Inducing Tropical Cyclones to Undergo Brownian Motion: A Comparison between Itô and Stratonovich in a Numerical Weather Prediction Model

AbstractStochastic parameterization has become commonplace in numerical weather prediction (NWP) models used for probabilistic prediction. Here a specific stochastic parameterization will be related to the theory of stochastic differential equations and shown to be affected strongly by the choice of stochastic calculus. From an NWP perspective the focus will be on ameliorating a common trait of the ensemble distributions of tropical cyclone (TC) tracks (or position); namely, that they generally contain a bias and an underestimate of the variance. With this trait in mind the authors present a stochastic track variance inflation parameterization. This parameterization makes use of a properly constructed stochastic advection term that follows a TC and induces its position to undergo Brownian motion. A central characteristic of Brownian motion is that its variance increases with time, which allows for an effective inflation of an ensemble’s TC track variance. Using this stochastic parameterization the authors...

[1]  H. Pan,et al.  Revision of Convection and Vertical Diffusion Schemes in the NCEP Global Forecast System , 2011 .

[2]  Liang Xu,et al.  Development of NAVDAS-AR: non-linear formulation and outer loop tests , 2006 .

[3]  Shepard A. Clough,et al.  Atmospheric radiative transfer modeling: a summary of the AER codes , 2005 .

[4]  Sharanya J. Majumdar,et al.  Characteristics of Ensemble Transform Kalman Filter adaptive sampling guidance for tropical cyclones , 2011 .

[5]  Liang Xu,et al.  Development of NAVDAS-AR: formulation and initial tests of the linear problem , 2005 .

[6]  A. Arakawa,et al.  Interaction of a Cumulus Cloud Ensemble with the Large-Scale Environment, Part I , 1974 .

[7]  Stanley G. Benjamin,et al.  Global Ensemble Predictions of 2009’s Tropical Cyclones Initialized with an Ensemble Kalman Filter , 2011 .

[8]  Z. Pu,et al.  Impact of Stochastic Convection on Ensemble Forecasts of Tropical Cyclone Development , 2011 .

[9]  Frederick H. Carr,et al.  A Prognostic Cloud Scheme for Operational NWP Models , 1997 .

[10]  R. L. Stratonovich.  A New Representation for Stochastic Integrals and Equations , 1966 .

[11]  Harold Ritchie.  Application of the semi-Lagrangian method to a multilevel spectral primitive-equations model , 1991 .

[12]  S. Majumdar,et al.  On the Ability of Global Ensemble Prediction Systems to Predict Tropical Cyclone Track Probabilities , 2010 .

[13]  Craig H. Bishop,et al.  A Local Formulation of the Ensemble Transform (ET) Analysis Perturbation Scheme , 2010 .

[14]  Kiyosi Itô.  Stochastic Differential Equations , 2018, The Control Systems Handbook.

[15]  Sarah C. Jones,et al.  Impact of perturbation methods in the ECMWF ensemble prediction system on tropical cyclone forecasts , 2012 .

[16]  James A. Hansen,et al.  The Impact of Noisy Physics on the Stability and Accuracy of Physics–Dynamics Coupling , 2013 .

[17]  Liang Xu,et al.  Preconditioning Representer-based Variational Data Assimilation Systems: Application to NAVDAS-AR , 2009 .

[18]  Verification of Ensemble-Based Uncertainty Circles around Tropical Cyclone Track Forecasts , 2011 .

[19]  Stuart Webster,et al.  Improvements to the representation of orography in the Met Office Unified Model , 2003 .

[20]  J. Louis.  A parametric model of vertical eddy fluxes in the atmosphere , 1979 .