Water balance of the Sudanese savannah woodland region

Abstract

The annual water balance for 39 grid cells covering the savannah woodland region of Sudan (10–16°N; 21–36°E) was determined and regional maps produced. Long-term (1961–1990) mean monthly climate data, National Forest Inventory data and Harmonized World Soil Database data for arenosols and vertisols, the two dominant soil types in the region, were used. Model validation was performed using daily data from a site in one of the grid cells and inter-annual (1961–1990) variation examined for another grid cell. Rainfall varied from 147 to 732 mm and only exceeded evapotranspiration for 18 of the grid cells, resulting in a small increase in soil moisture and runoff. Evapotranspiration accounted for, on average, 96% of rainfall and there was little difference between soil types. Drainage only occurred from AR soils and for four of the grid cells. Runoff varied from 0 to 89 mm for arenosols and from 0 to 109 mm for vertisols. The study provided useful insights into the spatial variability in water balance components across the region.

Editor D. Koutsoyiannis; Associate editor D. Gerten

Résumé

Le bilan hydrologique annuel de 39 cellules couvrant la région des savanes boisées du Soudan (10–16°N; 21–36°E) a été calculé et des cartes régionales ont été établies. Les données utilisées sont : les données climatiques mensuelles (1961–1990), les données des inventaires nationaux des forêts et la base harmonisée mondiale de données sur les sols pour les arénosols et les vertisols, les deux types de sols dominants de la région. La validation du modèle a été réalisée en utilisant les données journalières à partir d’un site de l’une des cellules de la grille et la variation inter-annuelle (1961–1990) observée pour une autre cellule de la grille. Les précipitations varient de 147 à 732 mm et dépassent l’évapotranspiration pour seulement 18 des cellules de la grille, ce qui entraîne une légère augmentation de l’humidité du sol et du ruissellement. L’évapotranspiration moyenne représente 96% des précipitations et il y a peu de différence entre les types de sols. Le drainage ne se produit qu’à partir des arénosols et pour seulement quatre des cellules de la grille. Le ruissellement varie de 0 à 89 mm pour les arénosols et de 0 à 109 mm pour les vertisols. L’étude a fourni d’utiles indications sur la variabilité spatiale des composantes du bilan hydrologique dans la région.

Key words:

• drylands
• evapotranspiration
• model validation
• savannah woodland
• Sudan
• water balance

Mots clefs:

• zones arides
• évapotranspiration
• validation du modèle
• savane boisée
• Soudan
• bilan hydrologique

1 INTRODUCTION

In arid and semi-arid regions (drylands), soil water availability is the main factor limiting plant growth, productivity and distribution (Fischer and Turner 1978, Webb et al. 1978, Stephenson 1990) and is strongly related to the amount of rainfall and evapotranspiration. Rainfall in dryland regions is not only low, but shows distinct seasonality and high spatial and temporal variation. The Sahel is currently experiencing a period of drought that began in the late 1960s (Le Houérou 1996), an increasing population growth and a decline in savannah woodland tree densities (Gonzalez 2001) threatening the health and livelihood of millions of people in the region.

Trees in the savannah woodlands of the Sahel are primarily Acacia species and occur as scattered individuals across the landscape (Griffith 1961, Bourliére and Hadley 1992). These trees protect against desertification and soil erosion, provide firewood, structural timber and non-timber products, and maintain habitats for plants, crops and animal production (Gonzalez 2001). Trees generally produce more litter and subsequently more soil organic matter than other types of vegetation, resulting in greater infiltration and retention of rainfall in the soil (Weltzin and Coughenour 1990, Githae et al. 2011). Planting trees in drylands can thus help restore degraded land and prevent desertification (FAO 2004). However, transpiration by the trees may exceed rainfall and so reduce the availability of soil water for growing crops and the flow of runoff to reservoirs (Malagnoux et al. 2007). Native trees are considered better than non-native species in this respect as they have been shown to conserve rather than deplete water resources (Ohte et al. 2003). Climate change in dryland regions may be expected to reduce tree densities and increase the extent of desertification (Hiernaux et al. 2009).

The water balance, in which rainfall is balanced against evapotranspiration, surface runoff, drainage and changes in soil water storage, is a useful way to assess and evaluate how rainfall is used in relation to soil type and vegetation. Evapotranspiration in arid and semi-arid regions is, by definition, greater than rainfall. Therefore, dryland regions are subject to a state of permanent evapotranspiration deficiency, a state to which native plants have adopted various strategies to allow them to cope (Fischer and Turner 1978). However, few water balance studies have been carried out for the savannah woodlands of the eastern Sahel region, an omission that is at least partly due to the lack of the necessary meteorological, vegetation and soil data.

In this paper we present the long-term (1961–1990) mean annual water balance for 39 grid cells covering the entire savannah woodland region of the Sudanese Sahel. This region is highly vulnerable to the availability of water resources (MEPD/HCENR 2003). The specific aims of the study were to determine how the water balance varies across the region in relation to rainfall, current woodland cover (above-ground biomass density) and soil type (arenosol vs vertisol). We hypothesized that evapotranspiration would be limited by the amount of rainfall and that soil moisture and runoff would be lower for sandy (AR) than for clay (VR) soils. A simple water balance model was used and maps of the resulting water balance components for the region produced using GIS mapping software. First, however, the model is described and validated using daily climate and soil moisture data that have been made available for a research site in one of the grids. As an example, the inter-annual variation in the water balance over the period 1961–1990 for one of the grid cells was also evaluated. The purpose of the study was to provide reference water balance information as part of a larger study dealing with carbon sequestration and impacts of climate change for the region (Alam and Starr 2013, Alam 2013, Alam et al. 2013).

