Journal of Hydrology: Regional Studies 12 (2017) 136–149

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Journal of Hydrology: Regional Studies

journal homepage: www.elsevier.com/locate/ejrh

Water scarcity, data scarcity and the Budyko curve—An MARK application in the Lower River Basin ⁎ Anne Gunkel , Jens Lange

Hydrology, Faculty of Environment and Natural Resources, University of Freiburg, Germany

ARTICLE INFO ABSTRACT

Keywords: Study region: Lower Basin, Eastern Mediterranean water-energy balance Study focus: Water scarcity and data scarcity are two of the main challenges for water Budyko curve management in the study region, therefore, all possible information should be extracted from Lower Jordan River Basin existing data. In this context, the Budyko framework offers possibilities not yet sufficiently Renewable water resources explored for evaluating the water-energy balance and estimating water availabilities. In this study, we applied a parametric Budyko type equation to the Lower Jordan River basin and compared data from global products, output of the hydrological model TRAIN-ZIN as well as values from literature. The curve shape parameters of the Budyko type curve fitted on different temporal and spatial scales were used to estimate renewable water resources with publicly available data for three subbasins. New hydrological insights for the region: The adjusted Budyko curves illustrate the influence of non- climatic factors such as vegetation or soil storage on the water-energy balance and a related relatively low efficiency of evapotranspiration, despite a high evaporative demand. Renewable water resources wereestimatedas25to30%ofprecipitationinaverage in most cases and were more strongly affected by inter-annual variabilities than by the variance between the different derived Budyko curves.

1. Introduction

Water management in several countries of the Eastern Mediterranean is challenged by water scarcity and data scarcity; despite a variety of studies, an integrated view of the local water system is still lacking. Through their endeavour for a holistic understanding of the environmental system, Darwinian approaches are means to tackle actual challenges in hydrological research and water resources assessment and management (Harman and Troch, 2014). The Budyko curve, a semi-empirical expression of the coupled water-energy balance (Yang et al., 2007) is one of the best investigated examples among the approaches discussed in the last years (Harman and Troch, 2014; Harte, 2002; Sivapalan et al., 2011; Wang and Tang, 2014). It describes how the ratio of atmospheric water supply, i.e. precipitation, and water demand, i.e. potential evaporation, drives the partitioning of precipitation into streamflow and evaporation (Berghuijs et al., 2014). Based on earlier work of Schreiber (1904) and Ol’Dekop (1911), Budyko (1974) proposed a non-parametric relationship for long-term averages and large basins that relates actual evapotranspiration AET to potential evapotranspiration PET and precipitation P. Subsequently, a variety of Budyko type models have been developed with similar shapes, but different functional forms (e.g. Choudhury, 1999; Donohue et al., 2012; Fu, 1981; Mezentsev, 1955; Milly, 1994; Pike, 1964; Turc, 1954; Yang et al., 2008; Zhang et al., 2004). They share Budyko’s assumption that evapotranspiration is limited by water in dry conditions and by energy in wet conditions (Zhang et al., 2004). Non-climatic influence on the data (Yang et al., 2007) can either be analysed as derivation from the Budyko curve (Donohue et al., 2010; Troch et al.,

⁎ Corresponding author at: Hydrology, Faculty of Environment and Natural Resources, University of Freiburg, Fahnenbergplatz, 79098 Freiburg, Germany. E-mail addresses: [email protected] (A. Gunkel), [email protected] (J. Lange). http://dx.doi.org/10.1016/j.ejrh.2017.04.004 Received 29 September 2016; Received in revised form 14 April 2017; Accepted 16 April 2017 Available online 17 May 2017 2214-5818/ © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/). A. Gunkel, J. Lange Journal of Hydrology: Regional Studies 12 (2017) 136–149

