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DIVISION S-6-SOIL & WATER MANAGEMENT & CONSERVATION

Characteristics and Modeling of Runoff Hydrographs for Different Tillage Treatments

^a Faculty of Environmental Sciences, Griffith Univ., Nathan QLD 4111, Australia
^b Dep. of Land Development, Bangkok, 10900 Thailand
^c Queensland Natural Resources, Toowoomba, QLD 4350, Australia
^d Australian Centre for International Agricultural Research, Canberra, ACT 2601, Australia

b.yu{at}mailbox.gu.edu.au

	ABSTRACT

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Conclusions REFERENCES

 
Surface runoff rate is a critical variable in determining the rate of soil erosion and sediment transport. Rainfall and runoff data at 1-min intervals from an experiment site at Khon Kaen, Thailand, were used to test a three-parameter runoff model originally developed for bare plots in relation to soil erosion studies. The site has a sandy soil with a slope of 3.6%. Plot length and width were 30 and 5 m, respectively. Four tillage treatments with three replicates each were considered: up- and down-slope cultivation, two contour cultivation treatments with tillage depth of 25 and 50 cm, respectively, and no tillage. Runoff data for 200 individual runoff hydrographs showed that runoff amount and peak runoff rate for the no tillage treatment were significantly less than those for other treatments at the site. On average, runoff amount and peak runoff rate for the no tillage treatment were 37 and 44%, respectively, of those for the up- and down-slope cultivation. Results for contour cultivation practices are between the two extremes, although the water retention was not greater with greater tillage depth as we originally thought would be the case at the site. For these 200 runoff events for the four treatments, the model for runoff hydrographs worked well, with an average coefficient of efficiency of 0.90 and an average standard error of 0.88 mm h^-1. The model performance is particularly good for large storm events with high volumetric runoff coefficient. The three model parameters vary considerably from event to event and from treatment to treatment. The initial infiltration amount was found to be inversely related to prior 10-d rainfall at the site; the spatially averaged maximum rate of infiltration can be related to the maximum retention or the Soil Conservation Service (SCS) Curve Number, and the hydrologic lag time is least variable among different storm events and tillage treatments, but tends to decrease with peak runoff rate.

Abbreviations: ACIAR, Australian Centre for International Agricultural Research • DSM, downhill simplex method • SCS, Soil Conservation Service

	INTRODUCTION

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Conclusions REFERENCES

 
SURFACE RUNOFF RATE plays a critical role in determining the rate of soil loss from agricultural lands. This is especially the case during large events with high stream power (Proffitt and Rose, 1991). In the Universal Soil Loss Equation (Wischmeier and Smith, 1978), the effect of rainfall and runoff is encapsulated in a rainfall and runoff factor, known as the R-factor, to represent the long-term climatic influence on soil erosion. As such, the R-factor should not be used to determine the soil loss on an event basis. In process-based water erosion models, runoff rate is explicitly required in order to determine the rate of soil loss. For example, in the Water Erosion Prediction Project (WEPP; Laflen et al., 1991; Flanagan and Nearing, 1995), which represents a new generation of process-based erosion models, the peak runoff rate is used to determine the rate of both interrill and rill erosion (Foster et al., 1995). In GUEST (Rose, 1993; Misra and Rose, 1996), a theoretical expression is derived for sediment concentration at the transport limit based on the stream power, which is in turn a function of the runoff rate. It is important therefore to predict runoff rates for given rainfall intensity, soil, and topographical characteristics.

