Hydrogeol J DOI 10.1007/s10040-016-1416-9

PAPER

Comparison of GRACE data and groundwater levels for the assessment of groundwater depletion in Jordan Tanja Liesch 1 & Marc Ohmer 1

Received: 13 November 2015 / Accepted: 3 April 2016 # Springer-Verlag Berlin Heidelberg 2016

Abstract Gravity Recovery and Climate Experiment (GRACE) derived groundwater storage (GWS) data are compared with in-situ groundwater levels from five groundwater basins in Jordan, using newly gridded GRACE GRCTellus land data. It is shown that (1) the time series for GRACEderived GWS data and in-situ groundwater-level measurements can be correlated, with R2 from 0.55 to 0.74, (2) the correlation can be widely ascribed to the seasonal and trend component, since the detrended and deseasonalized time series show no significant correlation for most cases, implying that anomalous signals that deviate from the trend or seasonal behaviour are overlaid by noise, (3) estimates for water losses in Jordan based on the trend of GRACE data from 2003 to 2013 could be up to four times higher than previously assumed using estimated recharge and abstraction rates, and (4) a significant time-lagged cross correlation of the monthly changes in GRACE-derived groundwater storage and precipitation data was found, suggesting that the conventional method for deriving GWS from GRACE data probably does not account for the typical conditions in the study basins. Furthermore, a new method for deriving plausible specific yields from GRACE data and groundwater levels is demonstrated.

Electronic supplementary material The online version of this article (doi:10.1007/s10040-016-1416-9) contains supplementary material, which is available to authorized users. * Tanja Liesch [email protected]

1

Division of Hydrogeology, Karlsruhe Institute of Technology, Institute of Applied Geosciences, Kaiserstr. 12, 76131 Karlsruhe, Germany

Keywords GRACE . Over-abstraction . Groundwater management . Groundwater statistics . Jordan

Introduction With the Gravity Recovery and Climate Experiment (GRACE) mission, continuous observations of short-term temporal variations in the Earth’s gravity field, which are mainly caused by changes in terrestrial water storage (TWS), have become available at an unprecedented resolution of a few hundreds of kilometres. Since the mission’s launch in 2003, researchers have used the gathered data to monitor TWS in regions all over the world and on various scales from global (Döll et al. 2014; Richey et al. 2015) to continental (Ahmed et al. 2014; Houborg et al. 2012; Moore and Williams 2014) and regional (Awange et al. 2014; Feng et al. 2013; Joodaki et al. 2014) to sub-regional (Famiglietti et al. 2011; Huang et al. 2015; Moiwo et al. 2009). GRACE data have also been used to calibrate regional groundwater models (Sun et al. 2012 and Hu and Jiao 2015). Recently, comprehensive overviews of GRACE data applications in hydrology were provided by Jiang et al. (2014) and Wouters et al. (2014). A focus that has become more and more important regarding population growth and climate change is the monitoring of changes in groundwater storage (GWS), which can be computed from GRACE observations using additional hydrologic data. Groundwater plays a major though often underestimated role in the supply of the world’s population. It has been estimated, that nearly half the world’s population rely on groundwater for their drinking-water supply (Morris et al. 2003) and about 40 % of the irrigated areas worldwide are equipped for irrigation with groundwater (Siebert et al. 2010). Furthermore, irrigated land produces about 40 % of the world’s food, and two-thirds of the world’s freshwater withdrawals are used by

Hydrogeol J

agriculture (Morris et al. 2003). This leads to the fact that in many regions of the world, groundwater withdrawals exceed natural recharge (Giordano 2009; Gleeson et al. 2012), and the resulting groundwater depletion is a major threat in many respects in the form of declining water supplies, increasing pumping costs, saltwater intrusion, land subsidence, negative ecological effects and maintaining the natural capital for future generations (Döll et al. 2014). It remains unclear though how the rate of global groundwater depletion compares to the rate of natural renewal and the supply needed to support ecosystems (Gleeson et al. 2012) since consistent data on global, or even regional, aquifer storage, recharge, and use are notoriously difficult to come by (Giordano 2009). For a sustainable use of groundwater, the understanding of GWS and the parameters influencing it is crucial though. A country where groundwater depletion due to excess abstraction is a major problem is Jordan. Jordan is considered to be one of the poorest countries worldwide in water resources, with available renewable water resources of an annual per capita share of about 145 m3 (MWI 2009). The renewable natural groundwater resources are estimated to about 275 million m 3 /year (MWI 2013), which are considered sustainable groundwater abstractions from wells and springs (safe yield). The actual groundwater abstraction exceeds the recharge by far and reaches approximately 160 % of the safe yield (MWI 2013), with about 50 % of the groundwater used for irrigation purposes. Among the groundwater basins which are most affected in Jordan are: the Amman-Zarqa Basin with an estimated deficit of −68.8 million m3/year between safe yield and abstraction, the Azraq Basin (−34.2 million m3/year), Dead Sea Basin (–22 million m 3/year), the Jordan Side Wadis Basin (−14.1 million m3/year) and the Yarmouk Basin (−5.9 million m 3 /year; MWI 2013; Fig. 1). In many well fields, the annual water level decline is between 1 and 2 m and even exceeds 2 m in same cases (MWI and BGR 2001). Due to limited availability of reliable data, most of these figures are only estimates though. Depletion rates are strongly affected by abstraction at numerous illegal wells and water level declines can only be measured at a few monitoring wells, which are mostly situated near major well fields and thus influenced by their drawdown cones. GRACE data could therefore provide valuable additional information concerning the assessment of regional groundwater losses. In the present study, classical time series analysis methods have been used for comparing in-situ groundwater level measurements of 22 monitoring wells in five groundwater basins in Jordan (Fig. 1) with GWS data obtained by GRACE, namely newly available spatial high-resolution GRCTellus land grid data, supported by the NASA MEaSUREs Program

(Landerer and Swenson 2012; Swenson 2012; Swenson and Wahr 2006), regarding their suitability for the assessment of groundwater depletion in the region. One often quoted shortcoming of the GRACE data is their relatively low spatial resolution, which was initially given with a minimum of about 200,000 km2 (e.g. Rodell and Famiglietti 2001). Wahr et al. (2004) showed that the accuracy strongly increases with the size of the monitored area since the required noise reduction by filtering for smaller areas also causes some loss of signal. In recent years, several studies applied GRACE data also for smaller basins. Longuevergne et al. (2010) showed that GRACE can be used effectively with basins as small as ∼ 200,000 km2. A study by Proulx et al. (2013) compared GRACE TWS data with combined changes in soil moisture and groundwater storage. They found a relatively poorer agreement for two basins of 66,000 and 38,000 km2 when compared with earlier studies for larger basins from Swenson et al. (2006), Strassberg et al. (2007) and Moiwo et al. (2009), and ascribe this to the increased noisiness of the GRACE data. In a recent study, Huang et al. (2015) state the signal-to-noise ratio is higher over regions where mass changes with large magnitude are highly concentrated, and GRACE can potentially detect mass changes within smaller areas. They found a good agreement of GRACE-derived GWS anomalies with the estimates based on in situ GW-level measurements for two regions of 54,000 and 86,000 km2 in the North China Plain. This confirms earlier studies of Famiglietti et al. (2011) and Scanlon et al. (2012), who found that large mass changes in the California Central Valley (52, 000 km2, USA) as a result of irrigation pumpage allow storage changes to be detected by GRACE. Recently, GRACE data (GRCTellus land grid) of a spatially higher resolution of 1 × 1° (about 100 × 100 km) were made available as a result of improved filtering algorithms. They also allow users to investigate smaller areas as well as to average over arbitrary regions. The better spatial resolution may come at the expense of larger errors though, and with increases in size of the averaging region, the errors generally decrease (Landerer and Swenson 2012). The five groundwater basins considered in the present study range from about 1,500 to 18,000 km2; thus, they are too small to be resolved by GRACE data. The regarded aquifers are part of much larger regional aquifer systems, which makes a comparison still suggestive, though it can only reflect regional- and large-scale coherences. The aggregation on groundwater basins has been applied to compare trends of groundwater losses, which are given on the groundwater basin scale by the local authorities.

