Importance of soil moisture measurements for inferring

Environmental Modelling & Software 18 (2003) 35–48www.elsevier.com/locate/envsoft

Importance of soil moisture measurements for inferring parametersin hydrologic models of low-yielding ephemeral catchments

S.A. Wooldridgea,∗, J.D. Kalmaa, J.P. Walkerb

a Department of Civil, Surveying and Environmental Engineering, The University of Newcastle, Callaghan, NSW, Australiab Department of Civil and Environmental Engineering, The University of Melbourne, Parkville, VIC, Australia

Received 21 March 2001; received in revised form 17 February 2002; accepted 16 April 2002

Abstract

Low-yielding catchments with ephemeral streams provide a stern test of the capability of conceptual catchment models forpredicting the hydrologic response of the natural landscape. Sustained periods of little or no flow mean that the information contentof the streamflow time-series for parameter estimation is limited. During periods with no streamflow, such ephemeral catchmentsalso offer no information on a catchment’s soil moisture status. As a result, parameters estimated solely from streamflow data areoften poorly identified and span a wide range of the feasible parameter space. These general observations were confirmed by anapplication of the conceptual VIC model in a 6 ha experimental catchment in eastern Australia. Using a Monte Carlo style assessmentof parameter uncertainty, it was shown that the simple three-parameter model was ill-posed when calibrated solely to the streamflowresponse. Failure of the calibration procedure to distinguish unique antecedent moisture storage conditions prior to large rainfallevents meant that the observed streamflow response could be replicated from a large envelope of potential parameter combinations.The inclusion of an estimated time-series index ofareal soil moisture status into the calibration procedure, however, significantlyreduced the number of feasible parameter combinations, and resulted in predictions that confirmed Bowen ratio measurements ofactual evapotranspiration. Attempts to further reduce parameter uncertainty by including the measured evapotranspiration data intothe joint calibration procedure were unsuccessful. The shortness of the measurement record was seen as a major factor inhibitingimprovement. The results of this study highlight the critical importance of antecedent moisture conditions on streamflow yields inephemeral catchments and point to the desirability of spatio-temporal soil moisture accounting. Future research efforts are discussedin terms of establishing the appropriate spatial and temporal resolution of soil moisture measurements needed to extend the resultsobserved for this small experimental study to larger catchments. 2002 Elsevier Science Ltd. All rights reserved.

Keywords:Ephemeral catchments; Conceptual catchment models; Soil moisture; Evapotranspiration; Joint calibration; Parameter uncertainty; MonteCarlo sampling

1. Introduction

Catchment models are hypotheses of the dynamicwater balance at the catchment scale. The identificationof such models requires validating the model hypothesesand, as part of that process, making inferences aboutmodel parameters. In this article, the issue of parameteridentification is considered in the application of concep-

∗ Corresponding author. Present address: The Australian Instituteof Marine Science, PMB No. 3, Townsville MC, QLD 4810, Australia.Tel.: +61-7-47534334; fax:+61-7-47725852.

E-mail address:[email protected] (S.A. Wooldridge).

1364-8152/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.PII: S1364-8152 (02)00038-5

tual catchment models in low-yielding ephemeral catch-ments.

Conceptual models typically involve a configurationof interconnected stores with mathematical transfer func-tions used to direct the movement of water betweenstores or into the stream. Although a mass balance isenforced for each store, the flux equations defining flowsinto and out of the stores are typically conceptual ratherthan physically based (Nash and Sutcliffe, 1970). Thisconceptual nature means that many of the parameters,state variables, and fluxes are not directly measurableand usually represent spatially and temporally lumpedcatchment characteristics. Consequently, although ratherparsimonious and not very data intensive, one of the

36 S.A. Wooldridge et al. / Environmental Modelling & Software 18 (2003) 35–48

distinguishing characteristics of conceptual models isthat the process of parameter inference relies heavilyupon calibration via inverse reasoning, typically to anobserved time-series of streamflow.

In low-yielding ephemeral catchments, parameteridentification by calibration to a streamflow record ishampered by the fact that the number of non-zero datapoints in the streamflow time-series may be quite small,even though the length of record is large. Thus, the infor-mation content of the streamflow time-series for para-meter identification is small. This presents particularproblems for models that generate surface runoff througha threshold process such as a spilling bucket. Duringcalibration the exceedence of the threshold may rarelyoccur and thus the bucket size is unidentifiable. This canlead to problems such as the existence of multiple optimawithin the feasible parameter space and the presence ofhigh interaction or correlation between subsets of fittedmodel parameters (see Duan et al., 1992; Freer et al.,1996). In more humid catchments this problem is oftennot as severe, as the information contained in the stream-flow series is likely to be rich enough to activate everymodel process several times during calibration (Ye etal., 1997).

A key outcome of ill-defined model parameters is thatit can no longer be assumed that accurate streamflowsimulation at the catchment outlet reflects accuratesimulation of internal catchment states and responses.This situation arises from the large number of modelparameter sets that produce virtually indistinguishablesimulated streamflow time-series even though the rela-tive contributions of the fluxes that make up the stream-flow vary greatly.

