## Abstract

Despite many strides made in the development of global circulation models as well as the expansive understanding of meteorological phenomena, many countries still lack sufficient meteorological information that can be conveniently utilized for a hydrologic outlook. This paper suggests a technique of processing the meteorological information, which is not only difficult to differentiate by reducing to a specific basin because of extensive data, but is also impossible to be led to a quantitative drought outlook because of its presentation in qualitative forms.

To assess the drought conditions, two indices were selected—the standardized precipitation index (SPI), which is a meteorological index, and the soil moisture index (SMI), an agricultural index. The long-range forecasts, provided by the Korea Meteorological Administration (KMA) to target the Korean peninsula, were used to predict these indices. As a means to convert the qualitative interval forecast into a quantitative probability forecast, previous data on temperature and precipitation were used to create a compatible probability distribution that was then divided into three intervals. Based on the interval forecast provided by the KMA, the forecast probability of corresponding intervals were differentiated and optimized for each study basin by modifying the probability adjustment coefficient. The quantified probability forecast established in this manner was applied to three basins in Korea, and was verified by applying the ranked probability skill score (RPSS). The results proved that accuracy was ensured in both SPI and SMI.

## 1. Introduction

An analysis on the characteristics of recent droughts that occurred in Korea shows shorter drought cycles and aggravating damages, thus emphasizing the importance of dealing with the aftermath as well as the preparations prior to the drought (Kwon et al. 2006). For an efficient management of drought, monitoring the current status and accurate forecasting of future progression must take precedence. Although many studies have been carried out even within Korea in terms of development of drought indices for assessing the drought condition (Choi et al. 1994; Yoon et al. 1997; Lee et al. 2006; Kang and Yoon 2002), there is an absence of research on drought outlook.

This research started off by examining international studies conducted on the subject of drought outlook methodology. Studies on outlook can be generally classified according to the used predictands, predictors, or models. While drought indices were primarily used as the predictands, which are the subjects of the drought outlook methodologies, the use of meteorological drought indices such as the standardized precipitation index (SPI) and the Palmer drought severity index (PDSI) were used in most cases (Lohani et al. 1998; Wedgbrow et al. 2002; Carbone and Dow 2005; T.-W. Kim et al. 2006; Cancelliere et al. 2007). Occasionally studies were forecasted by the use of low rainfall (Cordery 1999) or streamflow (Shrestha and Kostaschuk 2005) as the predictand. In cases where the drought index was used as the predictand, rainfall was essentially used as the predictor along with temperature and soil moisture. Recently, climate indicators such as the El Niño–Southern Oscillation (Vogt and Somma 2000; Tadesse et al. 2005; Morid et al. 2007), the North Atlantic Oscillation (Shrestha and Kostaschuk 2005; Morid et al. 2007), or sea surface temperature (Drosdowsky and Chambers 2001; Farokhnia et al. 2010) were used as the principle predictors. Among many countries, the United States actively employs its climate information, such as climate forecasts of the National Oceanic and Atmospheric Administration/Climate Prediction Center (NOAA/CPC), for the drought outlook (Carboneand Dow 2005; Steinemann 2006; Yoon et al. 2012; Yuan et al. 2011). In terms of models used for the outlook, the mainstream were those of nonlinear and linear regression, including artificial neural networks (Mishra and Desai 2006; Morid et al. 2007; Farokhnia et al. 2010), multiple linear regression models (Wedgbrow et al. 2002; Cacciamani et al. 2007; Mendicino et al. 2008), and autoregressive time series models (Paulo et al. 2005; Paulo and Pereira 2007; Cancelliere et al. 2007). Most of these drought outlook models were deterministic, but some recent studies employed probabilistic approaches (Cacciamani et al. 2007; Hwang and Carbone 2009). In comparison with such previous studies, the academic significance of this research is as follows: first, forecast information manufactured for the study basins were directly used as the input data. Second, the agricultural drought indices along with the meteorological drought indices were used as the predictands. Finally, the probabilistic format, which is currently preferred, was adopted to reflect forecast uncertainty.

