"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.

/pdf/parameter-estimation-and-inverse-problems-370q4164ci.pdf

Parameter estimation and inverse problems

Lightning in all corners of the world is monitored by one or more land- or space-based lightning locating systems (LLSs). The applications that have driven these developments are numerous and varied. This paper describes the history leading to modern LLSs that sense lightning radiation fields at multiple remote sensors, focusing on the interactions between enabling technology, scientific discovery, technical development, and uses of the data. An overview of all widely used detection and location methods is provided, including a general discussion of their relative strengths and weaknesses for various applications. The U.S. National Lightning Detection Network (NLDN) is presented as a case study, since this LLS has been providing real-time lightning information since the early 1980s, and has provided continental-scale (U.S.) information to research and operational users since 1989. This network has also undergone a series of improvements during its >20-year life in response to evolving detection technologies and expanding requirements for applications. Recent analyses of modeled and actual performance of the current NLDN are also summarized. The paper concludes with a view of the short- and long-term requirements for improved lightning measurements that are needed to address some open scientific questions and fill the needs of emerging applications.

An Overview of Lightning Locating Systems: History, Techniques, and Data Uses, With an In-Depth Look at the U.S. NLDN

. The knowledge of the lightning-induced nitrogen oxides (LNOx) source is important for understanding and predicting the nitrogen oxides and ozone distributions in the troposphere and their trends, the oxidising capacity of the atmosphere, and the lifetime of trace gases destroyed by reactions with OH. This knowledge is further required for the assessment of other important NOx sources, in particular from aviation emissions, the stratosphere, and from surface sources, and for understanding the possible feedback between climate changes and lightning. This paper reviews more than 3 decades of research. The review includes laboratory studies as well as surface, airborne and satellite-based observations of lightning and of NOx and related species in the atmosphere. Relevant data available from measurements in regions with strong LNOx influence are identified, including recent observations at midlatitudes and over tropical continents where most lightning occurs. Various methods to model LNOx at cloud scales or globally are described. Previous estimates are re-evaluated using the global annual mean flash frequency of 44±5 s−1 reported from OTD satellite data. From the review, mainly of airborne measurements near thunderstorms and cloud-resolving models, we conclude that a "typical" thunderstorm flash produces 15 (2–40)×1025 NO molecules per flash, equivalent to 250 mol NOx or 3.5 kg of N mass per flash with uncertainty factor from 0.13 to 2.7. Mainly as a result of global model studies for various LNOx parameterisations tested with related observations, the best estimate of the annual global LNOx nitrogen mass source and its uncertainty range is (5±3) Tg a−1 in this study. In spite of a smaller global flash rate, the best estimate is essentially the same as in some earlier reviews, implying larger flash-specific NOx emissions. The paper estimates the LNOx accuracy required for various applications and lays out strategies for improving estimates in the future. An accuracy of about 1 Tg a−1 or 20%, as necessary in particular for understanding tropical tropospheric chemistry, is still a challenging goal.

/pdf/the-global-lightning-induced-nitrogen-oxides-source-4n884kbcha.pdf

The global lightning-induced nitrogen oxides source

[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

The physics of lightning

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

Great Plains storms are known for their ability to produce severe weather. They are also prodigious producers of lightning; just how prodigious has been vividly illustrated by observations in central Oklahoma with a new Global Positioning System (GPS)-based lightning mapping system.The observations are useful not only for studying storm electrification but also provide a valuable indicator of storm structure and intensity.

The system maps lightning in three spatial dimensions by measuring the times at which impulsive VHF radiation events arrive at a network of ground-based measurement stations. Low-cost GPS receivers provide sufficient timing accuracy to produce high-quality pictures of the total lightning activity over a large area.

GPS‐based mapping system reveals lightning inside storms

Three-dimensional lightning mapping observations have been used to estimate the peak source powers radiated by individual VHF events of lightning discharges. The peak powers vary from minimum locatable values of about 1 W typically up to 10–30 kW or more in the 60–66 MHz passband of the receivers. An energetic positive bipolar event radiated in excess of 300 k W peak power. The strongest radiation sources tended to be observed in the upper part of storms, corresponding to the upper positive charge region, where the breakdown is of negative polarity. The results illustrate the bidirectional nature of intracloud discharges, with the largest source powers being along the negative portion of the discharge and an order of magnitude greater than the source powers along the positive portion. Overall, the source powers follow an approximate P−1 distribution for powers above about 100 W. The radiation sources indicate the location of the main charge regions in a storm; sample comparisons with radar data show that the main negative charge coincided with the precipitation core

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000GL011464

J. Harlin

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

GPS‐based mapping system reveals lightning inside storms

Observations of VHF Source Powers Radiated by Lightning