Drought Assessment using GRACE Terrestrial Water Storage Deﬁcit in Mongolia from 2002 to 2017

: Climate warming can result in increases in the frequency and magnitude of drought events, leading to water shortages and socioeconomic losses. Gravity Recovery and Climate Experiment (GRACE) satellite data have been used to monitor and estimate drought events. However, there is little information on detecting the characteristics of droughts in Mongolia due to sparse observations. In this study, we estimate the drought conditions in Mongolia using GRACE terrestrial water storage data during 2002–2017. Water storage deﬁcit (WSD) is used to identify the drought event and calculate the water storage deﬁcit index (WSDI). The WSDI was compared with the standardized precipitation index (SPI) and the standardized precipitation evapotranspiration index (SPEI). The results showed that there were two turning points of WSD in 2007 and 2012. Eight drought events were identiﬁed and the most severe drought occurred in 2007–2009 lasting for 38 months with a WSDI of − 0.98 and a total WSD of − 290.8 mm. Overall, the WSD and WSDI were e ﬀ ective in analyzing and assessing the drought severity in a region where hydrological observations are lacking.


Introduction
Drought is a type of natural hazard that plays a critical role in threatening various ecosystems and human societies, which has attracted much attention in ecology, hydrology, and meteorology [1]. Some studies indicate that the frequency and magnitude of droughts are projected to enhance in the future due to climate change [2,3]. It has been reported that an increase in drought intensity can lead to an imbalance of soil nutrients cycling in terrestrial ecosystems, which in turn affect ecosystem functions and stability [4]. Furthermore, droughts can lead to substantial loss of crop and economy. The recent drought in Mongolia is associated with major social and environmental change, including migration of several hundred herders to the capital city, drying of lakes, and declines in grassland productivity [5]. Thus, it is of great importance to monitor and characterize drought events and spatiotemporal pattern of water deficit.
Regional drought evaluation is traditionally dependent on site−level observations that provide high spatial and temporal resolution data [6]. Although field observations have high resolution in specific regions, the field monitors need installing of some instruments that are not only limited in space and time but are also costly in high human and material resources. Drought is characterized by total water deficit (e.g., soil water, surface water, groundwater) [7], which is hard to quantify over large regions for a long time due to limited observations and systematic monitoring. In recent years, remote sensing has been demonstrated to be a useful and cost−effective approach in accurately

GRACE Data
The GRACE space mission is a joint project between NASA (the US National Aeronautics and Space Administration) and the DLR (the German Aerospace Center) that can accurately measure the averaged time−variable components of the Earth's gravity field to monitor spatiotemporal variations of regional and global total water storage. The spatial resolution of GRACE data has been steadily improving and it currently 0.5° thanks to advances in processing of instrument data and post−processing of gravity field solutions. GRACE data is routinely calculated by various research groups producing monthly solutions based on 30 days of data [25]. The resulting Center for Space Research (CRS) mascon have no stripe errors and capture signal observed by GRACE within the measurement noise level; thus, GRACE RL05 CRS mascon products from the University of Texas Center for Space Research were used to estimate and characterize droughts. The grid data of GRACE total water storage from three GRACE data processing centers can be freely downloaded from the GRACE Tellus website. The monthly total water storage data, in units of equivalent water height [26][27][28] and with a 0.5° × 0. ; all the missing data were interpolated using the mean values before and after the missing month [28,29].

Meteorological Data
Surface and groundwater resources are scarce in Mongolia, making precipitation an important water source for local agriculture. Air temperature is also a significant factor in influencing variation in water storage. In this study, two meteorological parameters, precipitation and temperature, were used to analyze the water storage variation and drought severity. The U.S. National Climatic Data Center provided daily precipitation and air temperature data for 40 meteorological stations from 2002 and 2017. These sites are mainly located in the north of Mongolia (Figure 1), and thus, observations

GRACE Data
The GRACE space mission is a joint project between NASA (the US National Aeronautics and Space Administration) and the DLR (the German Aerospace Center) that can accurately measure the averaged time−variable components of the Earth's gravity field to monitor spatiotemporal variations of regional and global total water storage. The spatial resolution of GRACE data has been steadily improving and it currently 0.5 • thanks to advances in processing of instrument data and post−processing of gravity field solutions. GRACE data is routinely calculated by various research groups producing monthly solutions based on 30 days of data [25]. The resulting Center for Space Research (CRS) mascon have no stripe errors and capture signal observed by GRACE within the measurement noise level; thus, GRACE RL05 CRS mascon products from the University of Texas Center for Space Research were used to estimate and characterize droughts. The grid data of GRACE total water storage from three GRACE data processing centers can be freely downloaded from the GRACE Tellus website. The monthly total water storage data, in units of equivalent water height [26][27][28]  ; all the missing data were interpolated using the mean values before and after the missing month [28,29].

