A tightly bound soil–water scheme within an atmosphere–land–surface model

Journal of Hydrology 452–453 (2012) 51–63

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Journal of Hydrology

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A tightly bound soil–water scheme within an atmosphere–land–surface model

Rachel White ⇑, Ralf ToumiSpace and Atmospheric Physics Group, Imperial College London, Prince Consort Road, London SW7 2AZ, UK

a r t i c l e i n f o s u m m a r y

Article history:Received 10 May 2011Received in revised form 22 December 2011Accepted 10 May 2012Available online 29 May 2012This manuscript was handled by AndrasBardossy, Editor-in-Chief, with theassistance of Harald Kunstmann, AssociateEditor

Keywords:Catchment runoffTightly bound soil waterSoil water storageAtmosphere land–surface modelEvapotranspirationWRF regional climate modelling

0022-1694/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.jhydrol.2012.05.028

⇑ Corresponding author. Tel./fax: +44 2075941402.E-mail address: [email protected] (R. White).

The concept of tightly bound water, in which a reservoir of soil water is bound tightly within small soilpores but is still available for evapotranspiration, is parameterised for the first time within the land sur-face scheme of a fully-coupled regional-scale atmosphere-land surface model. The Weather Research andForecasting (WRF) regional climate model and the NOAH land surface scheme are selected and a casestudy is performed on the Olifants River Basin in the Limpopo region of South Africa. Accurate knowledgeof water availability in this water-stressed region is of great importance for adaptation and future waterpolicy. Results of a simulation forced by ERA40 re-analysis show that the standard land surface scheme isunable to reproduce the observed runoff despite rainfall and atmospheric conditions similar to observed.This version of the model over-estimates mean annual runoff by 120%. The tightly bound water schemeshows a significant improvement, reducing the bias to 22%.

The inclusion of the tightly bound water scheme has little effect on the basin average annual rainfalldespite increasing annual evapotranspiration. The tightly bound water physics dampens the responseof runoff to precipitation and provides additional de-coupling between precipitation and runoff, increas-ing the variability in this relationship. Simulations with the WRF model forced with both 1980s and2040s CCSM3 data show that the tightly bound water scheme significantly reduces runoff in different cli-mates and projects a greater relative future decrease in runoff, from 4% to 10% for the same precipitationdecrease of 2.5%. The scheme also affects the projected changes in spatially averaged 100-year return pre-cipitation and runoff with significance at the 0.9 confidence level.

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1. Introduction

Regional climate models are now frequently used to dynami-cally downscale results from general circulation models (GCMs)which are currently unable to produce information on the scalenecessary to assess and plan for climate change impacts.Dynamically downscaled simulations include the effects of regio-nal topography and land–surface impacts at a resolution that isnot computationally feasible with a GCM (Salathe et al., 2010;Caldwell et al., 2009). In recent years there has been extensivedevelopment of many regional climate models, including theWeather Research and Forecasting (WRF) model used in this study(Leung et al., 2006). There has been increasing use of the WRFmodel to dynamically downscale GCM results to spatial resolutionsof around 10–40 km (e.g. Salathe et al., 2010; Caldwell et al., 2009;Lo et al., 2008).

Land–atmosphere interactions are an important component ofany climate model. Changes to soil moisture, vegetation andland-use can feedback into the atmosphere. These feedbacks arecomplicated, non-linear and have been identified as a key sourceof uncertainty in climate models (Seneviratne et al., 2010; Pitman

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et al., 2009). Land–atmosphere feedbacks may be subject to signif-icant spatial variations with some regions of the world showingparticularly strong positive soil-moisture precipitation coupling(Koster et al., 2004). Recent studies on soil-moisture precipitationcoupling have looked at the effects of indirect interactions ratherthan simple moisture recycling (Hohenegger et al., 2009; Alfieriet al., 2008). Soil-moisture can impact on boundary-layer stabilityand precipitation formation and both positive and negative soil-moisture precipitation feedbacks have been simulated. In southernAfrica a negative feedback has been modelled (Cook et al., 2006;New et al., 2003). This was attributed to the decrease in surfacetemperatures caused by a shift from sensible to latent heating. Thisincreases atmospheric stability thus suppressing convective activ-ity. Soil moisture can also affect vegetation dynamics, which feed-back to the atmosphere through albedo and transpiration (Baudenaet al., 2008). Williams and Albertson (2005) suggest that vegeta-tion dynamics have only a minor influence on annual transpirationin water-limited ecosystems, with soil moisture playing a moredominant role. These complicated relationships highlight the needfor high resolution models in order to simulate regional wateravailability.

Many advances to land surface models have been made in re-cent years, often concentrating on the simulation of surface energyand water fluxes and their response to atmospheric conditions.

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52 R. White, R. Toumi / Journal of Hydrology 452–453 (2012) 51–63

(e.g. Ek et al., 2003). Other works have investigated the sensitivityof land surface models to changes in parameters (Rosero et al.,2010; Hogue et al., 2006), the addition of groundwater or phenol-ogy modules (Maxwell et al., 2011; Rosero et al., 2009; Jiang et al.,2009; York et al., 2002) and the parameterisation of runoff(Decharme, 2007). Rosero et al. (2010) conclude that inclusion ofa groundwater module tends to improve model results comparedto observations at wet study sites however, Rosero et al. (2009)show that this groundwater module tended to decrease modelrobustness with respect to parameters. Studies compare atmo-sphere-land surface model results to observations such as sensibleheat flux, latent heat flux, ground heat flux and ground tempera-ture but few studies compare simulation results to runoff or riverflow. There are many areas in which regional climate models sim-ulate latent heat fluxes poorly compared to observations (Godfreyand Stensrud, 2010; Feng and Houser, 2008; Hogue et al., 2005).

