The purpose of this EArly-concept Grant for Exploratory Research (EAGER) proposal is to develop an initial analysis of uncertainty in precipitation fluxes of water and nutrients at the scale of a small-watershed ecosystem. This effort complements preliminary studies of uncertainty in forest biomass and in stream loads. Uncertainty analysis is critical to the construction of ecosystem mass balances, one of the pillars of ecosystem science, but is rarely conducted or reported. Failure to address uncertainties can lead to important and erroneous conclusions, for example in identifying missing sources and sinks in ecosystem carbon or nutrient budgets. The activities proposed build upon a large amount of extant data and experience in constructing mass balances and will specifically utilize the unique weekly precipitation volume and chemistry data collected over many years from five watersheds at Hubbard Brook, New Hampshire. This is a great opportunity to help move ecosystem science into a more modern era of dealing with uncertainties in such datasets, which are generally quite common.
The broader impacts of the project are potentially transformative. The PI and colleagues hope to facilitate a cultural change that makes uncertainty analysis an accepted and expected practice in the construction of ecosystem budgets.
In most scientific disciplines, some kind of uncertainty analysis is used to report statistical confidence in results. Clearly, uncertainty is needed for determining the significance of observed differences, for analyzing trends over time or making predictions, and for guiding research investments by identifying which components contribute the most to the overall uncertainty. In ecosystem studies, however, it is not uncommon for uncertainty to be partially or even entirely ignored. The purpose of this project was to develop an initial analysis of uncertainty in precipitation fluxes of water and nutrients at the scale of a small-watershed ecosystem. Uncertainty in precipitation inputs to ecosystems 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. We developed 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 estimates monthly and annual wet deposition of solutes for each watershed and probability distributions for inference on predictive covariates. The model also partitions uncertainty due to measurement error, missing data, and poor model fit and provides estimates of environmental stochasticity. The value of this approach is that it accommodates differences in measurement scale between nutrient chemistry (6-20 days) and precipitation (daily), and it estimates uncertainty (as a variance) in both precipitation volume and chemistry measurements and integrates both sources of uncertainty into the derived flux estimate - at the scale of each rainfall gage and up to the watershed scale. Results Inter-annual variability in the precipitation volume (some years have more rain than others) is the largest source of "uncertainty" in the model (±53% (95% CI)). When calculating a 'mean flux' over multiple years (e.g., a decadal average flux) this inter-annual variability would be the largest component of the error bars. However, uncertainty in precipitation fluxes in a given year is much smaller. The uncertainty term for solute concentrations, based on duplicate collectors, was ±5% for sulfate, 7% for base cations, chloride, nitrate, and silica, and 8% for ammonium and phosphate, which are near detection limits. The greatest source of uncertainty within years was in the process model that uses elevation, aspect, and slope to predict volume of precipitation at a particular rain gage. This is important because it means that kriging or interpolation isn't all that accurate, during any sampling period. Over an entire year the uncertainty would be lower.
