Evaluating Sub-Grid Variability of Surface Fluxes with a Cellular Automata Version of the Wet-Dry DaisyWorld Model

We modified the ‘Daisyworld' model of Watson and Lovelock to consider the energy balance of vegetation with differing potential to evaporate water vapor across a two-dimensional landscape. High resolution spatial fields of surface temperature, latent heat exchange and net radiation are computed using cellular automata (CA). The CA algorithm considers competition between actively transpiring ‘wet-daisies' and ‘dry-daisies' for bare ground through temperature-dependent birth and death probabilities.

We examine how differences in biophysical properties (e.g. surface albedo and surface conductance) affect the composition and heterogeneity of the landscape and its energy exchange. And with high resolution and gridded spatial information, we evaluate bias errors and scaling rules associated with the sub-grid averaging of the non-linear functions used to compute surface energy balance. Among the key findings reported in the report, we observe that there are critical conditions, associated with albedo and surface resistance, when wet or dry/dark or bright ‘daisies' dominate the landscape. Second, we find that the heterogeneity of the spatial distribution of ‘daisies' depends on initial conditions (e.g. a bare field versus a random assemblage of surface classes). And third, the spatial coefficient of variation of land class, latent heat exchange, net radiation and surface temperature scale with the exponential power of the size of the averaging window. Though conceptual in nature, the two-dimensional ‘Wet/Dry Daisyworld' model produces a virtual landscape whose power law scaling exponent resembles the one derived for the spatial scaling of normalized difference vegetation index for a heterogeneous savanna ecosystem. This observation is conditional and occurs if the initial landscape is bare with two small colonies of ‘wet' and ‘dry' daisies.

Bias errors associated with the non-linear averaging of the surface energy balance equation increase as the coefficient of variation of the surface properties increases. Ignoring sub-grid variability of latent heat exchange produces especially large bias errors (up to 300%) for heterogeneous landscapes. We also find that spatial variations in latent heat exchange, surface temperature and net radiation, derived from our ‘Daisyworld' model, scale with the spatial variation in surface properties. These results suggest that we may be able to infer spatial patterns of surface energy fluxes from remote sensing data of surface features. ‘Wet-dry' Daisyworld, therefore, has the potential to provide a link between observations of landscape heterogeneity, deduced from satellites, and their interpretation into spatial fields of latent and sensible heat exchange and surface temperature.