As part of projects funded by the Australian Centre for International Agricultural Research (ACIAR), rainfall intensity and runoff rate were measured at 1-min intervals at a number of sites in Australia and Southeast Asia. One of the research objectives was to develop hydrologic models to predict runoff rates from rainfall rates for a range of soil types, slopes, slope lengths, and management practices in the tropical and subtropical regions of Australia and Southeast Asia. A three-parameter infiltration and runoff routing model was developed and validated using data from bare plots from six sites in Southeast Asia and Australia (Yu et al., 1997b). Apart from satisfactory performance of the model in terms of modeled hydrographs for these sites, two subsequent studies gave further support of the model as a tool for predicting runoff rate. Yu (1998) showed that one of the infiltration parameters is implicitly related to the widely used SCS Curve Number method for runoff estimation (Soil Conservation Service, 1985). Thus, the availability of the curve number values for a range of soil and land use would considerably facilitate the application of the infiltration and runoff routing model. Secondly, for 180 site–events, Yu (1999) showed that the model consistently outperformed the Green–Ampt infiltration model at the plot scale and at the small time interval for the six sites in Southeast Asia and Australia.

There are concerns about the model performance when there is substantial vegetative cover. While runoff data for a wide range of management practices were collected, they were not systematically used in the previous study of Yu et al. (1997b) because the uncultivated bare plot was the only treatment common to all sites, and because bare plots were of particular interest in relation to soil erosion research. Other treatments with respect to the crops used, surface cover management, and conservation strategies are highly site-specific, reflecting the local conditions and prevailing farmers' practices. There was a seventh site in the ACIAR network near Kohn Kaen, Thailand. The site was closed in 1992 and was not included as part of the project that led to the development of the infiltration and runoff routing model. Modeling runoff hydrographs was never attempted for the Khon Kaen site. Only annual crop yield, runoff, and soil and nutrient losses in summary form were presented (Sombatpanit et al., 1995). For this study, we reprocessed the rainfall and runoff data collected at the Khon Kaen site during 1989 to 1991. The 1-min hydrograph data was analyzed to address the following four research questions.

1. What are the effects of different cultivation treatments on both storm runoff amount and peak runoff rate?
   
2. How would the model perform when there is a substantial vegetative cover and a range of cultivation practices?
   
3. What factors would influence the model performance? In other words, can model performance be predicted?
   
4. What factors would determine the model parameter values?
   

The question of determining model parameters is of particular importance because model parameter values usually vary widely from event to event and site to site. A model adequate to describe the dynamic relationship between rainfall and runoff alone is insufficient because a model is of limited use unless its parameter values are known or can be readily estimated.

	Materials and methods

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Conclusions REFERENCES

 
Experiment Site and Rainfall–Runoff Data
The experimental site was located near Khon Kaen in the northeastern part of Thailand (102°50' E and 16°30' N) with an elevation of 195 m above sea level. Annual rainfall at the site is fairly consistent, varying from 1000 to 1200 mm. There is a distinct wet season from mid May to late October. The soil at the site is loamy sand to sandy loam with an average sand fraction (>0.2 mm) of 79%. There is some spatial variation in soil texture. For example, the sand fraction varied from 76 to 82% across all treatments.

Four treatments were considered in this experiment (Table 1) . Each of the four treatments were replicated three times. A fiber crop, roselle (Hibiscus sabdariffa L. var. Altissima), was planted for all treatments at the site. All 12 runoff plots were 30 m long and 5 m wide, and they were all hydrologically isolated as far as surface runoff was concerned. The land slope of these plots was 3.6%.

A rainfall threshold of 15 mm was used to extract large storm events when most soil and nutrient losses are likely to occur. Many of these large rainfall events were discarded because rainfall recorded by the two pluviometers was not consistent, or one of the two data loggers was apparently not functioning during the event, or the recording was affected by nearby lightning strikes. In the end, 20 storm events were selected for modeling purposes. The average rainfall amount for these events was 46.5 mm, varying from 15.2 to 266 mm. The difference in recorded rainfall between the two pluviometers was never >7%, with an average difference <1%. Of the 240 plot–events, 40 hydrographs were removed from further analysis because either the storm runoff was extremely small (<0.2 mm) or the data loggers seemed to have recorded no data for these plot–events. In the end, 200 runoff hydrographs were prepared for the four treatments with three replicates each.

