Assimilating shallow soil moisture observations into land models with a water budget constraint

Assimilating observations of shallow soil moisture content into land models is an important step in estimating soil moisture content. In this study, several modifications of an ensemble Kalman filter (EnKF) are proposed for improving this assimilation. It was found that a forecast error inflation-based approach improves the soil moisture content in shallow layers, but it can increase the analysis error in deep layers. To mitigate the problem in deep layers while maintaining the improvement in shallow layers, a vertical localization-based approach was introduced in this study. During the data assimilation process, although updating the forecast state using observations can reduce the analysis error, the water balance based on the physics in the model could be destroyed. To alleviate the imbalance in the water budget, a weak water balance constrain filter is adopted. The proposed weakly constrained EnKF that includes forecast error inflation and vertical localization was applied to a synthetic experiment. An additional bias-aware assimilation for reducing the analysis bias is also investigated. The results of the assimilation process suggest that the inflation approach effectively reduces the analysis error from 6.70 % to 2.00 % in shallow layers but increases from 6.38 % to 12.49 % in deep layers. The vertical localization approach leads to 6.59 % of the analysis error in deep layers, and the bias-aware assimilation scheme further reduces this to 6.05 %. The spatial average of the water balance residual is 0.0487 mm of weakly constrained EnKF scheme, and 0.0737 mm of a weakly constrained EnKF scheme with inflation and localization, which are much smaller than the 0.1389 mm of the EnKF scheme.

Assimilating Shallow Soil Moisture Observations into Land Models with a Water Budget Constraint

Incorporating observations of shallow soil moisture content into land models is an important step in assimilating satellite observations of soil moisture content. In this study, several modifications of an ensemble Kalman filter (EnKF) are proposed for improving this assimilation. It was found that a forecast error inflation-based approach improves the soil moisture content in shallow layers, but it can increase the analysis error in deep layers. To mitigate the problem in deep layers while maintaining the improvement in shallow layers, a vertical localization-based approach was introduced in this study. During the data assimilation process, although updating the forecast state using observations can reduce the analysis error, the water balance based on the physics in the model could be destroyed. To alleviate the imbalance in the water budget, a weak water balance constrain filter is adopted. The proposed weakly constrained EnKF that includes forecast error inflation and vertical localization was applied to a synthetic experiment and two real data experiments. The results of the assimilation process suggest that the inflation approach effectively reduce both the short-lived analysis error and the analysis bias in shallow layers, while the vertical localization approach avoids increase in analysis error in deep layers. The weak constraint on the water balance reduces the degree of the water budget imbalance at the price of a small increase in the analysis error.

The Impact of Stochastically Perturbed Parameterizations on Tornadic Supercell Cases in East China

The impact of stochastically perturbed parameterizations on short-term tornadic supercell ensemble forecasts (EFs) was evaluated using two tornado cases that occurred in eastern China. The initial condition (IC) perturbations of EFs were generated by a three-dimensional variational data assimilation system with perturbed radar data. The parameterization perturbations of EFs were produced by a stochastic procedure that was applied to diffusion and microphysics parameterizations. This procedure perturbed tendencies from both parameterizations and intercept parameters (INTCPs) of the microphysics parameterizations. In addition to individually perturbing these quantities, a combination of perturbations of diffusion and INTCPs was also examined. A resampling method was proposed to handle perturbations that vary substantially, and a vertical localization was applied to the microphysics tendency perturbations. The results indicated that combining perturbations of diffusion and INTCPs produced the intensity and path forecasts of the low-level vortex (LLV) that better match observations for a weak tornado case; this combination also had a positive impact on the LLV intensity forecast for a much stronger tornado case. This combination outperformed the stochastic procedures that perturbed only diffusion or INTCPs, which indicated that it is better to use both error representations. The vertical localization prevented the temperature tendency perturbations of microphysics from always suppressing storms in negative perturbation (<0.0) areas. The negative INTCP and diffusion perturbations benefited the strong LLV, which is consistent with that of the idealized case. The current stochastic procedure could not address the LLV displacement error that is caused by the IC error.

A Stochastic Perturbed Parameterization Tendency Scheme for Diffusion (SPPTD) and Its Application to an Idealized Supercell Simulation

Diffusion plays an important role in supercell simulations. A stochastically perturbed parameterization tendency scheme for diffusion (SPPTD) is developed to incorporate diffusive uncertainties in ensemble forecasts. This scheme follows the same procedure as the previously published stochastically perturbed parameterization tendencies (SPPT) scheme but uses a recursive filter to generate smooth perturbations. It also employs horizontal and vertical localization to retain the impact of perturbation in areas with strong shear. Three additional restrictions are added for the sake of integration stability; these restrictions determine the area and amplitude of the perturbation and the situation to suspend SPPTD. The performance of this scheme is examined by using an idealized supercell storm. The model errors are simulated using different resolutions in the truth run (1 km) and ensemble forecasts (2 km). The results indicate that the ensemble forecasts using SPPTD encompass the intensity and displacement of maximum updraft helicity in the truth run. This scheme yields better results than can be obtained using initial perturbations or larger computational mixing coefficients. The sensitivity of SPPTD to each of its parameters is also examined. The results indicate that the optimal horizontal and temporal scales for SPPTD are 40 km and 30 min, respectively. Moderately adjusting the spatiotemporal scale by 10 km or 10 min does not significantly change the SPPTD performance. In this case study, an ensemble size of 20 is sufficient. Perturbing the diffusion terms of all variables using the same approach does not provide additional benefits other than that of selected variables and thus requires further study.

Impact of MPEX Upsonde Observations on Ensemble Analyses and Forecasts of the 31 May 2013 Convective Event over Oklahoma

This study examines the impact of assimilating three radiosonde profiles obtained from ground-based mobile systems during the Mesoscale Predictability Experiment (MPEX) on analyses and convection-permitting model forecasts of the 31 May 2013 convective event over Oklahoma. These radiosonde profiles (in addition to standard observations) are assimilated into a 36-member mesoscale ensemble using an ensemble Kalman filter (EnKF) before embedding a convection-permitting (3 km) grid and running a full ensemble of 9-h forecasts. This set of 3-km forecasts is compared to a control run that does not assimilate the MPEX soundings. The analysis of low- to midlevel moisture is impacted the most by the assimilation, but coherent mesoscale differences in temperature and wind are also seen, primarily downstream of the location of the soundings. The ensemble of forecasts of convection on the 3-km grid are improved the most in the first three hours of the forecast in a region where the analyzed position of low-level frontal convergence and midlevel moisture was improved on the mesoscale grid. Later forecasts of the upscale growth of intense convection over central Oklahoma are improved somewhat, but larger ensemble spread lowers confidence in the significance of the improvements. Changes in the horizontal localization radius from the standard value applied to the MPEX sounding assimilation alters the specific times that the forecasts are improved in the first three hours of the forecasts, while changes to the vertical localization radius and specified temperature and wind observation error result in little to no improvements in the forecasts.