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.

Evapotranspiration (ET; evaporation + transpiration) is central to a wide range of biological, chemical, and physical processes in the Earth system. Accurate remote sensing of ET is challenging due to the interrelated and generally scale dependent nature of the physical factors which contribute to the process. The evaporation of water from porous media like sands and soils is an important subset of the complete ET problem. Chapter 1 presents a laboratory investigation into this question, examining the effects of grain size and composition on the evolution of drying sands. The effects of composition are found to be 2-5x greater than the effects of grain size, indicating that differences in heating caused by differences in reflectance may dominate hydrologic differences caused by grain size variation. In order to relate the results of Chapter 1 to the satellite image archive, however, the question of information loss between hyperspectral (measurements at 100s of wavelength intervals) laboratory measurements and multispectral (≤ 12 wavelength intervals) satellite images must be addressed. Chapter 2 focuses on this question as applied to substrate materials such as sediment, soil, rock, and non-photosynthetic vegetation. The results indicate that the continuum that is resolved by multispectral sensors is sufficient to resolve the gradient between sand-rich and clay-rich soils, and that this gradient is also a dominant feature in hyperspectral mixing spaces where the actual absorptions can be resolved. Multispectral measurements can be converted to biogeophysically relevant quantities using spectral mixture analysis (SMA). However, retrospective multitemporal analysis first requires cross-sensor calibration of the mixture model. Chapter 3 presents this calibration, allowing multispectral image data to be used interchangeably throughout the Landsat 4-8 archive. In addition, a theoretical explanation is advanced for the observed superior scaling properties of SMA-derived fraction images over spectral indices. The physical quantities estimated by the spectral mixture model are then compared to simultaneously imaged surface temperature, as well as to the derived parameters of ET Fraction and Moisture Availability. SMA-derived vegetation abundance is found to produce substantially more informative ET maps, and SMA-derived substrate fraction is found to yield a surprisingly strong linear relationship with surface temperature. These results provide context for agricultural applications. Chapter 5 investigates the question of mapping and monitoring rice agricultural using optical and thermal satellite image time series. Thermal image time series are found to produce more accurate maps of rice presence/absence, but optical image time series are found to produce more accurate maps of rice crop timing. Chapter 6 takes a more global approach, investigating the spatial structure of agricultural networks for a diverse set of landscapes. Surprisingly consistent scaling relations are found. These relations are assessed in the context of a network-based approach to land cover analysis, with potential implications for the scale dependence of ET estimates. In sum, this thesis present a novel approach to improving ET estimation based on a synthesis of complementary laboratory measurements, satellite image analysis, and field observations. Alone, each of these independent sources of information provides novel insights. Viewed together, these insights form the basis of a more accurate and complete geophysical understanding of the ET phenomenon.

Simple models of transpiration, e.g., the Penman-Monteith equation, treat atmospheric conditions as driving variables. In fact, transpiration modifies temperature and humidity throughout the convective boundary layer, creating feedbacks that stabilize the water use of vegetation. This thesis concentrates on the new empirical relationships proposed by Monteith (1995), for developing simple models of feedback, and then applies these relationships to data from the Oregon Cascades. Monteith showed that there is strong laboratory evidence to support a linear relationship between leaf transpiration rate and leaf conductance. If this relationship holds for vegetation in the field, simple models to explain the diurnal variation of canopy conductance can be developed. When this model was applied to data from a Douglas fir forest, canopy conductance changed in response to transpiration rate, rather than to saturation deficit, as has been previously assumed. Monteith also reanalyzed data from McNaughton and Spriggs (1989) which explored the dependence of the Priestley-Taylor coefficient alpha on surface parameters. He showed that there is a linear relationship between alpha and surface conductance. By combining this "demand function" with the physiological "supply function" described earlier, the PMPT model is developed in which evaporation rate depends on physical feedbacks in the convective boundary layer and physiological feedbacks within plants. The thesis will focus on the results of the research done using this model. The PMPT model will then be compared with other simple models of transpiration in order to determine its applicability. / Graduation date: 1997

Graduation date: 1994