The original rainfall and runoff data were in the form of tips per minute. The number of tips per minute was converted into rates in millimeters per hour using a calibration equation taking into account the dynamic change in tipping volume as a function of the tip rate (Calder and Kidd, 1978). Given the discrete nature of tipping bucket data, there is a systematic discrepancy in the observed rate and the true rate being sampled. The magnitude of this discrepancy depends on the plot area, bucket volume, and sampling frequency (Yu et al., 1997a). With an average tip volume of 8.4 L and plot area of 150 m², the standard error in the measured runoff rate at 1-min intervals would be 1.4 mm h^-1 using Eq. [4] in Yu et al. (1997a).

Stilling basins (4.5 m²), designed to encourage settling of the coarser sediment, were installed at the plot exit. Rainfall over these stilling basins can be an important component in measured runoff, especially during the relatively small event. Rainfall over the stilling basins was removed from runoff by multiplying the runoff rate by a coefficient such that volumetric water balance is achieved. In the calculation, 100% runoff from the stilling basins was assumed.

Infiltration and Runoff Model
The model used by Yu et al. (1997b) consists of two components. An infiltration component determines rainfall excess as a function of rainfall intensity and cumulative rainfall amount, and a routing component produces the runoff hydrograph at the plot exit so that the observed and modeled hydrographs can be compared. The rainfall excess rate, r_i (mm h^-1), for time interval i, can be expressed simply as

(1)

where p_i is the rainfall intensity (mm h^-1), t is the time interval (h), and F_o (mm) and I_m (mm h^-1) are model parameters. F_o represents the initial infiltration amount before runoff begins, and I_m is a spatially averaged infiltration capacity (the maximum possible rate of infiltration). Derivation of Eq. [1] is given elsewhere (Yu et al., 1997b).

A kinematic wave approximation was used to route the rainfall excess to plot outlet. A linear relationship between storage and runoff rate at the plot outlet is assumed to solve the storage equation in the discrete form

(2)

where K is a lag time (h) and q is runoff rate (mm h^-1). Here the average rate of inflow (rainfall excess rate) and outflow over two adjacent time intervals are used in the right-hand side of Eq. [2], while in Yu et al. (1997b) only the current rate of inflow and outflow (i.e., r_i and q_i) were used. This minor change in the algorithm would improve the numerical stability and conform to the standard finite difference scheme to solve the governing overland flow equation using the kinematic wave approximation (Chow et al., 1988; Singh, 1996). The assumption that storage is only a function of the runoff rate at the plot outlet led to an approximate analytical solution of the governing equation (Rose et al., 1983). The solution to Eq. [2] can be written simply as

(3)

where the routing parameter, , is related to the lag time, K, and time interval, t, by

(4)

Because of the change in the algorithm, there is a slight difference in the way the routing parameter is formulated compared with that in Yu et al. (1997b). A requirement of the improved algorithm is that the lag time should be greater than one-half the time interval. Otherwise, a negative (Eq. [4]) will cause the modeled runoff rate to oscillate between positive and negative values when the rainfall excess has ceased.

The hydrologic model, called SSRRM (Yu et al., 1997b), assumes an exponential distribution of the infiltration capacity in space and describes a positive relationship between rainfall intensity and rainfall excess. Spatial variability in the steady-state infiltration rate and saturated hydraulic conductivity has been widely noted (Nielsen et al., 1973; Sharma et al., 1980; Hawkins and Cundy, 1987; Loague and Gander, 1990). Similarly, the positive relationship between rainfall intensity and the apparent infiltration rate has also been widely observed (Cook, 1946; Moldenhauer et al., 1960; Hawkins, 1982; Flanagan et al., 1988; Yu et al., 1997b). Kinematic wave approximation and the discretization scheme (Eq. [2]) were widely used for numerically solving the governing equation for overland flows (Chow et al., 1988; Singh, 1996).

