All numerical models of the atmosphere operate at some set minimum resolution which, for example, may be represented by the spatial distance separating points at which measurable properties (e.g., temperature, moisture, wind etc.) are explicitly predicted. Processes operating at inherently smaller scales in the spaces between these points are termed "sub-grid scale", and must be approximated so that their net resolvable-scale impact is accounted for as accurately as possible. One common approach to this approximation for cloud and precipitation processes is termed "bulk microphysical parameterization." This project will investigate a new method for diagnosing and correcting systematic errors in such parameterizations through optimal inclusion (or "assimilation") of radar-observed precipitation fields into an ongoing model run. While traditional efforts to improve bulk microphysical parameterizations have centered on use of archived observations to better tune a myriad of internal parameters, the proposed approach aims to project available real-time radar observations onto a greatly reduced number of external parameters termed "contribution coefficients", allowing modulation of each individual process as a whole. The assembled research team will develop this approach in the context of a 4-dimensional variational data assimilation (4DVAR) system operating in junction with the widely distributed Weather Research and Forecasting (WRF) model at the National Center for Atmospheric Research. Efforts will initially be applied to a combination of orographic (mountain-induced) and frontally-forced storms whose atmospheric circulations are relatively simple capable of being well captured by the WRF model. Ultimately, however, the benefits of such an approach are likely to be greatest for global climate models whose large areal coverage will likely prohibit explicit inclusion of cloud microphysical processes for quite some time.
The intellectual merit of this study rests on developing improved estimates of cloud microphysical processes and their contributions to evolving storm structures, which will in turn allow a more objective assessment of the efficacy and suitability of individual bulk parameterization schemes for future use and improvement. This will initially be accomplished through assimilating widely available radar reflectivity observations into a cloud-resolving model for a variety of storm locations and types, but the approach will ultimately be amenable to inclusion of more advanced "polarimetric" radar observations or microphysical processes as those become widely available over the next decade. More accurate yet desirably efficient inclusion of cloud and precipitation processes in global models is an overarching goal of this research.
Broader impacts of this research include graduate student education and enhancements to community-based atmospheric model (WRF) used by a wide variety of U.S. and international investigators. The PI will also be training other students and researchers in data assimilation through teaching courses, individual mentoring, and hosting visitors from other institutions. Results of this research hold the potential to improve forecasts of the timing, location and intensity of precipitation events and associated societal impacts.
Motivation Predicting precipitation accurately is one of the biggest challenges in weather forecasting, resulting primarily from inability of Numerical Weather Prediction (NWP) models to represent well the physical processes of precipitation. These processes occur on small spatial scales that are not explicitly resolved in the models. A parameterized representation is used instead which is inevitably characterized with uncertainty. The uncertainty results from inabiity to represent well the full range of natural variability with a prescribed set of parameters and from incomplete understanding of the processes. For these reasons the microphysics parameterization uncertainty is the leading source of error for the precipitation prediction. Research Question The ensemble prediction approach has been introduced recently in NWP practice to reduce the errors due to the uncertainties within various physical parameterizations in the model, including the microphysics. The ensemble prediction is based on assumption that statistical mean of an ensemble of forecasts using different realizations of the parameterization would be more consistent with the verifying observations than each individual forecast because random errors would average out. The success of the ensemble forecasting depends on optimality of representation of the uncertainty in the leading sources of errors when forming the ensemble. The primary research question addressed in this project is : How to objectively estimate the microphysics parameterization uncertainty to improve the prediction of precipitation? Research Approach In this project a novel method for optimally representing the microphysics parameterization uncertainty using observations is investigated. The method is based on objective estimation of a joint distribution of possible values of parameters within the parameterization, using precipitation-sensitive observations. The objective estimation is performed by means of data assimilation numerical techniques. The project included three consecutive studies using a simplified NWP model of evolution of an idealized convective system. The microphysics parameterization in the model is representative of the parameterizations used in the NWP practice. Major Findings In the first study a fully nonlinear and computationally expensive, data assimilation technique was used to accurately solve the parameter estimation problem for 10 important physical parameters within the parameterization using radar reflectivity observations. The uncertainty of these parameters results from assuming them to be uniform across variety of natural conditions, and from inaccurate knowledge of the values. The estimates are expressed in terms of multi-parameter probability distribution of joint values of the parameters. Ten physical parameters were considered for two distinct precipitation regimes. For both regimes the computed probability distribution indicates complex nonlinear relationships between the different parameters and with the observations. The uncertainty was also found to vary with the precipitation regime. Although revealing about the properties of the parameterization, such uncertainty cannot be well represented in the NWP practice. Further analysis was performed to reformulate the representation of the uncertanty in terms of variations of non-dimensional multiplicative coefficients that were assigned to different individual parameterized processes. The new formulation was evaluated in the second study using the fully nonlinear data assimilation technique to ensure accuracy. The study results confirmed the validity of the new formulation. Most importantly, the ensemble prediction based on the uncertainty estimates for the process coefficients was shown to have significantly smaller errors than when the uncertainty was represented in terms of the original physical parameters. Another important finding from this study is that the uncertainty in terms of the process coefficients is nearly invariant to the precipitation regime. This finding suggested an important generalization of the microphysics parameterization uncertainty for the ensemble prediction: the stochastic uncertainty that is irreducible and related to natural physical randomness in the processes, referred to as aleatory. To ensure that benefits of the new formulation of the microphysics parameterization uncertainty could be realized in practice with a full-blown NWP model, it was necessary to also test applicability of a more practical quasi-linear data assimilation technique to this problem. In the third study a version of Ensemble Kalman Filter (EnKF) data assimilation technique was used to estimate the process coefficient parameters. This technique is chosen because it has been successfully applied to atmospheric state analysis in the NWP practice in support of the ensemble prediction. The major finding of the third study is that although the probability distributions using the EnKF and the full nonlinear technique exhibit similar primary features, the former simpler technique ehxibits tendency to produce less accurate ensemble forecast. It was found that this deficiency could be reduced by using a better, more informative prior ensemble distribution for the coefficients when using the EnKF technique. Further research is needed into this problem for applications with the full-blown NWP models. Relevance of the project results The project demonstrates the novel methodology for improving the precipitation forecasting by objective estimation of the aleatory uncertainty of the parameterized microphysical processes. The presented methodology is general and could be applied to any type of microphysical parameterization in the NWP models.