2 MATERIALS AND METHODS

2.1 Study region and grid cells

This study was carried out for the savannah woodland region (10–16°N; 21–36°E), referred to as the Acacia gum belt, of the former Sudan (now the Republic of the Sudan) (Fig. 1). We modelled the water balance for 39 1.0° latitude × 1.5° longitude grid cells (Haberlah 2005) that cover most of the savannah woodland region in Sudan. This grid size was used because it corresponds to the scale (1:250 000) at which National Forest Inventory (NFI) data are available (Glen 1996, FNC/MAF/FAO 1998). The NFI data enabled the woodland biomass to be estimated, and this was used to scale the crop coefficient parameter for calculating grid cell evapotranspiration (see Sections 2.2 and 2.4). The total area covered by the 39 grid cells is 0.8 × 10⁶ km². The vegetation cover is savannah, mostly grasses with scattered shrubs and trees, the density of which generally increases southwards. Typical tree species present include Acacia senegal, A. raddiana, A. seyal and A. laeta, but species such as Commiphora africana occur, and woody shrubs, including Salvadora, Leptadenia and several species of Grewia, are also common (Griffith 1961, Obeid and Eldin 1970). The soils in the centre and west of the region are mainly sandy soils classified (FAO) as arenosols (AR, locally named “Qoz”), and those in the eastern part are mainly clay soils classified as vertisols (VR, locally named “Gradud”) (Ayoub 1998, FAO/IIASA/ISRIC/ISS-CAS/JRC 2009).

Fig. 1 Map shows administrative divisions (in bold letters) of Sudan and the 39 grid cells (1.0° latitude × 1.5° longitude) utilized in the study.

2.2 Water balance model description

A simple, single-layer, capacity type water balance model for freely draining soils, WATBAL (Starr 1999), was used to calculate the water balance for savannah woodland vegetation for each grid cell and soil type:

(1)

where P is rainfall, ET is actual evapotranspiration, R is surface runoff, D is drainage and ∆SM is the change in soil water storage; all units in mm. The model can be run at monthly or daily time steps and is based on that presented by Bonan (1989). It requires climate data (temperature, precipitation and cloud cover) and data for a limited number of site, stand and soil parameters. Importantly, the relatively simple data input requirements means that the model, unlike more sophisticated and data demanding models, can be widely applied, and such simple models are more suited to arid and semi-arid regions than to humid regions (Pilgrim et al. 1988). The availability of data, particularly regional data, in dryland Africa is limited. Calculation of the modelled water balance components is described below.

2.2.1 Evapotranspiration

The Jensen-Haise alfalfa radiation equation (Jensen et al. 1990) was used to calculate reference crop evapotranspiration (ET_o) values (mm):

(2)

where λ is the latent heat of vaporisation (MJ kg^-1) (= 2.501 – 0.002 361T), C_T and T_x are site-specific temperature constants (°C), T is the air temperature (°C), and R_s is the global radiation (MJ m^-2 per day or month) for the site. The two site-specific temperature constants C_T and T_x are calculated as follows:

(3)

(4)

where Elev is the elevation of the site (m a.s.l.); and e₁ and e₂ are the site saturation vapour pressure (e^o kPa) at the mean daily maximum and minimum air temperatures, respectively, for the long-term warmest month of the year. The vapour pressures e₁ and e₂ were calculated using the Teten equation:

(5)

If global radiation data are available, then the values can be entered directly into the Jensen-Haise crop reference equation above (equation (2)). However, long-term global radiation data are not widely available, particularly for Africa, and R_s was therefore calculated from extraterrestrial solar radiation, R_a, and cloud cover, C, using an empirical equation developed by Black (1956) based on data from 88 stations from around the world:

(6)

Solar radiation, R_a, was calculated from the solar constant, solar declination, latitude and sunrise/sunset hour angles for the centre of the grid cell and the time of year using the Milankovitch equation (e.g. Allen et al. 1998, equation 21). Note that in Black’s equation, R_s and R_a are expressed in units of cal cm^-2 d^-1 and so unit conversion of the resulting R_s values has to be carried out before use in the Jensen-Haise crop reference equation. For the monthly water balance model, which was used to calculate the long-term annual water balance for each grid cell in this study, a ‘representative-day-of-the-month’ approach was used to calculate monthly R_s values, i.e. R_s is calculated for the day representative of each month and then multiplied by the number of days in the month (Klein 1977).

The Jensen-Haise ET_o values were converted into ET values in two steps: (a) taking into account the differences in plant and vegetation cover characteristics between the reference crop, alfalfa, and the savannah woodland; and (b) taking into account the availability of soil water that may be needed to meet any transpiration demand in excess of rainfall. The influence of the difference in plant and vegetation cover characteristics is accounted for by using a crop coefficient (K_c) (Allen et al. 1998):

(7)

where ET_c is the evapotranspiration demand of the savannah woodland in each grid cell. The crop coefficient, K_c, is an empirical dimensionless value that integrates the differences in the morphological and physiological characteristics of the plant that affect transpiration: height, albedo, canopy resistance and evaporation from bare soil. In our water balance model, we also integrated the differences in vegetation cover among the grid cells by using woodland biomass density values (Mg ha^-1) to scale K_c (as described in Section 2.4).

