"Parameter Estimation and Inverse Problems, 2/e" provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations containing errors, and how one may determine the quality of such a model. This book takes on these fundamental and challenging problems, introducing students and professionals to the broad range of approaches that lie in the realm of inverse theory. The authors present both the underlying theory and practical algorithms for solving inverse problems. The authors' treatment is appropriate for geoscience graduate students and advanced undergraduates with a basic working knowledge of calculus, linear algebra, and statistics. "Parameter Estimation and Inverse Problems, 2/e" introduces readers to both Classical and Bayesian approaches to linear and nonlinear problems with particular attention paid to computational, mathematical, and statistical issues related to their application to geophysical problems. The textbook includes Appendices covering essential linear algebra, statistics, and notation in the context of the subject. This book includes a companion website that features computational examples (including all examples contained in the textbook) and useful subroutines using MATLAB. It: includes appendices for review of needed concepts in linear, statistics, and vector calculus; features a companion website that contains comprehensive MATLAB code for all examples, which readers can reproduce, experiment with, and modify; offers an online instructor's guide that helps professors teach, customize exercises, and select homework problems; and, is accessible to students and professionals without a highly specialized mathematical background.

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Parameter estimation and inverse problems

Methane is an important greenhouse gas, responsible for about 20% of the warming induced by long-lived greenhouse gases since pre-industrial times. By reacting with hydroxyl radicals, methane reduces the oxidizing capacity of the atmosphere and generates ozone in the troposphere. Although most sources and sinks of methane have been identified, their relative contributions to atmospheric methane levels are highly uncertain. As such, the factors responsible for the observed stabilization of atmospheric methane levels in the early 2000s, and the renewed rise after 2006, remain unclear. Here, we construct decadal budgets for methane sources and sinks between 1980 and 2010, using a combination of atmospheric measurements and results from chemical transport models, ecosystem models, climate chemistry models and inventories of anthropogenic emissions. The resultant budgets suggest that data-driven approaches and ecosystem models overestimate total natural emissions. We build three contrasting emission scenarios-which differ in fossil fuel and microbial emissions-to explain the decadal variability in atmospheric methane levels detected, here and in previous studies, since 1985. Although uncertainties in emission trends do not allow definitive conclusions to be drawn, we show that the observed stabilization of methane levels between 1999 and 2006 can potentially be explained by decreasing-to-stable fossil fuel emissions, combined with stable-to-increasing microbial emissions. We show that a rise in natural wetland emissions and fossil fuel emissions probably accounts for the renewed increase in global methane levels after 2006, although the relative contribution of these two sources remains uncertain. © 2013 Macmillan Publishers Limited.

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Three decades of global methane sources and sinks

Hyperspectral remote sensing technology has advanced significantly in the past two decades. Current sensors onboard airborne and spaceborne platforms cover large areas of the Earth surface with unprecedented spectral, spatial, and temporal resolutions. These characteristics enable a myriad of applications requiring fine identification of materials or estimation of physical parameters. Very often, these applications rely on sophisticated and complex data analysis methods. The sources of difficulties are, namely, the high dimensionality and size of the hyperspectral data, the spectral mixing (linear and nonlinear), and the degradation mechanisms associated to the measurement process such as noise and atmospheric effects. This paper presents a tutorial/overview cross section of some relevant hyperspectral data analysis methods and algorithms, organized in six main topics: data fusion, unmixing, classification, target detection, physical parameter retrieval, and fast computing. In all topics, we describe the state-of-the-art, provide illustrative examples, and point to future challenges and research directions.

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Hyperspectral Remote Sensing Data Analysis and Future Challenges

TROPOMI on the ESA Sentinel-5 Precursor: A GMES mission for global observations of the atmospheric composition for climate, air quality and ozone layer applications

. The Global Fire Assimilation System (GFASv1.0) calculates biomass burning emissions by assimilating Fire Radiative Power (FRP) observations from the MODIS instruments onboard the Terra and Aqua satellites. It corrects for gaps in the observations, which are mostly due to cloud cover, and filters spurious FRP observations of volcanoes, gas flares and other industrial activity. The combustion rate is subsequently calculated with land cover-specific conversion factors. Emission factors for 40 gas-phase and aerosol trace species have been compiled from a literature survey. The corresponding daily emissions have been calculated on a global 0.5° × 0.5° grid from 2003 to the present. General consistency with the Global Fire Emission Database version 3.1 (GFED3.1) within its accuracy is achieved while maintaining the advantages of an FRP-based approach: GFASv1.0 makes use of the quantitative information on the combustion rate that is contained in the FRP observations, and it detects fires in real time at high spatial and temporal resolution. GFASv1.0 indicates omission errors in GFED3.1 due to undetected small fires. It also exhibits slightly longer fire seasons in South America and North Africa and a slightly shorter fire season in Southeast Asia. GFASv1.0 has already been used for atmospheric reactive gas simulations in an independent study, which found good agreement with atmospheric observations. We have performed simulations of the atmospheric aerosol distribution with and without the assimilation of MODIS aerosol optical depth (AOD). They indicate that the emissions of particulate matter need to be boosted by a factor of 2–4 to reproduce the global distribution of organic matter and black carbon. This discrepancy is also evident in the comparison of previously published top-down and bottom-up estimates. For the time being, a global enhancement of the particulate matter emissions by 3.4 is recommended. Validation with independent AOD and PM10 observations recorded during the Russian fires in summer 2010 show that the global Monitoring Atmospheric Composition and Change (MACC) aerosol model with GFASv1.0 aerosol emissions captures the smoke plume evolution well when organic matter and black carbon are enhanced by the recommended factor. In conjunction with the assimilation of MODIS AOD, the use of GFASv1.0 with enhanced emission factors quantitatively improves the forecast of the aerosol load near the surface sufficiently to allow air quality warnings with a lead time of up to four days.

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Biomass burning emissions estimated with a global fire assimilation system based on observed fire radiative power

Remote sounding of the atmosphere has proved to be a fruitful method of obtaining global information about the atmospheres of the earth and planets. This book treats the inverse problem of remote sounding comprehensively, and discusses a wide range of retrieval methods for extracting atmospheric parameters of interest from the quantities such as thermal emission that can be measured remotely. Inverse theory is treated in depth from an estimation-theory point of view, but practical questions are also emphasized, for example designing observing systems to obtain the maximum quantity of information, efficient numerical implementation of algorithms for processing of large quantities of data, error analysis and approaches to the validation of the resulting retrievals, The book is targeted at both graduate students and working scientists.

Clive D. Rodgers

Papers

Inverse Methods for Atmospheric Sounding: Theory and Practice