Predictive Capability of U.S.
OECD Phosphorus Loading-
Eutrophication Response Models

Mathematical models are being used with increasing frequency to estimate the responses of water bodies to changes in nutrient loadings, and to assist in developing and assessing the water quality benefits to be accrued from various eutrophication management options. Although the current models have various forms and varying degrees of complexity, two basic types of mathematical models have been developed recently for eutrophication modeling: "statistical" models and "dynamic" models.

Dynamic models consist basically of a series of interrelated differential equations which attempt to describe the biological, chemical, and physical reactions and interactions governing aquatic plant growth (usually algae), including nutrient loads and other driving forces, such as light and temperature. These equations are solved simultaneously, usually by computer, to give a quantitative expression of algal growth dynamics and other related lake responses (such as in-lake nutrient levels) over a given period. Such models are calibrated ("tuned") for a given water body by adjusting the values of the coefficients in the various equations to reflect the specific in-lake conditions for the various parameters included in the equations to the extent necessary to make model output match measured characteristics of the water body. Therefore, such models, because they were "system dependent" (that is, they must be readjusted for each water body), are not widely applicable to other water bodies having substantially different characteristics, or to the same water body if the driving force load or other characteristics are substantially changed. In addition, the data requirements for these models are usually very extensive. Because of such factors, the use of dynamic models has thus far generally been limited to site-specific examples. No dynamic model has been demonstrated to have appreciable predictive capability beyond the situations for which they were designed.

Prominent examples of dynamic models that have been developed for the North American Great Lakes include the phytoplankton model (Lake I) developed for Lake Ontario by Thomann et al.;^l,2 the dissolved oxygen (DO) model developed for Lake Erie by DiToro and Connolly;³ and the phytoplankton class succession model developed for Saginaw Bay, Lake Huron, by Bierman.⁴

A statistical or "empirical" eutrophication model, by contrast, is basically a statistical regression that quantifies a basic cause-and-effect relationship, and does not attempt to account for or characterize every component involved in the eutrophication process. The statistical models discussed in this paper were developed by plotting the value of the chosen measure of "effect" (that is, algal production as measured by a response parameter such as chlorophyll concentration) as a function of the factor exerting primary control over algal growth (P load suitably normalized), for each in a group of water bodies, and determining the line of best fit or regression through the individual points. Such models can be viewed, therefore, as statistical approaches relating nutrient (P) inputs and resultant eutrophication-related water quality responses to these inputs. They will not provide a detailed description of in-lake nutrient or algal dynamics, but rather, are formulated to describe the steady-state or equilibrium response. The data requirements are usually much less extensive for statistical models than for dynamic models.

Prominent examples of recent statistical models for assessing eutrophication include those of Vollenweider;^5-7 Dillon and Rigler;⁸ Larsen and Mercier;⁹ Jones and Bachmann;^l0 Rast and Lee;¹¹ Lee et al.;¹² Jones and Lee;¹³ and Vollenweider and Kerekes.¹⁴ While all of these models are in principle the same, the Rast and Lee^11,12 regressions, especially as expanded by Jones and Lee,¹³ have the largest, most varied data base and are hence likely to be most representative of the general case.

In this paper, the predictive capability of the "U.S. Organization for Economic Cooperation and Development (OECD)-Vollenweider-Rast-Lee and Jones" P load-response models is examined. This was done by collecting load and response data from the literature on water bodies that had undergone substantial P load reductions, both before and after the load changes. Only those water bodies with data sufficient to describe load and response characteristics both before and after loading changes were included in this analysis. The models were used to estimate the post-change equilibrium response, based on pre-change characteristics and the magnitude of load change. This prediction was then compared to the response measured after P load reduction occurred. Only by evaluating a model under substantially altered load conditions can its capability for predicting response be verified.

It must be emphasized that this analysis is not a strictly statistical exercise. Others have discussed the significance of the concept of uncertainty analysis in relation to statistical modeling efforts. The purpose of this paper is to describe the predictive capability of this statistical modeling approach by direct comparison of predicted and measured responses. It is felt that this description will have more immediate usefulness to lake or impoundment managers and decision-makers than a strictly statistical analysis. This latter aspect, however, is not to be ignored. The reader is referred to other sources for a detailed discussion of the associated statistics of this modeling approach.^15-17

The models presented herein are an outgrowth of the Cooperative Programme on Eutrophication Control of OECD. This program was initiated to define quantifiable relationships between nutrient loads and eutrophication-related responses of water bodies, which could be used as management tools in the assessment and control of eutrophication in lakes and impoundments. Through the OECD program, a detailed evaluation was made of loadings and responses of over 200 water bodies exhibiting a variety of trophic conditions and physiographic factors in about 20 nations around the world. These water bodies were grouped into four regional projects. Approximately 34 lakes and reservoirs in the U.S. were included in the OECD-North American Project. The OECD eutrophication study program is described in detail by Rast and Lee,¹¹ and Vollenweider and Kerekes.¹⁴

