Future drought analysis of SPI and EDDI considering climate change in South Korea

Prediction of drought is important for efficient water management, as the occurrence of droughts affects large areas over a long period. According to various climate change scenarios, it is reported that in the future, Korea’s climate is likely to increase in temperature with increasing rainfall. This increase in temperature will have a big impact on the evapotranspiration. The occurrence of drought begins mainly with two causes: lack of rainfall or an increase in evapotranspiration. Therefore, in this study, the impact of climate change on future droughts is revealed through the standardized precipitation index and the evaporative demand drought index. Two drought indices with different characteristics are used to examine the trend of future drought, and the SDF curve was derived to quantitatively analyze the depth of future drought. Future droughts are projected by applying future climate data generated from various climate models.


INTRODUCTION
The increase in temperature due to climate change is expected to increase severity and frequency of drought. In fact, the Intergovernmental Panel on Climate Change (IPCC) predicted that the annual average temperature of the Korean Peninsula would be about 2-4 C higher than the present by 2050, resulting in a subtropical climate (IPCC ). In addition, as the temperature has risen, the frequency of droughts in Korea has occurred 0.36 times per year by 2000, while it has increased sharply to 0.67 times in the last 15 years. The occurrence of droughts begins with changes in climate variables such as lack of precipitation and increased evapotranspiration. Such a condition is defined as a meteorological drought. When a meteorological drought occurs, depletion of soil moisture causes deterioration of plant growth and crop yield, which is defined as agricultural drought. Hydrological droughts are also defined as depletion of river flow or reservoir levels due to depletion of soil moisture. Drought is caused by natural phenomena such as changes in precipitation and evapotranspiration, and has a great impact on society both economically and environmentally.
In the field of drought monitoring, drought has been numerically interpreted using drought indices to respond to drought, and drought indices based on precipitation have been mainly used. The Standardized Precipitation Index (SPI; Mckee et al. ), the most widely known precipitation-based drought index, is an index that uses only precipitation. In many studies on drought, the cause of drought has been interpreted as a lack of precipitation, and SPI has been mainly used, and its utility as a drought However, since SPI does not take into account changes in other climate variables such as surface air temperature, there is a limitation that does not reflect the effects of climate change at all (Kempes et al. ; Zhang & He ). In fact, since an abnormal increase in surface air temperature due to climate change has a great influence on the frequency and severity of drought, it may not be reasonable to interpret drought using only precipitation.
Accordingly, in the field of drought monitoring, interest in evapotranspiration, an aspect of atmospheric moisture demand, has been increasing, and its importance has been proven through many studies (Vicente-Serrano et al. Taylor

METHODOLOGY AND MATERIALS Evaporative demand drought index
The EDDI is a new drought index based on the PET (E 0 ). EDDI focuses on E 0 , which is the moisture demand side of the atmosphere in interpreting the water exchange between surface and atmosphere. The interaction between the E 0 and the actual evapotranspiration (ET) in the drought onset and the persistent drought condition forms the physical basis of the EDDI, which can be explained by resulting in a slow transition of soil moisture. In this transitional period, sufficient soil moisture for ET is still available, so the ET increases as the E 0 increases (arrow 1 in Figure 1). As the dry condition continues, the elevated ET eventually depletes the soil moisture, and therefore, in a continuous drought condition, the ET decreases due to the depleted soil moisture (downward arrow 2 in Figure 1).
In this condition, the atmosphere requires more moisture due to the lack of previously moisture demand, which leads to a rise in E 0 (upper arrow 2 in Figure 1). In both of these drought conditions, E 0 increases, while ET reacts in opposite directions, so it can be seen that E 0 is more useful as an indicator of different conditions of drought.
The EDDI was verified by applicability assessment in Korea (Won et al. ) and the reproducibility of observed drought events was excellent, and the correlation with SPI was high. In addition, it was concluded that EDDI can be used as a drought index together with SPI and it can properly respond to various meteorological variables. Therefore, in this study, it was determined that EDDI can be utilized as much as the SPI which was used in the past, and it was applied to analyze future drought.

