Assessing Uncertainty in Estimates of Nitrogen Loading to Estuaries for Research, Planning, and Risk Assessment |
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Authors: | Glynnis Collins James N Kremer Ivan Valiela |
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Institution: | (1) San Francisco Bay Conservation Development Commission, 30 Van Ness Avenue, Suite 2011, San Francisco, California 94102, USA , US;(2) Department of Marine Sciences, University of Connecticut at Avery Point, Groton, Connecticut 06340-6097, USA , US;(3) Boston University Marine Program, Marine Biological Laboratory, Woods Hole, Massachusetts 02543, USA , US |
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Abstract: | Parametric (propagation for normal error estimates) and nonparametric methods (bootstrap and enumeration of combinations)
to assess the uncertainty in calculated rates of nitrogen loading were compared, based on the propagation of uncertainty observed
in the variables used in the calculation. In addition, since such calculations are often based on literature surveys rather
than random replicate measurements for the site in question, error propagation was also compared using the uncertainty of
the sampled population (e.g., standard deviation) as well as the uncertainty of the mean (e.g., standard error of the mean).
Calculations for the predicted nitrogen loading to a shallow estuary (Waquoit Bay, MA) were used as an example. The previously
estimated mean loading from the watershed (5,400 ha) to Waquoit Bay (600 ha) was 23,000 kg N yr−1. The mode of a nonparametric estimate of the probability distribution differed dramatically, equaling only 70% of this mean.
Repeated observations were available for only 8 of the 16 variables used in our calculation. We estimated uncertainty in model
predictions by treating these as sample replicates. Parametric and nonparametric estimates of the standard error of the mean
loading rate were 12–14%. However, since the available data include site-to-site variability, as is often the case, standard
error may be an inappropriate measure of confidence. The standard deviations were around 38% of the loading rate. Further,
95% confidence intervals differed between the nonparametric and parametric methods, with those of the nonparametric method
arranged asymmetrically around the predicted loading rate. The disparity in magnitude and symmetry of calculated confidence
limits argue for careful consideration of the nature of the uncertainty of variables used in chained calculations. This analysis
also suggests that a nonparametric method of calculating loading rates using most frequently observed values for variables
used in loading calculations may be more appropriate than using mean values. These findings reinforce the importance of including
assessment of uncertainty when evaluating nutrient loading rates in research and planning. Risk assessment, which may need
to consider relative probability of extreme events in worst-case scenarios, will be in serious error using normal estimates,
or even the nonparametric bootstrap. A method such as our enumeration of combinations produces a more reliable distribution
of risk. |
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Keywords: | : Nitrogen loading Estuaries Watershed Uncertainty Management Risk assessment |
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