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Journal of Hydrology: Regional Studies

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

Reconstructing hydro-climatological data using dynamicaldownscaling of reanalysis products in data-sparse regions –Application to the Limpopo catchment in southern Africa

Ditiro B. Moalafhia, Ashish Sharmab,⁎, Jason P. Evansc

a Department of Environmental Science, University of Botswana, Gaborone, Botswanab School of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW, Australiac Climate Change Research Centre, University of New South Wales, Sydney, Australia

A R T I C L E I N F O

Keywords:ReanalysesDynamical downscalingHydrological applicationsLimpopo basinSouthern Africa

A B S T R A C T

This study is conducted over the data-poor Limpopo basin centered over southern Africa usingreanalysis downscaled to useful resolution.

Reanalysis products are of limited value in hydrological applications due to the coarse spatialscales they are available at. Dynamical downscaling of these products over a domain of interestoffers a means to convert them to finer spatial scales in a dynamically consistent manner.Additionally, this downscaling also offers a way to resolve dominantatmospheric processes,leading to improved accuracy in the atmospheric variables derived. This study thus evaluateshigh-resolution downscaling of an objectively chosen reanalysis (ERA-I) over the Limpopo basinusing Weather Research and Forecasting (WRF) as a regional climate model.

The model generally under-estimates temperature and over-estimates precipitation over thebasin, although reasonably consistent with observations. The model does well in simulatingobserved sustained hydrological extremes as assessed using the Standardized Precipitation Index(SPI) although it consistently under-estimates the severity ofmoisture deficit for the wettest partof the year during the dry years. The basin's aridity index (I) is above the severe droughtthreshold during summer and is more severe in autumn. This practically restricts rain-fed agri-culture to around 3 months in a year over the basin. This study presents possible beneficial use ofthe downscaled simulations foroptimal hydrologic design and water resources planning in datascarce parts of the world.

1. Introduction

Africa is a data-poor continent, with significant gaps characterizing the rainfall and streamflow records across its major riverbasins. While a regional reanalysis for the continent offers an excellent means of addressing this limitation, computational expenseand lack of high quality ground observations make this a difficult task. An alternative to this is the dynamical downscaling of coarserscale reanalyzed datasets to interpolate it to finer spatial scales that are relevant to hydrological studies. We investigate here theviability of such an approach for hydrological applications with reference to the Limpopo catchment of southern Africa.

The Limpopo basin (Fig. 1), which covers an area of approximately 412 938 km2, falls within four countries: Botswana, Mo-zambique, South Africa and Zimbabwe. The basin has a diverse water use in which its middle to lower parts are dominated by

http://dx.doi.org/10.1016/j.ejrh.2017.07.001Received 15 June 2016; Received in revised form 24 March 2017; Accepted 4 July 2017

⁎ Corresponding author.E-mail address: a.sharma@unsw.edu.au (A. Sharma).

Journal of Hydrology: Regional Studies 12 (2017) 378–395

Available online 18 July 20172214-5818/ © 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/).

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agriculture while the upper parts are dominated by urban, industrial and mining water use sectors. The major urban centres for thecountries that make up the basin are situated either within or in the vicinity of the headwaters. A significant percent of the populationis rural and poor and hence socio-economically challenged (FAO, 2004). The basin has characteristic recurrent droughts that havesocio-economic implications on its resident population. The characteristically unreliable low rainfall accompanied with high eva-poration rates makes water availability an ever present challenge. Also, water abstraction rates over most of the sub-basins of theLimpopo are increasing and becoming unsustainably high as population continues to grow. As a consequence, a number of inter-basinwater transfer schemes (at potentially high costs and with politically risky debates for buy-ins from all concerned parties) continue todominate Southern African Development Community (SADC) forums facilitated through the regional bloc’s protocol on shared riversystems. Although reasonable efforts are being made to address the relatively severe water shortage in the Limpopo River Basinthrough such schemes, water demand management is being promoted over water supply management. A common need for opti-mizing such schemes is the availability of spatio-temporal hydrologic data records, which are of poor quality and coverage for thebasin, consistent with similar issues in many African catchments.

The present study assesses the possibility of using dynamical downscaling of selected reanalysis products as a means of for-mulating climate and hydrologic records over data sparse regions such as the Limpopo. Reanalysis is described as a climate orweather model simulation of the past that includes data assimilation of historical observations (Bengtsson et al., 2007). The use ofreanalysis products has increasingly been used in the field of climate research due, in part, to the lack of globally and temporallycomplete direct observations (Qian et al., 2006; Zhang et al., 2013). Reanalysis products have been used to drive land surface models,study the climate system and provide lateral boundary forcing for regional climate models (Decker et al., 2012). Although reanalysesuse some common station data, the products differ in various ways. They use different vertical and horizontal resolutions, dataassimilation methods, physical parameterizations and sea surface temperature prescriptions for boundary conditions. Mesinger et al.(2006) and Kanamitsu and Kanamaru (2007) argue that global reanalysis products can be usefully downscaled to provide greaterregional detail. A RCM with a relatively high fidelity is a useful tool in describing regional scale climate conditions and in producinghigh-resolution meteorological data (Bastola and Misra, 2014). The choice of which reanalysis to use has been left to the convenienceof individuals’ and their research team’s preferences and familiarity. This could then result in less than optimum meteorologicalforcing that may be limited in resolving the complex inter-play between processes at basin scale. The resultant inaccuracies willsubsequently propagate through any applications of the downscaled products and have consequences for water resources planning.Therefore, to use the high-resolution climate model simulations for hydrological and related enterprises, the global reanalysis beingdownscaled should have been carefully chosen to make sure that the most accurate lateral boundary conditions (LBCs) are used.Although improved simulations depend on various factors, starting with the most accurate LBCs is the first step in the right direction.This is desired for sustainable development of water resources where reliable and high resolution hydro-climatic data are necessaryfor making optimal decisions and planning.

