An evapotranspiration system was defined as six coupled, parallel subsystems defined by five rectangular and one radial, one-dimensional diffusion equations. A block diagram and system transfer function Were developed for each subsystem and the subsystems were coupled to obtain a block diagram of the evapotranspiration system. The soil heat transfer subsystem was assumed to be defined by the diffusion equation for a homogeneous soil of infinite depth with constant diffusivity and heat transfer by conduction only. The solution of the diffusion equation was obtained in the frequency domain as the frequency response function and in the time domain as the convolution integral. The frequency response function was used as an analytical model in the form of a gain and a phase function in conjunction with time series analysis to determine the system constant. A numerical solution of the convolution integral was used to determine soil heat diffusivity from arbitrary time distributions of temperature at two depths. The system response as the temperature at a depth was computed from an arbitrary time distribution of input temperature given the diffusivity. Results from time series analysis of analytically generated temperature data gave values for diffusivity from the gain and phase function of 16.24- and 16.21-cm²/hr, respectively. The value used to generate the data was 16.2 cm²/hr. The corresponding value of diffusivity obtained from a trial and error numerical convolution was 16.3 cm²/hr. Values of numerical convolution computed temperature, obtained after 72 hours to remove a starting transient, differed from the analytically correct temperatures by less than 0.1 ° C for an 8° amplitude or a 16° range. For 50 days of 6-hour interval temperatures the 95 percent confidence interval on diffusivity was within two percent of the analytically correct value. Soil temperature data for the 10- and 15-cm depth from an experiment where cold (4° C) irrigation water was applied, including the temperature data during the time of irrigation, was analyzed by time series analysis. The value of diffusivity obtained from time series analysis and the gain function was 14.7 cm²/hr compared to a range of 15.1 to 16.9 for amplitude and phase plots and 16.6 for a finite difference solution of the diffusion equation. The value from phase was 21.61 cm²/hr which is much higher due to the time-varying effects of diffusivity or improper alignment of the two time series. Confidence intervals for diffusivity were very wide because of the short period of record and because of heat transfer by moisture during the irrigation. Numerical convolution determined values of diffusivity of 15.1-and 14.9-cm²/hr for before and after irrigation indicated some change in soil heat diffusivity with time. Numerical convolution computed temperatures were within 0.17° C of the measured temperature except during and immediately after the application of the irrigation water. The maximum error between measured and computed temperature was 3.88° C. Time series analysis can be used to determine the soil heat diffusivity from arbitrary time distributions of temperatures at two depths. Confidence limits for diffusivity can be established by certain assumptions as a measure of the adequacy with which the diffusivity has been determined. Numerical convolution can also be used to determine soil heat diffusivity by trial and error from arbitrary time distributions of temperatures measured at two depths. Simulation of soil temperatures from arbitrary time distributions of measured input can be achieved by numerical convolution.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/190975 |
| Date | January 1971 |
| Creators | Clyma, Wayne,1935- |
| Contributors | Fangmeier, Delmar D., Matlock, William G., Sellers, William D., Warrick, Arthur W. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | Dissertation-Reproduction (electronic), text |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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