The temporal depth and spatial breadth of observations from platforms such as Landsat provide unique perspective on ecosystem dynamics, but the integration of these observations into formal decision support will rely upon improved uncertainty accounting. Monte Carlo (MC) simulations offer a practical, empirical method of accounting for potential map errors in broader ecosystem assessments. However, unless steps are taken across simulations to vary the probability density functions (PDFs) that control simulated map error, the large number of map units to which those PDFs are applied may cause convergence of mean simulated conditions and an artificial reduction of MC estimates of uncertainty. For MC simulation of errors in categorical maps, we introduce a technique we call “PDF weaving” which both: 1) allows variation of PDFs across simulations; and, 2) explicitly aligns the resulting range of simulated populations with estimates and uncertainties identified by traditional monitoring methods such as design-based inventories. This approach is based on solving systems of linear equations and inequalities for each simulation. Each system incorporates linear constraints related to the unchanging distribution of area among classes in the original map (akin to the fixed longitudinal “warp” on a loom) with variable linear constraints related to the class distribution to be simulated in any one iteration (analogous to the perpendicular, variable fibers of the “weft”). Additional constraints specify how many map units to treat as “correct” based on validation exercises at the map unit level. Solution of these systems provides PDFs which will simulate error at both the map unit level and the population level in a way that is consistent with validation exercises and available population-level estimates. We illustrated this approach in an assessment of the effects of wildfire and harvest on carbon storage over 20 years on a forested landscape in the western United States (US). This assessment utilized the Forest Carbon Management Framework (ForCaMF) approach,which is being implemented by the US National Forest System (NFS). Results showed that simulating map error through the use of dynamic PDFs can contribute significant, realistic uncertainty in a Monte Carlo analysis, but that impacts of fire and harvest on carbon storage may nevertheless be clearly identified and differentiated using remotely sensed maps of vegetation and disturbance.
Healey S.P., Urbanski S.P., Patterson P.L., Garrard C. (2014). A framework for simulating map error in ecosystem models. Remote Sensing of Environment, 150:207-217. 10.1016/j.rse.2014.04.028.