Quantifying uncertainty in ecology: Examples from small watershed studies
Monitoring elements 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 sinks and sources of nutrients and other elements, uncertainty in these fluxes is rarely reported in ecosystem budgets. This omission stems in part from the fact that each ecosystem is unique, making it challenging to identify replicate sampling units. Even in cases where replication may be possible, it is often prohibitively expensive to monitor the number of ecosystems required for an acceptable level of uncertainty. Without replication, it is still important to know the uncertainty in the measurements that go into describing ecosystem pools or fluxes. However, the calculations are complex and multiple sources of uncertainty are involved (e.g., missing data, biased observations, sampling error, analytical error). We illustrate the concept of error propagation in ecosystem studies using the net hydrologic flux of calcium 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 individual estimates of uncertainty to produce an overall value.
Sources of uncertainty in precipitation inputs that were identified and quantified in this study include: the model selected for interpolation among precipitation gages, precipitation collector efficiency (undercatch), collector measurement, gaps in precipitation volume, chemical analysis, and gaps in precipitation chemistry. Sources of uncertainty in stream water outputs include, watershed area, stage height measurement, stage-discharge relationship (rating curve), gaps in the stream flow record, and leakage (i.e. groundwater losses). The annual net hydrologic flux of calcium in the harvested and reference watersheds was calculated from 1963 through the present. Prior to the harvest, the difference in net hydrologic flux of calcium between the two watersheds was within the range of uncertainty. Following the harvest, the calcium flux in stream water exports from the harvested watershed increased and have remained high relative to the reference, but appear to be slowly returning to pre harvest levels. This example highlights the value of estimating uncertainty in studies where replication is impracticable, and demonstrates how uncertainty estimates improve confidence in comparisons.