Meteorological Data
Surface and groundwater resources are scarce in Mongolia, making precipitation an important water source for local agriculture. Air temperature is also a significant factor in influencing variation in water storage. In this study, two meteorological parameters, precipitation and temperature, were used to analyze the water storage variation and drought severity. The U.S. National Climatic Data Center provided daily precipitation and air temperature data for 40 meteorological stations from 2002 and 2017. These sites are mainly located in the north of Mongolia (Figure 1), and thus, observations in the southern region are limited. The small amount of missing climate data is interpolated with linear regression. Average monthly air temperature ranges from −20 • C to 20 • C with two distinctive warm and cold seasons (

GRACE−Based Water Storage Deficit Index
The water storage deficit index (WSDI) derived from the monthly deviation of GRACE TWSA is used to identify drought occurrences and to characterize their severity [21]; it is calculated by the following: , , , , where WSDi, j and TWSAi, j are the total water storage deficit and GRACE−inferred TWSA time series for the jth month in year i, respectively; j TWSA is the long term mean of TWSA for the same month (the jth month in a year), μ and σ are the mean and standard deviation of WSD time series, respectively. A negative WSD represents a deficit in total water storage, and a positive WSD denotes a surplus total water storage. A drought event occurs when a negative WSD lasts for three or more consecutive months [10]. Then WSDI can be calculated by standardizing WSD. The WSDI time series denotes the deviation of an individual month against average condition for that month, and its amount can be regarded as a proxy of drought intensity. To assess drought severity, a method that can capture the combined impact of water storage deficit and duration was used. Drought events can be expressed by the following formula [10]: where Se(t) is the severity of drought event t, M(t) is the average deficit of drought event t, that is the mean negative WSD in a drought event, and D(t) is the duration of drought event t, equal to the number of months between the starting and ending months of the drought event.

Standardized Drought Indices
Drought phenomena are usually monitored and characterized using standardized indices. In this study, SPI and SPEI derived from meteorological observations were used to characterize

GRACE−Based Water Storage Deficit Index
The water storage deficit index (WSDI) derived from the monthly deviation of GRACE TWSA is used to identify drought occurrences and to characterize their severity [21]; it is calculated by the following: where WSD i, j and TWSA i, j are the total water storage deficit and GRACE−inferred TWSA time series for the jth month in year i, respectively; TWSA j is the long term mean of TWSA for the same month (the jth month in a year), µ and σ are the mean and standard deviation of WSD time series, respectively. A negative WSD represents a deficit in total water storage, and a positive WSD denotes a surplus total water storage. A drought event occurs when a negative WSD lasts for three or more consecutive months [10]. Then WSDI can be calculated by standardizing WSD. The WSDI time series denotes the deviation of an individual month against average condition for that month, and its amount can be regarded as a proxy of drought intensity. To assess drought severity, a method that can capture the combined impact of water storage deficit and duration was used. Drought events can be expressed by the following formula [10]: where Se(t) is the severity of drought event t, M(t) is the average deficit of drought event t, that is the mean negative WSD in a drought event, and D(t) is the duration of drought event t, equal to the number of months between the starting and ending months of the drought event.

Standardized Drought Indices
Drought phenomena are usually monitored and characterized using standardized indices. In this study, SPI and SPEI derived from meteorological observations were used to characterize droughts in Mongolia and compared with the characterization obtained using WDSI values extracted from grid data of WDSI according to the location of meteorological stations.
The SPI is a precipitation−based drought index developed by McKee et al. (1993) [30] to define and monitor drought events at multiple time scales (1−, 3−, 6−, 12−, and 24−month). SPI can be calculated from long−term precipitation data with a probability density function and then transformed using an inverse normal function to monitor droughts with respect to different water resources [31]. However, disadvantages of SPI stem from the fact that only precipitation is considered without other meteorological factors and requires at least 20-30 years of monthly precipitation data, and 50-60 years, or more, is ideal. SPEI, developed from SPI, is calculated using precipitation and potential evapotranspiration (Equation 4 and 5). Precipitation was obtained from meteorological stations and potential evapotranspiration was estimated using the Thornthwaite method (Equation 6 and 7) that only relied on air temperature and latitude to calculate the monthly average day length.
where P is the probability of exceeding a threshold and can be calculated following Vicente et al.
where PET is potential evapotranspiration, T a is the mean monthly air temperature, I is the heat index, and a is a coefficient calculated by the heat index. The obtained PET values are corrected later according to the real of month and the theoretical sunshine hours for the latitude. The SPI, SPEI and WSDI can detect both dry and wet conditions, with negative values representing drought and positive values for wet conditions. Magnitudes of the three drought indices were used to assess the severity of droughts. The category of drought severity in accordance with McKee et al. (1993) [30] and Palmer (1965) [34] is shown in Table 1. Observation were used to calculate SPI and SPEI; therefore, the drought analysis results were regarded as reliable. Thus, SPI and SPEI were used to compare and assess WSDI values. Table 1. Drought severity category based on drought indices. SPI: standardized precipitation index; SPEI: standardized precipitation evapotranspiration index.

