Early View! Sources of uncertainty in estimating stream solute export from three headwater catchments

Yanai, R.D., N. Tokuchi, J.L. Campbell, M.B. Green, E. Matsuzaki, S.N. Laseter, C.L. Brown, A.S. Bailey, P. Lyons, C.R. Levine, D.C. Buso, G.E. Likens, J. Knoepp, K. Fukushima. 2014. Hydrological Processes.

Uncertainty in the estimation of hydrologic export of solutes has never been fully evaluated at the scale of a small-watershed ecosystem. We used data from the Gomadansan Experimental Forest, Japan, Hubbard Brook Experimental Forest, USA, and Coweeta Hydrologic Laboratory, USA, to evaluate many sources of uncertainty, including the precision and accuracy of measurements, selection of models, and spatial and temporal variation. Uncertainty in the analysis of stream chemistry samples was generally small but could be large in relative terms for solutes near detection limits, as is common for ammonium and phosphate in forested catchments. Instantaneous flow deviated from the theoretical curve relating height to discharge by up to 10% at Hubbard Brook, but the resulting corrections to the theoretical curve generally amounted to <0.5% of annual flows. Calibrations were limited to low flows; uncertainties at high flows were not evaluated because of the difficulties in performing calibrations during events. However, high flows likely contribute more uncertainty to annual flows because of the greater volume of water that is exported during these events. Uncertainty in catchment area was as much as 5%, based on a comparison of digital elevation maps with ground surveys. Three different interpolation methods are used at the three sites to combine periodic chemistry samples with streamflow to calculate fluxes. The three methods differed by <5% in annual export calculations for calcium, but up to 12% for nitrate exports, when applied to a stream at Hubbard Brook for 1997–2008; nitrate has higher weekly variation at this site. Natural variation was larger than most other sources of uncertainty. Specifically, coefficients of variation across streams or across years, within site, for runoff and weighted annual concentrations of calcium, magnesium, potassium, sodium, sulphate, chloride, and silicate ranged from 5 to 50% and were even higher for nitrate. Uncertainty analysis can be used to guide efforts to improve confidence in estimated stream fluxes and also to optimize design of monitoring programs.

This work is supported by the National Science Foundation (NSF) and the NSF Long-Term Ecological Research (LTER) Network Office. Many of the ideas implemented in this paper were developed in a meeting of a QUEST Working Group in March 2011. In June 2011, the Japanese Society for the Promotion of Science (JSPS) awarded a fellowship to Ruth Yanai, hosted by Naoko Tokuchi, to work on this project. The research at Gomadansan is supported by the staff of the Wakayama Experimental Forest of Kyoto University. The Hubbard Brook Experimental Forest is operated by the US Forest Service and the Hubbard Brook Research Foundation, and it forms part of the NSF LTER site network. Research at Coweeta Hydrologic Laboratory was funded by the US Forest Service, Department of Agriculture, Southern Research Station, and the NSF LTER (DEB-9632854 and DEB-0218001). Chemistry data for HBEF were obtained through funding from The A.W. Mellon Foundation and the NSF, including the LTER and LTREB programs.

Early View and Open Access! A climate of uncertainty: accounting for error in climate variables for species distribution models

Stoklosa, J., Daly, C., Foster, S. D., Ashcroft, M. B., Warton, D. I. (2014), A climate of uncertainty:
accounting for error in climate variables for species distribution models. Methods in Ecology and Evolution. doi: 10.1111/2041-210X.12217

The authors summarize:

1. Spatial climate variables are routinely used in species distribution models (SDMs) without accounting for the fact that they have been predicted with uncertainty, which can lead to biased estimates, erroneous inference and poor performances when predicting to new settings – for example under climate change scenarios.
2. We show how information on uncertainty associated with spatial climate variables can be obtained from climate data models. We then explain different types of uncertainty (i.e. classical and Berkson error) and use two statistical methods that incorporate uncertainty in climate variables into SDMs by means of (i) hierarchical modelling and (ii) simulation–extrapolation.
3. We used simulation to study the consequences of failure to account for measurement error. When uncertainty in explanatory variables was not accounted for, we found that coefficient estimates were biased and the SDM had a loss of statistical power. Further, this bias led to biased predictions when projecting change in distribution under climate change scenarios. The proposed errors-in-variables methods were less sensitive to these issues.
4. We also fit the proposed models to real data (presence/absence data on the Carolina wren, Thryothorus ludovicianus), as a function of temperature variables.
5. The proposed framework allows for many possible extensions and improvements to SDMs. If information on the uncertainty of spatial climate variables is available to researchers, we recommend the following: (i) first identify the type of uncertainty; (ii) consider whether any spatial autocorrelation or independence assumptions are required; and (iii) attempt to incorporate the uncertainty into the SDM through established statistical methods and their extensions.

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.  

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.