Use of reliable, skillful and high resolution data at basin scale cannot be overemphasized for semi-arid regions where under-standing the interplay of dynamic hydrologic processes continues to present a challenging task. Precipitation over semi-arid southernAfrica, for example, exhibits significant inter-annual variations with frequent droughts. Cyclones that bring intense rainfall, and oftenassociated floods, are increasingly common over the area. Droughts and floods account for 80% of loss of life and 70% of economiclosses that are linked to natural hazards in Sub-Saharan Africa (Vicente-Serrano et al., 2012; World Bank, 2010). Persistent droughtconditions are found to be the most significant climate influence on GDP per capita growth across the African continent (Brown et al.,2011).

This study undertakes a high resolution (10 km) downscaling of European Centre for Medium-Range Forecasts Reanalysis Interim(ERA-I) which is one of the two (2) reanalysis datasets that were recommended for the same domain using a 4-D evaluation of

Fig. 1. Elevation (m) of (a) all domains of the simulation, and (b) Limpopo basin within the inner domain.

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relevant lateral boundary condition (LBCs) fields at the same boundaries of the RCM (Moalafhi et al., 2016a). The ability of RCMs toreproduce observed characteristics has improved significantly over the years, but the use of output from RCMs could be limited whenthere are some systematic errors in global reanalysis LBC fields (Frei et al., 2003; Hagemann et al., 2004; Mooney et al., 2011;Moalafhi et al., 2016b). Since systematic biases for the current climate are unavoidable in GCMs/global reanalyses (Laprise et al.,2013), caution has to be taken to avoid propagating the biases through the downscaling process with far reaching implications on thesimulation products and any subsequent applications (Mehrotra and Sharma, 2015). Alternatively, biases of the downscaled productscan be corrected prior to use in hydrological studies. In this study, the reanalysis with the most accurate LBCs at the intendedboundaries of a RCM was taken as a cheaper option of reducing the biases without prior correction before downscaling. The studytakes advantage of dynamical downscaling that continues to be of help in converting reanalysis products to finer scales that are oftenrequired (Xu, 1999; Wilby et al., 2000; Fowler et al., 2007; Bastola and Misra, 2014; Wood et al., 2004; Rocheta et al., 2014). Anattempt is also made to demonstrate the usefulness of the resultant simulation products (temperature and precipitation) throughhydrological applications using the World Meteorological Organization (WMO)’s recommended Standardized Precipitation Index(SPI) and the aridity index (I) for analyzing droughts.

2. Methods and data

2.1. WRF-RCM design

The study uses a thirty-year regional simulation (1980–2010) made using the non-hydrostatic Weather Research and ForecastingWRF (ARW) model, version 3.6 (Skamarock et al., 2008). The WRF domain considered is centered over southern Africa (Fig. 1). Theinner domain uses a horizontal grid spacing of 10 km, and the outer domain a spacing of 50 km. Thirty Vertical levels were used inboth domains. During analysis, the first year of the simulations was discarded as model spin-up and 10 grid points along the boundaryof the inner domain left out as the relaxation zone. Initial and lateral conditions for the outer domain were derived from the ERA-Interim reanalysis. The lateral boundary conditions and sea surface temperature were both updated every 6 h using the reanalysisforcing. The ERA-I reanalysis is used following its overall best performance and recommendation over a southern African domaincovering the Limpopo basin (Moalafhi et al., 2016b).

Based on various studies using WRF as a regional climate model in Australia (Evans and McCabe, 2010) and southern Africa(Crétat et al., 2011; Boulard et al., 2012; Pohl et al., 2014; Ratna et al., 2013), WRF physical parameterizations adopted were: Single-Moment 5-class microphysics scheme; Rapid Radiative Transfer Model (RRTM) longwave radiation scheme; Dudhia shortwave ra-diation scheme; Yonsei University planetary boundary layer scheme; Betts-Miller-Janjic cumulus parameterization scheme and Noahland-surface scheme.

2.2. Observational datasets

The simulations are analyzed with regard to monthly near-surface temperature and precipitation fields from four (4) griddedobservational datasets (herein referred to as observations). For temperature, University of Delaware (UD) and the Climate AnomalyMonitoring System (GHCN_CAMS) datasets are considered while the University of Delaware (UD), Global Precipitation ClimatologyProject (GPCP), and Global Historical Climatology Network and The Climate Prediction Center (CPC) Merged Analysis ofPrecipitation (CMAP) are considered for precipitation. All four (4) data sets are available from NOAA/OAR/ESRL PSD, Boulder,Colorado, USA, from their Web site at http://www.esrl.noaa.gov/psd/.

