"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

SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography) is a spectrometer designed to measure sunlight transmitted, reflected, and scattered by the earth’s atmosphere or surface in the ultraviolet, visible, and near-infrared wavelength region (240–2380 nm) at moderate spectral resolution (0.2–1.5 nm, λ/Δλ ≈ 1000–10 000). SCIAMACHY will measure the earthshine radiance in limb and nadir viewing geometries and solar or lunar light transmitted through the atmosphere observed in occultation. The extraterrestrial solar irradiance and lunar radiance will be determined from observations of the sun and the moon above the atmosphere. The absorption, reflection, and scattering behavior of the atmosphere and the earth’s surface is determined from comparison of earthshine radiance and solar irradiance. Inversion of the ratio of earthshine radiance and solar irradiance yields information about the amounts and distribution of important atmospheric constituents and the spectral reflecta...

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SCIAMACHY: Mission Objectives and Measurement Modes

of uncertainty for the OTD global totals represents primarily the uncertainty (and variability) in the flash detection efficiency of the instrument The OTD measurements have been used to construct lightning climatology maps that demonstrate the geographical and seasonal distribution of lightning activity for the globe An analysis of this annual lightning distribution confirms that lightning occurs mainly over land areas, with an average land/ocean ratio of 10:1 The Congo basin, which stands out year-round, shows a peak mean annual flash density of 80 fl km 2 yr 1 in Rwanda, and includes an area of over 3 million km 2 exhibiting flash densities greater than 30 fl km 2 yr 1 (the flash density of central Florida) Lightning is predominant in the northern Atlantic and western Pacific Ocean basins year-round where instability is produced from cold air passing over warm ocean water Lightning is less frequent in the eastern tropical Pacific and Indian Ocean basins where the air mass is warmer A dominant Northern Hemisphere summer peak occurs in the annual cycle, and evidence is found for a tropically driven semiannual cycle INDEX TERMS: 3304 Meteorology and Atmospheric Dynamics: Atmospheric electricity; 3309 Meteorology and Atmospheric Dynamics: Climatology (1620); 3324 Meteorology and Atmospheric Dynamics: Lightning; 3394 Meteorology and Atmospheric Dynamics: Instruments and techniques;

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Global frequency and distribution of lightning as observed from space by the Optical Transient Detector

The radio occultation (RO) technique, which makes use of radio signals transmitted by the global positioning system (GPS) satellites, has emerged as a powerful and relatively inexpensive approach for sounding the global atmosphere with high precision, accuracy, and vertical resolution in all weather and over both land and ocean. On 15 April 2006, the joint Taiwan-U.S. Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC)/Formosa Satellite Mission 3 (COSMIC/FORMOSAT-3, hereafter COSMIC) mission, a constellation of six microsatellites, was launched into a 512-km orbit. After launch the satellites were gradually deployed to their final orbits at 800 km, a process that took about 17 months. During the early weeks of the deployment, the satellites were spaced closely, offering a unique opportunity to verify the high precision of RO measurements. As of September 2007, COSMIC is providing about 2000 RO soundings per day to support the research and operational communities. COSMIC RO dat...

/pdf/the-cosmic-formosat-3-mission-early-results-2bn1owr3dc.pdf

The COSMIC/FORMOSAT-3 Mission: Early Results

The influence of breaking gravity waves on the dynamics and chemical composition of the 60- to 110-km region has been investigated with a two-dimensional dynamical/chemical model that includes a parameterization of gravity wave drag and diffusion. The momentum deposited by breaking waves at mesospheric altitudes reverses the zonal winds, drives a strong mean meridional circulation, and produces a very cold summer and warm winter mesopause, in general agreement with observations. The seasonal variations of the computed eddy diffusion coefficient are consistent with the behavior of mesospheric turbulence inferred from MST radar echoes. In particular, it is found that eddy diffusion is strong in summer and winter but much weaker at the equinoxes and that this seasonal behavior has important consequences for the distribution of chemical species. Comparison between computed atomic oxygen and ozone, and the abundances of these constituents inferred from the 557.7-nm and 1.27-μm airglow emissions, reveals excellent agreement. The consistency between model results and these diverse types of observations lends strong support to the hypothesis that gravity waves play a very important role in determining the zonally averaged structure of the mesosphere and lower thermosphere.

The effect of breaking gravity waves on the dynamics and chemical composition of the mesosphere and lower thermosphere

A GPS-based system has been developed that accurately locates the sources of VHF radiation from lightning discharges in three spatial dimensions and time. The observations are found to reflect the basic charge structure of electrified storms. Observations have also been obtained of a distinct type of energetic discharge referred to as positive bipolar breakdown, recently identified as the source of trans-ionospheric pulse pairs (TIPPs) observed by satellites from space. The bipolar breakdown has been confirmed to occur between the main negative and upper positive charge regions of a storm and found to be the initial event of otherwise normal intracloud discharges. The latter is contrary to previous findings that the breakdown appeared to be temporally isolated from other lightning in a storm. Peak VHF radiation from the energetic discharges is observed to be typically 30 dB stronger than that from other lightning processes and to correspond to source power in excess of 100 kW over a 6 MHz bandwidth centered at 63 MHz.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999GL010856

A GPS‐based three‐dimensional lightning mapping system: Initial observations in central New Mexico

