We address two related questions. The first is about how to store information gained via data assimilation into the structure of the model so that this information is not lost outside the period of observation. We show the general (theoretical) strategy for storing this information, and propose a practical algorithm based on the EnFK. Doing this results in improved forecasts of energy and carbon fluxes from land surface models, as well as improved estimates of streamflow in a rainfall-runoff model.
Storing information in a model structure is done purely by statistical analysis of DA innovations, and so provides no insight about the adequacy of model hypotheses. We show that this type of insight can be gained by measuring how data assimilation changes the way information moves within the model. By treating the model as an information processing system we can visualize explicitly how assimilating observations changes strengths and time-scales of couplings between modeled variables. The insight here is that measuring Shannon-type information fluxes instead of mass and energy fluxes allows us to relate any variable with any other at any time-scale. We produce a concise set of statistics that are easily interpreted and directly highlight how DA effectively changes the way that the model behaves.
We applied the techniques described above to the Noah LSM after assimilating both in situ (FluxNet) and remote sensing (AMSR-E, MODIS) observations. Results indicate that major deficiencies in the way that Noah translates climatological boundary conditions into soil water states and surface energy and carbon fluxes are consistent across diverse soil regimes, climatic regimes, and biomes. This consistency suggests very particular ways in which to approach improving the structure of Noah, and also that the data assimilation methods we propose are capable of providing non-spurious insight.