The evapotranspiration demand (ET_c) is first met by the amount of effective rainfall, P_eff (described below), but if the demand is not satisfied by P_eff, then the unsatisfied part of the demand (ET_c*) is transferred to the store of available moisture in the soil. The amount of ET_c* that can then be satisfied by soil water (ET_SM) is a function of the amount of available soil moisture:

(8)

where SM is the available soil moisture content of the rooting zone (mm). The available soil moisture content is limited by the amount of water that can be held by the soil when at field capacity (SM_fc) and the amount of water that can be held when at permanent wilting point (SM_pwp). The withdrawal of available soil moisture first takes place at the ET_c* rate until a critical fraction of the available soil moisture content is reached (SM_crit); below this limit any further evapotranspiration demand on the soil moisture is met at a reduced rate (SM_rate) until the SM_pwp limit is reached. The SM_crit and SM_rate parameter values (0→1) depend on soil texture. That is, the fraction of the plant-available water capacity of the soil and the degree to which it can be used to meet the evapotranspiration demand are less in coarse textured soils than in finer textured soils.

The actual evapotranspiration term in the water balance equation, ET, is therefore calculated as:

(9)

(10)

2.2.2 Runoff

Rainfall in arid and semi-arid environments tends to occur in high-intensity events and can produce Hortonian overland runoff, even on coarse textured soils (Bryan and Yair 1982). Although this runoff may infiltrate the soil further down slope, or in more vegetated areas within a grid cell (Lesschen et al. 2009), we wished to include runoff (R) generation in the water balance calculations. To do this we used a simple rainfall–runoff threshold approach (Kirkby et al. 2005), in which runoff, R, is calculated as the amount of rainfall in excess of a threshold amount of rainfall (P_crit):

(11)

2.2.3 Drainage

Drainage, D, is the amount of water percolating from the soil layer of interest by gravity; that is, water held in the soil at tensions less than field capacity forms drainage and can contribute to groundwater recharge. Thus drainage only occurs when the soil moisture content is at or above field capacity (SM_fc):

(12)

where P_eff is the effective amount of rainfall (P_eff = P if P ≤ P_crit; P_eff = P – P_crit if P > P_crit). If the soil is not at field capacity, then water entering the soil recharges the soil moisture store.

2.2.4 Changes in soil moisture

Changes in soil moisture are simply calculated as the difference in the soil store of water between consecutive months (or days). Obviously, during a month, water may enter the soil and recharge the store only to be reused later on, resulting in no net change in soil moisture content at the end of the month.

2.3 Climate input data

The long-term water balance of each grid cell was calculated using long-term (1961–1990) monthly mean temperature (°C), precipitation (mm month^-1) and sunshine fraction (%) data generated for the centre of each grid cell. The climate estimator software tool, New_LocClim (FAO 2005, Grieser et al. 2006) was used to generate the data, including the long-term maximum and minimum air temperatures for the warmest month of the year. New_LocClim estimator was used in single point mode (grid cell centre) and Shepard’s inverse distance weighting interpolation method selected, which allows for up to 11 weather stations to be chosen for interpolation. Cloud cover in tenths was calculated from New_LocClim sunshine fraction values ((100 − sunshine fraction, %)/10).

For an assessment of the effects of inter-annual variation in climate on the water balance, the monthly water balance for one of the grid cells, Rashad, was determined for the 30-year period, 1961–1990. The Rashad grid cell was chosen because the long-term water balance had resulted in runoff, allowing us to assess the inter-annual variation in evapotranspiration, runoff and possibly also drainage components. In addition, it was one of eight grids selected for an assessment of climate change impacts on biomass and soil carbon (C) densities and evapotranspiration (Alam and Starr 2013). The climate data (monthly temperature, precipitation and cloud cover % for 1961–1990) were downloaded from the Climate Research Unit (CRU), University of East Anglia (CRU TS 2.1; Mitchell and Jones 2005). As the CRU TS 2.1 data are available in 0.5° × 0.5° grid cells, the data for the six CRU TS 2.1 grid cells corresponding to our 1° × 1.5° grid cell were averaged.

2.4 Model parameter values

The threshold value of rainfall at which surface runoff is generated (P_crit) was set at 140 mm per month in the case of AR soils and 130 mm per month in the case of VR soils. These values were established through adjustment and repeated runs of WATBAL and comparing the resulting annual runoff values with Budyko model values provided as additional information by New_LocClim and with values on a map of annual runoff for Africa produced using 1°  × 1° gridded data (Nicholson et al. 1997). The different P_crit values used for AR and VR soil types were used to reflect the difference in infiltration and permeability between the textures of these two soil types.

Grid cell crop coefficient, K_c, values were scaled to range between values of 0.6 and 1.0 for VR soils and between 0.4 and 0.8 for AR soils using grid cell tree biomass density values (Mg ha^-1) to reflect the density of vegetation cover and related variation in evapotranspiration. The grid cell tree biomass density values were derived from NFI stem volume (m³ ha^-1) data and wood density values (Alam et al. 2013). The NFI dataset is based on an inventory of 6160 plots (20 × 100 m) forming a 10 × 10 km grid south of latitude 16°N, but is only available as mean values for the national 1:250 000 maps corresponding to the 1.0° latitude × 1.5° longitude grid cells used in this study (Glen 1996, FNC/MAF/FAO 1998). While K_c values are available for food crops, they are rarely available for trees. Because of their interception capacity, trees tend to exhibit higher evapotranspiration rates than low crops, and K_c values for trees can therefore be expected to be >1, at least for forest/woodland with high stocking density and canopy cover. However, because of the open nature of savannah woodlands, K_c values can be expected to be relatively low, particularly on sandy soils where tree densities are less than on clay soils (Gaafar et al. 2006; Raddad et al. 2006). Various minimum and maximum values for setting the range of K_c were tested by comparing annual ET values with a map of ET for Africa presented in Nicholson et al. (1997) before deciding on the values given above. The K_c values used for each grid cell are presented in the Appendix (Table A1).