2013)orbyfitting a parametric curve (Li et al., 2013; Xu et al., 2013; Yang et al., 2007). Parametric Budyko type equations are equipped with a dimensionless free curve shape parameter without any a priori physical meaning (Li et al., 2013) that represents the influence of catchment characteristics (Wang et al., 2016). The frequently applied functional form of Fu (1981, in Chinese, revisited by Zhang et al., 2004)(see Chapter 3.3) resembles the equations of Choudhury (1999), Mezentsev (1955) and Yang et al. (2008). For a more detailed review of Budyko type equations, see Donohue et al. (2007) or Wang et al. (2016). In the last decade, several studies explored possibilities and limits of the approach on different scales and with a variety of purposes (Berghuijs et al., 2014; Donohue et al., 2010; Gentine et al., 2012; Greve et al., 2015; Li et al., 2013; Milly, 1994; O’Grady et al., 2011; Potter et al., 2005; Wang and Tang, 2014; Xu et al., 2013; Yang et al., 2007; Zhang et al., 2008, 2004). Their general aim is to understand controls on the water balance and its variability in space and time. The application of Budyko type curves on smaller temporal and spatial scales is debatable, since Budyko was originally developed for long-term averages (> > 1 year) and large catchments (> 10000 km2), assuming stationary hydrological conditions. However, several studies (e.g. Yang 2008; Zhang et al., 2008; Li et al., 2013) concluded that applications with an empirical curve shape parameter are legitimate on annual scales, while intra-annual applications are debatable (e.g. Zhang, 2008; see also the discussion in Wang et al., 2016). Very few studies on Budyko exist for the Middle East (Tarolli et al., 2012), although insights into the annual water-energy balance would be valuable in view of water scarcity and climate change. Budyko type studies are interesting under conditions of data-scarcity for several reasons: First, they do not rely on runoff data which are rare and uncertain in the Middle East, given numerous anthropogenic modifications, e.g. canals and dams, short measurements records and difficult data access; second, runoff makes up a small part of the water balance in drylandregionsliketheMiddleEast;andthird,theapproachcanbeusedforcomparingdataand,oncethecurveparameterisestimated,for calculating actual evapotranspiration based on the more commonly available data of precipitation and potential evapotranspiration (Zhang et al., 2004), as well as for extrapolation in space and time (Lebecherel et al., 2013; Yang et al., 2007). The Jordan River Basin is under great water stress (Comair et al., 2013). Its lower part, flowing from the outlet of Lake Kinneret to the , includes major parts of the population, industry, and irrigated agriculture of the Hashemite Kingdom of Jordan (Venot et al., 2008). Whereas water consumption increases, quality and quantity of local water resources decrease, groundwater recharge is decisive only during high intensity events (Ries et al., 2015; Sheffer et al., 2010) and the water balance is characterized by high variabilities in space and time (Gunkel and Lange, 2012). Regarding these challenges, the question arises if the Budyko approach generates additional information for water resources assessment in these specific conditions. The main aim of this study is to contribute to reliable estimates of the water balance and renewable water resources in the Jordan River region by establishing a Budyko type water-energy relation. We analysed and compared the Fu curves based on results of the hydrological model TRAIN-ZIN (Gunkel and Lange, 2012) and global data sets and derived renewable water resources as residual term of the water balance. Fu curves were chosen as functional form because they are parametric, but comparably simple and tested in different studies (e.g. Li et al., 2013; Zhang et al., 2008). In this study, the Fu approach is also used as a mean to integrate results from published studies for comparison and evaluation.

2. Study area

The Upper part of the Jordan River Basin (about 18300 km2)(Fig. 1) extends from the headwaters at Mt. Hermon to the Lake Kinneret (also known as Lake Tiberias or Sea of Galilee, 210 m bsl), in the borderland of , Syria and Lebanon. The study area, the Lower Jordan River Basin (LJRB, 16400 km2), comprises the river and all its tributaries between its exit of Lake Tiberias and the Dead Sea (410 m bsl). Yarmouk and are the largest of the 27 tributaries. The LJRB is located in the Eastern Mediterranean where the climate is a transition between the temperate European and the arid Sahara-Arabian climate; hot, dry summers and cool, wet winters are the prevailing seasons. Climate variability is generally high and the area has sharp climatic gradients. In the LJRB, precipitation is low in the and on the Jordan Highland Plateau in the East (less than 200 mm/year) and higher in the escarpments bordering the valley (up to 600 mm/year) (Gunkel and Lange, 2012). Mean daily temperature varies with altitude, the range between winter and summer temperatures is between 8 °C/24 °C in and Jerusalem and 15 °C/31 °C in the Jordan Valley (Exact, 1998). Soils in the LJRB correlate with lithology and reflect a wide range of physical characteristics (Singer, 2007). Soil formation is influenced by the local climate promoting xeric, i.e. dry, soil moisture regimes, but also by anthropogenic and aeolian impacts and the parent material varying from limestone areas to basalt plateaus. Alluvium and marly deposits dominate in the Jordan Valley, aridisols and inceptisols in other areas of the LJRB. Vegetation ranges from agricultural areas to almost bare soils, with a high percentage of grass- and shrublands (Gunkel and Lange, 2012). During the last decades, anthropogenic activities heavily altered the natural hydrological regime of the Lower Jordan River (e.g. Lowi, 1995). Today, its flow mainly consists of saline spring water, sewage and excess water from irrigation (FOME, 2010).

3. Methodology

3.1. TRAIN-ZIN

TRAIN-ZINisaconceptualmodelthatcombinesapproachesfordrylandareasonahigh,butflexible temporal and spatial scale. Each process is represented either more physically-based or more conceptually, depending on its supposed impact on the overall result. Principally, the user has several possibilities to adapt the model to the specifics of study area and data availability. Processes of runoff generation, evapotranspiration and percolation are calculated in regular grids. Runoff concentration is implemented conceptually with a Unit Hydrograph

137 A. Gunkel, J. Lange Journal of Hydrology: Regional Studies 12 (2017) 136–149

Fig. 1. (a) the Lower Jordan River Basin with all subbasins and the location of Auja spring (red point); (b) the radar derived precipitation (mm/a) of the average season in the study area (150 km range around location of rainfall radar) (Gunkel et al., 2012) and (c) a landuse map for the same area (Gunkel et al., 2012). approach and subbasins and channel flow processes including transmission losses are realized in a channel network of linked channel segments. Temporal resolution is flexible, evapotranspiration is simulated with a daily time step and the faster runoff generation processes with sub-daily time steps of several minutes. Evapotranspiration as major element of the water balance is calculated with a Shuttleworth- Wallace approach (Shuttleworth and Wallace, 1985) that is a better representation of the local conditions of non-closed vegetation canopies and the importance of soil evaporation than the popular Penman-Monteith approach.

