1. Introduction
2. Background
3. Research Methods
4. Results and Discussion
1. Lake Sammamish Data Analysis
2. Lake Washington Data Analysis
1. Temperature
2. Chlorophyll-A
3. Phosphorus
3. Phytoplankton Dynamics Modeling
1. Growth Rate
2. Grazing Rate
3. Settling Rate
5. Findings, Conclusions, and Future Work
1. Lake Sammamish
2. Lake Washington
3. Problems Encountered
4. Solutions and Future Work
6. References

The Urbanization and Water Quality course (CEWA 599/ZOO 572) is currently investigating the critical lake water quality issues in the Lake Washington and Lake Sammamish watersheds (Figure1).

Course objectives include:

• development of a spatially-explicit nutrient loading model that accounts for transfer of nutrients from watersheds into the surface waters of Lake Washington, Lake Sammamish, and other aquatic systems in the Seattle area;
• development of water quality simulation models for Lake Washington and Lake Sammamish which will predict the likely impact of modified P loading on the water quality of these lakes under various development and water resource management scenarios;
• calibration of the models described above to existing King County/Metro long term water quality records;
• use of the models to forecast future water quality responses to increasing urban sprawl, water diversions, and new sewage treatment facilities in the Seattle/Metro region during the next century;
• to attempt to solve a real world problem and to develop teamwork skills.¹

The "Lake Water Quality Monitoring Group" focuses on the second objective. Over the last several weeks, the group has conducted extensive data collection and analysis, and preliminary model construction. Efforts resulted in a "draft" working model at the conclusion of the Spring quarter.

Figure 1. Plan view of Lake Sammamish and Lake Washington with associated King County/Metro water quality monitoring stations.

The King County Department of Natural Resources is currently involved in several major regional initiatives (Regional Wastewater Services Plan, Endangered Species Response, and Regional Needs Assessment). To provide technical support, the County established the Sammamish-Washington Assessment Modeling Program (SWAMP) to provide water resource data and analysis in support of programs that protect water quality and prevent point and non-point pollution.

The goals of SWAMP are to:

• acquire water resource data for Lake Sammamish, Lake Washington and related influent streams;
• provide decision-makers with information necessary to meet applicable legal requirements for water quality;
• support implementation of the RWSP (Regional Wastewater Services Plan), and associated HCP (Habitat Conservation Plan);
• ensure compliance with the GMA (Growth Management Act);
• provide for King County Comprehensive Plan implementation; and,
• develop a model (assessment tool) to evaluate potential impacts to the Lake Sammamish, Lake Washington, Lake Union, and Ship Canal systems.²

The last goal is the focus of the University of Washington joint department course entitled "Urbanization and Water Quality." The course has been conducted as a workshop to investigate lake water quality issues in the Lake Washington and Lake Sammamish watersheds. The course participants are grouped according to the different aspects of the overall investigation. Investigation areas include Watershed Geography, Watershed Sources of Phosphorus Loading, Phosphorus Export from Watershed, and Lake Water Quality Modeling.

The Lake Water Quality Modeling Group has focused on the impact of phosphorus loading to both Lake Sammamish and Lake Washington. The approach involves two distinct efforts:

1) analysis of existing data to characterize both past and present lake conditions, and

2) development of a phytoplankton model to characterize biomass responses.

Lake data from several sources were collected and analyzed in an effort to establish baseline conditions for specific time intervals. The data for Lake Washington ranges from 1958 to present, and the Lake Sammamish data covers the period from 1979 to present. While the data represent an extensive record, many data gaps exist due to inconsistent sampling frequency during certain time periods. These data gaps create difficulty when calculating yearly and monthly averages. To reconcile these gaps, an interpolation method called Kriging was applied to generate a data set with biweekly values at 5-m depth intervals. This method takes irregularly spaced data and "replaces each missing value with a weighted calculation that minimizes the statistical variance of the array."³ The Macintosh program Transform^TM was used to interpolate data for Lake Washington, and the PC program Surfer^TM was used to generate the data for Lake Sammamish. Studied parameters include temperature, total phosphorus, ortho-phosphate, chlorophyll-a, nitrate-plus-nitrite and secchi depth.

The reconfigured data format also provided for easy import into the model. Model development has focused on defining the governing principles of algal growth dynamics. A phytoplankton biomass balance has been developed and incorporates growth, grazing, and sinking terms. Model software (STELLA) was utilized to study phytoplankton biomass dynamics under varying phosphorus loading scenarios.