Grid cell mean values for the plant-available water storage capacity parameters SM_fc and SM_pwp for AR and VR soils were calculated from field capacity (θ_fc) and permanent wilting point (θ_pwp) volumetric moisture contents, soil bulk density and soil layer thickness values. Values for θ_fc and θ_pwp for each soil type were derived using soil texture data (% sand, % silt and % clay) and the pedotransfer function developed by Saxton et al. (1986). The soil texture and bulk density (g cm^-3) values for the 0–30 cm and 30–100 cm soil layers for the two soil types in each grid cell were extracted from the Harmonized World Soil Database, HWSD (FAO/IIASA/ISRIC/ISS-CAS/JRC 2009). The HWSD soil map and associated soil mapping unit (SMU) attribute database covering the study region were imported into ArcGIS (version 9.2) and cut into polygons corresponding to the 39 grid cells. Using ArcGIS, we were then able to determine the area and access the soil data for all the SMUs of the two soil types in each grid cell, and calculate area-weighted mean soil texture and bulk density values for the two soil layers and soil types for each grid cell. Using these area-weighted values, SM_fc and SM_pwp values for the two layers were calculated and then summed to give soil type values for the upper 1 m of soil for each grid cell (Appendix, Table A1). As some grid cells did not have mapped soil units for AR and VR (areas of these soil types too small to be mapped), these grid cells were given the mean soil type values calculated from those grid cells that did have values. This was done so as to give a uniform spatial distribution of grid cell values for subsequent interpolation and mapping of the water balance components (see Section 2.6). Calculating the grid cell water balance using a constant soil depth, and for both soil types, facilitates the harmonized comparison of the water balance across the region in relation to the two major soil types and climate. Values for soil water parameters, SM_crit and SM_rate, were taken from those presented in Zahner (1967). Accordingly, SM_crit and SM_rate values of 0.25 and 0.50, respectively, were used for AR, and a value of 0.67 for both SM_crit and SM_rate for VR.

In the study of the inter-annual variation in the water balance for the Rashad grid cell, the same values were used for the parameters P_crit, K_c, SM_fc, SM_pwp, SM_crit and SM_rate as for modelling the long-term mean water balance of the Rashad grid cell for each year of the 30-year period. While it can be assumed that the soil hydraulic parameters will not have changed over this period, forest cover (and therefore K_c) may have done. However, there are no relevant data available to enable changes in forest cover to be taken into account and, in any case, the intention was to assess the effects of variation in climate on the water balance and not changes in vegetation.

2.5 Model validation

As grid cell scale empirical data for parameterizing WATBAL are not available, we sought to demonstrate the conceptual and operational validity (Rykiel 1996) of the model by comparing daily WATBAL soil moisture simulations with empirical measurements of soil moisture data from Demokeya in northern Kordofan (13.3°N, 30.5°E). Validating the model by examining soil moisture is considered particularly suitable because soil moisture integrates the effects of the other components of the water balance.

The Demokeya site, which falls within the Al Obeid grid cell (Fig. 1), is characterized as a sparse Acacia savannah with a tree canopy cover of 5–10%. The soil type is an arenosol, with 60–70% coarse sand, 20–30% fine sand and a small amount of clay, and has a reported field capacity of 15% and a permanent wilting point of 5% (Ardö 2013). Soil moisture and meteorological data were collected at the site during the period 2002–2012 as part of a long-term savannah woodland ecosystem study (Ardö 2013). The available dataset includes daily rainfall (mm), air temperature (°C), incoming global radiation (W m^-2), and volumetric soil moisture content measured at depths of 5, 15, 30, 60 and 100 cm using time-domain reflectrometry (Ardö 2013). The volumetric soil moisture values for each of the five depths were multiplied by the thickness of the layer that they were taken to represent (0–10, 10–22.5, 22.5–45, 45–80 and 80–100 cm, respectively), summed and multiplied by 10 to give a depth of water in mm for the upper 1-m soil layer (SM in WATBAL). The global radiation data (converted into MJ m^-2 d^-1) were used directly in the Jensen-Haise ET equation. Because of gaps and errors in the original datasets, daily data for the two periods 1 February 2005–20 April 2007 and 6 July 2007–19 January 2010 were used for validating WATBAL. A daily P_crit value of 40 mm (the two days with rainfall >40 mm were assumed to have generated surface runoff), SM_fc and SM_pwp values of 150 and 50 mm, respectively (as reported by Ardö 2013), SM_crit and SM_rate values of 0.25 and 0.5, respectively (for sand textured soils), and a K_c value of 0.41 (for Al Obeid grid cell) were used.

2.6 Mapping of grid cell water balance components

Maps showing the long-term mean annual temperature (MAT), mean annual precipitation (MAP) and the annual water balance components, ET, surface runoff and drainage across the study region were made using the data attributed to the grid cell centre and ArcMAP software (version 9.3) with the kriging interpolation method.

3 RESULTS

3.1 Model validation

The modelled and measured values of daily soil moisture content of the 1-m soil layer at the Demokeya site for the two time periods are displayed as time series plots in Fig. 2. The results show that WATBAL captured well the dynamics and level of soil moisture during the two study periods. The measured and modelled values are plotted against each other in Fig. 3. The fitted linear regression line has a coefficient of determination (R²) value of 0.84 and index of agreement (D) value of 0.87 (Legates and McCabe 1999).

Fig. 2 Daily rainfall and measured (Ardö 2013) and modelled (WATBAL) soil moisture contents during two periods, 1/2/05–20/4/07 and 6/7/07–19/1/10, for the Demokeya site, in northern Kordofan (Al Obeid grid cell).

