An initial vortex spindown, or strong adjustment to the structure and intensity of a hurricane’s initial vortex, presents a significant problem in hurricane forecasting, as with the NCEP Hurricane Weather Research and Forecasting Model (HWRF), because it can cause significantly degraded intensity forecasts. In this study, the influence of the self-consistent regional ensemble background error covariance on assimilating hurricane inner-core tail Doppler radar (TDR) observations in HWRF is examined with the NCEP gridpoint statistical interpolation (GSI)-based ensemble–three-dimensional variational (3DVAR) hybrid data assimilation system. It is found that the resolution of the background error covariance term, coming from the ensemble forecasts, has notable influence on the assimilation of hurricane inner-core observations and subsequent forecasting results. Specifically, the use of ensemble forecasting at high-resolution native grids results in significant reduction of the vortex spindown problem and thus leads to improved hurricane intensity forecasting. Further diagnoses are conducted to examine the spindown problem with a gradient wind balance. It is found that artificial vortex initialization, performed before data assimilation, can cause strong supergradient winds or imbalance in the vortex inner-core region. Assimilation of hurricane inner-core TDR data can significantly mitigate this imbalance by reducing the supergradient effects. Compared with the use of a global ensemble background error term, application of the self-consistent regional ensemble background covariance to inner-core data assimilation leads to better representation of the mesoscale hurricane inner-core structures. It can also result in more realistic vortex structures in data assimilation even when the observational data are unevenly distributed.

Nudging is a simulation technique widely used in sensitivity studies and in the evaluation of atmosphere models. Care is needed in the experimental setup in order to achieve the desired constraint on the simulated atmospheric processes without introducing undue intervention. In this study, sensitivity experiments are conducted with the Energy Exascale Earth System Model (E3SM) Atmosphere Model Version 1 (EAMv1) to identify setups that can give results representative of the model's long-term climate and meanwhile reasonably capture characteristics of the observed meteorological conditions to facilitate the comparison of model results with measurements. We show that when the prescribed meteorological conditions are temporally interpolated to the model time to constrain EAM's horizontal winds at each time step, a nudged simulation can reproduce the characteristic evolution of the observed weather events (especially in middle and high latitudes) as well as the model's long-term climatology, although nudging also leads to nonnegligible regional changes in wind-driven aerosol emissions, low-level clouds in the stratocumulus regime, and cloud and precipitation near the maritime continent. Compared to its predecessor model used in an earlier study, EAMv1 is less sensitive to temperature nudging, although significant impacts on the cloud radiative effects still exist. EAMv1 remains very sensitive to humidity nudging. Constraining humidity substantially improves the correlation between the simulated and observed tropical precipitation but also leads to large changes in the long-term statistics of the simulated precipitation, clouds, and aerosol lifecycle. Plain Language SummaryFor the development and application of numerical weather and climate models, it is often useful to constrain a numerical experiment so that the evolution of the meteorological conditions follows a specific pathway. One of the techniques to apply such constraints is nudging, which introduces additional terms to the model equations. This study performs and analyzes sensitivity experiments with an attempt to identify implementations of nudging that can provide sufficient constraints without severely interfering with the simulations.

Convergence testing is a common practice in the development of dynamical cores of atmospheric models but is not as often exercised for the parameterization of subgrid physics. An earlier study revealed that the stratiform cloud parameterizations in several predecessors of the Energy Exascale Earth System Model (E3SM) showed strong time step sensitivity and slower-than-expected convergence when the model's time step was systematically refined. In this work, a simplified atmosphere model is configured that consists of the spectral-element dynamical core of the E3SM atmosphere model coupled with a large-scale condensation parameterization based on commonly used assumptions. This simplified model also resembles E3SM and its predecessors in the numerical implementation of process coupling and shows poor time step convergence in short ensemble tests. We present a formal error analysis to reveal the expected time step convergence rate and the conditions for obtaining such convergence. Numerical experiments are conducted to investigate the root causes of convergence problems. We show that revisions in the process coupling and closure assumption help to improve convergence in short simulations using the simplified model; the same revisions applied to a full atmosphere model lead to significant changes in the simulated long-term climate. This work demonstrates that causes of convergence issues in atmospheric simulations can be understood by combining analyses from physical and mathematical perspectives. Addressing convergence issues can help to obtain a discrete model that is more consistent with the intended representation of the physical phenomena. Plain Language Summary Computer codes that simulate the time evolution of a physical system produce errors in the results due to the finite step sizes used to advance the calculations in time. These errors are expected to decrease as the time steps are shortened, at a rate determined by the characteristics of the equations and numerical methods. An earlier study revealed that the error reduction in several predecessors of the Energy Exascale Earth System Model (E3SM) was at a rate slower than expected. This study creates a simplified configuration of those models and investigates the causes of the unexpected behavior. We show that slow error reduction can be understood and improved by combining analyses from physical and mathematical perspectives. The required code modifications can lead to significant changes in the simulated long-term behavior of a full-fledged climate model. Furthermore, ensuring a proper rate of error reduction can help to obtain a computer code that is more consistent with the intended representation of the corresponding physical system.

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