Optimal ensemble size of ensemble Kalman filter in sequential soil moisture data assimilation

Abstract

The ensemble Kalman filter (EnKF) has been extensively applied in sequential soil moisture data assimilation to improve the land surface model performance and in turn weather forecast capability. Usually, the ensemble size of EnKF is determined with limited sensitivity experiments. Thus, the optimal ensemble size may have never been reached. In this work, based on a series of mathematical derivations, we demonstrate that the maximum efficiency of the EnKF for assimilating observations into the models could be reached when the ensemble size is set to 12. Simulation experiments are designed in this study under ensemble size cases 2, 5, 12, 30, 50, 100, and 300 to support the mathematical derivations. All the simulations are conducted from 1 June to 30 September 2012 over southeast USA (from −90°W, 30°N to −80°W, 40°N) at 25 km resolution. We found that the simulations are perfectly consistent with the mathematical derivation. This optical ensemble size may have theoretical implications on the implementation of EnKF in other sequential data assimilation problems.

A Method for Objectively Integrating Soil Moisture Satellite Observations and Model Simulations Toward a Blended Drought Index

“…Data assimilation techniques permit the modeled soil moisture (SM) to be corrected toward the observations with the correction degree determined by the error levels associated with each (Reichle & Koster, 2004). With satellite SM retrievals becoming widely and continuously available, it is consequently believed that a land data assimilation system that merges satellite retrievals and model estimates of soil moisture may provide more reasonable values of land surface state variables (Crow & Wood, 2003;Hain et al 2012;Koster et al, 2009;Kumar et al 2009;Reichle & Koster, 2004;Yin et al, 2015bYin et al, , 2015cXia et al, 2012;Zhan et al, 2012). In the most widely used ensemble Kalman filter (EnKF), still, satellite SM observations need to be bias-corrected to respect the assumption that retrieval errors are Gaussian-distributed.…”

An Intercomparison of Noah Model Skills With Benefits of Assimilating SMOPS Blended and Individual Soil Moisture Retrievals

“…Specifically, the error variances used a constant value (3%) as Land Information System (LIS) examples using Kumar et al (). Our particular application used 12‐member ensemble (Yin, Zhan, Zheng, Hain, et al, ) to update all four Noah SM states (0–10 cm, 10–40 cm, 40–10 cm, and 100–200 cm) using either SMOPS blended or individual SM retrievals. Perturbations of both forcing data and state variables are applied at each individual 30‐min Noah model time step.…”

“…The CTR run is a single realization (section ), while the ensemble size for the OLP run and the 6 DA cases was set as 12 that is the optimal ensemble size in a sequential SM assimilation system (Yin, Zhan, Zheng, Hain, et al, ). The Noah model under the ensemble condition was spun up by cycling 30 times through the period from 1 April 2015 to 30 June 2017, and then all of the six DA cases and the OLP run were conducted over the same period with 30‐min time step inputs and daily outputs.…”

“…What makes the SMOPS product unique is it provides a global blended SM data in near real time. Ongoing studies have indicated that model skills can be significantly enhanced with benefits of assimilating SMOPS blended (hereafter, SMOPS) SM product V2.0 that is a combination of SMOS, ASCAT, and WindSat (Nair & Indu, ; Yin et al, , Yin, Zhan, Zheng, Liu, et al, , Yin, Zhan, Zheng, Hain, et al, ). With the SMAP SM data becoming available, we developed the SMOPS product V3.0 that merges the SMOS, SMAP, AMSR2, ASCATA, and ASCATB SM retrievals.…”

Changes of Soil Moisture from Multiple Sources during 1988–2010 in the Yellow River Basin, China

“…Considering the different sources of errors, data assimilation approach, which uses the observational information to calibrate the model output, is used to produce more accurate soil moisture estimations. There are several data assimilation methods ranging from simple interpolation and optical interpolation to state-ofthe-art variation assimilation and Ensemble Kalman Filter assimilation [14][15][16][17].…”