Global spherical harmonic computation by two-dimensional Fourier methods

A method is presented for performing global spherical harmonic computation by two-dimensional Fourier transformations. The method goes back to old literature (Schuster 1902) and tackles the problem of non-orthogonality of Legendre-functions, when discretized on an equi-angular grid. Both analysis and synthesis relations are presented, which link the spherical harmonic spectrum to a two-dimensional Fourier spectrum. As an alternative, certain functions of co-latitude are introduced, which are orthogonal to discretized Legendre functions. Several independent Fourier approaches for spherical harmonic computation fit into our general scheme.     

Regional spatial inventories (cadastres) of GHG emissions in the Energy sector: Accounting for uncertainty

An improvement of methods for the inventory of greenhouse gas (GHG) emissions is necessary to ensure effective control of commitments to emission reduction. The national inventory reports play an important role, but do not reflect specifics of regional processes of GHG emission and absorption for large-area countries. In this article, a GIS approach for the spatial inventory of GHG emissions in the energy sector, based on IPCC guidelines, official statistics on fuel consumption, and digital maps of the region under investigation, is presented. We include mathematical background for the spatial emission inventory of point, line and area sources, caused by fossil-fuel use for power and heat production, the residential sector, industrial and agricultural sectors, and transport. Methods for the spatial estimation of emissions from stationary and mobile sources, taking into account the specifics of fuel used and technological processes, are described. Using the developed GIS technology, the territorial distribution of GHG emissions, at the level of elementary grid cells 2 km?×?2 km for the territory of Western Ukraine, is obtained. Results of the spatial analysis are presented in the form of a geo-referenced database of emissions, and visualized as layers of digital maps. Uncertainty of inventory results is calculated using the Monte Carlo approach, and the sensitivity analysis results are described. The results achieved demonstrated that the relative uncertainties of emission estimates, for CO₂ and for total emissions (in CO₂ equivalent), depend largely on uncertainty in the statistical data and on uncertainty in fuels’ calorific values. The uncertainty of total emissions stays almost constant with the change of uncertainty of N₂O emission coefficients, and correlates strongly with an improvement in knowledge about CH₄ emission processes. The presented approach provides an opportunity to create a spatial cadastre of emissions, and to use this additional knowledge for the analysis and reduction of uncertainty. It enables us to identify territories with the highest emissions, and estimate an influence of uncertainty of the large emission sources on the uncertainty of total emissions. Ascribing emissions to the places where they actually occur helps to improve the inventory process and to reduce the overall uncertainty.     

Spatial GHG inventory at the regional level: accounting for uncertainty

Methodology and geo-information technology for spatial analysis of processes of greenhouse gas (GHG) emissions from mobile and stationary sources of the energy sector at the level of elementary plots are developed. The methodology, which takes into account the territorial specificity of point, line, and area sources of emissions, is based on official statistical data surveys. The spatial distribution of emissions and their structure for the main sectors of the energy sector in the territory of the Lviv region of Ukraine are analyzed. The relative uncertainties of emission estimates obtained are calculated using knowledge of the spatial location of emission sources and following the Tier 1 and Tier 2 approaches of IPCC methodologies. The sensitivity of total relative uncertainty to change of uncertainties in input data uncertainties is studied for the biggest emission point sources. A few scenarios of passing to the alternative energy generation are considered and respective structural changes in the structure of greenhouse gas emissions are analyzed. An influence of these structural changes on the total uncertainty of greenhouse gas inventory results is studied.     

Mesoscale raised rim depressions (MRRDs) on Earth: A review of the characteristics,processes, and spatial distributions of analogs for Mars

Fields of mesoscale raised rim depressions (MRRDs) of various origins are found on Earth and Mars. Examples include rootless cones, mud volcanoes, collapsed pingos, rimmed kettle holes, and basaltic ring structures. Correct identification of MRRDs on Mars is valuable because different MRRD types have different geologic and/or climatic implications and are often associated with volcanism and/or water, which may provide locales for biotic or prebiotic activity. In order to facilitate correct identification of fields of MRRDs on Mars and their implications, this work provides a review of common terrestrial MRRD types that occur in fields. In this review, MRRDs by formation mechanism, including hydrovolcanic (phreatomagmatic cones, basaltic ring structures), sedimentological (mud volcanoes), and ice-related (pingos, volatile ice-block forms) mechanisms. For each broad mechanism, we present a comparative synopsis of (i) morphology and observations, (ii) physical formation processes, and (iii) published hypothesized locations on Mars. Because the morphology for MRRDs may be ambiguous, an additional tool is provided for distinguishing fields of MRRDs by origin on Mars, namely, spatial distribution analyses for MRRDs within fields on Earth. We find that MRRDs have both distinguishing and similar characteristics, and observation that applies both to their mesoscale morphology and to their spatial distribution statistics. Thus, this review provides tools for distinguishing between various MRRDs, while highlighting the utility of the multiple working hypotheses approach.     