Fig. 3 Scatter plot of the measured (Ardö 2013) and modelled (WATBAL) soil moisture contents for 1/2/05–20/4/07 and 6/7/07–19/1/10 for the Demokeya site, in northern Kordofan (Al Obeid grid cell). Dotted line is the 1:1 line.

3.2 Long-term mean annual water balances

Grid cell specific MAT, MAP and annual values of the water balance components for AR and VR soil types are given in Table 1 and the water balance components as percentages of MAP in Fig. 4. Grid-cell MAP values varied from 147 mm (Khartoum) to 732 mm (Al Roseires) and MAT from 24.2°C (Zalingei) to 29.2°C (Khartoum). MAT values were highest in the northeast and central-southern area of the study region, and MAP increased southwards across the study region (Fig. 5).

Table 1 Long-term mean annual temperature (MAT), mean annual precipitation (MAP) and modelled (WATBAL) water balance components for AR and VR soil types for each grid cell (see Fig. 1).

Map sheet grid	MAT, °C	MAP, mm	ET, mm		Runoff, mm		Drainage, mm
			AR	VR	AR	VR	AR	VR
Aba Island	28.6	289	289	289	0	0	0	0
Abu Gabra	28.0	466	466	458	0	8	0	0
Abu Matariq	28.0	644	608	588	36	56	0	0
Abu Zabad	26.6	452	452	448	0	4	0	0
Abyad	26.0	273	273	273	0	0	0	0
Al Fasher	24.6	334	334	329	0	5	0	0
Al Gebelain	27.9	384	384	383	0	1	0	0
Al Geteina	29.0	209	209	209	0	0	0	0
Al Kamlin	28.6	215	215	215	0	0	0	0
Al Nahud	27.8	315	315	315	0	0	0	0
Al Obeid	27.2	301	301	301	0	0	0	0
Al Quleit	26.7	373	373	373	0	0	0	0
Al Renk	27.4	567	555	561	0	6	12	0
Al Roseires	27.6	732	652	669	33	63	47	0
Buram	28.2	718	633	613	85	105	0	0
Dar Al Humr	28.3	583	583	567	0	16	0	0
Gebel Al Deir	27.0	482	475	455	7	27	0	0
Gedaref	28.7	440	423	409	17	31	0	0
Geneina	26.1	456	414	400	42	56	0	0
Idd Al Ghanam	27.5	550	518	498	32	52	0	0
Kadugli	26.8	587	557	543	30	44	0	0
Kagmar	28.8	162	162	162	0	0	0	0
Kaja Seruj	27.0	250	250	250	0	0	0	0
Karkoj	27.4	542	536	524	6	18	0	0
Kereinik	24.5	475	446	426	29	49	0	0
Khartoum	29.2	147	147	147	0	0	0	0
Kubbum	25.6	636	479	527	89	109	68	0
Muglad	28.5	471	471	471	0	0	0	0
Nyala	24.4	414	402	392	12	22	0	0
Qala’a Al Nahal	28.6	683	598	578	85	105	0	0
Rashad	26.5	676	640	620	36	56	0	0
Reira	29.0	211	211	211	0	0	0	0
Sennar	28.8	440	434	424	6	16	0	0
Sodiri	26.9	185	185	185	0	0	0	0
Taweisha	27.4	356	356	356	0	0	0	0
Umm Badr	25.5	165	165	165	0	0	0	0
Umm Dafog	26.2	642	591	571	51	71	0	0
Wad Medani	28.5	302	302	302	0	0	0	0
Zalingei	24.2	595	515	499	76	96	4	0
Mean	27.3	429	408	403	17	26	3	0
Minimum	24.2	147	147	147	0	0	0	0
Maximum	29.2	732	652	669	89	109	68	0
Std. Deviation	1.4	172	151	147	27	35	13	0

Fig. 4 Grid cell modelled long-term annual water balance components as a percentage of mean annual precipitation (MAP) for AR and VR soil types. Grid cells are ranked according to MAP (increasing to the right).

Fig. 5 Map showing distribution of mean annual precipitation (MAP) and mean annual temperature (MAT) across the study region (see Fig. 1 for location of study region in Sudan).

Grid cell mean annual ET for AR soils averaged 408 mm (95% of MAP) and varied from 147 mm (Khartoum) to 652 mm (Al Roseires) (Table 1). For VR soils, grid cell annual ET averaged 403 mm (94% of MAP) and ranged from 147 mm (Khartoum) to 669 mm (Al Roseires). Since ET is strongly limited by MAP in arid and semi-arid environments, the maps of ET for AR and VR soil types strongly resembled each other, and values increased southwards across the study region (Fig. 6).

Fig. 6 Map showing distribution of annual ET for AR and VR soil types across the study region (see Fig. 1 for location of study region in Sudan).

Grid cell mean annual runoff (R) varied from 0 to 89 mm (Kubbum) for AR soils and from 0 to 109 mm (Kubbum) for VR (Table 1). Annual runoff averaged across the region was 17 mm for AR and 26 mm for VR, corresponding to 4% and 6% of MAP respectively. For VR soils, runoff was produced on 23 of the grid cells, but only 17 of the grid cells in the case of AR. Runoff generally increased southwards across the study region, but was clearly greater in the southwestern and eastern areas than in the south-central area (Fig. 7).

Fig. 7 Map showing distribution of annual runoff for AR and VR soil types across the study region (see Fig. 1 for location of study region in Sudan).

Fig. 8 Map showing distribution of annual drainage for AR soil type across the study region (see Fig. 1 for location of study region in Sudan).