Parameter Estimation and Model Performance
The three parameters, namely F_o, I_m, and K were estimated by minimizing the sum of squared errors, SSE, between the observed (q_i) and modeled (_i) runoff rates, where

(5)

with n the event duration (min). The downhill simplex method (DSM) (Nelder and Mead, 1965) implemented in Press et al. (1992) was used to minimize the sum of squared errors. A set of approximate parameter values is needed to initiate the optimization process. The amount of rainfall prior to runoff was used as the initial value for F_o. A simple one-variable nonlinear water balance equation between runoff amount and total rainfall excess was solved for the initial value for I_m. The procedure to determine I_m for natural runoff events was described in detail by Yu et al. (1998). Preliminary estimation of the routing parameter, , involves a multivariate linear regression technique based on Eq. [3]. This gave rough estimates of individual parameter values before these values were refined simultaneously using more sophisticated techniques such as DSM. We found this approach to parameter estimation worked quite efficiently. It took <1 min to complete parameter estimation on ordinary PCs for the selected 200 hydrographs involving some 240000 individual rainfall and runoff observations.

Peak runoff rate, time to peak, and flow recession curve are important aspects of a hydrograph to consider. However, it is difficult to assess model performance based on multiple criteria because subjective weighting will have to be involved. In this study, as in Yu et al. (1997b), we use the coefficient of efficiency as a measure of model performance to characterize the overall fit between the observed and modeled hydrographs. The coefficient of efficiency, E (Nash and Sutcliffe, 1970), is defined as

(6)

where is the mean observed runoff rate. The coefficient of efficiency, E, is commonly used as a measure of model performance in hydrology (e.g., Loague and Freeze, 1985) and soil sciences (e.g., Risse et al., 1993). For a linear regression model, the coefficient of efficiency is identical to the familiar r². Generally speaking, E is much less than r². The value of E can vary from 1, when there is a perfect agreement, to -. A negative value of E means that model predictions are worse than predictions using a constant equal to the average observed value. It has been shown that the coefficient of efficiency is a much superior measure of goodness-of-fit for model validation purposes compared with the familiar r² or the co-efficient of determination (Willmott, 1981; Legates and McCabe, 1999).

Relationship Between the Infiltration Parameter I_m and the SCS Curve Number
Although the infiltration parameter I_m characterizes the spatial variability of the infiltration capacity (the maximum rate of infiltration) across the landscape, when integrated over a storm event and over the whole runoff plot, it can be shown that this parameter is intrinsically related to the widely used curve number for runoff estimation (Yu, 1998). Assuming that the rainfall intensity can be described by an exponential probability distribution, Yu (1998) showed that the runoff amount, Q_t, for a particular storm event can be expressed in terms of the effective rainfall and the spatially averaged infiltration capacity in the form

(7)

where P_t and Q_t (mm) are storm rainfall and runoff, respectively; T_e (h) is the effective storm duration from runoff commencement. Equation [7] shows that the product of the spatially averaged infiltration capacity and the effective storm duration (I_mT_e) plays the same role in Eq. [7] as does the maximum retention in the context of the SCS Curve Number method (Soil Conservation Service, 1985). Equation [7] further suggests that the infiltration parameter I_m may be estimated from the maximum retention, or the curve number, using

(8)

For a particular storm event when P_t and Q_t are measured, the maximum retention, S, (mm) for the event can be determined as

(9)

where the initial infiltration amount, F_o, for the event can be estimated by fitting the observed and modeled hydrographs as described above. Note that Eq. [9] is based on the SCS runoff equation without assuming that the initial abstraction (i.e., F_o in the current context) equals 0.2S. Hawkins (1973) presented a formula to calculate S when the initial abstraction is assumed to be 0.2S. Given S, the curve number can be easily determined if needed. The potential of using the maximum retention and, equivalently the curve number, to determine the infiltration parameter I_m will be explored below.