3.2. Data

For the Lower Jordan River Basin (LJRB), Fu-type curves are calculated based on data for hydrological years (1st of Oct to 30th of Sep) from different data sources described in the following section. One data set is the rainfall radar data as used as model input in Gunkel and Lange (2012), which is less reliable outside a 150 km range around the radar station. For reasons of comparability, only data inside this area is considered for all data (Fig. 1; about 10980 km2). Since not the same time periods are available for all data sources, the comparability of the periods is checked with a long term precipitation time series of the Jerusalem central meteorological station. This data was derived from Klein Tank et al. (2002) for the period 1960/61-1999/00 and from the Israel Meteorological Service (IMS) for the period 2000/01-2014/15.

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Table 1 Description of data sets for the LJRB (the column “Label” refers to the names used in this study; P: Precipitation, AET: Actual Evapotranspriration, PET: Potential Evapotranspriration).

Type Label Data set Source Time series Resolution

P Global CRU TS vs Climate Research Unit (CRU) at the 2000/01–2010/11 0.5 °, monthly 3.22, University of East Anglia Model Radar C-Band volume scanning system Extremes (1991/92, wet; 1998/99, dry; 1.4°x 1 km polar coordinates, 5 average, 2002/03) min AET, PET Global MOD16 NTSG 2000/01 − 2010/11 1 km2, daily (http://www.ntsg.umt.edu/project/ mod16) Model Model TRAIN-ZIN Extremes (1991/92, wet; 1998/99, dry; 250 × 250 m2, daily average, 2002/03)

Rainfall radar data was measured at Ben-Gurion international airport, close to (provided by E. Morin, Hebrew University of Jerusalem, Israel) (Table 1) and pre-corrected by a multiple regression approach (Morin and Gabella, 2007). Afterwards, it was regionalized to the LJRB and calibrated with ground stations (Gunkel and Lange, 2012). The three available years represent climatic extremes, as does the derived model output of TRAIN-ZIN for actual and potential evapotranspiration (Gunkel and Lange, 2012; Table 1). Out of several available global data sets for precipitation and evapotranspiration, two data sets were exemplarily selected for reasons of accessibility. Precipitation data from the Climate Research Unit (CRU) is a global gridded data set based on weather station records (Harris et al., 2014). The 2000/01-2010/11 period has been chosen to match the period of the MOD16 evaporation data, a land surface product calculated based on MODIS land cover data (Table 1). It is one of two operational global ETA products derived from remotely sensed data (Hu et al., 2015) and is widely known, as is the CRU data set. Additionally, both data sets have been applied to the area before (Comair et al., 2012). Available data was combined into different data sets: The first data set (hereinafter called model data) consists of radar rainfall and the related TRAIN-ZIN model output of AET and PET. Precipitation data of CRU and MOD16 AET and PET data are combined into the second data set which is hereinafter called global data. Additional data were available for several subbasins (Table 2): gauging station data were interpolated with inverse distance weighting for Wadi Qilt; basin wide estimates of the water balance of Wadi Faria were available from hydrological modelling (Gunkel et al., 2015); for the catchmentareaofAujaspring,datawereavailablefromastudyofSchmidt et al. (2014) (data courtesy of Sebastian Schmidt).

3.3. Fu curves

As a Budyko type curve, Fu’s equation (Fu, 1981; Zhang et al., 2004) relates the aridity index PET/P (also known as dryness index) to the evaporation index AET/P (van der Velde et al., 2014), including a dimensionless empirical curve shape parameter ω:

1 ⎡ ω⎤ω AET PET ⎛ PET ⎞ =1+ −1+⎢ ⎜ ⎟ ⎥ ⎢ ⎝ ⎠ ⎥ P P ⎣ P ⎦ (1) The aridity index AI is also applied to derive climate classifications for different zones: Hyper-arid (AI > 20), Arid (5 < AI ≤ 20), Semiarid (2 < AI ≤ 5), Dry sub-humid (1.5 < AI ≤ 2) and Humid (AI < 1.5) (UNEP 1992). Fig. 2 illustrates several curves where the Fu parameter ω varies from 1.5 to 2, and includes the climate classification. The Fu parameter represents the non-climatic influences on the water-energy balance and is often attributed to properties of soil, topography, and vegetation (Wang, 2016). The parameter ω of equation 1 was calibrated with values of P, PET and AET for different resolutions in space and time (mean annual value for the spatial mean of the LJRB; mean annual value for subbasins of the LJRB; annual values for the spatial mean; annual values for subbasins), each time for the two data sets (global and model) separately.

3.4. Renewable water resources

The long dry seasons result in very low soil storage levels towards its end (e.g. Ries et al., 2017; Ruiz-Sinoga et al., 2011) and in negligible inter-annual storage changes. Therefore, the residual term of the water balance (P-AET), i.e. the amount of precipitation

Table 2 Data available for several subbasins in the LJRB (P: Precipitation, AET: Actual Evapotranspiration, PET: Potential Evapotranspiration).

Subbasins Data Source Time series Resolution, Type

Wadi Qilt P, PET Palestinian Central Bureau of Statistics (PCBS) 2007/08-2014/15 Annual; stations and Wadi Faria P, PET, AET Gunkel et al., 2015 2004/5–2009/10 Annual; model data Auja spring catchment P, PET Schmidt et al., 2014 1967/68 − 2010/ Annual; model data 11

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Fig. 2. Fu curves for parameters between 1.5 and 2 and the classification of the aridity index according to UNEP, 1992. not evaporating, is calculated and referred to as renewable water resources (RWR) (European Commission, 2015) in this text. Where actual evapotranspiration data are not available, they can be estimated with the fitted regional ω parameter and be applied to calculate RWR. These estimates of renewable water resources were compared with those based on AET estimates from other sources, where available. Additionally, the influence of ω on the estimations of renewable water resources was calculated theoretically for a combination of ω, P and PET.

