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  • View in gallery

    The location of the study area in southwest China.

  • View in gallery

    The spatial coincidence among GRACE-MWD, GRACE-DSI, and SPEI03 by visual inspection for three anomalous droughts.

  • View in gallery

    The comparisons of GRACE-MWD against GRACE-DSI in strength of association and drought category coincidence. The strength of association measured by MIC between (a) GRACE-MWD and SPEI03 and (b) GRACE-DSI and SPEI03, both before discretization. The coincidence measured by ratio of agreement between (c) GRACE-MWD and SPEI03 and (d) GRACE-DSI and SPEI03, both after discretization. Three locations with different levels of ratio of agreement between GRACE-MWD and SPEI03 are marked in (c) and (d): location 1 (25.75°N, 102.75°E) with a ratio of agreement between 0.5 and 0.6, location 2 (30.75°N, 104.75°E) with ratio of agreement between 0.6 and 0.7, and location 3 (31.75°N, 100.75°E) with ratio of agreement between 0.7 and 0.8. In the line plots, the symbols are values of drought indices before discretization, and lines are smoothed values of symbols by locally weighted scatterplot smoothing.

  • View in gallery

    The unchanged land cover map in southwest China from the MODIS-derived LAI/fraction of photosynthetically active radiation (fPAR) scheme. The line plots compare GRACE-MWD with widely used remote sensing datasets including precipitation, land surface temperature, NDVI, and soil moisture at locations with different land covers: location 1 (32.13°N, 107.86°E) with deciduous broadleaf forest land cover, location 2 (28.88°N, 100.87°E) with evergreen needleleaf forest land cover, location 3 (25.87°N, 107.17°E) with savanna land cover, location 4 (30.70°N, 104.04°E) with urban land cover, location 5 (22.14°N, 101.84°E) with evergreen broadleaf forest land cover, and location 6 (32.20°N, 100.75°E) with grasses or cereal crops land cover.

  • View in gallery

    The ratio of agreement between (top) GRACE-MWD and SPEI at all grids for a time scale from 1 to 48 months. (bottom) GRACE-MWD and SPI at all grids for a time scale of 1 to 24 months. The red solid line indicates the mean; the black solid line indicates the median; upper and lower squares in each boxplot represent the top whisker (maximum value) and bottom whisker (minimum value), respectively. Five levels of agreement ranging from 0.5 to 0.9 with an increase of 0.1 are shown as different style of lines.

  • View in gallery

    The relationship between (a) peak-to-peak GRACE-MWD and the ratio of agreement and (b) peak-to-peak GRACE-MWD and peak-to-peak TWS. The red solid lines indicate a linear fit resulting from a linear model.

  • View in gallery

    EOF analysis on the original fields of MAC and the stationary annual cycle. Spatial structure for the MAC field of the (a) first EOF and (c) second EOF. Time series of the (e) first EOF and (g) second EOF. Spatial structure for the stationary annual cycle field of the (b) first EOF and (d) second EOF. Time series of the (f) first EOF and (h) second EOF.

  • View in gallery

    Stability test on the reference frames of MAC and the stationary annual cycle. The variation of MAC when a new year of GRACE data are added at (a) location 1, (c) location 2, and (e) location 3. The stationary annual cycle variation at (b) location 1, (d) location 2, and (f) location 3. The points selected, including 25.5°N, 102.5°E; 30.5°N, 104.5°E; and 31.5°N, 100.5°E, have different levels of ratio of agreement between GRACE-MWD and SPEI03.

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Drought Monitoring of Southwestern China Using Insufficient GRACE Data for the Long-Term Mean Reference Frame under Global Change

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  • 1 State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, and University of Chinese Academy of Sciences, Beijing, China
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Abstract

Global changes, such as human activities and climate change, increase the odds of worsening drought. The Gravity Recovery and Climate Experiment (GRACE) satellite provides an opportunity to monitor drought levels by the total amount of water, instead of using a small finite set of water cycle elements or indirect indicators. The potential gap lies in the insufficient size of the GRACE record. The database does not meet the requirements of a stationary annual cycle calculated over a relatively long period as recommended by the IPCC, and the disturbance from long-term global changes is often not considered. In this work, a GRACE-based modulated water deficit (GRACE-MWD) process for drought monitoring under the modulated annual cycle (MAC) reference frame in southwest China was proposed. GRACE-MWD achieved a higher ratio of agreement with the standardized precipitation evapotranspiration index at a time scale of 3 months (SPEI03): it ranged from 0.48 to 0.84, while the GRACE-based drought severity index (GRACE-DSI) ranged from 0.48 to 0.68. Compared with remote sensing datasets widely used in drought monitoring, GRACE-MWD data are less affected by seasonality from land-cover categories, which benefit from the MAC reference frame. The ratio-of-agreement metric for the study area showed that GRACE-MWD had a time scale between 7 and 11 months in reference to SPEI and the standardized precipitation index (SPI). The stability of the MAC reference frame to GRACE-MWD was further discussed when GRACE records were extended and was more stable than that of the stationary annual cycle. GRACE-MWD meets global changes via an adaptive reference frame, which is worthy of generalizing to global applications.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yaohuan Huang, huangyh@igsnrr.ac.cn

