King County Large Lakes Conductance Evaluation - Lake Sammamish model
For more than a year the conductance profiles in lakes Sammamish, Washington, and Union have been higher than has typically been observed (~1993-2022). Instrument checks by the King County Environmental Laboratory indicate that the instruments have been accurately calibrated. I explored historical trends in lake conductance and alkalinity and I evaluated trends in a number of tributary streams as a preliminary investigation into the cause(s) of the recently observed increases (see here).
Here I describe the development of a simple conductance (salt/conservative substance) model of Lake Sammamish to evaluate the connection between tributary and lake conductance trends. The approach follows an example provided by Chapra et al. (2009) that used used relatively simple mass-balance models to reproduce observed annual Great Lakes chloride trends.
The Lake Sammamish model
A simple mass balance model of a conservative substance, represented in this case by specific conductance (hereafter conductance), can be written as
\(dc/dt = [W(t) - Qo(t)c]/V\)
Where V = lake volume (km3), c = whole-lake annual average concentration (mg/L) or conductance (µS/cm), W = direct loading rate (kt/year), and Qo = outflow rate (km3/year). With calculated total annual loading rates from lake tributary inflows (W), annual outflow rates (Qo), and an initial lake concentration (c), the ordinary differential equation can be solved using the deSolve package in R (Sietaert et al. 2010).
Fortunately, I have already developed preliminary nutrient loading estimates for Lake Sammamish and Lake Washington for the period 2000-2023. I adapted the same methods to estimate conductance loading to Lake Sammamish. The overall approach is too complicated to describe in detail here, but basically I used the available long-term flow and routine stream water quality data to estimate daily and annual loading for Issaquah and Lewis creeks using the Kalman Weighted Regression on Time Discharge and Season (kWRTDS) function in the EGRET package in R (Hirsch et al. 2015). It was not possible to do this for other Lake Sammamish creeks due to lack of long-term flow data (e.g., Idylwood Creek, Pine Lake Creek, Ebright Creek) or lack of long-term stream water quality data (e.g., Laughing Jacobs Creek). Loading from the remaining watershed was extrapolated using watershed area scaling ratios and the respective Lewis and Issaquah loading estimates. Daily mean outflow measurements were available from the King County 51m stream flow gauging station at the outlet of Lake Sammamish.
The limiting factor is the outlet flow data, which is essential for the model to work. The daily discharge data from the Lake Sammamish outlet go back to August 2001. Therefore, the model is initiated in 2002.
I’ve plotted the results from the model and compared the model output to the annual average whole-lake conductance observations and the annual outlet flow data below.
I didn’t expect the model to fit the observations very well, but it looks like the fit of the model to the observations in any particular year is often within the error tolerance of the field conductivity sensor (±5%) which I think is pretty amazing considering the potential errors in the conductance loading estimate.
The observed and modeled trend inferred from a loess fit to the data indicates some large mismatches at the beginning (2002-2017). After 2017, the model seems to correspond more consistently with the year-to-year fluctuations in the observed values, including the sharp upward trend from 2021 to 2022. I’ll suggest that the better consistency between the model and observations beginning in 2018 is due in part to the change to the YSI EXO sonde and improved and more consistent sonde calibration.
A qualitative comparison of the outflow data to the conductance observations suggest to some degree a negative correlation between outflow and lake conductance, particularly for the later period (~2015-2021). I believe the lake outflow is a surrogate for the annual inflow. I could add a plot of total lake inflow but maybe not right now. The association of the large drop in outflow corresponding with the large increase in lake conductance in 2022 seems to confirm the hypothesis that the recent increase in lake conductance can be explained at least in part by the substantial decline in stream flow in the past couple of years.
What might be even more interesting than the current exercise would be the application of an inverse model (again following Chapra et al. 2012) to estimate the loading required to reproduce the available 60+ year time series of Lake Washington alkalinity observations. The largest challenge for that exercise would be (as in the Lake Sammamish example above) the extension of the current reliable outflow data which at this time only goes back to ~2000.