Raymond P. Canale

Long-term phenomenological model of phosphorus and oxygen for stratified lakes

Abstract A budget model is developed to predict the long-term response of a lake to changes in its phosphorus loading. This model computes total phosphorus and hypolimnetic oxygen concentrations, taking sediment-water interactions into account. The lake is treated as two segments: the water and a surface sediment layer. A total phosphorus budget for the water accounts for inputs due to external loading and recycle from the sediments. It reflects losses due to flushing and settling. The sediment layer gains total phosphorus by settling and loses total phosphorus by recycle and burial. The recycle from the sediments to the water is dependent on the levels of sediment total phosphorus and hypolimnetic oxygen. Hypolimnetic oxygen concentration is estimated with a semi-empirical model. The model is applied to Shagawa Lake. An analysis is performed to demonstrate how its predictions replicate in-lake changes not possible with simpler phosphorus budget models.

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.

Modeling fecal coliform bacteria—II. Model development and application

Abstract The episodic nature of their origin and the transience of the receiving water response make the modeling of fecal coliform bacteria contamination events particularly challenging. A two-layer mass balance model was developed to simulate spatial and temporal variability in fecal coliform bacteria concentrations in a polluted, urban lake. Independently validated submodels were used to estimate bacteria loads from tributary and point source discharges, to quantify mass transport and to determine losses due to sedimentation and death. The overall model was validated by successfully simulating spatial and temporal dynamics for dry weather conditions and two wet weather events. Sensitivity analyses indicate that the likelihood of violating public health standards is influenced by environmental conditions, e.g. light intensity and wind mixing. Model simulations are used to illustrate the impact of water quality management actions on bacteria levels at various locations in the lake. The general approach presented here and the techniques used to quantify model inputs may be of value in application to other systems.

Ecological Studies and Mathematical Modeling of Cladophora in Lake Huron: 5. Model Development and Calibration

The development of a mathematical model for calculating the spatial distribution and temporal variation in Cladophora biomass and selected forms of phosphorus at a site on Lake Huron is described. The model is intended for use in evaluating the utility of various phosphorus management strategies in reducing the nuisance growth of Cladophora in the Great Lakes. The model is composed of a transport component which accounts for bulk transfer and exchange of phosphorus within the system and a kinetic component which describes chemical and biological reactions. The kinetic component includes the effects of light, temperature, and internal phosphorus levels on Cladophora growth rate, aspects of phosphorus uptake, and the impact of sloughing and self-shading on standing crop. The numerical value of coefficients associated with kinetic equations have been independently determined through laboratory studies. The model has been calibrated to a data set collected in the vicinity of the Harbor Beach, Michigan, wastewater treatment plant. A satisfactory fit was achieved for model calculations and observed levels of Cladophora biomass, internal phosphorus, and soluble reactive phosphorus. The model has few degrees of freedom because the coefficient values were fixed from field and laboratory measurements. A standing crop of Cladophora biomass of 300 gDW/m2 with an internal phosphorus level of 0.35%P was characteristic of stations in the vicinity of the nutrient source. Soluble reactive phosphorus levels fluctuated widely due to mixing of the effluent plume with offshore waters, but averaged approximately 30 μgP/L. A distinct spatial trend was observed with Cladophora biomass, internal phosphorus, and soluble reactive phosphorus decreasing with distance from the point source of nutrients. The opportunity for model verification by perturbation through phosphorus removal is discussed.

Phosphorus models for eutrophic lakes

Abstract A model is developed for a highly eutrophic lake (White Lake, Michigan) which incorporates both the water and sediment systems and considers two forms of phosphorus—particulate and dissolved. Dynamic interactions of phosphorus between sediments and water are quantified by taking account particulate phosphorus sinking to the sediment-water interface and diffusion of dissolved phosphorus across the interface. Other model mechanisms include vertical eddy diffusion in the water; phosphorus transformation between the particulate form and the dissolved form in both the water and the sediment, diffusion of phosphorus in the interstitial water, and sedimentation in the sediments. Extensive field data have been used to determine the coefficients and parameters defined in the model formulations. Close agreement between the model calculations and the observed data is obtained, especially for the upper layers of the sediment. Sensitivity analysis for the model further substantiates the model calculations. It is found that two separate forms of phosphorus are necessary to gain detailed insight into the dynamics of phosphorus cycling in White Lake. The model also explains significant releases of phosphorus during anaerobic periods from the sediment to the hypolimnion of White Lake in summer. The general applicability of the model to lakes having different degrees of eutrophication must be determined by an examination and analysis of data from other systems.