Hydrogeol J

Fig. 1 a Groundwater basins in Jordan (based on USGS 1998, satellite image by ESRI World Imagery), and b location of the 22 monitoring wells in the study area, average annual rainfall (derived from TRMM 3B43 precipitation data), and major abstraction areas (based on MWI and GTZ 2004)

Data and methods Study area The study area is located in the northern and central part of the Hashemite Kingdom of Jordan, approximately between latitude 30–33° north and longitude 35–38° east. It comprises 22 wells in five groundwater basins—namely the Azraq Basin, Amman-Zarqa Basin, Dead Sea Basin, Side Wadis Basin, and Yarmouk Basin (Fig. 1). In all basins, groundwater levels are declining due to groundwater withdrawals. Most monitoring wells are situated in the vicinity of abstraction wells, and thus only show water levels that are directly influenced by pumping. Groundwater from wells and springs is the most important source of water supply in Jordan, providing more than half of the total water consumption (USGS 1998). Climate The climate in Jordan varies from Mediterranean (characterized by hot and dry summer months from May until September and cool winter months from November until March with short transitional seasons) in the north-western part over semi-arid areas in central Jordan to a continental arid climate in the southern and eastern parts. Precipitation occurs mainly during the winter months and ranges from about 600 mm in the northern Highlands (Margane et al. 2002) to less than 50 mm in the desert areas in the south and east (USGS 1998). About 90 % of the area experiences less than 200 mm of rainfall per year. Rainfall is often spatially and

temporally irregular, torrential and leads to flash floods (Hötzl et al. 2008; Dayan and Abramski 1983; Inbar 2000); furthermore, it is highly variable from year to year—up to more than 100 % around a long-term average (Margane and Zuhdy 1995). About 90 % of the total precipitation is lost to evapotranspiration, 5 % is runoff, and only about 5 % is available for groundwater recharge (USGS 1998). Groundwater recharge is estimated between 275 million m 3/year (Ministry of Water and Irrigation, MWI 2013) and 280 million m3/year according to model calculations (Margane et al. 2002). Hydrogeology of the groundwater basins Azraq basin The Azraq basin covers an area of about 18,000 km2 and is characterized by three principal aquifer systems. The BasaltRijam system is the main aquifer system, comprising hydraulically connected Quaternary alluvial deposits (Alluvium Aquifer), Tertiary and Quaternary basalts (Basalt Aquifer), and Tertiary limestones from the Belqua group (B4/B5 Aquifer, Fig. 2). The water of the Basalt-Rijam system is of good quality and is therefore used as the primary source of freshwater in the basin (USGS 1998). It is also used to supply the capital Amman with drinking water. Other aquifers of minor importance are the Amman-Wadi Sir Aquifer (B2/A7) with mainly limestone, chalk and chert of the Belqua and Ajlun group and the deeper Kurnub Sandstone Aquifer (Fig. 2). Groundwater recharge is estimated to 24

Hydrogeol J Fig. 2 Geological classification of relevant rock units and aquifers in the study area (compiled from Margane et al. 2002; USGS 1998 and MWI 2000). Units shaded in gray are absent in the study area

million m3/year and in 2013 abstraction rates were estimated to about 58.19 million m3/year, resulting in a deficit of 34.19 million m3/year (MWI 2013). Data for five monitoring wells, AR1–AR5 (Table 1), were available in the Azraq Basin, of which AR1 to AR4 are shallow wells in the Basalt-Rijam system with an average depth to the water table of about 20 m. AR5 is located in the deeper Amman-Wadi Sir aquifer (B2/A7) with more than 300 m depth to the water table (Table 1). The different behaviour of AR5 indicates different hydraulic properties of the aquifers Basalt-Rijam and B2/A7 and probably no or only a minor hydraulic connection, thus an averaging is not reasonable. For the analysis on basin averages, the aquifers have been regarded separately.

With nearly 700 wells, Amman-Zarqa is the basin with the highest abstraction rates, though data on groundwater abstractions tend to be incomplete and unreliable (Margane et al. 2002) and figures differ in different resources. For 2013, MWI (2013) estimates the abstraction rates at 156.3 million m3/year, resulting in a deficit of 68.8 million m3/year. Of the eight monitoring wells in the Amman-Zarqa basin used in this study, seven (AZ1-AZ7) are mainly screened in the Amman-Wadi Sir Aquifer (B2/A7), and one (AZ8) is screened in the deeper Hummar Aquifer (A4). Though the time series of the water levels show a similar behaviour for both aquifers, for the analysis on basin averages, the aquifers were considered separately.

Amman-Zarqa basin

Dead Sea basin

The Amman-Zarqa basin comprises an area of about 4, 000 km2 of which about 90 % is located in Jordan and 10 % in Syria. The main aquifer is formed by Basalt flows underlain by a carbonate rock sequence of the Amman-Wadi Sir formations (B2/A7; Al Mahamid 2005). The annual groundwater recharge was estimated to be about 22 million m3/year by Al Mahamid (2005) and 87.5 million m3/year by MWI (2013).

The Jordan part of the Dead Sea groundwater basin covers about 7,700 km2 along the Jordan Rift Valley and its escarpments. Groundwater represents the main source of freshwater and is withdrawn primarily from the Amman-Wadi Sir Aqifer (B2/A7). The average groundwater recharge by precipitation is about 57 million m3/year (USGS 1998 and MWI 2013). Minor withdrawals from Quaternary alluvial deposits along

Hydrogeol J Table 1

Groundwater monitoring wells used for the present study

Groundwater basin

Well

MWI well IDa

Locationb

Main aquiferc

PGE

PGN

Average depth to water table (m)

Azraq

AR1

F 1280

323,783

147,863

B4/5

18.89

Azraq Azraq

AR2 AR3

F 1022 F 1014

320,376 330,359

141,300 141,030

B4/5 B5, BS

26.22 15.04

Azraq Azraq

AR4 AR5

F 1060 F 3755

336,710 261,100

140,290 134,400

B4/5 B2/A7

22.83 314.49

Amman-Zarqa Amman-Zarqa

AZ1 AZ2

AL 3384 AL 1040

279,653 271,278

180,987 177,834

B2/A7 A7

136.54 104.69

Amman-Zarqa

AZ3

AL 1926

276,624

174,655

B2/A7

115.14

Amman-Zarqa Amman-Zarqa

AZ4 AZ5

AL 1043 AL 2699

266,987 257,800

171,506 170,600

A4-A7 B2/A7

73.69 65.21

Amman-Zarqa Amman-Zarqa

AZ6 AZ7

AL 1300 AL 1734

252,722 255,050

160,113 157,750

B2/A7 B2

55.47 58.01

Amman-Zarqa

AZ8

AL 1782

243,887

152,738

A4

105.42

Dead Sea

DS1

CD 1075

238,240

131,160

B2/A7

218.16

Dead Sea Dead Sea

DS2 DS3

CD 1212 CD 3340

253,720 260,000

115,400 105,000

B2/A7 B2/A7

190.22 242.37

Dead Sea Side Wadis Side Wadis

DS4 SW1 SW2

CF 3020 AE 1003 AB 3142

222,050 217,025 213,800

251,500 225,750 138,500

N/A B2/A7 Alluvium

101.82 124.09 23.68

Yarmouk Yarmouk Yarmouk

YM1 YM2 YM3

AD 1120 AD 1148 AD 3014

264,940 264,400 239,100

205,350 203,900 201,200

B2/A7 B2/A7 A4

173.09 156.36 184.08

a

Well identifier of the Jordan Ministry of Water and Irrigation (MWI)

b

Locations are given in Palestine Grid (PG) values

c

See Fig. 2 and text for explanation of main aquifer

the Dead Sea are partly also used for water supply. The abstraction is estimated to 79 million m3/year (MWI 2013) and the resulting deficit is 22 million m3/year. Three of the four monitoring wells in the Dead Sea basin have well screens in the Amman-Wadi Sir Aquifer (DS1–DS3). For DS4, no information is available, but the location, depth to the water table and water levels indicate a location in the Quaternary alluvial deposits of the Jordan Valley (Alluvium Aquifer). For the analysis on basin averages, the wells DS1–DS3 in the Amman-Wadi Sir Aquifer have been analysed together and DS4 has been analysed separately.

precipitation is about 15 million m3/year (USGS 1998). MWI (2013) estimates the abstraction to be 29.14 million m3/year, resulting in a deficit of 14.14 million m3/year. Of the two available monitoring wells, one (SW1) is screened in the Amman-Wadi Sir Aquifer, the other one (SW2) is located on the border to the Jordan Valley in the shallow Alluvium Aquifer, thus no representative average values could be obtained for the basin, but instead the analysis was done separately for both wells.

Side Wadis basin

The Yarmouk basin is located in the northern part of the Jordan Highlands and Jordan Plateau and comprises about 1, 500 km2. The Amman-Wadi Sir system (B2/A7) is the most important aquifer for water supply. The average recharge rate is estimated at about 40 million m3/year (USGS 1998), and thus is comparably high. With an estimated abstraction of 45.85 million m 3/year (MWI 2013), the deficit is 5.85 million m3/year. Two of the monitoring wells (YM1 and

The Side Wadis basin (sometimes also referred to as the Jordan Side Valleys basin) comprises an area of about 1, 900 km2. The Amman-Wadi Sir Aquifer (B2/A7) is the principal source of water supply, with secondary supplies available from the deeper Hummar Aquifer (A4) and Kurnub Aquifer (K). The average groundwater recharge by

