Inversion and Data Assimilation in Remote Sensing (eBook)

Estimation of Geophysical Parameters

Yajing Yan (Autor)

eBook Download: EPUB

2024
375 Seiten
Wiley (Verlag)
978-1-394-33228-1 (ISBN)

Infos

Remote sensing data are now the primary sources for observing Earth and the Universe. Data inversion and assimilation techniques are the main tools for estimating and predicting the geophysical parameters that characterize the evolution of our planet and the Universe, using remote sensing data.
Inversion and Data Assimilation in Remote Sensing explores recent advances in the inversion and assimilation of remote sensing data. It presents traditional and current neural network methods, as well as a number of topics where these methods have been developed or adapted to suit the specific nature of the field. The assimilation section covers prediction problems in volcanology and glaciology. Lastly, the inversion section covers biomass inversion using SAR images, bio-physio-hydrological inversion in coastal areas using multi- and hyperspectral images, and astrophysical inversion using telescope data.

Yajing Yan is a lecturer at the LISTIC laboratory, Université Savoie Mont Blanc, France. Her research focuses on multi-temporal InSAR analysis, remote sensing data fusion and assimilation, and machine learning.

Textauszug

1
Methods for Assimilation of Observations: Application to Numerical Weather Prediction

Olivier TALAGRAND

LMD/IPSL, CNRS, ENS, Université PSL, Institut polytechnique de Paris, Sorbonne Université, Paris, France

1.1 Introduction

This chapter presents a general description of assimilation of observations. The guideline of the presentation is the development of assimilation in the context of numerical weather prediction. The case of numerical weather prediction is rather emblematic in that it has led to the gradual development of more and more powerful numerical algorithms for assimilation of observations, which have in turn significantly contributed to the improvement of weather prediction, while they were at the same time expanding to many diverse applications.

Weather prediction, like many other fields of present science and technology, is now largely dominated by numerical modeling. Meteorological forecasts are basically produced by numerical models which, started from the observed meteorological conditions, compute the expected evolution of the relevant parameters (pressure, temperature, wind and humidity) over periods which, depending on the particular purpose at hand, may vary from a few hours or less, to weeks or months. The numerical models are built on the physical laws that govern the evolution of the flow (namely, the laws of conservation of mass, energy and momentum, or at least as accurate a formulation of those laws as can be obtained). These laws are discretized on an appropriate three-dimensional spatial grid and integrated in time over the period of the forecast. As an example, the present operational model of the European Centre for Medium-Range Weather Forecasts (ECMWF), located in Reading in England, is built on a grid which covers the whole volume of the atmosphere, with horizontal and vertical resolutions of about 9 km and 2 km, respectively. This leads for the description of the instantaneous state of the whole atmosphere to a vector with dimension over 109. Two daily forecasts are produced at present by evolving the state vector over a 10-day period (with a time step of 450 s).

With regard to the initial conditions from which the forecasts must be started, the observing system consists of a large variety of different instruments. Radiosondes are launched from ground stations at conventional synchronous “synoptic” hours. The ground stations are, however, concentrated over continents, mostly in developed countries. Satellites measure the radiation emitted by the planet, providing information on the thermal structure of the atmosphere. They cover the surface of the Earth more homogeneously than ground stations, but perform observations continuously in time. Other types of observations (as performed, for instance, by commercial planes or drifting buoys at the surface of the ocean) are also available. At present, the number of scalar observed quantities that are used in operational weather prediction over a 24-h period lies in the range 107–108.

A large fraction of these observations is distributed over time, and there is much more information in the observations distributed over 12 or 24 h, over which the flow can significantly evolve, than in synoptic observations performed at a given time. Assimilation is the process through which all that information is combined in order to define the initial conditions of the forecast. Its purpose can be precisely defined as estimating the state of the observed system as accurately as possible using all available relevant information. That information essentially consists of two different parts. The observations stricto sensu, on the one hand, may vary in nature, accuracy, as well as in spatial and temporal resolution and distribution, and the physical laws that govern the flow, on the other hand, are available in practice in the form of a numerical and necessarily approximate model.

