Journal of Hydrology 275 (2003) 49–66 www.elsevier.com/locate/jhydrol

Modeling the effects of a partial residue mulch on runoff using a physically based approach A. Findelinga,*, S. Ruyb,1, E. Scopelc,2 a

Programme Agronomie, CIRAD-AMIS, Montpellier 34398, France b Unite´ CSE, De´partement EA, INRA, Avignon, France c Programme GEC, CIRAD-CA, Montpellier, France Received 19 November 2001; accepted 7 January 2003

Abstract A partial covering mulch of residue on the soil strongly affects runoff dynamics, which consequently substantially reduces runoff amount. Experiments were conducted in la Tinaja (Mexico) on runoff plots (RPs) (20 m2) of four different treatments (bare, unplanted with 1.5 t ha21 of residue, planted with 1.5 and 4.5 t ha21 of residue), to characterize mulch effects. During one crop cycle, rainfall and runoff flow were recorded at a 20 s time step. Soil moisture, crop leaf area index, saturated hydraulic conductivity and sorptivity were also measured. Mulch increased the infiltration rate of the topsoil layer, concentrated overland flow and slowed it down by increasing roughness and pathway tortuosity. The physically based model developed accounts for these mulch effects on runoff. The model consists of a production and a transfer module. Each RP is considered as a microcatchment drained by a single channel. The production module accounts for rain interception by the plant and the mulch, soil retention and infiltration. The excess rainfall that cannot infiltrate defines runoff and is concentrated in the channel. The transfer module governs runoff flow out of the RP according to Darcy – Weisbach’s law. The model was calibrated on 12 events (five parameters). Fitted parameters provided high Nash efficiencies ranging from 0.721 to 0.828. Both runoff hydrographs and volumes were well simulated. A sensitivity analysis was carried out on eight parameters and a partial validation was done on 14 independent events. The model can be used as a predictive tool to assess the effect of various types of mulch on runoff. All its parameters are physical and can be measured or derived from literature. The model can also simulate inner variables of interest (water depth in the channel, infiltration in the channel and the hillslopes, etc.) at any time during rainfall. q 2003 Elsevier Science B.V. All rights reserved. Keywords: Runoff; Partial mulch; Modeling; Corn; Soil

1. Introduction

* Corresponding author. Fax: þ 33-467615642. E-mail addresses: [email protected] (A. Findeling), ruy@ avignon.inra.fr (S. Ruy), [email protected] (E. Scopel). 1 Fax: þ33-432722212. 2 Fax: þ33-467617160.

Experimental knowledge about the effects of a mulch of vegetative residue on runoff is well established. Savabi and Stott (1994) proved that this porous media can store significant amounts of liquid water. Rutter et al. (1971) and later Scopel et al. (1998) showed that a mulch partly intercepts the rain

0022-1694/03/$ - see front matter q 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-1694(03)00021-0

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A. Findeling et al. / Journal of Hydrology 275 (2003) 49–66

and cuts down the quantity of water reaching the soil. Gilley and Kottwitz, (1994) observed an increase in soil retention capacity due to the modification of soil microtopography by mulch elements. Also, mulch elements act as a succession of barriers that block runoff and increase roughness (Gilley et al., 1991; Gilley and Kottwitz, 1992; Weltz et al., 1992). Consequently, runoff pathways are generally more sinuous, and runoff flow velocity lower on mulched soils (Abrahams et al., 1994; Poesen and Lavee, 1991). Finally, mulch tends to develop and strengthen topsoil structure through soil protection, macro-fauna activity and the incorporation of organic matter, which usually provides a high infiltration rate (Rao et al., 1998; Scopel et al., 1998; Valentin and Bresson, 1992; Zachmann and Linden, 1989). However, very few authors have attempted to formalize or model these effects. Moreover, their models did not address all the previously listed effects but focused only on certain specific points. Gilley et al. (1991) modeled the uniform water flow on an impervious surface (, 7 m2) covered with glued residue, with the help of Darcy Weisbach’s law. Yu et al. (2000) used Manning’s equation to simulate overland flow on a mulched impervious soil (108 m2), at a 1 min time step. In both cases, modeling was in good agreement with experimental data and contributed to the determination of a friction factor that varies according to the type of residue used. However, the important role of the mulch in infiltration processes was not taken into consideration. Bristow et al. (1986), and later Bussie`re and Cellier (1994) and Gonzalez-Sosa et al. (1999), developed two similar mechanistic vertical 1D models to simulate the heat and water regimes of mulched soil. They simulated rain interception by mulch and percolation to the soil, and assumed that the rain that could not infiltrate into the soil was directly evacuated from the system, without considering runoff flow dynamics on the soil. The lack of accurate experimental data made calibration and validation of runoff processes impossible in these models. Based on the early experimental results of Scopel et al. (1998), the present study consists in quantifying and modeling all the important effects (rain interception, soil infiltration and retention, velocity and pathway geometry of runoff flow) of a partialcovering mulch of corn residue on runoff.

The methodology adopted consists of two parts: (1) obtaining a set of data that describe runoff dynamics at a short time step (20 s) on middle-scale runoff plots (RPs) (20 m2), (2) developing a physical model that accounts for the main processes that drive runoff on mulched soils, and calibrating and validating the latter on the experimental data.