The aspect of the atmosphere soil-moisture interaction that weconcentrate on in this study is the concept of tightly bound watervs mobile water. This is the idea that some water can becometrapped within small pores in the soil after which it does not moveunder standard hydraulic conduction or diffusion. This is a well-known concept within soil modelling communities (Larssonet al., 1999; Gazis and Feng, 2004) and is observable in the differ-ence in stable-isotopic compositions of soil water collected fromwick samplers (mobile water), suction lysimeters (mobile andsome tightly bound water) and cores (all soil water) (Landonet al., 1999; Brooks et al., 2010). Schemes modelling heat and mois-ture transport within the soil and coupling this to the atmosphereand boundary layer were developed as early as Zdunkowski et al.(1975) and Sievers et al. (1983). The tightly bound water processis partially represented in land–surface models by an increase inconductivity as the saturation ratio increases. Many models follow,for example, Cosby et al. (1984) where soil diffusivity and conduc-tivity are computed using saturation values and soil moisture con-tent combined with curve-fitting parameters. The saturation andcurve-fitting parameters are dependent on soil type. As describedin Yang et al. (1998), to determine the retention and hydraulic con-ductivity values for a given soil moisture via analytical methodswould require vast amounts of field data for application within aregional scale model. Such parameterisation of how these variablesvary with soil moisture is therefore necessary. The highlight of theBrooks et al. (2010) study (hereafter Brooks10) is the evidence that,whilst tightly bound water cannot travel through the soil to con-tribute to stream flow, it can be removed from the soil by evapo-transpiration. This removal of tightly bound water is currentlynot modelled in regional atmosphere-land surface models andhas the potential to change the soil-moisture precipitation feed-backs and impact on modelled stream-flow with respect to stan-dard models of soil water transport. This tightly bound waterphysics could be described with a full and consistent descriptionof soil water potential, diffusivity and conductivity such as thatpresented in Lebeau and Konrad (2010). However this would alsorequire very detailed knowledge of the evaporation and transpira-tion of water within different storage or transport regimes withinthe soil. In order to establish the general effect of this concept onregional climate simulations we use a simplified parameterisationdesigned to be applicable with a spatial resolution of the order of10 km. This paper presents the first parameterisation to includeevapotranspiration of tightly bound water within a regional atmo-sphere-land surface model. The tightly bound and mobile waterreservoirs are separated into two distinct categories instead ofmodelling a continuous pore size distribution. There is no maxi-mum infiltration rate into the tightly binding soil nor is the totalinfiltrated water split between the two soil reservoirs unless thetightly bound water reservoir is full. Modelling such processes ex-actly would require modelling of the diffusivity and conductivity of

water between pores of differing sizes. This first order approxima-tion should provide sufficient detail to investigate whether thescheme has a significant effect on the climate.

This paper is arranged as follows: the theory of the tightlybound water scheme and parameterisation within the NOAH landsurface model are described in Section 2. Section 3 details the test-ing of this new model within a case study region in South Africawith results and analysis. In Section 4 the results of simulationsforced with CCSM3 data using both original and modified modelsare presented in order to analyse the effect of the new scheme un-der different climate conditions and determine the impact on pre-dicted changes. The paper is concluded and discussed in Section 5.

2. Tightly bound water scheme within NOAH

2.1. The NOAH land surface scheme

The standard NOAH land surface model (Ek et al., 2003; Chenand Dudhia, 2001) is a medium complexity land surface schemeused in operational weather and climate forecasting. The modelcomputes soil temperature and soil moisture for each of four layers(with boundaries 0.1, 0.4, 1.0 and 2.0 m below the surface respec-tively) as well as single-layer canopy moisture and snow cover.Prognostic variables include turbulent heat fluxes, and both mois-ture and momentum fluxes. The model includes the root zone,evapotranspiration, soil drainage and runoff and takes into accountsoil textures, vegetation categories (based on the MODIS land-cov-er classification of the International Geosphere–Biosphere Pro-gramme) and climatologically derived monthly vegetationfraction and albedo. Vertical movement of water within the soilis described by a diffusive form of the Richard’s equation and massconservation in which both soil water diffusivity and conductivityare functions of the soil moisture content, H. These equations areshown for each of the four soil layers in

dz1@H1

@t¼ �D

@H@z

� �z1� Kz1 þ P � R� Edir � Et1 ð1Þ

dz2@H2

@t¼ D

@H@z

� �z1� D

@H@z

� �z2þ Kz1 � Kz2 � Et2 ð2Þ

dz3@H3

@t¼ D

@H@z

� �z2� D

@H@z

� �z3þ Kz2 � Kz3 � Et3 ð3Þ

dz4@H4

@t¼ D

@H@z

� �z3þ Kz3 � Kz4 � Et4 ð4Þ

In the above, dzi is the thickness of soil layer i, Hi the fraction of unitsoil volume occupied by water in layer i, D is the soil water diffusiv-ity, Kzi the hydraulic conductivity downwards out of layer i, P theprecipitation, R the surface runoff, Edir the direct evaporation andEti the transpiration out of soil layer i. Soil water diffusivity D is gi-ven by D = K(H)/(@W/@H) where W(H) is the soil water tensionfunction and K is the hydraulic conductivity. The NOAH model fol-lows Cosby et al. (1984) to compute K and W(H) by K(H) = KS(H/HS)2b+3 and W(H) = WS/(H/HS)b, where b is a curve-fitting param-eter which depends on soil type. KS and WS are respective values atsaturation and also depend on soil type. The infiltration is repre-sented by a conceptual parameterisation for subgrid treatment ofprecipitation and soil moisture and is related to the total unsatu-rated soil water capacity within the 2 m of soil (maximum soilwater storage–current soil water). The drainage from bottom soillayer is controlled solely by gravity. Direct evaporation occurs fromboth the uppermost soil layer and the canopy layer, and transpira-tion is calculated by the potential Penman–Monteith equation ad-justed for water availability. Vegetation and soil properties, such

R. White, R. Toumi / Journal of Hydrology 452–453 (2012) 51–63 53

as minimum canopy resistance, leaf area index porosity andhydraulic and diffusive conductivity, are static for a given soil orvegetation type and given in lookup tables.

2.2. Tightly bound water scheme – theory and implementation

The concept of a tightly bound reservoir of water held withinsmall soil pores and subsequent faster flow through larger poresis well established and the differential flow speeds and paths areconsidered important in modelling the transport of pollutantsthrough the soil matrix (Kutilek et al., 2009). Up until now how-ever, no-one has modelled the effect of the evapotranspiration ofthe tightly bound water reservoir of water on the water fluxes inthe area. Brooks10 presents evidence that the water taken up byvegetation is isotopically different to that which ends up in thestream-flow. This is supported by Dawson and Ehleringer (1991)who show that even streamside trees take up water that is isotopi-cally different to the stream water. Water from rainfall events atthe beginning of the wet season is retained in the small soil poreswith low matric potential. This water is used by vegetation butdoes not participate in translatory flow, mix with mobile wateror enter the stream. Subsequent rainfall does not displace thistightly bound water, travelling instead through larger pores toreach the groundwater and eventually the stream. This scheme isdepicted in Fig. 1.

Within the Mediterranean climate of the Brooks10 study site,transpiration is out of phase with the majority of the rainfall. Thewater from initial winter rains is locked into small pores and notreleased until significant transpiration occurs the following sum-mer. Brooks10 demonstrate that during early precipitation eventswhen the tightly bound water reservoir is being refilled runoffand stream-flow are significantly reduced. Once the tightly boundwater reservoir is full, stream-flow responds with increasing sensi-tivity to the precipitation. This implies that infiltration only startsto decrease significantly when the mobile-water pores are full upand is affected little by the saturation of the tightly binding reser-voir. We hypothesise that if this scheme were to be implementedin an area where the transpiration is in phase with the wet seasonthere could be a significant effect on predicted stream-flowthroughout the year. The tightly binding pores will provide a reser-voir of water that can be continuously emptied by transpirationand subsequently refilled throughout the wet season, removingthis water from that which may eventually enter the streams.