Yarmouk basin

Hydrogeol J

YM2) are located in the Amman-Wadi Sir Aquifer (B2/A7), the third (YM3) is screened in the deeper Hummar Aquifer (A4). Again, the analysis on basin averages was done for YM1 and YM2 to get representative average values of the Amman-Wadi Sir Aquifer (B2/A7) and separately for YM3 screened in the Hummar Aquifer (A4). Data Gravity Recovery and Climate Experiment (GRACE) data For the present study, the latest available GRACE GRCTellus land data, based on the RL05 spherical harmonics from the Center for Space Research at the University of Austin/Texas (CSR), NASA Jet Propulsion Laboratory (JPL) and the German Research Centre for Geosciences (GFZ; supported by the NASA MEaSUREs Program, Landerer and Swenson 2012; Swenson 2012; Swenson and Wahr 2006) were used. The data are provided in a grid of 1° in both latitude and longitude (about 100 × 100 km) and represent monthly values of surface mass change, adjusted by glacial isostatics and spatially smoothed with a destriping as well as a 300-km-wide Gaussian filter to remove noisy short wavelength spectral harmonic coefficients. The data were then multiplied by the provided scaling coefficients, which are intended to restore much of the energy removed by filtering. Sakumura et al. (2014) showed for CSR, GFZ, JPL solutions that the ensemble solution, using a simple arithmetic mean, reduces the noise in equivalent water height (EWH) by 5–10 mm RMS; therefore, for this study, the ensemble solution (arithmetic mean) of the CSR, GFZ and JPL solutions was used. Since 2011, data gaps in GRACE data are caused by battery management measures on the GRACE satellites. These gaps occur approximately every 5–6 months, and last for 4–5 weeks. The gaps were filled by linear interpolation of the adjacent months for this study. The provided GRACE data represent surface mass change anomalies relative to the 2004–2009 time-mean baseline. For the present study, data from 2003–2013 were used. The timemean baseline has been corrected accordingly. To get basinwide values, a weighted average of the gridded GRACE values for each groundwater basin has been computed. For error estimation, the provided values for leakage and measurement errors where used to compute weighted averages of the mean GRACE errors for each groundwater basin. Since short-term surface mass change anomalies are commonly ascribed to changes in water storage, the GRACE data are often referred to as a change in total or terrestrial water storage (ΔTWS), a term that comprises the total vertically integrated water content of groundwater, water in the unsaturated zone including soil moisture (SM), surface water storage (SW) and eventually snow water equivalent (SWE) and water stored in biomass (canopy storage; CS). Regarding the

groundwater contribution, auxiliary hydrological datasets for the other components have to be taken into account. Global Land Data Assimilation System (GLDAS) data To isolate changes in GWS from GRACE TWS, data from the NOAH land surface model of the Global Land Data Assimilation System (GLDAS, Rodell et al. 2004; Rodell et al. 2013, Fang et al. 2009) for SM, SWE, SW and CS have been used. The NOAH model was chosen after a thorough comparison with two other GLDAS hydrological models, namely VIC and CLM, which did not show any significant differences for the region. This observation corresponds to results of Tiwari et al. (2009) who compared four different GLDAS hydrological models including NOAH and CLM. The NOAH model was used, because its spatial resolution is much finer than that of the other models (0.25° vs. 1°) and thus more appropriate for smaller regions like the ones considered in this study. The monthly temporal resolution of the NOAH data is generated through temporal averaging of 3-h data. The average layer soil moisture gives an integrated value of the total column soil moisture in the upper 2 m in kg/m2. SW, SWE and CS are also given in kg/m2 and can thus be directly used as an equivalent water height (EWH) in millimetres. To fit the time line of the GRACE data, anomalies of the GLDAS data relative to the 2003–2013 time-mean baseline were computed. To get basin-wide values, weighted averages of the gridded GLDAS data for SM, SWE, surface runoff and CS were computed for each groundwater basin. Precipitation data For precipitation, two different datasets were used, data from the Tropical Rainfall Measuring Mission (TRMM) and reanalysis data from the Modern-Era Retrospective Analysis for Research and Applications (MERRA). The Tropical Rainfall Measuring Mission (TRMM) is a joint US–Japan satellite mission to monitor tropical and subtropical precipitation (Bolvin and Huffman 2015; Huffman et al. 2014; 2007). With the dataset 3B43 (TRMM and other sensors: monthly), a best-estimate precipitation rate and root-mean-square (RMS) precipitation-error estimate (in mm/h) from all global data sources, namely high-quality microwave data, infrared data, and analyses of rain gauges is available (Bolvin and Huffman 2015). The gridded estimates have a monthly temporal resolution and a 0.25° × 0.25° spatial resolution. The Modern-Era Retrospective Analysis for Research and Applications (MERRA) is a project by NASA’s Global Modeling and Assimilation Office (Reichle et al. 2011). Among many other parameters related to the hydrological cycle, it provides reanalysed precipitation data from several sources with a spatial relation of 0.5 × 0.67° (Rienecker et al. 2011).

Hydrogeol J

To get basin-wide values, weighted averages of the gridded precipitation data were computed for each groundwater basin. To fit the time line of the GRACE data, the anomalies of the data were adjusted relative to the 2003–2013 time-mean baseline. Though there are some differences in the precipitation values of TRMM and MERRA data (up to 8 mm/month for the monthly average over the regarded time period), the time series correlate generally well (R2 between 0.84 and 0.97). For a comparison of the data see the electronic supplementary material (ESM). In-situ groundwater monitoring and surface water data For the present study, monthly groundwater level data of 22 monitoring wells in five groundwater basins from January 2003 until December 2013 have been used (Fig. 1; Table 1). The data were provided by the Jordan Ministry of Water and Irrigation (MWI). Some of the wells had smaller data gaps, which were filled by linear interpolation. For the analyses on groundwater basin scale, the water levels from wells of the same basin and screened in the same aquifer have been averaged. To evaluate the influence of changes in surface-water storage, in-situ water-level data for the Dead Sea (obtained from the Israeli Central Bureau of Statistics) and Lake Tiberias (obtained from the Israel Water Authority) were used. For the Dead Sea, the relation of changes in surface area depending on water level was taken from Coyne et Bellier et al. (2012). Groundwater storage from GRACE, GLDAS and surface water level data For computing the anomalies in groundwater storage (GWS) for the groundwater basins, water in other compartments has to be subtracted from the GRACE TWS data. For this study, the GLDAS data for SM, SWE, SW and CS were taken into account. The contributions from SWE and CS are negligible, due to the mostly warm, arid climate and sparse vegetation in the region (< 1 mm EWH). The SW from GLDAS data shows minor changes for some basins in the winter month, especially for the Yarmouk basin, where precipitation is comparably high. The highest values of about 3.6 mm EWH was modelled for January 2013; however, GLDAS SW does not consider storage in lakes and reservoirs (e.g. Moore and Williams 2014; Richey et al. 2015). Figure 3 shows the time series for the GRACE TWS data, GLDAS SM and SW data as well as precipitation from TRMM data for comparison for the Yarmouk basin. Plots for the other basins are provided as ESM. Many studies neglect surface-water storage changes, although this can lead to accumulating errors in GWS estimates (Longuevergne et al. 2013; Kim et al. 2009; Proulx et al. 2013). For this reason, the study evaluated the possible

influence of the Dead Sea and Lake Tiberias, which are located on the edge and in the vicinity of the study area, respectively. Both exhibit strong changes of water levels in the regarded time period. In the Dead Sea, a regression of more than 1m water level per year and only minor seasonal changes can be observed, while Lake Tiberias shows strong seasonal changes of up to 4 m/year but only a small downward trend. Smaller reservoirs could not be taken into account due to a lack of available data. Since their total storage capacity sums up to more than 300 MCM (MWI 2013, while yearly variations are much smaller), this neglect possibly leads to errors in the computation of the GWS. For the Dead Sea and Lake Tiberias, changes in water volume were calculated from water level and surface area data. Their change in true basin storage (TBS, which equals the actual volume divided by regarded basin area) is quite high, but, as discussed by Longuevergne et al. (2013), assuming a uniform mass distribution can lead to under- or overestimation of the gravity signal. Therefore, the apparent basin storage (ABS), which describes how GRACE captures the actual gravity signal of a mass, has to be taken into account. ABS is strongly affected by the position of the mass relative to the regarded basin center, the basin area and the processing mode. Longuevergne et al. (2013) demonstrated with numerical experiments, that ABS diminishes quickly when point masses are located near the edge or outside of the basin. As applied by Mulder et al. (2015), the authors of this study used the results of Longuevergne et al. (2013) to approximate the ABS for the Dead Sea and Lake Tiberias from TBS. Regarding the groundwater basin area sizes and the distance to center/basin radius ratios, the corrective factor for TBS is below 0.1, meaning that ABS is actually less than 10 % of TBS. The actual influence by a parameter study was evaluated via applied stepwise values between 0.1 and 0 in 0.01 steps. In terms of ground truthing, the computed GRACE GWS data was then correlated with in-situ groundwater level data (see section ‘Time series analysis’ and section ‘Correlation of GRACE derived ΔGWS and groundwater level measurements’). The correlations are strongest with a corrective factor of zero and rapidly decrease with higher values. This actually implies that the contributions of the changes in water storage of the Dead Sea and Lake Tiberias on the GRACE TWS of the studied groundwater basins are negligible. Time series analysis The time series analysis comprised a modified Mann-Kendall test for autocorrelated data (Hamed and Rao 1998) to check the significance of the trends in the time series of the GRACEderived GWS and the water level data. Uncertainties in the trends of GRACE GWS and groundwater level measurements were estimated by propagating errors from the residuals of a least squares fit using the covariance matrix. The correlation

Hydrogeol J

Fig. 3 Time series for the GRACE TWS data, GLDAS soil moisture (SM) and surface water storage (SW) data, resulting groundwater storage (GWS) and precipitation from TRMM data for the Yarmouk basin. Values of TWS, SM, SW, and GWS are given in anomalies of

the equivalent water height (EWH) relative to the 2003–2013 timemean baseline. The contributions from snow water equivalent (SWE) and canopy storage (CS) are negligible (< 1 mm EWH) and therefore omitted in the diagram for clarity

of GRACE-derived GWS and the water level time series were done by cross correlation analyses and linear regressions of the time series. To account for uncertainties in the GRACE data, the GRACE time series were modelled with an ARIMA model and a following Monte-Carlo simulation of 10,000 realizations of the model, which were used for the correlation analyses. The residuals of the linear regression have been tested for serial correlation with the Durbin-Watson test (Durbin and Watson 1950, 1951). In a next step, the time series of the GRACE-derived GWS and the water level measurements were decomposed with the STL algorithm (Seasonal-Trend Decomposition Procedure Based on Loess, Cleveland et al. 1990). STL decomposes a time series into trend, seasonal and remainder component (additive decomposition) by iteratively minimizing the autocorrelaation in the remainder component. This is necessary for several reasons. First, the trend and the seasonal component have strong influence on cross correlations of time series. It is a well-known phenomenon that time series with a trend and a periodicity of the same duration (in case of seasonal data one year) strongly tend to show high cross correlations due to their autocorrelated nature (Yule 1926; Granger and Newbold 1974; Aldrich 1995). The usual significance tests on the coefficients tend to fail because of an autocorrelation in the errors; thus, it is much more convincing to perform crosscorrelation analyses on detrended and deseasonalized Bremainders^ of a time series. These remainders usually contain not only noise-like measurement errors, but also anomalous signals that deviate from the trend or seasonal behaviour and are therefore of special interest regarding cross correlations as well as possible causal relations.

