Drought detection in Java Island based on Standardized Precipitation and Evapotranspiration Index (SPEI)

This study reports a drought analysis which was carried out using the Standardized Precipitation and Evapotranspiration Index (SPEI) to determine the spatial and temporal level of drought risk in Java, Indonesia. Apart from using the SPEI, this study also used the SPI (Standardized Precipitation Index) as a comparison in detecting drought and also validated with historical drought occurrences. Temporal variations of SPI and SPEI values were discussed by considering different timescales (monthly to yearly). Pearson’s correlations between both drought indices were calculated to see how similar both indices were. Also, the Kolmogorov–Smirnov tests were used for the similarity test of two kinds of distributions. The results obtained from this analysis showed that the correlation coefficient between the SPI and SPEI models was relatively high on a monthly scale and consistently increased along with the increase of temporal scales but had a decreasing trend during the dry season. However, the SPI detected drought severity with an excessively high estimate in comparison with the SPEI. Greater spatial extents of drought estimation were also generated by SPI followed by SPEI in comparison to factual drought occurrences. As a consequence, SPEI becomes more moderate and SPI as a conservative approach for estimating drought events.


GRAPHICAL ABSTRACT INTRODUCTION
Drought is a natural phenomenon that occurs as a result of a high rainfall deficit (Wang & Asefa ). This later influences the agricultural sector in Indonesia directly. It was reported by Indonesian Statistics (BPS) that the potential financial loss due to drought in agriculture is estimated at three trillion rupiahs per year (BPS ). Additionally, beside having a direct impact on decreasing food productivity, drought can also have indirect environmental impacts, such as forest fires (Holden et al. ). Public Housing (PUPR), the availability rate of water for one person in Java Island is 1,169 m 3 /year and will continue to decline until 2040 when the availability rate of water for one person is limited to 476 m 3 /year, which is categorized as severe scarcity. Having the potential to cause severe impacts, drought has become a disaster that has received serious attention at both national and international levels, since it greatly affects people's activities in various sectors of life (Stampfli et al. ).
Drought that occurs slowly (called slow on-set drought) may have a severe long-term impact on various sectors of human life that needs to be anticipated. Therefore, mitigation efforts are needed to reduce any potential impacts of drought (Gebremeskel et al. ). One of the non-structural mitigation strategies that can be conducted is implementing early detection systems to monitor drought by creating a disaster risk distribution map. Disaster risk mapping is a starting point for raising public awareness, informing policymakers or authorities to encourage disaster management (Blauhut ).
In an early detection system, understanding the characteristics of drought is imperative. By identifying and representing drought characteristics and indicators, a drought index or a combination of drought indices is usually used (Blauhut ). A drought index consists of several drought indicators that can explain quantitatively the intensity, duration, and severity of drought (Wang & Asefa ).
Drought events can be analysed because several drought indices have been developed to detect and monitor drought events (Wang et al. ). Two drought indices that are often used for drought analysis are the Standardized Precipitation Index (SPI) and the Standardized Precipitation and Evapotranspiration Index (SPEI).
SPI is a drought index that has been standardized to measure rainfall anomalies and is the main indicator of drought recommended by the World Meteorological Organization (Stagge et al. ). The precipitation data used in this research is obtained from Global Precipitation, which has the advantage of providing precipitation data for a long time period from 1979 to 2020. The data are available almost in real-time for a whole continent so that the quality of the data is confirmed to be very good, in terms of both spatial and temporal coverages. The study location focuses on Java Island because according to the data compiled by the meteorological, climatological, and geophysical agency (BMKG), Java Island has been the island with the highest frequency of being hit by drought compared with the other islands in Indonesia for 30 years from 1979 to 2009 and is still prone to experiencing drought until now.
Beside that, the utilization of SPI and SPEI as the drought indices in this study is because these two indices are most often used, especially SPI as the main parameter in monitoring drought in Indonesia by the BMKG. The use of SPI as a comparison index is due to the existence of the same parameter as SPEI in analysing drought, namely precipitation. Additionally, apart from SPI and SPEI, there are various types of drought indices that are developed to suit the conditions of certain areas. One of them is the Hurst index, which is developed to determine annual and seasonal trends with hydrological and climatic variables in The paper is divided into four sections, namely Introduction, Methods, Results and discussion, and Conclusions. The first section describes the introduction of why this study is essential to conduct, the study location, and data available. Then, the methods of SPEI and SPI approaches as well as drought classification are explained in the section 'Methods'. Some research findings, such as behaviours of SPI and SPEI methods, for detecting droughts in terms of temporal and spatial characteristics are discussed in the section 'Results and discussion'. Finally, in the section 'Conclusions', the conclusion gives a brief summary of the findings and their implications.

