Feature Request: Calculate Total Spread

[icastorm]

Issue

An important function of the DART diagnostic toolkit is to compare the RMSE to the "total spread", which is defined in src/pydartdiags/obs_sequence/obs_sequence.py as the sqrt(sum(sd+obs_err_var)). Given the usefulness of the total spread value in a variety of contexts (temporal evolution, comparisons between observation types, vertical distribution, etc.), it seem appropriate to add a function that calculates the "total spread" of some set of observations to the plots.py script. Total spread plots could be added later as well.

Solution(s)

• To make calculating the total spread easier, the observation error variance should be added as a column to the dataframe created by the obs_sequence class. This would probably be a useful addition regardless.
• A function should be added to the plots.py script that, given a dataframe of observations with columns for observation error variance ensemble variance returns the "total spread" value given by sqrt(sum(ensemble_sd+obs_err_sd)). Here, ensemble_sd and obs_err_sd are the square roots of ensemble variance and observation error variance respectively.

Testing

• To ensure parity with the matlab diagnostic code base, total_spread values should be compared to those in the output of dart_diags

[hkershaw-brown]

Thanks @icastorm great request, currently totalspread is missing.

Here is how I was thinking about it with rmse and bias (I was focusing only on these for a demo of the plots!):

The column is single observation calculation, so squared error and bias are created as columns when we create the dataframe https://github.com/NCAR/pyDARTdiags/blob/7d1b167fb3cbe0d6bb8c33f02cffdb4274889fe0/src/pydartdiags/obs_sequence/obs_sequence.py#L86-L89

sq_err = (mean-obs)**2 bias = mean-obs

For rmse, this is over a group of observations, so you select the group of observations and get the rmse and bias for that group of obs. rmse = sqrt( sum((mean-obs)**2)/n ) bias = sum((mean-obs)/n

https://github.com/NCAR/pyDARTdiags/blob/7d1b167fb3cbe0d6bb8c33f02cffdb4274889fe0/src/pydartdiags/plots/plots.py#L133-L137

I think you're correct that we can treat totalspread in the same way. The function to calculate totalspread is the way to go.

obs_err_var is there as a column in the dataframe. There may be something funky going on if you are not seeing an 'obs_err_var' column

Longer term, I think we might want to split the diagnostic calculations into their own module - I'm guessing someone might want the calculations without necessarily making the plot.

[icastorm]

Sorry for the radio silence, its been a busy couple of weeks and I've been on a bit of a time crunch. I will hopefully be back to working on this next week though...