A comparative study of SPI, PCI, PCD, and RAI methods for estimating drought in the Palu River Basin, Indonesia

The Palu Watershed is vulnerable to extreme hydrological events, especially periods of heavy rains and prolonged dry seasons. This study aims to determine the drought index and the results of a comparison of the drought index between the Standardized Precipitation Index (SPI) and the Rainfall Anomaly Index (RAI), Rainfall Concentration Index (PCI), Rainfall Concentration Level (PCD), and Rainfall Concentration Period (PCP). The data used are monthly rainfall from Bora, Kalawara, Kulawi, Palolo, and Wuasa stations with observation periods from 1985 to 2021. The Pearson and Spearman correlation coefficients are used to determine the relationship between SPI and RAI, PCI, PCD, and PCP. RMSE and MAE are used to find out the absolute error in predictions. The results obtained show: PCI shows a uniform distribution of rainfall (76.57%) and moderately seasonal (32.43%) there is no distribution of seasonal and strongly seasonal rainfall, the dominant SPI is the normal category followed by mild and moderate drought, PCD and PCP show that rainfall is homogeneous and distributed throughout years and no rain is concentrated at any one time, Comparison of the relationship between SPI and RAI is very strong and significant compared to SPI versus PCI, SPI versus PCD and SPI versus PCP.


Introduction
The dynamics of the planetary climate, coupled with increased human activities, lead to changes in climate patterns that have a direct impact on natural ecosystems, extreme events, and socioeconomic systems.Experts agree that gradually increasing concentrations of GHGs, especially CO 2 , increase the greenhouse effect, leading to irreversible warming, affecting both natural and human systems [1], [2], [3], [4], [5].According to the IPCC (2021) [1], the human influence on global warming is indisputable, with rapid and widespread changes in the atmosphere, oceans, cryosphere, and biosphere [6].
The consequences of climate change are already evident in many parts of the world, especially in low and lower-middle countries, which, although they are not responsible for the majority of greenhouse gas emissions, are vulnerable to climate change.more vulnerable to climate change [7].It is commonly found in disaster-prone locations, where rainfall is highly variable, largely dependent on agriculture, and is the most climate-sensitive sector of the economy.
Extreme events are occurring with increasing frequency around the world, worrying the scientific community due to their large-scale impact.An event is said to be extreme when it presents an anomaly at the climate level.From a precipitation point of view, these events have a total amount of

Data sources
Data for this study were provided by the Sulawesi River Basin Office III, Central Sulawesi Island, and were obtained from the following five hydro-climate stations: Bora, Karawara, Klawi, Palolo, and Wuasa.The data series contains daily precipitation from 1985 to 2021.

Research methods
In this study, Thiessen's method was used to analyze regional precipitation.The Rainfall Concentration Index (PCI), the Normalized Precipitation Index (SPI), the Precipitation Concentration (PCD), the Time of Rainfall Concentration (PCP), and the Rainfall Anomaly Index (RAI) are used to analyze precipitation indicators.Correlation values, RMSE, and MAE were calculated to determine the relationship between the methods used.

