Numerical Weather Prediction and Data Assimilation

Petros Katsafados, Elias Mavromatidis, Christos Spyrou

• Publisher: Wiley-ISTE
• Year: 2020
• Print ISBN:
  9781786301413
• Edition: 1
• eBook ISBN:
  9781119701019
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

This book has as main aim to be an introductory textbook of applied knowledge in Numerical Weather Prediction (NWP), which is a method of weather forecasting that employs: A set of equations that describe the flow of fluids translated into computer code, combined with parameterizations of other processes, applied on a specific domain and integrated in the basis of initial and domain boundary conditions. Current weather observations serve as input to the numerical computer models through a process called data assimilation to produce atmospheric properties in the future (e.g. temperature, precipitation, and a lot of other meteorological parameters). Various case studies will be also presented and analyzed through this book.

1
The Primitive Equations

The primitive equations describing changes in the atmospheric motion and thermodynamics are based on the mathematical expressions of a complete set of conservation principles. These equations are applied to individual air parcels and, due to their accuracy, allow continued progress in NWP models. There are three fundamental physical principles that govern the atmospheric motions: the conservation of momentum (provides equations of the three-dimensional motion), the conservation of the dry air mass (this equation is known as the continuity equation) and, finally, the conservation of heat (based on the first law of thermodynamics). The set is completed by formulas related to the conservation of water (all phases: solid–liquid–gas), as well as with the equation of state for perfect gases. Spectral and grid point models use the same coupled set of governing equations to describe changes occurring at discrete locations within the forecast domain.

In order to extract the mathematical equations expressing the aforementioned principles, the system is usually analyzed using a differential control volume. In fluid dynamics, there are two types of control volume in use. The first type consists of a parallelepiped in fixed location on the Earth relative to the coordinate system (Eulerian framework), where the variables (e.g. B) and their derivatives (variable changes over time or space, for example ∂B/∂t or ∂B/∂x) are estimated. According to the second type, the control volume follows the fluid motion assuming that it always contains the same part of the fluid which comprises marked fluid particles (Lagrangian framework).

1.1. Wind forecast equations (conservation of momentum)

The conservation of momentum in the atmosphere comes from Newton’s second law of motion. According to this law, a body (e.g. air parcel) is accelerated when a force or a sum of forces is applied to it. The acceleration of the body is proportional to the applied force, inversely proportional to the body’s mass, while its direction is the same as the direction of the force. The acceleration can be written in vector form as:

[1.1]

Above,

is the sum of forces acting on the body (in Newton), m its mass (in kg) and

is the total or inertial acceleration (in ms^–2). The inertial acceleration is the rate of velocity’s change of the body in relation...

Table of contents

• Cover
• Table of Contents
• Preface
• Introduction
• 1 The Primitive Equations
• 2 Solving Methods in NWP Models
• 3 Domain Structures and Boundary Conditions
• 4 Introduction to Data Assimilation
• 5 Desert Dust Modeling
• 6 Simulations of Extreme Weather and Dust Events
• Appendices
• References
• Index
• End User License Agreement