Initial Soil Water Content as Input to Field-Scale Infiltration and Surface Runoff Models

Download Initial Soil Water Content as Input to Field-Scale Infiltration and Surface Runoff Models

Post on 22-Aug-2016




0 download


Initial Soil Water Content as Input to Field-ScaleInfiltration and Surface Runoff ModelsRenato Morbidelli & Corrado Corradini &Carla Saltalippi & Luca BroccaReceived: 9 March 2011 /Accepted: 13 January 2012 /Published online: 1 March 2012# Springer Science+Business Media B.V. 2012Abstract Evidence is given of the role of initial soil moisture content, i, in determining thesurface runoff hydrograph at field scale, that is a crucial element when distributed models forthe estimate of basin response to rainfall have to be formulated. This analysis relies uponsimulations performed by a model that, because of the necessity of representing theinfiltration of surface water running downslope into pervious saturated or unsaturated areas,uses a coupled solution of a semi-analytical/conceptual approach for local infiltration and anonlinear kinematic wave equation for overland flow. The model was applied to actualspatial distributions of i, earlier observed over different fields, as well as to a uniform valueof i assumed equal to the average value or to the value observed in a site characterized bytemporal stability. Our results indicate that the surface runoff hydrograph at a slope outlet ischaracterized by a low sensitivity to the horizontal heterogeneity of i, at least in the cases ofpractical hydrological interest. In fact, in these cases the correct hydrograph can be simulatedwith considerable accuracy replacing the actual distribution of i by the correspondingaverage value. Moreover, the surface hydrograph is sufficiently well reproduced eventhough a single value of i, observed at a site anyhow selected in the field of interest, isused. In particular, this extreme simplification leads to errors in magnitude on peak runoffand total volume of surface water with values typically within 10% and 15%, respectively.Keywords Hydrology . Surface runoff modeling . Soil water content1 IntroductionThe estimate of rainfall infiltration at field scale is a fundamental topic in hydrologicalapplications based on the use of rainfall-runoff transformations. In fact, the latter is frequentlyWater Resour Manage (2012) 26:17931807DOI 10.1007/s11269-012-9986-3R. Morbidelli (*) : C. Corradini : C. SaltalippiDepartment of Civil and Environmental Engineering, University of Perugia,via G. Duranti 93, 06125 Perugia, Italye-mail: renato@unipg.itL. BroccaResearch Institute for Geo-Hydrological Protection, National Research Council,Via Madonna Alta 126, 06128 Perugia, Italyrepresented through abstractions of the basin geometry into networks of elements with planesand channels (Hager 1984; Woolhiser et al. 1990; Singh 1996; Melone et al. 1998). Further, aconceptual approximation of the hydrological response from this basin structure requires toidentify: (1) an objective correspondence of each element with a specific watershed region, (2)an appropriate formulation of effective rainfall over the planes, and (3) the transformation ofeffective rainfall to direct runoff, through the mechanisms of overland flow and channel flow.In this context, infiltration is generally the main loss that limits the development ofeffective rainfall at field scale. Therefore, the estimate of the areal-average infiltration rate, I,is required. That becomes complicated by the spatial variability of soil hydraulic properties(Zhao et al. 2010), rainfall rate and initial soil water content. The spatial variability ofsaturated hydraulic conductivity, Ks, is generally assumed as the most important in compar-ison with those of the other soil hydraulic properties that influence the infiltration process(Russo and Bresler 1981; Dagan and Bresler 1983). At the same scale the spatial variabilityof rainfall rate, r, is considered less significant, also in the case of convective rainfalls(Goodrich et al. 1995; Morbidelli et al. 2006). Many studies have shown that the spatialvariability of Ks, assumed as a stochastic variable with a lognormal probability densityfunction (Nielsen et al. 1973; Warrick and Nielsen 1980; Sharma et al. 1987; Loague andGander 1990), can significantly affect the response of a slope to a uniform rainfall (Binley etal. 1989a,b; Saghafian et al. 1995; Corradini et al. 1998; Merz et al. 2002). Under theseconditions, several semi-analytical (Sivapalan and Wood 1986; Govindaraju et al. 2001) andsemi-empirical models (Smith and Goodrich 2000; Corradini et al. 2002) were proposed forthe estimate of the areal-average infiltration rate. Some formulations concerning the effectsof the joint spatial variability of Ks and r were also developed. Wood et al. (1986) used thetwo-term Philip equation to find approximate expressions for areal mean and variance ofinfiltration rates, however, their averaging operation occurred in space over a single reali-zation. Their relationship for areal average infiltration was validated by comparison withMonte-Carlo simulations, but the magnitude and the trend of the resulting errors were notspecified. Furthermore, Castelli (1996) developed a theoretical approach but under verysimplified conditions, particularly for the formulation of local infiltration rate. Govindarajuet al. (2006) and Morbidelli et al. (2006) proposed a more complete modelling to obtain theareal average infiltration, with a semi-analytical formulation and an additional componentthat describes empirically the run-on process consisting in infiltration of surface waterrunning from