4.1 Lake Sammamish Data Analysis

The interpolated Lake Sammamish data were used to characterize temperature, total phosphorus, ortho-phosphate, nitrate-plus-nitrite, chlorophyll-a, and secchi depth patterns on a biweekly basis (see Research Methods). The characterization was based on Station 0612, a deep-water station located in the center of the lake (Figure 1). This station was chosen to represent whole-lake conditions because the data for Station 0612 is consistent with the data for other stations. For example, Figure 2 illustrates the nitrate-plus-nitrite concentration similarity between Station 0612 and Station 0611 at 1 m. Graphs for the other parameters at all depths showed the same agreement between data. In addition, Station 0612 contains a more comprehensive data set than the other stations.

Figure 2. Nitrate plus nitrite concentration comparison between Station 0611 and Station 0612 at 1 m.

The original intention was to use biweekly averages from the available data set (1979 to 1999) to characterize the water quality of the lake. However, because of the extensive growth in the Lake Sammamish watershed over the last 10 years, averages from the 1990s were used to better represent the influences of recent urbanization on water quality.

Table 1 presents 1990s biweekly averages at 1-m and 25-m depths for temperature, total phosphorus, ortho-phosphate, and nitrate-plus-nitrite. The table also includes biweekly average values for secchi depth and for chlorophyll-a at 1-m. The 1-m and 25-m depths were chosen to characterize both the top and the bottom of the water column. Dissolved oxygen data were not included in these analyses as data were not provided from 1993 to present. Table 2 displays averages for November-April and May-October for 1990 through 1999. The two divisions represent the period of lake mixing (November-April) and the period of stratification (May-October), as determined by thermal profiles (Figure 3).

I₀: light intensity at the surface

K_t: attenuation coefficient for water and dissolved and particulate matter combined

Z: depth

If we assume the secchi disc disappears at 10% of surface light intensity, K_t can be calculated: K_t = -ln(0.1)/Z_SD where Z_SD is the secchi disc depth. ⁵

I₀ calculated:

SR: clear sky solar radiation

SC: sky cover (%)

The 0.5 in the formula denotes the surface light intensity usable in phytoplankton growth formulations. This corresponds to the visible range, which is typically about 50% of the total surface solar radiation used in the heat budget computations.⁶

II. Effects of light intensity on phytoplankton growth

We use the Steele formulation⁶, which is one of the most commonly used photoinhibition relationships:

q _L : relative photosynthesis

I: light intensity

I_S: optimum (saturating) light intensity

When depth and time are integrated, the Steele formulation becomes:

f_p: photoperiod (expressed as a fraction of the day)

Z₂-Z₁: depth interval

I_S: the optimum light intensity

We assume that phytoplankton growth is phosphorus-limited.

P: ortho-P concentration

k_sa: Michaelis-Menten half-saturation constant

G: zooplankton grazing rate

F_clad: cladocerans filtering rate (ml/ind-day)

Z_clad: cladocerans concentration (# of individuals per L)

F_cop: copepods filtering rate (ml/ind-day)

Z_cop: copepods concentration (# of individuals per L)

X: phytoplankton concentration (mgC/L)

q _T-graz :effects of temperature on zooplankton grazing

Despite the number of obstacles that we have encountered during the process of creating this model to describe the lacustrine response to phosphorus loading, we were succesful at producing a model that is fairly accurate in its description of algal growth dynamics in Lake Washington. However, our model provides merely a coarse characteization of very complex biophysical and geochemical processes that occur within Lake Washington. The utility of this model is that it can be interfaced with other models and it serves as a landmark from which future modeling efforts may originate. This tool that we have created could be potentially instrumental in deciding whether or not to implement new water conservation practices, such as water reuse, in King County, based on their foreseeable impacts on the water quality of Lake Washington.

The data that served as input into our model from Lake Sammamish have been collected mostly by King County and have been made available to us by Jonathon Frodge. We opted to use site 0612 which is one of the longest standing deepwater collection sites. This time series of data spans from 1979 to the present. However, the lack of consistency in collection and the paucity of data at different depths will greatly affect the resolution and predictive capability of our model. Although we were originally hoping to predict algal response to ortho-phosphate at several discrete depths, this may not be possible because much of our data is restricted to the surface. We have been able to generate biweekly averages for at least the surface of the epilimnion for the following parameters: temperature, ortho-phosphate, total phosphorus, light intensity, secchi depth, and photoperiod. The parameters which are either inadequate in resolution, or completely unavailable, are chlorophyll-a and zooplankton. Chlorophyll-a measurements are essential for the calibration and validation of the model, and zooplankton are an integral parameter in the model because they exert grazing pressure on the phytoplankton. Once values for these parameters are obtained we should be able to run the model for Lake Sammamish.