Abstract

Global changes, such as human activities and climate change, increase the odds of worsening drought. The Gravity Recovery and Climate Experiment (GRACE) satellite provides an opportunity to monitor drought levels by the total amount of water, instead of using a small finite set of water cycle elements or indirect indicators. The potential gap lies in the insufficient size of the GRACE record. The database does not meet the requirements of a stationary annual cycle calculated over a relatively long period as recommended by the IPCC, and the disturbance from long-term global changes is often not considered. In this work, a GRACE-based modulated water deficit (GRACE-MWD) process for drought monitoring under the modulated annual cycle (MAC) reference frame in southwest China was proposed. GRACE-MWD achieved a higher ratio of agreement with the standardized precipitation evapotranspiration index at a time scale of 3 months (SPEI03): it ranged from 0.48 to 0.84, while the GRACE-based drought severity index (GRACE-DSI) ranged from 0.48 to 0.68. Compared with remote sensing datasets widely used in drought monitoring, GRACE-MWD data are less affected by seasonality from land-cover categories, which benefit from the MAC reference frame. The ratio-of-agreement metric for the study area showed that GRACE-MWD had a time scale between 7 and 11 months in reference to SPEI and the standardized precipitation index (SPI). The stability of the MAC reference frame to GRACE-MWD was further discussed when GRACE records were extended and was more stable than that of the stationary annual cycle. GRACE-MWD meets global changes via an adaptive reference frame, which is worthy of generalizing to global applications.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yaohuan Huang, huangyh@igsnrr.ac.cn

1. Introduction

Droughts are a slow-onset, long-lasting, and wide-ranging phenomenon with noticeable social and economic impacts, and they are more complex than a lack of rainfall (Mishra and Singh 2010; Vicente-Serrano et al. 2010). Droughts have been expected to increase in frequency and severity in the future (at certain scales) as a result of global change (Dai 2011, 2013; Piao et al. 2010; Prospero and Lamb 2003; Trenberth et al. 2014). Recent droughts, including the Millennium Drought, which lasted from 1997 until late 2009 in Australia (van Dijk et al. 2013); the Amazon basin drought of 2005 (Xavier et al. 2010); the extreme drought in southwest China that lasted from 2009 to 2010 (Liu et al. 2014); and the prolonged and severe California drought that lasted from 2012 to 2014 (Griffin and Anchukaitis 2014), are only a few examples that place an emphasis on drought monitoring.

To monitor complicated droughts effectively, it is necessary to represent their total water deficits completely (including surface water, soil water, groundwater, or snow/ice; Famiglietti et al. 2011; Wang et al. 2014). However, in recent years, widely used indicators, such as the Palmer drought severity index (PDSI), the standardized precipitation index (SPI), and the standardized precipitation evapotranspiration index (SPEI), mainly rely upon subcomponents or proxies of total water deficit brought on by precipitation, temperature, wind speed, solar radiation, and other factors (Heim 2002; Mishra and Singh 2010). Satellite imagery–based drought monitoring has the advantage of easily accessing data with high spatial resolution, which is suitable for large-scale projects. Because these data mainly rely on proxies of digital numbers converted from radiation parameters, images often show information about the shallow surface of Earth (Anderson et al. 2011; Twomey 2013; Zhang and Jia 2013). Fortunately, the Gravity Recovery and Climate Experiment (GRACE) satellite provides an opportunity to determine the total amount of water by measuring the integrated bulk variables of terrestrial water storage (TWS) in the vertical continuum (AghaKouchak et al. 2015; Tapley et al. 2004a), under the hypothesis that observed changes in gravity are caused by changes in water (Chen et al. 2009; Tapley et al. 2004b).