Mann−Kendall Test
The Mann−Kendall (MK) test is a nonparametric method to identify the trend change within variables. The method has been used in studies to understand trends in time series of climate variables such as long−term precipitation, runoff, and evapotranspiration, as long as the time series values are independent of each other. The magnitude of the trend can be estimated by Thiel−Sen's slope. Positive values mean an increasing trend, and negative values mean a decreasing trend. This method is used to examine the trends of TWSA and drought indices to analyze water storage change and drought severity.

Variation of TWSA and WSD
Generally, the change of precipitation influences TWSA. However, considering TWSA as anomaly values, it is compared with precipitation anomaly that was defined as the difference between the mean monthly precipitation and observed monthly precipitation. Figure

Mann−Kendall Test
The Mann−Kendall (MK) test is a nonparametric method to identify the trend change within variables. The method has been used in studies to understand trends in time series of climate variables such as long−term precipitation, runoff, and evapotranspiration, as long as the time series values are independent of each other. The magnitude of the trend can be estimated by Thiel−Sen's slope. Positive values mean an increasing trend, and negative values mean a decreasing trend. This method is used to examine the trends of TWSA and drought indices to analyze water storage change and drought severity.

Variation of TWSA and WSD
Generally, the change of precipitation influences TWSA. However, considering TWSA as anomaly values, it is compared with precipitation anomaly that was defined as the difference between the mean monthly precipitation and observed monthly precipitation. Figure 3  The MK test is used to detect the spatial pattern of TWSA trend and the slope of the change (Figure 4). The most eastern and western areas of Mongolia show increasing trends in mean slope values from 0 to 0.4, and the southern and northern part showed declining trends with the mean slope values from 0 to −0.2. The declining trend is more severe in the southern region because of sparse vegetation, limited precipitation, and high temperature, indicating that Mongolia may face a threat of the decreasing water supply.  The MK test is used to detect the spatial pattern of TWSA trend and the slope of the change (Figure 4). The most eastern and western areas of Mongolia show increasing trends in mean slope values from 0 to 0.4, and the southern and northern part showed declining trends with the mean slope values from 0 to −0.2. The declining trend is more severe in the southern region because of sparse vegetation, limited precipitation, and high temperature, indicating that Mongolia may face a threat of the decreasing water supply. The WSD is calculated from GRACE−inferred TWSA using equation (1). The WSD has two apparent turning points that coincide with the change of TWSA (  Mean monthly TWSA gradually increases from January to July, then decreases from July to October, and shows a slight increase from October to December for Mongolia ( Figure 6). Although there were variations in TWSA between months, the change values were small in Mongolia at the national scale ( Figure 6). The inter−annual variations in WSD had no apparent seasonal change, although precipitation fluctuates significantly at a monthly scale ( Figure 2). However, comparing the TWSA and cumulative precipitation anomaly (Figure 7a), WSD and cumulative precipitation anomaly (Figure 7b), the correlation coefficients were 0.2 and 0.5, respectively. It indicates that The WSD is calculated from GRACE−inferred TWSA using equation (1). The WSD has two apparent turning points that coincide with the change of TWSA (  Mean monthly TWSA gradually increases from January to July, then decreases from July to October, and shows a slight increase from October to December for Mongolia ( Figure 6). Although there were variations in TWSA between months, the change values were small in Mongolia at the national scale ( Figure 6). The inter−annual variations in WSD had no apparent seasonal change, although precipitation fluctuates significantly at a monthly scale ( Figure 2). However, comparing the TWSA and cumulative precipitation anomaly (Figure 7a), WSD and cumulative precipitation anomaly (Figure 7b), the correlation coefficients were 0.2 and 0.5, respectively. It indicates that Mean monthly TWSA gradually increases from January to July, then decreases from July to October, and shows a slight increase from October to December for Mongolia ( Figure 6). Although there were variations in TWSA between months, the change values were small in Mongolia at the national scale ( Figure 6). The inter−annual variations in WSD had no apparent seasonal change, although precipitation fluctuates significantly at a monthly scale ( Figure 2). However, comparing the TWSA and cumulative precipitation anomaly (Figure 7a), WSD and cumulative precipitation anomaly (Figure 7b), the correlation coefficients were 0.2 and 0.5, respectively. It indicates that precipitation is important but not the sole factor for impacting TWSA. They show a turning point in 2008 in the series of WSD and cumulative precipitation anomaly. Precipitation, as an important water source, influences the change in water storage. Thus, these results indicate that the water storage deficit might be affected not only by climate variability but also human activities.
Water 2019, 11, 1301 8 of 14 precipitation is important but not the sole factor for impacting TWSA. They show a turning point in 2008 in the series of WSD and cumulative precipitation anomaly. Precipitation, as an important water source, influences the change in water storage. Thus, these results indicate that the water storage deficit might be affected not only by climate variability but also human activities.