2. Theory Because we worked on a soil that tended to crust, we assumed that the topsoil layer strongly controlled infiltration (Vandervaere et al., 1998). Based on this concept, the model developed is composed of a production module for estimating runoff volume and a transfer module for assessing its flow dynamics to the plot outlet. The system on which the model was applied consisted of a RP that was simplified to a micro-catchment of two hillslopes drained by a single central channel (Fig. 1). The central channel had an average slope of 0.07 and was assumed to be of constant width, occupying a fraction 0 , al # 1 of plot width (l ¼ 2 m). The hillslopes had an average slope of 0.05. 2.1. Runoff production The production module accounts for rain interception by the plant and the mulch, and soil retention and infiltration. It defines runoff production as an excess of rain that cannot infiltrate or be stored, and is evacuated in the channel. Concerning rain interception, the distinction between the hillslopes and the channel was not taken into account. The plant and the mulch had a maximum water storage capacity, respectively, Rp;max and Rm;max (m), defined by: Rp;max ðtÞ ¼ aLAI LAIðtÞ

ð1aÞ

Rm;max ðtÞ ¼ aBm Bm ðtÞ

ð1bÞ

where t is time starting from the beginning of each rainfall event (s), aLAI ¼ 2 £ 1024 ; an empirical coefficient (m) derived from Brisson et al. (1998), LAI the leaf area index of the plant (m2 m22), aBm ¼ 0:355 £ 1023 an empirical coefficient (m ha t21) derived from Arreola Tostado (1996), and Bm the mulch biomass (t ha21). Plant and mulch water

A. Findeling et al. / Journal of Hydrology 275 (2003) 49–66

51

Fig. 1. Conceptual diagram of the model (case of a planted and mulched plot).

storage are set at zero at the beginning of each rainfall. When rain starts, the plant intercepts all the rain till plant storage, Rp (m), reaches its maximum value: ( DRp ¼

DR;

Rp , Rp;max

0;

Rp ¼ Rp;max

ð2Þ

where R is the cumulative rain (m). This simplified approach causes an overestimation of the plant interception, when the plant coverage is low. However, the interception is very small for small values of LAI and this overestimation is negligible. When throughfall onto the soil and the mulch begins, mulch interception, Rm (m), is proportional to mulch coverage, tc (m2 m22), till it reaches its maximum value: 8 0; > > < DRm ¼ tc DR; > > : 0;

Rp , Rp;max Rp ¼ Rp;max and Rm , Rm;max ð3Þ Rp ¼ Rp;max and Rm ¼ Rm;max

The amount of rain, which is not intercepted by the mulch, is transmitted to the soil. This transmission is total when mulch storage reaches its maximum value. The cumulative amount of rain reaching the soil, Rs

(m), is governed by: 8 0; > > < DRs ¼ ð1 2 tc ÞDR; > > : DR;

Rp , Rp;max Rp ¼ Rp;max and Rm , Rm;max Rp ¼ Rp;max and Rm ¼ Rm;max ð4Þ

Infiltration rate in the soil, qi (m s21), is defined: qi ¼ ð1 2 al Þqih þ al qic

ð5Þ

where qih and qic are the hillslopes and channel contributions, respectively (m s21). Infiltration rate is 21 controlled by a potential infiltration rate qpot i (m s ), defined by the law of Philip (1957): qpot i ðtÞ ¼

Sðus ; u0 Þ 1 pffi þ ð1 þ mÞKs 3 2 t

ð6Þ

where S is the soil sorptivity (m s21/2) for initial and saturated water content, respectively, u0 and us (m3 m23), m is a parameter ranging from 0 to 1 (Haverkamp et al., 1999) and set to 0, Ks is the soil water conductivity at saturation (m s21), and t is the elapsed time from the beginning of rain (s). Hydraulic properties and initial conditions are supposed to be the same for hillslopes and channel, which lead to a single value for qpot i : When the water cannot infiltrate totally into the soil on hillslopes (Fig. 1), a residual amount

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A. Findeling et al. / Journal of Hydrology 275 (2003) 49–66

hh (m), remains on the surface: qih Dt ¼ min½hh þ DRs ; qpot i Dt

ð7aÞ

Dhh ¼ DRs 2 qih Dt

ð7bÞ

This amount is stored till it reaches the soil surface retention capacity hs (m), and is later infiltrated. The potential excess, hh;excess ¼ max½hh 2 hs ; 0 (m), is concentrated in the central channel with a one time step delay (20 s) (Eq. (13)), which is in good agreement with the concentration law of Gregory (1982) for a hillslope length of 1 m, a slope of 0.05, a Manning’s roughness coefficient of 0.01, and a typical rainfall intensity of 6 mm h21 (Table 1). In the channel, infiltration is governed as on the hillslopes

and the potential residual amount of water, hc (m), is calculated from the amount of rainfall and infiltration: qic Dt ¼ min½hc þ DRs ; qpot i Dt

ð8aÞ

Dhc ¼ DRs 2 qic Dt

ð8bÞ

Runoff transfer begins if water depth in the channel exceeds zero and water is evacuated from the plot. The runoff flow is described in Section 2.2. 2.2. Runoff transfer The transfer module deals with runoff flow in the channel (Fig. 1), and takes into account pathway tortuosity and soil and mulch friction. It is based on

Table 1 Definition and main characteristics of the 26 rain events used for modeling Rain event Calibration

Day of year (d)

Duration (h)

Amount (mm)

Validation

1c 1v 2c 2v 3c 4c 3v 5c 4v 5v 6c 6v 7v 8v 9v 7c 8c 10v 9c 11v 12v 10c 11c 12c 13v 14v

Intensity (mm h21) Average

Maximum

184 187 187 188 210 213 220 224 237 238 239 239 243 245 249 249 252 254 255 261 262 272 272 274 278 285

2.41 0.34 0.30 0.16 0.43 2.87 0.88 0.88 0.59 1.41 0.51 0.76 0.76 0.53 1.41 2.25 1.48 0.47 1.53 0.42 1.87 1.08 1.17 1.25 0.63 0.23

16.9 1.6 3.2 2.0 7.8 8.0 4.6 4.8 4.8 7.4 4.5 1.5 3.6 2.0 4.1 5.6 6.9 3.2 6.4 1.6 2.0 7.6 3.6 4.1 3.0 2.6

