Weather forecasting is one of the most vital tasks in many applications ranging from severe weather hazard systems to energy production. Numerical weather prediction (NWP) systems are commonly used state-of-the-art atmospheric models that provide point forecasts as deterministic predictions arranged on a three-dimensional grid. However, there is always some level of error and uncertainty in the forecasts due to inaccuracies of initial conditions, the chaotic nature of weather, etc. Such uncertainty information is crucial in decision making and optimization processes involved in many applications. A common representation of forecast uncertainty is a Prediction Interval (PI) that determines a minima, maxima and confidence level for each forecast, e.g. [2°C, 15°C]-95%. In this study, we investigate various methods that can model the uncertainty of NWP forecasts and provide PIs for the forecasts accordingly. In particular, we are interested in analyzing the historical performance of the NWP system as a valuable source for uncertainty modeling. Three different classes of methods are developed and applied for this problem. First, various clustering algorithms (including fuzzy c-means) are employed in concert with fitting appropriate probability distributions to obtain statistical models that can dynamically provide PIs depending on the forecast context. Second, a range of quantile regression methods (including kernel quantile regression) are studied that can directly model the PI boundaries as a function of influential features. In the third class, we focus on various time series modeling approaches including heteroscedasticity modeling methods that can provide forecasts of conditional mean and conditional variance of the target for any forecast horizon. iv All presented PI computation methods are empirically evaluated using a developed comprehensive verification framework in a set of experiments involving real-world data sets of NWP forecasts and observations. A key component is proposed in the evaluation process that would lead to a considerably more reliable judgment. Results show that PIs obtained by the ARIMA-GARCH model (for up to 6-hour-ahead forecasts) and Spline Quantile Regression (for longer leads) provide interval forecasts with satisfactory reliability and significantly better skill. This can lead to improvements in forecast value for many systems that rely on the NWP forecasts.

Uncertainties in Numerical Weather Prediction is a comprehensive work on the most current understandings of uncertainties and predictability in numerical simulations of the atmosphere. It provides general knowledge on all aspects of uncertainties in the weather prediction models in a single, easy to use reference. The book illustrates particular uncertainties in observations and data assimilation, as well as the errors associated with numerical integration methods. Stochastic methods in parameterization of subgrid processes are also assessed, as are uncertainties associated with surface-atmosphere exchange, orographic flows and processes in the atmospheric boundary layer. Through a better understanding of the uncertainties to watch for, readers will be able to produce more precise and accurate forecasts. This is an essential work for anyone who wants to improve the accuracy of weather and climate forecasting and interested parties developing tools to enhance the quality of such forecasts. Provides a comprehensive overview of the state of numerical weather prediction at spatial scales, from hundreds of meters, to thousands of kilometers Focuses on short-term 1-15 day atmospheric predictions, with some coverage appropriate for longer-term forecasts Includes references to climate prediction models to allow applications of these techniques for climate simulations

An Introduction to Numerical Weather Prediction Techniques is unique in the meteorological field as it presents for the first time theories and software of complex dynamical and physical processes required for numerical modeling. It was first prepared as a manual for the training of the World Meteorological Organization's programs at a similar level. This new book updates these exercises and also includes the latest data sets. This book covers important aspects of numerical weather prediction techniques required at an introductory level. These techniques, ranging from simple one-dimensional space derivative to complex numerical models, are first described in theory and for most cases supported by fully tested computational software. The text discusses the fundamental physical parameterizations needed in numerical weather models, such as cumulus convection, radiative transfers, and surface energy fluxes calculations. The book gives the user all the necessary elements to build a numerical model. An Introduction to Numerical Weather Prediction Techniques is rich in illustrations, especially tables showing outputs from each individual algorithm presented. Selected figures using actual meteorological data are also used. This book is primarily intended for senior-level undergraduates and first-year graduate students in meteorology. It is also excellent for individual scientists who wish to use the book for self-study. Scientists dealing with geophysical data analysis or predictive models will find this book filled with useful techniques and data-processing algorithms.