One obvious and well-documented way to increase theinformation content available for parameter estimationis to augment streamflow data with other kinds ofhydrologic information relevant to the prediction task(see for example, Mroczkowski et al., 1997; Franks etal., 1998). Examples of multiple responses include stre-amflow and stream chemical tracer data at differentlocations within a catchment and measurable internalhydrologic fluxes or states such as soil moisture, satu-rated areas, piezometric levels, and evapotranspiration atselected locations. Such data represent a much richersource of information about the catchment water balancedynamics than do streamflow data alone. General state-ments relating multiple data sources with improved para-meter identification, however, have been shown to be notuniversal. It has been shown, for example, that aug-menting streamflow with ‘point’ groundwater measure-ments does little to reduce parameter and predictiveuncertainty (e.g. Seibert et al., 1997; Kuczera andMroczkowski, 1998). Areal soil moisture, however,would appear to provide a valuable source of additionalinformation, especially for ephemeral catchments during

periods with no streamflow, and thus no information oncatchment-average soil moisture status.

Soil moisture content is a major control on hydrolog-ical processes for both storm and interstorm periods.During storm periods it influences the partitioning ofprecipitation into infiltration and runoff (for saturationexcess processes). For interstorm periods, soil moisturedetermines whether the soil column can meet the atmos-pheric demand for moisture; either at the surface (baresoil evaporation) or in the root zone (transpiration) andit thus affects the partitioning between latent and sens-ible heat fluxes. In this way, the soil moisture content isthe link between the surface energy and water balances.

In most conceptual models there is some represen-tation of soil moisture status, but validation against fielddata is often difficult because of at least two problems.Firstly, field measurements of soil moisture content aremade at the point scale while conceptual models providean estimate for a specified area, producing a disparity inscales. Secondly, soil moisture is highly variable inspace, meaning that individual point measurementsrarely if ever represent the spatial average of even smallareas. This necessitates that areal values are estimatedfrom many point measurements.

The hydrological literature contains few examples ofcatchment studies where distributed measurements ofsoil moisture values have been compared with valuessimulated by conceptual catchment models. Johnstonand Pilgrim (1976) showed a comparison between soilmoisture modelled with a simple conceptual model andsoil moisture data obtained from field measurements,providing an independent assessment of model perform-ance. Kuczera (1983) used soil moisture and throughfallmeasurements with a conceptual rainfall-runoff model.He noted that the use of data on runoff, soil moisture andinterception with catchment models can yield substantialreductions in the uncertainty of model parameters.Kalma et al. (1995) described a comparison betweensimulated soil moisture resulting from both a fixed andvariable storage conceptualisation and a soil moistureindex based on point measurements to show the potentialof conceptual models to make useful predictions of soilmoisture status at the catchment scale. Western et al.(1999) demonstrated that simulated time-series of spati-ally average soil moisture storage achieved with a quasi-distributed conceptual model was consistent with theobserved soil moisture characteristics. The statistical dis-tribution of soil moisture storage assumed in the model,however, was shown to differ from that observed.

This article aims to re-examine the usefulness of con-ceptual models for soil moisture prediction at the catch-ment scale. This is done via a case study application ofthe conceptual variable infiltration capacity (VIC) model(Wood et al., 1992) in a 6 ha experimental catchmentlocated in eastern Australia. The low-yielding catch-ment, which is representative of a large number of catch-

37S.A. Wooldridge et al. / Environmental Modelling & Software 18 (2003) 35–48

ments in semiarid regions of Australia, was chosen tobe a stern test of the capability of the VIC model. TheVIC model uses a statistical distribution to characterisethe spatial variation in soil moisture storage. For the cur-rent study, this distribution is determined explicitly bycalibration against combinations of surface runoff, soilmoisture and evapotranspiration data. Monte Carlo basedassessment of parameter uncertainty resulting from indi-vidual and joint calibrations leads to the main contri-bution of the article, namely to provide insight into thevalue of field measured soil moisture, evapotranspirationand surface runoff data for parameter inference andhydrological prediction in low-yielding ephemeral catch-ments.

2. Study area

The 6 ha Nerrigundah experimental catchment islocated in the Williams River catchment, approximately11 km north-west of Dungog, New South Wales, Aus-tralia (Fig. 1). The catchment runs east to west with arelief of 27 m. Hillslopes range from 3 to 22%, with themain drainage line having an average slope of 9%. Aver-age annual rainfall is 1000 mm and areal potential eva-potranspiration is 1600 mm. The soil type is a moder-ately well drained clay-loam duplex with an A horizonof approximately 30–40 cm and a clay B horizon from50 to over 100 cm deep. Measurement of bulk densityfrom 19 spatially distributed soil core samples indicatethat the mean porosity for the catchment is approxi-mately 50–55% v/v, while permeameter measurementsindicate that the saturated hydraulic conductivity of theA horizon is an order of magnitude larger than that ofthe B horizon (Walker et al., 2001).

3. Measurements

For the 908-day period of investigation (28.10.1996–07.04.1999) undertaken in this study, a variety of hydro-meteorological variables were measured. A weatherstation continuously measured net radiation, atmosphericpressure, wind speed and direction, relative humidity, airtemperature, rainfall, soil heat flux and soil temperatureat various depths. Apart from rainfall, all measurementswere made at 1-min intervals, with the average takenevery 10 min. Rainfall was recorded for each tip of the0.2 mm tipping bucket pluviometer.

A 45 cm Parshall flume at the catchment outlet moni-tored surface runoff. A second pluviometer was locatedat the flume, and four collecting rain gauges were distrib-uted throughout the catchment to check the spatial varia-bility of rainfall. The additional gauges showed that rain-fall at Nerrigundah was spatially uniform at both theevent and seasonal scales.