	Results

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Conclusions REFERENCES

 
We present results in three parts: (i) the effect of different treatments on runoff characteristics, (ii) model performance for different treatments and factors that influence the model performance, and (iii) event-to-event variation in model parameter values among different treatments.

Runoff Characteristics for Different Treatments
Rainfall characteristics in terms of rain amount, peak intensity, and duration and number of storm events can be regarded as essentially the same for the four treatments (Table 2) . The contrast in runoff amount and peak runoff rate can therefore be considered as entirely the result of the effects of various treatments applied. On average, runoff amount from the no tillage treatment was only 37% that from plots with the farmers' practice. The average runoff amount with no tillage was significantly (P < 0.001) less than those with other treatments, and the runoff amount is not significantly different among the other three treatments. The volumetric runoff coefficient, which is the ratio of total runoff to total rainfall, decreased from 18% for farmers' practice to 7% for no tillage. Runoff amount for contour cultivation (Treatments 2 and 3) was between farmers' practice and no tillage.

In summary, no tillage decreased both runoff amount and peak runoff rate, the decrease being greater for runoff amount than for peak runoff rate. It was originally thought that an increase in tillage depth would encourage water retention. However, tillage to a 50-cm depth actually resulted in a greater amount of runoff and higher peak runoff rate than that for a tillage depth of 25 cm for the site.

Model Performance
Table 3 shows a summary of the estimated parameter values and the coefficient of efficiency for the four different treatments. The consistently high value of E shows that the overall performance of the model is good for all the treatments. The average coefficient of efficiency for all treatments is 0.90 (Table 3), and the median is 0.94. The average standard error (standard deviation of the model residuals) is 0.88 mm h^-1, or 63% of the magnitude of the sampling error of 1.4 mm h^-1 in the discrete runoff data at 1-min intervals.

View this table: [in this window] [in a new window]   Table 3 Average (± one standard deviation of the mean) parameter values, standard error and coefficient of efficiency.

View larger version (21K): [in this window] [in a new window]   Fig. 1 A storm event at Khon Kaen with rainfall intensity and observed and modeled runoff rates, all at 1-min intervals. The treatment was contour cultivation with subsoiling. With Fo = 22.4 mm, Im = 119 mm h-1, K = 5.24 min, and E = 0.90, this event was selected as typical of the 200 hydrographs used (see Table 3 for comparison)

View larger version (21K): [in this window] [in a new window]   Fig. 2 The relationship between gross runoff coefficient and the coefficient of efficiency for all plot–events

(10)

View larger version (17K): [in this window] [in a new window]   Fig. 3 The relationship between prior 10-d rainfall and the average initial infiltration amount for the Khon Kaen site. The error bars represent one standard deviation among the four treatments with three replicates each. For two of the 20 events, error bars are not used because there were fewer than two estimated Fo values for the two events

For the spatially averaged infiltration capacity, I_m, (the maximum possible rate of infiltration), the trend in the mean was not as clear as that in the initial infiltration amount. While I_m for the no tillage treatment was more than twice as high as that for the farmers' practices, the average infiltration capacity for the two treatments with contour cultivation was actually lower than that for the farmers' practice, and I_m for subsoiling and contour cultivation (Treatment 3) was the lowest of all treatments (Table 2). The low I_m for Treatment 3 with a greater tillage depth explains why the peak runoff rate for this treatment was higher than that for Treatment 2. The difference in the mean between Treatment 2 and 3, however, was not significant because of the relatively high variability of this parameter.

The parameter I_m was most variable of the three in the infiltration and runoff model. Estimated value of I_m varied from 0.66 to 2150 mm h^-1 for the 200 plot–events. To test the analytical relationship between the maximum retention and the infiltration capacity (Eq. [8]), the maximum retention was determined using Eq. [9] for the 200 plot–events. A linear regression model with a zero intercept was used to relate the parameter I_m to the maximum retention, resulting in

(11)

A scatter plot of I_m against the S/T_e ratio is presented for the 200 plot–events in Fig. 4 . The linearity between the two variables held for a wide range of I_m values (Fig. 4), although the constant of proportionality in the regression Eq. [11] was not unity as Eq. [8] would suggest.