Assimilation is one of many inverse problems that are encountered in many fields of science and technology. Inverse problems arise in situations when we want to know the state of a system (often a physical system, but not necessarily so), while the available data are not in the format appropriate for the purpose at hand. They are encountered, for instance, in solid Earth geophysics (when we want to know the internal structure of the planet), non-destructive probing of structures of various types, navigation of aircraft, spacecraft or any mobile object, as well as in many other applications as described in the other chapters of the book. In most of these problems, data are affected with some uncertainty, and we may wish to know the resulting uncertainty on the final estimate. From a mathematical point of view, uncertainty is conveniently described by probability distributions. This leads to the fact that many inverse problems are stated as problems in Bayesian estimation, namely determining the probability distribution for the state of the system of interest, conditioned by the available data. Indeed, although the basic nature of the problems considered may be very different, the mathematical equations that are used for solving these problems are often the same (as can be seen in several chapters of this book).

It is in this general Bayesian perspective that assimilation of meteorological observations is described and discussed below. Compared to other inverse problems, there are two specific difficulties in assimilation of meteorological observations. Firstly, the observations used are distributed in time, so that the complex nonlinear dynamics of the atmospheric flow, and in particular the instabilities that constantly develop in the flow, must be taken into account. Secondly, as shown by the numbers given above, the numerical size of the problems to be solved is extremely large. This difficulty is aggravated by the need for the forecast that will follow to be delivered in time. Those two specific difficulties have had a very strong impact on the development of assimilation of meteorological observations.

Oceanography is another domain where assimilation of observations has been used early. The dynamics of the ocean is very similar to that of the atmosphere, with different spatial and temporal scales. Due to its opacity to any form of electromagnetic radiation, the ocean is much more difficult to observe than the atmosphere. However, similar problems arise as in meteorology, and much of what is said below also applies to the ocean. Actually, assimilation of oceanographic observations is at the origin of several of the developments that are described in the following.

Section 1.2 presents a classical and relatively simple problem in Bayesian estimation in the linear and Gaussian case. The relatively simple algorithm called optimal interpolation (OI) is described in section 1.3 as an application of that elementary linear and Gaussian approach. The main algorithms that are used in operational assimilation, namely, Variational Assimilation and Ensemble Kalman Filter (EnKF), are presented and discussed as extensions of the same approach in section 1.4. A new class of algorithms, namely Particle Filters, is then described and discussed (section 1.5). The new methods of artificial intelligence (AI) and machine learning (ML) are briefly presented in section 1.6, and various extensions and applications of assimilation are described in section 1.7.

Early studies on assimilation of meteorological and oceanographical observations are as follows: Daley (1991); Ghil and Malanotte-Rizzoli (1991); Talagrand (1997); Kalnay (2002). More recent studies are as follows: Asch et al. (2016) and Carrassi et al. (2018).

In the following, E() denotes the expectation of a (scalar or vector) random variable. N (a, C) denotes the multidimensional Gaussian probability distribution with expectation a and covariance matrix C (with a similar transparent notation for a uni-dimensional Gaussian probability distribution).

1.2 The linear and Gaussian case

A simple estimation problem is as follows: we want to determine the unknown state vector x of the system of interest, belonging to state space S, with dimension n. The known available data are supposed to make up a vector z, belonging to data space D, with dimension m. The data vector is related to the unknown x through the relationship:

[1.1]

where the data operator Γ is a known linear operator from state space into data space, and ζ is an unknown “error”, meant to represent the effect of all possible uncertainties in the link between x and z (instrumental and/or representativeness errors, inaccuracies in the specification of Γ, etc.). Assume that the error ζ is a random Gaussian variable, with expectation 0 and covariance matrix S (ζ ~ N (0, S)) (if the expectation of ζ was not 0, but known, it would have to be first subtracted from z). The probability distribution of x, conditioned to z, is then the Gaussian distribution N (xa, Pa), with:

[1.2]

[1.3]

These quantities are properly defined under the only condition that rankΓ = m. This is a determinacy condition, which means that z contains information, either...

Produkt-Details

• Erscheint lt. Verlag: 29.10.2024
• Reihe/Serie: ISTE Consignment
• Sprache: englisch
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: biomass inversion • bio-physio-hydrological inversion • data assimilation • data inversion • glaciology • hyperspectral images • neural network methods • remote sensing • volcanology
• ISBN-10: 1-394-33228-9 / 1394332289
• ISBN-13: 978-1-394-33228-1 / 9781394332281