601 2044 2141 2538 1578 1749 2357

2006 1794 2257 1927 2258 1524 1980 1544

2007 1794 2370 3237 2778 1789 2293 1940

2008 1623 1621 1899 2227 1406 2264 1639

2009 1538 1909 1793 1816 1291 1393 1376

2010 3145 3101 3285 3773 2902 3172 3100

2011 1468 1637 2027 2540 1466 1852 1685

2012 1714 1439 2213 2407 1600 2450 1730

2013 1140 1477 1421 1869 1353 1464 1527

2014 1124 1442 1392 2034 888 1496 1790

2015 1437 1878 1777 2188 1440 2256 1669

2016 2756 3734 3316 3875 2798 3684 3356

(8)

Year Annual Rainfall Data (mm)

Srengat Sumberingin Talun Wlingi Wonodadi Kalimanis Bantaran

2017 1747 2756 1912 2816 1661 2534 2060

2018 1505 2004 1923 2377 1637 1710 2002

2019 1202 1786 1445 1942 1390 1491 2474

2020 1829 2893 2401 2803 2061 2322 3886

2021 1980 2643 2441 2139 2168 2621 3692

Design rainfall was calculated using the SMADA Distrib 2.13 apps and plotted in Figure 2. The calculation of the design rainfall used the Log Normal, Gumbel, and Log Pearson type III methods.

Then, the goodness of fit testing was performed to find the suitable method for Abab sub-watershed.

The goodness of fit testing results for the design rainfall using the Log Normal, Gumbel, and Log Pearson type III methods showed that the Log Normal method was the most suitable for the Abab sub-watershed region. The utilized goodness of fit tests were the Chi-Squared tests as shown in Table 4, and Kolmogorov-Smirnov tests in Table 5. From the calculations of the goodness of fit testing as above, it was found that for the Chi-Squared test, the Log Normal method passed the test with α = 1%. Meanwhile, for the Kolmogorov-Smirnov test, the three methods passed the test with α = 5%, where Log Normal had the smallest calculated value. The Summary of Log-Normal Calculation is shown in Table 6.

Table 4. Summary of Calculations for the Chi-Squared Test of the Three Methods

No Rain Station

Results

Log-Normal Gumbel Log Pearson

X²hit 5% 1% X²hit 5% 1% X²hit 5% 1%

1 Birowo 9.158 Rejected Accepted 12.842 Rejected Rejected 18.63 Rejected Rejected 2 Bondogerit 1.500 Accepted Accepted 5.500 Accepted Accepted 3.500 Accepted Accepted 3 Garum 1.789 Accepted Accepted 4.421 Accepted Accepted 3.368 Accepted Accepted 4 Gogolatar 3.500 Accepted Accepted 2.000 Accepted Accepted 2.500 Accepted Accepted 5 Judeg 4.947 Accepted Accepted 3.895 Accepted Accepted 4.947 Rejected Accepted 6 Kademangan 7.053 Rejected Accepted 10.211 Rejected Rejected 6.526 Rejected Accepted 7 Kaliputih 6.500 Rejected Accepted 10.000 Rejected Rejected 6.500 Rejected Accepted 8 Kaulon 4.000 Accepted Accepted 1.500 Accepted Accepted 2.500 Accepted Accepted 9 Kepanjenlor 2.000 Accepted Accepted 2.000 Accepted Accepted 2.000 Accepted Accepted 10 Kesamben 1.263 Accepted Accepted 0.737 Accepted Accepted 0.211 Accepted Accepted 11 Klampok 3.368 Accepted Accepted 5.474 Accepted Accepted 3.895 Rejected Accepted 12 Lodoyo 3.368 Accepted Accepted 2.316 Accepted Accepted 3.368 Accepted Accepted 13 Mangunan 5.000 Accepted Accepted 12.500 Rejected Rejected 2.500 Accepted Accepted 14 Ngrendeng 6.500 Rejected Accepted 5.500 Accepted Accepted 6.500 Rejected Accepted 15 Slemanan 1.000 Accepted Accepted 2.500 Accepted Accepted 1.000 Accepted Accepted 16 Srengat 1.000 Accepted Accepted 3.500 Accepted Accepted 1.500 Accepted Accepted 17 Sumberingin 1.000 Accepted Accepted 1.000 Accepted Accepted 1.000 Accepted Accepted 18 Talun 1.789 Accepted Accepted 1.789 Accepted Accepted 1.789 Accepted Accepted 19 Wlingi 0.500 Accepted Accepted 3.000 Accepted Accepted 0.500 Accepted Accepted 20 Wonodadi 3.000 Accepted Accepted 4.500 Accepted Accepted 2.000 Accepted Accepted 21 Kalimanis 2.000 Accepted Accepted 4.000 Accepted Accepted 2.000 Accepted Accepted 22 Bantaran 1.500 Accepted Accepted 1.000 Accepted Accepted 2.500 Accepted Accepted

