The Liang-Kleeman Information Flow-based Machine Learning And Its Application To The Forecast Of Typhoon Trajectories

For more than half a century,the progress of weather forecasting has been mainly credited to numerical modeling.As all kinds of data accumulate,artificial intelligence(AI)methods have gradually shown their power.Traditionally the AI methods do not have causality taken into consideration.But for a dynamical system such the weather system,its temporal dimension contains important “cause-effect" information ——"effect " must not occur before “cause”.How to identify and describe the causality within a dynamical system,and combine it with machine learning is hence very important not only in the field of meteorology but also in the whole field of artificial intelligence.Traditionally causal inferences are belonging to statistics,and are mostly axiomatically formulated,making it difficult to obtain a precise and quantitative assessment.To address these problems,Liang(2014,2016)established,based on a physical discovery in information flow by Liang and Kleeman(2005),a rigorous formalism from first principles for causal inference.This is the Liang-Kleeman information flow analysis,or Liang causality analysis that may be referred to as in the literature.As a dynamical system,atmospheric internal processes have involved complex multiscale and nonlinear cross-scale interactions,to which multiscale energetics analysis provides a natural approach.However,existing multiscale energetics methods have difficulty in handling non-stationary processes;in fact,they may even have conceptual problem in representing multiscale energetics.These above issues have not been resolved until the advent of multiscale window transform(MWT)by Liang and Anderson(2007).Based on MWT,Liang(2016)developed a theory of canonical transfer,and a methodology called localized multiscale energy and vorticity analysis(MS-EVA),to tackle the complex multiscale interactions.In this thesis,these theories/tools are used to diagnose the dynamical mechanisms underlying the genesis,evolution,and decay of typhoons.We then utilize these dynamical findings,in combination with the Liang-Kleeman information flow analysis results,construct an AI model for the forecasting of the typhoon tracks.Overall,the following major issues are addressed in the treatise.I.What are the internal dynamical processes within the atmosphere governing the development of a typhoon? Which processes account for typhoon movement?Using ERA-Interim reanalysis data with a resolution of 0.25° and 6 hours,we put those atmospheric processes in the northwest Pacific Ocean on scales more than 32 days,between 1-32 days and less than 1 day into three different scale windows,namely,the background circulation window,typhoon scale window and high-frequency disturbance window,respectively.Based on the results of MS-EVA,it is found that non-adiabatic heating is the dominant source of energy.The non-adiabatic heating and the localized baroclinic canonical transfers from the background circulation to the typhoon scale strengthens typhoons via buoyancy conversion from available potential energy(APE)to kinetic energy(KE);in the kinetic energy balance,the dominant source is barotropic canonical transfer from the background circulation to the typhoon scale,and,secondly,at the low-level,the pressure working.The sink of kinetic energy is mainly through pressure gradient force in the middle and upper troposphere,and through frictional dissipation and spatial transport in the lower troposphere.For typhoon movement,the asymmetric kinetic energy balance plays an important role.The barotropic canonical transfer from the background circulation to the typhoon-scale,and the transport of typhoon-scale KE have obvious asymmetric structures.In particular,the former tends to be in the form of a dipole at the center of the typhoon.Most importantly,the typhoon moves in the direction of the dipole,i.e.,the direction from the positive barotropic canonical transfer center to the negative center.In the composite pattern of the sudden northward turning cases,the shift from the southeast(positive)-northwest(negative)baroclinic transfer dipole to the southwest(positive)-northeast(negative)dipole is completed 36-12 hours before the sudden turning of the typhoon.That is to say,the sudden turning of a recurvatured typhoon can be predicted 12 hours or more in advance.II.How to determine the predictors for typhoon track forecasting through dynamical analysis and information flow/causality analysis?Generally,except for the asymmetrically distributed barotropic canonical transfer and those well known ones such as steering flow,it is difficult to determine which internal dynamical processes have significant influence on the typhoon movement.We hence employ the Liang-Kleeman information flow analysis to establish the predictors influencing the typhoon trajectories.In order to handle the piecewise continuous data like those of typhoon,we generalize the existing causal inferences based on Liang-Kleeman information flow,which are designed for time series(Liang,2014),to discontinuous series(e.g.,cross-sectional data and panel data).This results in an algorithm,called Algorithm-IF,which is validated with a linear stochastic model,a highly chaotic deterministic system and a real problem in economics.By the causality analysis results with Algorithm-IF,the following predictors are selected for typhoon track forecasting: the location(longitude and latitude)of the typhoon,the latitudinal variability 0-6 h ahead,the maximum wind speed,and the longitudinal location and minimum pressure 6-12 h ahead,some principal components of a)850h Pa: barotropic canonical transfer,the zonal,meridional and vertical components of the KE transport on the typhoon scale,and the zonal and meridional components of pressure gradient force on the typhoon scale;b)500h Pa:the zonal component of the KE transport on typhoon scale,the KE transport on typhoon scale by background circulation,and the zonal and vertical components of pressure gradient force on typhoon scale;c)300h Pa: the zonal and meridional components of the KE transport on typhoon scale and that part contributed by the background circulation III.How to build the causality-based typhoon trajectory forecasting model? What are the advantages of the model?Finally,we combine deep learning with the information flow-based causality analysis to construct a causality-based artificial intelligence model for the typhoon trajectory forecasting.Based on the dynamics and predictors for typhoons as diagnosed,the longitude and latitude variability 6-48 hours in the future are henceforth predicted.Substituting them into the error back propagation(BP)neural network and convolutional long and short-term memory neural network(Conv LSTM),respectively,the typhoon trajectory forecasting model is hence trained.The average error(2015-2016)for the track in the next 24/48 hours is 135/202 km for the BP neural network model,and 106/157 km for the Conv LSTM.The 48-h forecast error of the Conv LSTM is comparable to that with forecasts in the China Meteorological Administration(CMA),though so far only coarsely resolved data are used.Most importantly,the forecast of the recurvature of a typhoon is a notoriously difficult problem in meteorology,but our model is promising.For example,the causality-based Conv LSTM shows a good performance for the 2015 typhoons Linfa and Nangka in the test set,whose trajectories changed abruptly and failed the CMA forecasts.