Fig. 1. The Nerrigundah experimental catchment, showing thelocation of the measurement sensors.

The soil moisture profile was continuously monitoredat 15 min increments using five Virrib soil moisture sen-sors (Komin, Technical Data) installed at depths of 10,15, 20, 30 and 40 cm for an individual point in the catch-ment, located at the weather station. The spatial variationof soil moisture profiles was periodically monitored withtime domain reflectometry (TDR) probes of variouslengths up to the maximum of 1 m or bedrock at 13 sitesdistributed throughout the catchment. The location ofthese sites is displayed in Fig. 1. The spatial TDR soilmoisture measurements were made on 40 days (atapproximately 2-week intervals) during the experi-mental period.

3.1. Intensive intersampling period

For a 24-day intensive soil moisture sampling period(04.03.1999–28.03.1999), evapotranspiration measure-ments were made with a Campbell Scientific Bowenratio system. The Bowen ratio system was located next


to the weather station and measured sensible and latentheat fluxes over 15-min time intervals. The location ofthe system achieved the required fetch-to-height ratio of1:150 (Heilman et al., 1989) for the predominant south-east wind direction. Based on spatial TDR soil moisturemeasurements for the top 40 cm during the intensivemeasurement period, it was considered that the moistureconditions at the Bowen ratio measuring site wereslightly drier than the catchment-wide ‘average’ . Itshould also be noted that above average soil moistureconditions were present during the intensive samplingperiod relative to the entire measurement period.

Fig. 2 displays the time-series of soil moisture (%v/v), latent heat flux (W/m2) and daily-accumulatedactual evapotranspiration (mm/day) for the 24-day inten-sive measurement period. The period corresponded to agradual lowering of soil moisture content from 42 to36% v/v over the first 16 days of measurement before a15 mm rain event on 20.03.1999 and a 30 mm rain eventon the 22.03.1999 resulted in a rise in soil moisture con-tent back to 45% v/v, with a subsequent lowering to 40%v/v over the following 6 days.

4. Soil moisture analysis

The 13 spatially distributed measurements of soilmoisture were discontinuous in time (i.e. approximately

Fig. 2. Measured soil moisture (% v/v), latent heat flux (W/m2) anddaily-accumulated actual evapotranspiration (mm/day) for the 24-dayintensive measurement period.

one measurement every 2 weeks) while the Virrib soilmoisture sensors at the weather station provided a con-tinuous soil moisture time series for an individual point.In order to recover a continuous record of areal soilmoisture, a merging of the two data sets was performed.The idea was to utilise the spatial measurements toobtain instantaneous catchment average soil moistureestimates, and then to statistically regress these arealestimates against the corresponding point measurements.The resulting relationship would thus allow for thereconstruction of a continuous areal estimate from thecontinuous point record.

Following the methodology of Kalma et al. (1995) asoil moisture index approach was utilised in an effort toaggregate the spatial (point-scale) soil moisture measure-ments to a single quantity that was representative ofareal soil moisture availability within the catchment. Foreach spatial location and for each day of measurement,the local value of the volumetric moisture content of thetotal soil profile (SM∗, % v/v) was measured with theTDR equipment. The soil moisture index SMI∗ at eachlocation was then defined by

SMI∗ � (SM∗�SM∗min) / (SM∗

max�SM∗min) � A /B (1)

where A � (SM∗�SM∗min) is the removable component

of total soil moisture (% v/v) and B � (SM∗max�

SM∗min) represents the maximum soil moisture storage

capacity (% v/v) at that point (with values obtained forthe entire sampling period). SMI∗ values thus rangebetween 0 and 1. Finally, with SMI∗ estimated for eachlocation, it was assumed that for each day of measure-ment, the areal soil moisture storage could be estimatedfrom SMI∗∗(�A /�B) based on all measurements on thatday. The utility of the index approach can be seen in thecomparison plots of Fig. 3a and b. Fig. 3a shows theactual measured temporal variation of the soil moisturecontent (% v/v) in the top 40 cm for a dry (Profile 2),intermediate (Profile 4) and wet (Profile 8) catchmentlocation. Fig. 3b shows the corresponding plot using theindex approach, and highlights the improved similaritybetween the profiles when using the index approach.

The temporal dynamics of the areal soil moistureindex (SMI∗∗) based on the 13 spatial locations wascompared to the corresponding point moisture index(SMI∗), as measured at the continuous Virrib monitoringsite. As a result of soil disturbance during installation,a 10-month ‘settling-in’ period of the Virrib sensors wasallowed in an effort to permit the soil to re-establishequilibrium conditions. The comparison was thereforenot attempted until day 315 (22.08.1997) of the experi-mental campaign, resulting in a total of 40point/spatial combinations.

Fig. 4 shows the plot of these 40 point/spatial soilmoisture index combinations, along with a fitted cubicpolynomial resulting from the regression between bothquantities. The nature of the polynomial is likely to inte-


Fig. 3. (a) Measured temporal variation of the soil moisture content(% v/v) in the top 40 cm for a dry (Profile 2), intermediate (Profile4) and wet (Profile 8) catchment location, and (b) the correspondingtemporal variation using the soil moisture index approach.