This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the development fields discussed, to demonstrate their mathematical complexity and, more importantly, to encourage mathematicians to contribute to the further success of such practical applications as weather forecasting and climate change projections. Written by leading experts in the field, the book provides an attractive and diverse introduction to areas in which mathematicians and modellers from the meteorological community can cooperate and help each other solve the problems that operational weather centres face, now and in the near future. Readers engaged in meteorological research will become more familiar with the corresponding mathematical background, while mathematicians working in numerical analysis, partial differential equations, or stochastic analysis will be introduced to further application fields of their research area, and will find stimulation and motivation for their future research work.

The purpose of this thesis is to examine and advance North American weather predictability from weather to subseasonal time-scales. Specifically, it focuses on 1) developing machine learning/deep learning methods and models to improve predictability through numerical weather prediction (NWP) post-processing on weather time-scales (0-7 days) and 2) examining the physical mechanisms which govern the evolution of the predictable components and noise components of teleconnection modes on subseasonal time-scales (7 days-1 month). NWP deficiencies (e.g., sub-grid parameterization approximations), nonlinear error growth associated with the chaotic nature of the atmosphere, and initial condition uncertainty lead initial small forecast errors to eventually result in weather predictions which are as skillful as random forecasts. A portion of these forecast errors are inherent to the NWP models alone, systematic biases. The first two chapters develop cutting-edge vision-based deep-learning algorithms to advance the current state-of-the-art NWP post-processing and correct these systematic biases. Using dynamic forecasts of North Pacific integrated vapor transport (IVT) as a test case, we develop post-processing systems which are spatially aware, readily encode non-linear predictor interaction, easily ingest ancillary weather variables, and have state of the art training methods that systematically prevent model overfitting. Further, we outline a framework to quantify uncertainty in single-point (deterministic) forecasts using neural networks. The uncertainty is shown to be probabilistically rigorous, leading to calibrated probabilistic forecasts which outperform or compete with calibrated dynamic NWP ensemble systems for IVT under atmospheric river conditions. The second half of this thesis shifts focus to subseasonal time scales and examines predictability in the Pacific North American (PNA) sector in boreal winter. Particularly, it investigates the physical mechanisms involved in the intraseasonal modulation of atmospheric Signal-to-Noise (SN), and how it is affected by slowly varying climate modes (ENSO and MJO). These mechanisms are further explored using a fully-coupled hindcast of the 20th century, showing that the increased SN leads to high model forecast skill at subseasonal timescales in particular forecast windows of opportunity. Additionally, we reveal the MJO as the largest growing mode of tropical forecast uncertainty which directly influences PNA forecast certainty.

This textbook provides a comprehensive yet accessible treatment of weather and climate prediction, for graduate students, researchers and professionals. It teaches the strengths, weaknesses and best practices for the use of atmospheric models. It is ideal for the many scientists who use such models across a wide variety of applications. The book describes the different numerical methods, data assimilation, ensemble methods, predictability, land-surface modeling, climate modeling and downscaling, computational fluid-dynamics models, experimental designs in model-based research, verification methods, operational prediction, and special applications such as air-quality modeling and flood prediction. This volume will satisfy everyone who needs to know about atmospheric modeling for use in research or operations. It is ideal both as a textbook for a course on weather and climate prediction and as a reference text for researchers and professionals from a range of backgrounds: atmospheric science, meteorology, climatology, environmental science, geography, and geophysical fluid mechanics/dynamics.

Numerical models have become essential tools in environmental science, particularly in weather forecasting and climate prediction. This book provides a comprehensive overview of the techniques used in these fields, with emphasis on the design of the most recent numerical models of the atmosphere. It presents a short history of numerical weather prediction and its evolution, before describing the various model equations and how to solve them numerically. It outlines the main elements of a meteorological forecast suite, and the theory is illustrated throughout with practical examples of operational models and parameterizations of physical processes. This book is founded on the author's many years of experience, as a scientist at Météo-France and teaching university-level courses. It is a practical and accessible textbook for graduate courses and a handy resource for researchers and professionals in atmospheric physics, meteorology and climatology, as well as the related disciplines of fluid dynamics, hydrology and oceanography.