saturated areas downslope over a pervious soil. The possibility to replacethe spatially varying infiltration rate by the average infiltration rate was investigated byTayfur and Singh (2004) but specifically in the context of models for sediment transport.However, all these models dont consider the possible effects of spatial variability of initialsoil water content, i, that has to be appropriately clarified.In a simulation study, using the Coweeta catchment topography, North Carolina, Graysonet al. (1995) considered two patterns of soil moisture with the same properties of mean,variance and correlation length. They showed that, assuming a pattern spatially random andthe other organized by a wetness index, very different responses to given rainfall inputs wereproduced. Similar results were also obtained by Merz and Plate (1997), Merz and Brdossy(1998) and Bronstert and Brdossy (1999). However, rather different results were derived inother investigations (Goodrich et al. 1994; Aubert et al. 2003; Longobardi et al. 2003;Corradini et al. 2008; Brocca et al. 2009b). In particular, for two sub-basins of the WalnutGulch experimental watershed, Goodrich et al. (1994) found that the knowledge of theremotely sensed average initial soil moisture was sufficient as input to rainfall-runoff modelsin semi-arid regions, provided the rainfall was known with a great spatial resolution.Grayson and Western (1998) suggested that a network with a limited number of moisture1794 R. Morbidelli et al.sensors could provide soil moisture time series potentially usable as antecedent conditiondata. Therefore, these indicative wetness conditions derived by satellite, and/or a few localmeasurements at surface (see also Tombul 2007), might be sufficient to establish antecedentconditions for a rainfall-runoff event in alternative to detailed spatial measurements (Korenet al. 2008). Recently, Brocca et al. (2009a, 2010) from spot measurements carried out indifferent experimental plots located in the Upper Tiber River (Central Italy) investigated thespatial pattern of the volumetric soil moisture at the surface. The results stated that, at fieldscale, i can be usually assumed as a random variable characterized by a probability densityfunction of normal type, set equal to zero for negative values, and coefficient of variationequal to0.1. Moreover, they found that a limited number of sampling points representativeof all the values observed in each experimental field was sufficient to determine averageconditions at basin scale (see also Vachaud et al. 1985), but they did not quantify theinfluence of this approximation on overland flow generation.Considering the results aforementioned someway contrasting, the main objective of thispaper is to improve the knowledge of the role of spatial variability of initial soil moisture onthe overland flow generated at the field scale. The proposed study takes into account theinfiltration of rainfall and, in addition, of overland flow running downslope into pervioussaturated or unsaturated areas (run-on process) that none of the above-mentioned inves-tigations considered earlier. Theoretical results have been obtained starting from the Broccaet al. (2009a, 2010) experimental data and combining a local infiltration model earlierproposed for complex rainfall patterns (Corradini et al. 1997) with a nonlinear kinematicwave approximation for overland flow. The second objective is to address the problemconcerning the number of soil moisture measurements to be sampled for an appropriateestimate of the field scale surface runoff hydrograph.2 Statement of the ProblemAs a geometrical simplification of a natural hillslope we represent it by a single plane ofslope S0. The soil is assumed to be vertically homogeneous, but the initial soil water contentis considered to vary through the soil surface according to experimental observations byBrocca et al. (2009a, 2010). Given a time varying rainfall rate, r, the generation of surfacerunoff will be governed by the combined effects of the processes of rainfall infiltration andrun-on. Figure 1 provides a simple scheme of the interacting processes along a strip of therainfallsaturated cellunsaturated cellrunoninfiltrationoverland flowslope outlett1t2t3rainfallsaturated cellunsaturated cellrunoninfiltrationoverland flowslope outlett1t2t3Fig. 1 Schematic representationof the mechanisms contributingto the generation of the surfacerunoff hydrograph at the fieldscale. A single strip at threedifferent times t1< t2slope at three different times t1< t2< t3. As it can be seen, in this example at the time t1 thereare only unsaturated cells subjected to rainfall infiltration, while at the time t2 there aresaturated cells with rainfall infiltration and unsaturated cells with infiltration due to bothrainfall and run-on; lastly, at the time t3 all the strips contribute to the overland flow at theslope outlet.Local infiltration is described by assuming one-dimensional flow into independentvertically homogeneous columns, following the scheme adopted by Corradini et al.