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Error Propagation in Determining Hydraulic Conductivities from Successive Water Content and Pressure Head Profiles¹

ABSTRACT

The flux of water in unsaturated soils can be determined indirectly by using Darcy's Law. The critical part of this approach is the determination of the hydraulic conductivity at a given depth and time. In this paper we analyze the relative errors of hydraulic conductivities determined from a transient drainage field experiment. Knowing the errors of this method would be useful in planning future experiments. It allows putting limitations on the conclusions to be drawn from such experiments and it further allows re-examination of already published field data.

In the wet range of the conductivity function errors are 20–30% of the k-value. In the range where k-values are small, the relative errors may be > 100%. Errors stemming from tensiometer readings are significant when the hydraulic gradient is < 0.3 mbar · cm^-1. During the early stage of the transient drainage experiment these errors are always considerable and are more important than other errors. On the other hand, the errors in the measured water content changes are dominant when drainage is slowed down due to desaturation of the soil.

The errors contained in the conductivity, k, are calculated by means of error propagation equations. These errors are also simulated using the Monte Carlo technique. The simulation shows that the conductivity errors predicted by explicit error propagation equations are optimistic minimum estimates.

¹ This paper is part of a cooperative investigation between the Univ. of California, Riverside and Berkeley, made at the Kearney Hort. Field Stn., Parlier, California. Supported in part by the National Science Foundation Grant no. GI 34733X. The senior author was supported by the Swiss National Science Foundation.

² Assistant Research Soil Physicist, Univ. of California, Riverside; Assistant Research Soil Chemist, Univ. of California, Berkeley; and Professor of Soil Physics, Univ. of California, Riverside, respectively.

Received for publication February 16, 1976. Accepted for publication June 29, 1976.

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