Fig. 4. Comparison between the continuous point moisture index(SMI∗) and the areal soil moisture index (SMI∗∗) for all days of spatialsoil moisture measurement.

grate the effects of a number of features, making exactphysical explanation difficult. Firstly, the shape is likelyto reflect the fact that the continuous soil moisturemeasurements were made at a comparatively drylocation within the catchment. It is also likely to accountfor differences in the measurement techniques. The Vir-rib sensors (at various depths) consist of two horizontallyinserted stainless steel concentric circular rings(electrodes of diameter 28 and 20 cm), which allow soilmoisture measurement by means of an electro-magneticfield generated around the two electrodes. The TDR sen-sors, on the other hand, measure the down and returntravel time of an electro-magnetic wave for two verti-cally inserted stainless steel probes of known length.While both approaches make use of the dielectricproperties of water, the structural differences in theapproaches are likely to result in slight differences inhow the measurements respond to temporal changes insoil water content.

Fig. 5 displays the result of the regression edited, con-tinuous point moisture index (SMI∗ (point-edit)), whichcan subsequently be interpreted as a continuous estimateof areal soil moisture index. Also shown for comparisonpurposes is the corresponding soil moisture index(SMI∗∗) resulting from the 13 spatial profiles. It can beseen that there is good agreement between the continu-ous and instantaneous estimates, which engenders con-fidence in utilising the developed areal estimates fordescribing the catchment average soil moisture status.Potential inaccuracies induced by the largely unknownparameter uncertainty of the regression relationshipshould, however, be kept in mind for the modelling thatis to follow.

5. Description of the VIC model

The conceptual water balance model used here is thesingle layer VIC model (Wood et al., 1992; Sivapalan

Fig. 5. Comparison of the regression edited, continuous point moist-ure index (SMI∗ (point-edit)), and the corresponding spatial moistureindex (SMI∗∗) resulting from the 13 spatial profiles.


and Woods, 1995; Kalma et al., 1995). Fig. 6a providesa schematic illustration of the soil moisture distributionapproach that forms the basis of the VIC model. TheVIC model assumes that scaled infiltration (i.e. storage)capacity is a random variable with its cumulative distri-bution function given by the Xinanjiang distribution(Zhao et al., 1980). The distribution function allows fora variable bucket conceptualisation that allows runoffgeneration and evapotranspiration to vary within an area(e.g. lumped catchment). Here, we apply the modifieddistribution function (Kalma et al., 1995), whichincludes a minimum storage level for the initiation ofsurface runoff (see Fig. 6b). The cumulative distributionof the scaled (i.e. normalised) storage capacity, s, isgiven by

Fig. 6. (a) Distribution approach towards variability in catchmentstorage capacity, and (b) schematic of the VIC hydrologic model con-ceptualisation (after Kalma et al., 1995).

s � 1�(1�smin)(1�a)1/b (2)

where a represents the saturated fraction of the totalcatchment area, smin, the threshold for overland flow andb, the model parameter giving the concave-up shape forvalues less than 1 and convex-up for values greater than1. Storage capacity at any point in a catchment is definedas the maximum depth of rainfall, which can infiltrateat that point. The scaled storage capacity, s, is the localstorage capacity divided by the largest storage capacityat any point in the catchment.

The soil moisture status for the entire catchment canbe described by the scaled soil moisture variable, v,which represents the actual scaled soil moisture in stor-age at every point of the catchment. Antecedent soilmoisture is indicated by v0. Those points on the landsurface with s � v0 are considered to be saturated,before any rain begins. If all soil water in the catchmentis assumed to be held in saturated soil, then the scaledsoil moisture can be written as v0 � y0 / zmax, where y0

is the height of saturated soil above bedrock (forlocations that are not already totally saturated) and zmax

the maximal soil depth across the catchment (y0 isassumed to be constant throughout the catchment). Fora given v (equal to s at saturation), the fraction of landsurface which is saturated is denoted by a, and the totalsoil moisture held in the catchment denoted by w. Givenvalues of b and smin, any one of v, w or a is sufficientto define the moisture status for the entire catchment.Kalma et al. (1995) specify all of these functionalrelationships.

The VIC model therefore produces a time series of w,the total moisture storage for the entire catchment. If thew values are divided by wc, the maximum possible valueof w when all the soil is saturated, then the ratio w /wc

is a catchment-scale wetness index. For the modifiedXinanjiang distribution (Eq. (2))

wc � smin � (1�smin) / (b � 1) (3)

Within the current VIC formulation, catchment-scaleevapotranspiration is calculated by integrating a point-scale model of evapotranspiration over the catchment-wide distribution of soil moisture conditions. The two-parameter point-scale model results in local evapotran-spiration Es being estimated as a function of local soilmoisture via the following step function

Es /Ep � [(v � yc) /s]h

for (v � yc) � sEs /Ep (4)

� 1 for (v � yc)�s

where Ep is the potential evapotranspiration from a uni-formly wetted surface, v, the level of soil moisture (equalto s at saturation), s, the local maximum of soil moisture,yc, the scaled capillary fringe thickness and h, a propertyof the soil and vegetation types, assumed to be constantin space. The total actual catchment evapotranspiration


Ea may then be found (see Sivapalan and Woods(1995) by

Ea /Ep(v,yc) � �1

0

Es /Ep(s;v,yc)Fs(s)ds (5)

Subsurface runoff in the VIC model is calculated asa linear function of average soil moisture storage, andsurface runoff is calculated by a simple water balance.

