Observation Error Estimate

[jzwart]

I have been using values between 0.5-1C as observation error for mean daily stream temperature in DRB segments, but I was hoping to make this estimate a little more robust and based on variation within the stream segment and sensor accuracy. Thermistor accuracy is around 0.2C sd based on accuracy from some of the better thermistors out there. And I've been looking into variation within stream segments using output files from the delaware-model-prep pipeline (specifically this step, which takes the mean of multiple obs/reach). 
When there are multiple sites / reach-date, most only have ~2 sites / reach-date but there are a handful of sites with 10+ sites / reach-date.

Below is the standard deviation of temperature observations for reaches with multiple sites for a given reach-date

And the coefficient of variation to take into account any variation in mean temperature

Below are the mean temperature CV's for a given PRMS reach plotted against the number of dates where the given reach had multiple sampling locations (each point is a PRMS reach). Could use this to filter out only those sites with many dates with multiple sampling locations.

I was wondering if we know any more information about where the sites are located or maybe what reaches would be good candidates for estimating within reach temperature variation. For now, assuming a ~1 C sd for mean daily temperature for a reach might work OK based on the plots above, but I'd like to hear any thoughts about how to go about estimating this variation.

[limnoliver]

Interesting Jake. One quick thought is to see how the variability relates to either the distance between the observations, or the length of the reach. My guess is that the reaches that have a lot of sites per date are also really big, which would intuitively increase the potential for variation across the reach? If this is true, you could scale your assumed SD value according to how long the reach is?

[aappling-usgs]

Variability along reaches came to mind for me, too, though I also wonder if you want to try to capture any of that variability (with the idea that model-predicted temperatures should perhaps be representative of the whole reach? but I don't know if this is appropriate).

The CVs well above 0.5 raise my eyebrows - a standard deviation that's >50% of the mean temperature for a reach-day seems like a lot!! Good thing there aren't too many of these.

[jzwart]

Thanks for the input and I'll look into how reach length and/or distance between observations relates to variability in observations. If there is a strong relationship between variability and reach length then varying obs SD by reach length might make sense.

And I'm not sure any of the details on the CV's above 0.5 - I can look into these to see if they are during winter months and /or are far apart by distance

[jordansread]

I'd expect temperature errors to be systematic (bias in the sensor) or potentially correlated with flow (low flows might be more heterogenous, so your measurement might not be representative). I think you are already going down the second path, but do the error methods involve a way to treat the error as bias per-sensor instead of random through time?

[jzwart]

Good points, I think including error correlated with flow would be pretty easy to include. Calculating error per sensor might be a little more work that I was hoping to do, unless you mean estimating sensor error based on reach (e.g. length) and condition (e.g. low flow vs high flow).

[jzwart]

Chatted with USGS uncertainty project folks. USGS thermistors have to be within 0.2C of a calibration thermometer, and many are likely closer to 0.01C difference. Variation within a stream cross-section and for a stream reach is a bit more difficult to estimate and will vary from stream to stream - but most point measurements should be within 1C of the average cross-sectional measurement. They thought that assuming a 0.5-0.8 C standard deviation for observations of a point applied to a stream reach was a reasonable estimate, but it'll vary by stream reach.