(9)

Table 5. Summary of Calculations for the Kolmogorov-Smirnov Test of the Three Methods

No Rain Station

Results

Log Normal Gumbel Log Pearson

X²hit 5% 1% X²hit 5% 1% X²hit 5% 1%

1 Birowo 0.177 Accepted Accepted 0.197 Accepted Accepted 0.221 Accepted Accepted 2 Bondogerit 0.096 Accepted Accepted 0.087 Accepted Accepted 0.130 Accepted Accepted 3 Garum 0.161 Accepted Accepted 0.123 Accepted Accepted 0.145 Accepted Accepted 4 Gogolatar 0.117 Accepted Accepted 0.103 Accepted Accepted 0.119 Accepted Accepted 5 Judeg 0.083 Accepted Accepted 0.101 Accepted Accepted 0.115 Accepted Accepted 6 Kademangan 0.176 Accepted Accepted 0.183 Accepted Accepted 0.238 Accepted Accepted 7 Kaliputih 0.171 Accepted Accepted 0.139 Accepted Accepted 0.165 Accepted Accepted 8 Kaulon 0.126 Accepted Accepted 0.102 Accepted Accepted 0.135 Accepted Accepted 9 Kepanjenlor 0.086 Accepted Accepted 0.054 Accepted Accepted 0.131 Accepted Accepted 10 Kesamben 0.077 Accepted Accepted 0.080 Accepted Accepted 0.144 Accepted Accepted 11 Klampok 0.104 Accepted Accepted 0.148 Accepted Accepted 0.115 Accepted Accepted 12 Lodoyo 0.125 Accepted Accepted 0.089 Accepted Accepted 0.152 Accepted Accepted 13 Mangunan 0.171 Accepted Accepted 0.152 Accepted Accepted 0.146 Accepted Accepted 14 Ngrendeng 0.186 Accepted Accepted 0.150 Accepted Accepted 0.183 Accepted Accepted 15 Slemanan 0.083 Accepted Accepted 0.073 Accepted Accepted 0.149 Accepted Accepted 16 Srengat 0.085 Accepted Accepted 0.118 Accepted Accepted 0.164 Accepted Accepted 17 Sumberingin 0.119 Accepted Accepted 0.095 Accepted Accepted 0.117 Accepted Accepted 18 Talun 0.134 Accepted Accepted 0.124 Accepted Accepted 0.152 Accepted Accepted 19 Wlingi 0.095 Accepted Accepted 0.090 Accepted Accepted 0.107 Accepted Accepted 20 Wonodadi 0.091 Accepted Accepted 0.128 Accepted Accepted 0.154 Accepted Accepted 21 Kalimanis 0.106 Accepted Accepted 0.111 Accepted Accepted 0.163 Accepted Accepted 22 Bantaran 0.105 Accepted Accepted 0.118 Accepted Accepted 0.153 Accepted Accepted

Table 6. Summary of Log-Normal Calculation

No Rain Station Returning Period, Log Normal Method (mm)

2 5 10 25

1 Birowo 97.850 113.410 122.520 133.030

2 Bondogerit 90.890 117.320 134.090 154.610

3 Garum 90.320 102.840 110.070 118.350

4 Gogolatar 86.140 99.930 108.010 117.340

5 Judeg 94.820 115.560 128.160 143.110

6 Kademangan 99.440 117.200 127.730 139.990

7 Kaliputih 108.100 128.950 141.410 156.020

8 Kaulon 90.310 110.320 122.490 136.960

9 Kepanjenlor 98.320 118.420 130.530 144.810

10 Kesamben 97.300 123.030 139.100 158.560

11 Klampok 100.980 126.970 143.140 162.650

(10)

