Preface

*It's alright, sweetie. In the information age of ridiculously enormous and complex data set, everybody feels stupid, unless one has the right tools and methodology to deal with. Anonymous*

This book provides a comprehensive introduction to data assimilation, a vital tool used mostly in atmospheric science and oceanography. Ensemble data assimilation methods have been applied with remarkable success in several real-life historymatching problems. However, performance is severely degraded as data assimilation methods are based on Gaussian assumptions. This problem can be overcome with artificial neural networks, machine learning, and deep learning. The synergy of these complementary technologies leverages their benefits and results in the emergence of one of the most efficient tools for handling linear and non-linear models predicting the evolution of the atmosphere. This hybrid approach emulates hidden, chaotic dynamics and predicts future states with desired accuracy. The most known use of data assimilation is predicting the state of the atmosphere using meteorological data. Data assimilation is a vital step in numerical modeling, specifically in the atmospheric sciences and oceanography. However, even with a good understanding of the underlying physical laws that drive it, its chaotic nature makes it extremely difficult to determine the state of the environment, specifically atmospheric variables like temperature, humidity, pressure, and so on, with accuracy in a given spatio-temporal domain. This book presents the material in a clear, simple style and examines the many challenges and opportunities in the field of data assimilation.

I would like to convey our appreciation to all authors for their contributions. I owe special thanks to Author Service Managers Ms. Ivana Barac and Ms. Sara Debeuc, and Commissioning Editor Ms. Klara Mestrovic, at IntechOpen, London, UK, for their kind support and great efforts in bringing this book to fruition. In addition, I am grateful to all those who worked behind the scenes and assisted in formatting the book.

> **Dr. Dinesh G. Harkut** Dean and Associate Professor, Department of Computer Science and Engineering, Prof Ram Mehge College of Engineering and Management, Badnera-Amravati, M.S., India

**1**

**Chapter 1**

Assimilation

*Dinesh G. Harkut*

**1. Introduction**

Introductory Chapter: Data

that are either causality or empirically derived and can be:

3.Based on either continuous space or discrete space

4.Operates in either discrete time or continuous time domain

1.Static model or dynamic model

time series of data on unemployment, etc.

2.Stochastic model or deterministic model

Our life is highly influenced and affected by the uncertainty in predicting the outcome of various phenomena and human activities. All the activities are highly influenced by predictions like uncertainty in predicting natural phenomena like rains, heat waves, short-term climate change, cyclone, tornados, or revenue prediction/projection by state/central government while preparing budgets and, GDP growth while formulating financial policies or predicting stock prices/indices by individual investors. These predications are based on some relevant class of models

Irrespective of the model used or its origin, solution computed or predictions generated were based on several prerequisite unknown controlling parameters along with initial conditions, boundary conditions variables those are based on some estimation: observations of the phenomenon in question like observed pressure distribution around the eye of the hurricane, data from radars or satellites, the

Data assimilation is basically a process of fusing data with the model for the singular purpose of estimating the unknown variables. One can obtain an instantiation of the model once these estimates are available, which in turn then run forward in time to generate the requisite forecast products for public consumption. Basic mathematical principles and tools along with conventional methods like Kalman filters and variational approaches, which find applications in dynamic data assimilation include: linear algebra, multivariate calculus, estimation theory, finite dimensional optimization theory, chaos, and nonlinear dynamics. It refers to the computation of the conditional probability distribution function of the output of a numerical model describing a dynamical process, conditioned by observations. Numerical prediction of atmospheric evolution is critically dependent on the initial conditions provided to it. It is a technique by which numerical model data and observations are combined to obtain an analysis that best represents the state of the phenomena of interest. It is the process of updating model forecasts (priors) with information