No drainage (D) was produced from VR soils for any of the grid cells and drainage from AR soils only occurred for four of the grid cells (Table 1). The highest annual drainage value was 68 mm (Kubbum), corresponding to 1% of MAP. The grid cells that produced drainage values for AR soils were located in the southeastern and western areas of the study region (Fig. 8).

3.3 Water balance inter-annual variation

The annual water balance components over the 30-year period 1961–1990 for the Rashad grid cell are presented in Fig. 9 and Table 2. Annual rainfall ranged from 339 (1984) to 970 mm (1963), with a coefficient of variation (CV) of 20% (Table 2), and generally declined over the 30-year period (Fig. 9). The annual mean temperature ranged from 26.2 (1961) to 28.8°C (1987), with a CV of 2.8%, and increased over the period. Of the water balance components, ET showed the least inter-annual variation (CV: 13%) and no trend. Surface runoff showed the most inter-annual variation (CV: 92% for arenosols, 81% for vertisols), being zero in very dry years for both soil types. The inter-annual variation in drainage (percolation below 1 m) was relatively small for AR and large for VR (Table 2), but was zero in the driest years for both soil types. The mean end-of-month plant-available moisture content of the soil (SM – SM_pwp) was generally higher for vertisols than for arenosols, but the inter-annual variation was similar for both soil types.

Table 2 Descriptive statistics of annual rainfall, temperature and WATBAL modelled water balance components for AR and VR soil types for the Rashad grid cell (11.5°N, 30.75°E) during 1961–1990.

	Rainfall	Temp.	Arenosols (mm)				Vertisols (mm)
	(mm)	(°C)	ET	Runoff	Drainage	SM^a	ET	Runoff	Drainage	SM
Minimum	339	26.2	297	0	0	1	343	0	0	0
Maximum	970	28.8	509	229	291	34	677	260	139	49
Mean	654	27.3	396	68	189	26	519	89	47	37
Coefficient of variation, %	20	3	13	92	36	23	13	81	77	29

^aSM = end-of-month mean plant-available soil moisture content of upper 1 m soil.

Fig. 9 Annual rainfall and WATBAL modelled water balance components for AR and VR soil types for the Rashad grid cell (11.5°N, 30.75°E) during 1961–1990. Mean annual temperatures (MAT, °C) during the same period are given on the secondary y-axis.

3.4 Grid cell long-term mean monthly water balances

The monthly water balance averaged over the 39 grid cells is presented separately for AR and VR soil types in Fig. 10. The rainy season occurred between May and October; outside this period, rainfall was negligible. Rainfall was high enough for the soil to be recharged during the period July–January for AR soils (totalling 63 mm) but for a shorter period (July–October) for VR soils (totalling 6 mm); otherwise soil water contents at the end of the month were reduced to permanent wilting point values. However, there was a soil water deficit (SM_fc – SM) for each month, averaging 69 mm for AR soils and 133 mm for VR soils, which reflected a monthly evapotranspiration deficit (ET_c – ET) averaging 217 mm for both soil types. Surface runoff was generated during July and August for both soil types when rainfall was the highest and above P_crit values, and drainage (percolation below 1 m) occurred during August and September, but only for AR soils. There was still soil moisture available to plants at the end of the month from July–October in the case of vertisols; for arenosols there were greater amounts that were available for longer. The greater soil moisture levels in the AR soils enabled greater ET during September and October compared to VR.

Fig. 10 Grid cell mean (n = 39) monthly water balances for AR and VR soil types.

4 DISCUSSION

Water scarcity in African drylands is projected to increase over time due to increasing population and changes in climate, land use and land cover (Hassan et al. 2005). A simple water balance model, such as described in this study, can be used for assessing how these factors are related and interact, and for planning mitigation against water scarcity. Unfortunately, appropriate climate data, particularly global radiation and evapotranspiration, and hydrological data (runoff, soil moisture) for running, validating and calibrating such models are rarely available for Africa. However, the soil hydraulic property and crop coefficient values used for the water balance modelling of each grid cell were derived using an objective methodology and based on HWSD soil data (FAO/IIASA/ISRIC/ISS-CAS/JRC 2009) and woodland inventory (FNC/MAF/FAO 1998) data. The input climate data generated from New_LocClim are also based on an extensive database of meteorological observations (FAO 2005). While perhaps not the best-performing method, the Jensen-Haise crop reference evapotranspiration equation has been shown to give reasonably accurate results compared to the FAO Penman-Monteith standard method and to have the advantage of requiring limited input data (Jensen et al. 1990). Nowadays, models using remote sensing techniques and data, such as the Surface Energy Balance Algorithm for Land (SEBAL) (Bastiaanssen et al. 2005), can be used to estimate the spatial and temporal variation in ET for use in water balance calculations. However, using such methods was beyond the scope of this study. Furthermore, the results of the model verification using the detailed and daily data from the Demokeya site demonstrated both the conceptual and operational validity of the model (Rykiel 1996) and its suitability for calculating the water balance of the grid cells. Undoubtedly, a better fit to the Demokeya measured soil moisture data could have been achieved through calibration of the soil water holding parameters. At least the SM_pwp (parameter value, based on the permanent wilting-point moisture content reported by Ardö (2013), appears to be too low (~10 mm) according to modelled soil moisture values. Nevertheless, given the availability of data for the region, we consider that the results from WATBAL are both reasonable, useful and fit for purpose.