In order to parameterise this tightly bound water (TBW) schemewithin the NOAH land surface model we split the soil into two dis-tinct reservoirs – the standard soil with mobile water (large pores;

Fig. 1. The TBW scheme. Schematic diagram showing the tra

hereafter mobile-water soil) and soil with tightly bound water(smaller pores; hereafter tightly binding soil). This requires twoadditional global variables, SMOIS_TBW, denoting the fractionalmoisture content of the tightly binding soil at each soil level andSICE_TBW, giving the fractional frozen water content. An addi-tional tuneable parameter, TBWfrac, gives the fraction of the soilthat constitutes the tightly bound water reservoir and is assumedto be independent of soil type. The moisture content of each soilreservoir is stored as a saturation fraction as in the standard modeland input/output fluxes are adjusted with TBWfrac to take accountof the reduced volume of each soil type. The properties of the mo-bile-water soil are considered to be those given by the standardlook-up tables for the NOAH model. Those of the tightly bindingsoil are identical to mobile-water soil with the exceptions of thesaturated soil hydraulic conductivity Dksat(=KS) = 0.0 ms�1 andthe saturated soil diffusivity Dwsat(/WS) = 0.0. As soil conductivityK and diffusivity D are calculated from the saturated values, settingthese to zero effectively removes the conduction and diffusionterms from the equations. There is therefore no movement ofwater within the tightly binding soil, including zero drainage fromthe lowest soil level. The new prognostic equations for the volu-metric tightly binding soil moisture are shown in

dz1@H1tbw

@t¼ P � R� Edir tbw � Et1 tbw ð5Þ

dz2@H2tbw

@t¼ P2 � Et2 tbw ð6Þ

dz3@H3tbw

@t¼ P3 � Et3 tbw ð7Þ

dz4@H4tbw

@t¼ P4 � Pmob � Et4 tbw ð8Þ

Pi is the remainder of the infiltration for which there was noremaining capacity in the above i � 1 layers of tightly binding soil.Variables subscripted with tbw are for the tightly binding soil reser-voir. In the equation for the top level of the mobile-water soil theP–R term is replaced by the Pmob term in Eq. (8), denoting theinfiltration for which there was no remaining capacity in the wholetightly binding reservoir. The soil moisture fractions of the tightlybinding soil are updated first in order to calculate Pmob beforeupdating the moisture fractions of the mobile-water soil. Theinfiltration function is calculated using the unsaturated capacityof the mobile-water soil only, on the assumption that it is withinthis matrix that the water will initially travel before percolating into

nsport of water within the tightly bound water scheme.


the smaller pores if tightly binding capacity allows. This models theeffect on stream-flow seen in Brooks10.

Both the direct evaporation and the transpiration are calculatedbased on the total soil moisture content of the whole soil. Withoutfield measurements of the evapotranspiration from tightly bindingsoil relative to mobile-water soil we simplify the physics and re-duce the number of tuneable variables by assuming that evapora-tion and transpiration do not happen preferentially from either soiltype. The evaporative fluxes are attributed to each soil type basedon the form of the evaporative equations themselves. For example,the direct evaporation is calculated as in

Edir ¼ bð1:0� SHDFACÞ � ETP in which

b ¼ ðH1 �HdryÞHS �Hdry

� �Fxexp

ð9Þ

The variable SHDFAC gives the fraction of the gridbox that is shadedby vegetation and ETP is the potential evapotranspiration calculatedby a Penman-based energy balance approach. Fxexp = 2.0, the stan-dard value for this parameter, chosen and justified in Ek et al.(2003). Hdry is the fractional saturation value of the soil belowwhich no direct evaporation occurs and HS the saturated soil watercapacity. It is assumed in the standard model that direct evapora-tion only occurs from the unshaded fraction of each gridbox. Eq.(10) shows how direct evaporation from the tightly binding soil isthen calculated. There is an equivalent equation for mobile-watersoil direct evaporation.

Edir tbw ¼ Edir �btbw

btbw þ bmob

� �ð10Þ

btbw ¼ ðTBWfrac � ðH1tbw �HdryÞÞFxexp;

bmob ¼ ðð1:0� TBWfracÞ � ðH1mob �HdryÞÞFxexp

The distribution of the total transpiration flux is calculated in asimilar manner (Eq. (11)), based on the original transpirationcalculation.

ETtbwðiÞ ¼ ETðiÞ � ctbwðiÞctbwðiÞ þ cmobðiÞ

� �ð11Þ

ctbwðiÞ ¼ ðTBWfrac � ðHtbwðiÞ �HwltÞ;

cmobðiÞ ¼ ð1:0� TBWfracÞ � ðHmobðiÞ �HwltÞ

Hwlt is the fractional saturation wilting point of the soil belowwhich no transpiration occurs.

The soil temperature is calculated under the assumption thatthe two moisture reservoirs are in thermal equilibrium. An averageof the soil moisture fractions for the tightly binding and mobile-water soils is used for the temperature calculations. Frozen soilwater content is calculated separately for each reservoir. Surfacerunoff is calculated as before, as the difference between rainfalland infiltration. Underground runoff is the drainage from the low-est level of the mobile-water soil. The new NOAH model conserveswater to the same accuracy as the original model.

This implementation of a TBW scheme is very simplified and as-sumes that a linearisation of the soil pore distribution into two dis-tinct categories is valid. In addition we assume that within eachtimestep the infiltrated water is able to percolate into the smallpores, even in the lowest level. To improve the validity of both thisassumption and the standard NOAH assumption that the amountof infiltration at each timestep is dependent on the soil capacityof the whole 2 m of soil, the soil water fluxes within the TBWscheme are updated every 60 min instead of every timestep(approximately 1 min in this study). Ideally this should apply onlyto the infiltrated water, however for simplicity it applies to all

water fluxes within the soil. All heat fluxes and the water fluxesto the atmosphere continue to be calculated every timestep sothe atmosphere response time is unchanged. The value of 1 hwas chosen as timesteps of this order are generally used whenhydrological land–surface models such as NOAH are forced withobservational data (e.g. Wood et al., 1998). The sensitivity of theTBW scheme to this timestep is investigated in Section 3.5.

3. Case study: The Olifants basin, South Africa

To test the effects of the TBW scheme we use the NOAH modelwithin the WRF regional climate model to simulate rainfall andrunoff in the Olifants River catchment in the Limpopo region ofSouth Africa. South Africa has been identified in previous studiesas a country facing significant environmental and social challengesas a result of global climate change and predicted populationgrowth (Collier et al., 2008; Meadows, 2006; Tadross et al.,2005). There is concern over potential changes to regional wateravailability due to changes in precipitation and evaporation (deWit and Stankiewicz, 2006). The Limpopo region of South Africais a semi-arid region characterised by strong inter-annual and in-ter-seasonal variability in rainfall. The Olifants basin is already cat-egorised as water-stressed by the Department of Water Affairs(DWA) in South Africa (McCartney et al., 2004). For the OlifantsRiver an ecological reserve of 8.6 mm per year has been assignedby the DWA (McCartney et al., 2004). This ecological or environ-mental reserve was developed under the 1995 National WaterAct in South Africa and is designed to quantify the annual mini-mum water requirement to meet basic human needs and ensureenvironmental sustainability of the river ecology. Water demandin the area is predicted to increase in the future due to miningactivity and increased domestic and agricultural use. It is thus veryimportant to have predictions of the potential changes in wateravailability in this region. Due to the complicated relationship be-tween rainfall and runoff (Jones et al., 2006) it is necessary to mod-el current runoff accurately for any projected changes to havevalue. This area has rainfall and evaporation in phase and so we ex-pect to see an impact on runoff throughout the year with thetightly bound water scheme.