A second reason for decomposition was the isolation of the seasonal component. To compare GRACE derived GWS, which is given as a difference to the mean of the time baseline and has the dimension of an equivalent net water height, to changes in the in-situ groundwater level (potentiometric water level in the aquifer), the specific yield of the aquifer has to be taken into account. Others have compiled the in-situ groundwater level measurements into equivalent water height by using literature values of the specific yield for their study area (e.g. Feng et al. 2013; Houborg et al. 2012; Huang et al. 2015; Moiwo et al. 2009; Rodell et al. 2007, 2009; Scanlon et al. 2012; Shen et al. 2015; Strassberg et al. 2009; Swenson et al. 2006; Yeh et al. 2006). For Jordan, values of the specific yield tend to vary from different resources (e.g. for the B2/A7 aquifer from 0.01 to 0.07). Rodell et al. (2007) emphasize that inaccurate estimates of specific yield significantly influences the amplitude of groundwater fluctuations, particularly when specific yields are small. For this reason a new approach was applied by comparing the amplitudes of the seasonal components of the GRACE-derived GWS with that of the in-situ groundwater level changes, assuming that they represent the same change in equivalent water height. Thus average specific yields for the groundwater basins were derived. The third reason for decomposition was to isolate the trend component, which can also be compared. If the trend component (after converting insitu water levels to equivalent water height by using the aforementioned obtained specific yield) still shows different slopes for GRACE-derived GWS and the in-situ groundwater level measurements, the depletion of the groundwater is either under- or overestimated by the

Hydrogeol J

Figure 4 shows the time series of GRACE-derived GWS and the averaged in-situ measured water levels of YM1 and YM2 in the Yarmouk basin, that correlate well with an R2 value of 0.74 (for plots of the other basins, see the ESM), along with the results of the error estimation by Monte-Carlo simulation. For plotting reasons, the groundwater levels were adjusted by the specific yield (see section ‘Analysis of seasonal variations and specific yield’) and trend ratio (see section ‘Analysis and comparison of trend components’), which has no influence on the cross correlation though. The error for the GRACEderived GWS comprises the error for the TWS and the errors for the soil moisture, snow water equivalent, SW and CS from GLDAS data. The error in the GRACE TWS data sums up the leakage error and the measurement error in the filtered, scaled GRACE data and is provided with the monthly grids (Landerer and Swenson 2012; Swenson and Wahr 2006). Weighted averages of the GRACE TWS errors for each basin are shown in Table 2. Since no published error estimates for the monthly GLDAS data from the 0.25 × 0.25 gridded NOAH model were available, as well as no other models in

this resolution for comparison, an error of 15 % as proposed by Famiglietti et al. (2011) was assumed. The uncertainties in the GRACE data have been taken into account by modelling the original GRACE GWS time series with an ARIMA model and a following Monte-Carlo simulation of 10,000 realizations of the model. The median, lower and upper quartile for R2 of the correlation analyses for the realizations are shown in Table 2 in addition to the R2 value for the original time series. Probability distribution of R2, p-value, and mean residuals of the correlation analyses for the realizations by Monte-Carlo simulation are shown in Fig. 4 for YM1–YM2 and for the other basins and wells in the ESM. The correlation of the time series of the GRACE-derived GWS and the in-situ groundwater-level time series for the five groundwater basins and grouped by aquifer show R2 results between 0.55 and 0.74 for the original time series of the four basins with representative values (average of at least two wells; Table 2). The smaller values are based on only one well and thus probably not representative, though AZ8 shows an exception with an R2 of 0.75. The median R2 values of the Monte-Carlo analyses are about in the same range, confirming a good approximation of the time series with the chosen ARIMA models. The lower and upper quartiles are in the range 0.2–0.8, with median p-values below 0.05 (with exceptions for wells DS4 and SW2), classifying the correlations as significant. The R2 values seem to be fairly high, compared with other studies on larger areas and regarding the fact that the GRACE data signal-to-noise ratio is expected to be too low for such

Fig. 4 a Time series of GRACE-derived GWS (error shown by gray shading) and averaged in-situ measured groundwater levels of wells YM1 and YM2 in the Yarmouk basin. For plotting reasons, the groundwater levels were adjusted by the specific yield of 0.02 and trend

ratio of 2.24. Probability distribution of b p-values, c R2 values, and d mean residuals of the correlation analyses of 10,000 realizations of an ARIMA model for the GRACE GWS time series by Monte-Carlo simulation

in-situ measurements compared to the basin wide trend in GRACE-derived GWS.

Results and discussion Correlation of GRACE derived ΔGWS and groundwater level measurements

Hydrogeol J

small regions. The values are about as high as the ones found by Huang et al. (2015) for two regions of 54,000 and 86, 000 km2 in the North China Plain (R2 between 0.65 and 0.60 for the monthly time series) and exceed the values found by Moiwo et al. (2009) for the Hai River Basin (China) with a size of more than 300,000 km2 (R2 = 0.31). Moore and Fisher (2012) found about the same correlation strength for a study area of 190,000 km2 in Yemen (R2 range 0.56–0.79) and Proulx et al. (2013) found a correlation of R2 between 0.64 and 0.75 for two regions of 38,000 and 66,000 km2 in South Dakota (USA). The highest R2 values in our study are found for the Amman-Wadi As Sir aquifer, which covers a fairly large area, indicating that the large scale GRACE signal correlates well to the in-situ groundwater measurements. Decomposition Before decomposition, the time series were verified for trends by a modified Mann-Kendall test for autocorrelated data (Hamed and Rao 1998). All trends where classified as significant on a 0.05 level, with an exception for the water level data of well DS 4. The results are shown in Table 2. Figure 5 shows an example for the decomposed GRACEderived GWS time series of the Yarmouk groundwater basin (decomposed time series for GRACE derived GWS and insitu groundwater level measurements for all basins are provided in the ESM). The seasonal component shows variations of about 50 mm EHW, which are slightly increasing over the 11year time span. The highest groundwater storages are found in the winter months (January–February), followed by a steep decrease over spring to summer, with a small interim high in June–July. The lowest values are measured in October, with a steep rise until February again. The trend component shows a slight increase of the groundwater storage from 2003 until 2006, followed by a sharp decline from 2006 until 2009 and a more stable period from 2009 to 2013.

This can be explained from a hydrogeological point of view by the different geology of the basins. In the AR basin, the Basalt-Rijam system (Basalt and B4/B5) is the main aquifer system, while in the AZ, SW and YM basin, the Amman-Wadi Sir (B2/A7) aquifer dominates, thus dominating the seasonal amplitude of the GRACE GWS signal. Since values for the specific yield of the BasaltRijam system found in literature are only estimates (MWI and GTZ 2004), a comparison is not possible, but a value of about 0.005 for basalt seems possible, though at the lower end of a reasonable range. For the Dead Sea basin, the situation is not that clear. Since 3 out of 4 wells in this basin are screened in the B2/A7 aquifer, the average water level trend, which is comparable to the other basins, seems explainable. Though the B2/A7 aquifer is the dominant aquifer for freshwater withdrawal (because of water quality reasons) it is not the only aquifer. The Quaternary alluvial deposits form a second aquifer, in which waterlevel fluctuations are also expected (thus influencing GRACE derived GWS data). The specific yield obtained by DS4 for the alluvial deposits is 0.2, which seems quite reasonable for an unconfined alluvial aquifer. The errors of this analysis can be estimated when taking the errors of the GRACE data into account. Errors in measured groundwater levels are usually low (in the range of 10–50 mm maximum). With seasonal amplitudes for the groundwater levels between 2 and 17 m roughly (with an exception of DS4 with only 0.36 m), the errors in the measured groundwater levels are negligible. The amplitudes of the seasonal GRACE GWS signals amount to between 8 mm EWH for the AR basin and 27 mm EWH for the YM basin, while the errors are in a range of 30–50-mm EWH, and have been taken into account to compute an error range for the specific yield (Table 2). It can be assumed though, that the errors are widely averaged out by the decomposition process, since the amplitude of the seasonal component is computed as an average over the whole time period of 11 years.