Compared with commonly used drought indices and satellite-based approaches that characterize subcomponents of shallow surface water deficits, GRACE-based TWS enables researchers to incorporate the relevant hydrological variables to fully characterize drought propagation and recovery and associated human activities, such as irrigation and water transfer projects (Wu et al. 2013; Wu et al. 2006). TWS estimates from GRACE have been widely used in drought monitoring assessments at the regional scale (Swenson et al. 2008; Swenson and Milly 2006; Thomas et al. 2014; Yirdaw et al. 2008). These assessments include the standardized drought severity index based solely on GRACE TWS estimates (GRACE-DSI; M. Zhao et al. 2017) and some practical applications of drought monitoring tools incorporating GRACE information (http://drought.unl.edu/MonitoringTools.aspx).

Driven by global changes, the complexity of drought has increased severely (Bates et al. 2008). Drought estimation needs to consider the underlying variation in trends of water resource storage at long time scales that consider global changes (Haddeland et al. 2014; Milly et al. 2008; Pahl-Wostl 2007). However, previous studies have focused only on the stationary annual cycle, which is always calculated from climate variable averages over relatively long periods (e.g., 30 years) as the baseline (Hallegatte et al. 2007; IPCC 2013; Zhu et al. 2008). GRACE, which was launched in 2002, has insufficient time series data to calculate long-term mean reference frames for GRACE TWS–based approaches. Furthermore, existing mean reference frames are derived from long-term data accumulation that ignores changes from earthquakes, water conservation projects, and climate change. The water deficits extracted from long-term mean reference frames may suffer from this interference.

To overcome these limitations, we developed a new drought index called GRACE-based modulated water deficits (GRACE-MWD) that uses the modulated annual cycle (MAC) reference frame (Chen et al. 2013; Moron et al. 2012; Qian et al. 2011; Wu et al. 2008) and allows the annual cycle to change over years. The results from GRACE-MWD were compared to SPEI and GRACE-DSI data from southwest China. We also analyzed the relationship between drought monitoring results from GRACE-MWD and satellite-based drought monitoring datasets that include precipitation, land surface temperature, normalized difference vegetation index (NDVI), and soil moisture. Finally, we discussed the MAC reference frame, which GRACE-MWD relies on, via empirical orthogonal function (EOF) analysis and verified the stability when GRACE records are extended in metrics of standard deviation to evaluate the merit of the solution we proposed.

2. Data and methodology

a. Study area

The study area is in southwest China and consists of the Chongqing municipality and four provinces, including Guangxi, Yunnan, Guizhou, and Sichuan, with a total area of approximately 1.36 × 106 km2 (Fig. 1). The region is complicated in terms of its topography, which covers the Yunnan–Guizhou Plateau, the Sichuan basin, the southeastern Tibetan Plateau, part of the Southeast Hills, and transitional zones with an elevation difference of more than 6000 m. The area has a subtropical monsoon climate and generally experiences an annual precipitation of over 900 mm. There are abundant water resources in this area, and it is the origin of many large rivers, such as the Yangtze River and the Pearl River. However, the area has frequently suffered from droughts since 2000 (such as the extreme summer 2006 drought in Sichuan, Chongqing, and Yunnan; the prolonged drought of southwest China from autumn 2009 through spring 2010; and the severe drought in southwest China in autumn 2011), which have caused serious economic losses, environmental damage, and human suffering (Huang et al. 2015; Li et al. 2015).

Fig. 1.
Fig. 1.

The location of the study area in southwest China.

Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0869.1

b. Data sources

1) GRACE TWS

We used GRACE-derived monthly terrestrial water storage (http://grace.jpl.nasa.gov) that is based on the Release 05 spherical harmonics from the University of Texas Center for Space Research (CSR), the National Aeronautics and Space Administration (NASA) Jet Propulsion Laboratory (JPL), and the GeoForschungsZentrum Potsdam (GFZ) for the period from April 2002 to December 2015, with 1° spatial resolution. The data expressed gravity anomalies captured by GRACE after postprocessing (Landerer and Swenson 2012; Swenson 2012; Swenson and Wahr 2006). The anomalies were in the centimeter range, which is equivalent to water thickness, and were scaled to restore the energy attenuated by the data processing in this study. The total combined leakage error and measurement error of the study area is ±19.56 mm 27.59 km3 after decorrelation from adjacent grid points (Landerer and Swenson 2012).