6.9 4.8 10.7 12.5 18.2 2.8 5.3 5.5 8.1 5.3 8.8 1.9 4.8 3.8 2.9 2.5 4.6 6.8 4.2 3.9 1.1 7.1 3.1 3.2 4.7 11.3

108.0 36.0 68.6 36.0 72.0 9.0 36.0 36.0 36.0 36.0 72.0 6.0 18.0 12.0 9.0 12.0 36.0 36.0 18.0 12.0 2.3 72.0 12.0 36.0 36.0 36.0

Minimum Maximum Average Median

0.16 2.87 1.02 0.82

1.5 16.7 4.7 4.1

1.1 18.2 6.0 4.8

2.3 108.0 34.6 36.0

A. Findeling et al. / Journal of Hydrology 275 (2003) 49–66

53

the semi-empirical law of Darcy –Weisbach (Gilley et al., 1991): sffiffiffiffiffiffiffiffiffi 8gSo h ð9Þ v¼ f

starting the following iteration, by accounting for runoff discharge and hillslopes inflow:

where v is the horizontal runoff flow velocity (m s21), g the acceleration of gravity (m s22), So the slope of the rough surface (– ), h the thickness of the flowing water (m), and f the Darcy – Weisbach friction factor ( – ). The presence of mulch on the soil increases the length and tortuosity of runoff pathways. The flow occurs with lateral movements along an apparent shallower slope in the channel (Findeling, 2001). This effective flowing slope Se (– ) is derived from soil surface slope So (– ), with the help of a trigonometric calculus:

where 1=al and (1 2 al Þ=al are concentration factors of the water in the channel depending on the relative width of the latter. An example of the dynamics of most variables of the model is given in Fig. 2, for a typical rain event.

sin a Se ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi with So ¼ tan a 2 t 2 sin2 a

ð10Þ

where a is the angle between horizontal and soil surface (rad), and t the pathway tortuosity ( –), defined as the ratio between real length of a trajectory and direct length between the top and the bottom of this trajectory. The similar effect on the hillslopes is neglected. Mulch elements also acts as a succession of physical obstacles that block runoff and delay its flow (Findeling, 2001). These complex mulch effects may be considered to be greater roughness on mulched soil than on bare soil, and are included in the model as a friction factor f that increases with mulch biomass. Allowing for mulch specificity and assuming that the channel has a negligible retention capacity, we define the potential runoff flow velocity in the channel as vpot (m s21): sffiffiffiffiffiffiffiffiffiffi 8gSe hc pot ð11Þ v ¼ f The runoff flow per unit surface q (m s21) is then derived from vpot by assuming a uniform flow in the central channel and respecting the limitation of the amount of available water in the channel: qDt ¼

al h c min½vpot Dt; L L

ð12Þ

where L ¼ 10 m is the length of the RP. The residual amount of water in the channel is actualized before

Dhc ¼ 2

1 1 2 al qDt þ hh;excess al al

ð13Þ

3. Material and methods Experimental data (rain and runoff dynamics), soil, mulch and plant properties, and parameters describing runoff flow were required to calibrate and validate the model. This information was obtained from measurements on different plots and is described in the subsections below. The methodology adopted for modeling consisted of three steps: (1) calibration of runoff production and transfer modules by means of an iterative procedure; (2) sensitivity analysis; (3) validation of the model. 3.1. Experiments Experiments were performed from July to October 1998 (crop cycle) in la Tinaja (Mexico-State of Jalisco) on 4 RPs, under natural rain in a semi-arid climate. It was surrounded by metal plates and runoff water was collected in a drum (180 l) located at its outlet. When the first drum was full, a partitioning device extracted one fifth of the excess runoff, which was then stored in a second drum. Each RP formed a single replication of a specific treatment (Table 2), identically repeated since 1995: direct drilling of corn with 4.5 t ha21 of corn residue mulch (RP4.5P), direct drilling of corn with 1.5 t ha21 of corn residue mulch (RP1.5P), no tillage and no plant with 1.5 t ha21 of corn residue mulch (RP1.5), and bare soil (RP0). Crop LAI was measured on RP4.5P and RP1.5P every week with a radiation interception measuring device (picqhelios model). The mulch was composed of vegetative corn residue (canes, leaves, etc.) from the previous crop, which were brought in from adjacent plots and spread out homogeneously on the soil.

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A. Findeling et al. / Journal of Hydrology 275 (2003) 49–66

Fig. 2. Dynamics of some intermediate variables of the runoff-infiltration process simulated by the model for rain event 5c (Table 1) and plot RP4.5P (Table 2).

Mulch elements were left at the surface and decomposed along the crop cycle. We assumed a mulch biomass degradation based on a decreasing exponential law with extinction factor aBm ¼ 7:02 £ 1023 d21 (Arreola Tostado, 1996). Mulch coverage was derived from previous measurements (Arreola Tostado, 1996). The RPs were on a sandy-silt soil (16.5% clay, 23.9% silt and 59.5% sand) with a bulk density of 1500 kg m23. The soil was assumed to possess homogeneous hydraulic properties within each RP. As RPs were small and thus very sensitive to invasive measurements, soil hydraulic properties were roughly estimated by measurements on adjacent plots with the same treatments. Water content at saturation us (m3 m23), hydraulic conductivity at saturation Ks

(m s21), and intrinsic soil sorptivity Sðus ; 0Þ (m s21/2) were measured with the help of the 1D Beer – Kan method (de Condappa, 2000; Haverkamp et al., 1998), with 10 averaged replications (Table 2). Since this method ignores 3D fluxes and so gives rise to a slight overestimation of Ks ; the measured values of Table 2 were taken as upper bound values. Soil moisture was measured every week in the 0 –20 cm layer of the RPs with buried TDR probes (four replications per plot). These measurements were not continuous enough to constraint the model but permitted to assess the initial soil water content u0 of each event. Rainfall and runoff dynamics were measured with an electric pluviograph and pressure sensors located at the bottom of each drum. These instruments were connected to a Campbell CR10 datalogger operating