[1] The location accuracy of the New Mexico Tech Lightning Mapping Array (LMA) has been investigated experimentally using sounding balloon measurements, airplane tracks, and observations of distant storms. We have also developed simple geometric models for estimating the location uncertainty of sources both over and outside the network. The model results are found to be a good estimator of the observed errors and also agree with covariance estimates of the location uncertainties obtained from the least squares solution technique. Sources over the network are located with an uncertainty of 6–12 m rms in the horizontal and 20–30 m rms in the vertical. This corresponds well with the uncertainties of the arrival time measurements, determined from the distribution of chi-square values to be 40–50 ns rms. Outside the network the location uncertainties increase with distance. The geometric model shows that the range and altitude errors increase as the range squared, r2, while the azimuthal error increases linearly with r. For the 13 station, 70 km diameter network deployed during STEPS the range and height errors of distant sources were comparable to each other, while the azimuthal errors were much smaller. The difference in the range and azimuth errors causes distant storms to be elongated radially in plan views of the observations. The overall results are shown to agree well with hyperbolic formulations of time of arrival measurements [e.g., Proctor, 1971]. Two appendices describe (1) the basic operation of the LMA and the detailed manner in which its measurements are processed and (2) the effect of systematic errors on lightning observations. The latter provides an alternative explanation for the systematic height errors found by Boccippio et al. [2001] in distant storm data from the Lightning Detection and Ranging system at Kennedy Space Center.

Accuracy of the Lightning Mapping Array

Observations of radio emissions from thunderstorms were made during the summer of 1996 using two arrays of sensors located in northern New Mexico. The first array consisted of three fast electric field change meters separated by distances of 30 to 230 km. The second array consisted of three broadband (3 to 30 MHz) HF data acquisition systems separated by distances of 6 to 13 km. Differences in signal times of arrival at multiple stations were used to locate the sources of received signals. Relative times of arrival of signal reflections from the ionosphere and Earth were used to determine source heights. A distinct class of short-duration electric field change emissions was identified and characterized. The emissions have previously been termed narrow positive bipolar pulses (NPBPs). NPBPs were emitted from singular intracloud discharges that occurred in the most active regions of three thunderstorms located in New Mexico and west Texas. The discharges occurred at altitudes between 8 and 11 km above mean sea level. NEXRAD radar images show that the NPBP sources were located in close proximity to high reflectivity storm cores where reflectivity values were in excess of 40 dBZ. NPBP electric field change waveforms were isolated, bipolar, initially positive pulses with peak amplitudes comparable to those of return stroke field change waveforms. The mean FWHM (full width at half maximum) of initial NPBP field change pulses was 4.7 μs. The HF emissions associated with NPBPs were broadband noise-like radiation bursts with a mean duration of 2.8 μs and amplitudes 10 times larger than emissions from typical intracloud and cloud-to-ground lightning processes. Calculations indicate that the events represent a distinct class of singular, isolated lightning discharges that have limited spatial extents of 300 to 1000 m and occur in high electric field regions. The unique radio emissions produced by these discharges, in combination with their unprecedented physical characteristics, clearly distinguish the events from other types of previously observed thunderstorm electrical processes.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1998JD200045

A distinct class of isolated intracloud lightning discharges and their associated radio emissions

Radio frequency observations of cloud-to-ground lightning in Florida have been analyzed to document a number of features of the lightning. The observations have been made using an interferometer system which determined the direction to the lightning radiation as a function of time during close lightning discharges. Observations are presented for about 50 radiating events during five multiple-stroke, normal-polarity flashes to ground. The results confirm and extend results of a similar study of New Mexico lightning by Rhodes et al. (1994). Dart leaders, in-cloud K events, and attempted leaders are found to be the same phenomena, namely, a negative-polarity streamer that propagates horizontally and/or vertically to ground at estimated speeds of about 10 7 ms −1 down to 10 6 ms −1 . The step or impulsive fast electric field change produced by some K events is found to be caused by positive breakdown back at the starting point of the negative streamer, after the streamer has progressed over some or all of its distance. This breakdown appears to initiate a forward stroke along the streamer channel which can renew the breakdown at the front end of the channel. K breakdown which happens to occur during a continuing current discharge to ground produces an M event (channel brightening) when it connects with the conducting channel to ground. The step fast field change of the M events is found to be produced at the time of connection inside the cloud ; no fast field change is detected when this breakdown reaches ground that would be associated with a return stroke. M events can also be initiated by fast (10 7 ms −1 ) positive streamers which often propagate away from the leader source region within a few milliseconds of the arrival of a return stroke back in the source region. These streamers often generate an even faster negative recoil event back along their extent which propagates down the channel to ground, as the M event. In all cases the current increase or channel brightening produced by K and M events is predicted to occur in a forward direction, that is, toward or down the channel to ground, in the same direction as the initiating negative streamer. Positive breakdown is detected only immediately following return strokes or during some K streamers. In both cases the electric stresses are expected to be very large, suggesting that positive breakdown which produces a conducting channel is difficult to initiate. Results for one flash suggest that negative charge was left at low altitude by the initial stroke to ground ; this forced the subsequent leaders to develop a new path to ground, first as series of attempted leaders and then as a dart-stepped leader.

Ronald J. Thomas

Papers

A GPS‐based three‐dimensional lightning mapping system: Initial observations in central New Mexico

Accuracy of the Lightning Mapping Array

Accuracy of the Lightning Mapping Array

A distinct class of isolated intracloud lightning discharges and their associated radio emissions

Radio interferometric observations of cloud-to-ground lightning phenomena in Florida