Inverse problems are a research topic for each branch in the geosciences: geophysics (geodynamics/tectonics, gravimetry, magneto-tellurics) and space geophysics (including magnetosphere, ionosphere), meteorology, oceanography, hydrology, environmental science, Earth observation (remote sensing), special issues (such as the pedosphere or cryosphere) and even geo-engineering. In all of these research fields, scientists have developed techniques for solving inverse problems appearing in these different disciplines. For ‘The Meeting of the Americas’, a Conference promoted by the American Geophysical Union, on 8–12 August 2010, in Foz do Iguassu (Brazil), we held a technical session on ‘Inverse Problems in Geosciences’ (session IN22A). The session was an opportunity for scientists from different research areas to describe the inversion methods used and/or developed. The intention was to promote contact among different branches of geosciences to spread the information to other areas.
Data assimilation is a special kind of inverse problem. Therefore, we invited researchers working in this area to attend the session. Data assimilation is an essential procedure for operational prediction system. Numerical weather prediction was the first application for data assimilation. However, for all prediction systems, in which an evolution mathematical model is employed, data assimilation is necessary. Therefore, for a forecasting system for ocean circulation, environmental prediction, hydrology, ionospheric dynamics or other applications in planning, such as human health (cancer treatment) or tectonic movements, data assimilation must be used.
Inverse problems and data assimilation are two well-established fields. These procedures can also be understood as very sophisticated schemes for data analysis. The combination of a mathematical model with observations to gain more knowledge is a tendency in the twenty-first century. Taking the twentieth century as a reference, the scientific challenge before the twentieth century was to find out the nature laws (equations) in mechanics, thermodynamics, electromagnetism, and even in biology and sociology. During the twentieth century, the scientific challenge was to develop a means to solve the complicated equations governing the natural phenomena. A new machine emerged on the scene: the computer. This was one of the most important contributions in the last century. Now, we can solve (approximately) the mathematical equations in a given model, and it becomes possible to scientifically conquer the problem of modern weather prediction for several days ahead. Indeed, computer simulation is now another way to gain understanding. This is another paradigm for getting and developing our understanding, the former two were from the empiricism and rationalism schools. For this century, a new path is emerging to acquire knowledge: data science. We are living in an exponential world: the amount of data is growing without precedent. Maybe, this is a scientific challenge after the twentieth century. Inverse problems and data assimilation have already been born embedded in data science, and they will remain so. Geosciences will be enhancing their relevance and application.
For this special issue, several techniques are employed to address inverse problems in calibration – an inverse problem of parameter estimation, applied to a surface model (it is used to represent the soil and the communication channel for information changing between the soil and atmosphere) and a hydrological model, determining the precipitation field for the atmospheric model, data assimilation. And finally, one paper is dedicated to the use of a traditional data assimilation scheme applied to solve an inverse problem: quantification of moisture in the soil.
We thank the contributors.
Our special acknowledgments to Prof. George Dulikravich, Founder and Editor-in-Chief of the IPSE journal, who agreed to give us the opportunity of this special issue.
Finally, we thank the referees. They did a good critical examination of the selected papers, improving the final version of these papers. Thank you very much.
Referee list:
Gerson P. Almeida, Ceara State University (UECE), Brazil
Mark Asch, University of Picardy Jules Verne, France
Jonathan D. Beezley, University of Colorado (UC-Denver), USA
João P. Braga, Federal University of Minas Gerais (UFGM), Brazil
Alexandre A. Costa, Ceara State University (UECE), Brazil
Ana Paula Cuco, Embraer (Brazilian Aeronautics Company), Brazil
Luiz Gustavo Goncalves, National Institute for Space Research (INPE), Brazil
Lili Lei, Pennsylvania State University (PennState), USA
Juan Martín Bravo, Federal University of Rio Grande do Sul (UFRGS), Brazil
Il-Ju Moon, JeJu National University, South Korea
Maelle Nodet, National Institute for Research in Computer Science and Control (INRIA), France
Juan Ruiz, University of Buenos Aires (UBA), Argentina
Chris Snyde, University Corporation for Atmospheric Research (UCAR), USA
Justin Schoof, Southern Illinois University (SIU), USA
Gilvan Sampaio, National Institute for Space Research (INPE), Brazil
Haroldo F. de Campos Velho
National Institute for Space Research (INPE), Sao Jose dos Campos, Brazil
Valéria C.F. Barbosa
National Observatory (ON), Rio de Janeiro, Brazil
Steven Cocke
Florida State University, Tallahassee, FL, USA
Special Issue Guest Editors