Analysis of seasonal variations and specific yield

Analysis and comparison of trend components

The specific yields, Sy, computed by dividing the amplitudes of seasonal component time series of GRACE-derived GWS and in-situ groundwater-level measurements are shown in Table 2. The values for the Amman-Wadi Sir aquifer in the Amman-Zarqa (AZ), Side Wadis (SW) and Yarmouk (YM) basin (Sy between 0.02 and 0.05) are about in the same range as values found in literature (e.g. Bender et al. 1989 with about 0.01–0.03 for the B2/A7 aquifer; MWI and BGR 2001 and Margane et al. 2002 with both Sy values at 0.05 for the B2/A7 as well as the B4/B5 aquifer); while the values for the Azraq (AR) and Dead Sea (DS) basins (Sy, 0.004–0.005) are about a magnitude lower, though the value of the AR basin is only based on one well.

All but one time series, the one for the GRACE-derived GWS as well as the in-situ groundwater level measurements, show negative trends regarding the time span from 2003 to 2013 (Table 2). An exception constitutes well DS4, screened in the alluvial aquifer of the Dead Sea basin, with no significant trend. The average trends in water level declines from the in-situ groundwater-level measurements show values between –0.35 and –3.52 m/a, which is equivalent to values of –1.60 to – 183.4 mm/year in equivalent water height, using the specific yield for conversion. The trends in the GRACE-derived GWS show a range from –2.6 to –16.1 mm/year in equivalent water height. A comparison of the trends shows (except for DS4 and

–14.14 –5.85

–29.45 ± 1.29

–23.63 ± 1.10

SW

YM

e

d

c

b

0.56 (< 0.001) 0.45 (< 0.001) 0.68 (< 0.001) 0.75 (< 0.001) 0.66 (< 0.001) 0.14 (< 0.001) 0.73 (< 0.001) 0.06 (0.005) 0.74 (< 0.001) 0.40 (< 0.001)

R2 original time series (p-value)

0.005 (0.001–0.009) 0.004 (0.001–0.008) 0.018 (0.010–0.026) 0.026 (0.015–0.038) 0.004 (0.001–0.007) 0.20 (0.08–0.46) 0.052 (0.001–0.055) 0.005 (0.001–0.012) 0.021 (0.001–0.017) 0.028 (0.001–0.078)

Specific yielda

R2 values: lower quartile/median/upper quartile of 10,000 Monte Carlo simulations

Water level trend in EWH/trend in GRACE derived GWS

Computed by averaged water level trend of wells multiplied by average specific yield

Corrected p-value of modified Mann-Kendall trend test in brackets

Range according to error estimation in brackets

–22.00

–44.58 ± 2.49

DS

a

–68.80

–59.17 ± 2.88

AZ

56.2

–34.19

1,468

YM

52.1

–47.28 ± 3.33

1,894

SW

34.7

AR1–AR4 AR5 AZ1–AZ7 AZ8 DS1–DS3 DS4 SW1 SW2 YM1–YM2 YM3

AR

7,726

DS

54.0

Basalt-Rijam Amman-Wadi Sir Amman-Wadi Sir Hummar Amman-Wadi Sir Alluvium Amman-Wadi Sir Alluvium Amman-Wadi Sir Hummar

Wells

Water deficit according to MWI (2013) [million m3/year]

4,131

AZ

31.2

Aquifer

Estimated water loss from GRACE derived GWS [million m3/year]

18,046

AR

Average GRACE TWS error [mm EWH]

Basin

Area [km2]

Results of the specific yield, trend analyses and correlation analyses

Basin

Table 2

0.25/0.57/0.74 (< 0.03) 0.28/0.62/0.80 (< 0.03) 0.30/0.63/0.79 (< 0.03) 0.33/0.65/0.79 (< 0.03) 0.40/0.69/0.81 (< 0.02) 0.06/0.13/0.19 (0.051) 0.18/0.48/0.71 (< 0.04) 0.03/0.11/0.20 (0.083) 0.28/0.61/0.78 (< 0.03) 0.17/0.40/0.55 (< 0.04)

0.62 0.54 0.54 0.71 0.75 0.26 0.67 0.18 0.69 0.32

Durbin-Watson statistic (d) original time series

–4.17 ± 0.08 –10.69 ± 0.16 –28.74 ± 0.52 –68.24 ± 2.01 –8.43 ± 0.29 3.38 ± 0.60 –183.40 ± 5.10 –1.60 ± 0.22 –36.13 ± 0.54 –18.52 ± 0.87

–0.85 ± 0.02 (p < 0.001) –2.41 ± 0.04 (p < 0.001) –1.58 ± 0.03 (p < 0.001) –2.56 ± 0.08 (p < 0.001) –2.13 ± 0.07 (p < 0.001) 0.02 ± 0.003 (p = 0.16) –3.52 ± 0.10 (p < 0.001) –0.35 ± 0.05 (p = 0.03) –1.72 ± 0.03 (p < 0.001) –0.66 ± 0.03 (p < 0.001)

R2 of Monte-Carlo simulationse (p-value)

Average water level trend in EWH [mm/year]c

Average water level trend [m/year]b

1.43E-02 (0.175) 3.71E-02 (0.027) 2.00E-04 (0.877) 2.18E-02 (0.091) 5.19E-07 (0.994) 2.02E-02 (0.105) 1.87E-02 (0.124) 1.52E-04 (0.889) 2.11E-02 (0.096) 6.39E-02 (0.004)

R2 remainder (p-value)

–16.09 ± 0.75 (p < 0.001)

–15.55 ± 0.68 (p < 0.001)

–5.77 ± 0.32 (p = 0.001)

–14.32 ± 0.70 (p < 0.001)

–2.62 ± 0.18 (p = 0.003)

Trend GRACE-derived GWS [mm/year]b

2.13 2.18 1.97 2.19 1.97 2.15 2.08 1.98 2.02 2.13

Durbin-Watson statistic (d) remainder

1.59 (1.46–1.75) 4.08 (3.75–4.45) 2.01 (1.88–2.15) 4.76 (4.41–5.16) 1.46 (1.34–1,60) –0.59 ((–0.73)–(–0.46)) 11.79 (10.98–12.67) 0.10 (0.09–0.12) 2.24 (2.11–2.39) 1.15 (1.05–1.26)

Trend ratiod

Hydrogeol J

Hydrogeol J

Fig. 5 Decomposition of the GRACE-derived GWS time series of the Yarmouk basin: original time series (data), seasonal, trend and remainder component

SW2) that the trends from the in-situ groundwater-level measurements are about 1.2–11.8 times steeper than for the GRACE-derived GWS, with an average trend ratio of 2.4. This indicates that the declines computed from in-situ groundwater level measurements tend to overestimate the trends for the entire aquifers, which can be explained by the fact that the monitoring wells are often situated near abstraction well fields and thus exhibit water levels influenced by their drawdown cones. When the trends from GRACE-derived GWS are converted in deficits into million m3/year using the basin areas, the values show greater differences to the ones from MWI (2013), which are based on estimated recharge and abstractions (Table 2). For the AmmanZarqa basin, the trend estimated by GRACE-derived GWS is somewhat lower (59 vs. 69 million m3/year) than that estimated by MWI, while for the other basins, they are much higher. For the Azraq Basin, the trend estimated by GRACE-derived GWS is about a third higher (47 vs. 34 million m3/year) and for the Dead Sea basin and the Side Wadis basin, about twice as high (45 vs. 22 million m3/year and 30 vs. 14 million m3/ year). For the Yarmouk basin, it is about four times as high (24 vs. 6 million m3/year). The reasons for these discrepancies are most probably shortcomings either in the estimations of the recharge rates or abstraction rates, since these estimates, especially regarding abstraction rates, tend to differ greatly.

Cross correlations of the remainder time series When applying the Durbin-Watson test (Durbin and Watson 1950, 1951) to our time series of the GRACE GWS and in-situ water-level measurements, values for the Durbin-Watson statistics (d) are between 0.18 and 0.75, thus confirming a strong autocorrelation in the residuals. This implies that though the correlation seems quite strong, it is widely dependent on the trend and seasonal component and thus cannot be referred to as significant in a statistical sense. There are several famous examples of time series that show a high correlation because of a trend and seasonal variations but have clearly no obvious causal relation (e.g. Aldrich 1995; Hipel and McLeod 1994). Though this is probably not the case here, since a causal relationship is highly presumable, it can still be interpreted in a manner, that the correlation is mainly caused by the fact that the two time series have a trend and a common seasonality. For the assessment of a significant correlation and thus a more resilient causal relation, the cross correlation of the remainders that contain noise-like measurement errors on the one hand, but also anomalous signals that deviate from the trend or seasonal behaviour on the other hand, is therefore more meaningful. Thus, correlation analyses with the detrended and deseasonalized remainders of the time series, which were obtained by additive decomposing (see section ‘Decomposition’), have been performed. The remainders show only very weak correlations (R2 < 0.1). Only two of the cross correlations (AR5 and

