Using the probably approximately correct (PAC) learning hypothesis, we have conducted experiments using clustered computers, high-performance workstations and ad-hoc grids of personal computers, to develop an analytical model for, and demonstrate asymptotic convergence of simple parallel search in the parameter space of complex environmental models such as the Soil and Water Assessment Tool (SWAT). SWAT calibration for hydrological flow, N and P is, for our test cases, superior to current genetic algorithms, as well as to SWAT-CUP, a multi-paradigm calibration solver and to its components. With more complex models, there is no current alternative to our approach in a realizable wall-clock time.