Derivation of PET
In this study, the Penman-Monteith method was used to derive PET. The Penman-Monteith method is an improved version of the Penman FAO-24 method by the Food and Agriculture Organization (FAO), it is known to be highly applicable since it can be used under limited meteorological data as well as provides consistent values for crop water requirement worldwide.
The American Society of Civil Engineers (ASCE), and the World Meteorological Organization (WMO) are also recommended for this method. It was studied that this method is more appropriate than the Penman method (Penman ) for prediction future PET and for drought indices such as EDDI or SPEI using PET (Dewes et al.

).
To use this method, meteorological data on surface air temperature, relative humidity, radiation and wind speed are required and the daily PET can be estimated as follows (Allen et al. ): where ET SZ is the standardized reference evapotranspiration (mm day À1 ); R n is the net radiation (MJ m À2 day À1 ); G is the soil heat flux density (MJ m À2 day À1 ); T is the surface air temperature ( C); u 2 is the wind speed at a 2 m height(m s À1 ); e s is the saturated vapor pressure (kPa); e a is the actual vapor pressure (kPa); Δ is the slope of the vapor pressure-temperature curve (kPa C À1 ), and γ is the psychrometric constant (kPa C À1 ). C n and C d can be determined by the aerodynamic roughness. Since the G is relatively small compared to the R n , the G can be neglected.
In Korea, the observational radiative data for estimating PET is incomplete, so the method of estimating solar radiation data proposed by Allen et al. () was used. This method calculates the solar radiation energy (R s ) reaching the earth surface using the difference between the daily maximum temperature and the daily minimum temperature as follows: where R s is the extraterrestrial radiation which changes with respect to the location and date of the observation site. The T max is the daily maximum air temperature ( C), T min is the daily minimum air temperature ( C), and k rs is the empirical coefficient, which can be calculated as follows: where P is the mean atmospheric pressure (kPa); P 0 is the mean atmospheric pressure at sea level (101.3 kPa); k r0 is an adjustment factor and has a value of 0.17 in inland and 0.20 in coastal areas. Once the solar radiation data is constructed, the net radiation can be obtained using the method proposed by Allen et al. ().

Drought index formulation
The calculations for both SPI and EDDI were based on the SPI estimation formula developed by Mckee et al. ().
SPI is simple since this index only uses precipitation, and is now mainly used by KMA. SPI and EDDI are calculated using moving-averaged monthly precipitation or PET for a given time-scale. The optimal probability density function for each month of the moving-averaged monthly time series is estimated, and is applied to the moving-averaged monthly time series to construct its monthly cumulative probability time series. The drought index is the value obtained by applying the monthly cumulative probability time series inversely to the standard normal distribution.
The probability distribution used is a two-parameter Gamma distribution, and its probability density function is given by where x is the moving-averaged monthly precipitation or PET; α is the scale parameter; and β is the shape parameter.
The parameters α and β are estimated for each month using the method of probability weighted moments. Table 1 shows the drought classification according to the SPI and EDDI.
The above drought index calculation method is to express the drought in the region as a relative value of each month time series. However, since the drought index for the future period should be calculated based on the amount of change in the future compared to the present, the method of calculating the drought index based on the observational data cannot be equally applied. The future drought index Z f can be estimated as follows based on the relative amount of precipitation or evapotranspiration over the current period.
where x f is the moving-averaged data of the future period; F p is the Gamma cumulative distribution function of the present data; G À1 is the standard normal inverse cumulative distribution.
Climate data simulated from GCMs or RCMs should be bias-corrected since there are biases with observations.
Quantile Mapping (QM), one of the commonly used biascorrection methods, is a method of mapping the probability distribution of simulation data to the probability distribution of observation data by using the cumulative probability distribution of observation data and simulated data from climate models (Hashino et al. ). However, the relative ranking of climate model simulated data remains unchanged after the bias correction using QM. In other words, since the drought index is estimated as the relative value of each data, there is no significant difference in the drought index with or without bias correction. As a representative example, the data simulated by MM5 RCM driven by MPI-ESM-LR GCM was used to compare each drought index before and after bias correction (Figure 2). Figure 2 shows that the  were used, and the used climate variables were the daily averaged surface air temperature, maximum and minimum surface air temperature, wind speed, relative humidity and precipitation. In addition, future climate change scenario data was used for future drought analysis. Future climate data was simulated using Global Climate Models (GCMs) and Regional Climate Model (RCMs). Since data generated from GCMs has limitations due to low resolution and relatively simple physics, more accurate and more detailed climate data are required and such data can be obtained by using RCM that can simulate detailed regional characteristics. Therefore, a total of 8 model

