A method to assess the uncertainty of Benfratello’s estimate of the irrigation deficit in a semiarid area and its GIS based application for anthropogenic and climate change scenarios

Benfratello's conceptual method, to estimate the irrigation deficit for agricultural districts in semiarid or arid climate, firstly came to light in 1961. The method generalizes previous Thornthwaite (1948) and Thornthwaite and Mather (1955) water balances to assess the irrigation deficit as the difference between the maximum evapotranspiration, exerted by the plant in full irrigation conditions and traditionally estimated with the Thornthwaite formula, and the actual evapotranspiration provided by the available soil water. Since its first appearance, it has been applied to the study of many areas in Southern Italy. Due to its simplicity and to the small number of required parameters, Benfratello's method might be regarded to as an effective tool to assess the effects of climatic, landuse and anthropogenic changes on the soil water balance and on the irrigation deficit.

In the previous General Assembly we presented a GIS based application of Benfratello's method to the case study of the semiarid Capitanata plane (4550 km², Southern Italy), which is one of the most important agricultural districts in Italy. With this contribution we present a further theoretical development of the method that allows to simply estimate in closed form the uncertainity of the calculated irrigation deficit, once known the uncertainty of the required climatic variables (temperature and precipitation). Our procedure is based on a local linearization of the core—function of Benfratello’s method, which presents the decrease of the available soil water, during the dry season, as a function of the potential soil water loss, given by the difference between the maximum evapotranspiration demand and the precipitation. The maximum evapotranspiration was in this case determined by means of the Hargraves formula, according to FAO procedure in case of limited availability of meteorological data. The estimate of the uncertainty can be easily performed in both the cases in which the field capacity is completely or only partially restored during the wet season. As a test case, the method was then applied to some sites in the Capitanata plane and extended to the whole plane through a GIS application, with fair results if compared with the required water volumes declared by the local irrigation consortium.