Vegetation optimality explains the convergence of catchments on the Budyko curve
Authors: Nijzink Remko Christiaan , Schymanski Stanislaus Josef 
Published: March 2022

Abstract. The Budyko framework puts the long-term mean annual evapo-transpiration (ET) of a catchment in relation to its maximum possible value determined by the conservation of mass (ET can not exceed mean annual precipitation) and energy (ET can not exceed mean annual net radiation) in the absence of significant storage contributions. Most catchments plot relatively close to this physical limit, which allowed to develop an empirical equation (often referred to as the Budyko curve) for estimating mean annual evaporation and runoff from observed net radiation and precipitation. Parametric forms of the curve often use a shape parameter (n), that is seen as a catchment characteristic. However, a satisfying explanation for the convergence and self-organization of catchments around such an empirical curve is still lacking. In this study, we explore if vegetation optimality can explain the convergence of catchments along a Budyko curve and in how far n can be seen as a catchment characteristic. The Vegetation Optimality Model (VOM) optimizes vegetation properties and behaviour (e.g. rooting depths, vegetation cover, stomatal control), to maximize the difference between the total carbon taken up from the atmosphere and the carbon used for maintenance of plant tissues involved in its uptake, i.e. the long-term net carbon profit (NCP). This optimization is entirely independent of observed ET and hence the VOM does not require calibration for predicting ET. In a first step, the VOM was fully optimized for the observed atmospheric forcing at five flux tower sites along the North Australian Tropical Transect, as well as 36 additional locations near the transect and six Australian catchments. In addition, the VOM was run without vegetation for all sites, meaning that all precipitation was partitioned into soil evaporation and runoff. For comparison, three conceptual hydrological models (TUWmodel, GR4J and FLEX) were calibrated for the Australian catchments using the observed precipitation and runoff. Subsequently, we emulated step changes in climate by multiplying precipitation (P) by factors ranging between 0.2 and 2, before running the VOM and hydrological models without changing the vegetation properties or model parameters, emulating invariant catchment characteristics under a changed climate. In a last step, the VOM was re-optimized for the different P amounts, allowing vegetation to adapt to the new situation. Eventually, Budyko curves were fit by adapting the parameter n to the model results. This was carried out for both multiple sites simultaneously and for each individual study site, thereby assuming that n is a site specific characteristic. The optimized VOM runs tracked relatively close to a Budyko curve with a realistic n value and close to observations, whereas the runs without vegetation led to significantly lower evaporative fractions and unrealistically low n values compared with literature. When fitting n to individual catchments, changes in P led to changes in n (increasing n for decreasing P) in all model runs (including the three conceptual models) except if the VOM was re-optimized for each change in P, which brought the value of n back close to its value for the unperturbed P in each catchment. For the re-optimized VOM runs, the variation in n between catchments was greater than within each catchment in response to multiplications of P with a factor 0.2 to 2. These findings suggest that optimality may explain the self-organization of catchments in Budyko space, and that the accompanying parameter n does not remain constant for constant catchment and vegetation conditions as hypothesized in the literature, but in fact emerges through the adaptation of vegetation to climatic conditions in a given hydrological setting. Moreover, the results suggest that n might initially increase in response to suddenly reduced P, and only slowly returns to its original, catchment-specific value, as vegetation re-adjusts to the new climate over decades and centuries. This may constitute a new basis for the evaluation and prediction of catchment responses to climatic shifts.