Table 2 Plant, mulch and soil experimental measurements on the four RPs (uncertainty in brackets, minimum and maximum in square brackets) Plot

RP4.5P RP1.5P RP1.5c RP0 a b c

Plant

Soila

Mulch

Type

Maximum LAI (m2 m22)

Initial biomass Bm (t ha21)

Coverage rate tc (–)

Hydraulic conductivityb Ks (1026 m s21)

Intrinsic sorptivity S (1024 m s21/2)

Corn Corn None None

3.1 2.7 0.0 0.0

4.5 1.5 1.5 0.0

0.70 0.30 0.30 0.00

25.0 17.6 17.6 1.94

6.00 4.38 4.38 1.50

(0.5) (0.5) (0.0) (0.0)

(0.2) (0.2) (0.2) (0.0)

(0.05) (0.05) (0.05) (0.00)

Soil parameters were estimated on adjacent plots. At saturation ðus ¼ 0:420 m3 m23 Þ: This plot had direct drilling of corn with 3.0 t ha21 of mulch from 1995 to 1997.

[6.89; 42.7] [6.16; 29.0] [6.16; 29.0] [0.08; 4.49]

[2.18; 8.61] [1.89; 6.82] [1.89; 6.82] [0.60; 2.12]

A. Findeling et al. / Journal of Hydrology 275 (2003) 49–66

at a 20 s time step. Water temperature in the drums was measured (thermocouple) to correct thermal drift of the sensors according to previously performed laboratory calibration. When measuring pressures, allowances were made for sediment deposit on the sensors and at the bottom of the drums. Technical problems due to the erratic working of the partitioning device prevented us from using rain events that produced more runoff than the first drum capacity, which corresponded to a runoff amount of about 9 mm. We included only the small or medium rain events for this work. A specific runoff experiment was designed to provide an in situ estimation of some key runoff parameters of the model. These measurements were performed to confirm the assumption of the model and to initialize the calibration procedure of the latter. They were carried out at the beginning of the cycle (day 187). Two artificial and constant water flows (Qlow ¼ 5:13 ^ 0:50 £ 1025 m 3 s 21 and Qhigh ¼ 2:14 ^ 0:29 £ 1024 m 3 s 21) which correspond to usual runoff flows, were distributed regularly along the top of each plot. Measurements were performed on each RP when runoff flow had reached a stationary regime. Flow velocity, v (m s21), and flow thickness, h (m), were measured in the main rills. v was measured considering the time necessary for a colored plume to flow across a section of 3 m (three replications) whereas h was measured with a ruler (five replications). Pathway tortuosity, t (– ), was calculated as the ratio between the real trajectory length and the direct length between the top and the bottom of this trajectory (three replications). Real length was measured with a cord that was placed along runoff pathways. Proportion of the plot width occupied by the flow, al (– ), could not be measured accurately because there was no clear distinction between emerged and submerged soil. al was estimated visually for the high value of water flow in the center part of each plot. The impact of the lack of precision on al will be discussed in the sensitivity analysis. 3.2. Modeling 3.2.1. Calibration of the model From the 26 rain events used (Table 1), 12 events produced a significant runoff volume on

55

the four RPs. All these events were necessary to explore satisfactorily the high variability of the hydrological regime of la Tinaja (rain amount, maximum rain intensity, duration, temporal structure of the rain intensity). Besides, these events had the highest signal amplitude (rain and runoff intensity) and thus the lowest sensitivity to measurement errors. The model was calibrated with these 12 events to maximize the scope of the calibration. The remaining events were used for validating the model. The observed variables were the runoff flow per unit surface, qobs (m s21), and the cumulative runoff volume per unit surface, Vobs (m). The former was used in the calibration procedure of the model and the latter was eventually used for comparison with the model outputs. The model was calibrated on five parameters (Table 3): (i) soil water conductivity at saturation, Ks ; and soil intrinsic sorptivity, Sðus ; 0Þ; which were roughly estimated on adjacent plots, (ii) soil surface retention capacity, hs ; which was not measured, and (iii) proportion of the plot width occupied by the flow, al ; and friction factor, f ; which were difficult to assess accurately. A direct calibration of all the parameters with the help of an automatic non-linear optimizer does not always provide a relevant solution. The minimum of the error function may indeed be poorly defined for so many parameters. To avoid this eventuality we split the parameters into two sets: (i) Ks ; S and hs ; and (ii) al and f : Both sets were calibrated with a controlled iterative procedure. Each iteration had two steps. In the first step, al and f were kept constant and Ks ; S and hs were optimized. In the second step, temporary best values of Ks ; S and hs were used, and al and f were optimized. Best values of the latter parameters were then used to start the next iteration. For the first iteration, al and f were set to measured values of Table 4. For each step, optimization consisted in maximizing a Nash efficiency criterion, Eq ( –): N ð X ½ ½qði; tÞ 2 qobs ði; tÞ2 dt

Eq ¼ 1 2

i¼1 N ð X ½ ½qobs ðiÞ 2 qobs ði; tÞ2 dt

ð14Þ

i¼1

where N is the number of considered rain events ( –), q the simulated runoff flow per unit surface (m s21),

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A. Findeling et al. / Journal of Hydrology 275 (2003) 49–66

Table 3 Definition of the ranges used for the calibration of the model parameters Parameter Symbol

