Measuring the amount and chemistry of rainfall at a precipitation station is relatively straightforward. However, estimating the input of rain water and solutes to ecosystems requires interpolation between the precipitation stations. Various methods of interpolation are used in precipitation and atmospheric deposition studies (Garcia et al. 2008, Weathers et al. 2006), but the uncertainty in the interpolation is rarely reported or used in estimating uncertainty in deposition estimates.
John Campbell conducted a preliminary analysis of spatial uncertainty in rainfall amounts using data from the Hubbard Brook Experimental Forest in New Hampshire. Hubbard Brook uses eleven precipitation gauges to estimate annual precipitation for six adjacent experimental watersheds. Thiessen polygons (Viessman and Lewis 1996) are used to define the area characterized by each of these eleven precipitation estimates, and precipitation to each watershed is calculated as the sum of the areas contributed by each polygon. He compared this to several other interpolation methods (spline, inverse distance weighting, kriging, and regression modeling) and found differences of less than 1% across the methods for annual precipitation of the nine watersheds at Hubbard Brook (Figure 1). The error associated with model selection is thus likely to be small. The error within the models describing precipitation amounts (e.g. model or parameter error in the regression) has yet to be estimated. Accounting for uncertainty in solute deposition is further complicated by the spatial and temporal mismatch between volume and chemistry samples, with fewer samples typically collected for solute chemistry than for rainfall volume. Additional challenges to be addressed in estimates of atmospheric inputs are associated with the difficulty of monitoring dry deposition and cloud deposition and their interaction with vegetation structure.
Shannon LaDeau will develop a hierarchical regression model that can accommodate the spatial and temporal mismatches in precipitation volume and chemistry observations, using weekly data sampled from five watersheds at Hubbard Brook. The regression will estimate monthly and annual wet deposition of solutes for each watershed and probability distributions for inference on predictive covariates. The model will also partition uncertainty due to measurement error, missing data, and poor model fit and will provide estimates of environmental stochasticity. Methods for spatial interpolation of regressions will be explored and impacts on annual budgets compared, including spatial analyses packages in ArcView, R (e.g, ModelMap package) and Bayesian kriging methods in OpenBUGS (i.e., geoBugs).
We also have support from the LTER Network Office for a Synthesis Working Group to further develop approaches to estimating uncertainty in precipitation fluxes. We will extend our model protocol and results to similar data from other LTER sites.