2) Drought severity index

We adopted SPEI grids at a 3-month time scale (SPEI03) from the Global SPEI database (http://digital.csic.es/handle/10261/128892) with 0.5° spatial resolution and 1-month temporal resolution to characterize the drought conditions in southwest China during April 2002–December 2015. The data were chosen because they combine the sensitivity of PDSI, evaporation demand changes, and the multitemporal nature of SPI (Vicente-Serrano et al. 2010). A 3-month time scale was used for the SPEI monitoring, and the characteristics of drought in the study area were recorded (H. Zhao et al. 2017).

3) Satellite-based drought monitoring datasets

We compared the GRACE-MWD results with five remote sensing datasets that are commonly used in large-scale drought monitoring to analyze temporal characteristics after the annual cycle was removed. These data are monthly 0.25° (resolution) precipitation products from the Tropical Rainfall Measuring Mission (Zhang and Jia 2013), monthly 0.05° land surface temperature data (MOD11C3), monthly 0.05° NDVI data (MOD13C2), yearly 0.05° land-cover type data (MCD12C1) from NASA (Karnieli et al. 2010), and daily 0.25° soil moisture data from the European Space Agency Climate Change Initiative program (Liu et al. 2011).

c. GRACE-MWD

We applied the MAC reference frame to monthly TWS variability based on the ensemble empirical mode decomposition (EEMD) method (Wu and Huang 2009), which decomposes a nonlinear and nonstationary signal into a high-frequency component that has a time scale of 12 months, a modulated annual cycle that is dominated by a quasi-annual time scale, and a low-frequency component with a time scale longer than 1 year (Wu et al. 2008). The remarkable properties of the EEMD have led to powerful signal-processing algorithms in many geophysical fields (Hawinkel et al. 2015; Qian et al. 2011, 2009; Ruzmaikin and Feynman 2009; Wang et al. 2015). The MAC was extracted from a monthly TWS series for grids based on Wu et al. (2008) and Qian et al. (2011). We calculated GRACE-MWD as
eq1
where is the terrestrial water storage of the kth grid, and is the modulated annual cycle of the kth grid.

To match these results to the preexisting drought categories, we discretized the GRACE-MWD based on the ranking percentiles introduced by the U.S. Drought Monitor (Svoboda et al. 2002), which has been widely used in drought grading (Potop et al. 2014; H. Zhao et al. 2017; M. Zhao et al. 2017). The GRACE-MWD data were classified into five categories (Table 1) and postprocessed by identifying the one that lasted 3 or more months as final drought monitoring results (Thomas et al. 2014).

Table 1.

The ranking percentiles for each drought category in dry conditions of GRACE-MWD and SPEI.

Table 1.

d. Evaluation of GRACE-MWD

We examined the temporal coincidence between GRACE-MWD and SPEI03 and the temporal coincidence between GRACE-DSI and SPEI03 during the entire study period. SPEI data were aggregated to 1° using a simple majority-based scheme to match the resolution of the other two datasets (Ershadi et al. 2013). The temporal coincidence was measured via the maximal information coefficient (MIC), which captures linear and nonlinear associations (Reshef et al. 2011) between two drought indices at each grid cell. The MIC method captures the strength of the correlation by the degree of data concentration and does not assume prior distributions of data (e.g., normal distribution) and forms of correlation (e.g., exponential correlation, linear correlation). Moreover, we examined the ratio of agreement between GRACE-MWD and SPEI03 after discretization and the ratio of agreement between GRACE-DSI and SPEI03 after discretization. The ratio of agreement was measured by considering when two drought indices have the same drought category, divided by the total number of months at each grid. The formula is as follows:
eq2
where is the ratio of agreement at grid , and are time series of drought monitoring results from two different indices, is the number of same drought results at the grid, and is the length of a time series.

Furthermore, we evaluated the spatial coincidence among GRACE-MWD, GRACE-DSI (M. Zhao et al. 2017), and SPEI03 by visual inspection of three anomalous droughts. The droughts selected were the extreme summer 2006 drought in Sichuan, Chongqing, and Yunnan that was part of extreme drought of the Changjiang River in 2006 (Dai et al. 2008); the prolonged drought in southwest China from autumn 2009 through spring 2010, which is a once-in-a-century drought (Lu et al. 2011); and the severe drought in southwest China in autumn 2011, which is a once-in-a-50-yr drought (Lu et al. 2014). The characteristics of severity, spatial distribution, and duration were used to identify the differences and similarities of these three methods.