3.1. Model set-up

The regional climate model used in this study is the fully-com-pressible non-hydrostatic Advanced Research Weather Researchand Forecasting V3.2.1 model developed at the National Centerfor Atmospheric Research. There are a number of options for eachof the model physics packages which include cloud and precipita-tion microphysics, cumulus parameterisation, longwave and short-wave radiation, planetary boundary layer physics, surface layerscheme and representation of the land surface, including soil lay-ers. The model uses the sigma pressure coordinate in the verticalwhich aids simulation of flow over complex topography. Furtherdetails on the WRF model are given by Skamarock and Klemp(2008).

A high-resolution domain covering the Olifants catchment areaat 12 km spatial resolution is nested using one-way nesting insidea 36 km resolution domain. The position of each domain, topogra-phy of the area and outline of the Olifants basin are shown in Fig. 2.This set-up allows for a sufficiently large domain to avoid potentialspurious dynamic effects at the lower boundary (Seth and Giorgi,1998), whilst keeping computational costs reasonable. The modeluses 28 levels in the vertical. The defaults for relaxation zone widthand nudging strength at the lateral boundaries are used. The seasurface temperature is updated at 6-hourly intervals.

Fig. 2. Olifants basin and domain. Locations of the WRF domains, showingtopography at the domain resolution and the outline of the Olifants River Basin.


Physical options were selected from preliminary testing to sim-ulate precipitation over the region as accurately as possible. TheWRF double-moment 6-class scheme includes prediction equa-tions for both mass and number concentration for each species,allowing a more robust treatment of particle size distributionsthan single-moment schemes. Convective processes are parame-terised by the Betts–Miller–Janjic scheme, radiation modelledusing the RRTM and Dudhia schemes for longwave and shortwaverespectively, the planetary boundary layer by the MYNN Level 2.5scheme and the surface layer physics by the corresponding MYNNsurface layer scheme.

The WRF model is evaluated for the Olifants basin for a 10 yearsimulation forced by ERA-40 Re-Analysis data produced by theEuropean Centre for Medium-Range Weather Forecasting(ECMWF) and distributed by the British Atmospheric Data Centre(ECMWF, 2006). It is assumed that since the ERA-40 data produce

a

c

Fig. 3. Basline ERA climatologies, STD and TBW. (a) Rainfall climatology. (b) Runoff clim2 m temperature difference, ERA_TBW–ERA_STD. All data area averaged over the OlifantHY1920–89. All root mean square errors (RMSE) are within respect to the DWA observa

precipitation fields closer to CRU observations than the NCEP/NCAR re-analysis, the water vapour fields are also more realistic.One month spin-up is allowed for the soil moisture fields to relaxfrom the initial conditions. The simulation runs over hydrologicalyears (HY; October–September for this region) 1979–1989. Forthe standard model run no parameters are changed from the de-faults. In the TBW simulation TBWfrac = 0.5 and a tuneable param-eter, refkdt, is altered from its default value of 3.0 to 5.0.

3.2. Results

This section details the results for the 10 year simulations,comparing both the standard model (ERA_STD) and the new TBWmodel (ERA_TBW) with available observations.

3.2.1. RainfallMonthly rainfall is calculated for the Olifants catchment area

using the basin outline shown in Fig. 2 and a climatology con-structed. This climatology is shown in Fig. 3a compared to clima-tologies from ERA40 and the CRU TS3.0 rainfall dataset (Mitchelland Jones, 2005) for the same period, and an observational clima-tology for the catchment provided by the DWA (McCartney et al.,2004) for HY1920–1989. Precipitation over the region is very wellsimulated compared to the observations, as shown by the rootmean square error (RMSE) values shown on the graphs (all with re-spect to DWA). The RMSE for CRU gives an estimate of the uncer-tainty in the observational data. Table 1 presents the total annualvalues, showing that the TBW scheme has decreased mean annualprecipitation by 1.3%.

Maps of annual mean rainfall are shown in Fig. 4. Qualitativelythe ERA_STD model produces the same spatial patterns as observa-tions although ERA_STD does not simulate the high rainfall bandover the escarpment that runs approximately northwest–south-east across the basin. This is not unexpected as even with a resolu-tion of 12 km our domain will be unable to produce the steeptopographical gradients present over this region. The maximumvalues are also lower in the ERA_STD results but again this is tobe expected due to resolution differences. In general the mapresults have good agreement and since the basin average valuesare in very good agreement with observations there is no reasonto increase the resolution. Fig. 4c shows the annual mean

b

d

atology. (c) Evapotranspiration difference, ERA_TBW–ERA_STD. (d) Monthly means basin. CRU, ERA40 and WRF runs are shown with data from HY1979–89, DWA fortions.

Table 1Average annual values of rainfall, runoff, evapotranspiration and potential evapora-tion, given in mm/year. ERA_TBW–ERA_STD is shown in the ‘Diff’ column. DWAobservations are for HY1920–89, all other HY1979–89.

DWA obs. ERA_STD ERA_TBW Diff.

Rainfall (mm) 535.6 564.7 557.5 �7.2Runoff (mm) 37.55 82.8 45.9 �36.9Sub-surface runoff as% of total 30–55 36 43 7Evapotranspiration (mm) N/A 477.5 501.3 23.7Potential evaporation (mm) N/A 2307 2284 �22.8


zdifference between ERA_STD and ERA_TBW. Whilst the basinaverage annual mean difference is small, there are local variationsof up to ±15%. These changes exist in both grid-scale rainfall andrainfall parameterised by the cumulus scheme.

3.2.2. RunoffFig. 3b shows the corresponding runoff climatology for the ba-

sin. Despite the standard model producing accurate annual averagerainfall the runoff is over-estimated by 120% compared to the DWAnaturalised runoff. This naturalised flow data is taken fromMcCartney et al. (2004) and is calculated by the Water SituationAssessment Model. This model uses river flow data and informa-tion about water releases from all the dams and reservoirs in thesystem to synthesise natural flow conditions. Even taking into ac-count probable inaccuracies in the naturalised runoff (estimated to

Fig. 4. (a) Rainfall maps. Map of ERA_STD mean annual rainfall HY1979–89 for compariso(2004). (c) Map of the percentage difference between mean annual rainfall for ERA_TBW

be approximately 10%), given the close correlation between modeland observational rainfall it is clear that the original NOAH landsurface model is not reproducing the correct physics to simulaterunoff in the Olifants area. Implementation of the tightly boundwater scheme produces results which are in much better agree-ment with the naturalised flow results. The data in Table 1 showthat the discrepancy in average annual runoff between observa-tions is reduced to 22% with the use of the TBW scheme.