4. Results

4.1. Aridity index

Mean annual precipitation measured in Jerusalem, one of the few stations in the region with a long continuous daily precipitation record, is compared to averages of the subsets of this data considered in the further analyses. The upper panel of Fig. 3 shows annual values for Jerusalem (1981-2014) with a long term mean of 530 mm/a together with the means of the same data set of the periods 2000/01-2010/11 (global data set, 506 mm/a), 2007/08-2014/15 (Wadi Qilt, 466 mm/a), 2004/05-2009/10 (Wadi Faria, 479 mm/ a) and for the three years of radar data (LJRB, model data, 1991/92, 1998/99, 2002/03). The data for precipitation in these subbasins and periods are given in the lower panel of Fig. 3 and in Table 5. For the LJRB, precipitation and evapotranspiration for both data sets are summarized in Fig. 4. The average of the radar derived precipitation in the model data set is with 309 mm/a higher than the global data set value of 270 mm/a, as is its range between the subbasins (160 − 660 mm/a compared to 203- 515 mm). Actual evapotranspiration (AET) is higher for model data in most cases and in average (215 vs. 198 mm/a) and has a higher variance between the subbasins. For precipitation and actual evapotranspiration, the discrepancies between both data sets do not vary systematically between the basins. Potential evapotranspiration (PET) shows only minor variations between the subbasins, but a major difference as a function of method. The average value of PET is 1112 mm/a for the model data set, while the satellite derived value is higher in all subbasins and amounts to 1899 mm/a in average. Consequently, aridity indices (AI) are lower for model than for the global data. For model data, the mean value is 3.6, with a range between 1.6 and 7.0. The mean for satellite data is 7.0, the range between 3.7 and 9.4. According to the UNEP classification, average value and almost all subbasins values for model data are clearly in the semi-arid range, whereas the mean aridity index and some of subbasins of the other data set indicate arid climates.

4.2. Fu curves on different scales

4.2.1. Mean annual values The Fu curves based on the temporal mean of the three modelled years as well as on the ten years considered in the global data set are plotted in Fig. 5. If the curves are fitted based on the subbasins, ω values are similar for model and global data (1.55 and 1.5 resp.) and the coefficient of determination is low in both cases (0.34 and 0.35 resp.). Fitting to the mean values of the LJRB area results in very similar results (1.48 for model data and 1.58 for the global data set). For the single subbasins (Fig. 5), the global data show two

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Fig. 3. A. Long-term time series of precipitation for Jerusalem with annual variation and long term average from 1960/61-2014/15 plotted from 1980/81 for reasons of visibility; data compiled from Klein Tank et al., (2002) (1960/61-1999/00) and the Israel Meteorological Service Database (IMS), http://data.gov.il/ims (2000/01- 2014/15). The dark grey bars indicate the considered years for rainfall radar and hydrological modelling. The coloured lines show the average in Jerusalem data for the periods considered in the subbasins. B. Local annual precipitation (points) and precipitation averages (lines) for the subbasin data. Note that in case of the LJRB model data only the average of three years, not of the entire period is calculated (dashed line). distinct groups for Eastern and Western basins, whereby the Eastern basins show higher aridity indices and plot mostly above the mean curve, whereas the western basins are below this curve. Also in model data, Eastern basins are predominantly above the curve and show more scatter around the curve, but the difference between the two groups is smaller than in the global data.

4.2.2. Spatial means, single years For spatial means and single years (Fig. 6), modelled data have a lower ω value (1.57) than the global data set (1.66) and a higher coefficient of determination (0.79 compared to 0.26). For the global data set, single years even plot above the water limit line.

4.2.3. Spatially distributed, single years If the Fu curves are fitted for each subbasin individually for all available years, their ω values range considerably between the basins, from 1.42 to 2.43 for model data and from 1.28 to 2.63 for the global data set. However, the average calculated based on this data is close to each other (1.7 and 1.67 for model and satellite data, respectively). The coefficients of determination vary considerably, with mostly high values and an average of 0.79 for model data (range 0.04 to 0.99), and lower value for the global data set (0.28, range 0 to 0.5).

4.3. Integrating literature values

In the relevant literature, only very few studies provide all necessary data for Budyko curves, they are summarized in Table 3. Fig. 7 compares these studies with results from TRAIN-ZIN model and global data sets, whereby the latter have generally higher aridity indices than model and literature data. Although differences in aridity index are high, values are often comparably similar in

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Fig. 4. Annual means of precipitation (upper), potential evapotranspiration (middle) and actual evapotranspiration (lower) for the subbasins of the Lower Jordan River Basin for model and global data. Colour code indicates the climate classification of the aridity code, as determined with the particular data set. evaporative index, specifically for model and literature values.