6. Application of the VIC model

6.1. VIC simulations

For the current application of the VIC model a dailytime step was used. Results are based on the 908-dayperiod between 28.10.1996 and the 07.04.1999. Potentialevapotranspiration (Ep) for the period was calculatedwith the Penman–Monteith model, following the meth-odology outlined by Smith et al. (1991). Net radiation,temperature, humidity and wind data were obtained fromthe Nerrigundah weather station. Daily rainfall was takenas the average of the measured volumes obtained fromthe two pluviometers within the catchment. Both rainfalland potential evapotranspiration were assumed to be spa-tially uniform.

Simulations began on 28.10.1996 with the initial con-dition of zero available water storage (i.e. maximumsimulated saturation deficit). To allow the internal statevariables to reach equilibrium, an 8-month period wasallowed before any calibration of the model parameterswas performed. Other parameters that were set prior tothe calibration included the conceptual maximum soildepth for active soil water movement (Dmax � 1 m, esti-mated from soil core data), the hydrologically activeporosity (�q � qsat�qpwp � 0.38m3 /m3), the estimatedheight of the capillary fringe divided by Dmax (yc �0.16m/m) and the subsurface recession constant (kc �0.0).

6.2. Parameter optimisation

Calibration of the VIC model parameters b, Smin andh was performed with the nonlinear regression softwarenlfit (Kuczera, 1994) using a sum of squared errorsobjective function. The parameter search strategyemployed the robust shuffled complex evolution methodof Duan et al. (1992) searching over a large hypercubein parameter space; the number of complexes was setequal to the number of fitted parameters. Though not asefficient as gradient search strategies, it virtually guaran-tees termination close to the global optimum (Kuczera,1997).

The VIC model was jointly calibrated to combinations

of daily streamflow, soil moisture and evapotranspirationtime series data from the Nerrigundah catchment. Thejoint calibration strategy, based on the work of Kuczera(1983), required care in its implementation. The key stepwas specification of a weight matrix, �, which deter-mines how much weight is assigned to each fittedresponse. Misspecification of the weights can result inpoor fits for some responses. To guard against this, itwas decided to initially fit each response separately withs2

i , i � 1,…,m, being the residual variance from mobserved time series. The weight matrix was theninitialised to zero except for the diagonal elements,which were set to

��1i,i � 1 /s2

i i � 1,…,m (6)

This ensured that the joint calibration did not giveundue weight to any particular response. After the firstjoint calibration the weight matrix was updated using thejoint residual vectors.

To assess the worth of the different data sources interms of parameter identification, a thorough uncertaintyanalysis was undertaken for the optimal parameter sets.This was achieved by directly computing the posteriorprobability distribution of each parameter. The posteriorprobability distribution represents what is known abouta parameter given the available data. All things beingequal, the more a posterior distribution concentrates itsprobability mass about a particular value the more pre-cise (or certain) the knowledge of that parameter will be.

Monte Carlo-based methods provide a useful tool forsampling from the posterior distribution. Two genericMonte-Carlo sampling approaches exist: namely impor-tance sampling and Markov chain sampling. Kuczeraand Parent (1998), provide a complete description ofboth approaches, and emphasize that Markov chain sam-pling is a more efficient method as it adapts to the trueshape of the posterior distribution via a random walkprocess. For the present application, the Markov chainsampling methodology of Kuczera and Parent (1998)was adopted, resulting in the implementation of theMetropolis algorithm (Metropolis et al., 1953). Thealgorithm was used to generate five parallel sequences,each with 2500 samples. Each sequence was started atthe most probable parameter value. The first 500 samplesin each sequence are discarded, leaving a total of 10,000samples. The parameter covariance and Metropolis sca-ling were updated after every 500 samples. An accept-able R statistic (Gelman et al., 1997) indicated approxi-mate convergence.

7. Results and discussion

7.1. Calibration to streamflow

In a general sense, calibration of the VIC model tostreamflow involved optimising the model parameters to


ensure that the minimum soil moisture deficit (smin�v)following a prolonged dry period would generate thecorrect amount of streamflow for the next large rainfallevent. This could be achieved by adjusting either thethreshold depth to overland flow, smin, or the evaporationparameter, b (which would then change v). Table 1apresents the Metropolis-sampled posterior mean andstandard deviation of the three fitted VIC parametersobtained from calibration against the observed stream-flow record. Fig. 7a presents the corresponding plot ofthe observed and predicted streamflow responses. Thegood agreement between responses as indicated by therelatively high Nash and Sutcliffe (1970) coefficient ofefficiency (i.e. E2 � 0.90), implies that the VIC modelwas able to successfully capture the streamflow responseof the catchment to precipitation and other climaticinputs. The large standard deviations associated with theposterior means of the fitted parameters, however, sug-gest a high degree of uncertainty associated with theoptimal parameter estimates. This high degree of uncer-tainty is demonstrated by the plot of the posterior densitydistribution of the 10,000 Metropolis samples for the band smin (Fig. 8a) and, b and h (Fig. 8b) parameters. Bothplots indicate a high degree of parameter interaction, andsuggest that an equally acceptable streamflow predictioncould occur from over a wide range of the feasible para-meter space. Presumably this parameter interaction is aresult of the previously mentioned fact, that for adequaterunoff prediction with the VIC model following dry per-iods (a common occurrence in ephemeral catchments),it is not strictly necessary that the actual level of soil

