Comparison of first‐order error analysis and Monte Carlo Simulation in time‐dependent lake eutrophication models

Abstract

Estimates of variance for a nonlinear, seasonal food chain, nutrient cycle eutrophication model of Saginaw Bay, Lake Huron, calculated by first‐order variance propagation and Monte Carlo analyses, do not always agree. A comparison of estimates of state variables indicates that Monte Carlo means are most like the measurements, whereas Monte Carlo medians are most like the deterministic model output. Best agreement between Monte Carlo and first‐order estimates of both state variable values and their variances occurs when Monte Carlo output distributions are symmetric. Under these conditions, both estimates are measures of variance associated with total populations (i.e., all algae). Those distributions, however, change dramatically in time for most state variables. For asymmetric distributions, first‐order variance estimates measure variability about the typical component of the total population (i.e., the typical algal species) and Monte Carlo variance estimates measure variability of the mean component (which is more reflective of the total). One must be cognizant of these differences when estimating variance associated with model projections.