(1998). The model proposed earlier by Corradini et al. (1994) and then reformulated byCorradini et al. (1997) is selected to determine the infiltration rate in each column, consid-ering that it was found to be very accurate by using the Richards equation as a benchmark.The flow problem is simplified by assuming an initial soil water content, i, invariant withdepth, z, and approximating the dynamic wetting profile, (z), by a distorted rectanglerepresented in functional form through a shape factor (1) which depends on the surfacewater content, 0. Combining the continuity equation and a depth-integrated form of theDarcy law, the following relation is obtained:d0dt 0 i b 0 I 0 0 i db 0 d0 b 0 h i q0 K0 0 i G i; 0 b 0 p K0I 0 1where t is the time; q0 is the downward water flux at the surface; K0 is the hydraulicconductivity at the surface; I is the cumulative dynamic infiltration depth; p is a quantitydepending on the profile shape and linked with ; G(i, 0) is the net capillary drivedepending on both the suction head, , and hydraulic conductivity, K, as:G i; 0 1K0Zy 0 y i K dy 2The model requires the knowledge of the functional forms of hydraulic soil properties,which are expressed according to the parameterization adopted by Smith et al. (1993) as:K Ks rs r 32 l=3y yb rs r c l=" #1 c= d 4where s is the volumetric water content at natural saturation; r is the residual volumetricwater content; 1 is the pore size distribution index; yb is the air entry head, which is given ina tabular form for soil texture classes (Rawls et al. 1983); and c and d are empiricalcoefficients. The downward water flux at the soil surface, q0 , may be formally expressed as:q0 r v0 unsaturated surface 5q0 f saturated surface 6where v0 represents the run-on in terms of discharge per unit surface, estimated as specifiedin the following. The quantity f denotes the infiltration capacity derived from Eq. 1 with1796 R. Morbidelli et al.d0/dt00. All the parameters in Eqs. 14 are considered to be constant through the slope,except the initial soil water content.Surface runoff is routed over the plane by the kinematic wave equation with flowresistance expressed by the Manning law (Woolhiser and Goodrich 1988; Singh 1996;Venkata et al. 2008). We have:@h@t @ahm@x r q0 7where h is the depth of flow at time t and position x; a 1=n S1=20 , with n Manningroughness coefficient; m05/3 and !hm at the slope outlet represents the discharge per unitwidth. The upper boundary condition and the initial condition are:h 0; t 0 and h x; 0 0 8By Eq. 5 we observe that over an unsaturated elementary area r-q0 of Eq. 7 is equal to -v0,while on a saturated surface r-q0 represents the effective rainfall rate. The quantity v0 isobtained through the solution of Eq. 7 in the adjacent upstream area. With the support ofprevious numerical simulations (Schmid 1989), we neglect the influence of overland flowdepth on the infiltration rate.The discharge at the slope outlet is given by:Qt a hm x L; t B 9with L and B length and width of the slope, respectively. In principle Q(t) is dependent on thespatial distribution of i through Eq. 1. We note that, in principle, for natural surfaces withirregular microtopography, flow dynamics should be represented in two dimensions by thediffusion wave approximations (Govindaraju et al. 1992; Tayfur et al. 1993; Tayfur andSingh 2004), while the use of the bi-dimensional kinematic wave approximation (Tayfur2001) would be inappropriate. However, for the case of a plain with smooth surface it iswidely recognized that the one-dimensional kinematic wave approximation provides anappropriate representation of the surface runoff hydrograph (see for example Giakoumakisand Tsakiris 2001). Our mathematical formulation is supported by the fact that our primaryobjective is not to maximize the accuracy in simulating the surface runoff hydrograph but toinvestigate its sensitivity to different spatial representations of soil moisture content. On theother hand, it is expected that the choice of a slope with erratic microtopography determinesan irregular bi-dimensional overland flow and therefore mitigates the role of the spatialvariability of i.3 Numerical Approach, Study Soils and Selected Rainfall EventsNumerical solutions of the kinematic wave equation coupled with the infiltration equationwere carried out over two different planes: the first-one, 60 m long and 50 m wide, thesecond-one 120 m long and 90 m wide, both with 4% slope along a specific direction.Equation 7 was solved by the Lax-Wendroff finite difference scheme using n00.15 sm1/3.A square grid of 10 m10 m was used for representing the soil moisture spatial variability.For a given soil moisture distribution we computed the overland flow response to a specificrainfall pattern at the slope outlet. Because of the one-dimensional flow paths along thex-direction, for a given set of values the contribution to discharge from each strip wastreated independently and the contributions of all the strips summed to form Q(t). TheInitial Soil Water Content as Input to Field-Scale Infiltration 1797computations were performed by adopting a 1.0 m long and 10 m wide grid to meet stabilityrequirements of the numerical procedure. This size of the grid was found to be the minimumfor which Q(t) changed appreciably as a result of the distortion associated with therepresentation of the run-on process. In fact, for the numerical solution we assumed thatthe discharge at the upper boundary of a grid element wetted immediately the entire element,while it physically takes some time before the wetting front advances over the same element.We selected a soil representative of a clay loam that is typically found in a region ofCentral Italy where measurements of spatial distribution of i were earlier carried out byBrocca et al. (2009a, 2010). The main hydraulic features of this soil that are required for theestimate of infiltration rate are given in Table 1.For this study we selected as i the values of soil water content observed by Brocca et al.