“Wet/dry Daisyworld”: a conceptual tool for quantifying the spatial scaling of heterogeneous landscapes and its impact on the subgrid variability of energy fluxes

We modified the “Daisyworld” model of Watson and Lovelock to consider the energy balance of vegetation with differing potential to evaporate water vapour across a 2-D 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. This paper examines 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 subgrid averaging of the nonlinear functions used to compute surface energy balance. Among our key findings 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 2-D “wet/dry Daisyworld” model produces a virtual landscape whose power-law scaling exponent resembles the one derived for the spatial scaling of a 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 nonlinear averaging of the surface energy balance equation increase as the coefficient of variation of the surface properties increases. Ignoring the subgrid 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.