This paper intends foremost to introduce the drought indices that are deemed useful in Korea. Most drought indices include meteorological variables such as precipitation and temperature, thus accurate prediction of such meteorological variables is a prerequisite to drought outlook. However, such highly useful meteorological information has not been sufficiently provided in Korea; therefore, they have almost never been applied to the drought outlook. Nevertheless, it is rarely the case that the given information is perfectly suitable for immediate use. This problem is not only a matter for Korea but also for other countries, except for a few developed ones that are in need of a technique to utilize the meteorological information in practice. Therefore, this study attempts to propose a research direction for them. Given these environments, what is actually crucial is a research that adequately processes and utilizes the given information. Therefore, this research has investigated domestic meteorological information applicable to drought outlook and has studied methods of rendering such information useful, thus proving the originality of this study.

## 2. Methodology

### a. Drought indices

This study selected SPI and the soil moisture index (SMI) in order to examine drought in terms of two aspects: meteorology and agriculture. Since studies on SPI and SMI have already been carried out for decades (Nagarajan 2003), this paper will only briefly outline these indices. The applied drought indices were each classified into five categorized ratings: wet, normal, mild drought, severe drought, and extreme drought. Originally, the SMI and SPI indices had six and seven categories, respectively, but both indices were reclassified into five categories in a manner that assigned 50%, 40%, 5%, 3%, and 2% of the occurrence probabilities based on the historical observation for the wet, normal, mild drought, severe drought, and extreme drought categories, respectively. With this reclassification procedure, both indices maintain consistency in the expression of drought. For further specifications of this classification, refer to the research of Ahn et al. (2010).

#### 1) Standardized precipitation index

Designed by McKee et al. (1993), SPI is a representative meteorological drought index and is also the most frequently used index throughout the world. He created this index based on the idea that drought is initiated by the decrease of precipitation, which causes a shortage of water relative to the actual demand for water. According to Bonaccorso et al. (2003), SPI enables drought monitoring over various time frames, thus permitting the comparison of different areas with various climate conditions, and is also acknowledged as a meteorological index encompassing such strengths.

The process of measuring the SPI consists of three steps: first, the time frame has to be set to a specific period, then the shortfall of precipitation per time is calculated, and finally the impact of each source of water supply on drought is assessed. To calculate the SPI, one must establish a time series of cumulative precipitation per time that can be constructed by the moving accumulation method in which monthly precipitation is continuously amassed in terms of specific time frames. The cumulative precipitation time series is computed by monthly measurements and the result is then divided by the cumulated number of months, thereby yielding the moving average precipitation during the considered months. When a duration time series is formulated, this model is analyzed based on each month to calculate the optimal probability distribution, which is used to estimate the cumulative probability of individual variants. With the application of the standard normal deviate, the average precipitation index is then produced. Among various time units of SPI, SPI-3, which used a moving window average with a window length of 3 months, was chosen in this study since previous research by Lee et al. (2006) concluded that it was the most appropriate index for studies in the Korean peninsula.

#### 2) Soil moisture index

The SMI, which is the most popular agricultural index, was applied by O. K. Kim et al. (2006) on the research of the Korean peninsula. Soil moisture is the key element in computing the SMI and it can be calculated in various ways. The most accurate and popular method is to directly measure the degree of soil moisture by installing the sensor and measurement. However, the Korean research environment is insufficiently equipped to use this method; therefore, a measurement based on the soil moisture balance model was used. Based on a few assumptions, Eqs. (1) and (2) represent a brief summary of the inflow and outflow of water in the soil throughout a specific period of time:

In the equations above, ΔSMC stands for the amount change of soil moisture, RF for rainfall, DR for surface drainage, DP for deep percolation, and ET for evapotranspiration. Here SM_{t} is the degree of soil moisture of the subject month, while *t* stands for the month in consideration. In this soil moisture model, the Penman–Montheith method was adopted for the evapotranspiration while the Natural Resources Conservation Service (NRCS) method was adopted for the surface drainage and the deep percolation which is calculated based on the field capacity.