The University of Delaware (UD) dataset, which was developed by compiling together data from a large number of stations bothfrom the Global Historical Climate Network (GHCN2), the Global Synoptic Climatology Network, the Global Summary of the Day(GSOD) from NCDC and the archives of Legates and Willmott monthly and annual station records (Legates and Willmott 1990a,1990b), covers the years 1900–2010 at grid resolution of 0.50 × 0.50. This dataset has received a wide applicability by the researchcommunity (Hao et al., 2013; Rawlins et al., 2012; Sheffield et al., 2012). The GHCN_CAMS temperature dataset is a combination oftwo large individual data sets of station observations collected from the Global Historical Climatology Network version 2 and theClimate Anomaly Monitoring System (GHCN + CAMS). The dataset, which is credited for its use of some unique interpolationmethods (Fan and van den Dool, 2008), is available at 0.50 by 0.50 grid resolutions from 1948 to April 2015. The Climate PredictionCenter (CPC) Merged Analysis of Precipitation (CMAP; Xie and Arkin, 1997), which has also been investigated over Africa (Lélé et al.,2015), is a monthly dataset consisting of monthly averaged precipitation rates obtained by merging gauge observations, estimatesinferred from a variety of satellite observations, and the NCEP–NCAR reanalysis. The data is on a 2.5° by 2.5° grid resolution andcovers the period from 1979 to present. The GPCP dataset is probably the most commonly used dataset for global precipitation,including use in climate and hydrology related studies over southern Africa (Crétat et al., 2011; Boulard et al., 2012; Pohl et al.,2014). The dataset was developed by merging rain gauge, satellites, and sounding observation data to estimate monthly rainfall on a2.50 by 2.50 grid resolution from 1979 to present (Adler et al., 2003). The observations were interpolated to the 0.0880 (about 10 km)common grid resolution of the downscaled products (i.e., WRF simulations).

2.3. Analysis and data handling

Error statistics based on mean bias, RMSE and temporal correlation are quantified both annually and seasonally. In an attempt toaccount for uncertainties among the different gridded observations considered, the Observational Range Adjusted (ORA)

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computation of error statistics is adopted to evaluate the model performance against all observational datasets collectively (Evanset al., 2015). This method considers the model to have no error when it falls within the range of the observational datasets. When themodel is outside this range the error is the difference between the model and the nearest observation. This is achieved by creating apseudo-observational time series which equals the model value when the model falls within the observational range, and takes themaximum or minimum observation value when the model falls above or below the observational range respectively. This approachuses all available gridded observational datasets by putting them together into a single pseudo-observation time series. By doing this,the levels of uncertainty among the different gridded observational datasets are reduced. Since when the simulation result falls withinthe range of observations the pseudo-observation time series matches the simulation perfectly (there is no error), the ORA corre-lations are higher than correlations with any one observational dataset. Indeed, if the simulation always falls within the observationalrange (that is, it cannot be distinguished from the observations) it will receive a correlation of 1 even though it does not match any ofthe observational datasets perfectly. However, if one of the observational datasets is always higher than the others and the simulationis always higher than this dataset then the correlation will be exactly the correlation with this highest dataset. The pseudo-ob-servation series, ObsORA, can be represented by;

ObsORA = Model if Obsmin ≤ Model≤ Obsmax

ObsORA = Obsmin if Model < Obsmin

ObsORA = Obsmax if Model > Obsmax (1)

where ObsORA is the Observational Adjusted Range (ORA) valueObsmin is the minimum value from all the observationsObsmax is the maximum value from all the observationsModel is the model valueThe ORA adjusted values are then used in computations of error statistics. The differences of the means between the model and

the ORA pseudo-observation series is given by Mean Bias as

−M ObsORA (2)

where M is model averaged temperature or precipitation and ObsORA is averaged observed temperature or precipitation.The RMSE is calculated as

∑= ⎛

⎝⎜ − ⎞

⎠⎟

=

RMSEn

M Obs1 ( )i

n

i ORA i1

2

(3)

where n is the number of time steps, ObsORAi and Mi are the observations and model product values respectively for time i = 1,…,n.Temporal correlation coefficient is used to evaluate the goodness-of-fit by performing linear regression between observational

range adjusted (ORA) and models’ temperature or precipitation.

∑∑ ∑

=− −

− −=r

Obs Obs M M

Obs Obs M M

( )( )

( ) ( )i

nORA ORA i

i

nORA ORA i

ni

1

2 2

i

i (4)

where ObsORA and M are observational range adjusted (ORA) and model mean values respectively.The analysis is also done using the Nash and Sutcliffe (1970) efficiency and variance for assessment of how well the simulations fit

the observations and levels of variability in observed and downscaled data. The Nash and Sutcliffe efficiency, E, is defined as oneminus the sum of the absolute squared differences between the predicted and observed values normalized by the variance of theobserved values.

∑∑

= −−

−=

=

EO M

O O1

( )

( )i

ni i

i

ni

12

12

(5)

where Oi and Mi are the observations and model product values respectively for time i = 1,…,n and O is the observations mean.Variance, σ2, is defined as the average squared deviation of each ith datum from the mean.

∑=

−σ

x xn

( )i22

(6)

where xi and x are model or observations ith datum for time i = 1,…,n and x is the mean.The evaluation of the downscaled temperature and precipitation fields is also extended through a drought analysis which is one of

the biggest challenges in water resources management and related sectors like agriculture in the region. The StandardizedPrecipitation Index (SPI) and Aridity Index (I) are used in this study.

