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Analysis of Soil Water Content and Temperature Using State-space Approach¹

ABSTRACT

Several statistical methods have been developed to smooth or interpolate observations taken spatially and temporally. Most of these methods require that the observations manifest stationarity, meaning that the expected value of the observations is constant over the domain considered. The authoregressive moving average method requires the above condition but can also be used to estimate missing observations. The exponential smoothing method is available for nonstationary time or space series but generally requires evenly spaced observations. The state-space model can be used for smoothing or estimating and forecasting a relatively short, nonstationary series of observations. A first order state-space model was used here to estimate the missing observations of 0- to 5-cm gravimetric soil water content. This was accomplished using joint analysis of observed water content and soil surface temperatures from a sorghum field irrigated by two line source irrigation system. The parameters of the model indicated the degree of spatial correlation between the two measured parameters. The expectation maximization algorithm and Kalman smoothed estimators were used to estimate the first order state-space model parameters by maximum likelihood.

¹ Contribution from Dep. of Land, Air and Water Resources, Univ. of California, Davis.

² Graduate Student and Professors, respectively, Dep. of Land, Air and Water Resources, Univ. of California, Davis, CA 95616. This research was supported by the Kearney Foundation of Soil Science.

Received for publication March 22, 1984. Accepted for publication January 17, 1985.

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