4.4. Estimations of renewable water resources

The influence of the derived ω values on estimations of actual evapotranspiration and available water in the study area (Table 4)was calculated depending on combinations of precipitation and potential evapotranspiration. If the mean annual ω values for the LJRB are estimated from global data (1.58) and model data (1.48) (see section 4.2), the differences in renewable water resources are below 40 mm/ a. In contrast, the ω valueof2.6,correspondingtotheoriginalBudykocurve,giveshigherdifferences, up to 200 mm/a. Mean annual renewable water resources (RWR) for the considered periods can be calculated directly, without the Budyko curve, and are 55 mm/a for the global data set and 80 mm/a for model data (Fig. 8). The values evaluated for the subbasins (Table 5) are mostly higher, whereby the absolute values depend on the methodology. Wadi Qilt has the lowest renewable water resources in the study, only 9 mm/a RWR are estimated for a ω of 2.6. In all other cases, differences based on the methodology or the ω value are less

Fig. 5. Fu curve compared for model data (circles) and satellite data (triangles): The black symbols indicate mean value of LJRB, the coloured points averages for the subbasins of the LJRB (brown to yellow: West of the Jordan Valley and Jordan Valley, dark green to light green: East of Jordan Valley, whereby darker colour indicate Northern basins). The lines are Fu curves based on the mean LJRB values for model (solid) and global (dashed) data.

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Fig. 6. Fu curves for model and global data as spatial average of the LJRB for all available years. than 15% of the water balance and all other estimations are between 20 and 46% of the water balance. Inter-annual variability (Fig. 8) is high in the long-term record for the Auja Spring basin, where annual renewable water resources reach values below 50 and above 600 mm/a. For cases where satellite derived actual evapotranspiration is higher than the CRU data precipitation, RWR as difference between precipitation and evapotranspiration is even negative for single years.

5. Discussion

5.1. Aridity index

Due to the high temporal variability in the region, identical time periods for all data sets would be advisable, but are not available. However, if the considered periods are examined in the Jerusalem rainfall data, the averages are relatively similar to the long term mean. The three years chosen for hydrological modelling are an exception, because they have been selected as extreme seasons. An influence of the time periods on the results cannot be excluded nevertheless. The difference in mean annual value for the LJRB between the two data sets (global and model) is low, compared to the high derivations between precipitation and actual evapotranspiration estimates from these data sets in the different subbasins. The derivations between the data sets in the different basins are not systematic, if compared between the basins, and show that the methods perform differently in the individual climatological, hydrological and geographical conditions that characterize the basins. The well-known uncertainties when applying different estimation methods in hydrology (e.g. Beven, 2012; Mittermaier, 2008) must be kept in mind, as they are diminished, but not abolished by modern approaches like radar or satellite data. In contrast, differences in potential evapotranspiration (PET) are systematic and striking and raise the question if one of them is considerably erroneous. Weiß and Menzel (2008) compared four different equations for potential evapotranspiration in the Jordan River region. The values differed within the region, but even more between the methods (e.g. 1200 mm for Penman Monteith grass or alfalfa reference evaporation, 1500 mm/a for corrected Class A pan evaporation and 1950 mm/a estimated by the Priestley Taylor approach). The Israel Meteorological Service (IMS) offers publicly available evapotranspiration data for one station in the study region (Bet Shaan Valley Eden farm), with a mean annual PET of about 1650 mm/a with the Penman Monteith method and 1600 mm/a for corrected Class A pan evaporation (assuming a pan coefficient of 0.7 as in Weiß and Menzel (2008)). For the Auja spring, Schmidt et al. (2014) estimate 1140 mm potential evapotranspiration with the Hargreaves equation (period 1967-2010). Although most of these numbers represent point estimates only, they illustrate the variance of PET estimates and a lacking standard

Table 3 Water balances studies in the Jordan River Basin area (P: Precipitation, PET: Potential evapotranspiration, AET: Actual evapotranspiration, R: Recharge, all values in mm/a).

Source Area (Size) Period P PET AET R

Alkhoury (2011) Wadi Kafrein (161 km2) 1980-2008 428 1928 251 132 Hartmann et al., 2012 Faria spring (30 km2) 1971-2001 679 2275 472 201 Moshe, 2008 Wadi Faria (139 km2) 1960-2000 660 1400 385 Rimmer and Salingar Upper Jordan River Basin (UJRB) (738 km2) 1970-2000 958 1100 226 641 (2006) Schmidt et al., 2014 Wadi Auja (49 km2) 1967-2010 543 1140 365 178

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Fig. 7. Literature values for the JRB compared with fitted Fu curves for data from model and global data sets (spatial and temporal mean). for hydrological modelling (Oudin et al., 2005), even for the definition of PET (Allen, 2006). Besides the general uncertainties of PET estimates, the chosen data products are subject to specific shortcomings. MODIS16 data relies on an improved method for estimating potential evapotranspiration, based on the Penman Monteith equation and driven by daily meteorological reanalysis data and MODIS derived vegetation data (Mu et al., 2011). However, validation with eddy covariance flux towers revealed an average mean absolute bias values for AET of 24.1% (Mu et al., 2011). Information on the specific reliability in drylands is rare, but some studies indicate higher differences to other products in semi-arid and arid areas (Trambauer et al., 2014; Hu et al., 2015). Uncertainties in the model output are due to uncertainties in input data, parametrization and model structure. For the re-calculated precipitation data from CRU, errors in station data and in deriving gridded values from this data are the main sources of uncertainty (Zhao and Fu, 2006; Zhuo et al., 2014), whereby variations of ± 20% can be assumed (Zhao and Fu, 2006). In addition, the high climatic gradient in the study area (Ries et al., 2016) together with the varied topography decreases the quality of PET estimates of all methods. In these conditions, the selection of a single data set for each water balance element appears somehow arbitrary. Comparisons of different remote sensing derived products have been conducted (Chen et al., 2017; Hu et al., 2015; Mueller et al., 2013), but are not the focus of this study. In practice, selecting a single data product as an input for an environmental modelling task may not be rarely done (e.g. Comair et al., 2012; Pande et al., 2012). In this situation, although it is neither possible to define the “real” PET value nor to assess the quality of modelled and global data PET unequivocally, the Budyko based analysis delivers some information on the plausibility of the data. The question arises which of the PET data sets with the highly different values is more trustable and how much their differences impact the resulting analyses. Indeed, mainly due to high PET values, AI values for the global data set are significantly higher than for the model data and partly in the arid range, which does not agree with other climate classifications of the region (e.g. Goldreich, 2012). Second, AET is higher in parts than P. Although this may be caused by water input in addition to precipitation (Greve et al., 2016), it may as well be attributed to input not only from different data sources, but even from different data types (global gauging stations vs. satellite derived). Third, the coefficients of determination for fitting the Fu parameter ω are mostly lower than for model data. All results discussed in the following sections are influenced by the discussed uncertainties in general and particularly in the global data set. However, PET values do not seem to be influential for AET estimates in this and in other studies. The variance between PET products was higher than between derived AET estimates (Trambauer et al., 2014) or the uncertainty related to the AET product was not dependent on the choice of the PET or precipitation product (Greve et al., 2014). Weiß and Menzel (2008) conclude that not the absolute value of PET, but the derivation of actual from potential evapotranspiration values is apparently most relevant in the case of water resources assessment.

