David W. Dilks

Development of Bayesian Monte Carlo techniques for water quality model uncertainty

A new technique, Bayesian Monte Carlo (BMC), is used to quantify errors in water quality models caused by uncertain parameters. BMC also provides estimates of parameter uncertainty as a function of observed data on model state variables. The use of Bayesian inference generates uncertainty estimates that combine prior information on parameter uncertainty with observed variation in water quality data to provide an improved estimate of model parameter and output uncertainty. It also combines Monte Carlo analysis with Bayesian inference to determine the ability of random selected parameter sets to simulate observed data. BMC expands upon previous studies by providing a quantitative estimate of parameter acceptability using the statistical likelihood function. The likelihood of each parameter set is employed to generate an n-dimensional hypercube describing a probability distribution of each parameter and the covariance among parameters. These distributions are utilized to estimate uncertainty in model predictions. Application of BMC to a dissolved oxygen model reduced the estimated uncertainty in model output by 72% compared with standard Monte Carlo techniques. Sixty percent of this reduction was directly attributed to consideration of covariance between model parameters. A significant benefit of the technique is the ability to compare the reduction in total model output uncertainty corresponding to: (1) collection of more data on model state variables, and (2) laboratory or field studies to better define model processes. Limitations of the technique include computational requirements and accurate estimation of the joint probability distribution of model errors. This analysis was conducted assuming that model error is normally and independently distributed.

Exploring the dynamics and fate of total phosphorus in the Florida Everglades using a calibrated mass balance model

Abstract The Everglades protection area, which encompasses five Water Conservation Areas (WCA), Everglades National Park (ENP), and a network of canals, levees, structures, and pump stations, exhibits elevated nutrient concentrations in the water and sediments, primarily as a result of phosphorus loads in agricultural runoff. A mass balance model was developed to predict phosphorus fate and transport in the Everglades Protection Area that could result from proposed phosphorus reduction strategies. The modeled area is about a 7000 km 2 region that is divided into 642, 3.2×3.2 km cells, plus additional cell areas for canals. Phosphorus is transported between model cells and canals in accordance with output from a regional hydrology model. Simulated water column phosphorus dynamics within each cell and canal is further controlled by a simple, apparent net settling rate coefficient that integrates the effects of chemical, biological, and physical processes, and leads to net deposition of phosphorus in the sediments. After specification of external phosphorus loads (surface water and atmospheric wet and dry deposition) and system boundary conditions, the model was calibrated to available field data. The calibration procedure consisted of varying the apparent net settling rate coefficients in the WCA and the ENP. The goodness of fit of predicted water column total phosphorus concentrations varied temporally and spatially. Sediment phosphorus net deposition rates calculated by the model matched well with in situ observations where available. The model indicates that phosphorus in seasonal rainfall is a dominant influence on water column phosphorus dynamics in remote areas of the Everglades, whereas phosphorus dynamics in cells directly downstream of runoff inputs exhibit well-documented, nutrient gradients in receiving waters and sediments that could not be caused by rainfall alone. The model suggests that reductions of phosphorus concentrations leaving agricultural areas at the north end of the system will lead to lower concentrations entering ENP at the south end of the system.

Artificial substrata for reducing periphytic variability on replicated samples

Periphyton accrual (chlorophyll a) was evaluated utilizing two different geometrically shaped artificial glass substrata. The first consisted of small coverslips attached to a glass slide (Dilks & Meier 1981), while the other method employed both horizontally and vertically oriented small culture tubes. Sufficient numbers of each type were placed in Fleming Creek (Ann Arbor, Michigan), a second order temperate stream, to permit four collections of three replicates for each type at 5-day intervals. With the exclusion of the first collection (after 5 days), the variability among the replicates was less than 8 percent. Analysis of the chlorophyll a data by ANOVA and simple linear regression showed least amount of variation in horizontally positioned test tubes, followed by those of vertical orientation, and then by the coverslips. The highest concentration of periphyton biomass measured in chlorophyll a was, however, observed in the vertically placed test tubes. The coverslips and horizontally incubated tubes collected comparable concentrations of chlorophyll a over the exposure period.

The Use of Coverslips in Estimating Periphyton Accrual

ABSTRACT A new method of using artificial substrates for quantitative periphyton measurement was given preliminary testing over a 30 day period in Fleming Creek, Washtenaw County, Michigan. Results were encouraging, as this technique was found to be less time consuming than other methods. It also appears that this new procedure could be a valuable tool in addressing the problem of high variability between replicate periphyton samples. In this experiment variation of chlorophyll a concentrations between glass slides was reduced to 4%.

Periphytic oxygen production in outdoor experimental channels

Abstract The contribution of periphytic oxygen was quantified in outdoor artificial streams. A factorial design was employed to determine the effect of stream velocity and light on periphytic growth, measured as chlorophyll α. Results showed that periphytic oxygen production can be estimated by the equation: mg O 2 h −1 mg Chl a =0.85 × 10 −4 × Light Intensity (ft. candles) + 0.061 =0.91 × 10 −3 × Light Intensity (1x) + 0.061 for light intensities to 5000 ft-candles (53,800 lx). Stream velocity was found to be statistically insignificant in affecting oxygen production, but was a factor in periphyton accural and species composition. Gross oxygen production exceeded respiration by a factor of three.