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Abstract
A numerical analysis of the nonlinear heat diffusion equation has been carted out to bring to light a heretofore little-understood type of instability that can be encountered in many numerical modeling applications. The nature of the instability is such that the error remains bounded but becomes large enough to prevent proper assessment of model results. For the sample problem under investigation, the nonlinearity is introduced through a diffusion coefficient that depends on the Richardson number which, in turn, is a function of the dependent variable. Our analysis shows that the interaction of short-wavelength and inter-mediate-wavelength solution components can induce nonlinear instability if the amplitude of either component is sufficiently large. Since the unstable solution may not wander far from the true solution, the error can be difficult to detect. A criterion, given in terms of a restriction on the Richardson number, guarantees local (short-term) stability of the numerical scheme whenever the criterion is satisfied. Numerical results obtained using a boundary-layer model with GATE Phase III data are presented to support the theoretical conclusions.
Abstract
A numerical analysis of the nonlinear heat diffusion equation has been carted out to bring to light a heretofore little-understood type of instability that can be encountered in many numerical modeling applications. The nature of the instability is such that the error remains bounded but becomes large enough to prevent proper assessment of model results. For the sample problem under investigation, the nonlinearity is introduced through a diffusion coefficient that depends on the Richardson number which, in turn, is a function of the dependent variable. Our analysis shows that the interaction of short-wavelength and inter-mediate-wavelength solution components can induce nonlinear instability if the amplitude of either component is sufficiently large. Since the unstable solution may not wander far from the true solution, the error can be difficult to detect. A criterion, given in terms of a restriction on the Richardson number, guarantees local (short-term) stability of the numerical scheme whenever the criterion is satisfied. Numerical results obtained using a boundary-layer model with GATE Phase III data are presented to support the theoretical conclusions.
Abstract
Accurate cloud and precipitation forecasts are a fundamental component of short-range data assimilation/model prediction systems such as the NOAA 3-km High-Resolution Rapid Refresh (HRRR) or the 13-km Rapid Refresh (RAP). To reduce cloud and precipitation spinup problems, a nonvariational assimilation technique for stratiform clouds was developed within the Gridpoint Statistical Interpolation (GSI) data assimilation system. One goal of this technique is retention of observed stratiform cloudy and clear 3D volumes into the subsequent model forecast. The cloud observations used include cloud-top data from satellite brightness temperatures, surface-based ceilometer data, and surface visibility. Quality control, expansion into spatial information content, and forward operators are described for each observation type. The projection of data from these observation types into an observation-based cloud-information 3D gridded field is accomplished via identification of cloudy, clear, and cloud-unknown 3D volumes. Updating of forecast background fields is accomplished through clearing and building of cloud water and cloud ice with associated modifications to water vapor and temperature. Impact of the cloud assimilation on short-range forecasts is assessed with a set of retrospective experiments in warm and cold seasons using the RAPv5 model. Short-range (1–9 h) forecast skill is improved in both seasons for cloud ceiling and visibility and for 2-m temperature in daytime and with mixed results for other measures. Two modifications were introduced and tested with success: use of prognostic subgrid-scale cloud fraction to condition cloud building (in response to a high bias) and removal of a WRF-based rebalancing.
Abstract
Accurate cloud and precipitation forecasts are a fundamental component of short-range data assimilation/model prediction systems such as the NOAA 3-km High-Resolution Rapid Refresh (HRRR) or the 13-km Rapid Refresh (RAP). To reduce cloud and precipitation spinup problems, a nonvariational assimilation technique for stratiform clouds was developed within the Gridpoint Statistical Interpolation (GSI) data assimilation system. One goal of this technique is retention of observed stratiform cloudy and clear 3D volumes into the subsequent model forecast. The cloud observations used include cloud-top data from satellite brightness temperatures, surface-based ceilometer data, and surface visibility. Quality control, expansion into spatial information content, and forward operators are described for each observation type. The projection of data from these observation types into an observation-based cloud-information 3D gridded field is accomplished via identification of cloudy, clear, and cloud-unknown 3D volumes. Updating of forecast background fields is accomplished through clearing and building of cloud water and cloud ice with associated modifications to water vapor and temperature. Impact of the cloud assimilation on short-range forecasts is assessed with a set of retrospective experiments in warm and cold seasons using the RAPv5 model. Short-range (1–9 h) forecast skill is improved in both seasons for cloud ceiling and visibility and for 2-m temperature in daytime and with mixed results for other measures. Two modifications were introduced and tested with success: use of prognostic subgrid-scale cloud fraction to condition cloud building (in response to a high bias) and removal of a WRF-based rebalancing.