### b. Drought outlook methodology

#### 1) Available meteorological information

To predict the drought index, the values of precipitation and temperature are required. It is because precipitation is an input variable for both SPI and SMI, while temperature is an input variable for SMI through evapotranspiration. Under such conditions, this study has examined how the outlook of precipitation and temperature is provided in Korea. The Korea Meteorological Administration (KMA) issues a product of long-range forecasts on precipitation and temperature during the upcoming three months from a given month. These KMA forecasts are generated by the Climate Prediction Division of KMA, which combines various long-term simulation models such as the Global Data Assimilation and Prediction System (GDAPS), the United Model (UM), and the Multimodel Ensemble (MME) given by the APEC Climate Center (APCC). They suggest their predictions as qualitative formulations among three categories which are “more than average,” “similar to average,” and “less than average.” This paper will refer to this categorization as above normal (AN), normal (*N*), and below normal (BN), respectively, and the classification of each interval provided by the KMA are shown in Table 1. This long-range forecasting regards the entire Korean peninsula as a unitary region and is published on a monthly basis.

The hit ratio was applied to determine the accuracy of the long-range forecasting. The hit ratio is any value between 0 and 1 where 1 represents perfect forecasting. The period of observation was from May 2008 to December 2009 during which 20 tests were carried out on three study basins, which are described in detail in section 3a. Results are shown in Table 2—they imply that the forecast information is adequate for use as all three intervals yield more than 33% in terms of arbitrary probability prediction.

However, there are two obstacles to applying this forecast information in order to produce the drought forecast. One problem is that the forecast data are expressed in qualitative terms and should thus be converted to quantitative values. Moreover, the coverage of outlook is too vast and the range of information has to be reduced to a size of the study basins.

#### 2) Transforming to quantitative forecasts

To solve the problems mentioned above, the given meteorological information was processed in the following manner. 1) First, distributions compatible with the precipitation and temperature data were estimated for the study basins during the past (usually of the last 30 years), and they were labeled “prior distributions.” As had been suggested by Wilks (1995) on the estimation of distribution, normal distribution was applied to temperature, whereas gamma distribution was applied to precipitation. Quantiles presented at the breakpoints of intervals (called terciles in Table 1) were acquired from each estimated distribution. In terms of temperature, the tercile of BN and *N* was labeled *t*_{1} and that of *N* and AN was labeled *t*_{2}; as for precipitation, the tercile of BN and *N* was *r*_{1} and that of *N* and AN was *r*_{2}. This way, the prior distribution was divided into three intervals and the prior probability for each interval was also obtained. 2) When the forecast fell into one of the three categories—AN, *N*, and BN—weighted probability was given to the prior distribution. For example, if this month’s forecast is AN, the probability of interval AN would be increased by *α*, whereas the probability of interval BN, which is relatively less likely to occur, is decreased by probability of *α*. Yet, the probability of occurrence of *N* is kept unchanged. However, if the forecast for this month is *N*, the probability of *N* will be increased by *α*, while the probabilities of other intervals—AN and BN—are decreased by *α*/2.

Consequently, *t*_{1} and *t*_{2} (or *r*_{1} and *r*_{2} for precipitation) acquired new cumulative probabilities, and a new distribution corresponding to these values was estimated—this is titled “posterior distribution.” More specifically, this is the process from which two parameters of a bivariate probability distribution are induced when two quantiles and the corresponding cumulative probabilities are given. In this study, it is assumed that the posterior distributions of temperature and precipitation each follows the normal distribution and the gamma distribution, respectively. 3) A total of 1000 random numbers were generated from each distribution in order to be entered into the drought equation. Specifically, 1000 values of drought outlook were calculated and used to formulate a distribution to construct a probability outlook of the drought index. 4) Now the stage of deciding the value of *α* (probability adjustment coefficient) remains. In this paper, the probability adjustment coefficient was constructed through trial and error in which the value of *α* was varied and determined so that the probability forecast score of the study basins would be the highest during the verification period. Value of *α* was increased by 0.05, and the most widely used ranked probability skill score (RPSS) was adopted for the probability forecast score:

Here, *J* denotes the number of the classes, and the cumulative probabilities of the forecasts *Y _{j}* and the observations

*O*are defined as and , where

_{j}*Y*and

_{j}*O*are the probability of the forecast and observation, respectively, for the class

_{j}*i*(Weigel et al. 2007). The maximum value of RPSS is 1, which represents a perfect forecast, while the magnitude of negative values is proportional to the degree of inaccuracy of the forecast. The value of RPSS is greater than 0 when it scores higher than the naive forecast, therefore the value of 0 serves as the criteria that determines the usability of the forecast information. It can be concluded that the process of determining the value of

*α*is in fact a question of optimization in finding the decision variable

*α*by using RPSS as an objective function. Following the five steps, not only is the qualitative forecast transformed into quantitative data, but the extensive weather information—which was initially given in common to many basins—is broken down and reduced to forecasts that are optimal for the characteristics of each individual basin.

## 3. Application

### a. Application overview

In the application of the meteorology for drought outlook proposed in this study, three basins from Korea were selected—Andong-dam basin, Hwanggang basin, and Milyanggang basin along the Nakdong River (Fig. 1). The Nakdong River is 521.5 km long and has the second largest drainage area of 23 817 km^{2} in Korea, corresponding to 24.1% of the South Korean territory. The hydrology of this basin is affected by the monsoon climate. In total, 65% of the annual precipitation is concentrated during the three months ranging from July to September, while the remaining 35% is dispersed during the nine remaining months. Therefore, drought is an important issue in regards to the Nakdong River basin.

Figure 1 shows the regional locations of the study basins. The studied period was in the dry season—from September 2008 to May 2009—during which monthly analysis was carried out. The flood season was excluded because, as aforementioned, drought rarely occurs during this time of year. The KMA long-range forecasting method made forecasts of the 3 consecutive months after the subject month, and was conducted 27 times (=3 different lead times × 9 months from September 2008 to May 2009) for each basin. In addition, RPSS was scrutinized while constantly increasing the value of *α* by 0.05, starting from 0, in order to determine the optimal probability adjustment coefficient appropriate for the study basins. Figure 2 illustrates an example of application of the probability adjustment coefficient to the Andong-dam basin. It shows the distributions of both temperature and precipitation based upon the determined value of *α* as 0.15. The bold dotted lines represent the average temperature and precipitation, while the unbroken lines show the posterior distribution obtained from applying the probability adjustment coefficient yielded from the use of a BN forecast.

### b. The SPI outlook and investigation

As mentioned earlier, the SPI drought outlook was tested by means of increasing the probability adjustment coefficient by 0.05 at each time of testing. Figure 3a shows the outlook results of the Andong-dam basin in December, January, and February—three months following the subject month, November—based on the probability adjustment coefficient of 0.10. Figure 3b uses the same probability adjustment coefficient value and shows the predicted results based on December as the subject month. In the outlook of December from Fig. 3, the probability of mild drought is the highest with 75% chance of occurrence, and severe drought shows a probability of 6%. Finally, it is also observed that there is a 19% probability of not having drought. A general overview of Figs. 3a,b indicates that the probability of drought will be highest in January, while it is expected that this problem would be completely resolved by March. Table 3 shows the results of RPSS calculations on the probability outlooks of each study basin. A close look at Table 3 shows that the Andong-dam basin yields the highest accuracy. The outlook on the Hwanggang basin yields the lowest values, yet all values of RPSS are positive. These results prove that the meteorology developed in this paper is substantially valid.

### c. The SMI outlook and investigation

Figure 4a provides the SMI outlook results of the Andong-dam basin during the three consecutive months following November (i.e., the subject month) when the probability adjustment coefficient is 0.10. Figure 4b shows outlook results based on the same probability adjustment coefficient but of a different month (i.e., December). Compared to Fig. 3, Fig. 4 reports inconsistency between the calculated values of SMI and SPI. For example, Fig. 3 shows that December of 2008 and January and February of 2009 are classified as mild drought, severe drought, and mild drought, respectively, in terms of the observed SPI while Fig. 4 shows normal, normal, and wet conditions, respectively, for the same months in terms of the observed SMI. This would be because ET was low but SMC was not low during the period; the precipitation was also low. Therefore, SMI did not classify the period as a drought while SPI, which depends only on the precipitation, did so.