No Rain Station Returning Period, Log Normal Method (mm)

2 5 10 25

12 Lodoyo 81.530 100.140 111.510 125.050

13 Mangunan 128.690 160.610 180.350 204.080

14 Ngrendeng 90.190 108.570 119.630 132.670

15 Slemanan 102.920 123.910 136.540 151.440

16 Srengat 102.360 138.610 162.440 192.370

17 Sumberingin 97.820 116.240 127.230 140.080

18 Talun 90.090 102.310 109.360 117.400

19 Wlingi 106.060 133.580 150.710 171.400

20 Wonodadi 108.840 143.080 165.090 192.310

21 Kalimanis 97.980 119.080 131.870 147.020

22 Bantaran 76.630 95.520 107.200 121.220

Figure 2. Chart of Log Normal Distribution in the SMADA Application

3.2. Mapping Results

The distribution of design rainfall was mapped using the interpolation techniques of Inverse Distance Weighted (IDW), Kriging, and Spline. The execution of spatial interpolation required data on the coordinates of all rain stations and calculation results for design rainfall of each return period.

After plotting, a comparison analysis was performed to find the best method.

From Figure 3, for the return period of 2 years, the IDW method resulted in interpolated values at 76-129 mm, and the interpolation lines was quite smooth, with the rain stations as the center point for interpolation lines. For the Kriging method, the interpolated values were at 77-129 mm with broken interpolation lines, particularly on the upper left. Meanwhile, for the Spline method, the interpolated values were at 64-151 mm, with smooth interpolation lines that on average precisely passed through the rain station points.

From Figure 4, for the return period of 5 years, the interpolation lines appeared to become denser.

For the IDW method, the interpolated values were at 95-161 mm with interpolation lines that are quite smooth and more even with the rain stations at their center points. The Kriging method's interpolated values were 96-161 mm, with many interpolation lines broken on the upper left, center, and right. Finally, for the Spline method, the interpolated values were 72-188 mm, with denser and all interpolation lines passing through the rain station points.

(11)

48 Fiqri, Harisuseno, Fidari: Mapping of Design Rainfall of Various Return Periods for Abab Sub-Watershed 3.2.1. Return Period of 2 Years

Figure 3. Mapping Results, 2-Year Return Period (a) IDW (b) Kriging (c) Spline

3.2.2. Return Period of 5 Years

(a) (b)

(c)

IDW KRIGING

SPLINE

(mm) (mm) (mm)

(a) (b)

(c)

IDW KRIGING

SPLINE

(mm) (mm) (mm)

(12)

49 Fiqri, Harisuseno, Fidari: Mapping of Design Rainfall of Various Return Periods for Abab Sub-Watershed 3.2.3. Return Period of 10 Years

From Figure 5, for the return period of 10 years, the density of interpolation lines appeared to increase further. The IDW method had interpolated values at 107-180 mm, and the interpolation lines were quite smooth. However, there were several breaks, and the rain stations were the center points of interpolation lines. The Kriging method had interpolated values at 108-180 mm, with many interpolation lines still with breaks on the upper left, center, and right. Meanwhile, the Spline method had interpolated values at 77-213 mm, with even denser interpolated lines and all interpolation lines still passing through the rain station points.

3.2.4. Return Period of 25 Years

(a) (b)

(c)

IDW KRIGING

SPLINE

(mm) Kriging 10th (mm) (mm)

(a) (b)

(c)

IDW KRIGING

SPLINE

(mm) Kriging 25th (mm) (mm)

(13)

From Figure 6, for the return period of 25 years, the interpolation lines appeared to become even denser. The IDW method had interpolated values at 117-204 mm, and the interpolation lines were still quite smooth with the rain stations as the central points of the interpolation lines, indicating that the interpolation results depended on distance. Greater distances mean the values will also be further off from the data. The Kriging method had interpolated values at 118-204 mm, with still many interpolation lines with many breaks on the upper left, center, and right, as the Kriging method results in calculations that are imperfect if there are large value differences at close distances. Meanwhile, the Spline method had interpolated values at 82-243 mm, with all interpolation lines passing through the rain station points, which was more suitable for creating contours. The interpolation results with the Spline method showed the largest value for the maximum interpolation value and the smallest value for the minimum interpolation value.

