Determining the shortwave field
Shortwave radiation (0.3-3um) is the main source of heat to the lake. It depends on two things:
1. The position of the sun in the sky;
2. Latitude and longitude
3. Cloud cover.
#1 and #2 can be determined for the model grid as a function of time pretty precisely. #3 is a bit more difficult.
I have taken MODIS imagery for 2008 and compared the image intensity at a set of pixels located roughly around the location of my surface buoy in 2008. I then compare this image intensity to the fraction of the clear-sky shortwave that is reaching the buoy. The fit, while noisy, suggests the expected relationship:
when the image intensity is high (i.e. R, G, and B values are large) the image is very white, indicating the presence of clouds, and the resulting observed shortwave fraction is small. And vice versa. I'm currently using the quadratic fit shown, though I'm tempted to switch back to the linear fit, because it does a good job of going to 1 as the image intensity goes to zero.
Given this relationship, I can take a MODIS image from a given day and combine it with the astronomical prediction of clear-sky radiation to make an estimate of how much radiation should be reaching the surface at every point.
One big drawback: I'm using MODIS imagery since it is easy to access right now (through NOAA GLERL's CoastWatch program). Ice also appears white, so I am biasing the forcing towards the low side in the winter, since I count ice as clouds. In the long run, I'm going to identify a satellite product that tells us about atmospheric moisture instead of using color.