Table 1Metropolis sampled, posterior mean and standard deviation of the threefitted VIC parameters resulting from calibration to (a) streamflow data,(b) joint streamflow and soil moisture data (c) joint streamflow andevapotranspiration data and, (d) joint streamflow, soil moisture andevapotranspiration data

Parameter Mean Standard deviation

(a) Calibration to streamflow datab 2.32 1.065smin 0.19 0.016h 1.08 0.146(b) Calibration to streamflow � soil moisture datab 2.91 0.170smin 0.33 0.008h 2.02 0.054(c) Calibration to streamflow � evapotranspiration datab 0.865 0.063smin 0.463 0.049h 4.41 0.347(d) Calibration to streamflow � soil moisture � evapotranspirationdatab 2.68 0.168smin 0.31 0.010h 2.19 0.082

Fig. 7. Streamflow calibration. Comparison of observed and modelpredicted (a) streamflow, (b) areal soil moisture status and (c) evapo-transpiration.

moisture in storage (i.e. v) needs to be predicted cor-rectly, only that the minimum soil moisture deficit

(smin � v)

is correct. Subsequently, there are many ways in whichb, smin and h can interact to ensure that the correct vol-ume of runoff is achieved.

As an independent check of the usefulness of the stre-amflow calibrated VIC model as a predictor of thedynamic catchment water balance, a comparison was


Fig. 8. A plot of the posterior probability surface for the VIC model parameters; (a) b and smin and (b) b and h resulting from calibration solelyto streamflow data. Each plot is based on 10,000 samples as generated by the Metropolis algorithm.

made between model predicted soil moisture status andactual evapotranspiration, and the equivalent quantitiesas obtained by field measurement. Fig. 7b displays thecomparison of the areal wetness index obtained fromthe merged point and spatial field analysis (SMI∗ (point-edited)) and that produced by the VIC model (w /wc). Itcan be seen that while the temporal trace of relativecatchment wetness shows good agreement, the absolutevalues are rarely consistent. On average, over the entireperiod of investigation, the model simulates the catch-ment as being drier than reality. Although only a rela-tively short record, comparison of observed and pre-dicted actual evapotranspiration for the 24-day Bowenratio measurement campaign (Fig. 7c) suggests that apossible reason for the drier prediction of soil moisturestatus could be due to the fact that the model para-meterisation results in an over-prediction of actual eva-potranspiration for relatively wet conditions. Theessence of the evapotranspiration scheme utilised by theVIC (as described by Eq. (4)) is that the actual evapor-ation from bare-soil and vegetated surfaces is a fraction of the energy-limited (potential) rate, Ea � Ep, where is non-linearly related to soil moisture availability. Theperformance of this type of evapotranspiration schemehas traditionally been shown to become less satisfactoryas the modelling time-scale is reduced, leading to anoverestimation of evaporation during wet periods, andunder-estimation during dry periods (Chen et al., 1996).Because there are significant no-flow periods in the cali-bration record, within which there is no informationavailable to infer the correct temporal evolution of soilmoisture status, it is likely that the evapotranspirationrates resulting from such a scheme are not sufficientlyconstrained by the streamflow response alone.

7.2. Joint calibration involving streamflow and soilmoisture

Table 1b presents the Metropolis sampled, posteriormean and standard deviation of the three fitted VICmodel parameters obtained from joint calibration to theobserved streamflow and areal soil moisture data. Thecorresponding plots of observed and predicted stream-flow (Fig. 9a) and areal soil moisture status (Fig. 9b)resulting from the two optimised time-series, show thatwhile streamflow predictability is similar in comparisonto the single streamflow calibrated model, soil moistureprediction is considerably more consistent with thejointly calibrated model. Weiss and Smith (1998) explainthat it is common for the fit of each individual data setbased on a joint calibration to be worse than the fit ofeach data set using the estimates from that data set. Theimprovement in the prediction of the internal soil moist-ure state variable also corresponds with a significantreduction in the standard deviations associated with themean posterior parameter values of the optimal para-meter set (Table 1b). This reduction in parameter uncer-tainty is reflected in the constrained posterior density dis-tributions for the b and smin (Fig. 10a) and, b and h (Fig.10b) parameters.

From Fig. 9 it is clear that the inclusion of the soilmoisture data in the calibration process has providedadditional information with which to accept or rejectcompeting model parameterisations. This additionalinformation can be reconciled with the fact that by forc-ing the model to reproduce the time-series of soil moist-ure status, the acceptable range of the evaporation para-meter h is necessarily reduced. Because of the


Fig. 9. Joint streamflow and soil moisture calibration. Comparisonof observed and model predicted (a) streamflow, (b) areal soil moisturestatus and (c) evapotranspiration.

competing interaction of smin and b, the constraining ofb must similarly constrain the acceptable range of smin.

