Mathematical Description of Rooting Profiles of Agricultural Crops
and its Effect on Transpiration Prediction by a Hydrological Model

The geometry of rooting systems is important for modelling water flows in the soil-plant-atmosphere continuum. Measured information about root density can be summarized in adjustable equations applied in hydrological models. We present such descriptive functions used to model root density distribution over depth and evaluate their quality of fit to measured crop root density profiles retrieved from literature. An equation is presented to calculate the mean root half-distance as a function of depth from root length density profiles as used in single root models for nutrient and water uptake. To assess the importance of the shape of the root length density profile in hydrological modelling, the sensitivity of actual transpiration predictions of a hydrological model to the shape of root length density profiles is analysed using 38 years of meteorological data from southeast Brazil. The cumulative root density distributions covering the most important agricultural crops (in terms of area) were found to be well described by the logistic function or the Gompertz function. Root length density distribution has a consistent effect on predicted relative yield, but the common approach to predict transpiration reduction and irrigation requirement from soil water storage or average water content is shown to be only partially supported by simulation results.