We compared GRACE-MWD with remote sensing datasets that are commonly used in large-scale drought monitoring, which examined temporal characteristics of datasets on different land-cover types. These datasets are limited to measuring the deep soil water and groundwater (Houborg et al. 2012), which have been increasingly influenced by human activities, such as irrigation and interbasin water transfer (Rodell et al. 2009). Meanwhile, these data have various responses on different land-cover types. For example, vegetation has a buffering effect on the change of temperature and precipitation, brings a seasonal variation on NDVI, and influences the soil moisture measurement (Brown et al. 2008; Wang et al. 2014). We extracted unchanged land cover from MCD12C1 datasets during the data period and randomly selected a single location representing each land-cover type to compare GRACE-MWD via these remote sensing datasets. The power spectrum analysis was employed to identify the dominant frequency of the signal for each remote-sensed dataset at each position (Parsons et al. 2017). The dominant frequency at the highest spectral density was used to depict the main periodic characteristics of the time series. To obtain the details of the trend, a simple linear regression was used to model the time series of the remotely sensed datasets as a function of time (Raynolds et al. 2008).

Because droughts are a multiscalar phenomenon (McKee et al. 1993), the temporal scale of GRACE-MWD was tested against the SPEI and SPI datasets to determine a specific time scale for monitoring and managing water resources. The SPI was calculated based on the precipitation from the Climate Research Unit (CRU) time series dataset (Mitchell and Jones 2005). The SPEI data have a time scale from 1 to 48 months, and SPI has a time scale from 1 to 24 months. A boxplot was applied to the ratio of agreement in each grid at different time scales to map GRACE-MWD to a certain time scale in view of the current drought measurements. The ratio of agreement greater than certain thresholds that range from 0.5 to 0.9, with an increase of 0.1, was taken into consideration to assist in the detection of optimal time scales.

3. Results

GRACE-MWD, GRACE-DSI, and SPEI03 were calculated and compared for three severe droughts over the past 10 years and are shown in Fig. 2. The results show similarities and differences. For the extreme drought in 2006, GRACE-MWD captured droughts in Sichuan, Chongqing, and Yunnan, while GRACE-DSI and SPEI03 left out the drought in Yunnan (Huang 2009). GRACE-DSI exaggerated the drought in northern Sichuan. For the severe drought in 2011, GRACE-MWD also performed well and did not exaggerate the situation, like GRACE-DSI and unlike SPEI03. GRACE-DSI exaggerated the drought in terms of both severity and distribution. In view of the prolonged drought from 2009 to 2010, GRACE-MWD may miss critical drought features, as it produces similar drought monitoring results as GRACE-DSI does, which is not as severe as SPEI03. In contrast with the results of GRACE-MWD, GRACE-DSI tends to give a more serious and extensive drought situation in most cases via a comparison of these three droughts.

Fig. 2.
Fig. 2.

The spatial coincidence among GRACE-MWD, GRACE-DSI, and SPEI03 by visual inspection for three anomalous droughts.

Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0869.1

Moreover, further comparisons of GRACE-MWD against GRACE-DSI were in accordance with SPEI03, which was conducted via both the correlation of the real values before discretization and the ratio of agreement between drought categories (Fig. 3). As shown in Figs. 3a and 3b, the MIC before discretization between GRACE-MWD and SPEI03 ranges from 0.21 to 0.41, which is slightly smaller than that between GRACE-DSI and SPEI03, which ranges from 0.19 to 0.48. This may be caused by seasonal signals of GRACE-DSI and SPEI03. After discretization of these three drought indices, the ratio of agreement between GRACE-MWD and SPEI03 exceeds that between GRACE-DSI and SPEI03. The ratio of agreement between GRACE-MWD and SPEI03 ranges from 0.48 to 0.84 (Fig. 3c), and the ratio of agreement between GRACE-DSI and SPEI03 ranges from 0.48 to 0.68 (Fig. 3d).

Fig. 3.
Fig. 3.

The comparisons of GRACE-MWD against GRACE-DSI in strength of association and drought category coincidence. The strength of association measured by MIC between (a) GRACE-MWD and SPEI03 and (b) GRACE-DSI and SPEI03, both before discretization. The coincidence measured by ratio of agreement between (c) GRACE-MWD and SPEI03 and (d) GRACE-DSI and SPEI03, both after discretization. Three locations with different levels of ratio of agreement between GRACE-MWD and SPEI03 are marked in (c) and (d): location 1 (25.75°N, 102.75°E) with a ratio of agreement between 0.5 and 0.6, location 2 (30.75°N, 104.75°E) with ratio of agreement between 0.6 and 0.7, and location 3 (31.75°N, 100.75°E) with ratio of agreement between 0.7 and 0.8. In the line plots, the symbols are values of drought indices before discretization, and lines are smoothed values of symbols by locally weighted scatterplot smoothing.

Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0869.1

The line plots with the ratio of agreement between GRACE-MWD and SPEI03 at three levels (0.5 ≤ r < 0.6, 0.6 ≤ r < 0.7, and 0.7 ≤ r < 0.8) show a certain degree of detail in the temporal data. GRACE-MWD (black solid line) has a higher period than GRACE-DSI and SPEI03 at each location. The average period of GRACE-MWD in the above locations is 17 months, the average period of GRACE-DSI is 15 months, and the average period of SPEI is 9 months. The vibration amplitude of GRACE-MWD is different than GRACE-DSI and SPEI03 at a ratio of agreement between 0.5 and 0.6, while it is similar to GRACE-DSI and SPEI03 at a ratio of agreement between 0.6 and 0.8. (The vibration amplitude is the difference between the maximum and minimum values in a drought monitoring time series at one grid.) The relationship between amplitude and ratio of agreement is detailed in section 4a.

We evaluated GRACE-MWD by comparing widely used indicators of remote sensing datasets after the land cover was set as the control variable (Fig. 4). The frequency at the highest spectral density was extracted to characterize the periodicity of different time series. GRACE-MWD tends to have the most power, with interannual frequencies from 22 to 90 months in different land covers, indicating that the MAC processing effectively removed seasonal fluctuations. The precipitation exhibits more spectral power during seasonal frequencies from 2 to 6 months in different land covers. This shows the seasonality effects of precipitation may not be properly eliminated using the stationary annual cycle. The seasonality may have effects on drought propagation (Van Loon et al. 2014). The land surface temperatures provide opposite performances for the day and night. The daytime temperature has major fluctuations in the urban land cover of 20 months and has fluctuations between 3 and 7 months in other land covers. The nighttime temperature in the urban land cover has a major fluctuation of 4 months and has fluctuations from 11 to 36 months in other land covers. The influence of human activities should be considered in drought monitoring that is based on temperatures, which may result from the urban heat island effect.

Fig. 4.
Fig. 4.

The unchanged land cover map in southwest China from the MODIS-derived LAI/fraction of photosynthetically active radiation (fPAR) scheme. The line plots compare GRACE-MWD with widely used remote sensing datasets including precipitation, land surface temperature, NDVI, and soil moisture at locations with different land covers: location 1 (32.13°N, 107.86°E) with deciduous broadleaf forest land cover, location 2 (28.88°N, 100.87°E) with evergreen needleleaf forest land cover, location 3 (25.87°N, 107.17°E) with savanna land cover, location 4 (30.70°N, 104.04°E) with urban land cover, location 5 (22.14°N, 101.84°E) with evergreen broadleaf forest land cover, and location 6 (32.20°N, 100.75°E) with grasses or cereal crops land cover.

Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0869.1

The NDVI shows a seasonal frequency of 9 months in deciduous broadleaf forest and interannual frequencies of more than 12 months in other land covers. The regression caught a significant upward trend for NDVI in land covers of grasses or cereal crops (k = 0.14, R2 = 0.42), urban (k = 0.15, R2 = 0.42), and savanna (k = 0.11, R2 = 0.35) at a significance level of 0.01, which may result from afforestation projects or CO2-enhanced vegetation productivity (Lambin and Linderman 2006; Martínez and Gilabert 2009). These influences over the land covers may be valuable for drought monitoring that is based on NDVI. The soil moisture has a major fluctuation of 11 months in the urban land cover, but suffers from missing values in other land covers, which may be obstructed by snow cover or soil temperatures below zero (Dorigo et al. 2015). As the soil moisture record from satellite microwave retrievals is unreliable over urban areas (An et al. 2016), regression analysis is abandoned.

As shown in Fig. 5, the mean ratio of agreement of GRACE-MWD versus SPEI and SPI is greater than 0.6 for all time scales. The boxes indicate that the middle 50% of the ratio of agreement varies between a 25% and 75% increase with the time scale in each plot, which means an increase in heterogeneity of the ratio of agreement exists for each grid. In view of the agreement between GRACE-MWD and SPEI, the mean ratio of agreement is displayed in red solid lines and reaches a maximum of more than 0.65 on time scales of 7–11 months. This result recurs for the second maximum of more than 0.63 on time scales of 28–32 months. The mean ratio of agreement between GRACE-MWD and SPI reaches a maximum of more than 0.65 on time scales of 8–12 months.