The grid cell water balance results were characterized by evapotranspiration that was equal or almost equal to rainfall. As a result, soil moisture contents were brought close to permanent wilting point most of the time, with runoff and drainage only occurring for grid cells receiving the highest rainfall. Our regional map of annual ET values showed good agreement with that presented by Nicholson et al. (1997) for the same region and grid cell, and the values were strongly correlated with Bodyko ET values produced by New_LocClim (r = 0.91 for both soil types). Evapotranspiration accounted for 75–100% of grid-cell MAP for AR soils and for 83–100% of grid cell MAP for VR soils. While vertisols clearly had larger available soil moisture storage capacities (SM_fc – SM_pwp) than arenosols ( = 134 mm for VR and 74 mm for AR), the generally equal or slightly lower annual ET values for vertisols can be attributed to the fact that proportionally more of the available soil water is held at greater tensions in clay (fine texture) than in sandy (coarse texture) soils. Also, infiltration during wet periods can be expected to be less for vertisols than for arenosols, because of low conductivity rates of clay and closure of cracks formed during dry periods. These differences in soil properties also explain why grid cell runoff is greater and drainage lower for vertisols than for arenosols. The parallel relationship between monthly ET and rainfall for both soil types clearly shows that ET in dryland environments is mainly determined by the amount of rainfall, and vegetation cover and soil type have little influence.

Evapotranspiration consists of interception, transpiration and evaporation from the soil. These separate components of ET are difficult to model without detailed data and complex modelling, and are not separated in WATBAL. Interception losses in dryland environments may be relatively more important than in humid environments, but it is highly variable and depends on rainfall intensity and duration, and canopy cover characteristics (Dunkerley 2000). Wilcox et al. (2003) reported interception losses from rangeland (dryland) ecosystems in North America of between 1% and 80% of the annual water budget, but they were generally between 20% and 40%. Depending on the extent of bare soil, evaporation from bare soil can account for a significant proportion of ET in arid and semi-arid regions (Wilcox et al. 2003). Other studies, however, suggest that bare soil evaporation in dryland environments soon becomes negligible after rainfall (Williams and Albertson 2005).

We used a single K_c value based on grid cell mean tree biomass densities derived from forest inventory data to convert reference crop evapotranspiration (ET_o) values into potential ET values appropriate for the tree cover present. While some savannah woodland species are evergreen, others shed their leaves during the dry season so that canopy cover varies during the year (Murphy and Lugo 1986, Sarmiento and Monasterio 1992, Timberlake et al. 2010). Changes in canopy cover may therefore be expected to affect ET, and using K_c values that change during the season in response to changes in canopy cover may be expected to produce more reliable ET estimates (Allen et al. 1998). We tested the effect of using seasonal K_c values by varying monthly K_c from 25% (during dry periods when deciduous species would have shed their leaves) to 100% (during wet periods when canopy would be at maximum cover) of the fixed K_c value for the Khartoum grid cell (low MAP) and the Rashad grid cell (relatively high MAP). The results showed that there was no difference in the annual ET (also runoff and drainage) values for the two grid cells using seasonal and fixed K_c values.

The plant-available soil moisture was calculated for the 1-m layer, this being the depth to which soil data were available. While the maximum depth of the tree roots in drylands may exceed 1 m (Canadell et al. 1996), and so increase the amount of available water for evapotranspiration (Zhang et al. 2001), studies have found that different types of dryland vegetation cover (varying combinations of grass and wood) have little or no significant effect on water use (Kabat et al. 1997, Williams and Albertson 2005). This is further confirmation that ET in dryland regions is limited by rainfall rather than by the characteristics of the vegetation and availability of soil water. That there is plant-available water at the end of some months, particularly in the case of AR soils, suggests that biomass production could potentially be increased during these months.

Savannah woodlands have canopies that are sparse and of mixed species, and a ground cover that is heterogeneous (grass and bare soil). This makes modelling infiltration, surface runoff and evapotranspiration in drylands difficult (Wallace et al. 1991). This difficulty is further increased by the stripped pattern of vegetation cover typical of drylands and its effects on runoff and run-on (Cornet et al. 1992, Dunkerley 2002), and by the soil crusting and sealing formed by the impact of rain drops during heavy rainfall events (Abu-Awwad 1997, Francis et al. 2007). Grid cell annual runoff accounted for up to 17% of MAP on VR soils and for up to 14% on AR soils, and was strongly correlated with the Bodyko runoff values produced by New_LocClim (r = 0.77 for AR and 0.83 for VR soils). Our regional map of annual runoff was also in good agreement with the high-resolution map of annual runoff for the region presented in Nicholson et al. (1997). The WATBAL model uses a simple rainfall threshold approach to allocate an amount of rainfall to surface runoff. A more sophisticated approach to model surface runoff production based on rainfall amount, and distribution and surface morphology, such as described by Kirkby et al. (2005), could be expected to improve the estimation of runoff.

Groundwater recharge is generally very small in drylands, commonly only a few millimetres or less per year (Wilcox et al. 2003). Across our study region, drainage from below 1 m depth only occurred for AR soils and then only from four of the grid cells. Drainage from VR soils was zero across the entire region. Although vertisols develop cracks, which would allow for greater infiltration than their soil texture suggests, these cracks only develop during prolonged dry periods and close during wet periods. Thus, contrary to what is reported by many researchers, there is no deep drainage from these soils as a result of cracking (Abdelhadi et al. 2000). Thus, the cracks are assumed to be closed when the monthly rainfall is at P_crit values, the rainfall amount at which surface runoff is generated in WATBAL.

The variation in water balance components, exemplified by the Rashad grid cell, showed that ET had the lowest inter-annual variation and runoff the greatest. Evapotranspiration is known to be conservative and to show relatively little inter-annual variation because it is primarily driven by radiation, which does not vary greatly from year to year. The inter-annual variation in plant-available soil moisture content was also relatively low and similar for both soil types. However, the inter-annual variation in drainage did differ considerably between the two soil types, with the VR soils showing greater inter-annual variation than the AR soils. The greatest inter-annual variation was in runoff. Relatively small differences in rainfall therefore have a significant impact on runoff and formation of wadis across the region. Climate change is generally expected to increase the inter-annual variation in the water balance (Huntington 2006), posing a considerable challenge to water security in drylands.