Regional rainfall
Precipitation that occurs in an area is called zonal precipitation calculated by the Polygon Thiessen equation [9], [10], [11], [12], [13]:  (1997) and is an index that allows one to determine the concentration or seasonality of rainfall [15], [16] according to its monthly variation, allowing to detect changes in meteorological conditions in Vietnam.certain places, as well as d surveying extreme phenomena.risk event for this variable [17], [18].The PCI equation looks like this: where  is the monthly rainfall of month i.According to Oliver (1980) [14], a uniform distribution of precipitation is indicated by values below 10, with higher values indicating more concentrated precipitation.Therefore, the seasonal precipitation concentrations are classified according to Table 1.[19] defines SPI as a mathematical algorithm for detecting and characterizing precipitation anomalies related to expected weather conditions.For example, a negative SPI value indicates below-average rainfall and a positive value indicates above-average rainfall.SPI is commonly used to monitor drought conditions and excessive rainfall.The World Meteorological Organization (WMO) strongly recommends its use.Therefore, it is possible to compare different regions and climate zones.Also, to compute this metric, the first step is to find a probability density function that best fits the frequency distribution of precipitation on the desired time 1311 (2024) 012056 IOP Publishing doi:10.1088/1755-1315/1311/1/0120564 scale.Among the various distributions proposed in the literature, the gamma distribution is widely used in climatology and is therefore used in this study to represent the theoretical distribution of these variables.The gamma distribution determined by its probability density function is: where a > 0 is the shape parameter, b > 0 is the scale parameter, and x > 0 is the precipitation.The gamma function is given by: To estimate the parameters a and b, Thom [20]'s maximum likelihood method is used, according to equation ( 8)- (10): where n is the number of observations in the sample, x is the average precipitation, and xi is the observed precipitation.Using the outcome parameter, the cumulative rain event probability G(x) is calculated on the desired time scale according to equation (8): Note, however, that the gamma function is undefined at x = 0. Since the historical precipitation series may contain zeros, the cumulative probability is: where q is the probability of a zero value in the analyte, calculated as q = m/n, where m is the number of events without precipitation and n is the number of observations.Finally, the cumulative probabilities H(x) are transformed into a normally distributed random variable (Z) with a mean of 0 and a standard deviation of 1. SPI values are obtained according to equations ( 10) and (11).Table 2 shows the SPI classification for the dry season and the rainy season.
,  0 < () ≤ 0.5 ( 10) ,  0.5 < () ≤ 1.0 (11) where c 0 = 2.515517; c 1 = 0.802853; c 2 = 0.010328; d 1 = 1.432788; d2 = 0.189269, and d3 = 0.001308.PCD and PCP are two indicators that can be used to quantitatively describe the concentration and distribution of rainfall during the year at a given location [21], [22].PCD is an index showing the distribution of total rainfall in a year and 12 months.PCP is the period (month) of the total rainfall of a year.PCD and PCP calculations are based on monthly precipitation data (r), the radius vector of the trigonometric circle, and the angle that determines the month of the year.Using this decomposition of vectors, on the level, equations ( 12) and ( 13) can be expressed by: where i represents the number of months of the year and q is the angle relative to each month of the year, ranging from 00 to 3600.Rx and Ry represent the sum of vector projections representing monthly precipitation for x and y.Axis, or according to equations ( 14) and ( 15), the PCD and PCP values are: The PCD value varies between 0 and 1, with a value closer to 0 indicating more precipitation.Rainfall is distributed all year round, but the values are close to 1 point, which concentrates rainfall in one area, in a short time.PCP is expressed in degrees and indicates the wettest month.Focus for a year.Table 4 shows the relationship between the PCP values and the corresponding month.Another parameter used in this study is the RAI to identify extreme anomalies.Classification of drought in the order of forward and reverse in rainy time series and wet period with different intensities.This index's main feature is that since only precipitation data needs to be calculated, the procedure is simple and suitable for applications such as: Use in semi-arid and/or tropical areas.Equations ( 16) and ( 17) were used to determine RAI [6]: where P is the observed rainfall (mm) of the year for which the RAI will be calculated, P is the annual mean precipitation of the historical series (mm), and M and X represent the mean of the ten values highest and lowest annual rainfall in the historical series (mm), respectively.From the values found, the precipitates can be classified according to Table 4.  [23]).[24].The correlation coefficient using Pearson correlation coefficient shows the degree of correlation between regression analysis and causal relationship and ranges from 1.0 ≥ r ≥ -1 [25], [26], [27], [28].Meanwhile, the root mean square error (RMSE) is a measure of error based on the difference between two corresponding values to measure the accuracy of the data.The mean absolute error (MAE) indicates the absolute error of the difference between the model and the observed values.In this study, the accuracy of each model is determined by the formula below.
We also use Spearman's correlation coefficient to check if the conclusion is consistent with Pearson's correlation coefficient (Table 5).The scoring criteria for the Pearson Correlation Scale are presented in Table 6.The results show that over the analyzed period, the Palu Basin is homogeneous (76.57%) and moderately seasonal (32.43%).During this time there is no seasonal distribution and high seasonal rainfall.Figure 2b.
shows the average annual PCI for the Palu River basin over the 37 years analyzed.The results show that the mean of the index is 9.68 (even), a maximum of 12.52 (seasonal average), and a minimum of 8.49 (even).Based on this PCI index, in the Palu River basin, rainfall is unevenly distributed in all areas.These values show that in these places most of the annual rainfall is concentrated in a short time, which can lead to drought, major impacts on water resources and water supply as well as floods.The dominant SPI is the normal category, followed by mild drought and moderate drought.The average SPI is 0.01 which is classified as normal, the minimum SPI is -2.52 which occurs in November 2019 which is classified as extreme drought, and the maximum SPI is 6.39 which occurs in November 2012 which is classified as extreme wet.The SPI value chart shows that dry years occurred in 1987, 1989, 1994, 1996, 2002, 2006, 2016, and 2019.Meanwhile, wet years occurred in 1991, 2012, and 2020 when extreme rain occurred.Wet years cause flooding in these locations, while dry years cause shortages of raw water supplies and decreased agricultural production. .This shows that the rainfall is homogeneous and well-distributed throughout the year in the Palu Watershed.PCP (Figure 5), it is observed that no rainfall is concentrated at one time and all is evenly distributed throughout the year in the Palu Watershed.1985, 1987, 1989, 1997, 2009, 2011, 2015, and