The separation of surface and underground runoff is an impor-tant aspect of simulating runoff. Surface runoff occurs instanta-neously with precipitation whereas underground runoff lagsbehind precipitation due to transport time within the soil. Obser-vationally based estimates of this separation for the Olifants regiongive an approximate value of between 30% and 55% for the propor-tion of total runoff from underground (Xu and Beekman, 2003; As-ton, 2000). The underground runoff as a percentage of the totalrunoff increases in the TBW model. The TBW implementation thusreduces the surface runoff proportionally more than the under-ground runoff. Both models produce values that are within the ex-pected range.

3.2.3. EvapotranspirationThe climatological difference in monthly evapotranspiration

(the sum of direct soil evaporation and vegetation transpiration)between the ERA_STD and ERA_TBW models is presented inFig. 3c. There are no observational datasets for actual evaporation

n with (b) observational mean annual rainfall for HY1920–89 from McCartney et al.and ERA_STD runs.

Fig. 5. Rainfall–runoff relationships, ERA. Rainfall–runoff relationships for bothERA_STD and ERA_TBW experiments. Linear lines of best fit are shown along withthe equations and R2 values.


or transpiration, however potential evaporation comparison withmeasurements collected by the DWA gives good agreement, witha slight over-estimate by both WRF simulations (comparison notshown). The TBW scheme produces 5.0% more evaporation overthe year than the standard scheme. Potential evaporation de-creases by 1% in the TBW run, therefore the increased moisturefluxes to the atmosphere can be wholly attributed to the increasein soil water available for evapotranspiration in the TBW scheme.

Although there is an increase in basin average evapotranspira-tion which will increase the total column water vapour, there isno increase in annual average precipitation. This increase in atmo-spheric water may be offset by increases in atmospheric stabilitydue to the shift in the ratio of sensible to latent heating at the sur-face and subsequent decreases in surface temperature, as sug-gested by Cook et al. (2006). This is supported by resultsshowing a decrease in the climatological 2 m temperature(Fig. 3d) for the ERA_TBW experiment compared to ERA_STD witha climatological pattern matching the increase in evapotranspira-tion. This temperature decrease explains the reduction in potentialevaporation seen in Table 1.

3.3. Runoff coefficient and uncertainty

The runoff coefficient is defined as the fraction of rainfall con-verted to runoff. This can vary with location, climate, soil and veg-etation type and the intensity of the rainfall. Heavy rainfall of shortduration will produce more runoff than equivalent drizzle over alonger period. The runoff coefficient is also dependent on theamount of rainfall in previous months through the moisture con-tent of the soil, which affects both the infiltration of current rainfalland the underground runoff.

By considering annual totals instead of monthly values the ef-fect of the time lag between infiltration and underground runoff

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is reduced. Fig. 5 shows the relationship between annual total rain-fall and runoff for both ERA_STD and ERA_TBW. In the followinganalysis we approximate the relationship as linear for thisrelatively small range as R2 values show little difference betweenlinear, power-law and exponential fits. Fig. 5 also presents theequations of the best fit lines, showing that a steeper gradient ex-ists for ERA_STD compared to ERA_TBW. The ERA_TBW schemeacts to dampen the runoff response over the range of rainfall valuesseen. Regression analysis shows that the difference in these gradi-ents is statistically significant at the 0.90 confidence level.

There is an intrinsic uncertainty in predicting runoff from rain-fall and the fact that the rainfall itself is only known with a finiteaccuracy adds additional runoff uncertainty. For the ERA_STD mod-el the standard error in runoff is 12.9 mm, 16% of the mean runoffvalue. The uncertainty in the runoff calculation from a known per-centage error in the rainfall is found for the mean rainfall value,neglecting the additional uncertainty in the rainfall–runoff

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relationship: an x% uncertainty in rainfall translates to a 2x% uncer-tainty in runoff. If the uncertainty in the annual rainfall is greaterthan 8% then this rainfall uncertainty produces a larger uncertaintyin the predicted runoff then the uncertainty in the rainfall–runoffrelationship itself.

This analysis is repeated for the ERA_TBW model. The standarderror increases to 28%, while the translation of a rainfalluncertainty into the runoff calculation remains similar. The imple-mentation of the TBW scheme increases the variability in therainfall–runoff relationship. This is physically consistent with thechanges introduced with the TBW scheme as the runoff, particu-larly sub-surface, is now influenced by increased evaporation,and thus by atmospheric variables other than precipitation. Thiscan also be seen in the R2 values for each trend, displayed on thegraph in Fig. 5.

3.4. Precipitation and runoff extremes

Two possibilities exist for the study of the impact of the TBWscheme on extreme events. The first is the study of the mechanicalimpact on the dynamics of individual extreme events, and the sec-ond to analyse the impact on the statistical probabilities of suchevents. Here we present the latter, using a Gumbel distributionto model daily extreme values of precipitation and surface runoff.

By fitting the annual maximum daily rainfall for each of the10 years to a Gumbel distribution, the daily precipitation 100-yearreturn value (the maximum daily rainfall amount that is expectedto occur on average once every 100 years) is calculated for eachgrid-box. These return values are shown in Fig. 6a and b forERA_STD and ERA_TBW for an area just covering the Olifants basin.In the following, significance is defined by the 0.90 confidence leveland is tested using the two-sample Student’s t-test statistic underthe assumption of equal variances. The TBW scheme increases thearea average return value significantly by 6.3 mm, 6.5%. Fig. 6a andb shows that the location of the highest maximum daily rainfallhas been shifted by the TBW scheme and the absolute value of thismaximum has increased, showing that the scheme has a strongereffect on extreme precipitation on an individual grid-box level thanon a spatially averaged mean, as for the annual mean precipitationin Section 3.2.

This analysis is repeated for the daily surface runoff 100-yearreturn value. Surface runoff was chosen as it is generally responsi-ble for localised flooding. These results are presented in Fig. 6c andd. The changes in spatial distribution reflect the changes in the pre-cipitation results. The TBW scheme decreases the surface runoff re-turn value significantly by 6.0 mm, or 26%, despite the increase inspatial mean precipitation return value.

Table 2Summary of rainfall and runoff results for 4 months of TBW simulation, showing therunoff response with different timesteps for the water flux equations of the NOAHscheme (Noahdt).