The Standardized Precipitation Index (SPI) was designed by McKee et al. (1993) and is one of the most popular indices formeasuring aridity, which considers only precipitation (Wang et al., 2014; Tao et al., 2015; Asadi Zarch et al., 2015). SPI is defined asthe difference between precipitation on a time series (xi) and the mean value (x ), divided by the standard deviation (σ).

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= −SPI x xσ

i(7)

The index quantifies precipitation deficit on multiple time scales to reflect different water resources (Livada and Assimakopoulos,2006) based on the probability of recording a given amount of precipitation. The probabilities are standardized so that an index ofzero indicates the median precipitation amount, a negative index indicates dry conditions, and a positive index indicates wet con-ditions. The SPI values can be interpreted as the number of standard deviations by which the observed anomaly deviates from thelong-term mean. In this study the SPI is calculated on 3-, 6- and 12-month durations to reflect short-, medium- and long-termmoisture conditions. The 3-month SPI (SPI-3) reflects short-term moisture conditions and provides seasonal estimation of pre-cipitation while the 6-month SPI (SPI-6) provides information on anomalous streamflow and reservoir levels. SPI at 12-monthdurations (SPI-12) are helpful for reservoir and groundwater levels at longer time scales. Computation of SPIs starts with rawprecipitation data being fitted to a gamma or a Pearson Type III distribution, and then transformed to a normal distribution. In thisstudy, the commonly used Pearson III distribution is selected to fit the monthly precipitation data. Pearson III distribution has mostlybeen used since the pioneering work of Guttman (1998,1999). Key among its advantages as put forward by Guttman (1998) is thatalthough it gives essentially equivalent results to the 2-parameter gamma distribution fit, it is superior in instances where monthlyand seasonal precipitations are zero. This is particularly important for the region of this study where monthly precipitations of zeroare common.

To further analyze for aridity variations where both precipitation and temperature are considered, we also compute the aridityindex. Aridity index (I) is defined by de Martonne (1926) and WMO (1975, 2012) for studying irrigation demands and is computed as,

=+

I PT

1210ii

i (8)

where Pi and Ti are monthly total precipitation (mm) and mean near-surface temperature (°C), respectively. Generally, irrigation isnecessary when Ii ≤ 20 (mm/°C), and thus the aridity index is used to identify the months when irrigation is necessary. These monthsare referred to as drought months.

Following the idea of Atmospheric Moisture Storage (Wasko and Sharma, 2009) inspired by the well-established procedure forestimating the storage capacity of a water supply reservoir (Ripple, 1883), an attempt is made to look at the consistency of the modelprecipitation with gridded global observations and the precipitation available from two (2) stations in the upper Limpopo catchment.A precipitation mass curve is developed with storage requirement fixed by the largest of the differences between crests and theirimmediate respective troughs. Here, we look at similarities of the precipitation mass curve plots and the resultant storage require-ments at the locations of the two stations. This is the most viable demonstration of the usefulness of the model precipitation forstorage requirements related applications as no discharge data is available over the basin for streamflow comparisons to be made.Precipitation mass curve representing cumulative monthly precipitation minus demand is constructed with 90% of average monthlygridded ORA precipitation here taken as constant demand figure that also includes evaporation losses and any mandatory releases.This is done for precipitation at the two individual stations with model and gridded observations precipitation taken at the nearestgrid points to the individual stations locations.

3. Results and discussions

Computation of error statistics (mean bias, RMSE and temporal correlation) for near-surface temperature (i.e., at 2 m) (K) andtotal surface precipitation (mm) is performed at the annual and seasonal time scale. Near surface temperature and especially pre-cipitation are also analyzed for closeness of fit to model simulations with variance also computed to investigate relative variability ofthe variables within the datasets with one station within the basin where continuous precipitation data covering the period of study(1980–2010) was available. The analysis is also extended to assess sustained water deficit through Standardized Precipitation Index(SPI) and aridity index (I) in which the downscaled temperature and precipitation’s usefulness for hydrology and related applicationsin this semi-arid environment is demonstrated.

The summer season (December-January-February or DJF for the southern hemisphere) is particularly critical as the season whenmost precipitation is received, when field ploughing begins, and for providing significant inflow into surface storages and recharge ofgroundwater aquifers. Also the Autumn (MAM) season, which follows the summer season (DJF), is critical for moisture sustenance ofrain-fed crops which sustains the region’s populace.

3.1. Temperature and precipitation

Annual temperature simulated by the model (WRF_ERA-I) and averaged over the basin falls between the UD and GHCN_CAMSobservational datasets (Table 1). The simulations are very close to the observations with variability of the simulated temperatureslightly lower than that from both the observational datasets. UD annual temperature fits the simulated temperature better thanGHCN_CAMS temperature. Spatially, the simulated annual temperature closely resembles that from the individual observations andORA (Fig. 2).