Hydrogeol J

YM3) were classified as significant on a 95 % confidence level (p < 0.05), and another two (AZ8 and the averaged YM1–YM2) on a 90 % confidence level (p < 0.1). The result of the correlation analyses of the remainder components suggest that either anomalous signals that deviate from the trend or seasonal behaviour are superimposed by noise or that the method for deriving GWS from GRACE TWS data by subtracting SM, SW, snow water equivalent and CS has some shortcomings. Comparison of changes in water storage with precipitation from TRMM and MERRA data To assess if the poor correlation of the remainder time series of GRACE GWS and groundwater level data is mainly due to the fact that GRACE data cannot resolve such small regions for an insufficient signal-to-noise ratio or if there also might be a systematic error due to shortcomings in the algorithm of deriving GWS from GRACE data, the monthly changes in the GRACE-derived GWS, the changes in the soil moistures and the changes in the groundwater levels have been compared with precipitation data of the TRMM and MERRA projects. Precipitation is, together with evapotranspiration, runoff and abstraction, the main parameter that causes short-term variations in water storage. The components have a complicated relationship, which varies according to climatic, hydrogeological and land use conditions. Evapotranspiration is widely dependent on temperature and available water but also on land use. Evapotranspiration happens either from surface water or soil moisture in the upper soil layers (either physically as evaporation or as transpiration by plants), but in some cases for shallow water tables also direct evapotranspiration of groundwater is possible. In the case of Jordan with mostly deep water tables and sparse vegetation though, variations in the water table are mainly caused by abstraction, which is in turn often influenced by precipitation and temperature, especially when the pumped water is used for irrigation. Changes in SW are mostly dependent on precipitation and temperature. Soil moisture is mostly dependent on climate, but it is also influenced by land use and especially by irrigation. To compare the changes in the GRACE-derived GWS, soil moisture and groundwater levels with precipitation data, the GRACE GWS, soil moisture and groundwater-level time series have been differentiated to obtain monthly changes in the storage components. The comparison with the precipitation data by cross correlations should show if the precipitation influences the particular storage component and if so, at what time lag. For the same reasons as already mentioned, this was also done with the remainder time series to eliminate the seasonal component and separate anomalous signals that deviate from the seasonal behaviour in the remainder. The positive peaks in the remainder of the precipitation data can be

interpreted as anomalous precipitation signals in the normally dry season, while the negative peaks represent unusually dry periods with little precipitation in normally wet seasons. These signals can reveal correlations in a more resilient way, which are otherwise superimposed by the seasonal behaviour. Regarding time span from 2003–2013, no overall trend in precipitation was detected. As expected, the change in soil moisture is strongly correlated to precipitation at a small time lag of zero to 1 month, showing that the soil moisture immediately responds to precipitation events, and thus confirming the suitability of the used NOAH soil moisture model for the region. For the groundwater level, a positive correlation at a small time lag might also be expected, indicating a negative change in groundwater storage (a loss) for negative signals in the precipitation remainder (unusually dry periods with little precipitation in normally wet seasons) due to increased pumping for irrigation and vice versa. A direct influence of precipitation on the groundwater level by infiltrating water can be mostly excluded due to small groundwater recharge rates and high depths to the water tables; however, the expected effect is not clearly confirmed by the data. Only for some wells in the Amman-Wadi Sir aquifer (AR5, DS1–DS3 and YM1– YM2) can a significant but low positive correlation at a time lag of one month be observed and there is no significant correlation at a short time lag for the other wells. One reason might be that a large part of the irrigated agriculture is done in green houses and therefore abstraction for irrigation purposes is independent of the actual precipitation. Correlations that are classified as significant at longer time lags up to several years for some wells could be due to stochastical reasons, since they are neither consistent within basins or aquifers, nor can they be explained reasonably. Cross correlation functions for precipitation and soil moisture as well as for precipitation and groundwater levels can be found in the ESM. When comparing the remainder component of the precipitation data with the changes in the GRACE-derived GWS remainder, an interesting observation could be made. The changes in the GRACE-derived GWS remainder show a significant positive correlation with the precipitation remainder at a time lag of about 5 years for the Yarmouk, the Side Wadis and the Amman-Zarqa basins. A comparison of the remainder time series of changes in the GRACE-derived GWS and precipitation from TRMM data for the Yarmouk basin along with the cross correlation function is shown in Fig. 6 (for other basins and MERRA data, see the ESM), where the black bar at a negative time lag of 5 years indicates a significant correlation (the black bars beyond the significance level for positive time lags can be neglected, since this would imply that the groundwater storage leads the precipitation, which is apparently not possible). For the Dead Sea basin, there are two positive correlations classified as significant at time lags of about 26 and 36 months, of which the latter are also present

Hydrogeol J

Fig. 6 Comparison of the remainder time series of changes in the GRACE-derived GWS and precipitation from (a–b) TRMM data and (c–d) MERRA data for the Yarmouk basin and associated cross correlation functions (ccf), showing a significant positive correlation at

a time lag of about 5 years (dashed blue lines indicate significance levels). Cross correlation function for the other groundwater basins can be found in the ESM

in the Azraq basin (not as distinct, but for the TRMM data still significant). Additionally there is a low but significant positive correlation for the Azraq basin for a time lag of about 15 months. The results are very similar for the TRMM and MERRA precipitation data despite the afore-mentioned differences in the data and the resulting uncertainties, though the overall correlations are slightly higher for the TRMM data. This result implies that anomalous precipitation events may have an impact on the changes in the GWS component derived from GRACE data by a time delay of several months up to 5 years, depending on the dominating aquifer. It has to be admitted though, that the correlations are low and the time series of the GRACE data as well as the precipitation data are spatially correlated to a certain degree, which makes it more likely that similar correlations are found for neighbouring basins. As this time-lagged cross correlation cannot be observed in the changes in groundwater storage derived by in-situ groundwater level data, a possible explanation lies in the method of obtaining GWS from GRACE data by subtracting the remaining vertical water components. In this context, Strassberg et al. (2009) noticed that under irrigated areas the variability in the soil moisture in the upper 2 m accounts for 76–98 % of the total variability depending on the estimation method; hence a

variability of moisture in strata deeper than 2 m (intermediate zone), which is not accounted for in the GLDAS NOAH model, could possibly contribute to the error. This observation has also been made by other authors, e.g. Swenson et al. (2006) and Yeh et al. (2006). The effect could be of increased importance in areas with deep water tables like in most parts of Jordan and especially when the soil layer is sparse or absent, thus allowing more rapid percolation of water to layers deeper than 2 m as well as easier evaporation from the intermediate zone. Since water in the intermediate zone is not subtracted from the GRACE TWS, it is still included in the derived GWS component (which, correctly in a hydrogeological sense, is not the storage of groundwater, but the sum of groundwater and water in the intermediate zone at the time). The time lags of several months up to several years seem possible for a travel time through the intermediate zone under the prevailing hydrogeological conditions. It is especially interesting that the longer time of 5 years is found for the groundwater basins with dominating deep aquifers (Amman-Wadi Sir and Hummar) and the shorter time lag of several months for the Azraq and Dead Sea groundwater basins with dominating shallow aquifers (Basalt-Rijam and Alluvium). A further possible explanation might be the underestimation of changes in surface-water runoff and storage. Rainfall in the Middle East

Hydrogeol J

is often irregular and torrential, and rather leads to surface runoff as flash floods than seeps into the soil. This is especially the case for anomalous precipitation events in the transition periods in spring and autumn, when intense thunderstorms, with extreme rain rates (Dayan et al. 2001) can lead to severe floods—as described by Dayan and Abramski (1983) and Inbar (2000)—which emerge from local rainfall and probably are too spatially small regarding the observation scale.

Conclusions Comparisons of GRACE-derived groundwater storages to insitu groundwater-level measurements in Jordan from 2003 to 2013 show a good agreement (R2 between 0.55 and 0.75). The highest R2 values are found for the Amman-Wadi As Sir aquifer, which covers a fairly large area, indicating that the largescale GRACE signal correlates well to the in-situ groundwater measurements. However, it can be shown that the correlation is widely dependent on the trend and seasonal component. When performing correlation analyses with the detrended and deseasonalized time series, only 2 out of 10 time series show a significant but very weak cross correlation, suggesting that either anomalous signals that deviate from the trend or from the typical seasonality are superimposed by noise or that the method for deriving groundwater storage GWS from GRACE data has some shortcomings. Comparisons of GRACE-derived changes in GWS and precipitation data show a significant correlation at a time lag of several months up to 5 years, depending on the dominating aquifer, while a correlation of changes in groundwater storage derived by in-situ groundwater-level measurements to precipitation at a small time lag is only partly supported by the data. The effect can be explained by reactions of the water table to abstractions for irrigation purposes, which are subject to the weather conditions, except for regions where the majority of agriculture is cultivated in green houses. The time-lagged correlation of GRACE-derived changes in GWS and precipitation possibly suggests that the model for deriving groundwater storage by subtracting SM, SW, SWE and CS from GRACE TWS data might not be suitable for the study area. A possible explanation for the correlation at this time lag could either be the neglect of the water in the intermediate zone or an insufficient consideration of SW like flash floods and artificial reservoirs. For the study area in Jordan, it was possible to estimate water losses based on an 11-years’ trend in large-scale, regional GRACE-derived GWS (2003–2013). The figures show up to four times higher water deficits than previously assumed using estimated recharge and abstraction rates for the Yarmouk basin, about two times higher deficits for the Dead Sea and Side Wadis basins, and a third higher for the Azraq basin; while for the Amman-Zarqa basin, the deficit computed based on GRACE

data is slightly lower. Though GRACE-based estimates are based on a regional scale, and thus averaging data over a larger area, leading to higher uncertainties, and the time span of 11 years is too short to be representative of the current climate, it can be assumed, that the deficits based on recharge and abstraction rates tend to underestimate actual groundwater losses in the region. In spite of the limited resolution of GRACE data, associated with high uncertainties and a rather low signal-to-noise ratio for smaller regions, GRACE data at the present stage can still support regional studies on groundwater depletion, especially in terms of estimation of trends in long-term groundwater depletion and where other reliable data are sparse. A direct correlation of GRACE data to groundwater levels is largely dependent on the seasonal and trend component, though, thus making in-situ groundwater-level measurement not redundant at this time. This might well change with the GRACE follow-on mission that is planned to launch in 2017, and which could provide data of an up to five times higher spatial resolution (Thales Alenia Space 2010). Acknowledgements The authors would like to thank Ali Subah from the Ministry of Water and Irrigation (Amman, Jordan) for providing the groundwater level data and two anonymous reviewers for helpful suggestions. GRACE GRCTellus Land data are available at http://grace.jpl.nasa.gov, supported by the NASA MEaSUREs Program. The precipitation data used in this study were acquired as part of the Tropical Rainfall Measuring Mission (TRMM). The algorithms were developed by the TRMM Science Team. The data were processed by the TRMM Science Data and Information System (TSDIS) and the TRMM office; they are archived and distributed by the Goddard Distributed Active Archive Center. TRMM is an international project jointly sponsored by the Japan National Space Development Agency (NASDA) and the US National Aeronautics and Space Administration (NASA) Office of Earth Sciences. Data were processed using R (R Core Team 2015).