As an independent check of the value of the reducedparameter uncertainty, Fig. 9c shows the 24-day time-series of observed and predicted actual evapotranspir-ation resulting from the joint streamflow and soil moist-ure calibrated model. Comparison of the plot to the cor-responding predictions resulting from the streamflowcalibrated model (Fig. 7c) shows that the jointly cali-brated model results in considerably improved predictionof evapotranspiration, with predictions being surpris-

ingly accurate given the conceptual simplicity of the eva-potranspiration routine. The improvement in evapotran-spiration prediction highlights the importance of accuratesoil moisture accounting when evapotranspiration rou-tines based on Ea � Ep relationships are applied at thesmall-catchment scale. The comparatively poor evapo-transpiration estimates from the 23.03.1999 to26.03.1999 could possibly be related to measurementerror, as rain fell during this period and could have inter-fered with the measurement sensors of the Bowen ratiosystem. Assuming the data to be true could, however,allude to the above-mentioned deficiency with this styleof evapotranspiration routine that results in over-esti-mation of evapotranspiration for the wet conditions.

A question that deserves to be asked about the jointsoil moisture calibration is, ‘Would the same constrain-ing of the parameters occur for a humid, energy limitedcatchment as opposed to a water limited ephemeralcatchment?’ While the answer to this question obviouslylies in a repeat application, initial reasoning would tendto suggest not. For the humid catchment with abundantwater supply, the VIC model conceptualisation wouldconsistently result in the local soil moisture storagelevel, v, being above smin. The correct simulation ofevaporation and runoff would therefore only require thatthe changes in soil moisture be correct and not necessar-ily require the absolute values of soil moisture to be cor-rect. Specifying soil moisture correctly may therefore notprovide improved simulation of fluxes such as evapo-transpiration and streamflow for humid catchments. Insuch situations it may prove more beneficial to investi-gate the integrated value of soil moisture status (i.e. satu-rated area fraction).

7.3. Joint calibration involving streamflow andevapotranspiration

The measured 24-day evapotranspiration record wasutilised to investigate the ability of a joint calibrationbased on streamflow and evapotranspiration to aid inparameter identification and thereby constrain parameteruncertainty. Theoretically, if the evapotranspiration rec-ord could be considered representative of the areal esti-mate, and if it was of a sufficient length to contain thedynamics of both the wetting and drying of the soil pro-file for a variety of catchment wetness conditions, thenone would expect it to be a rich source of informationwith which to condition the internal dynamics of themodel.

Table 1c presents the Metropolis-sampled posteriormean and standard deviation of the three fitted VIC para-meters obtained from joint calibration to the observedstreamflow and evapotranspiration data. Examination ofthe parameter values for the optimal parameter setreveals a considerably smaller value of b and largervalues of smin and h compared to the previous parameter


Fig. 10. A plot of the posterior probability surface for the VIC model parameters; (a) b and smin and (b) b and h resulting from joint calibrationto streamflow � soil moisture data. Each plot is based on 10,000 samples as generated by the Metropolis algorithm.

combinations. The result of these parameter changes interms of changes in model function can be reconciled asfollows. The smaller value of b will result in lower levelsof saturation over all soil moisture levels and lead toreduced surface runoff for a given rainfall input. Thelarger value of smin means a greater level of antecedentwetness needs to be exceeded before the initiation ofsurface runoff. Finally, the larger value of h means areduced rate of evapotranspiration, although this will beoffset to some extent by higher average soil moisturelevels. A consequence of these parameter changes is aless dynamic catchment in terms of runoff and evaporat-ive fluxes, meaning that more water is held in storage.

The result of this parameterisation in terms of pre-dicted streamflow, soil moisture and evapotranspirationcan be seen in Fig. 11. Due to the joint conditioning,the parameterisation results in good predictions of thestreamflow and evapotranspiration responses. The pre-dicted soil moisture response, however, shows a poorcorrelation with the observed equivalent, with a moreconstant (i.e. less dynamic) soil moisture variation.Clearly, the evapotranspiration and streamflow fluxeshave been achieved at the expense of non-realistic soilmoisture conditions. By maintaining the catchment in a‘wet’ state, the streamflow and evapotranspiration vol-umes have been simulated with lower rates of evapotran-spiration and streamflow per unit surface area in unittime.

The poorly constrained posterior probability densitydistributions for the b and smin (Fig. 12a), and b and h(Fig. 12b) parameters, confirm the uncertainty associatedwith the model parameterisation. It should be noted thatthe y-axis scale describing the variation of smin (Fig. 12a)and h (Fig. 12b) is different from the earlier equivalent

plots and those which are to follow. In the case of smin

(Fig. 12a), the y-axis scale is threefold larger, and forh (Fig. 12b), the y-axis scale is eightfold larger. In acomparative sense therefore, there is considerably morevariation in the smin and h parameters for the case whenoptimisation is based on the joint streamflow and evapo-transpiration record.

The inability of the evapotranspiration data to provideconstrained, physically realistic, parameter estimates isa possible consequence of the Bowen ratio measure-ments not being representative of the ‘averaged’ evapo-transpiration behaviour of the catchment (e.g. due to soilmoisture and atmospheric boundary layer variabilityetc.). Given the reasonably homogeneous nature of thecatchment, a more likely reason is that the evapotranspir-ation record was too short to capture the full spectrum ofsoil moisture/evapotranspiration conditions experiencedwithin the catchment. Because the measuring period onlycorresponded with the catchment being in a relativelywet state, the parameterisation was not forced to be rep-resentative of the total dynamics experienced by thecatchment.