Comparison of WSDI with Other Drought Indices
WSDI is a better indication of drought intensity to quantify the magnitude of drought severity. Figure 8 shows the comparison between WSDI and two widely used drought indices, SPI and SPEI, in different time scales in Mongolia from 2002 to 2017. The trend of WSDI is in agreement with the trend of SPEI−06 and SPI−06. Thus, the 6−month time scale can effectively show the terrestrial water storage deficit change from the GRACE satellite.
The smoothed WSDI, SPEI, and SPI time series also display consistent characteristics with respect to the time of peaks and troughs (Figure 8). In addition, the differences among drought indices are the result of different input variables and methodologies used to calculated. Another source of error may arise from differing spatial scales of the gridded WSDI and point scale of SPEI and SPI.  precipitation is important but not the sole factor for impacting TWSA. They show a turning point in 2008 in the series of WSD and cumulative precipitation anomaly. Precipitation, as an important water source, influences the change in water storage. Thus, these results indicate that the water storage deficit might be affected not only by climate variability but also human activities.

Comparison of WSDI with Other Drought Indices
WSDI is a better indication of drought intensity to quantify the magnitude of drought severity.

Comparison of WSDI with Other Drought Indices
WSDI is a better indication of drought intensity to quantify the magnitude of drought severity.

Drought Events Detected by Drought Indices
By definition, a drought event occurs when negative WSD lasts for three or more consecutive months; eight drought events were confirmed based on WSD during the 2002-2017 period. The mean and peak values of WSD, Se from eight drought periods and the WSDI of Mongolia are shown in Table 2. In addition, the values and drought severity categories based on SPEI, SPI and WSDI of stations also are displayed in Table 3.  Statistics results of WSD values showed that the period from 2007/02 to 2009/12 was the most extensive drought period, followed by the period from 2011/08 to 2012/07, with durations of 38 and 12 months, respectively. The drought duration from 2011/08-2012/07 was shorter than that from 2007/02-2009/12, but the maximum average water deficit occurred with a value of −10.0 mm. In addition, the maximum peak deficits recorded were in 2008/03 and 2015/01 with −16.6 mm and −16.2 mm respectively, the drought duration only six months from 2014/12 to 2015/05. Figure 10 shows the overall drought severity in Mongolia using negative WSD values and a cumulative negative WSD from 2002 to 2017 to analyze and better quantify the intensity of each drought event. The values of drought severity (Se) calculated by equation 3 are shown in Figure 10. Large values of WSDs with longer durations are representative of more severe droughts. Among the eight drought events observed during the study period, the drought event during 2007/02-2009/12 was the most extensive deficit period, lasting 38 months. This event displays the highest total water deficit of −290.8 mm. The drought period from 2011/08-2012/07 lasted for 12 months with a severity of −120.4 mm. The two periods were rated as long−term drought events. Additionally, the other periods were regarded as minor droughts or temporary episodes of dryness in Mongolia, lasting for several months. Drought severity levels are used to characterize drought intensity. Three indices with the highest values were classified according to Table 1. The different drought severity levels are displayed in Table 2 Figure 11 and Figure 12 to discern the change of drought severity. The largest area affected by drought (D1 and D2) occurred in the 2011-2012 drought event, which caused 71% of Mongolia to suffer a mild drought (D1) and 19% for a moderate drought (D2). From 2007 to 2008, 79% of Mongolia area suffers mild drought (D1), 29% moderate drought (D2), 5% for severe drought (D3) and 1% extreme drought (D4). The frequency of D0 from SPEI and SPI was the highest, while frequencies of D0 and D1 from WSDI were similar to one another ( Figure 12). Overall, most of Mongolia experiences mild drought, and severe drought occasionally, although there were differences among these drought indices.  Drought severity levels are used to characterize drought intensity. Three indices with the highest values were classified according to Table 1. The different drought severity levels are displayed in Table 2. Differences in drought levels existed among these drought indices for the same drought events.  