Table 4 Influence of ω parameter on estimations of actual evapotranspiration and renewable water resources RWR (mm/a) of different combinations of precipitation P (mm/a) and potential evapotranspiration PET (mm/a) (ω: Fu parameter (−), AI: Aridity index (−), AET: Actual evapotranspiration, (mm/a)).

P PET AI AET (mm/a) RWR (mm/a)

ω = 1.48 ω = 1.58 ω = 2.6 ω = 1.48 ω = 1.58 ω = 2.6

200 1000 5 139 151 194 61 49 6 200 2000 10 156 167 198 44 33 2 600 1000 1.6 303 337 505 297 263 95 600 2000 3.3 378 416 567 222 184 3

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Table 5 Renewable water resources RWR (mm/a and %) in the LJRB, for different periods and subbasins (ω: Fu parameter, P: Precipitation, mm/a, PET: Potential evapotranspiration, mm/a, PCBS: Palestinian Central Bureau of Statistics).

Location Time period P (mm/a) PET (mm/ RWR (mm/ RWR Method Source or Type of input data a) a) (%)

LJRB 2000-2010 269 1899 55 20 Water balance Global data set, P: CRU PET: MOD16 LJRB 1991/92, 1998/99, 2002/ 309 1112 80 26 Model Model data set 03 (Gunkel and Lange, 2012) Wadi Qilt 2007-2014 379 2129 108 28 Fu (ω = 1.48) PCBS Wadi Qilt 2007-2014 379 2129 91 24 Fu (ω = 1.58) PCBS Wadi Qilt 2007-2014 379 2129 9 2 Fu (ω = 2.6) PCBS Wadi Faria 2004 − 2009 506 1215 157 31 Model (Gunkel et al., 2015) Wadi Faria 2004 − 2009 506 1215 210 42 Fu (ω = 1.48) (Gunkel et al., 2015) Auja Spring 1981 − 2014 528 1140 172 33 Model (Schmidt et al., 2014) Auja Spring 1981 − 2014 528 1140 241 46 Fu (ω = 1.48) Station and model data (Schmidt et al., 2014)

5.2. Fu curves on different scales

Calculations of ω values for different scales and for global and model data range between 1.48 and 1.7, whereby higher ω values indicate more AET for the same aridity index. Trends of increasing ω value with higher resolution show a scale-dependency known from previous studies (Choudhury, 1999; Xu et al., 2013): larger basins lead to lower ω. The variance in the individual ω estimates for subbasins and annual data illustrate the degree of variability in the area that is averaged out in long term means. However, these individual values for subbasins would be interesting for local predictions; further studies are required to increase the validity of these first results, where coefficients of determinations are comparably low, and explore the robustness and possible regionalization of Fu parameters. Despite the discrepancies in PET, both methods estimate relatively similar ω values. However, the scatter of mean annual values for the subbasins (Fig. 5) is lower for the model based estimations. For both data sets, the cluster of subbasins appears to be related to location and topography, with most Eastern subbasins plotted above the fitted curve. For the same AI, more evapotranspiration is predicted in the Eastern basins than the Western basins. Since the basins west and east differ in several basin characteristics, further studies could investigate their influence on the efficiency of evaporation in the study region, whereby aspect or vegetation might be promising candidates. For model data, the Zarqa river basin is an outlier, due to a high AI caused by low annual precipitation. This subbasin has low mean annual precipitation values due to its extension into drier climates, but also into the outer limit of the radar range (Gunkel and Lange, 2012). Conditions in basins where climatic and catchment characteristics lead to such low ω values are not favourable for evapotranspiration (Zhang et al., 2004). Since the ω parameter is related to the ability of a watershed to retain water for evapotranspiration (Zhou et al., 2015), the low values in the study region indicate less developed retention capacities and less efficient actual evapotranspiration. However, studies on the influence of catchment characteristics on Budyko parameters show

Fig. 8. Water availability either derived directly from the water balance (triangles and solid lines) or estimated with Fu’s equation (points and dashed lines) for different data sources and periods: Model data (1991/92, 1998/99 and 2002/03) and global data (2000/01-2010/11) for the LJRB (grey); Model and Fu derived values for Auja Spring catchment (1981/82 to 2000/2001; based on (Schmidt et al., 2014), green) and Wadi Faria (2004/05 to 2009/10, based on (Gunkel et al., 2015), purple); Wadi Qilt estimates with several parameters, based on input data of PCBS (2007-2014, dark red).