From Table 1, WRF_ERA-I gives the highest annual precipitation (639.42 mm) than the individual observational datasets (UD,GPCP and CMAP). When compared with precipitation at a station (Mahalapye: lat 23.01 0S, lon 26.83 0E) within the basin, the modelsimulations still give the highest precipitation with UD ranking lowest. Precipitation averaged over the basin also appears to be

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consistently higher than that at the station for all the observational datasets and the model simulations (Fig. 3). This implies that thesimulated precipitation could be consistent with station data over the basin. Spatially, the models simulated annual precipitation isclosest to ORA derived precipitation than it is to the individual observational datasets (Fig. 4). Variability of annual precipitation atthe station is comparable to that derived using individual observational datasets but closely matches that from the model simulations(Table 1). Through the Nash-Sutcliffe efficiency index, model simulations are clearly closest to station precipitation than to theindividual observational datasets precipitation (Table 1). Use of ORA derived precipitation reduces average precipitation, and re-duces variability while improving the closeness of the combined observational datasets to model simulations.

Table 1Annual precipitation (mm) and temperature (K) levels, variance and Nash-Sutcliffe efficiency for the datasets averaged over the study area and at a station (Mahalapye:Lat 23.01 0S; Lon 26.83 0E) within the area.

Dataset Levels Variance Nash-Sutcliffe efficiency

Over the area At a station Over the area At a station Over the area At a station

Precipitation (mm)UD 501.43 401.37 28.49 16.33 −64.21 −38.03CMAP 555.46 443.47 19.66 14.43 −91.23 −36.40GPCP 579.84 469.47 22.35 17.09 −73.34 −33.17WRF 639.42 504.56 26.58 23.67ORA 548.75 438.10 16.86 9.89 −64.75 −29.94Station 448.98 23.94 −1.05

Temperature (K)UD 293.68 0.37 −51.51GHCN 293.72 0.35 −81.08WRF 293.48 0.25ORA 293.66 0.27 −40.97

Fig. 2. Annual temperature (K) for (a) UD, (b) GHCN_CAMS, (c) ORA, and (d) WRF.

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3.1.1. Mean bias (model-observations)3.1.1.1. Temperature at 2 m above ground level. WRF forced by ERA-I (WRF_ERA-I) generally under-estimates temperature at annualand seasonal time scales except spring (SON), as shown in Table 2. The cold bias (under-estimations) for autumn (MAM), and summer(DJF) may result in under-estimation of evaporation rates for these seasons which are critical for various stages of crop growth. It isduring these seasons that most recharge of groundwater storages also occurs. The model’s best seasonal performance is duringsummer (DJF), while autumn (MAM) has the worst performance, slightly inferior to spring (SON). It is noticeable that the model doesnot generally do well over the eastern-most part of the Limpopo basin over Mozambique and south-eastern parts over South Africa(Fig. 5). These areas show the largest warm bias (temperature over-estimations) especially for autumn and summer seasons which arethe wettest part of the year. Summer and Autumn also have a general overestimation in the extreme east of the basin. This is the areawith relatively high temperatures associated with the warm and humid southward-flowing Mozambique current especially duringsummer.

In a study by Moalafhi et al. (2016b), WRF_ERA-I simulations evaluated over austral summer months (DJF1998/99-DJF2009/10)and using NCEP2 (National Centre for Environmental Prediction/National Centre for Atmospheric Research Reanalysis2) surfacetemperature as observations (same as in Ratnam et al., 2011) were found to be much improved than WRF_NCEP2 simulations (NCEP2downscaled using WRF) in Ratnam et al. (2011) who downscaled NCEP2 using WRF over a domain that covered the same and currentdomain but at a horizontal resolution of 30 km. The comparisons were made assuming that the use of different version of WRF did notaffect the results considerably. Both studies used the same long wave radiation, planetary boundary layer and Noah land-surfaceschemes, among others. WRF_ERA-I summer surface temperature biases were reduced than in WRF_NCEP2. Even at a coarser re-solution of 50 km, WRF_ERA-I biases were found to be slightly better than in WRF_NCEP2 simulations at 30 km horizontal. Thefindings resonate with findings in Moalafhi et al. (2016a) on a framework for choosing the reanalysis with the most accurate lateralboundary conditions (LBCs) for regional climate modeling which subsequently inspired use of ERA-I reanalysis over the same do-main.

3.1.1.2. Surface precipitation. The model over-estimates precipitation (wet bias) annually, and especially during summer (DJF – bias50 mm) and to a lesser extent spring (SON) (Table 2). The least bias is in winter (JJA) at −1.48 mm. The over-estimation ofprecipitation by the model in summer leads to over-estimation of moisture availability during this wettest part of the year. Whenconsidering the seasons individually, the performance does not vary much across the Limpopo basin (Fig. 6) with the exception ofsummer. The highest seasonal bias of the summer (DJF) is due to the model’s over-estimation of precipitation at the highestelevations which largely occur in South Africa. Apart from this precipitation over-estimation (wet biases), the rest of the simulationagrees well over the basin with bias averaging close to zero.

3.1.2. Root mean squared error (RMSE)3.1.2.1. Temperature at 2 m above ground level. Model performance considering RMSE is similar to that for mean bias with best andworst performances during summer (DJF) and autumn (MAM) respectively. Over the whole basin, RMSEs vary more than the meanbias over the seasons (Fig. 7). The model struggles particularly during the autumn season with largest temperature errors over thesouth west to west and northern parts of the basin. This spatial pattern is to some extent also visible for spring (SON). The winter(JJA) has the best performance generally over the central to the southern part of the Limpopo basin which is dominated by urban andagricultural water use sectors. The model also has good performance for most of the Limpopo basin during summer.