Study location
The study location was Java Island, which is situated between 113 48 0 10″ to 113 48 0 26″ East Longitude and 7 50 0 10″ to 7 56 0 41″ South Latitude as shown in Figure 1. Java Island has a total area of 138,793 km 2 with a length from east to west of 1,033 km, and within its central position, it has a width of about 104 km, while in the western part, the width is about 98 km and the eastern part is about 107 km. Administratively, Java Island consists of six provinces: four provinces include Banten with the provincial capital of Serang, West Java with the provincial capital of Bandung, Central Java with the provincial capital of Semarang, and East Java with the provincial capital of Surabaya; two special areas at the provincial level, namely Jakarta and Yogyakarta. Furthermore, Banten province consists of six districts/cities, Jakarta province consists of five municipalities, West Java province consists of 25 districts/cities, Central Java province consists of 35 districts/cities, Yogyakarta province consists of five districts/cities, and East Java province consists of 38 districts/cities. Java Island has an annual average temperature of 22 -29 C, and usually during the day and the dry season, the temperature in the coastal area can reach up to 34 C, while the average humidity is around 75%. Meanwhile, the annual rainfall ranges from 1,773 to 3,710 mm. Based on the distribution of average monthly rainfall, Java Island has a monsoon type that makes it experience only two seasons, namely the dry season that occurs from April to September (dry months) and the rainy season that occurs from October to March (wet months).

Drought historical data
To anticipate the occurrence of drought, future projections could be carried out to determine the recurring drought period by utilizing historical data. Drought historical data are recorded data from reports of previous droughts that have occurred in a certain time period. Drought historical data of Java were obtained through the Indonesian Disaster Information Data (DIBI) recorded by the National Disaster Management Agency (BNPB), and the available data taken were from 2003 to 2019. These data contained coordinates of the location, name of the district/city and province, number of victims (injured, died, evacuated, and missing), material losses, and a description of the events that were recorded directly at the disaster site. Drought historical data would be used for validation coupled with the results of the SPI and SPEI analyses to identify a correlation between the two. As for the total data on drought events in Java Island, it is illustrated by Figure 2.

Precipitation data
In this research, precipitation data were obtained from Global Daily Precipitation (CPC-Global). CPC-Global was developed by the National Oceanic and Atmospheric Administration (NOAA), which is the first product of the CPC Unified Precipitation Project (Sun et al. ). This project is devoted to creating an integrated set of precipitation  Furthermore, CPC-Global is able to provide daily precipitation data, while in drought analysis, the timescale used is monthly. Therefore, the daily precipitation data would be accumulated into monthly data. To analyse drought based on SPEI, the form of data used is usually that which comprises more than 40 years, and the data from CPC-Global have fulfilled the requirement in this regard. In contrast to data from satellites such as Tropical Rainfall Measuring Precipitation data is said to be better and more reliable.
Moreover, the data from CPC-Global have a grid resolution of 0.5 × 0.5 . Since the grid size for precipitation is different from the evaporation grid size (0.25 × 0.25 ), the precipitation grid size was converted into the evaporation grid size first. The following illustration is the image for the precipitation and evaporation data grids ( Figure 3).