3.3. Comparison Analysis

The utilized comparison methods were Root-Mean-Square Error (RMSE) and Nash-Sutcliffe Efficiency (NSE) [10]. The compared data were designed rainfall data for the field (Log-Normal) with data from interpolation results by three methods (IDW, Kriging, and Spline). Other similar studies resulted in different conclusions. For example, [4] a study comparing methods of rainfall interpolation in East Java concluded that IDW interpolation has a smaller error. Meanwhile, [5]

Another study comparing data interpolation methods for the potential of solar energy in South Jakarta concluded that Spline had more precise results. Finally, [6] stated that Kriging was more accurate for the research on the accuracy of interpolation methods on the mapping of groundwater-surface in Sleman Regency. As such, it was still impossible to determine which calculation was the best and perfect for creating these isohyet maps. However, at the end of the analysis, it would be possible to determine which of the three methods was the best and most accurate for interpolation calculations to create isohyet maps for design rainfall.

The resulting interpolation values from the three methods appeared quite similar compared to the distribution Log Normal. In addition, the 20-year data span resulted in interpolation values that approached the condition of field data. The followings are the field data and interpolation results for return periods of 2, 5, 10, and 25 years in the form of charts as seen in Figure 7.

Figure 7. Chart of Interpolation Results and Log Normal Distribution Calculation

(14)

3.3.1. Root-Mean-Square Error (RMSE)

The RMSE values obtained for the IDW method were small or close to 0 for the Kriging method were farther from 0 with larger return periods, and for the Spline method were close to 0 though not as small as IDW. Therefore, it may be regarded that the IDW method had the smallest error values, followed by the Spline method which had quite small error values that approached zero. Lastly, the Kriging method had larger error values as the return period increased. The Summary of RMSE calculations results are shown in Table 7.

Table 7. Summary of RMSE Calculation Results

No Method RMSE

2 5 10 25

1 IDW 0.007 0.010 0.012 0.016

2 Kriging 0.163 0.232 0.288 0.363

3 Spline 0.117 0.178 0.229 0.298

3.3.2. Nash-Sutcliffe Efficiency (NSE)

NSE has criteria or indicators for evaluating the model's resemblance to field data [11]. For example, the NSE values obtained for the IDW, Kriging, and Spline methods were between 0.75 and 1, which are very good criteria. The Summary of NSE calculation results is shown in Table 8.

Table 8. Summary of NSE Calculation Results

No Method NSE

2 5 10 25

1 IDW 0.9999 0.9999 0.9999 0.9999

2 Kriging 0.9998 0.9997 0.9997 0.9997

3 Spline 0.9999 0.9998 0.9998 0.9998

4. Conclusion

Based on the results, using the Log Normal method, the calculation of design rainfall with return periods of 2, 5, 10, and 25 years using the SMADA Distrib 2.13 application for the Abab sub- watershed is most suitable. The calculation that passed the goodness of fit tests, as the Kolmogorov- Smirnov test and Chi-Squared test, was the Log Normal method, and thus the Log Normal method was chosen as the method to be used based on the goodness of fit testing. Through calculations by the IDW, Kriging, and Spline methods with return periods of 2, 5, 10, and 25 years, it is found that the interpolation values of the IDW and Spline methods have sufficient similarity to the field data.

In contrast, the interpolation values of Kriging have large differences as the return period becomes larger. From the resulting interpolation maps, the IDW and Spline methods result in smooth interpolation lines, and the results of Spline interpolation produce lines that pass through several rain station points. With the Kriging method for return periods of 2, 5, 10, and 25 years, the interpolation lines are quite smooth, but there are interpolation lines with breaks. The results of comparing isohyet rainfall distribution maps made with the IDW, Kriging, and Spline methods by using the RMSE and NSE methods show that RMSE calculations for IDW have the smallest error values, for Spline have quite small error values close to zero, and for Kriging have large error values as the return period became larger. Meanwhile, from the results of NSE calculations, the IDW, Kriging, and Spline methods are good evaluation criteria, as all the calculation results have values from 0.75-1. This research shows that the IDW method is selected to create the design rainfall map for the Abab sub- watershed with the resulting smooth interpolation lines, the smallest RMSE values close to 0, and the NSE values closest to 1.

Acknowledgments

For this study, the authors would like to express gratitude to the Department of Public Works and Housing of Blitar Regency for the permission to request rainfall data and the Brantas River Authority to provide map data.