The outlook results for December in Fig. 4b indicate that severe drought has the highest probability of occurrence (43%), while there is a 38% chance of extreme drought. Mild drought is likely to occur with a probability of 8%, normal 9%, and wet 2%. In contrast to Fig. 4a, Fig. 4b produced results that forecast lower probability of drought. This discrepancy is caused by the fact that the Andong-dam basin had experienced only a small amount of precipitation during November. Thus, when the forecast was made based on November as in Fig. 4a, the outlook predicted severe progression of drought. However, when December became the subject month, drought was expected to be less severe since there was a greater amount of precipitation during this month. This implies that the meteorology applied in this paper is a technique that best reflects the actual weather conditions. Accuracy of the applied probability outlook can be seen in Table 4, and the overall accuracy is lower compared to the SPI. The reason is that whereas the SPI requires only one variable, precipitation, the SMI requires both precipitation and potential evapotranspiration as variables; an increased number of variables contributes to the growth of uncertainty. Nevertheless, the SMI is still sufficiently valid as a drought outlook methodology since its computed results maintain RPSS values that are considerably greater than zero.

### d. Determination of the optimal probability adjustment coefficient

This study quantifies the KMA long-range forecasts, which is qualitatively expressed, and determines the optimal probability adjustment coefficient, thereby subdividing the general forecast information so as to target specific basins. This process is based on the stationary trait, which assumes that the probability adjustment coefficient with the highest RPSS value during the previous testing period will also yield accurate forecast results at the study basins in the future. In sum, the RPSS values of each basin are shown in Tables 3 and 4. In each table, the underlined characters indicate the highest RPSS values for optimal probability adjustment coefficients. In other words, when using the KMA long-range forecasting for the drought outlook in the three basins—Andong-dam basin, Hwanggang basin, and Milyanggang basin—simple recalibration of interval probabilities from the prior distribution to 0.05, 0.10, and 0.00, respectively, will suffice. The difference of the probability adjustment coefficients among each basin is due to their individual hydrologic characteristics.

## 4. Conclusions

This research has developed a method that can best forecast drought conditions from the given meteorological information. To make use of the drought outlook, Korean meteorological information was examined, and the long-range forecasts provided by the KMA were decided as suitable in the application of the new method. Initially, this study faced two problems—converting and reducing the nationwide forecast information into regional scales, and quantifying information that are given in qualitative forms—but they were soon resolved by the application of SPI and SMI as drought indices. To verify the probability forecast, RPSS was used as a means to evaluate accuracy. The obtained results showed that the maximum values of SPI and SMI were 0.60 and 0.69, respectively. In addition, the RPSS values of SPI and SMI yielded average results of 0.53 and 0.44, respectively, in the study basins. Finally, appropriate probability adjustment coefficients for each model basin were calculated in the process of breaking down the KMA long-range forecasts into regionally applicable information.

However, the meteorological information used in this article showed an average accuracy of the 34% hit ratio for precipitation and 39% for temperature. This rate of accuracy shows that the information is just barely sufficient as forecast information. The reason for such uncertainty is that not only is it difficult to predict the climate but there are also limitations to producing a forecast when considering the Korean peninsula as a unitary region. Thus, it should be noted that a study is also required in regards to the accuracy of the meteorological information, which is the primary data of this research. Increased precision of the basic forecast data used in this study will improve the accuracy of the drought outlook meteorology as well. Therefore, along with research such as this article—which combines meteorological data and hydrology—studies should be done to improve the accuracy of the meteorological information.

## Acknowledgments

This research was carried out as a part of the “Climate Change Adaptation and Projection for Hydrology in Korea” study in support of the Korea Institute of Construction and Transportation Technology Evaluation and Planning (KICTEP).

## REFERENCES

*Methods and Tools for Drought Analysis and Management,*G. Rossi et al., Eds., Springer, 29–48.