Fortunately, we were given access to Professor Edmondson’s data obtained from 1956 to the present near Madison Park, in the deepest part of the lake. Surprisingly enough this data required very little interpolation because during the summer months samples were usually collected every two weeks. For Lake Washington we have also generated a biweekly data set for the following variables: temperature, total phosphorus, ortho-phosphate, light intensity, photoperiod, secchi depth, and chlorohpyll-a. At this point the only data we have yet to obtain for the completion of our model is zooplankton abundance, which will be made available.

During the course of this exercise we have experienced difficulties with many aspects of the model. Initially, we had grandiose ideas of creating a 3 dimensional model that would capture all of the spatial and temporal variability in algal growth as a response of phosphorus loading. However, we quickly realized that not only was such a model an unobtainable objective for this brief course but that it may be cumbersome and unnecessary. Instead we have opted for a much simpler design for our model.

For Lake Washington, our modeling effort focuses primarily on the epilimnetic waters as determined from thermal profiles. This approach is inappropriate for Lake Sammamish, as an appreciable amount of phosphorus may be re-entering the water column during seasonal periods of anoxia. How to handle the seasonal variability in phytoplankton and zooplankton has been another obstacle. The output of our model is directly related to the phytoplankton growth rates and zooplankton grazing rates that appear as parameters within the equations of our model. From the literature we know that these growth rates and grazing rates vary considerably as a function of species. We also know from the data that species dominance changes during different seasons in both lakes. Given this, do we change our growth rates and grazing rates according to season to more accurately depict actual seasonal fluctuations that occur in the lakes, or do we assume constant growth and grazing rates so as to introduce less error into our model?

Because we have been working on one isolated portion of this larger project, a recurring concern of ours has been how our model will interface with the models developed by other groups. Our concerns were brought to the forefront when we learned that all of the other groups were expressing their estimates of phosphorus dynamics in the watershed in terms of total phosphorus, whereas we are primarily interested in ortho-phosphate. The most important input parameter for our model is the amount of ortho-phosphate, as this is the phosphorus fraction that is biologically accessible to algae. We are currently exploring ways in which to reconcile the difference between ortho-phosphate and total phosphorus.

From the inception of this process we have been conceptualizing a model calibrated to empirical data that will take as its primary input ortho-phosphate, and will predict the algal response in terms of chlorophyll-a:

However, in aggregating several pre-existing models from the literature into a single model for our purpose we quickly realized that one of the parameters contained within our model was the very same Chlorophyll-a that we were intending to model. We have not quite resolved how we will rectify this obvious circularity within our model.

We have also encountered difficulties in interpolating our data using the Kriging technique within Transform. Some of the interpolated values for ortho-phosphate and chlorophyll-a do not make sense intuitively.

5.4 Solutions and Future Work

We must first tackle the fundamental circularity currently contained within our model, as this is crucial before we can make any further progress on this project. There are two potential solutions to this problem: 1) we can figure out a means of removing chlorophyll-a as an input parameter into our model, or, 2) we can use a surrogate parameter in our model instead of chlorophyll-a. The first solution may be possible because the only reason that chlorophyll-a is included in our model is to determine zooplankton grazing rates and subsequent growth rates. The second solution may be possible if we could use an alternative parameter such as phytoplankton counts instead of chlorophyll-a.

Once our model is rectified we must reconcile the difference in currency between the different groups working on this project. The easiest way of alleviating major problems is to have all groups work in terms of ortho-phosphate instead of total phosphorus. However, at this point in the project it may be impossible to have the other groups provide us with ortho-phosphate data, as they have spent the entire quarter researching total phosphorus. An alternative solution is to devise a means of predicting ortho-phosphate values from total phosphorus values. These values are readily available from the lake data and may be sufficiently correlated so that we may only have to conduct a linear correlation to generate ortho-phosphate from total phosphorus. An initial correlation is present in Figure 10.

Model output for depth interval 0-2.5m

Model output for depth interval 2.5 to 7.5m