The validity of a simple statistical model for estimating fluvial constituent loads: An Empirical study involving nutrient loads entering Chesapeake Bay

Abstract

We consider the appropriateness of "rating curves" and other log linear models to estimate the fluvial transport of nutrients. Split-sample studies using data from tributaries to the Chesapeake Bay reveal that a minimum variance unbiased estimator (MVUE), based on a simple log linear model, provides satisfactory load estimates, even in some cases where the model exhibited significant lack of fit. For total nitrogen (TN) the average difference between the MVUE estimates and the observed loads ranges from -8% to +2% at the four sites. The corresponding range for total phosphorus (TP) is -6% to +5%. None of these differences is statistically significant. The observed variability of the MVUE load estimates for TN and TP, which ranges from 7% to 25% depending on the case, is accurately predicted by statistical theory.

Chemical characteristics of particulate organic matter from a small, mountainous river system in the Oregon Coast Range, USA

“…a Historical data on TSS concentrations determined by the USGS and Oregon DEQ (grey crosses). The lines in each graph represent rating curves determined from the data acquired in this study using the ''quasi-maximum likelihood estimator'' approach described by Cohn et al (1992) (Eq. 1).…”

“…Data from the Santa Clara River are from Masiello and Druffel (2001); data from the Alsea River are from this study. The lines in (a) represent rating curves estimated using the ''quasi-maximum likelihood estimator'' approach described by Cohn et al (1992) (Eq. 1).…”

“…where b 0 and b 1 are regression coefficients, C i is the constituent concentration, Q t is the instantaneous discharge and s is the standard error of residuals (e.g., Cohn et al 1992). This quasi-maximum likelihood method to fit the data corrects for retransformation bias associated with using log linear regressions to calculate loads (e.g., Cohn 1995;Wheatcroft and Sommerfield 2005).…”

Capturing Spatial Variability of Biogeochemical Mass Exchanges and Reaction Rates in Wetland Water and Soil through Model Compartmentalization

“…where Q = inflow (m 3 =s); N = number of inflow observations in the calibration data set; and ln Q = average natural logarithm of inflow observations (Cohn et al 1992). Table 1 presents the regression statistics and coefficient values for constituents of interest that were generated by LOADEST.…”

An export coefficient modeling approach to estimate organic matter and nutrient loadings from point and non point sources into the Fuji river, Japan

“…c. Estimate loadings by regression modelling using the measured, estimated discharge and water quality concentration. A seven parameter log linear model (Cohn et al, 1992) was used to estimate loadings from each sub basin using water quality concentrations along with observed and estimated discharges. The model calculates loads of nutrients (and other constituents) carried by rivers employing a statistical regression model, where the constituent concentrations are estimated based on stream flow and time/season.…”