Evaporation data
Apart from precipitation, evaporation is an integral component that is used to detect changes in the hydrological cycle and estimate the impact of climate change on water resources (Ghorbani et al. ). In this research, the evaporation data were obtained from GLEAM (Global Land-surface Evaporation: the Amsterdam Methodology).  . And it provided daily evaporation data, while in a drought analysis, the timescale used is monthly. Therefore, the daily evaporation data would need to be accumulated first into monthly data. However, for certain times such as the dry season or summer where the rate of rainfall is minimum, the possibility of rainfall accumulation does not exist (zero precipitation), especially for short periods that occur in between 1 and 3 months. In previous SPI studies that have been reviewed by Stagge et al. (), to solve the zero precipitation, the SPI value is set based on the historical occurrence (%) of periods with zero precipitation in the following equation:

SPI development
where p represents the probability distributions for accumulated precipitation, F(x, λ) is the parametric univariate distribution functions, and x, p o is the historical ratio of periods with zero precipitation.
Nonetheless, this method causes a problem because it provides the maximum SPI value. The average SPI value in the normal distribution should be 0; meanwhile, the value is in between two conditions, 50% is in wet conditions and the other 50% is in dry conditions. In this method, the average SPI value has increased so that the where n is the total number of samples in the reference period, p and F(x, λ) are the probability distribution and the parametric univariate distribution functions for samples that match parameter λ with detectable precipitation accumulation.
After all the probability value has been calculated, the distribution of the SPI value can then be computed.
The SPI values require selecting an appropriate parametric probability distribution to convert climate water balance accumulation into standard normal distribution.  To develop a drought index based on SPEI, it is necessary to ensure that the quality of the precipitation and evaporation data use is complete. SPEI uses the difference between monthly precipitation and PET. After PET is obtained, then the climate water balance for the ith month (D i ) can be calculated by reducing the value of precipitation for the ith month (P i ) with evaporation potential for the ith month (PET i ) as in the following equation: SPEI is standardization based on the GEV distribution.
With the GEV distribution, the observed variable will be limited to observing only the maximum or minimum value, which is independent and identically distributed.
The probability density function f(x) of the GEV distribution is shown in the following equation: where μ, σ, and ξ are parameters of location, scale, and shape, respectively, that have been estimated using the maximum probability. The cumulative GEV distribution function F(x) can be calculated in the following equation:

Drought classification
The drought index is the main variable for assessing the effects of drought and for determining variations in drought characteristics such as duration, intensity, and severity. In this study, the drought analysis will be calculated on a differ- Drought can also be classified based on the frequency of occurrence according to WMO (), drought is divided into four categories as listed in Table 2.

RESULTS AND DISCUSSION
The goodness of fit statistics To prove that the distribution recommended by Stagge et al.
() is valid and fits with the spatial conditions of Java Island, it is necessary to evaluate the suitability of the distribution known as the goodness of fit (GOF) statistics. The GOF is conducted to test the fit between the observed results (empirical distribution) and the expected results (theoretical distribution  This test takes the dataset as its argument and returns the p-value so that H 0 will be rejected if the p-value is <0.05. This study investigates time-series datasets (SPI and SPEI) from grid points over Java with different timescales (1-12 months) whether the observation datasets are able to be modelled reasonably by gamma and GEV distributions, respectively. In addition, the datasets are also classified into 12 different months (January-December) separately. Tables 3 and 4 present the number of the grid points (in %) statistically accepted for different timescales and months. In the grid points, the data generated from the theoretical distribution match the empirical distribution data.
In Table 3, the percentage of acceptance rates for the gamma distribution using the KS, AD, and CVM tests shows values that are not much different from one another.
During 12 months (January-December) with varying scales of time, the percentage value tended to fluctuate but was not significant. In general, the number of the grid points statistically accepted is above 93% of Java for all 12 months and different timescales. This indicated that the gamma distribution is suitable to model rainfall amount in Java for different seasons and a variety of timescales.
Similar to the gamma distribution, the GEV distribution is also fit to the observation datasets (rainfall minus evapotranspiration), which is used for the SPEI model. The percentage of acceptance rate among all grid points in Java shows a very high rate. In fact, In general, drought indices derived by the SPI method present systematically lower than the SPEI approach, particularly for the upper thresholds from À1 to À2 as shown in Figure 4.
This means drought severity generated by SPI reveals systematically higher other than SPEI for a given month. Figure 4 presents a monthly temporal variation of drought indices for   In their research, the frequency of drought decreased from the highest to the lowest margin in summer, autumn, spring, and winter, respectively. However, the results of our research are contradictory to those in Gurrapu et al.
(), as the study concluded that the correlation between SPI and SPEI was weaker in winter and relatively stronger in summer, autumn, and spring. The correlation between the two analyses during winter was weaker but positive, whereas the correlation in April was weaker and negative, which was probably due to the increased river flow from rapid snowmelt.
The difference in results may be due to different conditions in the study area. In Java, there are only two seasons and there is no snow, so during the dry season, when the temperature increases, the area will become drier. It is different from the study reported in the research by Gurrapu et al. (), where there is snow in the research location so that with the increasing temperature, the water availability in the area increases due to snowmelt.