145 A. Gunkel, J. Lange Journal of Hydrology: Regional Studies 12 (2017) 136–149 comparably complex relations, depending on local conditions, scale of investigation etc. (e.g. Donohue et al., 2007; Gentine et al., 2012; Li et al., 2013). Controlling factors may include precipitation intensity, seasonality, slope and limited soil water storage capacity. Applications in smaller catchments showed an increasing influence of vegetation (Li et al., 2013; Xu et al., 2013; Zhou et al., 2015). Smaller values are apparently associated with steep slopes, high precipitation intensity and lower plant available water storage capacity (Zhang et al., 2004). These conditions prevail in the study area as they do in semi-arid and arid areas in general, where the short and spotty nature of rainfall events does not lead to continuous availability of soil moisture necessary for high evapotranspiration values (Wheater et al., 2008). In addition, seasonality in the wet winter season of Mediterranean climate leads to a seasonal shift between rainfall and evaporative demand and to a surplus of water (precipitation minus PET) in winter. This favours percolation and runoff, but hinders evapotranspiration (Williams et al., 2012; Milly, 1994). Additionally, vegetation influences the ratio of evapotranspiration; grasslands for example, one of the dominating land use types in the areas, cannot evaporate as efficiently as forests with their deeper roots, lower aero dynamic resistances, and higher and more persistent leaf area (Zhang et al., 2004). Vegetation type and cover are strongly influenced by availability of water and energy (Yang et al., 2009), but influence the partinioning of water into evapotranspiration in turn. Some studies improved the estimations of water balances by incorporatingy vegetation characteristics like vegetation cover or rooting depth into the Budyko framework (e.g. Donohue et al., 2007; Yang et al., 2009; Li et al., 2013). However, precipitation dynamics are more relevant than vegetation cover at annual scale in the study of Donohue et al. (2010) and the non-closed vegetation canopies prevailing in semi-arid areas might be less influential than richer vegetation types. The connection between vegetation and water balance appears to complex, as effects might be scale-depending (Li et al., 2013) and regionally different (Wang et al., 2016), but is not the focus of this research. For longer periods, anthropogenic land use changes would add to the effect of natural variation in vegetation. Although Fu parameters are relatively stable for all conditions, annual values appear to work better for model data, even regarding the fact that the three considered seasons are extreme seasons in this case. This might be related to the problem of global data discussed above. The validity of Budyko approaches for annual values and small basins are a topic of dispute in recent literature, but in this study, the results are even plausible for the extreme years selected in the model data (Fig. 6). Extreme cases are relevant information in the non-linear climatic conditions of the study area, as indicated by a previous study of the authors that estimates annual renewable water resources to range between 11 and 216 mm for dry and wet extreme resp. (Gunkel and Lange, 2012).

5.3. Integrating literature values

The derived ω values are distinctly lower than the value of 2.6 corresponding to the original Budyko curve, relatively low compared to literature values. For Australian basins, Zhang et al. (2004) found values between 1.7 and 5, whereby forests had higher ω averages (2.84) than grasslands (2.55). Li et al. (2013) report a slightly smaller range (1.3-3) for major global river basins, with an average value of 2.0; the study of Xu et al. (2013) revealed a median of 2.6 for smaller basins in the U.S., and of 1.8 for larger basins, in both cases with a considerable range (1-4.9 and 1.3-4.6, resp.). In contrast to these global studies, few studies address explicitly dryland regions, but if so, the averages are in the same order of magnitude as our results. For the dry Niger basin (AI=3.59), Li et al. (2013) estimated a ω of 1.55; Greve et al. (2014) assumed a ω of 1.6 for African data. An investigation of 108 catchments in the non- humid regions of China confirmed the general applicability of Fu’s formula for long-term means and inter-annual variability of the water balance in that region. The median ω was 2.9 for the complete dataset, but between 1.3 and 1.8 for the drier inland river basins (Yang et al., 2007). Literature values on water balances can be integrated into the Budyko curve for overview and comparison, since they either plot on the same Fu curve or deviate due to discrepancies and errors. Thereby, shifts in the x-axis direction of the Budyko diagram are related to PET, along the y axis to AET. In the present study, the low availability of water balance studies with all necessary information published limits the informative value of the analysis. However, some conclusions are possible (Fig. 7): For Wadi Auja, all three available data sets are different mainly in terms of aridity index and the effectiveness of evapotranspiration appears to be represented correctly. For Wadi Faria, results from TRAIN-ZIN and Moshe (2008) are very similar, despite their different methodology, whereas the satellite derived data have a higher aridity index. In general, very small differences occur in vertical direction, i.e. literature values support the low ω values.