Benefits of dealing with uncertainty in greenhouse gas inventories: introduction

The assessment of greenhouse gases emitted to and removed from the atmosphere is high on the international political and scientific agendas. Growing international concern and cooperation regarding the climate change problem have increased the need for policy-oriented solutions to the issue of uncertainty in, and related to, inventories of greenhouse gas (GHG) emissions. The approaches to addressing uncertainty discussed in this Special Issue reflect attempts to improve national inventories, not only for their own sake but also from a wider, systems analytical perspective—a perspective that seeks to strengthen the usefulness of national inventories under a compliance and/or global monitoring and reporting framework. These approaches demonstrate the benefits of including inventory uncertainty in policy analyses. The authors of the contributed papers show that considering uncertainty helps avoid situations that can, for example, create a false sense of certainty or lead to invalid views of subsystems. This may eventually prevent related errors from showing up in analyses. However, considering uncertainty does not come for free. Proper treatment of uncertainty is costly and demanding because it forces us to make the step from “simple to complex” and only then to discuss potential simplifications. Finally, comprehensive treatment of uncertainty does not offer policymakers quick and easy solutions. The authors of the papers in this Special Issue do, however, agree that uncertainty analysis must be a key component of national GHG inventory analysis. Uncertainty analysis helps to provide a greater understanding and better science helps us to reduce and deal with uncertainty. By recognizing the importance of identifying and quantifying uncertainties, great strides can be made in ongoing discussions regarding GHG inventories and accounting for climate change. The 17 papers in this Special Issue deal with many aspects of analyzing and dealing with uncertainty in emissions estimates.     

Young (late Amazonian), near-surface, ground ice features near the equator, Athabasca Valles, Mars

A suite of four feature types in a ∼20 km² area near 10° N, 204° W in Athabasca Valles is interpreted to have resulted from near-surface ground ice. These features include mounds, conical forms with rimmed summit depressions, flatter irregularly-shaped forms with raised rims, and polygonal terrain. Based on morphology, size, and analogy to terrestrial ground ice forms, these Athabascan features are interpreted as pingos, collapsing pingos, pingo scars, and thermal contraction polygons, respectively. Thermal Infrared Mapping Spectrometer (THEMIS) data and geological features in the area are consistent with a sedimentary substrate underlying these features. These observations lead us to favor a ground ice interpretation, although we do not rule out volcanic and especially glaciofluvial hypotheses. The hypothesized ground ice that formed the mounds and rimmed features may have been emplaced via the deposition of saturated sediment during flooding; an alternative scenario invokes magmatically cycled groundwater. The ground ice implicit in the hypothesized thermal contraction polygons may have derived either from this flooding/ground water, or from atmospheric water vapor. The lack of obvious flood modification of the mounds and rimmed features indicates that they formed after the most recent flood inundated the area. Analogy with terrestrial pingos suggests that ground ice may be still extant within the positive relief mounds. As the water that flooded down Athabasca Valles emerged via a volcanotectonic fissure from a deep aquifer, any extant pingo ice may contain evidence of a deep subsurface biosphere.     

Verification of compliance with GHG emission targets: annex B countries

The focus of this study is on the preparatory detection of uncertain greenhouse gas (GHG) emission changes (also termed emission signals) under the Kyoto Protocol. Preparatory signal detection is a measure that should be taken prior to/during negotiation of the Protocol. It allows the ranking of countries under the Protocol according to their realized versus their agreed emission changes and in terms of both certainty and credibility. Controlling GHGs is affected by uncertainty and may be costly. Thus, knowing whether each nation is doing its part is in the public interest. At present, however, countries to the United Nations Framework Convention on Climate Change (UNFCCC) are obliged to include in the reporting of their annual inventories direct or alternative estimates of the uncertainty associated with these, consistent with the Intergovernmental Panel on Climate Change’s (IPCC) good practice guidance reports. As a consequence, inventory uncertainty is monitored, but not regulated, under the Kyoto Protocol. Although uncertainties are becoming increasingly available, monitored emissions and uncertainties are still dealt with separately. In our study we analyze estimates of both emission changes and uncertainties to advance the evaluation of countries and their performance under the Protocol. Our analysis allows supply and demand of emissions credits to be examined in consideration of uncertainty. For the purpose of our exercise, we make use of the Undershooting and Verification Time concept described by Jonas et al. (Clim Change doi:10.1007/s10584-010-9914-6, 2010).