(2009a, 2010) by a portable Time Domain Reflectometry. Many sequences of measurementsin different fields located inside the Vallaccia basin (area 60 km2) were carried out. In a givensampling day, soil moisture measurements were usually collected over regular grids in eachfield, characterized by uniform structure and use of soil, of extension between 3000 m2 and10800 m2. In this study we have selected data sets representative of a very large range ofinitial conditions. The main characteristics of the selected fields (Castel Rigone, Molino,Preggio and Colorso, hereafter denoted as CRI, MOL, MON and COL, respectively) andsoil moisture measurements in different periods are summarized in Table 2.The surface runoff hydrographs were derived for a variety of synthetic experimentsinvolving real rainfall patterns and design hyetographs referred to Central Italy.4 Analysis of ResultsIn principle, distributed or semi-distributed rainfall-runoff models should consider the spatialvariability of soil hydraulic properties, rainfall rate and initial soil moisture at the field scale.The problem has been widely examined with results that substantially agree for the first twoquantities. On the other hand, the role of the last quantity does not appear sufficiently clearand a possible representation based on the assumption of i as a random variable wouldmake the models considerably complex. Therefore, in the light of this problem we haveexamined the effects of the spatial variability of initial soil moisture on the overland flowhydrographs produced in each experimental field under different time-varying rainfall rates.Many observed soil moisture spatial distributions, together with their simplified representations,have been considered as potential initial distributions of i. In particular, a simple representationrelies on the observed soil moisture in a site that, through a temporal stability analysis, was earlierfound to be representative of a specific field (Brocca et al. 2010).Table 1 Hydraulic quantities ofthe study soil (for symbols see text) Property Study Soils 0.55r 0.08yb (mm) 400Ks (mmh1) 0.751 0.2c 5d (mm) 1001798 R. Morbidelli et al.Table2Maincharacteristicsoftheselectedfieldsandobservedsoilmoisturedistributions(Broccaetal.2009a,2010)FieldSoilTextureLandUseFieldDimens.(mxm)Spacing(m)NumberMeasur.PointsDateMeanValue(%)Stand.Dev.(%)MoistureDistributionPeculiarityCRISiltyclayandsandGrass60501030Feb22,200746.31.1HMVMay25,200712.21.7LMVMOLGravelGrass60501030Mar30,200729.51.3HMVMay25,200710.11.5LMVMONSandyloamGrass60501030Feb16,200749.13.3HMVMay25,200720.13.8LMVApr26,200721.25.8HCVCOLSandyloamGrass1209010108May5,200524.86.7LMVDec2,200539.74.8HMVHMV,Samplingdaywiththehighervalueofthemeanaveragesoilmoistureforthespecificfield(seeBroccaetal.2010);LMV,Samplingdaywiththelowervalueofthemeanaveragesoilmoistureforthespecificfield(seeBroccaetal.2010);HCV,Setofvalueswiththehighercoefficientofvariationforallsamplingdaysandfields(seeBroccaetal.2010).Initial Soil Water Content as Input to Field-Scale Infiltration 1799Representative results produced by the same observed rainfall pattern of convective type,selected among the natural events occurred in the Vallaccia River Basin, are shown in Figs. 2and 3. The surface runoff hydrographs of Fig. 2 were obtained for the CRI field. As it can beseen, the hydrograph is practically independent of the spatial distribution of i. In fact, thecurves obtained for the real distribution or for constant values of i, equal to the average inthe field and to the measurement in the site characterized by temporal stability, are verysimilar. We note that the results of Fig. 2 were obtained starting from a very humid soil.Under particularly dry soil initial conditions, Fig. 3 illustrates the results obtained for theMOL field where the observed moisture content was generally lower than those in the otherfields of Table 2. The shapes of the hydrographs are rather similar to those shown in Fig.2.A similar analysis was performed at the MON field where the average soil moisture wastypically the maximum observed at the field scale. Two sample events, with surface hydro-graphs generated by a low intensity natural rainfall of frontal type, are represented in Figs. 4and 5. The hydrographs of Fig. 4, simulated starting from a high average soil moisture,indicate that the approximation of the natural spatial distribution of i by the average valueleads to a shape of the hydrograph rather similar to the actual one, while the peak dischargeand the total volume of surface water become underestimated of 13% and 23%, respectively.On the other hand, the adoption of the i observed in a temporally stable site produces acurve with minor errors. In addition, Fig. 5 shows that much greater relative errors areassociated with experiments involving a very low value of initial soil moisture. Specifically,the hydrograph derived through the value of i measured in a temporally stable site ischaracterized by values of peak discharge and total volume of surface water overestimated ofabout 123% and 130%, respectively, while for i assumed equal to the areal-average valuethe same quantities are underestimated of 54% and 75%, respectively. In any case, the lasterrors are linked with an experiment that generates a very limited volume of surface water.Some simulations were also carried out for design hydrographs. As it could be expected,because in these conditions the design hyetographs generally involved rainfall rates largerthan those considered in the experiments of Figs. 2 and 3, the representation of the spatialheterogeneity of i was found to be needless, even for return periods typical of hydraulicstructures of minor importance (equal to 25 years).0.00E+005.00E-031.00E-021.50E-022.00E-022.50E-02Discharge (m3 /s)i,vi,mi,t0.61605101520Time (h)Rainfall Rate (mm)0.50 0.5 1 1.5 2Time (h)e i,vi,mi,t16Time (h)1.0Fig. 2 Comparison of simulated surface runoff hydrographs at the study slope outlet (60 m long and 50 mwide) for different initial soil water distributions: values spatially variable, i,v; average value of i,v at eachsite (0.463), i,m; and value observed at a site characterized by temporal stability (0.457) considered constantthrough the field, i,t. Soil moisture observed on February 22, 2007 at CRI experimental field by Brocca et al.