Rainfall (mm) Runoff (mm) Runoff coefficient

Noahdt = 60 416.8 26.8 0.064Noahdt = 600 407.5 24.2 0.060Noahdt = 1800 419.4 22.0 0.053Noahdt = 3600 417.2 20.8 0.051

3.5. Sensitivity of NOAH model to parameters

Land–surface models should be tuned in order to produce themost accurate results in a particular area. The NOAH model useslook-up tables for parameter values based on soil and vegetationtypes for each grid-box. Rosero et al. (2010) have shown that theseparameters are not necessarily transferable solely based on vegeta-tion type and some are more sensitive to local climatic forcing thanthe specific land cover classification. In this section we investigatethe effects of changing some basic model parameters to testwhether the results of the TBW implementation could be repro-duced by simply modifying existing parameters. This is not de-signed to fully test the sensitivity of the model. We also studythe sensitivity of the TBW model to changes to the new parameterTBWfrac and the altered parameter Refkdt to determine how tune-able this new scheme could be to other regions. Lastly, we look atthe effect of changing the water flux timestep, Noahdt.

A single standard simulation is run with parameter changes in-tended to reproduce the effects of the TBW implementation asmuch as possible (named ERA_STD_2). The basic concepts are theincrease of infiltration to reduce the surface runoff and the increaseof evapotranspiration to remove this water from the soil matrix. Allparameters were kept within the ranges specified either by theNOAH documentation or as documented by Hogue et al. (2006).The parameters changed are described below.

– Refkdt, a tuneable parameter controlling the proportion of rain-fall infiltrated into the soil; Increased from 3.0 to 6.0 in order toIncrease infiltration and decrease surface runoff.

– Dksat (m/s), a parameter specifying saturated soil hydraulicconductivity and thus the soil hydraulic conductivity K for allsaturation values; Values decreased by 20% for each soil type(minimum value of 5.00E�7) in order to decrease downwardmotion of water through the soil allowing more time for evapo-transpiration, though significant decrease would decreaseinfiltration.

– RSmin and RSmax (s/m), minimum and maximum stomatalresistance; RSmin default values decreased by 50% for each veg-etation type (minimum value of 40.0); Rsmax decreased from5000 to 3000 in order to decrease vegetation stomatal resis-tance, increasing transpiration.

The parameter changes had the desired effect and decreased thetotal annual runoff. However, the runoff decreased by only10.2 mm/year compared to a decrease of 36.8 mm/year for theERA_TBW run. The underground component of runoff contributedto 44% of the total runoff which is within the observational esti-mates. The total annual evaporation increased by 15.4 mm/yearin ERA_STD_2 compared to ERA_STD, however this is still11.3 mm/year less than the ERA_TBW run. An additional parameterthat could have been changed is Fxexp as the WRF model is notedto produce values closer to observed evaporation for a semi-aridenvironment when Fxexp = 1 (Peters-Lidard et al., 2008). A singleyear experiment showed that this change does have a noticeableeffect on runoff reducing the annual total by a further 4.2 mm. Thisis still not sufficient to reproduce the effect of the TBW simulation.It is noted that use of this parameter change could further improvethe TBW simulation compared to observations.

Simulations of ERA_TBW with different values of TBWfrac andRefkdt are also performed. The results demonstrate that the TBWscheme has the tunability to be adapted to areas with different cli-mates and/or soil compositions. The sensitivity of the model to therange of the two parameters chosen (maximum decrease of11.0 mm/year in total runoff) is 31% of the sensitivity to addingthe TBW scheme in the first place (decrease of 36.2 mm/year).

As discussed in Section 2.2 the time-step of water flux updateswithin the soil (Noahdt) is increased from the model timestep of60 s in order to improve the validity of assumptions made in thesimplification of the TBW scheme. The results of simulations of4 months during the wet season (October–January) are shown inTable 2 for Noahdt of 60, 600, 1800 and 3600 s. Due to the non-lin-earity of the precipitation response to atmospheric variables, slight


changes in evaporation caused by the change in soil moisture with-in the scheme result in changes in precipitation. Increasing thetimestep decreases the runoff response, or coefficient of runoff,via increased infiltration. Increasing the timestep decreases therunoff, thus decreasing the bias the TBW scheme has with respectto the observations. There is no systematic effect on rainfall, sug-gesting that the small precipitation changes seen can be attributedto the internal variability within the model.

3.6. Discussion of case study

The strengths of the TBW scheme are that it is based on thephysical principles shown experimentally in Brooks10 and that itcan significantly improve model predictions compared to observa-tions as demonstrated in this study. Due to the complex interac-tions between rainfall and runoff there are a number of factorsthat have the potential to affect the model results in a similar man-ner. The main points are addressed below.

– Incorrect parameters. Section 3.5 shows that the NOAH modeldoes not have sufficient sensitivity to the commonly tunedparameters to reproduce the results obtained with the TBWscheme.

– Incorrect basic model concepts, such as a free-draining lowerboundary and a stationary water table at 2 m depth. Yorket al. (2002) look at the effect of coupling an interactive aquiferto a single-column model including atmosphere and land sur-face physics. The inclusion of the aquifer produced slightlymore runoff. Rosero et al. (2010) conclude that at wet sitesthe inclusion of a groundwater module may improve modelresults compared to observations. These studies indicate thatsuch additions could not have sufficient impact on the standardNOAH model runoff to produce significant improvement in theOlifants region.

– Incorrect atmospheric climate and hence inaccurately calcu-lated evaporation. A comparison of model climatological basinpotential evaporation with measurements from the DWA (notshown) shows that the WRF model slightly over-estimatespotential evaporation over this region, thus this cannot be thecause of the under-estimation of actual evapotranspiration.

– Missing physical concepts within the model. This includes thebehaviour of tightly bound water as implemented in this study.

– There is thus a strong argument that the inclusion of the TBWscheme is not only physically justifiable but that the improve-ment obtained could not be easily produced by other means.

4. Climate simulations

The effect of the TBW scheme on the Olifants basin for the pres-ent day climate has been established and presented in Section 3.We now present results from the WRF model forced with CCSM3.0general circulation model data (Collins et al., 2006) for both thepresent day and the future A1B scenario in order to analyse the im-pact of the TBW scheme under different climates, particularlywhen it has been tuned to a different (ERA_STD) climate. This pro-vides evidence for how the scheme may perform in other geo-graphical areas with different climates and whether the TBWscheme has an impact on projections of climatic changes. Simula-tions are run for HY1979–99 (C1980s) and for HY2039–59(C2040s). The set-up for the CCSM runs is identical to that de-scribed in Section 3.1 with the WRF model boundaries forced byCCSM3.0 data. The model CO2 is updated for the C2040s runs to525 ppmv in line with the A1B scenario for 2050. The sea surfacetemperatures are updated every 6 h with CCSM values.