References Ahmed M, Sultan M, Wahr J, Yan E (2014) The use of GRACE data to monitor natural and anthropogenic induced variations in water availability across Africa. Earth Sci Rev 136:289–300. doi:10.1016/j. earscirev.2014.05.009 Al Mahamid J (2005) Integration of water resources of the Upper Aquifer in Amman-Zarqa basin based on mathematical modeling and GIS, Jordan. Freiberg Online Geol 12:223 Aldrich J (1995) Correlations genuine and spurious in Pearson and Yule. Stat Sci 10:364–376 Awange JL, Gebremichael M, Forootan E, Wakbulcho G, Anyah R, Ferreira VG, Alemayehu T (2014) Characterization of Ethiopian mega hydrogeological regimes using GRACE, TRMM and GLDAS datasets. Adv Water Resour 74:64–78. doi:10.1016/j. advwatres.2014.07.012 Bender H, Hobler M, Klinge H, Schelkes K (1989) Investigations of groundwater resources in central Jordan. Desalination 72:161–170. doi:10.1016/0011-9164(89)80033-5 Bolvin D, Huffman G (2015) Transition of 3B42/3B43 Research product from monthly to climatological calibration/adjustment. NASA, Washington, DC. http://pmm.nasa.gov/sites/default/files/document_ files/3B42_3B43_TMPA_restart.pdf Accessed 11 Jan 2016

Hydrogeol J Cleveland RB, Cleveland WS, McRae JE, Terpenning I (1990) STL: a seasonal-trend decomposition procedure based on loess. J Off Stat 6: 3–73 Coyne et Bellier and Tractebel Engineering and KEMA (2012) Red SeaDead Sea Water Conveyance Study Program, Draft final feasibility study report summary. http://siteresources.worldbank.org/ INTREDSEADEADSEA/Resources/Feasibility_Study_Report_ Summary_EN.pdf. January 2016 Dayan U, Abramski R (1983) Heavy rain in the Middle East related to unusual jet stream properties. Bull Am Meteorol Soc. doi:10.1175/ 1520-0477(1983)064 Dayan U, Ziv B, Margalit A, Morin E, Sharon D (2001) A severe autumn storm over the Middle East: synoptic and mesoscale convection analysis. Theor Appl Climatol 69:103–122. doi:10.1007/ s007040170038 Döll P, Fritsche M, Eicker A, Müller Schmied H (2014) Seasonal water storage variations as impacted by water abstractions: comparing the output of a global hydrological model with GRACE and GPS observations. Surv Geophys 35:1311–1331. doi:10.1007/s10712-014-9282-2 Durbin J, Watson GS (1950) Testing for serial correlation in least squares regression, I. Biometrika 37:409–428 Durbin J, Watson GS (1951) Testing for serial correlation in least squares regression, II. Biometrika 38:159–177 Famiglietti J, Lo M, Ho S, Bethune J, Anderson K, Syed T, Swenson S, de Linage C, Rodell M (2011) Satellites measure recent rates of groundwater depletion in California’s Central Valley. Geophys Res Lett 38:L03403. doi:10.1029/2010GL046442 Fang H, Beaudoing HK, Rodell M, Teng WL, Vollmer BE (2009) Global Land data assimilation system (GLDAS) products, services and application from NASA hydrology data and information services center (HDISC). Proceedings of the ASPRS 2009 Annual Conference, Baltimore, MD, March 2009, pp 8–13. http://www.asprs.org/a/ publications/proceedings/baltimore09/0020.pdf Feng W, Zhong M, Lemoine J-M, Biancale R, Hsu H-T, Xia J (2013) Evaluation of groundwater depletion in North China using the Gravity Recovery and Climate Experiment (GRACE) data and ground-based measurements. Water Resour Res 49:2110–2118. doi:10.1002/wrcr.20192 Giordano M (2009) Global groundwater? Issues and solutions. Annu Rev Environ Resour 34:153–178. doi:10.1146/annurev.environ.030308. 100251 Gleeson T, Wada Y, Bierkens MF, van Beek LP (2012) Water balance of global aquifers revealed by groundwater footprint. Nature 488:197– 200. doi:10.1038/nature11295 Granger CW, Newbold P (1974) Spurious regressions in econometrics. J Econ 2:111–120 Hamed KH, Rao AR (1998) A modified Mann-Kendall trend test for autocorrelated data. J Hydrol 204:182–196. doi:10.1016/S00221694(97)00125-X Hipel KW, McLeod AI (1994) Time series modelling of water resources and environmental systems. Elsevier, Amsterdam Hötzl H, Möller P, Rosenthal E (2008) The water of the Jordan Valley: scarcity and deterioration of groundwater and its impact on the regional development. Springer Science & Business Media, Heidelberg, Germany Houborg R, Rodell M, Li B, Reichle R, Zaitchik BF (2012) Drought indicators based on model-assimilated Gravity Recovery and Climate Experiment (GRACE) terrestrial water storage observations. Water Resour Res 48(7). doi:10.1029/2011wr011291 Hu L, Jiao JJ (2015) Calibration of a large-scale groundwater flow model using GRACE data: a case study in the Qaidam Basin, China. Hydrogeol J 23:1305–1317. doi:10.1007/s10040-015-1278-6 Huang Z, Pan Y, Gong H, Yeh PJF, Li X, Zhou D, Zhao W (2015) Subregional-scale groundwater depletion detected by GRACE for both shallow and deep aquifers in North China Plain. Geophys Res Lett 42:1791–1799. doi:10.1002/2014gl062498

Huffman GJ, Bolvin DT (2014) The climate data guide: TRMM— Tropical Rainfall Measuring Mission. NASA, Washington, DC. ftp://precip.gsfc.nasa.gov/pub/trmmdocs/3B42_3B43_doc.pdf. Accessed 22 July 2015 Huffman GJ, Adler RF, Bolvin DT, Gu GJ, Nelkin EJ, Bowman KP, Hong Y, Stocker EF, Wolff DB (2007) The TRMM multisatellite precipitation analysis (TMPA): quasi-global, multiyear, combinedsensor precipitation estimates at fine scales. J Hydrometeorol 8:38– 55. doi:10.1175/jhm560.1 Inbar M (2000) Episodes of flash floods and boulder transport in the Upper Jordan River. The Hydrology-Geomorphology Interface: Rainfall, Floods, Sedimentation, Land Use. Proceedings of the Conference onDrainage Basin Dynamics and Morphology, IAHS Publ, Jerusalem, no. 261 Jiang D, Wang J, Huang Y, Zhou K, Ding X, Fu J (2014) The review of GRACE data applications in terrestrial hydrology monitoring. Adv Meteorol 2014:1–9. doi:10.1155/2014/725131 Joodaki G, Wahr J, Swenson S (2014) Estimating the human contribution to groundwater depletion in the Middle East, from GRACE data, land surface models, and well observations. Water Resour Res 50: 2679–2692. doi:10.1002/2013wr014633 Kim H, Yeh PJF, Oki T, Kanae S (2009) Role of rivers in the seasonal variations of terrestrial water storage over global basins. Geophys Res Lett 36(17). doi:10.1029/2009gl039006 Landerer FW, Swenson SC (2012) Accuracy of scaled GRACE terrestrial water storage estimates. Water Resour Res 48(4). doi:10.1029/ 2011wr011453 Longuevergne L, Scanlon BR, Wilson CR (2010) GRACE Hydrological estimates for small basins: evaluating processing approaches on the High Plains Aquifer, USA. Water Resour Res 46(11). doi:10.1029/ 2009WR008564 Longuevergne L, Wilson CR, Scanlon BR, Crétaux JF (2013) GRACE water storage estimates for the Middle East and other regions with significant reservoir and lake storage. Hydrol Earth Syst Sci 17: 4817–4830. doi:10.5194/hess-17-4817-2013 Margane A, Zuhdy Z (1995) Groundwater resources of northern Jordan, vol 1: rainfall, spring discharge and baseflow, part 1—rainfall in Jordan. Report Technical Cooperation Project no. 89.2105.8, BGR-WAJ Technical Cooperation Project, Amman, Jordan Margane A, Hobler M, Almomani M, Subah A (2002) Contributions to the hydrogeology of northern and central Jordan. Geologisches Jahrbuch Reihe C, Heft 68. Schweizerbart, Hannover, Germany Ministry of Water and Irrigation (MWI) (2000) Outline hydrology of the Amman-Zarqa Basin. http://pdf.usaid.gov/pdf_docs/Pnacp586.pdf. Accessed January 2002 Ministry of Water and Irrigation (MWI) (2009) Water for life: Jordan’s water strategy 2008–2022. http://www.semide.net/media_server/ files/K/g/JO_Water-Strategy09.pdf. Accessed June 2015 Ministry of Water and Irrigation (MWI) (2013) Jordan water sector facts and figures 2013, Amman, Jordan. http://www.mwi.gov.jo/sites/enus/Documents/W.%20in%20Fig.E%20FINAL%20E.pdf. Accessed June 2015 Ministry of Water and Irrigation (MWI), Federal Institute for Geosciences and Natural Resources (BGR) (2001) Groundwater resources of northern Jordan, vol 4: contributions to the hydrogeology of northern Jordan. Report Technical Cooperation Project no. 89.2105.8, BGR-WAJ Technical Cooperation Project, Amman, Jordan Ministry of Water and Irrigation (MWI), German Technical Cooperation (GTZ) (2004) National water master plan of Jordan: balancing resources and demands. Ministry of Water and Irrigation (MWI), German Technical Cooperation (GTZ), Ammam, Jordan Moiwo JP, Yang YH, Li HL, Han SM, Hu YK (2009) Comparison of GRACE with in situ hydrological measurement data shows storage depletion in Hai River basin, northern China. Water SA 35:663–670 Moore S, Fisher JB (2012) Challenges and opportunities in GRACEbased groundwater storage assessment and management: an