(2010). Hydrographs obtained under a natural rainfall pattern1800 R. Morbidelli et al.An overall analysis of our results obtained over fields of 3000 and 10800 m2 indicatesthat the spatial variability of the initial soil moisture does not affect appreciably thegeneration of surface runoff at the field scale. In fact, infiltration under intense storms ofshort duration can be accurately described by adopting the soil moisture obtained as averagevalue through the field or that measured at a site characterized by temporal stability.Furthermore, in the events with rainfalls of moderate intensity and considerable duration asimilar simplification can be used, because the actual spatial distribution of i is crucial onlywhen the volume of surface water is very limited and the rainfall-runoff transformationbecomes not useful in the hydrological practice.In spite of our aforementioned results indicate that distributed rainfall-runoff models canavoid considering the heterogeneity of i at field scale, an alternative representation of soil0.00E+001.00E-032.00E-033.00E-034.00E-035.00E-036.00E-037.00E-038.00E-030 0.5 1 1.5 2Time (h)Discharge (m3 /s)i,vi,mi,t0.616Time (h)0.5 1.0Time (h)i,vi,mi,t16Rainfall Rate (mm)05101520Fig. 3 Comparison of simulated surface runoff hydrographs at the study slope outlet (60 m long and 50 mwide) for different initial soil water distributions: values spatially variable, i,v; average value of i,v at eachsite (0.101), i,m; and value observed at a site characterized by temporal stability (0.121) considered constantthrough the field, i,t. Soil moisture observed on May 25, 2007 at MOL experimental field by Brocca et al.(2010). Hydrographs obtained under a natural rainfall pattern0.00E+001.00E-032.00E-033.00E-034.00E-035.00E-036.00E-037.00E-038.00E-039.00E-030 1 2 3 4 5 6 7 8Discharge(m3 /s)i,vi,mi,t0.6 0.6 0.6 (h)RainfallRate(mm).......7.00E-03.Time(h)iri,vi,mi,t0.6 0.6 0.6 2.0 3.0 4.0 5.0 6.0Fig. 4 Comparison of simulated surface runoff hydrographs at the study slope outlet (60 m long and 50 mwide) for different initial soil water distributions: values spatially variable, i,v; average value of i,v at eachsite (0.491), i,m; and value observed at a site characterized by temporal stability (0.537) considered constantthrough the field, i,t. Soil moisture observed on February 16, 2007 at MON experimental field by Brocca etal. (2010). Hydrographs obtained under a natural rainfall patternInitial Soil Water Content as Input to Field-Scale Infiltration 1801moisture through the areal-average value or the value observed at a site earlier characterizedas temporally stable is required. Therefore while the models can be simplified, extendedexperimental observations have to be in any case performed. In this context, we haveexamined the possibility of reducing the experimental burden by selecting the essentialmeasurements to be carried out.Figure 6 shows, for very dry initial conditions, the sensitivity of the surface runoffhydrograph generated under a rainfall event of convective type to the number of sensorsused for estimating the areal-average value of i. The curves obtained using 30 sensors, and10 or 3 sensors anyhow selected among them are substantially superimposed. On this basis,0.00E+001.00E-052.00E-053.00E-054.00E-055.00E-056.00E-057.00E-058.00E-059.00E-051.00E-04Time (h)Discharge (m3 /s) i,vi,mi,t0.6 0.6 0.6 (h)Rainfall Rate (mm) 1.0 2.0 3.0 4.0 5.0 6.00 1 2 3 4 5 6 7 8i,vi,mi,t0.6 0.6 0.6 (h)Fig. 5 Comparison of simulated surface runoff hydrographs at the study slope outlet (60 m long and 50 mwide) for different initial soil water distributions: values spatially variable, i,v; average value of i,v at eachsite (0.201), i,m; and value observed at a site characterized by temporal stability (0.199) considered constantthrough the field, i,t. Soil moisture observed on May 25, 2007 at MON experimental field by Brocca et al.(2010). Hydrographs obtained under a natural rainfall pattern0.00E+001.00E-032.00E-033.00E-034.00E-035.00E-036.00E-037.00E-038.00E-039.00E-030 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2Time (h)Discharge(m3 /s)i,vi,3i,100.61605101520Time (h)RainfallRate(mm)0.5 1.0i,vi,3i,10160.5 1.0Fig. 6 Comparison of simulated surface runoff hydrographs at the study slope outlet (60 m long and 50 mwide) for different initial soil water distributions: values spatially variable, i,v; values assumed invariant withposition and obtained by averaging 3 (i,3) and 10 (i,10) random measurements, respectively. Soil moistureobserved on May 25, 2007 at CRI experimental field by Brocca et al. (2010). Hydrographs obtained under anatural rainfall pattern1802 R. Morbidelli et al.for the same rainfall event the extreme hypothesis with 1 sensor has been also taken intoaccount. Figure 7 compares the surface hydrograph estimated through the complete set ofobservations available in a representative field and those obtained by using only themaximum and the minimum values of i. The errors in magnitude on peak discharge andvolume of surface water are rather limited and in any case with values within 10% and 15%,respectively. A similar analysis has been carried out for surface runoff