Comparison of SPI and SPEI values with historical droughts
Three historical drought events were selected as samples to where El Nino with a weak category was also hitting Java.
Therefore, the three drought events that occurred in different years would be discussed. This would later be compared with the historical droughts recorded by DIBI. One point to consider is when the drought event in DIBI is recorded at the beginning of the month, the drought data recorded in the previous month will be used, while those recorded at the end of the month will use the drought data for that particular   This indicates that SPI is very conservative and SPEI is more moderate in estimating drought events.

Effect of different timescales on similarity of the SPI and SPEI
A scatter plot was used for analysing between SPI and SPEI for determining how closely both indices are related. There was a significant positive correlation between SPI and SPEI, which is seen from the tendency of the data to gather around the diagonal line. The results of the correlation analysis are set out in Figure 6. The SPI and SPEI can actually be used to calculate the drought index for a variety of different timescales. In this study, a different timescale will be used ranging from 1 to 12 months. Most studies have only used fewer timescales such as 1, 3, 6, and 12 months, while this study has the advantage of being more detailed in order to see the correlation between SPI and SPEI.
To determine more detail about the relationship between SPI and SPEI which was on different timescales, the correlation coefficient and the KS test were used. The difference in SPI and SPEI values may be due to differences in data variables used as input to calculate the drought index. For example, in the event of the same drought, the SPI index may show a value of 1, while the SPEI may show a value of 3. This is possible because the SPI only calculates drought events based on the rainfall rate, while the SPEI identifies drought events not only based on the rainfall rate but also the evapotranspiration of the region. This view is supported by Gurrapu et al. () who write that the differences in the variables used as input data in analysing drought will affect the value of the drought index.
The correlation between SPI and SPEI is consistently increasing along with the longer the timescale used. It can be seen from the box plot in Figure 7 that the value of the correlation coefficient is above 0.9 for all timescales. This showed that the relationship between SPI and SPEI is strong. The 1-to 6-month timescale tends to have a higher significant increase in the correlation coefficient value than the 7-to 12-month timescale, which has a slight increase in the value of the correlation coefficient. Then, in Figure 8 that depicts the results of the KS Test, the p-value in the 1-to 2-month timescale tends to have a significant increase and then becomes stable up to the 7-month timescale. However, in the 8-month timescale, the p-value continues to decline up to the 12-month timescale. This indicates that the timescale for the long term is better than the short to medium term.
For the drought index, especially from the SPI and SPEI analyses, the use of different timescales will result in different implications from one another (Nam et al. ). Thus, those calculations of drought with different timescales are often used as information to determine water resources management policies in the short, medium, and long term.
The timescales that are often used to measure drought   values are 1-, 3-, 6-, and 12-month timescales. The drought index with a 1-month timescale is included in the shortterm period, the 3-and 6-month timescale is included in the medium-term period, and the 12-month timescale is included in the long-term period (Nam et al.  Figure 9. The frequency rate for SPI will fluctuate more, as the severity of drought increases with the timescale used, whereas for the SPEI with the timescale used, the more severe the level of drought, the more stable the frequency rate. The results of moderate, severe, and extreme droughts are presented in Figure 9. It can be seen that for moderate drought, the highest frequency based on the SPI was 12.18%, while based on the SPEI was 14.32%. Then, the highest frequency, for severe drought, based on the SPI was 6.2%, while based on the SPEI was 7.69%. Meanwhile, for extreme drought, the highest frequency based on the SPI was 6.84%, while based on the SPEI was 3.21%. SPEI has a higher frequency for moderate and severe droughts than SPI, while for extreme drought, the frequency generated by SPI is higher. This indicates that in detecting drought, SPI assesses drought at a more severe level than SPEI.
From the above explanation, it can be concluded that in general the frequency rate for the SPEI is much more stable than that for the SPI, and the drought frequency produced by the SPEI is higher than that by the SPI. With regard to two of the three types of drought frequency, moderate and severe, the SPEI recorded a drought frequency value higher than the SPI. This is due to the existence of the evapotranspiration variable in the SPEI. This feature allows identifying drought events even when the rainfall is not available, so that the index can still be used to capture drought events and calculate the frequency of drought events. Meanwhile, the SPI's extreme drought frequency is higher than that of the SPEI's. Furthermore, the pattern shown for the change in the frequency value against time caused by the SPI and SPEI marks one thing in common, namely the possibility of fluctuations for all types of drought. However, overall the SPEI's drought frequency is more stable than that of the SPI's.
These results are supported by research conducted by Tirivarombo et al. (). The study found that the SPI was superior in capturing extreme drought events compared with the SPEI. The reason is that when identifying drought that only considers the variable of rainfall, the SPI of which input data are only the rainfall variable will be better to identify extreme drought than the SPEI. The results of the correlation analysis between the SPI and SPEI clearly show that rainfall is the main cause of the drought. It should be noted that the existence of PET becomes important at longer timescales since the correlation is stronger.

