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Quantifying uncertainty in ecology: Examples from small watershed studies

Campbell, John L., Ruth D. Yanai, Mark B. Green, Carrie Rose Levine, Mary Beth Adams, Douglas A. Burns, Donald C. Buso, Mark E. Harmon, Shannon L. LaDeau, Gene E. Likens, William H. McDowell, Jordan N. Parman, Stephen D. Sebestyen, James B. Shanley and James M. Vose. In preparation for Frontiers in Ecology and the Environment.


Measurement from ecosystems are often reported without taking uncertainty into account. This omisison stems in part from the fact that each ecosystem in unique, making it difficult to replicate sampling units. Without replication, it is still important to know the uncertainty in the measurements that go into describing ecosystem pools or fluxes, a challenge that is commonly encountered in small watershed studies. One of the initial QUEST working groups was tasked with developing methods for quantifying uncertainty in small watershed applications. John Campbell is leading this effort, which uses examples from watersheds operated by LTER, USGS and USFS.


HJ Andrews Experimental Forest and LTER (Blue River, OR); Biscuit Brook (Frost Valley, NY); Coweeta Hydrologic Laboratory and LTER (Otto, NC); Fernow Experimental Forest (Parsons, WV); Hubbard Brook Experimental Forest and LTER (West Thornton, NH); Luquillo Experimental Forest and LTER (Luquillo, Puerto Rico); Marcell Experimental Forest (Grand Rapids, MN) ; Niwot Ridge LTER (Roosevelt National Forest, CO); Sleepers River Research Watershed (Danville, VT).

Funding Sources

The NSF LTER Network Office funded a Working Group to quantify uncertainty in hydrologic input -output budgets in 2011.

Uncertainty of precipitation inputs including model uncertainty and natural variability

LaDeau, S., J.L. Campbell, M.B. Green, R.D. Yanai. In preparation for Atmospheric Environment


under construction.


National Science Foundation EArly-concept Grant for Exploratory Research (EAGER) Award # 1216092, and a second LTER Synthesis Working Group grant.

Uncertainty of streamwater outputs in five contrasting headwater catchments including model uncertainty and natural variability

Brent Aulenbach, Doug Burns, Jamie Shanley, Ruth Yanai, Kikang Bae, Adam Wild, Yang Yang, Yi "Tony" Dong
In preparation for ?


There are many sources of uncertainty in estimates of streamwater solute flux. Flux is the product of discharge and concentration (summed over time), each of which has measurement uncertainty of its own. Discharge can be measured almost continuously, but concentrations are usually determined from discrete samples, which increases uncertainty dependent on sampling frequency and how concentrations are assigned for the periods between samples. Gaps between samples can be estimated by linear interpolation or by models that that use the relations between concentration and continuously measured or known variables such as discharge, season, temperature, and time. For this project, developed in cooperation with QUEST (Quantifying Uncertainty in Ecosystem Studies), we evaluated uncertainty for three flux estimation methods and three different sampling frequencies (monthly, weekly, and weekly plus event). The constituents investigated were dissolved NO 3 , Si, SO 4 , and dissolved organic carbon (DOC), solutes whose concentration dynamics exhibit strongly contrasting behavior. The evaluation was completed for a 10-year period at five small, forested watersheds in Georgia, New Hampshire, New York, Puerto Rico, and Vermont. Concentration regression models were developed for each solute at each of the three sampling frequencies for all five watersheds. Fluxes were then calculated using (1) a linear interpolation approach, (2) a regression-model method, and (3) the composite method – which combines the regression-model method for estimating concentrations and the linear interpolation method for correcting model residuals to the observed sample concentrations. We considered the best estimates of flux to be derived using the composite method at the highest sampling frequencies. We also evaluated the importance of sampling frequency and estimation method on flux estimate uncertainty; flux uncertainty was dependent on the variability characteristics of each solute and varied for different reporting periods (e.g. 10-year, study period vs. annually vs. monthly). The usefulness of the two regression model based flux estimation approaches was dependent upon the amount of variance in concentrations the regression models could explain. Our results can guide the development of optimal sampling strategies by weighing sampling frequency with improvements in uncertainty in stream flux estimates for solutes with particular characteristics of variability. The appropriate flux estimation method is dependent on a combination of sampling frequency and the strength of concentration regression models.


Biscuit Brook (Frost Valley, NY), Hubbard Brook Experimental Forest and LTER (West Thornton, NH), Luquillo Experimental Forest and LTER (Luquillo, Puerto Rico), Panola Mountain (Stockbridge, GA), Sleepers River Research Watershed (Danville, VT)


The NSF LTER Network Office funded a Working Group to quantify uncertainty in hydrologic input-output budgets in 2011. Retreats in fall 2011 and spring 2012 In the Fall of 2012 and the Spring of 2013, four students at SUNY Environmental Science and Forestry joined the effort as class projects.

Spatial variance of precipitation: optimizing interpolation efficiency and mitigating uncertainties

Joshua A Roberti1, Jeffrey R Taylor1, 2, Ruth D Yanai3, Adam Skibbe4, Xuesong Zhang5, and Lloyd Swift6. 1National Ecological Observatory Network (NEON), Boulder, CO 80301; 2Institute of Arctic and Alpine Research, University of Colorado-Boulder; 3SUNY College of Environmental Science and Forestry, Syracuse, NY; 4Konza Prairie Biological Station, Kansas State University, Manhattan, KS;5Pacific Northwest National Laboratory, Richland, WA; 6Coweeta Hydrologic Laboratory, Otto, NC.


Fifty-six years of precipitation data from over one hundred gauges were analyzed to determine the spatial distribution that describes a majority of the annual precipitation variance within the Coweeta Hydrologic Laboratory Watershed in North Carolina, USA.  Common interpolation methods (e.g., kriging, etc.) were used to quantify the significance of individual gauges relative to the total variance of annual precipitation within the watershed.  Gauges were then removed from the analysis in ascending order of their importance and as a function of the interpolation methods to derive an optimal sampling regime.  The resulting regime i) explains a majority of the system’s total variance, ii) identifies spatial correlations among gauges as functions of local climatic characteristics, and iii) optimizes sampling efficiency as a function of the spatial uncertainty of annual precipitation within the Coweeta Watershed.  This regime was then applied to other regions with similar and different topographic and climatic features. Although such features vary among watersheds, we argue that spatial uncertainties associated with scarcely sampled networks can be evaluated using a densely sampled network, such as the Coweeta.


Coweeta Hydrologic Laboratory, Otto, NC.

Quantifying uncertainty in gap filling of long-term hydrologic datasets for nutrient budgets: case studies from the LTER network

Craig R. See, Jeremy Hayward, Ruth D. Yanai, Doug Moore, Mark B. Green
In preparation for tbd.


All long term datasets contain missing or unusable data (gaps). While many of these gaps are inevitable, when calculating solute inputs from precipitation or outputs from streamflow, it is not possible to simply omit missing values. The uncertainty associated with gap-filling estimates is not commonly reported or propagated into flux estimates. We hope to characterize the causes of these gaps across sites for both volume and solute chemistry in long-term precipitation and steamflow datasets. To quantify the uncertainty associated with different gap-filling methods, we are applying them to a series of "fake gaps," and comparing the estimates with measured values.


HJ Andrews Experimental Forest and LTER (Blue River, OR); Coweeta Hydrologic Laboratory and LTER (Otto, NC); Hubbard Brook Experimental Forest and LTER (West Thornton, NH); Sevilleta National Wildlife Refuge (Socorro, NM)


Datasets were collected under several cycles of NSF LTER programs.