Stochastic phosphorous model for Onondaga Lake

Abstract A probabilistic phosphorus model that utilizes the Monte Carlo technique was developed and applied to address water quality management issues for Onondaga Lake, N.Y. Several analyses were conducted to support model development: (1) evaluation of the loading and concentration of phosphorus in the lake; (2) determination of the natural variability of flow and non-point loading to the lake; (3) validation of a deterministic total phosphorus model for the lake; and (4) examination of the uncertainty associated with the phosphorus model using Monte Carlo techniques. Simulations with the probabilistic model have been used to evaluate the significance of year-to-year changes in rainfall, the level and variability of point sources, operation at METRO and uncertainty in the model coefficients. The results indicate that substantial reductions in loading from point sources and some control of non-point sources are necessary to achieve distinct improvements in water quality in the lake. Furthermore, significant year-to-year differences in phosphorus concentration are expected in the lake in response to natural variations in rainfall and runoff.

Performance, reliability and uncertainty of total phosphorus models for lakes—I. Deterministic analyses

Water quality problems in many lakes are closely related to the concentration of total phosphorus. Several total phosphorus models have been developed over the years that may be suitable to study these problems. However, some models may be more appropriate than others depending on the management objectives of the model and the mechanisms that affect the dynamics of various forms of phosphorus in the lake. These mechanisms include stratification, partitioning of total phosphorus into soluble and particulate forms, sediment interactions, and algal uptake and recycle. This paper analyzes the mechanisms, performance, and reliability of several total phosphorus models for lakes. Recommendations are made concerning the most appropriate model for Shagawa Lake, Minnesota. Part II of this paper extends these procedures to include uncertainty analysis using Monte Carlo stochastic techniques.

Ecological Studies and Mathematical Modeling of Cladophora in Lake Huron: 7. Model Verification and System Response

This manuscript describes the verification of a calibrated mathematical model designed to predict the spatial and temporal distribution of Cladophora about a point source of nutrients. The study site was located at Harbor Beach, Michigan, on Lake Huron. The model is intended to have a widespread utility for evaluating the impact of phosphorus removal on the nuisance growth of Cladophora. Therefore, verification was attempted by implementing phosphorus removal at the study site. Phosphorus removal efficiencies at the Harbor Beach, Michigan, wastewater treatment plant averaged 80–90% following the implementation of alum precipitation. The average loading of soluble reactive phosphorus was reduced from 1.35 kg P/day in 1979 to 0.20 kg P/dayin 1980. The standing crop, areal distribution, and duration of abundance of Cladophora biomass were considerably reduced in 1980. Lower ambient levels of soluble reactive phosphorus resulted in a reduction of internal phosphorus from about 0.34% P in 1979 to 0.14% P in 1980 for sites in the vicinity of the nutrient source. The growth rate of Cladophora is directly related to internal phosphorus levels in a phosphorus limited environment. Productivity calculations indicate an 80% reduction in standing crop and gross productivity and a 90% reduction in sloughed biomass. Beach accumulation of sloughed algae was sharply reduced in 1980. Model predictions of the response of Cladophora populations to reductions in phosphorus loading agreed well with field observations. It is concluded that the verified model is suitable for examination of the impact of various phosphorus management strategies on the growth of Cladophora.

Phosphorus Uptake Dynamics as Related to Mathematical Modeling of Cladophora at a Site on Lake Huron

Abstract Cladophora is a significant symptom of eutrophication in Lakes Erie and Ontario and is a local problem associated with nutrient perturbations in Lakes Huron, Michigan, and Superior. This paper presents results of measurements of phosphorus uptake rates as a function of internal phosphorus levels by Cladophora growing near Harbor Beach, Michigan. Cladophora collected near the Harbor Beach wastewater treatment plant had high levels of internal phosphorus and low (or even negative) phosphorus uptake rates. Cladophora distant from the wastewater treatment plant had low internal phosphorus levels and rapid phosphorus uptake rates. The experimental results are discussed in terms of quantitative kinetic formulations which may be incorporated into mathematical models useful for predicting the response of Cladophora to alternative management and control strategies. Preliminary model simulations of Cladophora biomass, internal phosphorus, and external phosphorus are qualitatively similar to observed field data.

Development and Testing of a Total Phosphorus Model for Onondaga Lake

ABSTRACT Adynamic two-layer mass balance model for total phosphorus (TP) is developed for culturally eutrophic Onondaga Lake, NY, and tested for the May 1987 through 1990 period. The model accommodates key processes in the lakes phosphorus cycle, including settling of the particulate fraction of TP, sediment release, and vertical mass transport Model development and testing were supported by a comprehensive program of field and laboratory measurements and experiments, to determine model coefficients and external loads, and to establish temporal and vertical distributions of lake TP concentrations. The model performs well in tracking documented interannual, seasonal, and vertical distributions of TP in the lake, and thus is appropriate as a management tool to evaluate management scenarios aimed at abating the lakes cultural eutrophication problem.