3.1.2.2. Surface precipitation. In terms of the magnitude of error, the model exhibits larger errors in the wetter seasons of the year.Here, summer (DJF) has the largest errors (53.66 mm) of all the seasons followed by autumn (10.97 mm). Spring season has thesmallest RMSE. Similar to mean bias, RMSEs are fairly uniform over the Limpopo basin across all seasons except during summer(Fig. 8). While errors are generally less than 50 mm (for autumn, spring and winter), the summer season has high RMSEs over highelevation parts of the basin reaching values as high as 280 mm at small areas over the extreme south.

The largest wet biases are observed over high altitude areas as also found in other RCMs studied including WRF over the region(e.g., Kalognomou et al., 2013). Generally, differences in annual precipitation are in agreement with those found over a similardomain involving RegCM4 (Li et al., 2015). The models’ wet bias towards south-eastern part of the basin is similar to the findings ofKalognomou et al. (2013) and Ratnam et al. (2011) while the model’s largest dry bias over Mozambique to the extreme east was also

Fig. 3. Annual precipitation (mm) showing consistently higher precipitation averaged over the area than at a station (Mahalapye: Lat 23.01 0S; Lon 26.83 0E) for thedatasets.

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revealed in Ratnam et al. (2011) through downscaling NCEP2 through WRF over a similar domain for the austral summer (DJF)between 1998/99 and 2009/10 and at a coarser resolution of 30 km. Ratnam et al. (2011) findings were comparable to WRF_ERA-Idownscaled over the same and current domain in Moalafhi et al. (2016b), but a little worse. Favre et al. (2015) also evaluated theability of 10 COordinated Regional climate Downscaling Experiment-Africa (CORDEX) RCMs (including WRF) forced by ERA-I re-analysis data between 1989 and 2008 to reproduce the spatial distribution of annual cycles of precipitation over southern Africa. In

Fig. 4. Annual precipitation (mm) for (a) UD, (b) CMAP, (c) GPCP, (d) ORA, and (e) WRF.

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that study, they found that in most models, higher elevation regions have a wet bias and coastal fringes have neutral to dry bias.

3.1.3. Temporal correlationTemporal correlation of modelled temperature exhibits greater values at an annual scale (0.69) with the worst correlation during

spring at 0.52. Over all the seasons, temperature is better correlated over the southern part of the basin (Fig. 9). The eastern-most partof the basin, especially over Mozambique, is generally less correlated. Precipitation is clearly better correlated than temperature. Allseasonal correlations are greater than annual. The model performs best towards the eastern part of the Limpopo basin over all theseasons (Fig. 10).

3.2. Aridity indices

3.2.1. Standardized precipitation index (SPI)The Standardized Precipitation Index (SPI) is computed at 3-, 6-, and 12-monthly durations to cover short-, medium-, and long-

term drought for moisture availability for crop use, streamflow, and surface and groundwater storage levels. A specific SPI-n (e.g.,SPI-3) provides a comparison of precipitation over a specific n-month period with the full historical record. The computed SPI valuesare interpreted through aridity levels as summarized in Table 3 below.

The SPI-3, SPI-6 and SPI-12 are computed for the full study period (1981–2010). Contour plots are made for the driest year (1992)and the wettest year (2000) of the study period (1981–2010) based on the ORA and WRF_ERA-I monthly precipitation. Moisture

Table 2Observational Range Adjusted (ORA) mean bias of annual and seasonal temperature and precipitation showing thatthe model generally under-estimates temperature and over-estimate precipitation over the Limpopo basin.

Timescale Temperature (K) Precipitation (mm) Bias

DJF −0.14 50.15MAM −2.38 −6.37JJA −0.31 −1.48SON 2.16 2.83Annual −0.19 90.67

Fig. 5. Observational Range Adjusted (ORA) Bias of mean seasonal Temperature (K) showing the model’s notable poor performances over the extreme east andsouthern parts of the basin.

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Fig. 6. Observational Range Adjusted (ORA) Bias of mean seasonal Precipitation (mm) shows more bias during summer.

Fig. 7. Observational Range Adjusted (ORA) RMSE of mean seasonal Temperature (K) shows more spatial variations than mean bias.

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Fig. 8. Observational Range Adjusted (ORA) RMSE of mean seasonal Precipitation (mm) showing more uniform performances except during summer.

Fig. 9. Observational Range Adjusted (ORA) temporal correlation of mean seasonal Temperature (K).

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accumulated up to the end of February and May is chosen to coincide with the ends of the summer and autumn months respectively.This captures precipitation accumulated during these two seasons individually and when combined through analyzing at SPI-3 andSPI-6 respectively. The results for different months are summarized in Table 4 below.

The model precipitation computed SPIs capture the directions (wet/dry conditions) of the deficit based on observations very well.

Fig. 10. Observational Range Adjusted (ORA) temporal correlation of mean seasonal Precipitation (mm).

Table 3Standardized Precipitation Index (SPI) general interpretation.