5.4. Estimations of renewable water resources

This study shows that the application of the traditional Budyko curve (ω = 2.6) would result in unrealistic high evapotranspira- tion and low renewable water resources for this area. In contrast, regionally calibrated ω values lead to estimations of renewable water resources that correspond comparably well with the other results, if available (Table 3, Table 5), taking into account the simplicity of the approach. For example, estimates for the Auja spring catchment agree well with the results of Schmidt et al. (2014) in many cases, but mostly for wetter years. All results are mostly between 100–200 mm/a, with differences due to methodology. Renewable water resources estimated for the Lower Jordan River basin in total are lower than for the three subbasins considered. Of these three, Wadi Qilt, the subbasin with the highest AI, has not only the lowest absolute RWR, but also the lowest RWR relative to precipitation. This shows the non-linearity in the water balance known from other studies (Gunkel and Lange, 2012; Hartmann et al., 2014; Ries, 2016), where the share of evapotranspiration increases with aridity. However, data for evaluating these results for Wadi Qilt are missing. For water management, the inter-annual variability is relevant that is most obvious in the Wadi Auja data. Despite a relative high average of renewable water resources in this basin, very low amounts of water refresh the natural water resources in some years, which is neglected in the long term means normally used to calculate annual sustainable water yield of an area. On the

146 A. Gunkel, J. Lange Journal of Hydrology: Regional Studies 12 (2017) 136–149 other hand, extreme wet years as the 1991/92 season stress water infrastructure by delivering outstanding quantities of water (see Gunkel and Lange (2012) for a more detailed analysis of regional drought and flood conditions). Only a small part of the annual renewable water will run off as surface runoff. The major part that does not evaporate will percolate through the unsaturated soil zone and reach deeper layers. Subsequently, it can either reach deep groundwater or create spring flow, thereby possibly leaving the (surface) basin. Both aspects are not included in this study.

5.5. Implications

Conditions of data scarcity in the study area, efforts for obtaining and preparing data and computing time limit the applicability of hydrological models like TRAIN-ZIN. In this context, several possibilities for applying the Budyko framework exist and are explored in this study: Extrapolating of fitted ω values in space and time for subsequent estimates of annual renewable water resources is a useful approach in the sense of predictions in ungauged basins (Blöschl, 2013; Hrachowitz et al., 2013). Comparing literature values within the Budyko framework contributes to comparative hydrology (Wagener et al., 2007; Zhuo et al., 2015). The method can also be used to evaluate and compare results from model and other data sources to check their plausibility, similar to finding behavioural models (Schaefli et al., 2011). However, the issue of scale in Budyko should not be neglected. Although several authors state its applicability for lower temporal and spatial resolution (Yang 2008; Lu Zhang et al., 2008), it was originally developed for the large scale and annual means and its theoretical foundation for smaller scales requires further investigation. However, in (semi-)arid areas with their high spatial and temporal variability in the water balance, mean values are of limited informative value and in this study, data do not challenge the relation between energy and water input, as first postulated by Budyko, not even for high resolutions. The general assumption in Budyko type equations, steady-state conditions, is generally not problematic at mean annual scales, but requires neglecting inter- annual changes in soil storage for applications at sub-annual or inter-annual time scales (Greve et al., 2016). In the Eastern Mediterranean, inter-annual changes in soil storage are expected to the negligible due to the high evaporative demand and the dry summers (e.g. Ries et al., 2017; Ruiz-Sinoga et al., 2011).

6. Conclusions

Results of the hydrological model TRAIN-ZIN and of global data sets were used for applying a Budyko type approach in the water and data scarce Lower Jordan River basin. Differences in the input data influenced the results more as the spatial and temporal scales considered. High derivations from the original Budyko curve promote parametric approaches and a comparably low value of the Fu parameter ω points towards a low evaporation efficiency in the study area. Possible causes are relatively low water storage capacities, high intensity precipitation events and the seasonality of Mediterranean climate. Similar Fu curves are known from other dry regions of the world, however, relatively few studies explored the application of Budyko under conditions of water and data scarcity so far. Several beneficial aspects of the approach exist though, for example establishing long term water-energy balances for ungauged basins or investigating climate change effects. Limitations are mainly caused by the availability and reliability of input data. Since all data sets have their shortcomings, relying on a single data source, e.g. data derived from global data products like MODIS, is hazardous, and quality checks of input data should be mandatory. This is especially relevant since the non-linearity of processes in drier environment increases the sensitivity of runoff and water supply to precipitation uncertainties (Fekete et al., 2004; Vorosmarty, 2000). The influence of differences between ω values from various scales on estimations of renewable water resources is negligible compared to inter-annual variability. Consequently, the long term annual means derived are relatively stable, given the general high uncertainties in water assessment in the area. In the long term, about 30% of precipitation input is not evaporated, but inter-annual variability implies that the informative value of long term means is limited, since they neither represent flood nor drought conditions. Considering the very low runoff coefficients in the area, hydrological modelling should rather focus on evapotranspiration and groundwater recharge, its long term values and its variability, which are of interest for water management. The estimations of renewable water resources in this study are relevant in this regard, but must be supported in future studies. These should consolidate the first estimations of Fu parameters in the region from this study and should concentrate on annual scales relevant for water management. The limited informative value of single studies in the region and the urgent need for more measurements and new data sources, as it is known from other studies, is evident from the results of this study. However, with the relative stable Fu parameter estimates, this study fosters positive results for exploring an alternative approach towards stable estimates of natural water resources. It further illustrates the generally low efficiency of evapotranspiration as well as the great variability of estimates of renewable water resources around an average of approximately one third of precipitation.

Acknowledgments

We have to thank Sebastian Schmidt for providing data from his work on the Wadi Auja spring and Thorsten Wagener for ideas and comments that improved the manuscript considerably. We are also grateful to three anonymous reviewers for their helpful comments. The article processing charge was funded by the German Research Foundation (DFG) and the University of Freiburg in the funding programme Open Access Publishing.

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