4.1. Base-line and future results

The rainfall and runoff climatologies for C1980s STD and TBWsimulations are presented in Fig. 7a and b along with the DWAclimatology and RMSE values with respect to DWA values. The biasin annual total rainfall for C1980s_STD is 13%, a similar magnitudeto that between ERA_STD and DWA. However, the RMSE (with re-spect to the DWA climatology) value of 23.9 mm/month showsthat the shape of the C1980s climatology has a large bias, com-pared to the RMSE of the ERA_STD simulation of 8.9 mm/month.The precipitation from the CCSM global model itself has a RMSEof 24.9 mm/month with respect to the DWA values. The bias inprecipitation climatology is therefore introduced by the forcingdata, not by the WRF model. The C1980s_STD average annual2 m temperature (air temperature 2 m from the surface) is verysimilar to the ERA_STD simulation in both climatology, with aRMSE of less than 1 K/month, and spatial distribution. The spatialdistribution of the 2 m temperature is highly dependent on alti-tude explaining the close correlation between the two simulations.

As the standard methodology for estimating future changesusing GCM results we will take the difference between the presentday and future simulations. Provided that any precipitation biasbetween simulated and real climate is temporally constant thehigh RMSE will not affect our results.

The effect of the TBW scheme on all three climates is summa-rised in Table 3. There is no robust effect on precipitation, howeverall other changes are robust and largely consistent across the threecomparisons. Runoff is decreased the most in ERA40, though thiscould be partially due to the TBW scheme having been tuned tothis particular climate. The percentage of total runoff from sub-sur-face is increased in all simulations, but by significantly more inC1980s and C2040s than in ERA40. The increases in evaporationand slight decrease in potential evaporation are consistent in mag-nitude in all three climates.

The C2040s climate shows a basin average annual mean tem-perature increase of 2.2 K, slightly greater than the increase of2 K projected by the CCSM model itself. Fig. 7c and d shows theprojected changes in rainfall and runoff for the STD and TBW mod-els. There is a projected decrease of approximately 3% in the annualtotal rainfall, with increases only over the late rainy season fromJanuary to April. The TBW scheme projects a slightly larger de-crease in rainfall. The TBW simulation projects a greater decreasein annual runoff (13%) than the STD simulation (4%). We normalisethis change to the STD projection of rainfall change to obtain theTBW runoff change excluding the additional decrease in rainfallwith respect to the STD simulation. Using the power-law relation-ship between rainfall and runoff for the C2040s TBW climate, de-scribed later in Section 4.2, it can be calculated that the extradecrease in rainfall in the TBW simulation should have resultedin an additional decrease of approximately 1.4 mm, or 3%, in therunoff. Taking this into account the remaining decrease of 10% isstill over twice as high as the 4% decrease projected by the originalscheme. The TBW scheme therefore projects a greater decrease inavailable water in the future than the STD simulation for a 2.4% de-crease in rainfall.

4.2. Runoff coefficient and uncertainty

The analysis completed in Section 3.3 is repeated for both CCSMsimulations. Fig. 8 presents the rainfall–runoff relationships forC1980s and C2040s. Unlike the ERA40 simulations, power-lawand exponential relationships show consistently higher R2 valuesfor both simulations and thus the best fit relationships shownare power-law (chosen over exponential for physical consistencyat zero rainfall, x = 0). Statistical regression analysis shows thatthe exponentials in the power-law relationships are not

Table 3Percentage changes of TBW-STD for basin annual average values for the threeclimates. The runoff value is normalised to STD rainfall using the relationships inSection 4.2 to remove the change in runoff due to slight changes in rainfall.

ERA (%) C1980s (%) C2040s (%)

Rainfall �1.2 +0.5 �0.9Runoff �43 �36 �39Sub-surface runoff% +19 +35 +37Evapotranspiration +5.0 +6.2 +5.3Potential evapotranspiration �0.8 �1.0 �1.0

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Fig. 8. Rainfall–runoff relationships, CCSM. Rainfall–runoff relationships for (a)C1980s STD and TBW, (b) C2040s STD and TBW. Power-law lines of best fit areshown along with the equations and R2 values.

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Fig. 7. C1980s and predicted changes to C2040s (a and b) show precipitation and runoff climatologies respectively for C1980s_STD and C1980s_TBW (HY1979–99) comparedto the DWA observations for HY1920–89. The simulated changes to precipitation and runoff for C2040s–C1980s for STD and TBW experiments are shown in (c and d).


statistically different between the STD and TBW simulations due tothe uncertainty on this relationship. This uncertainty is caused byfactors such as annual temperature, wind and humidity (all affect-ing evaporation) and the temporal distribution of rainfall, concern-ing both intensity and seasonal distribution.

The power-law rainfall–runoff relationships calculated here canbe used to calculate the expected future decrease in C2040s runoffdue solely to the simulated changes in precipitation. For the STDsimulation the 11.3 mm precipitation decrease should correspondto a 3.5 mm decrease in runoff, which matches that simulated.For the TBW simulation the �18.0 mm precipitation change shouldresult in a runoff decrease of 3.5 mm. This is only 60% of that sim-ulated. This suggests that the TBW runoff is more sensitive to otherclimatic changes such as the increase in surface temperature whichwill increase potential evapotranspiration, or to the temporal dis-tribution of precipitation. This is in agreement with the resultsshowing a larger uncertainty on the rainfall–runoff relationshipsfor the TBW simulations compared to the STD, seen in the R2 valuesin Fig. 8.

4.3. Precipitation and runoff extremes

We look at the ecological reserve for the Olifants basin andwhether the probability of the annual runoff of any 1 year beingbelow this threshold changes in the future. In particular we lookat whether the TBW scheme affects any change seen. Milly et al.(2002) caution that at least 30 years of data is often required forextremes analysis. Since our intention is not to provide an absoluteprediction of any changes but to establish whether the implemen-tation of the TBW scheme may affect any predicted changes, the20 years of data that we use here should be sufficient.

Both log-normal and gamma distributions are fitted to 70 yearsof DWA total annual naturalised runoff data. The log-normal fit de-scribes the probability of annual runoff below the ecological re-serve of 8.6 mm as 0.92%, or a 1 in 110 year event. The gammadistribution models the probability as 2.7%, or a 1 in 40 year event.Given that in the 70 years of data available this event has notoccurred, we assume that the log-normal distribution betterdescribes the tail end of the runoff distribution.

The log-normal percentile of 0.92% is applied to the C1980s datato find the C1980s equivalent of the ecological reserve (20.4 mm


for STD and 7.9 mm for TBW). This normalises the analysis to theDWA runoff values and thus the bias between C1980s and observa-tions is negated. The probability of annual runoff below this nor-malised ecological reserve is then found for the C2040s data andcompared to the present day value. The results for both STD andTBW experiments show a decrease in the probability of annualrunoff below this threshold, despite the overall decrease in averageannual runoff. The STD simulation projects a future probability of0.71% and the TBW scheme gives 0.49%.

Jackknife resampling analysis (Li et al., 2008) was performed onboth the C1980s and C2040s data in order to obtain an estimate ofthe uncertainty of these probabilities. Jackknife resampling is aform of Monte Carlo analysis where multiple datasets are createdby the alternate deletion of each value from the original dataset.Resampling is often used as a first step towards the definition ofuncertainty bands (Prudhomme et al., 2003). The decrease in prob-ability shown by the STD model is not statistically significant; thedecrease shown by the TBW model is significant to the 0.90 confi-dence level. The difference between the two models is notsignificant.