Vollenweider,^5,7 as part of his work in the OECD eutrophication study program, developed overall empirical relationships between areal annual total phosphorus loads normalized by mean depths and hydraulic residence times in the expression [L(P)/(z/T)]/(1+ T)},) and annual average chlorophyll concentrations for a number of European lakes. In his loading expression, L(P) is the areal, annual total P load in mg P/m^2.y , z is mean depth in m, and T is hydraulic residence time in years. The expression z/T is also given the notation q_s. As discussed by Vollenweider and Kerekes,¹⁴ this normalized loading expression is theoretically equal to and can be empirically related to the mean, in-lake, steady-state total P concentration. Rast and Lee¹¹ followed Vollenweiders approach for the U.S. OECD water bodies by relating their phosphorus loads to their chlorophyll concentrations, and deriving a regression similar to Vollenweiders. Using the U.S. OECD data base, Rast and Lee¹¹ also developed regressions between P load (normalized by mean depth and hydraulic residence time) and Secchi depth, and between normalized P load and hypolimnetic oxygen depletion rate. These were presented and discussed by Rast and Lee¹¹ and Lee et al.¹²

Since that time, the authors¹³ have evaluated the P load and eutrophication response characteristics of approximately 40 more water bodies in the U.S. Jones and Lee¹³ have slightly modified the U.S. OECD load-response regressions for Secchi depth and chlorophyll based on the addition of these water bodies but have found that these approximately 40 additional U. S. water bodies did not substantially alter the lines of best fit based on the U.S. OECD data alone. Figure 1 shows the regressions developed by Jones and Lee,¹³ which include the U.S. OECD data and other data evaluated by Rast and Lee.¹¹ They are based on water bodies having a wide variety of morphologic and hydrologic characteristics and geographic locations, ranging from small, shallow lakes and impoundments, to the Great Lakes, including Lake Superior. They include water bodies with trophic conditions ranging from oligotrophic to hypereutrophic. Lee has also found that the U.S. OECD load-response relationships are applicable to the approximately 200 other OECD water bodies evaluated in the OECD eutrophication study program. As discussed in a subsequent section of this paper, Lee and Jones¹⁸ expanded this approach to develop a relationship between P load and fish yield in water bodies.

Figure 1: Phosphorus load: Eutrophication response relationships for US water bodies (after Jones and Lee13).

PROCEDURE AND ANALYSIS

The predictive capability of the U.S. OECD eutrophication modeling approach, and Jones and Lee¹³ regressions was examined by comparing the predicted and measured responses of water bodies subjected to substantial changes in their phosphorus loads. The authors surveyed the eutrophication literature for pertinent, requisite data to determine load-response couplings for as many such water bodies as possible for before and after the P load change. No attempt was made to select certain types or classes of water bodies. Because data for phosphorus loads and water body conditions both before and after changes in the phosphorus loads were needed, sufficient information was found for only about 15 water bodies, located in the U.S., Canada, and Sweden. A number of these water bodies were not included in this evaluation, however, because they were found to violate one or more of the significant basic premises that must be fulfilled to reliably use the OECD eutrophication modeling approach. These omissions, as well as the general conditions that must be met, are discussed in a subsequent section. Further, during preparation of this paper, a paper by Smith and Shapiro¹⁹ was published that discussed chlorophyll-phosphorus concentration relationships. Those authors sources were examined to determine if adequate P loading information was provided so their water bodies could be included in this paper. As discussed in a subsequent section, few of the water bodies discussed by Smith and Shapiro could be included herein.

The general locations, phosphorus loads, and hydrologic and morphometric characteristics of the water bodies evaluated herein are presented in Table 1. Corresponding data on chlorophyll concentrations, Secchi depth transparencies, and hypolimnetic oxygen depletion rates are presented in Table 2. The columns labeled "Pre-" and "Post-" in Table 2 refer to conditions prior to, and following initiation of phosphorus control programs, respectively.

Table 1: Summary of data on phosphorus loads and morphometric and hydrologic characteristics.

Lee et al.⁵⁵ discussed an interesting application of the predictive capability of these models to evaluate the change in water quality characteristics (specifically, hypolimnetic oxygen depletion) of Lake Mendota, Wis., between the early 1900s and present. Based on the U.S. waterbody line of best fit (Figure 4), current oxygen depletion rates and P loading, and the reported oxygen depletion rates for 1906-1909, an estimate was made of the P load in 1906-1909. This loading and a literature value for Secchi depth for 1916 was plotted on the P loading-Secchi depth model (Figure 3). It was found to plot close to the line of best fit. Even more remarkable was the fact that this coupling was "up" the line of best fit from Lake Mendotas current position, giving credibility to the assumptions made. Such a "retrospective" approach can be useful in defining the water quality of a water body at some time in the past (by knowing changes in land use) or in determining the impact certain activities of the past may have had on water quality. In the case of Lake Mendota, it was used to conclude that the demise of the cold water fish, cisco, was the result of increased development of the Lake Mendota watershed principally as increased urban area and more intensive agriculture. The land-use changes increased the P loading, which produced greater amounts of phytoplankton, which in turn increased the rate of deoxygenation of the hypolimnion immediately below the thermocline, which finally made this water (the cisco niche) uninhabitable for them.

