Explicitly include GPP, ER, Gas exchange in model outputs

[jsadler2]

One possible approach to adding process guidance to the vanilla deep learning model is to explicitly represent the DO mass balance by outputting GPP, ER, and Gas exchange:

Baseline LSTM (#40):

Proposed:

[amcarter]

A couple more ideas for this version of the model:

1. We could add process guidance based on physical relationships between stream slope, width and depth with gas exchange (K)
2. Both GPP and ER could be constrained to have a degree of autocorrelation (unless there is high precipitation possibly)

[amcarter]

Also, an option for farther down the road would be to take this approach but then add on a second layer of neural network after the GPP, ER and K are predicted that included a subset of the original predictors. This would allow for non-deterministic relationships between metabolism and oxygen concentrations that arise because of variation in stream temperatures, differences in groundwater inputs, or other types of process error.

[amcarter]

One more thought - could we also estimate water temperature? Meaning that the estimated variables would be:

If so, then we could calculate DO saturation, and then have equations like the ones above to calculate DO max/mean/min:

I'm still don't fully understand the h, W, and b terms - so I apologize if these equations don't make sense!