Scale range Category description

[+, −] 2.00 and above/below Exceptionally [wet, dry][+, −] 1.60–1.99 Extremely [wet, dry][+, −] 1.30–1.59 Severely [wet, dry][+, −] 0.80–1.29 Moderately [wet, dry][+, −] 0.51–0.79 Abnormally [wet, dry][+, −] 0.50 Near normal

Table 4Average Standardized Precipitation Index (SPI) for the driest (1992) and wettest (2000) years at 3-, 6- and 12-month durations based on WRF_ERA-I and ORA between1981 and 2010 over the Limpopo basin show that the model computed SPIs reasonably reproduce the observations. The indicated month is the last month included inthe SPI duration.

Average SPI-3 Average SPI-6 Average SPI-12

WRF_ERA-IFebruary May February May February May

1992 (dry) −1.47 −1.54 −1.67 −1.88 −1.43 −1.972000 (wet) −0.41 1.26 0.95 1.02 0.89 1.21

ObservationsFebruary May February May February May

1992 (dry) −1.79 −1.99 −2.02 −2.21 −1.64 −2.362000 (wet) −0.31 1.05 1.03 0.82 1.62 1.51

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The model, however, under-estimates the severity of all three SPI durations for the driest year. For the wettest year under all three SPIdurations, the basin is under wet conditions (Table 4). It is, however, noted that SPI-3 for summer (i.e. moisture accumulated over 3months up to February 2000) is showing dry conditions (i.e. negative SPI) from both the model and the observations though nearnormal. The model slightly over-estimates this severity. The model is found to over-estimate the moisture availability at SPI-3 andSPI-6 for May of the wettest year (2000), while the rest are under-estimations. This means that the model slightly under-estimatesmoisture availability for the wettest years while over-estimating it for the driest years. This shows the challenges in using thesimulated precipitation for these extreme situations (Fig. 11).

According to Fig. 8, the driest year has a SPI-3 at the end of the summer (DJF) mostly less than −1.3 and thus the basin generallyis severely dry. The model conceals the severity of the moisture deficit since it depicts almost the whole of the extreme east that fallswithin Mozambique as normal to moderately wet. The observations on the other hand show a more uniform dryness across the entirebasin. The wettest year shows fairly uniform wet conditions (i.e., SPIs on the positive side).

Looking at the end of autumn (Fig. 12), the southern part of the basin over South Africa, the region’s industrial hub, is stronglyaffected with an SPI of −2 to −3 and thus exceptionally dry. The model under-estimates the extent of this aridity over eastern partsof the basin in South Africa and Mozambique. For the wettest year, the situation is better as SPI shows wet conditions especially fromcentral to south eastern and eastern parts of the Limpopo basin.

Time series of the model and observations computed SPI over the basin are highly correlated at 0.85, 0.83 and 0.82 for SPI-3, SPI-6 and SPI-12 respectively. The model gives some over-estimation of average SPI timeseries at SPI-12 while under-estimations areevident for SPI-3 and SPI-6. (Table 5).

3.2.2. Aridity indexAridity index (I), based on both the model simulations and ORA, averaged over the basin ranges between 40.50 mm/°C and

2.59 mm/°C considering the seasons and annually for both the model and the observations (Table 6). The aridity index computedfrom the model simulations and averaged over the basin is found to be consistently higher (Fig. 13) and highly correlated over timewith that computed from observations. During summer, the Limpopo basin usually has an aridity index above the 20 mm/°C severedrought threshold implying that rain-fed agriculture can thrive (Fig. 14). The highest elevation corresponds to regions with thehighest aridity index. The situation, however changes for the worse in autumn where moisture availability, which is still critical tosustain crop production towards flowering, becomes less available. This demonstrates that rain-fed agriculture is generally restrictedto only 3 months of the summer in limited areas of the basin. The temporal and spatial limitation of moisture availability in thisregard also limits sustenance and replenishment of surface and groundwater storages.

Fig. 11. February Standardized Precipitation Index (SPI) for the driest (1992) and wettest (2000) years at 3-month durations based on (a) WRF_ERA-I and (b) RangeAdjusted Observations between 1981 and 2010 show that the model under-estimates the severity of moisture deficit to the east for the driest year.

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Aridity index averaged over the basin from both the observations and the model are highly correlated over time at 0.85 (also seeFig. 15). There is no significant trend over time, however a number of years barely cross the 20 mm/C threshold indicating marginalcapacity for crop production in these years. WRF_ERA-I simulates these years well.

3.3. Precipitation storage requirements

Continuous monthly precipitation data spanning the study period (1981–2010) is available for two stations in the upper Limpopo

Fig. 12. May Standardized Precipitation Index (SPI) for the driest (1992) and wettest (2000) years at 3-month runs based on (a) WRF_ERA-I and (b) ORA between1981 and 2010 showing that southern parts of the basin are more susceptible to drought conditions.

Table 5SPI summary over the basin showing general near normal conditions.

SPI-3 SPI-6 SPI-12

ORAAverage −0.00130 0.00046 0.00014% fraction negative 51.4 48.2 52.4

WRF_ERA-IAverage −0.00228 −0.00004 0.00015% fraction negative 47.3 49.9 50.7

Table 6Aridity Index averages and error statistics over the basin at seasonal and annual time scales showing that the model errors are largest in summer.

ORA WRF_ERA-I Bias RMSE Temporal correlation

DJF 32.78 40.50 7.73 8.57 0.70MAM 14.23 17.29 3.06 3.88 0.68JJA 2.59 3.54 0.94 1.20 0.69SON 11.33 12.01 0.68 1.37 0.84Annual 15.03 17.83 3.97 6.52 0.85

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Fig. 13. Aridity Index showing model simulations giving consistently higher values.