(15)

References

[1] Blitar Regency Regional Disaster Management Agency (Badan Penanggulangan Bencana Daerah Kabupaten Blitar), “The BNPB Team Verifies Bridges Damaged by the Disaster in Blitar Regency (Tim BNPB Melakukan Verivikasi Jembatan Rusak Akibat Bencana di Kabupaten Blitar),” 2021.https://bpbd.blitarkab.go.id/read/8628/agenda-kegiatan/tim-bnpb- melakukan-verifikasi-jembatan-rusak-akibat-bencana-di-kabupaten-blitar.html (accessed March 11, 2022).

[2] Ningsih, Dewi Handayani Untari, “Thiessen Polygon Method for Forecasting Rainfall Distribution for Certain Periods in Areas Without Rainfall Data (Metode Thiessen Polygon untuk Ramalan Sebaran Curah Hujan Periode Tertentu pada Wilayah yang Tidak Memiliki Data Curah Hujan),” Jurnal Teknologi Informasi 17(2): 154-163, 2012.

[3] Adam, Riandi Ashab, “Comparative Analysis of the Use of Arithmetic Methods, Thiessen Polygons and Isohyets in Calculation of Regional Average Rainfall (Jangkok Watershed Site Study) ((Analisis Perbandingan Penggunaan Metode Aritmatika, Poligon Thiessen Dan Isohyet Dalam Perhitungan Curah Hujan Rerata Daerah) (Studi Lokasi DAS Jangkok)),”

Jurusan Teknik Sipil, Universitas Mataram, 2019.

[4] Kurniadi, Hanif, Erlita Aprilia, Joko Budi Utomo, Andang Kurniawan, and Agus Safril,

“Comparison of IDW and Spline Methods in Rainfall Data Interpolation (Perbandingan Metode IDW Dan Spline Dalam Interpolasi Data Curah Hujan),” Prosiding Seminar Nasional Geotik 2018. 1(1): 213-220, 2018.

[5] Fitri, Silvy Rahmah, Edi Saadudin, and Bono Pranoto, "Comparison of Inverse Distance Weighted (IDW), Natural Neighbor, and Spline Interpolation Methods for Condensing Solar Energy Potential Map Data (Perbandingan Metoda Interpolasi Inverse Distance Weighted (IDW), Natural Neighbour, Dan Spline Untuk Perapatan Data Peta Potensi Energi Surya),"

Jurnal Ketenagalistrikan dan Energi Terbarukan 13(1): 27-38, 2014.

[6] Sejati, Sadewa Purba, “Comparison of the Accuracy of the IDW and Kriging Methods in Mapping the Groundwater Table (Perbandingan Akurasi Metode IDW dan Kriging dalam Pemetaan Muka Air Tanah),” Majalah Geografi Indonesia 33(2): 49-57, 2019.

[7] Soemarto, CD, Engineering Hydrology (Hidrologi Teknik), Malang: UB Press, 1987.

[8] Triatmojo, B, Applied Hydrology (Hidrologi Terapan), Malang: UB Press, 2013.

[9] Junita Monika Pasaribu Dan Nanik Suryo Haryani, "Comparison of Dem Srtm Interpolation Techniques with Inverse Distance Weighted (IDW), Natural Neighbor and Spline Methods (Perbandingan Teknik Interpolasi Dem SRTM Dengan Metode Inverse Distance Weighted (IDW), Natural Neighbor Dan Spline)", Jurnal Penginderaan Jauh Vol. 9 No. 2. Lapan, 2012.

[10] Moriasi, D. N., M. W. Gitau, N. Pai, and P. Daggupati, "Hydrologic And Water Quality Models: Performance Measures And Evaluation Criteria." Journal of American Society of Agricultural and Biological Engineers 58(6): 1763-1785, 2015.

[11] Suhartanto, Ery, Evi Nur Cahya, and Luluil Maknun, “Runoff Analysis Based on Rainfall Using an Artificial Neural Network (ANN) Model in the Upper Brantas Sub-Das (Analisa Limpasan Berdasarkan Curah Hujan Menggunakan Model Artifical Neural Network (ANN) di Sub Das Brantas Hulu),” Jurnal Teknik Pengairan 10(2): 134-144, 2019.