Figure 3: Phosphorus Loading-Shecchi Depth Couplings before and after P Load Changes.

Figure 4: Phosphorus Loading: Hypolimnetic oxygen depletion rate couplings before and after P load changes.

Smith and Shapiro¹⁹ have discussed the efficacy of empirical models for assessing eutrophication in water bodies. They have examined the relationship between the in-lake total P and chlorophyll concentrations in several water bodies in the U.S., Canada, and Sweden (most of which are included herein) and concluded that reduction in the total P concentrations in these water bodies are typically accompanied by consistent declines in their chlorophyll levels, although they have also expressed the view that all water bodies do not respond in an "identical" manner to P reductions, and that the "unique" responses of each lake will contribute to the variability of such models. Rast and Lee⁵⁶ and these authors concur in these basic conclusions although Rast and Lee⁵⁶ also point out problems inherent in both the data base and the analyses of Smith and Shapiro. When such problems are appropriately considered in the analyses, Rast and Lee have concluded that, for the purpose of lake management, the Smith and Shapiro¹⁹ relationships present adequate predictions within well-defined confidence intervals. In addition, it should be recalled that the P loading term [(L(P)/q_s)/(1 +T] defines the predicted in-lake, steady-state total P concentrations⁷ within the statistical limitations defined by Vollenweider and Kerekes.¹⁴ Accordingly, if the P loading term were substituted for the average in-lake total P concentration (after appropriate data transformation) in the graphs of Smith and Shapiro, the resulting correlation would likely be similar to the P load-chlorophyll correlation expressed in Figure 2. The reader is referred to Rast and Lee⁵⁶ for a more detailed discussion analysis of the work of Smith and Shapiro within the context of water body management for the effective control of eutrophication.

Implications for Section 314A lake restoration. With all the load alterations that have been undertaken for water bodies around the world and with the tens of millions of dollars that have been spent on such water quality management over the past 10 to 20 years, it is amazing to the authors that adequate load and response data for before and after P loading changes are available on fewer than a dozen water bodies. Lee⁵⁷ pointed out over 10 years ago that money should be spent as part of "lake restoration" to develop a data base whereby a reliable procedure to predict the impacts on water quality - beneficial uses of water bodies could be developed and evaluated. Unfortunately, such monies were not made available. It is indeed fortuitous that there are "before" and "after" data available on at least some water bodies. Certainly a greater portion of the Section 314A lake classification money should have been earmarked for pre-P load change (or other restoration) studies of water bodies, as well as follow-up post-load change studies. The 314A activities should have been used as learning tools to help with future water body evaluation and restoration. Without such studies and subsequent overall evaluations of those study results, knowledge of potential benefits to be derived from water body "restoration" techniques will not be substantially advanced. While the U.S. OECD load-response models will reliably predict the impact of altering P loads to many water bodies for recreational water management, there are other beneficial uses of concern to the public for which there is a need for additional information to develop and evaluate relationships between load and response. Lee and Jones³⁸ have developed a manual on conducting studies of the type needed to develop an adequate "before" and "after" data base for evaluating the impact of altered loads on water quality. Any lake restoration effort should be accompanied by a 3-year, pre-change study and a 3-year, post-change study, of the type described by them.

Credits. The authors wish to thank R. Vollenweider, Canada Center for Inland Waters, Burlington, Ontario, and C. Forsberg, Uppsala University, Uppsala, Sweden, for their review of and comments on this paper. The assistance of H. Bernhardt, Postfach, West Germany, in providing information on Wahnbach Reservoir, and of S.O. Ryding, Uppsala University, Uppsala, Sweden, in providing comments on the paper and information on several Swedish lakes is also acknowledged. Support for preparation of this paper was provided by the Department of Civil Engineering and Water Resources Center, Texas Tech University, Lubbock, Tex..

Authors. W. Rast is a scientist with the U.S. Geological Survey, Sacramento, Calif. At the time of preparation of this paper, he was an environmental scientist with the International Joint Commission, Washington, D.C. R. Anne Jones is a research associate and lecturer in the Department of Civil Engineering at Texas Tech University. G. Fred Lee is professor of civil engineering at Texas Tech University, Lubbock. Correspondence should be addressed to G. Free Lee, Dept. of Civil Engineering, Environmental Engineering Program, Box 4089, Lubbock, TX 79409.

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