Ks Sðus ; 0Þ hs al f

Range Unit

RP4.5P

1026 m s21 1024 m s21/2 mm – –

RP1.5P

RP1.5

RP0

Min

Max

Min

Max

Min

Max

Min

Max

0.00 0.00 0.00 0.05 0.5

25.0 6.00 1.40 0.90 20

0.00 0.00 0.00 0.05 0.1

17.6 4.38 1.40 0.90 15

0.00 0.00 0.00 0.05 0.1

17.6 4.38 1.40 0.90 15

0.00 0.00 0.00 0.05 0.1

1.94 1.50 1.40 0.90 10

and qobs ðiÞ the average measured runoff flow per unit surface for a given event i (m s21). In practice, we defined a calibration range for each parameter and each RP (Table 3). The ranges of Ks and S were based on the upper bound values obtained from measurements and the usual spatial variability of one order of magnitude for such parameters. The range of al was imposed by its physical limits. The range of f was based on measurements and plausible extreme values (Weltz et al., 1992). The range of hs was derived from literature (Kamphorst et al., 2000). For step one, we scanned the 3D matrix defined by the ranges of parameters Ks ; S and hs and calculated the corresponding values of Eq (113 simulations). The best triplet of parameters was manually determined with the help of Eq contour maps. For step two, the same method was applied to al and f (102 simulations). The procedure was repeated until convergence, which was reached after three iterations and provided a set of five adjusted parameters for each RP.

3.2.2. Sensitivity analysis A one-at-a-time analysis of the sensitivity of the model was carried out on the five calibration parameters plus three additional parameters: the effective slope Se ; the coefficient of rain interception by plant aLAI ; and by mulch aBm (Table 5). The relative variation of the parameters dk;l (–) was defined as:

dk;l ¼

pk;l 2 pk if pk – 0 pk

ð15aÞ

dk;l ¼

pk;l 2 pk otherwise ppk

ð15bÞ

where k [ {1; …; 8} is the index of parameter (– ), l [ {1; …; lk } the index of current value of the considered parameter (– ), lk the number of values taken by parameter number k ( –), pk and pk;l ; the optimum value and current value l of parameter number k; respectively, and ppk ¼ minl=pk;l –0 lpk;l l the smallest non zero value of parameter k in absolute

Table 4 Experimental characterization of runoff flow for two artificial and constant water flows (uncertainty in brackets) Parameter

Tortuosity t Eff. slope Se Flow depth h Velocity v Friction f Occupation al a

Not measured.

Unit

– % mm m s21 – –

RP4.5P

RP1.5P and RP1.5

RP0

Qlow

Qhigh

Mean value

Qlow

Qhigh

Mean value

Qlow

Qhigh

Mean value

1.54 4.5 3.50 0.07 2.63 NMa

1.38 5.0 8.25 0.12 2.26 0.15

1.46 4.8 – 0.09 2.45 0.15

1.31 5.3 3.00 0.17 0.43 NM

1.26 5.5 6.00 0.21 0.60 0.20

1.28 5.4 – 0.19 0.52 0.20

1.11 6.3 2.00 0.20 0.25 NM

1.06 6.6 3.50 0.35 0.15 0.40

1.09 6.4 – 0.27 0.20 0.40

(0.08) (0.3) – (0.03) (1.50) (0.15)

(0.03) (0.2) – (0.02) (0.24) (0.10)

(0.05) (0.3) – (0.08) (0.10) (0.10)

A. Findeling et al. / Journal of Hydrology 275 (2003) 49–66 Table 5 Definition of the ranges of the parameters used for the analysis of sensitivity Parameter Unit

Ks Sðus ; 0Þ hs al f Se aLAI aBm

m s21 m s21/2 m – – – m m ha t21

Parameter Number of Range index k values lk 1 2 3 4 5 6 7 8

7 7 9 10 7 7 8 8

[0:1p1 ðjÞ; 10p1 ðjÞ] [0:1p2 ðjÞ; 10p2 ðjÞ] [0.0; 2.0] [0.05; 0.99] [0:1p5 ðjÞ; 10p5 ðjÞ] [0:1p6 ðjÞ; 10p6 ðjÞ] [0; 10p7 ðjÞ] [0; 10p8 ðjÞ]

terms. Detailed information about the parameters and their ranges is given in Table 5. Model sensitivity was studied through two significant output variables: the maximum runoff flow, qm (m s21), and the cumulative runoff volume per unit surface, V (m). The sensitivity j (– ) was expressed for each variable and each parameter as :

jðX;dk;l Þ¼

N 1 X 4N i¼1 X Xði;p1 ðjÞ;…;pk;l ðjÞ;…;p8 ðjÞÞ  21 ð16Þ  Xði;p1 ðjÞ;…;pk ðjÞ;…;p8 ðjÞÞ j

where X[{qm ;V} is the type of variable, and j[{ RP0;RP1:5;RP1:5P;RP4:5P} the index of RP. 3.2.3. Validation of the model Using optimized parameters, the model was tested as a predictive tool on the 14 rain events that were not used for calibration (Table 1). It was noted that this validation was only partial as validation events had light rain amount and intensity. The model could therefore not be tested in conditions of substantial runoff production, especially for RP4.5P. However, the validation permitted to estimate roughly the scope of the calibrated model.

4. Results 4.1. Experiments The results of the artificial runoff experiment are presented in Table 4. Tortuosity increased almost