hydrographs producedby a natural rainfall event of frontal type involving much lower intensities (see Fig. 8). Theuse of a single extreme value of observed initial soil moisture leads to relative errors inmagnitude up to 22% for the peak value and 66% for the total volume of surface water,however the quantity of surface water involved is very reduced. Our results suggest that thewater content observed in a site randomly selected in the field study can be used as initialuniform value of i in rainfall-runoff modelling.This analysis showing the small role of spatial heterogeneity of i gets stronger if spatialvariability of saturated hydraulic conductivity, Ks, is also considered. In fact, in natural soilsthe spatial variabilities of i and Ks were found considerably different, with a coefficient ofvariation of Ks (typically between 0.3 and 1.0) much larger than that of i coming out fromour earlier measurements. Furthermore, the spatial variability of Ks was found to have asignificant role on areal infiltration for a wide range of conditions (Corradini et al. 2002).From these elements, it can be deduced that the spatial variability of Ks leads to mask theeffects of the heterogeneity in initial soil moisture on the surface water hydrograph.Further, we note that the results we have obtained at the COL field are similar to those wehave shown in this section for the other fields of smaller dimensions and in addition thesediffer from the earlier ones presented in some other investigations. However, such differ-ences can be ascribed to well-defined elements as the representation of the run-on processand the main characteristics of the study regions. In any case, at least for heavy rainfall rates,the results are not contrasting because our simulations refer to fields with uniform character-istics of both structural type and soil use, while Grayson et al. (1995), Merz and Brdossy(1998) and Bronstert and Brdossy (1999) used simulations at a larger scale where thesecharacteristics were spatially variable and associated with large coefficients of variation of0.00E+001.00E-032.00E-033.00E-034.00E-035.00E-036.00E-037.00E-038.00E-039.00E-030 0.5 1 1.5 2Time (h)Discharge(m3 /s)i,vi,1Mi,1m0.61605101520Time (h)RainfallRate(mm) i,vi,1Mi,1m16Time (h)0.5 1.0Fig. 7 Comparison of simulated surface runoff hydrographs at the study slope outlet (60 m long and 50 mwide) for different initial soil water distributions: values spatially variable, i,v; values assumed invariant withposition and equal to the maximum (i,1M) and minimum (i,1m) observed values, respectively. Soil moistureobserved on May 25, 2007 at CRI experimental field by Brocca et al. (2010). Hydrographs obtained under anatural rainfall patternInitial Soil Water Content as Input to Field-Scale Infiltration 1803i. The last statement is also supported by an investigation on the role of run-on. We havefound that, for any experimental situation examined here, the surface runoff hydrographsestimated with and without run-on are practically coincident. On the other hand, for largecoefficients of variation of i the same comparisons reveal that the run-on is still unimportantwhen heavy rainfall rates are involved, while, as it can be seen in Fig. 9, it reducesconsiderably the effects of spatial variability in soil water content for low intensity rainfalls.The representative event shown in Fig. 9 is referred to a coefficient of variation of i equal to0.4 (see, for example, Minet et al. 2010).Alternatively, we have verified that the application of the diffusion hydrodynamic modelproposed by Hromadka and Yen (1986) (see also Corradini et al. 1989) does not modify therole of the spatial variability of initial soil moisture content.0.00E+005.00E-051.00E-041.50E-042.00E-042.50E-043.00E-043.50E-048543210Time (h)Discharge(m3 /s)i,vi,1Mi,1m0.6 0.6 0.6 (h)RainfallRate(mm) i,vi,1Mi,1m0.6 0.6 0.6 2.0 3.0 4.0 5.0 6.06 7Fig. 8 Comparison of simulated surface runoff hydrographs at the study slope outlet (60 m long and 50 mwide) for different initial soil water distributions: values spatially variable, i,v; values assumed invariant withposition and equal to the maximum (i,1M) and minimum (i,1m) observed values, respectively. Soil moistureobserved on March 30, 2007 at MOL experimental field by Brocca et al. (2010). Hydrographs obtained undera natural rainfall pattern0.00E+001.00E-042.00E-043.00E-044.00E-045.00E-046.00E-040 1 2 3 4 5 6 7 8Time (h)Discharge (m3 /s)0.6 0.6 0.6 3 5 7 9 11 13Time (0.5 h)Rainfall Rate (mm) without run-onwith run-onFig. 9 Comparison of surface runoff hydrographs computed at the study outlet (60 m long and 50 m wide)with and without run-on. Initial soil moisture distribution of normal type with average value of 0.274 andcoefficient of variation equal to 0.4. Hydrographs obtained under a natural rainfall pattern1804 R. Morbidelli et al.5 ConclusionsIn the representation of surface runoff hydrographs at the field scale, both as an independentmodel and a fundamental component of distributed modeling for estimating the basinresponse, the infiltration process requires to consider the random spatial variability both ofsaturated hydraulic conductivity, Ks, and initial soil moisture content, i. The role of the firstquantity is widely recognized and many specific empirical and conceptual/semi-analyticalformulations have been proposed in the scientific literature in the last 10 years. On the otherhand, contrasting results concerning the weight of the spatial heterogeneity of i have beenpresented and thus a modelling describing the interaction between the spatial variability ofKs and i has not been sufficiently investigated. In