Soil Moisture Assimilation With the Ensemble Kalman Filter in Support of NASA's Seasonal-to-Interannual Prediction Project
Rolf H. Reichle, Jeffrey P. Walker, Randal D. Koster, Michele M. Reinecker and Paul R. Houser
The goal of the NASA Seasonal-to-Interannual Prediction Project (NSIPP) is to develop the use of existing and planned remote sensing observaton systems together with in situ data for improved predictions of seasonal-to-interannual variations. The prediction of precipitation over land at seasonal time scales is naturally a foremost objective of NSIPP. Seasonal climate forecasting must rely on the correct initialization of the slow components of the Earth system, namely, the land surface and the oceans. Although the ocean has the longer memory of the two, ocean conditions appear to have limited impact on predictability outside the tropics (Evenson, 1997). By contrast, the memory associated with the land surface, in particular soil moisture, is likely to be the chief source of mid-lattitude forecast skill. Recent results (Koster et al., 2000) demonstrate the potential predictability of precipitation over land associated with soil moisture.
In this paper we examine the feasibility of using the Ensemble Kalman filter (EnKF) (Evenson, 1994) for optimal soil moisture initialization. The EnKF is based on the propagation of an ensemble of model trajectories whose spread gives an estimate of the uncertainty of the soil moisture estimates. The forecast error covariances that are needed for the update are derived from the ensemble. The EnKF is an attractive option for land surface applications because 1) it is relatively easy to implement even if the land surface model equations include thresholds and other nonlinearities, 2) it is able to account for a wide range of possible model errors, 3) it provides information on the accuracy of its estimates, and 4) its sequential structure is convenient for processing remotely sensed measurements in real-time. On the other hand, the EnKF relies on a number of assumptions and approximations which may compromise its performance in certain situations. Most notably, the size of the ensemble is quite limited in large-scale applications.
In a series of synthetic (identical-twin) experiments we use the EnKF to assimilate near-surface soil mositure into the NSIPP Catchment Model of North America (Koster et al., 2000). Ultimately, the goal is to assimilate directly L-band (1.4 GHz) and C-band (6.6 GHz) passive microwave brightness data. Our land model uses the hydrological catchment as the fundamental land surface unit. Within each catchment, the variability of soil moisture is related to characteristics of the topography. This modeled variability allows the partitioning of the catchment into several areas representing distinct hydrological regimes, wherein distinct (regime-specific) evaporation and runoff parameterizations are applied.
We assess the quality of the soil moisture estimates and the associated evapotranspiration by comparing the estimates to the (synthetic) true fields as well as by examining the innovations sequence. The innovations are defined as the difference between the observations and the soil moisture forecast prior to the update. They are also available when actual observations are assimilated. The quality of the soil moisture estimates is mainly influenced by 1) the size of the ensemble, 2) nonlinearities in the hydrological model, 3) large-scale three-dimensional error correlations in the hydro-meteorological forcings, and 4) errors in the model formulation. Initial results indicate that the EnKF is a flexible and robust data assimilation option which gives satisfactory estimates even for moderate ensemble sizes.
References
Evensen G., 1994. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. Journal of Geophysical Research, 99(C5): 10143-10162.
Evensen G., 1997. Progress during TOGA in understanding and modeling global teleconnections associated with tropical sea surface temperatures. Journal of Geophysical Research, 103: 14291-14324.
Koster, R.D., M.J. Suarez and M. Heiser, 2000. Variance and predictability of precipitation at seasonal-to-interannual time scales. Journal of Hydrometeorology, 1(1):26-46.
Koster, R.D., M.J. Suarez, A. Ducharne, M. Stieglitz, and P. Kumar, 2000. A catchment-based approach to modeling land surface processes in a GCM. Part 1: Model structure. Journal of Geophysical Research – Atmospheres, 105(D20): 24809-24822.