View larger version (20K): [in this window] [in a new window]   Fig. 4 The relationship between the ratio of maximum retention to storm duration and the spatially averaged infiltration capacity for all plot–events. The insert shows the low values more clearly

View larger version (19K): [in this window] [in a new window]   Fig. 5 The relationship between peak runoff rate and lag time for all plot–events

	Discussion

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Conclusions REFERENCES

 
The infiltration and runoff model considered by Yu et al. (1997b) has been tested for a number of bare plots in Australia and Southeast Asia and has been shown to perform better than the Green–Ampt model for natural storm events (Yu, 1999). We are able to show that the model does a good job of describing the dynamic relationship between rainfall and runoff at a small time scale of 1 min for four different tillage treatments under a wide range of hydrologic conditions in terms of the gross runoff coefficient. A model that reproduces the observations is important for successful prediction of runoff hydrographs at ungauged sites. However, the highly variable nature of the model parameters makes it difficult to predict the runoff hydrograph in isolation. The relationships for model parameters identified here suggest that information on the antecedent rainfall and potential runoff should be needed to determine the model parameters.

The initial infiltration amount varied inversely with the antecedent rainfall. This suggests that a time series of rainfall is required to quantify the antecedent moisture condition and subsequently the parameter F_o. The lag parameter, while somewhat varying with the runoff rate, may be held constant for given slope length and steepness for practical purposes. The most difficult parameter to determine is the spatially averaged infiltration capacity. It is encouraging to find a close relationship between the maximum retention in the context of the SCS Curve Number method and the infiltration parameter because the well-established SCS Curve Number method may be used to derive a parameter on infiltration rate for hydrograph prediction in an operational sense. The relationship between S and I_m, however, also suggests that predicting runoff hydrographs is fundamentally difficult for individual storm events, and for events with small runoff amounts especially. It is generally established that the maximum retention, or the curve number, varies widely between storm events. The SCS Curve Number method works in the mean, and the method was never intended to match individual storms (Ponce and Hawkins, 1996). A possible solution to this problem with parameter estimation for hydrograph prediction would be a two-step approach. First, continuous water balance is undertaken to predict event or daily runoff amount only. Secondly, runoff hydrographs are determined using the predicted antecedent moisture condition and runoff amount for individual events.

	Conclusions

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Conclusions REFERENCES

 
Rainfall and runoff data for 200 hydrographs at 1-min intervals from the Khon Kaen site were used to determine the effects of tillage treatments on runoff characteristics and to test a three-parameter model for runoff hydrographs originally developed for bare plots in relation to soil erosion studies. Runoff data from these storm hydrographs showed that runoff amount and peak runoff rate for the no tillage treatment were significantly less than those for other treatments at the site. On average, runoff amount and peak runoff rate for the no tillage were 37 and 44%, respectively, of those for the up- and down-slope cultivation. Results for contour cultivation practices are between the two extremes, with water retention not increasing with greater tillage depth. For the 200 plot–events of the four treatments, the model for runoff hydrographs worked well, with an average coefficient of efficiency of 0.90 and an average standard error of 0.88 mm h^-1. The model performance was particularly good for large storm events with high volumetric runoff coefficients. The three model parameters varied considerably from event to event and from treatment to treatment. The initial infiltration amount was found to be inversely related to prior 10-d rainfall at the site; the spatially averaged maximum rate of infiltration was related to the maximum retention parameter for the SCS Curve Number method. The hydrologic lag time was the least variable parameter among different storm events and tillage treatments, tending to decrease with increasing peak runoff rates.

Received for publication September 17, 1999.

	REFERENCES

TOP ABSTRACT INTRODUCTION Materials and methods Results Discussion Conclusions REFERENCES

 

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