Parameter estimation technique for a water balance model and application to measured data

Currently, remote sensing techniques provide the most feasible capability to monitor soil moisture over a range of space and time scales, such as passive microwave radiometric measurements in the 1-5 GHz range. It is found that variations in the brightness temperature are related most closely to the moisture content in a shallow near surface region, even if the actual sensing depth depends on the magnitude of surface moisture and shape of the moisture profile. Moreover the algorithm to transform the brightness temperature into soil moisture needs the calibration of soil texture and vegetation parameters. A new method has been developed to estimate the parameters of a water balance model’s components (actual evapotranspiration, drainage plus runoff) as functions of the soil moisture and of the estimated parameters. The technique requires limited information, that is measured precipitation plus potential evapotranspiration and measured soil moisture; in particular, the method doesn’t need the storage but only an index of the soil moisture content and this makes it easy to apply to remotely sensed measures of soil moisture. The mathematical model is essentially based on the mass conservation equation of all the hydrological processes and used under the hypothesis of stationary conditions; it’s proposed to be an efficient model in term of number of parameters. The method proposed is based on the Bayes’s theorem and compares two possible ways for finding the solution, the maximum likelihood principle and the expected value criterion. The solution is the set of parameter values that permits to reconstruct the fluxes of actual evapotranspiration and drainage plus runoff relative to the surface soil volume. The method’s skills are evaluated using synthetic data, both at point and hillslope scales, using all the available observations (30 years time series), and true data for shorter periods of one year or few years. The measured data were achieved during the field campaign in the Toce river basin, North of Italy (in 1999), and during more campaigns in USA (whose data were downloaded from Ameriflux website). The estimation technique is able to estimate the water balance components in different soil and climatic conditions, both at point-scale and hillslope scale. 1 Dipartimento I.I.A.R., sezione Idraulica, Politecnico di Milano, Piazza L. da Vinci, 32 20133 MILANO, ITALY Tel.: 02 2399 6235 Fax: 02 2399 6207 [email protected]