57

linearly with mulch biomass, its average from 1.09 on RP0 to 1.46 on RP4.5P (Table 4). Corresponding effective slope decreased from 0.064 to 0.048. Friction factor, derived from velocity and flow depth (Eq. (11)), was strongly affected by mulch biomass and increased on average from 0.20 on bare soil to 2.45 on RP4.5P. Width occupation varied from about 0.15 on mulched plot to approximately 0.40 on bare soil. Unsubmerged mulch elements acted like microdams and tended to concentrate the flow, whereas bare soil let it spread more widely. We present the runoff coefficients (RC) for 26 rain events distributed over the 1998 crop cycle on Fig. 3. These experimental results showed that the four treatments were separated event per event and on average at the cycle scale (RC ¼ 0:05 for RP4.5P, RC ¼ 0:16 for RP1.5P, RC ¼ 0:22 for RP1.5, and RC ¼ 0:44 for RP0). The differences between RC were highly significant ðp ¼ 0:001Þ for all the treatments, except for RP1.5 and RP1.5P ðp ¼ 0:18Þ: RP0 recorded the greatest RC ranging from 9 to 80% throughout the experiment. This plot was bare and crusted (Table 2) and had no rain interception. A strong mulch effect was observed when comparing RP1.5 with RP0. The small amount of residue in RP1.5 dramatically cut down runoff (0% , RC , 57%). Mulch intercepted up to 5% of the rain and increased friction and pathways tortuosity (Table 4), which slowed the flow down. It also improved infiltration rate by soil protection. A comparison of RP4.5P and RP1.5P showed that mulch biomass had an important impact on runoff. RC was seldom greater than 0% and never exceeded 23% for RP4.5P, whereas it was often substantial for RP1.5P (0% , RC , 48%). An increase in mulch biomass enhanced the mulch effects (interception of up to 16% for RP4.5P). Finally, a slight plant effect was observed when comparing RP1.5P with RP1.5, especially in the second part of the cycle when the crop was well developed. Soil protection and rain interception by the plant (up to 5%) were probably the main factors that contributed to the decrease of RC by 5– 15%. Cumulative and instantaneous hyetograph and runoff hydrographs were obtained for every event given in Table 1. Measured runoff dynamics showed general common characteristics that can be represented by the event 5c (Fig. 4). Curves of Fig. 4a

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A. Findeling et al. / Journal of Hydrology 275 (2003) 49–66

Fig. 3. Effect of treatments on runoff coefficient (26 events, 1998 crop cycle).

were ordered like cumulative runoff and never crossed, which proved that at any time during a rain event runoff followed the previously observed pattern. The general shape of the cumulative hydrographs did not vary significantly with treatment (except RP4.5P which sometimes had no runoff). They were similar to rain dynamics and may be deduced from the latter by means of a storage threshold and a reduction factor according to the treatment used. Ponding time varied significantly according to rain intensity but were also generally ordered (Fig. 4b): the quickest pondings were observed in RP0 (no interception and low infiltration rate), while RP1.5 and RP1.5P had intermediate ponding times,

and RP4.5P, which had the highest interception (mulch and plant) and infiltration rate, recorded the highest ponding time (sometimes infinite). Instantaneous runoff flow was the highest on RP0, medium on RP1.5P and RP1.5 (with values slightly greater for RP1.5) and the lowest on RP4.5P, which was consistent with all the previous results. 4.2. Modeling 4.2.1. Calibration of the model Calibrated parameters are given in Table 6. Except for RP4.5P, calibrated Ks and Sðus ; 0Þ followed

Fig. 4. Effect of treatments on runoff dynamics for event 5c: measured runoff amount (a) and measured runoff intensity (b).

A. Findeling et al. / Journal of Hydrology 275 (2003) 49–66

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Table 6 Optimal value of the parameters and performance of the calibrated model for the 12 calibration events (uncertainty in brackets) Parameter, variable

Unit

RP4.5P

RP1.5P

RP1.5

Ks Sðus ; 0Þ hs al f

1026 m s21 1024 m s21/2 mm – –

15.0 1.20 0.00 0.15 15.0

5.28 1.53 0.00 0.15 5.0

2.64 1.75 0.00 0.15 5.0

Runoff flowa Eq Slope Origin sres R2

– – mm h21 mm h21 –

0.725 0.832 20.047 1.248 0.736

Runoff amount P V P V P obs ½V 2 Vobs 

mm mm mm

6.3 8.5 22.2

(0.009) (0.024)

0.786 0.927 20.245 1.967 0.794 16.9 22.5 25.6

(0.009) (0.038)

0.721 1.001 0.105 2.589 0.763 29.1 27.4 1.7

RP0 0.19 0.75 0.20 0.45 1.5

(0.010) (0.051)

0.828 1.064 20.224 2.447 0.865

(0.008) (0.051)

46.2 46.9 20.7

a Slope, origin, residual standard deviation and determination coefficient derive from linear regression between q and qobs of the 12 calibration events (2921 values per RP).

the same trend as measurements with mulch application rate (Table 2). The low value of calibrated Sðus ; 0Þ for RP4.5P was due to the high ratio Ks =Sðus ; 0Þ; which provided the highest sensitivity to Ks and the lowest sensitivity to Sðus ; 0Þ; through the linkage between Ks and Sðus ; 0Þ in Eq. (6). This mathematical artifact does not mean that sorptivity was low in RP4.5P. A simulation was carried out with and Ks ¼ 1:25 £ 1025 m s21 Sðus ; 0Þ ¼ 2:40 £ 1024 m s21/2, which respect the experimental trend of Table 2. This simulation provided an efficiency of 0.707, only 2.5% lower than the maximum efficiency (Table 6). Calibrated hs ; al ; and f were sound in spite of high values of friction factor that will be analyzed in the discussion. The simulation was satisfactory for the 12 contrasted events with efficiencies ranging from 0.721 for RP1.5 to 0.828 for RP0 (Table 6). Regression between simulated and observed runoff flow gave slopes in the range of 0.832 – 1.064 with origins always lower in absolute terms than 0.25 mm h21, and determination coefficients in 0.736 – 0.865. Residual standard deviation never exceeded 2.6 mm h21. The total amount P P of observed and simulated runoff (respectively,P Vobs and V), and the bias on runoff volume ( ½V 2 Vobs ) are given in Table 6, for the whole crop cycle. The total

