Investigation of Uncertainty in Infiltration Using First Order Analysis
Abstract
In modeling infiltration, the soil water retention parameters are needed for the specific soil types. These parameters can be obtained by fitting water content versus matrix-potential data when available for the specific soils. The fitted parameters generally contain estimation errors (i.e., uncertainty). When specific data are not available, published information for the soil water retention parameters for various soil types may be used, however it is important that the uncertainty in the parameters be considered in the modeling. A goal of this study was to investigate the use of the first order analysis approach which includes covariances between the parameters to quantify the infiltration uncertainty. To investigate the uncertainty in infiltration caused by the uncertainty in the soil water retention parameters, a one-dimensional vadose-zone model with three soil layers was developed that includes vegetative cover and irrigation periods during a six month growing season. The flux at the bottom of the model was considered to be an estimate of the total infiltration for the period. Published data for the mean values and covariances for the various parameters were used for each soil type. The mean value of infiltration was obtained based on the mean values for the parameters. In the first order analysis approach, the calculation of the variance requires an estimation of the first derivative of the infiltration with each of the parameters. These first derivatives are usually approximated in discrete form by running the model with small changes about the mean value for each parameter and dividing by the change in the parameter. The best application of the first order analysis approach requires that the response (i.e., infiltration) be linear about the mean value, thus the "smaller" the change in parameter about the mean the more likely the linearity condition will hold. The question then becomes what constitutes a small change. Changes in the parameters of 5% and 2.5% of the mean values, as well as, changes based on the standard deviations for the various parameters were considered. The approximation of the first derivatives obtained from adding and subtracting 1/16 of the standard derivation (assuming a normal distribution, this corresponds to 2.5% of the area under the distribution on either side of the mean) was determined to yield satisfactory results. The variance of the infiltration was obtained considering the covariance of the parameters and compared to the calculated variance when only the variance of each parameter was included. The variance in the infiltration was approximately 9% smaller when the complete parameter covariance information was used compared to the value when only the parameter variances were included.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2001
- Bibcode:
- 2001AGUFM.H31B0244J
- Keywords:
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- 1829 Groundwater hydrology;
- 1875 Unsaturated zone