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Model Error in HWRF Surface Layer and Boundary Layer Parameterizations

Principal Investigators:

Project Members:

Collaborating Scientists:
  • Sundararaman Gopalakrishnan, NOAA/AOML/HRD
  • Vijay Tallapragada, NOAA/NCEP/EMC
  • Jian-Wen Bao, NOAA/ESRL/PSD

Funding Information:
  • Funding Agency: NOAA-NWSPO
  • Award Number: NA12NWS4680010
  • Funding Period: 01/01/2012-12/31/2013 (no-cost extension granted until 12/31/2014)
  • Award Amount: $213,386

  • Investigate the representation of model error in ensemble-based estimates of background error covariances. We envision our results to be of significant scientific and practical value for both ensemble-based and ensemble/variational hybrid data assimilation systems with NOAA's Hurricane Weather Forecasting and Research (HWRF) model. Specifically, we will target processes within the surface-layer (SL) and boundary-layer (BL) parameterizations of the HWRF model because they are known to control vortex dynamics in the inner core of a hurricane and therefore directly relate to the forecast of intensity. We aim to apply the findings of SL and BL uncertainty to our Hurricane Ensemble Data Assimilation System (HEDAS) to understand how accounting for such uncertainties in an ensemble could improve data assimilation itself.
  • Quantify the structures of the HWRF SL and BL and the variabilities therein relative to those observed due to the uncertainties in surface momentum and heat exchange coefficients and specific BL parameters that control vertical eddy diffusivity and BL depth.
  • By using information obtained from above as to the expected mean values and variances of the surface momentum and heat exchange coefficients and specific BL parameters, quantify the impact of accounting for the variability in SL and BL parameters in the HEDAS ensemble on the performance of HEDAS and the resulting estimates of vortex structure and TC intensity in such HEDAS analyses.
  • Quantify the impact of accounting for the variability in SL and BL parameters in the HEDAS ensemble on the evolution of vortex structure and intensity in the short-range (up to 24 hours) deterministic/ensemble forecasts initialized with the corresponding HEDAS vortex analyses.
  • Examine how frequently improvements in SL/BL structures in HEDAS analyses lead to improvements in the forecast of these structures.

The figure below summarizes our approach in a schematic:


We expect systematic differences to develop in the SL and BL between an idealized HWRF model run and observations. We will initialize our model runs with a balanced vortex/environment combination that is consistent with composite observations obtained in steady-state mature hurricanes. As these observed SL/BL structures are sub-sampled within steady-state hurricanes, they are expected not to vary much in time (solid green in figure), so that any model deviation from such structure can be attributed entirely to the model’s SL and BL formulations (solid purple in figure). To assess model sensitivity to SL and BL parameters, we will then proceed to perturb parameters about the assumed mean values. The magnitudes of these perturbations will be consistent with the variability in observations, when available. Using identical initial balanced vortices and environments as before, idealized HWRF ensembles will be constructed where ensemble members only differ in their perturbed parameter values, thereby altering their trajectories as compared to the mean model SL/BL structure. This ensemble of possible model SL/BL trajectories is depicted with the purple shading in figure. The resulting model SL/BL variability at the end of the simulation period will then be compared against model bias, as well as the corresponding observed uncertainty, through means of statistical significance. 


  • We constructed a composite axisymmetric vortex (wind, pressure, temperature, and moisture fields) that is objectively obtained from a vast database of Doppler radar wind, flight level, dropsonde, and buoy observations in hurricane conditions, to carry out sensitivity experiments in a controlled environment. The figure below shows some characteristics of this initial vortex, as well as how it evolves in 48-72 h during the control simulation:

Initial Observed Vortex

It can be seen that generally reasonable structure is obtained for tangential wind speed as well as radial wind speed below 8-10 km altutide at initial time. Structure at higher altitudes is more difficult to obtain because of lack of Doppler radar data at these locations. To fill these gaps, several HEDAS analyses for Hurricane Earl (2010) are used as low-weight background. HEDAS analyses used for this purpose were carried out with the latest versions of HWRF and HEDAS (see Aksoy et al. 2013 for details on HEDAS analyses). Interpolation procedures are the same as used for the thermodynamic fields.

  • An ocean-coupled, idealized HWRF capability has been developed that allows for hurricane simulations in sheared environments. These simulations can be initialized with any axisymmetric vortex structure. The following picture summarizes how environmental characteristics were perturbed in various experiments:

Environment Perturbations

  • We have carried out extensive sensitivity tests for shear, storm speed, SSTs, temperature and moisture perturbations in the PBL and middle troposphere, initial intensity and RMW, as well as model parameters that control horizontal and vertical diffusion and momentum and heat fluxes. These perturbation experiments are summarized in the table below:

Perturbation Experiments

  • We are currently in the process of evaluating the impact of these parameter perturbations on the idealized simulations. While this can be carried out in many different ways, we have found that the response function method provides an objective measure of the comparative impacts of the various parameters perturbed. For more information on the response function, we recommend consulting Tong and Xue (MWR, 2008). Here, for each parameter, we calculate an average response that takes into consideration a number of scalar metrics for the various dynamical/thermodynamic aspects of a simulation. The figure below summarizes our findings based on the response function:

Average Response Function

Several features here are noteworthy. First of all, over the range of values specified, parameters appear to have varying degrees of overall impact on the simulations. The impact is actually even greater than it appears in the figure, because the the y-axis is plotted on log scale. In other words, each horizontal grid line represents a 10-fold increase in impact. Another significant outcome is that some PBL parameters appear to have comparable magnitudes of impact on the simulations as some of the environment parameters like shear and SST that one would naturally expect. Finally, for all parameters, impact seems to taper off as perturbation magnitudes increase, pointing to the nonlinear nature of the simulations.


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