This result has a number of implications. Firstly, itwould appear that multiple discontinuous measurementperiods for a range of soil moisture conditions may proveto be more beneficial than a long continuous measure-ment record obtained under similar moisture conditions.Secondly, and in a related fashion, when undertakingjoint calibrations with variables of different measure-ment periods, a method of weighting each response vari-able that takes into consideration the range of ‘ realised’responses during the conditioning period relative the‘potential’ range (over all conditions) may be beneficial.While the current study re-confirms the inability of stre-


Fig. 11. Joint streamflow and evapotranspiration calibration. Com-parison of observed and model predicted (a) streamflow, (b) areal soilmoisture status and (c) evapotranspiration.

amflow (especially for ephemeral conditions) to stronglyconstrain model behaviour, it would appear that toomuch weight was given to the period for which evapo-transpiration measurements were undertaken.

7.4. Joint calibration involving streamflow, soilmoisture and evapotranspiration

The final component of this study investigated thepotential of observed streamflow, areal soil moisture andevapotranspiration data to provide improved constraint

of parameter estimates. Table 1 presents the Metropolis-sampled posterior mean and standard deviation of thethree fitted VIC parameters obtained from the joint cali-bration. It can be seen that the optimal parameter set isvery similar to that determined using only the streamflowand soil moisture data. However, comparison of theassociated standard deviations for the model parametersindicates a slight deterioration with the inclusion of theevapotranspiration data. This is confirmed by the slightlyless constrained posterior probability density distri-butions for the b and smin (Fig. 13a), and b and h (Fig.13b) parameters. Such a result would appear to suggestthat the additional information in the evapotranspirationrecord (above that contained by the streamflow and soilmoisture data) is limited. This is likely a consequenceof the limitations of the evapotranspiration data outlinedin the previous section. Although not shown, investi-gation of the fitted streamflow, areal soil moisture statusand evapotranspiration time-series also showed that theslight improvement gained in predicting the evapotran-spiration response (in comparison to the joint streamflowand soil moisture parameterisation) was at the expenseof the soil moisture response.

8. Conclusions and recommendations

This study has illustrated how a simple three-para-meter version of the conceptual VIC model is ill-posedwhen calibrated to the streamflow time-series for a 6 haephemeral catchment. The fact that a streamflowresponse is an integrated result of both quick-flow andslow-flow processes, combined with the fact thatextended periods with no streamflow offer no infor-mation on the catchment’s soil moisture status, makesthe process of inferring the compartmentalisation of stor-age within the catchment largely unachievable. As aconsequence, the internal soil moisture state and evapo-transpiration flux of the model, while being able to pro-vide a trace of the temporal dynamics, have only limitedcorrespondence in terms of the correct absolute values.

The inclusion of an additional measure of areal soilmoisture status was shown to provide significant con-straint of the feasible parameter space, by providingadditional information regarding the correct compart-mentalisation of storage. This result confirms sugges-tions by Jakeman and Hornberger (1993) who concludedwith regard to the robust application of conceptual mod-els that “ information on the flow needs to be obtainedfrom time-series data on the inputs and outputs of aboutevery second storage that is separately parameterised” .If, for example, with three or more connected storages,one has flow data only into the first and out of the laststorage, then the uncertainties of estimating the charac-teristic hydrological properties of all these storages willbe extremely high.


Fig. 12. A plot of the posterior probability surface for the VIC model parameters; (a) b and smin and (b) b and h resulting from joint calibrationto streamflow � evapotranspiration data. Each plot is based on 10,000 samples as generated by the Metropolis algorithm.

Fig. 13. A plot of the posterior probability surface for the VIC model parameters; (a) b and smin and (b) b and h resulting from joint calibrationto streamflow � soil moisture � evapotranspiration data. Each plot is based on 10,000 samples as generated by the Metropolis algorithm.

For the present study, the availability of spatially dis-tributed measurements of soil moisture was a key factorin defining a meaningful catchment-scale soil moistureindex. While these measurements were obtained usingonly modest equipment, for larger catchments it wouldbecome increasingly difficult to maintain such a sam-pling density. This raises an important question. If someform of ‘ internal’ moisture measurement is required toprovide confidence in the application of conceptual mod-els for use in catchment management studies and otherapplications, ‘To what level of detail should thesemeasurements be made, both spatially and temporally?’

Recent studies indicate that it might be possible to obtainreliable areal estimates of soil moisture from a limitednumber of point measurements, if the locations of thesemeasurements are chosen thoughtfully (Grayson andWestern, 1998). Our work with the VIC model withinthe Nerrigundah catchment also suggests that the mostimportant time to optimise the model in terms of thecorrect soil moisture storage (i.e. antecedent conditions)is the dry period prior to a significant runoff event. Whilepredicting the onset of significant runoff events is prob-lematic, historical/seasonal rainfall-runoff informationmay provide clues for suggesting appropriate sampling


times. It may be therefore that it is not necessary to haveextravagantly detailed spatial and temporal soil moisturepatterns to provide significant parameter constraintwithin land surface models. The utility of such sugges-tions will be the focus of additional research efforts.

Acknowledgements

Special thanks are made to John Russell, the ownerof the Nerrigundah catchment. John provided free accessto his land and willing cooperation throughout this pro-ject. A grateful acknowledgement is also made to GeorgeKuczera for his insightful comments and assistance withthe parameter-fitting package nlfit (Kuczera, 1994).Improvements to the current version of the manuscriptwere aided by the constructive suggestions of twoanonymous reviewers.

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