Fig. 5.
Fig. 5.

The ratio of agreement between (top) GRACE-MWD and SPEI at all grids for a time scale from 1 to 48 months. (bottom) GRACE-MWD and SPI at all grids for a time scale of 1 to 24 months. The red solid line indicates the mean; the black solid line indicates the median; upper and lower squares in each boxplot represent the top whisker (maximum value) and bottom whisker (minimum value), respectively. Five levels of agreement ranging from 0.5 to 0.9 with an increase of 0.1 are shown as different style of lines.

Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0869.1

Overall, the proportion of agreement is greater than 0.5 between GRACE-MWD and SPEI. The red solid line decreases with time scale, which has three peaks at time scales of 1 (0.97), 29 (0.85), and 41 months (0.81). The proportion of agreement greater than 0.6 in the green line has two peaks at time scales of 7 (0.64) and 34 months (0.57). The proportion of agreement greater than 0.7 in the blue line reaches a value of more than 0.33 at a time scale from 9 to 14 months. The other two levels, including the proportion greater than 0.8 and the proportion greater than 0.9, increase with time scale. Combined with the boxplot, the optimal time scale should be 7–11 months to map GRACE-MWD to a certain time scale based on SPEI and SPI.

4. Discussion

a. Relationships between GRACE-MWD amplitude and ratio of agreement

GRACE-MWD extends the previous studies that represented the droughts in standardized drought indices, such as PDSI (Palmer 1965), Z index (Palmer 1965), and SPI (McKee et al. 1993). GRACE-DSI also follows the same method. The spatial patterns of the ratio of agreement for the two drought indices are different. GRACE-MWD has an uneven ratio of agreement, which is higher in the north and lower in the south. (The lower values are equivalent to GRACE-DSI.) GRACE-DSI is even across the study area. As GRACE-DSI benefits from the standard deviation adjustment (M. Zhao et al. 2017), we interpret the spatial patterns to the following mechanisms; the amplitudes of the time series result in the uneven patterns of GRACE-MWD.

The scatterplot results (Fig. 6) further validate our interpretation. The peak-to-peak amplitude of GRACE-MWD shows a significant negative correlation between ratios of agreement (r = −0.83, R2 = 0.68), and it has a significant positive correlation between the amplitudes of TWS (r = 0.97, R2 = 0.92). The patterns of GRACE-MWD are mainly influenced by the amplitude of the TWS data themselves. GRACE-MWD has a higher ratio of agreement distributed in clustered patterns in the north. The phenomenon shows that a certain global partitioning scheme may further improve the local ratio of agreement. This partitioning scheme may be related to hydrological zoning, meteorological zoning, or rainfall zoning and is worth further exploration.

Fig. 6.
Fig. 6.

The relationship between (a) peak-to-peak GRACE-MWD and the ratio of agreement and (b) peak-to-peak GRACE-MWD and peak-to-peak TWS. The red solid lines indicate a linear fit resulting from a linear model.

Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0869.1

b. Comparisons with stationary annual cycles

GRACE-MWD differs from the previous studies because it employs the MAC reference frame, which allows the annual cycle to change from year to year (Wu et al. 2008). In previous studies based solely on GRACE, such as Thomas et al. (2014) and M. Zhao et al. (2017), the stationary annual cycle was used as a reference frame, which is independent of the year for a relatively long period. The stationary annual cycle is recommended by the IPCC and widely adopted in research. The differences between the MAC and stationary annual cycle were discussed in depth by Wu et al. (2008) and Huang and Wu (2008). Thus, we mainly focus on the GRACE applications via MAC analysis and the stationary annual cycle extracted from GRACE in the study area.

To compare between the spatial and temporal structures, GRACE-MWD and the stationary annual cycle employ EOF analysis. The results (Fig. 7) show that the spatial patterns are almost the same, which means that the two reference frames contain consistent information. The temporal patterns of MAC resemble those of the stationary annual cycle. Time series of EOF decomposition for MAC change over time rather than being fixed; thus, they are adaptive to time. MAC may adapt to long-term changes, such as climate change, by temporal variability and avoid priori assumptions, such as data that are linear or stationary (Huang and Wu 2008).

Fig. 7.
Fig. 7.

EOF analysis on the original fields of MAC and the stationary annual cycle. Spatial structure for the MAC field of the (a) first EOF and (c) second EOF. Time series of the (e) first EOF and (g) second EOF. Spatial structure for the stationary annual cycle field of the (b) first EOF and (d) second EOF. Time series of the (f) first EOF and (h) second EOF.

Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0869.1

The previous studies based on GRACE may be affected by insufficient data accumulation, which does not meet the recommendation from the IPCC to calculate a stationary annual cycle reference frame. The stability of the reference frame is especially important for this situation. MAC and the stationary annual cycle were extracted each year, beginning in 2003 (Fig. 8), in view of the three different levels of the ratio of agreement. Both MAC and the stationary annual cycle vary when new data are added. To measure the variance, the standard deviation was calculated for MAC and the stationary annual cycle. The mean standard deviation for MAC is 0.68, while the stationary annual cycle has a mean standard deviation of 0.92. If the first 4 months of MAC are not taken into account, then the mean standard deviation reduces to 0.52. This shows that MAC, as a reference frame, has stability when new data are added. Additionally, the first 4 months of MAC have a standard deviation from 0.77 to 2.60, which is obviously different from the whole set. This phenomenon, which is inevitable for finite time series, results from the end effects of MAC inherited from empirical mode decomposition (Barnhart et al. 2011; Lin et al. 2012).

Fig. 8.
Fig. 8.

Stability test on the reference frames of MAC and the stationary annual cycle. The variation of MAC when a new year of GRACE data are added at (a) location 1, (c) location 2, and (e) location 3. The stationary annual cycle variation at (b) location 1, (d) location 2, and (f) location 3. The points selected, including 25.5°N, 102.5°E; 30.5°N, 104.5°E; and 31.5°N, 100.5°E, have different levels of ratio of agreement between GRACE-MWD and SPEI03.

Citation: Journal of Climate 31, 17; 10.1175/JCLI-D-17-0869.1

The MAC, which contains similar information to the stationary annual cycle and is more stable than the stationary annual cycle in this study, is an alternative reference frame worthy of exploration for drought monitoring. The switch of reference period for stationary annual cycles generates a gap used for comparison between studies and changes the past drought events as GRACE’s record length grows. A reference frame that is adaptive to the nature of the data may be able to avoid this dilemma. Under climate change, the adaptive reference frame of MAC deals with nonlinear nonstationary data, which implies a wider application in terms of drought monitoring and climate change detection (Lee and Ouarda 2012; Qian et al. 2011).

With MAC as a reference frame, GRACE-MWD may fill the gap of the insufficient GRACE data record and be reliable for seasonality removal. GRACE-MWD benefits from adaptions of MAC, while GRACE-DSI benefits from variance adjustment. The two GRACE-based drought monitoring indices have gone one step further with respect to the stationary annual cycle, which incorporates more information other than the mean value (the first moment). Though GRACE-DSI contains information about the variance (the second moment), it lacks information on higher-order moments. In view of this, GRACE-MWD may be an alternative solution for drought monitoring applications.

5. Conclusions

In this paper, we presented a GRACE-based modulated water deficit for drought monitoring under the MAC reference frame in southwest China and achieved a ratio of agreement with SPEI03 ranging from 0.48 to 0.84. GRACE-MWD hits the drought situation twice in accordance with SPEI03 for the three severe droughts over the past 10 years in the examined study area. It achieved similar results once consistent with GRACE-DSI for the prolonged drought from 2009 to 2010 by visual inspection. Compared with remote sensing datasets, which widely used satellite-based drought monitoring approaches, GRACE-MWD suffers less from seasonality and trends on different land-cover categories. We map GRACE-MWD to the current multiscalar drought indices by examining the ratio of agreement with SPEI, which has a time scale from 1 to 48 months, and SPI, which has a time scale from 1 to 24 months. In view of the ratio of agreement, the time scale of GRACE-MWD is between 7 and 11 months in the study area.

There is a significant negative correlation between the ratio of agreement and amplitude for GRACE-MWD data according to the Pearson correlation value of −0.83. GRACE-MWD can reach a higher ratio of agreement when the amplitude of TWS is adjusted, which needs further exploration. The MAC, which GRACE-MWD relied on, contains similar information as the stationary annual cycle and is more stable in standard deviation metrics when the GRACE records are extended. The GRACE-MWD method we proposed provides an alternative choice for drought monitoring based on GRACE. The GRACE data guarantee a rigorous water balance–based solution to drought monitoring and promise a spatial and temporal resolution improvement on the GRACE Follow-On mission. Future work will focus on the global application of GRACE-MWD.

Acknowledgments

This research was supported and funded by the National Key Research and Development Program of China (Grants 2017YFB0503005 and 2016YFC0401404).

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