Conclusions
Based on the analysis and discussion carried out, it can be concluded: (i) PCI shows uniform distribution of rainfall (76.57%) and moderately seasonal (32.43%) no distribution of seasonal and strongly seasonal rainfall (ii) The dominant SPI is the normal category, followed by mild drought and moderate drought (iii) PCD and PCP show that the rainfall is homogeneous and distributed throughout the year and no rain is concentrated at one time (iv) Comparison of the relationship between SPI and RAI is very strong and significant compared to SPI versus PCI, SPI versus PCD, and SPI versus PCP The four methods of analyzing the drought index show that there will be no drought at the work location.This has a big impact on the agricultural sector, raw water supply, and industry in supplying water.

2. 1 .
Description of study The survey site is located in the Palu Basin, 0°55'12.61'' to 0°58'26.38''South latitude and 119°52'23.82''to 119°52'18.24'' East longitude.The Palu River is formed by the confluence of two main rivers, the Miu River and the Gumbasa River, and empties into Palu Bay.The Palu River is 90 km long and flows from southeast to northwest along the long valley of the Palu Koro fault.The Palu River originates in the Kulawi Mountains in Sigi District, Central Sulawesi, Indonesia.The area of the Palu River basin is 3,005.33km².The study location is shown in Figure 1 below.

Figure 2 .
Figure 2. PCI in the Palu Watershed from 1985 to 2021 (a.Relative frequency, b.Variation) 3.1.2.Standardized Precipitation Index (SPI) Figure 3 and Table7present the monthly SPI distribution of the Palu Watershed from 1985 to 2021.The dominant SPI is the normal category, followed by mild drought and moderate drought.The average SPI is 0.01 which is classified as normal, the minimum SPI is -2.52 which occurs in November 2019 which is classified as extreme drought, and the maximum SPI is 6.39 which occurs in November 2012 which is classified as extreme wet.The SPI value chart shows that dry years occurred in1987, 1989, 1994, 1996, 2002, 2006, 2016, and 2019.Meanwhile, wet years occurred in 1991, 2012, and 2020 when extreme rain occurred.Wet years cause flooding in these locations, while dry years cause shortages of raw water supplies and decreased agricultural production.

Figure 3 .
Figure 3. Distribution of the SPI in the Palu Watershed

Figure 4 .
Figure 4. PCD in the Palu Watershed for the period from 1985 to 2021.

Figure 5 .
Figure 5. PCP in the Palu Watershed for the period from 1985 to 2021

Table 1 .
Classification of the precipitation concentration index

Table 3 .
The month corresponding to each PCP value

Table 4 .
Rainfall Anomaly Index rating

Table 7 .
Distribution of the SPI in the Palu Watershed Annual Rainfall Anomaly Index for the period from 1985 to 2021 in the Palu Watershed3.2.Comparative rainfall indicesFigure7displays the relationship between SPI and the rainfall index for the period 1985 to 2021.From the figure, it can be seen that the relationship between SPI and RAI is very significant and strong where the variance (R 2 ) is close to one, while the correlation between SPI versus PCI, SPI versus PCD, and SPI versus PCP is very weak with the variance (R 2 ) close to zero.This is reinforced by the distribution pattern of the drought index, which is the same pattern only with SPI versus RAI, while for the others, the distribution pattern is very different from the SPI.

Table 8 .
Relationship between SPI and Index Rainfall (a.RAI, b.PCI, c.PCD, d.PCP)Table 8 shows a comparison of the values of SPI versus RAI, PCI, PCD, and PCP in the period 1985 to 2021.It can be seen that only SPI versus RAI has a strong to very strong correlation, while the correlation between SPI versus PCI, PCD, and PCP is weak.RMSE and MAE values are also small when compared to other correlations except for SPI versus PCD.This indicates that the quality of the RAI model is better than PCI and PCP in analyzing the drought index.Comparison of SPI values versus rain index (RAI, PCI, PCD, PCP)