this context, an interesting approach thatneglects the run-on process has proposed by Craig et al. (2010). In any case, the first issue tobe addressed in advance is to extend the analyses earlier carried out on the effects of thevariability of i for a given uniform Ks. This work accomplishes this objective.Our results indicate that for the estimate of the surface runoff hydrograph at a slope outletthe actual spatial distribution of i can be generally approximated with good accuracy by thecorresponding areal-average value or the i value observed at a site characterized bytemporal stability. In addition, our simulations show that, at least in the situations of majorinterest, the hydrograph is sufficiently well reproduced through a single measurement of iperformed at a site anyhow selected in the field of interest. These results point out that thesurface runoff hydrograph is characterized by a low sensitivity to spatial variations of i atleast when rainfalls of high intensity are involved. A similar behaviour has been found evenfor very humid soils under natural frontal rainfalls of low intensity. On the other hand, thissensitivity is much more pronounced for particularly dry soils under natural frontal rainfallof low intensity even though these situations determine a small amount of surface water andare therefore of minor interest in the hydrological practice.An overall analysis of our results suggests that, at the field scale, the spatial heterogeneityof i can be disregarded and therefore the fundamental quantity to be described as a randomvariable is the saturated hydraulic conductivity. On the other hand, when a larger scale thatincludes several fields with different structures and/or soil uses has to be considered, thevariability of both Ks and i should be represented by adopting as basic element a componentof deterministic type linked with the main trend of these two quantities.Acknowledgment This research was mainly financed by the Italian Ministry of Education, University andResearch and by the Cassa di Risparmio di Perugia Foundation.ReferencesAubert D, Loumagne C, Oudin L (2003) Sequential assimilation of soil moisture and streamflow data in aconceptual rainfall runoff model. J Hydrol 280:145161Binley A, Elgy J, Beven K (1989a) A physically based model of heterogeneous hillslopes, 1, Runoffproduction. Water Resour Res 25(6):12191226Binley A, Elgy J, Beven K (1989b) A physically based model of heterogeneous hillslopes, 2, Effectivehydraulic conductivities. Water Resour Res 25(6):12271233Brocca L, Melone F, Moramarco T, Morbidelli R (2009a) Soil moisture temporal stability over experimentalareas in Central Italy. Geoderma 148:364374Brocca L, Melone F, Moramarco T, Singh VP (2009b) Assimilation of observed soil moisture data in stormrainfall-runoff modeling. J Hydrolog Eng ASCE 14(2):153165Brocca L, Melone F, Moramarco T, Morbidelli R (2010) Spatial temporal variability of soil moisture and itsestimation across scales. Water Resour Res 46:W02516. doi:10.1029/2009WR008016Initial Soil Water Content as Input to Field-Scale Infiltration 1805Bronstert A, Brdossy A (1999) The role of spatial variability of soil moisture for modeling surface runoffgeneration at the small catchment scale. Hydrol Earth Syst Sci 3:505516Castelli F (1996) A simplified stochastic model for infiltration into a heterogeneous soil forced by randomprecipitation. Adv Water Resour 19(3):133144Corradini C, Melone F, Singh VP (1989) A simple approximation of the hydrograph downstream of a floodedarea. Nord Hydrol 20:179190Corradini C, Melone F, Smith RE (1994) Modeling infiltration during complex rainfall sequences. WaterResour Res 30(10):27772784Corradini C, Melone F, Smith RE (1997) A unified model for infiltration and redistribution during complexrainfall patterns. J Hydrol 192:104124Corradini C, Morbidelli R, Melone F (1998) On the interaction between infiltration and Hortonian runoff. JHydrol 204:5267Corradini C, Govindaraju RS, Morbidelli R (2002) Simplified modelling of areal average infiltration at thehillslope scale. Hydrol Process 16:17571770Corradini C, Morbidelli R, Saltalippi C, Flammini A (2008) Ruolo del contenuto di acqua iniziale del suolosullinfiltrazione media areale, XXXI Convegno Nazionale di Idraulica e Costruzioni Idrauliche, Perugia,912 settembre 2008, 18Craig JR, Liu G, Soulis ED (2010) Runoff-infiltration partitioning using an upscaled Green-Ampt solution.Hydrol Process. 24(16):23282334Dagan G, Bresler E (1983) Unsaturated flow in spatially variable fields, 1, Derivation of models of infiltrationand redistribution. Water Resour Res 19(2):413420Giakoumakis S, Tsakiris G (2001) Experimental validation of a linearized kinematic wave equation for micro-catchment water harvesting design. Water Resour Manag 15:235246Goodrich DC, Schmugge TJ, Jackson TJ, Unkrich CL, Keefer TO, Parry R, Bach LB, Amer SA (1994) Runoffsimulation sensitivity to remotely sensed initial soil water content. Water Resour Res 30(5):13931406Goodrich DC, Faurs J-M,Woolhiser DA, Lane LJ, Sorooshian S (1995)Measurement and analysis of small-scaleconvective storm rainfall variability. J Hydrol 173:283308Govindaraju RS, Kavvas ML, Tayfur G (1992) A simplified model for two-dimensional overland flows. AdvWater Resour 15:133141Govindaraju RS, Morbidelli R, Corradini C (2001) Areal infiltration modeling over soil with spatially-correlatedhydraulic conductivities. J Hydrol Eng 6(2):150158Govindaraju RS, Corradini C, Morbidelli R (2006) A semi-analytical model of expected areal-average infiltrationunder spatial heterogeneity of rainfall and soil saturated hydraulic conductivity. J Hydrol 