amount of runoff was well simulated for unplanted plots and somewhat underestimated for planted plots (up to 5.6 mm). Observed and simulated runoff hydrographs of two contrasted events (1c and 5c) are represented in Fig. 5. We generally observed a good agreement between simulation and observation for both events. For event 1c (Fig. 5a – d), intensity peaks were well reproduced even at the beginning when intensity was low. However, intensity was underestimated for RP1.5 (10 mm h21). Event 5c had a lighter rain intensity (Fig. 5e – h). Its intensity peaks were correctly reproduced with discrepancies lower than 5 mm h21. The advance of the model for RP1.5 and RP0 (3 min) was due to a model structural imperfection that will be debated in the discussion. 4.2.2. Sensitivity analysis For all the parameters except for the third ðk – 3Þ; relative variation dk;l was defined by Eq. (15a). For parameter hs ðk ¼ 3Þ; d3;l was defined using Eq. (15a) for RP0 and Eq. (15b) with p3 ¼ 0:2 mm for the other plots. Model sensitivity j is presented in Fig. 6 for both output variables qm and V against the relative variation of each parameter. General behavior of the model proved consistent: j was an increasing function of Se and a decreasing function of all other parameters. The highest sensitivity was observed for

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Fig. 5. Comparison of observed and simulated runoff hydrographs for two calibration events (1c on the left and 5c on the right).

A. Findeling et al. / Journal of Hydrology 275 (2003) 49–66

Ks and S for both output variables. For output variable qm ; the model had a substantial sensitivity to f and Se that governed runoff flow dynamics. Sensitivity was intermediate for hs ; aBm and al which accounted for rain retention, rain interception and relative width of the flow. As aLAI had the lowest incidence, it justified the use of an approximate value obtained from literature. For output variable V; parameters hs and aBm had the second highest impact on sensitivity. This is logical because these parameters quantified rain interception and thus runoff production. Sensitivity was moderate for aLAI and al ; which characterized the interception of rain by the plant and the proportion of the plot surface generating runoff, respectively. The lack of precision on al had consequently a small impact. Finally, f and Se ; which mainly affected runoff propagation had a small impact on runoff volume sensitivity. 4.2.3. Validation of the model Main characteristics of validating simulations are given in Table 7. Statistical results of RP4.5P proved

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poor because runoff dynamics were very small. The difference between observed and simulated runoff amount was small in absolute terms (1.2 mm). For RP1.5P and RP1.5, efficiencies were higher (, 0.5) and linear regression between observation and simulation gave slopes in the range of 0.452 – 0.492 with origins lower in absolute terms than 0.03 mm h21 and determination coefficients within the 0.499 – 0.527 range. Residual standard deviation remained lower than 0.7 mm h21. Small slopes meant an underestimation of runoff flow which led to a slight underestimation of runoff amount (, 3 mm). For RP0, efficiency was the highest (0.661) and linear regression was closer to the y ¼ x axis, with a determination coefficient of 0.721 and a residual standard deviation of 1.6 mm h21. The total runoff amount was well simulated. Observed and simulated runoff hydrographs of two validation events (4v and 5v) are represented in Fig. 7. Flows in RP4.5P are very small and thus difficult to reproduce. The model proved sensitive enough to respond to event 4v but did not simulate runoff for

Fig. 6. Model sensitivity on maximum runoff flow (a– b) and runoff volume (c –d) for the four RPs.

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Table 7 Performance of the calibrated model for the 14 validation events (uncertainty in brackets) RP4.5P Runoff flowa Eq Slope Origin sres R2

– – mm h21 mm h21 –

20.013 0.096 0.002 0.142 0.200

Runoff amount P V P V P obs ½V 2 Vobs 

mm mm mm

0.2 1.4 21.2

RP1.5P

(0.004) (0.003)

0.499 0.452 20.030 0.456 0.681 1.7 4.4 22.8

RP1.5

(0.007) (0.011)

0.527 0.492 20.009 0.661 0.665 3.2 6.6 23.5

RP0

(0.008) (0.016)

0.661 0.824 0.226 1.623 0.721

(0.012) (0.041)

15.7 16.2 20.5

a Slope, origin, residual standard deviation and determination coefficient derive from linear regression between q and qobs of the 14 calibration events (1898 values per RP).

event 5v. For the other treatments, we observed a good agreement between simulation and observation for both events. Intensity peaks were all qualitatively reproduced even if some discrepancies of about 5– 10 mm h21 appeared, especially for event 4v (Fig. 7a– d). The advance of the model was observed for RP1.5 and RP0 as during the calibration of the model.

5. Discussion In this work, specific experiments were designed to assess quantitatively the main effects of a partial covering mulch of corn residue on runoff. Measurements showed that runoff was dramatically cut down by mulch, even for a small amount of residue. Runoff coefficient was reduced by 50% on average by applying only 1.5 t ha21 of residue. This behavior was due to both short-term and long-term effects. At the cycle scale, the mulch stored up to 1.6 mm by rain interception, which reduced runoff production. Runoff was concentrated in channels, which were more sinuous and rougher when mulch biomass was high. Pathway tortuosity and friction significantly slowed down runoff flow (Table 4) and delayed runoff propagation. These phenomena were in agreement with previous investigations (Abrahams et al., 1994; Gilley et al., 1991; Savabi and Stott, 1994; Scopel et al., 1998). At the four-cycles scale (1995 – 1998), the decomposition of the successive mulches, even

with small amounts of residue, provided a continuous organic cover made of small pieces of residue, which protected efficiently the physical topsoil structure (Findeling, 2001). Besides, this structure was also stabilized by an increase in the soil organic matter content and a higher macrofauna activity (Scopel and Findeling, 2001). Consequently, mulched soil developed higher water conductivity and sorptivity than bare soil (Table 2), and had a higher potential infiltration rate. A gap was observed in the literature between experimental knowledge on mulches and modeling the effects of mulch on runoff. Models in literature only partially take mulch effects on runoff into account (Yu et al., 2000; Gonzalez-Sosa et al., 1999). We proposed a physically based model to account for the observed mulch effects. Its originality lies in the representation of pathway tortuosity by an effective slope and the concentration of runoff flow in a main channel, whereas the usual models are generally based on a homogeneous flow taking up the whole width (Gilley et al., 1991; Yu et al., 2000). All the model parameters have a physical meaning. They can consequently be measured or estimated, which is a big help when using the model as a predictive tool in different contexts (soil, mulch, slope, etc.). The sensitivity analysis showed that soil hydraulic properties (Ks and S) had a determining effect on runoff, which is in accordance with the modeling assumption of a system controlled mainly by

A. Findeling et al. / Journal of Hydrology 275 (2003) 49–66

Fig. 7. Comparison of observed and simulated runoff hydrographs for two validation events (4v on the left and 5v on the right).