CONCLUSIONS
The conclusions drawn from the results and discussions can be explained as follows.
A comparison between the SPI and SPEI values to temporal variation shows that the correlation between the two indices is quite high for all months for the 1-month timescale. However, this correlation has decreased in the dry months (dry season). In almost all months, the SPI and SPEI values have similar margins with no significant difference, and the SPI value is always below the SPEI value. Yet, in the dry months, the SPEI value is far below the SPI value.
This indicates that the temperature variable affects the correlation between the SPI and SPEI because during the dry season the evaporation rate increases more rapidly, resulting in a lower SPEI value than in normal conditions.
The SPI is more conservative in detecting drought than the SPEI. This is indicated by the fact that the SPI detects an overestimation compared with the SPEI and historical data on drought events in Indonesia. Besides, the difference in the timescale used in the analysis will affect the correlation between the SPI and SPEI. The correlation between the SPI and SPEI will get stronger as the timescale used increases.
Then for moderate and severe droughts based on the SPEI, the SPEI shows a higher frequency than the SPI, while for extreme drought, the frequency shown by the SPI is higher. This is because when drought takes into account only the rainfall, the SPI that has one indicator in the form of rainfall will be better at identifying extreme drought than SPEI. The results of the correlational analysis between the SPI and SPEI clearly show that rainfall is the main cause of drought. However, evaporation indicators are also important, especially on a longer timescale where their existence affects the correlation between the SPI and SPEI.
By comparing the two indices, it can be seen how the characteristics and correlations between the SPI and SPEI are. Also, we could identify further the influence of precipitation and evaporation parameters in analysing drought in Java Island. Therefore, this research is expected to be one of the sources of information that can help related parties, especially the BMKG in monitoring drought in Indonesia.