Hydrogeol J example from Yemen. Water Resour Manag 26:1425–1453. doi:10. 1007/s11269-011-9966-z Moore P, Williams SDP (2014) Integration of altimetric lake levels and GRACE gravimetry over Africa: inferences for terrestrial water storage change 2003–2011. Water Resour Res 50:9696–9720. doi:10. 1002/2014wr015506 Morris BL, Lawrence ARL, Chilton PJC, Adams B, Calow RC, Klinck BA (2003) Groundwater and its susceptibility to degradation: a global assessment of the problem and options for management. Early Warning and Assessment Report Series, United Nations Environment Programme, Nairobi, Kenya Mulder G, Olsthoorn TN, Al-Manmi DAMA, Schrama EJO, Smidt EH (2015) Identifying water mass depletion in northern Iraq observed by GRACE. Hydrol Earth Syst Sci 19:1487–1500. doi:10.5194/ hess-19-1487-2015 Proulx RA, Knudson MD, Kirilenko A, VanLooy JA, Zhang X (2013) Significance of surface water in the terrestrial water budget: a case study in the Prairie Coteau using GRACE, GLDAS, Landsat, and groundwater well data. Water Resour Res 49:5756–5764. doi:10. 1002/wrcr.20455 R Core Team (2015) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/. Accessed April 2016 Reichle RH, Koster RD, De Lannoy GJM, Forman BA, Liu Q, Mahanama SPP, Touré A (2011) Assessment and enhancement of MERRA land surface hydrology estimates. J Clim 24:6322–6338. doi:10.1175/jcli-d-10-05033.1 Richey AS, Thomas BF, Lo M-H, Famiglietti JS, Swenson S, Rodell M (2015) Uncertainty in global groundwater storage estimates in a total groundwater stress framework. Water Resour Res 51:5198–5216. doi:10.1002/2015WR017351 Rienecker MM, Suarez MJ, Gelaro R, Todling R, Bacmeister J, Liu E, Bosilovich MG, Schubert SD, Takacs L, Kim GK, Bloom S, Chen JY, Collins D, Conaty A, Da Silva A, Gu W, Joiner J, Koster RD, Lucchesi R, Molod A, Owens T, Pawson S, Pegion P, Redder CR, Reichle R, Robertson FR, Ruddick AG, Sienkiewicz M, Woollen J (2011) MERRA: NASA’s modern-era retrospective analysis for research and applications. J Clim 24:3624–3648. doi:10.1175/jcli-d11-00015.1 Rodell M, Famiglietti JS (2001) An analysis of terrestrial water storage variations in Illinois with implications for the Gravity Recovery and Climate Experiment (GRACE). Water Resour Res 37:1327–1339. doi:10.1029/2000wr900306 Rodell M, Houser P, Uea J, Gottschalck J, Mitchell K, Meng C, Arsenault K, Cosgrove B, Radakovich J, Bosilovich M (2004) The global land data assimilation system. Bull Am Meteorol Soc 85:381–394 Rodell M, Chen J, Kato H, Famiglietti J, Nigro J, Wilson C (2007) Estimating groundwater storage changes in the Mississippi River basin (USA) using GRACE. Hydrogeol J 15:159–166. doi:10. 1007/s10040-006-0103-7 Rodell M, Velicogna I, Famiglietti JS (2009) Satellite-based estimates of groundwater depletion in India. Nature 460:999–1002 Rodell M, Kato H, NASA/GSFC/HSL (2013) GLDAS Noah Land Surface Model L4 monthly 0.25 × 0.25 degree Version 2.0. Goddard Earth Sciences Data and Information Services Center (GES DISC), Greenbelt, MD. doi:10.5067/9SQ1B3ZXP2C5. Accessed July 2014 Sakumura C, Bettadpur S, Bruinsma S (2014) Ensemble prediction and intercomparison analysis of GRACE time-variable gravity field models. Geophys Res Lett 41:1389–1397. doi:10.1002/ 2013gl058632

Scanlon BR, Longuevergne L, Long D (2012) Ground referencing GRACE satellite estimates of groundwater storage changes in the California Central Valley, USA. Water Resour Res 48(4). doi:10. 1029/2011wr011312 Shen H, Leblanc M, Tweed S, Liu W (2015) Groundwater depletion in the Hai River Basin, China, from in situ and GRACE observations. Hydrol Sci J 60:671–687. doi:10.1080/02626667.2014.916406 Siebert S, Burke J, Faures JM, Frenken K, Hoogeveen J, Döll P, Portmann FT (2010) Groundwater use for irrigation: a global inventory. Hydrol Earth Syst Sci 14:1863–1880. doi:10.5194/hess-14-18632010 Strassberg G, Scanlon BR, Rodell M (2007) Comparison of seasonal terrestrial water storage variations from GRACE with groundwater-level measurements from the High Plains Aquifer (USA). Geophys Res Lett 34(13). doi:10.1029/2007gl030139 Strassberg G, Scanlon BR, Chambers D (2009) Evaluation of groundwater storage monitoring with the GRACE satellite: case study of the High Plains aquifer, central United States. Water Resour Res 45(5). doi:10.1029/2008wr006892 Sun AY, Green R, Swenson S, Rodell M (2012) Toward calibration of regional groundwater models using GRACE data. J Hydrol 422– 423:1–9. doi:10.1016/j.jhydrol.2011.10.025 Swenson SC (2012) GRACE monthly land water mass grids NETCDF RELEASE 5.0. Ver. 5.0. PO.DAAC, CA, USA. doi:10.5067/ TELND-NC005 Swenson S, Wahr J (2006) Post-processing removal of correlated errors in GRACE data. Geophys Res Lett 33(8). doi:10.1029/2005gl025285 Swenson S, Yeh PJF, Wahr J, Famiglietti J (2006) A comparison of terrestrial water storage variations from GRACE with in situ measurements from Illinois. Geophys Res Lett 33(16). doi 10.1029/ 2006gl026962 Thales Alenia Space (2010) Assessment of a Next Generation Mission for monitoring the variations of Earth’s gravity. Final report of the Next Generation Gravity Mission (NGGM) study. Thales Alenia Space, Cannes. http://www.iapg.bgu.tum.de/mediadb/5746123/5746124/ 04_ao7317_rd4-nggm_finalreport_issue2.pdf. Accessed 11 Jan 2016 Tiwari VM, Wahr J, Swenson S (2009) Dwindling groundwater resources in northern India, from satellite gravity observations. Geophys Res Lett 36(18). doi:10.1029/2009gl039401 US Geological Survey (USGS) (1998) Overview of Middle East water resources: water resources of Palestinian, Jordanian, and Israeli interest. Report compiled for the Executive Action Team, Middle East Water Data Banks Project (EXACT), US Geological Survey, Reston, VA Wahr J, Swenson S, Zlotnicki V, Velicogna I (2004) Time‐variable gravity from GRACE: first results. Geophys Res Lett 31. doi:10.1029/ 2004GL019779 Wouters B, Bonin JA, Chambers DP, Riva RE, Sasgen I, Wahr J (2014) GRACE, time-varying gravity, Earth system dynamics and climate change. Reports on Progress in Physics. Phys Soc 77:116801. doi: 10.1088/0034-4885/77/11/116801 Yeh PJF, Swenson S, Famiglietti J, Rodell M (2006) Remote sensing of groundwater storage changes in Illinois using the Gravity Recovery and Climate Experiment (GRACE). Water Resour Res 42(12). doi: 10.1029/2006WR005374 Yule GU (1926) Why do we sometimes get nonsense-correlations between time series? A study in sampling and the nature of time-series. J R Stat Soc 89:1–63