Severity-Duration-Frequency (SDF) curve
The SDF curve replaces rainfall intensity with drought severity in the Rainfall Intensity-Duration-Frequency (IDF) curve used in flood analysis and is a useful tool for determining drought characteristics for the region (Park et al. ). In order to derive SDF curves, the annual maximum drought severity time series of each drought index should be constructed. However, unlike rainfall, droughts do not occur on a yearly basis, and long-term droughts continue into the next year, so the annual maximum time series may not be suitable for drought frequency analysis. Therefore, this study constructed the drought severity time series by applying the Peak-Over-Threshold (POT) concept. First, we set the threshold to identify the drought events, define the start of the drought event when the drought severity of each drought index exceeds the threshold, and define the end of the drought event when it falls below the threshold.
The identified drought events consisted of drought severity and drought duration as shown in Figure 3. In many studies using SDF curves, a drought severity time series has been constructed by extracting drought severity and drought duration from drought event as shown in Figure 3    events was set at a value greater than 1.0 for EDDI and less than À1.0 for SPI.
where N f is the number of drought events in the future, N p is the number of drought events in the present, and CP is the percentage of change in the probability of future drought experience. The calculated rate of change is divided into RCP scenarios and is shown in Figure 6. If the rate of change exceeds 100%, the probability of future drought experience is increased, and if it is less than 100%, the probability of future drought experience is less than the present.
In the case of SPI, drought experience is likely to decrease at most of the six sites, with the exception of some model combinations. In particular, the Seoul site is likely to reduce the probability of future drought experiences in all future ensembles. EDDI has shown an increased probability of future drought experience at all future climate ensembles at all sites, and projects a rate of change of at least 200%. This means that in the future, the probability of experiencing a drought is at least twice that of the present. In RCP8.5 scenario, where a relatively higher surface air temperature is projected, a rate of change of more than 500% may occur at the four sites except Daegu and Daejeon sites. However, the Gwangju site shows a rate of change of about 250%, indicating that the difference between climate model combinations is relatively large. In summary, the SPI is generally expected to reduce the probability of future droughts, but some climate model combinations show an increased chance of droughts, and thus no clear change in the pattern of drought occurrences could be identified. On the other hand, EDDI has shown that the probability of occurrence of future drought increases relatively clearly, but it can be seen that the uncertainty is very large.

SDF curves
In this section, the SDF curve is used to quantitatively analyze changes in the severity of future droughts. The future drought  sites, it was projected that for all durations under RCP 4.5 scenario, the severity of future droughts would be greatly reduced in all eight future climate ensembles. In some ensembles, the future drought severity is intensified over the present severity under RCP 8.5 scenario, but for most ensembles, the future drought severity is projected to be similar to or less than the present severity. Other sites were also projected that future drought severity under RCP 4.5 scenario would likely be significantly less than present severity, with RCP 8.5 scenario showing greater uncertainty among ensembles. Figure 9 shows the present and future SDF curves using for PET estimation. It is also true that doubts are raised that future drought severity will increase to that extent.
The future trends of SPI and EDDI are due to the future behavior of the climate variables (i.e., precipitation and PET) on which the indices depend, respectively. The drastically different trends of two drought indices projecting future droughts using the same future climate ensembles at the same sites will have a significant impact on which drought index will be applied to future projections of future droughts.

CONCLUSIONS
In the future, rainfall is likely to increase due to climate change. Nevertheless, there is also the possibility that the   drought will intensify due to the increase in temperature.
Since SPI, which has been mainly used for drought analysis, is calculated only by considering precipitation, there is a limit to applying SPI to the establishment of drought adaptation measures that reflect the effects of global warming.