Approaches to scaling up physiologically based soil-plant models in space and time

Many broad-scale, environmental phenomena can be investigated by extrapolating from detailed study of events at a small scale. This paper evaluates approaches to the use of physiologically based soil-plant models for addressing broad-scale, environmental issues. When the space and time domains of a soil-plant simulator are extended, there is an increase in the variability of soil, plant, and weather variables, which can be dealt with by what is called extended-range modeling, ERM. There may also be a gain of phenomena not represented at the small scale, which can be dealt with by what is called phenomena-added modeling, PAM. As an example of ERM, a Monte Carlo procedure, called Latin hypercube sampling, is used to estimate annual photosynthate production of an oak-hickory forest under three atmospheric CO(2) concentrations. Phenomena-added modeling is illustrated by scaling up spatially from a vegetated plot to a watershed, and scaling up temporally from a physiological model with hourly time steps to a forest-succession model operating on annual time steps. Where large-scale processes take place on a time scale similar to, or faster than, that of small-scale processes (plot-watershed case), less computation is required if the small-scale processes are built into the large-scale model and ERM is conducted with the expanded model. Phenomena-added modeling may be conducted by information transfer from a small-scale simulator to a large-scale simulator. This is also possible with Latin hypercube sampling by using the output frequency distributions from the small-scale model as input distributions for the large-scale model. The final outputs at the large scale are also frequency distributions, and these can be used to determine confidence intervals for statistical comparisons among modeling scenarios. The ERM and PAM methods are data and computer intensive; nevertheless, they can fill an important need for addressing large-scale issues that cannot be adequately addressed through other scaling up methods.