5 CONCLUSIONS

Using a simple monthly water balance model, a programme for generating long-term climate data for any location, National Forest Inventory data, and soils data from a global database we were able to produce reliable and harmonized annual and monthly water balances for 39 1° × 1.5° grid cells covering the savannah woodland region of Sudan and for the two dominating soil types, arenosols and vertisols. The water balances provide useful insights into the spatial variability in evapotranspiration, runoff, drainage and changes in soil moisture across the region. The need for more empirical meteorological, hydrological and soil studies and data in the region is emphasized.

Disclosure statement

No potential conflict of interest was reported by the authors.

APPENDIX

Table A1 WATBAL parameter values for each grid cell (see Fig. 1 for location of study region in Sudan).

Map sheet	Map sheet centre		Elevation (m a.s.l.)	Tmax^(a) (°C)	Tmin^(b) (°C)	Arenosols			Vertisols
	Lat. °N	Long. °E				Kc^(c)	SMfc^(d) (mm)	SMpwp^(e) (mm)	Kc	SMfc(mm)	SMpwp(mm)
Aba Island	135	32.25	380	41.1	24.8	0.5	133	59	0.7	451	317
Abu Gabra	115	26.25	440	39.8	24.7	0.5	132	59	0.7	451	317
Abu Matariq	105	26.25	440	38.9	24.2	0.7	132	58	0.9	451	317
Abu Zabad	125	29.25	580	38.9	23.8	0.5	134	59	0.7	451	317
Abyad	135	26.25	740	38.6	23.2	0.4	132	58	0.6	451	317
Al Fasher	135	24.75	900	36.6	21.3	0.6	132	58	0.8	451	317
Al Gebelain	125	32.25	400	39.9	24.9	0.4	133	59	0.6	451	317
Al Geteina	145	32.25	360	41.4	24.6	0.5	133	59	0.7	451	317
Al Kamlin	155	33.75	460	42.1	24.1	0.4	131	57	0.6	451	317
Al Nahud	125	27.75	520	39.6	24.3	0.4	134	60	0.6	452	317
Al Obeid	135	30.75	580	39.5	24.6	0.4	133	59	0.6	451	317
Al Quleit	135	29.25	620	39.3	23.8	0.4	133	59	0.6	452	317
Al Renk	115	32.25	400	38.0	24.0	0.5	131	57	0.7	451	317
Al Roseires	115	33.75	540	39.3	22.2	0.6	132	59	0.8	453	319
Buram	105	24.75	480	38.3	25.7	0.8	131	57	1.0	451	317
Dar Al Humr	105	27.75	440	39.6	24.3	0.6	132	58	0.8	451	317
Gebel Al Deir	125	30.75	540	38.8	24.1	0.5	132	59	0.7	451	317
Gedaref	145	35.25	560	40.8	25.2	0.5	132	59	0.7	451	317
Geneina	135	21.75	780	38.5	22.3	0.5	133	60	0.7	450	318
Idd Al Ghanam	115	24.75	580	38.7	24.3	0.6	131	57	0.8	451	317
Kadugli	115	29.25	640	38.6	23.9	0.5	137	62	0.7	451	317
Kagmar	145	30.75	440	40.5	24.8	0.4	131	58	0.6	452	317
Kaja Seruj	135	27.75	600	39.7	23.3	0.4	133	59	0.6	452	317
Karkoj	125	33.75	460	40.8	22.8	0.7	132	59	0.9	451	317
Kereinik	135	23.25	880	38.2	19.0	0.6	131	57	0.8	452	317
Khartoum	155	32.25	400	41.6	25.8	0.4	132	58	0.6	451	317
Kubbum	115	23.25	640	37.3	21.2	0.7	133	59	0.9	451	318
Muglad	115	27.75	440	39.4	25.8	0.5	133	59	0.7	451	317
Nyala	125	24.75	900	36.1	19.7	0.5	132	58	0.7	451	317
Qala’a Al Nahal	135	35.25	540	40.3	24.7	0.5	132	59	0.7	451	317
Rashad	115	30.75	660	38.2	23.5	0.6	131	57	0.8	451	317
Reira	155	35.25	440	42.2	24.6	0.4	131	57	0.6	451	317
Sennar	135	33.75	400	41.0	21.9	0.5	132	59	0.7	451	317
Sodiri	145	29.25	520	40.8	24.3	0.4	132	58	0.6	452	317
Taweisha	125	26.25	560	39.7	23.9	0.4	132	58	0.6	451	317
Umm Badr	145	27.75	740	36.9	22.9	0.4	132	58	0.6	452	317
Umm Dafog	105	23.25	520	37.5	22.3	0.8	137	63	1.0	451	318
Wad Medani	145	33.75	420	41.6	24.3	0.5	132	59	0.7	451	317
Zalingei	125	23.25	840	38.2	18.4	0.6	131	57	0.8	451	316
Mean	129	29.06	558	39.4	23.5	0.5	132	59	0.7	451	317
Minimum	105	21.75	360	36.1	18.4	0.4	131	57	0.6	450	316
Maximum	155	35.25	900	42.2	25.8	0.8	137	63	1.0	453	319

^{(a) & (b)} Long-term air maximum and minimum temperatures for the warmest month of the year;

^(c) Crop coefficient values are calculated based on the grid cell biomass carbon densities;

^(d) Soil moisture content at field capacity;

^(e) Soil moisture content at permanent wilting point.