Uncertainty in the net hydrologic flux of calcium in a paired‐watershed harvesting study

Monitoring solutes in precipitation inputs and stream water exports at small watersheds has greatly advanced our understanding of biogeochemical cycling. Surprisingly, although inputs to and outputs from ecosystems are instrumental to understanding sources and sinks of nutrients and other elements, uncertainty in these fluxes is rarely reported in ecosystem budgets. We illustrate error propagation in input-output budgets by comparing the net hydrologic flux of Ca in a harvested and reference watershed at the Hubbard Brook Experimental Forest, New Hampshire. We identify sources of uncertainty and use a Monte Carlo approach to combine many sources of uncertainty to produce an estimate of overall uncertainty. Sources of uncertainty in precipitation inputs included in this study were: rain gage efficiency (undercatch or overcatch), gaps in measurements of precipitation volume, selection of a model for interpolating among rain gages, unusable precipitation chemistry, and chemical analysis. Sources of uncertainty in stream water outputs were: stage height-discharge relationship, watershed area, gaps in the stream flow record, chemical analysis, and the selection of a method for flux calculation. The annual net hydrologic flux of Ca in the harvested and reference watersheds was calculated from 1973 through 2009. Relative to the reference watershed, the harvested watershed showed a marked increase in Ca flux after it was cut in 1983-1984, and slowly declined toward pretreatment levels thereafter. In 2009, the last year evaluated, the 95% confidence intervals for the annual estimates approach the 95% confidence intervals of the pretreatment regression line, suggesting that the increased net loss of Ca in the harvested watershed may soon be indistinguishable from the reference. Identifying the greatest sources of uncertainty can be used to guide improvements, for example in reducing instances of unusable precipitation chemistry and gaps in stream runoff. Our results highlight the value of estimating uncertainty in watershed studies, including those in which replication is impractical.