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Updating snow in CLM #253

@timhoar

Description

@timhoar

Use case

Assimilation experiments that update the snow in CLM require a partitioning function that redistributes the
posterior (diagnostic) SWE into the (prognostic) snow variables - which have an arbitrary number of layers.
Most snow observations are of snowcover fraction or snow water equivalent (SWE). It is useful to provide these
diagnostic quantities (frac_sno and H2OSNO, respectively) from the CLM history files as part of the DART vector.
However, updating each layer of the prognostic variables (H2OSOI_LIQ, H2OSOI_ICE) directly through the ensemble
correlation may not result in a posterior SWE that matches the posterior SWE in H2OSNO.

Note that we have never attempted to create snow from scratch. Nor have we ever attempted to change things like grain size or the amount of black carbon. Also, and perhaps most importantly, if one ensemble member did not have (unobserved) snow-related quantities, the (unobserved) snow-related values were left unchanged in ALL ensemble members. This is different than a failed forward operator. The forward operator can calculate a meaningful value if there is snow in the gridcell, but when the state is being updated - anything in the cutoff radius is considered. (It may be clearer to state that if there were only 79 values on the unobserved axis (think snow ice in layer 5) and 80 estimates of the observed SWE, the regression is ill-defined.)

Is your feature request related to a problem?

This is really a feature request, but if there is a problem, it is that updating the prognostic variables directly does not result in a SWE consistent with the observations.

Describe the your prefered solution

Maintain the original ratios of snow in each active layer, but modify the amount of snow in each layer such that the
resulting SWE matches the desired posterior SWE. The most logical place to do this is in dart_to_clm since it
reads both the posterior variables from DART and the original variables from CLM (which are needed to calculate the original ratios of snow in the layers). This removes the consideration that each ensemble member may have a different number of active snow layers in each column.

Eroding the snow is easy. Increasing snow is harder. Creating snow from scratch is impossible.

Describe any alternatives you have considered

Ideally, I suspect it is most appropriate to modify the atmospheric forcing to provide new snow.

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