Figures 11 and 12 to discern the change of drought severity. The largest area affected by drought (D1 and D2) occurred in the 2011-2012 drought event, which caused 71% of Mongolia to suffer a mild drought (D1) and 19% for a moderate drought (D2). From 2007 to 2008, 79% of Mongolia area suffers mild drought (D1), 29% moderate drought (D2), 5% for severe drought (D3) and 1% extreme drought (D4). The frequency of D0 from SPEI and SPI was the highest, while frequencies of D0 and D1 from WSDI were similar to one another ( Figure 12). Overall, most of Mongolia experiences mild drought, and severe drought occasionally, although there were differences among these drought indices. The drought severity of the area in Mongolia affected by different drought levels is assessed. The spatial distribution of drought areas represented the change process of different drought levels. The statistical results show the area's change suffering from different drought levels. The time series of the monthly area percentage in different drought levels are shown in Figure 11 and Figure 12 to discern the change of drought severity. The largest area affected by drought (D1 and D2) occurred in the 2011-2012 drought event, which caused 71% of Mongolia to suffer a mild drought (D1) and 19% for a moderate drought (D2). From 2007 to 2008, 79% of Mongolia area suffers mild drought (D1), 29% moderate drought (D2), 5% for severe drought (D3) and 1% extreme drought (D4). The frequency of D0 from SPEI and SPI was the highest, while frequencies of D0 and D1 from WSDI were similar to one another ( Figure 12). Overall, most of Mongolia experiences mild drought, and severe drought occasionally, although there were differences among these drought indices.

Conclusion
We evaluated drought events on Mongolia over the period from 2002 to 2013 based on GRACE data. It is clear that GRACE satellites provide considerable insights to the field of hydrology, revealing information about large−scale groundwater depletion and droughts. WSD and WSDI were used to analyze and characterize the identified drought events. Additionally, WSDI values were compared with SPEI and SPI and similarities and differences in the drought classification among these drought indices were discussed.
The Because of the computation methods, data, spatial scales, and the category standards of the indices, differences were found in the results. Overall, although there were some differences between WSDI, SPI, and SPEI, the changing trend and occurred time of peak of these drought indices were consistent. Meanwhile, it captured the major drought events occurring over a large spatial area. Thus, it may be an ideal substitute for large−scale regions with scarce hydro−meteorological sites.

Author Contributions:
The manuscript was primarily written by W.Y., with Y.L. and T.S. contributing to its preparation and English check. Y.C. supervised the research and critically reviewed the draft.

Conclusions
We evaluated drought events on Mongolia over the period from 2002 to 2013 based on GRACE data. It is clear that GRACE satellites provide considerable insights to the field of hydrology, revealing information about large−scale groundwater depletion and droughts. WSD and WSDI were used to analyze and characterize the identified drought events. Additionally, WSDI values were compared with SPEI and SPI and similarities and differences in the drought classification among these drought indices were discussed.
The and lasted 38 months with the total WSD of −290.75 mm, although the average water storage deficit of −7.65 mm was less than that in 2011/08-2012/07 of −10.03 mm. The eight drought events analyzed were classified into different drought severity levels based on different drought indices. Because of the computation methods, data, spatial scales, and the category standards of the indices, differences were found in the results. Overall, although there were some differences between WSDI, SPI, and SPEI, the changing trend and occurred time of peak of these drought indices were consistent. Meanwhile, it captured the major drought events occurring over a large spatial area. Thus, it may be an ideal substitute for large−scale regions with scarce hydro−meteorological sites.

Author Contributions:
The manuscript was primarily written by W.Y., with Y.L. and T.S. contributing to its preparation and English check. Y.C. supervised the research and critically reviewed the draft.