Numerical modeling of simultaneous tracer release and piscicide treatment for invasive species control in the Chicago Sanitary and Ship Canal, Chicago, Illinois

Abstract

In December 2009, during a piscicide treatment targeting the invasive Asian carp in the Chicago Sanitary and Ship Canal, Rhodamine WT dye was released to track and document the transport and dispersion of the piscicide. In this study, two modeling approaches are presented to reproduce the advection and dispersion of the dye tracer (and piscicide), a one-dimensional analytical solution and a three-dimensional numerical model. The two approaches were compared with field measurements of concentration and their applicability is discussed. Acoustic Doppler current profiler measurements were used to estimate the longitudinal dispersion coefficients at ten cross sections, which were taken as reference for calibrating the longitudinal dispersion coefficient in the one-dimensional analytical solution. While the analytical solution is fast, relatively simple, and can fairly accurately predict the core of the observed concentration time series at points downstream, it does not capture the tail of the breakthrough curves. These tails are well reproduced by the three-dimensional model, because it accounts for the effects of dead zones and a power plant which withdraws nearly 80 % of the water from the canal for cooling purposes before returning it back to the canal.

Appendix: Model efficiency statistics

Different statistics comparing measured and simulated data can be used to evaluate model accuracy [25]. Among those, the following were considered: Nash-Sutcliffe efficiency (NSE), ratio of the root-mean-square error (RMSE) to the standard deviation of measured data (RSR), and percent bias (PBIAS).

The Nash-Sutcliffe efficiency (NSE) is computed as:

$$\begin{aligned} {\mathrm{{NSE}}} = 1 - \frac{{\sum \nolimits _{i = 1}^n {{{\left( {Y_i^{obs} - Y_i^{sim}} \right) }^2}} }}{{\sum \nolimits _{i = 1}^n {{{\left( {Y_i^{obs} - \overline{{Y^{obs}}} } \right) }^2}} }} \end{aligned}$$

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where $Y_i^{obs}$ and $Y_i^{sim}$ are the ith observed and simulated data, respectively; $\overline{{Y^{obs}}}$ is the mean of observed data; n is the total number of observations. NSE can range from $-\infty$ to 1. ${\mathrm{{NSE}}} = 1$ means a perfect match of simulated data to the observed data. The closer NSE is to 1, the more accurate the model is. A coefficient value between 0 and 1 is generally considered to be acceptable.

The ratio of the root-mean-square error to the standard deviation of measured data (RSR) is computed as:

$$\begin{aligned} \mathrm{{RSR}} = \frac{{\mathrm{{RMSE}}}}{{\mathrm{{STDE}}{\mathrm{{V}}_{\mathrm{{obs}}}}}} = \frac{{\sqrt{\sum \nolimits _{i = 1}^n {{{\left( {Y_i^{obs} - Y_i^{sim}} \right) }^2}} } }}{{\sqrt{\sum \nolimits _{i = 1}^n {{{\left( {Y_i^{obs} - \overline{{Y^{obs}}} } \right) }^2}} } }} \end{aligned}$$

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RSR is the ratio of the root-mean-square error (RMSE) to the standard deviation (STDE) of the measured data. $\mathrm{{RSR}} = 0$ means perfect match between simulated and observed data. The closer RSR is to 0, the more accurate the model is.

The percent bias (PBIAS) is computed as:

$$\begin{aligned} \mathrm{{PBIAS}} = \frac{{\sum \nolimits _{i = 1}^n {\left( {Y_i^{obs} - Y_i^{sim}} \right) } }}{{\sum \nolimits _{i = 1}^n {Y_i^{obs}} }} \times 100 \end{aligned}$$

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PBIAS is expressed as a percentage and the optimal value is 0 %. The closer PBIAS is to 0 %, the more accurate the model is. Positive values indicate that the model underestimates the observed data, and negative values indicate that the model overestimates them.