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the potential infiltration rate of the topsoil layer. Although the sensitivity to S was higher, Ks remains the main parameter that drives runoff because its natural variability is far higher than that of S (Table 2). The physical and geometrical properties of the flow (f ; Se and al ) had a slighter impact but contributed to improving simulation of runoff dynamics. Parameters characterizing water storage and interception (hs ; aBm and aLAI ) mainly affected production processes, and thus, runoff volume. The physical structure of the model made it possible to monitor meaningful intermediate variables at any time during any rain event. Fig. 2 shows the behavior of six key variables on RP4.5P, which includes plant and mulch effects. The rain event 5c was broken up in five periods named (a) to (e). During period (a), the rain began and was completely intercepted by the plant, till plant storage, Rp ; reached its maximum value. During period (b), the plant could not intercept more water and let rain fall to the soil. The mulch intercepted rain proportionally to its coverage and let the remainder reach the soil and infiltrate into the soil as dRs=dt , qpot i : Period (c) started when mulch storage, Rm ; had reached its maximum storage capacity and all the rain was transmitted to the soil. Period (d) began when the soil could not infiltrate all the water and the excess rain was concentrated in the central channel ðhc . 0Þ and produced runoff ðq . 0Þ: During this period infiltration qi could be greater than instantaneous rain intensity dR=dt; because the water of the channel could be reinfiltrated. In the end, rain intensity decreased and did not make up for losses of the channel by infiltration and evacuation at the plot outlet. Period (e) started when the empty channel no longer produced runoff and infiltration was equal to rain intensity, as was the case during period (c). The coherence of this detailed analysis of the simulated dynamics showed that the model was structurally consistent. This work also has several limitations. To start with, the experimental layout did not have treatment replications, which hampered the differentiation of treatment effects from artifacts due to the specific properties of the plots in runoff response. Replications of the four treatments studied existed but were set up belatedly in 1997, on a gentler slope (, 0.03), and

fitted with a device for measuring total runoff amount. After only two cycles, average runoff coefficients of those plots resembled the runoff coefficients of the studied plots, which suggested that the effect of treatment prevailed. The scope of our work was limited, as the heaviest rain events could not be used for technical reasons. The model was calibrated on the 12 most substantial events and validated on the 14 remaining events that were not varied enough to explore thoroughly the prediction capacity of the model. We could verify the model consistency and its ability to separate the treatments, but an additional validation on experimental data will be necessary to rigorously assess model robustness and its range of application. In the model, water storage in mulch and plant was set at zero at the beginning of each rain event. This was not realistic for two consecutive rains or when rain occurred at night and dew had dampened the mulch and the plant. The use of infiltration law of Philip is questionable for the beginning of rainfall of low intensity: potential infiltration strongly decreased with time whereas little water infiltrated the soil thereby leading to an underestimation of potential infiltration and an overestimation of runoff. A time compression approach that adapts the time variable to the temporal evolution of the rain intensity (Corradini and Melone, 1992) should partially solve this problem. However, a more detailed analysis that takes into account infiltration as a soil-limited and rainfall-limited process (Swartzendruber, 1974) appears necessary to significantly improve modeling. Finally, no time lag was assumed for simulating the time necessary for water flowing in the channel to reach the plot outlet, which led to an early estimation of runoff. This bias was partially counterbalanced by an overestimation of the calibrated friction factor f ; on average 5 –10 times greater than usual friction (Weltz et al., 1992; Yu et al., 2000). A quick calculation showed that for current velocities, time lag to flow from the center of the channel to the plot outlet was approximately 15 s for RP0 and 75 s for RP4.5P, while advance of simulated runoff ranged on average from 80 s for RP0 to 220 s for RP4.5P. This difference between time lags may be explained by a longer hillslope to channel time lag. Accounting better for the latter in the model would probably improve the modeling significantly.

A. Findeling et al. / Journal of Hydrology 275 (2003) 49–66

6. Conclusion The objective of this work was to quantify and model the main effects of residue mulch on runoff processes. The experimental layout showed that runoff was dramatically cut down by mulch, even for a small amount of residue. In the short run (0 – 1 year), mulch intercepted rain, enhanced water flow concentration by dam effect, and slowed down runoff flow by increasing roughness and pathway tortuosity. In the long run (4 years), mulch ensured high topsoil water conductivity and sorptivity. Measurements did not permit us to tackle the dynamics of hydraulic properties evolution. A physically based model was developed to account for these effects on runoff in terms of dynamics and volume. Its parameters have a physical meaning and can be measured either directly (Ks ; S; t and al ), or indirectly (aLAI ; hs and f ). The model was successfully calibrated on 12 events. A sensitivity analysis showed that soil hydraulic properties ðKs and S) had the greatest impact on runoff for our plots. Although it was only partially validated, the calibrated model simulated satisfactorily the runoff dynamics in the four studied plots.

Acknowledgements Financial and technical support from Centro Internacional de Mejoramiento del Maı´z y Trigo (CIMMYT) as well as Institut National de la Recherche Agronomique (INRA) is gratefully acknowledged. Special thanks to Jean-Claude Gaudu for his efficient technical assistance.

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