Integrating discrete and continuous data

[jds485]

A few questions with the theme of how to integrate the discrete and continuous samples for prediction models. I'd expect these questions have come up for other projects and would appreciate lessons learned and insights. @jsadler2 @aappling-usgs

1. "Will we want padded time series, or just the available data? Does it make a difference from a modeling perspective?"
   Originally posted by @lekoenig in Add daily nwis data to project pipeline #8
2. Do we need an ActivityStartTime.Time for discrete samples to be useful? About 6% (~6000 samples) do not have a time recorded.
3. I'd expect most discrete sites have just one sample per day. I think Lauren merged sites with multiple in a day to one per day. Is that right? This leads to a question of how to treat these samples for daily prediction.

Here are my thoughts:

Static prediction model:
Discrete sites: If they have NAs, we can safely drop them. Same as having no sample info for that time.
Continuous sites - daily average: NAs can be dropped. We may also consider dropping days if they have few measurements on a given day. Could implement a cutoff for number of non-NA time steps required to compute a daily average.

Time-aware prediction model:
Discrete sites: Pad at the timestep of prediction? It seems like that would increase file size by a lot. I'd expect the code would be faster if we check that these discrete sites have data in each timestep.
Continuous sites: Yes, I think padding with NAs is useful at the timestep of prediction. For example, if we predict hourly and have 4 NAs in that hour, we set to NA. If we have at least one measurement, we use the average of those measurements. Could create a function that accepts the timestep and timeseries and outputs the timeseries on the simulation timestep.

[jds485]

In response to item 3 above

I'd expect most discrete sites have just one sample per day. How should we treat these samples for daily prediction?

Assuming we want to predict a daily average, we could use the high-frequency sample sites to derive an error model that results from using discrete samples as the daily average value. We can treat the daily average from the high-frequency sample records as the true daily average, and then compute the error obtained from using only one sample per day from the continuous record. That would allow us to estimate the error distribution associated with using daily discrete samples to represent the daily average values. It might be conditional on site features and could vary by season and/or flow conditions. But even with those nuances, we would have an estimated error distribution that we can use to describe the tolerable model error for the discrete samples.

[jsadler2]

Discrete sites: Pad at the timestep of prediction? It seems like that would increase file size by a lot. I'd expect the code would be faster if we check that these discrete sites have data in each timestep.

With our previous modeling with flow and temperature, we have padded the data for all of the segments. This ensures the output data for all of the segments is the same shape (has the same number of values, including nans) which is what Tensorflow is expecting. The size of the observation data (even padded) has never been very big, so I don't think we need to be concerned about that.