316:184194Grayson RB, Bloschl G, Moore ID (1995) Distributed parameter hydrologic modelling using vector elevationdata: THALES and TAPES-C. In: Singh VP (ed) Computer models of watershed hydrology. WaterResources Publications, Highlands Ranch, Colorado, pp 669696Grayson RB, Western AW. (1998). Towards areal estimation of soil water content from point measurements:time and space stability of mean response. J. Hydrol 207:6882Hager WH (1984) A simplified hydrological rainfall-runoff model. J Hydrol 74:151170Hromadka TV II, Yen CC (1986) A diffusion hydrodynamic model (DHM). Adv Water Resour 9(3):118170Koren V, Moreda F, Smith M (2008) Use of soil moisture observations to improve parameter consistency inwatershed calibration. Phys Chem Earth 33(1718):10681080Loague K, Gander GA (1990) R-5 revisited, 1, Spatial variability of infiltration on a small rangelandcatchment. Water Resour Res 26(5):957971Longobardi A, Villani P, Grayson RB, Western AW (2003) On the relationship between runoff coefficient andcatchment initial conditions. Proc. MODSIM 2003 International Congress on Modelling and Simulation,Modelling and Simulation Society of Australia and New Zealand Inc., Townsville, Australia, 2:867872Melone F, Corradini C, Singh VP (1998) Simulation of the direct runoff hydrograph at basin outlet. HydrolProcess 12:769779Merz R, Brdossy A (1998) Effects of spatial variability on the rainfall runoff process in a small loesscatchment. J Hydrol 212213:304317Merz R, Plate EJ (1997) A analysis of the effects of spatial variability of soil and soil moisture on runoff.Water Resour Res 33(12):29092922Merz B, Brdossy A, Schiffler GR (2002) Different methods for modelling the areal infiltration of a grass fieldunder heavy precipitation. Hydrol Process 16:13831402Minet J, Laloy E, Lambot S, Vanclooster M (2010) Effect of GPR-derived within-field soil moisturevariability on the runoff response using a distributed hydrologic model. Hydrol Earth Syst Sci Discuss7:89478986Morbidelli R, Corradini C, Govindaraju RS (2006) A field-scale infiltration model accounting for spatialheterogeneity of rainfall and soil saturated hydraulic conductivity. Hydrol Process 20:146514811806 R. Morbidelli et al.Nielsen DR, Biggar JW, Erh KT (1973) Spatial variability of field measured soil-water properties. Hilgardia42(7):215259Rawls WJ, Brakensiek DL, Soni B (1983) Agricultural Management effects on soil water processes: Part I.Soil water retention and Green-Ampt parameters. Trans ASAE 26(6):17471752Russo D, Bresler E (1981) Soil hydraulic properties as stochastic processes, 1, Analysis of field spatialvariability. Soil Sci Soc Am J 45:682687Saghafian B, Julien PY, Ogden FL (1995) Similarity in catchment response, 1, Stationary rainstorms. WaterResour Res 31(6):15331541Schmid BH (1989) On overland flow modelling: can rainfall excess be treated as independent of flow depth?.J. Hydrol 107:18Sharma ML, Barron RJW, Fernie MS (1987) Areal distribution of infiltration parameters and some soilphysical properties in lateritic catchments. J Hydrol 94:109127Singh VP (1996) Kinematic wave modeling in water resources: surface water hydrology. John Wiley andSons, New YorkSivapalan M, Wood EF (1986) Spatial heterogeneity and scale in the infiltration response of catchments. In:Gupta VK, Rodrguez-Iturbe I, Wood EF (eds) Scale problems in hydrology. Water Science andTechnology Library, D. Reidel Publishing Company, Dordrecht, Holland, pp 81106Smith RE, Goodrich DC (2000) A model to simulate rainfall excess patterns on randomly heterogeneousareas. J Hydrol Eng 5(4):355362Smith RE, Corradini C, Melone F (1993) Modeling infiltration for multistorm runoff events. Water ResourRes 29(1):133144Tayfur G (2001)Modeling two-dimensional erosion process over infiltrating surfaces. J Hydrol Eng 6(3):259262Tayfur G, Singh VP (2004) Numerical model for sediment transport over nonplanar, nonhomogeneoussurfaces. J Hydrol Eng 9(1):3541Tayfur G, KavvasML,Govindaraju RS, StormDE (1993) Applicability of St.Venant equations for two-dimensionaloverland flow over rough infiltrating surfaces. J Hydraul Eng 119(1):5163Tombul M (2007) Mapping field surface soil moisture for hydrological modelling. Water Resour Manag21:18651880Vachaud GA, Passerat de Silans A, Balabanis P, Vauclin M (1985) Temporal stability of spatially measuredsoil water probability density function. Soil Sci Soc Am J 49:822828Venkata RK, Eldho TI, Rao EP, Chithra NR (2008) A distributed kinematic wave-Philip infiltration watershedmodel using FEM, GIS and remotely sensed data. Water Resour Manag 22:737755Warrick AW, Nielsen DR (1980) Spatial variability of soil physical properties in the field. In: Hillel D (ed)Applications of soil physics. Academic, New York, pp 319344Wood EF, Sivapalan M, Beven K (1986) Scale effects in infiltration and runoff production. Proc. of theSymposium on Conjunctive Water Use, IAHS Publ. N. 156, BudapestWoolhiser DA, Goodrich DC (1988) Effect of storm rainfall intensity patterns on surface runoff. J Hydrol102:335354Woolhiser DA, Smith RE, Goodrich DC (1990) KINEROS, A Kinematic Runoff Erosion Model, U.S. Dep. ofAgric., Agric. Res. Serv., Rep. ARS-77Zhao P, Shao M, Wang T (2010) Spatial distributions of soil surface-layer saturated hydraulic conductivity andcontrolling factors on dam farmlands. Water Resour Manag 24:22472266Initial Soil Water Content as Input to Field-Scale Infiltration 1807Initial Soil Water Content as Input to Field-Scale Infiltration and Surface Runoff ModelsAbstractIntroductionStatement of the ProblemNumerical Approach, Study Soils and Selected Rainfall EventsAnalysis of ResultsConclusionsReferences


View more >