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Estimating Soil Temperature by Linear Filtering of Measured Air Temperature¹

ABSTRACT

Linear dynamic filtering techniques were used to model the relationship between time series of average daily air temperature and soil temperature at the 10-cm depth. The data utilized consisted of 730 consecutive daily observations of these two variables measured at Brawley, Calif., for the period 1 Jan. 1962 to 31 Dec. 1963. The soil temperature measurements were made in a bare and level Holtville silty clay soil completely exposed to the sum. Spectral analysis procedures were used to first identify and then to obtain the factors for filtering the frequency components contributing most to the variance of each temperature series. The annual cycle (frequency 2 rad d^–1 ÷ 365) contributed 82.30 and 91.10%, respectively, and the semiannual cycle (frequency 2 rad d^–1 ÷ 365) contributed, respectively, 2.36 and 1.56%, of the variance of the air and soil temperature series. The analysis also showed that the annual and semiannual cycles of the soil temperature series lagged the corresponding cycles of the air temperature series by 2.5 and 10.4 d, respectively. After removing the annual and semiannual cyclic components from each series, Box-Jenkins transfer function modelling techniques were used to describe the filter relating the residual stochastic series. The transfer function was then used in conjunction with the results of the spectral analysis to yield a relation for estimating the soil temperature at the 10-cm depth using the air temperature as input. The residual variance of this estimation was 58.5% less than the residual variance using a linear regression equation.

¹ Contribution from the Dep. of Soil and Environmental Sciences, Univ. of California, Riverside, CA 92521.

² Respectively, Postgraduate Research Soil Scientist and Professor of Agricultural Engineering, Univ. of California, Riverside.

Received for publication February 14, 1983. Accepted for publication May 24, 1983.

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