To study precipitation and surface runoff 100-year return val-ues the analysis produced in Section 3.4 is repeated for the CCSMdata. Again, stated significance is at the 0.9 confidence level. Forboth the C1980s and C2040s there is no significant change in pre-cipitation between the STD and TBW simulations. Both climatesshow a significant decrease in runoff of 6.0 mm (C1980s) or8.3 mm (C2040s).

The STD simulation projects a future decrease in area mean pre-cipitation return value of �6.0 (5.4%) whilst the TBW projects a de-crease of 3.2 mm (3.0%). Both of these are significant, as is thedifference between the projected changes for TBW compared toSTD. The STD scheme projects no significant future decrease in sur-face runoff whilst the TBW scheme projected a significant decreaseof 2.5 mm (12.0%). Again, the difference between the simulatedchanges of the STD and TBW models is significant.

5. Conclusions

Water is thought to exist in a tightly bound form within smallsoil pores where it is still available for evapotranspiration. In thispaper this concept is simplified and parameterised for the firsttime within an atmosphere-land surface model. The WRF regionalclimate model is selected and a case study of the Olifants River Ba-sin in the Limpopo region of South Africa performed using ERA40re-analysis data as lateral-boundary forcing. The results show thatthe standard land surface scheme is unable to reproduce the ob-served runoff despite being forced with rainfall and atmosphericconditions similar to those observed, with an over-estimate of120% on the naturalised annual mean runoff. The TBW schemeshows a significant improvement, reducing this bias to 22%.

The inclusion of the TBW scheme has little effect on the basinannual average rainfall despite increasing annual evapotranspira-tion. Analysis of 2 m air temperature shows a cooling with theuse of the TBW scheme indicating that this result is consistent withincreased atmospheric stability as suggested by Cook et al. (2006).Simulations for the same region with the WRF model forced withCCSM3 data provide a means of testing the TBW scheme behaviourunder different climates. The TBW scheme significantly reducedrunoff in all simulations. The proportional decrease in runoff isgreatest in the ERA40 simulation, though this could be partiallydue to the TBW scheme having been tuned to this particular cli-mate, and least in C1980s. We conclude that the existence of a res-ervoir of tightly bound water may have greater effect on climateswith longer and less intense rainy seasons (ERA40 vs C1980s)and also in warmer climates (C2040s vs C1980s). These are

physically consistent conclusions as increasing the duration ofthe rainy season or the surface temperature is likely to increaseevaporation from the tightly bound water reservoir during therainy season when the largest effect on runoff is seen. Furtherstudy in other areas and climates is required to confirm these con-clusions. Simulations of runoff in other semi-arid regions may ben-efit from the inclusion of this scheme. For example Hogue et al.(2005) find that the NOAH land surface model consistently un-der-estimates the latent heat fluxes in a semi-arid area in southernArizona whilst Feng and Houser (2008) also find that the NOAHmodel under-estimates evaporation and consequently over-esti-mates runoff in the Mississippi river basin. The new parameterisa-tion may bring most benefit to areas with a strong seasonal cycleand high potential evaporation during the wet season. There mayalso be benefit to precipitation simulation in regions with a Medi-terranean climate if the region has strong soil–moisture–precipita-tion coupling. Water from the winter wet season may be stored inthe tightly binding soil for evaporation in the following summerwhich may impact on summer rainfall simulation.

Inclusion of the TBW scheme increases the projected relativedecrease in both total and underground runoff in future simula-tions, suggesting that implementation of the new physics consid-ered here is important for accurate simulation of future runoffchanges in semi-arid regions.

The implementation of the tightly bound water physics damp-ens the response of the runoff to precipitation forcing and providesadditional de-coupling between the precipitation and the runoff,increasing the variability in this relationship. With the rainfall–runoff relationships calculated for the Olifants basin, an x% uncer-tainty in rainfall translates approximately to a 2x% uncertainty inrunoff for all climates and both the standard and TBW models.Analysis of the CCSM 20 year simulations suggests that the rain-fall–runoff relationship is not linear, but is modelled better by apower-law or exponential equation. These results have implica-tions for rainfall–runoff models which utilise a static runoff coeffi-cient, such as the Urban Runoff and Basin Systems used in Bullardet al. (2007).

We provide evidence that the new physically-based TBWscheme significantly improves the simulation of runoff in the Oli-fants River Basin and may well be applicable to other regions withsimilar climates.

The TBW scheme may also have an effect on the simulation ofextreme rainfall and run-off events. A significant increase in thespatially averaged precipitation return value is seen in with theTBW scheme compared to the STD scheme for the simulationforced by ERA data, whilst a decrease in extreme runoff is projectedas expected from the effect on annual average runoff. The increasein extreme precipitation agrees in principle with current literaturesuggesting that extreme events are dominated by moisture supply(e.g. Trenberth, 2011), however as significant increases are notseen in the CCSM simulations further study is required to confirmthis effect. Both schemes project a decrease in the spatially aver-aged precipitation return value for the C2040s compared to theC1980s, with the least decrease shown by the TBW model. The dif-ference between the two projections is significant at the 0.90 con-fidence level. The scheme may also have some impact on thechange in the probability of annual runoff below the ecological re-serve in the Olifants basin. A jackknife test suggests that the TBWscheme projects a significant decrease in the probability of annualrunoff below this threshold. However, as discussed in Li et al.(2008), this method can under-estimate the variance in some casesand so further simulations are required to fully establish the signif-icance and robustness of this result.

The tightly bound water scheme has introduced a new param-eter, TBWfrac, to the land surface model, governing the fractionof the soil which consists of small pores. This is currently


determined by tuning the model to observations and therefore itwould be of significant value to perform field study work in orderto obtain a physical basis for these estimates, including its varia-tion with soil type. Observationally based values for the evapora-tion from tightly bound pores would also be of use. Investigationinto the comparative effect of parameterising the tightly boundwater concept with a more realistic continuous soil pore distribu-tion over the discrete 2-mode distribution modelled in this studywould be worthwhile. A number of studies have looked at the im-pact of including groundwater modules within land–surface mod-els and it would be valuable to determine the interaction betweensuch modules and the parameterisation of tightly bound soil water.

Acknowledgements

The authors would like to thank the AXA Research Fund for pro-viding funding for this work. We are grateful to the ECMWF for theRe-Analysis data obtained through the BADC provided by NERC. BPplc (Upstream Environmental Technology Program) is thanked forsupport. CCSM 6-hourly output was converted to WRF inputformat using code provided by Peter Caldwell at the Lawrence Liv-ermore National Lab, CA. The useful comments of two anonymousreviewers have helped improve this manuscript.

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A tightly bound soil–water scheme within an atmosphere–land–surface model