Fig. 14. Seasonal aridity index based on the model simulations over the study period showing that summer is generally free from moisture deficits.

Fig. 15. Aridity index from the model for the whole study period over the basin showing a marginal downward trend.

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basin on the Botswana side. The stations are Ramotswa Station (lat 24.88 0S; lon 25.87 0E) and Mahalapye (lat 23.01 0S; lon 26.830E). Precipitation mass curves are developed based on WRF-ERA-I and the gridded ORA precipitation at the individual stations alongwith that based on precipitation at the individual stations. The 90% monthly average constant demand is based on ORA precipitationand made common to the three mass curves. An estimation of precipitation (mm) equivalent moisture that needs to be stored basedon the 90% of average monthly precipitation demand figure is fixed by the largest of the differences between crests and theirrespective immediate troughs. This concept is equivalent to the rationale adopted in developing reservoir storage capacities as per theResidual Mass curve, but from an atmospheric storage viewpoint (Wasko and Sharma, 2009)

The mass curves based on the WRF_ERA-I are found to reasonably reproduce the general patterns of those based on station dataand ORA precipitation, although the model’s wet bias at the individual stations is evident (Fig. 16). The model is found to under-estimate the storage requirement by 37% and 9% for Ramotswa Station and Mahalapye respectively with reference to the stationrainfall. Use of ORA precipitation on the other hand also under-estimates storage requirements but at 15% for both the locationsusing the same reference. The under-estimation of storage requirements by the model at the two station locations is as a result of themodel’s over-estimation of precipitation at the two locations and generally over the basin. What is interesting in these results is thepresence of similar critical periods where the mass curve increases suddenly (as in 1996, and, to a lesser extent in 1988). This suggeststhe low frequency variability attributes important for reservoir storage estimation are being replicated in both gridded and themodelled rainfall over the basin.

4. Conclusions

This study evaluated a high-resolution dynamical downscaling of an objectively chosen global reanalysis (ERA-I) over Limpopobasin in southern Africa for its hydrological properties over this data-sparse basin. Demonstration of the levels of errors of thedownscaled temperature and precipitation fields using the Standardized Precipitation Index (SPI) and the aridity index (I) as mea-sures of sustained water deficit was performed. Further assessment of the downscaled product to serve as a proxy for surface storagerequirements validated the utility of the downscaled product in an operational context.

Water availability is central to all socio-economic undertakings and observational or derived datasets form the basis for estab-lishing its abundance or lack thereof. The findings reveal that the downscaled ERA-I do not closely resemble the observations intemperature, and generally under-estimate temperature during summer and autumn. The model exhibits bias in both temperatureand precipitation over the eastern-most part of the Limpopo basin over Mozambique and south to south-eastern parts over SouthAfrica which receives some of the largest precipitation over the basin. This is especially noticeable for temperature during the wettestparts of the year with the temperature under-estimation that could result in under-estimation of evaporation rates for these criticaltimes of the year. The model over-estimates precipitation during summer and under-estimates temperature in all seasons except

Fig. 16. Precipitation mass curves based on WRF_ERA-I and ORA precipitation compared with those from (a) Ramotswa Station and (b) Mahalapye with a common90% of average monthly precipitation demand based on ORA precipitation.

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spring. Temperature is found to be better correlated over the southern part of the basin while precipitation shows better correlationstowards the east.

The simulation products are found to be useful in simulating climatic drought over the Limpopo basin. The model under-estimatesmoisture deficit severity for all the 3-, 6-, and 12-month duration SPIs during the driest year. Moisture accumulated for autumnduring the driest year shows that the southern part of the basin, which contains the region’s industrial hub, is most affected, being“exceptionally dry” in some areas. Use of downscaled precipitation generally results in under-estimating the severity of this aridityespecially over central to eastern parts of the basin over South Africa and Mozambique.

During summer, the Limpopo basin is usually above the severe aridity index drought threshold implying that rain-fed agriculturecan on average thrive although the situation changes for the worse in autumn where moisture availability, which is still critical tosustain crop production towards flowering, decreases. This restricts rain-fed agriculture to only 3 months in a year. The downscaledproduct successfully captures this strong seasonality in aridity.

It is further revealed that the downscaled precipitation can fairly be useful for storage related applications over the basinespecially with limited data available and challenges of sourcing any available data from the member countries sharing the basin.This further gives some confidence that with bias corrections of the LBCs prior to downscaling and/or correction of the simulationproducts before subsequent hydrological-related applications, dynamical downscaling of reanalysis with the most accurate LBCscould be useful for semi-arid environments with limited data. It must, however, be emphasized that improved monitoring is neededalong with integrated shared databases if optimum and sustainable utilization of the limited and dwindling water resources are to berealized.

Conflict of interest

The authors hereby declare that there is no conflict of interest whatsoever either financial/personal interest or belief that couldhave affected the objectivity of the manuscript being submitted.

Acknowledgements

We acknowledge funding support from the University of Botswana and the Australian Research Council (FT110100576 andFT100100197) that helped carry out this research. This research was undertaken with the assistance of resources from the NationalComputational Infrastructure (NCI), which is supported by the Australian Government.

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