Spatially resolving methane emissions in California: constraints from the CalNex aircraft campaign and from present (GOSAT, TES) and future (TROPOMI, geostationary) satellite observations

We apply a continental-scale inverse modeling system for North America based on the GEOS-Chem model to optimize California methane emissions at 1/2° × 2/3° horizontal resolution using atmospheric observations from the CalNex aircraft campaign (May–June 2010) and from satellites. Inversion of the CalNex data yields a best estimate for total California methane emissions of 2.86 ± 0.21 Tg a−1, compared with 1.92 Tg a−1 in the EDGAR v4.2 emission inventory used as a priori and 1.51 Tg a−1 in the California Air Resources Board (CARB) inventory used for state regulations of greenhouse gas emissions. These results are consistent with a previous Lagrangian inversion of the CalNex data. Our inversion provides 12 independent pieces of information to constrain the geographical distribution of emissions within California. Attribution to individual source types indicates dominant contributions to emissions from landfills/wastewater (1.1 Tg a−1), livestock (0.87 Tg a−1), and gas/oil (0.64 Tg a−1). EDGAR v4.2 underestimates emissions from livestock, while CARB underestimates emissions from landfills/wastewater and gas/oil. Current satellite observations from GOSAT can constrain methane emissions in the Los Angeles Basin but are too sparse to constrain emissions quantitatively elsewhere in California (they can still be qualitatively useful to diagnose inventory biases). Los Angeles Basin emissions derived from CalNex and GOSAT inversions are 0.42 ± 0.08 and 0.31 ± 0.08 Tg a−1 that the future TROPOMI satellite instrument (2015 launch) will be able to constrain California methane emissions at a detail comparable to the CalNex aircraft campaign. Geostationary satellite observations offer even greater potential for constraining methane emissions in the future.

Study on Electronic Industry with an Application of Rectilinear Embedding in VLSI Placement

The electronic industry has developed quickly in last few years, with the rapid growth of Very Large Scale Integration technology. Placement layout is considered as the original step in VLSI physical design. The rectilinear embedding, which originates from graph theory, has wide range of application in VLSI placement. In this paper, we constructed a mathematical model for VLSI placement. Firstly, the VLSI placement was converted to quadrangulation by using rectilinear embedding speculative knowledge. Then we provided generating functions for two types of quadrangulations with graph multiple parameters. And the explicit formulae were obtained by employing Lagrangian inversion. Furthermore, we found the relationship between outerplanar graph and Hamilton graph, so the counting result of Hamilton quadrangulation was derived. The quadrangulation calculation can be applied to the establishment of arithmetical algorithms, which can be widely used in the optimization of VLSI placement.

An Application of Rectilinear Embedding in VLSI Placement

The VLSI (Very Large Scale Integrated Circuits) technology has developed rapidly in recent years, with a lot of advanced electric products emerging. Placement layout is regarded as the initial step in VLSI physical design. Its quality has a direct effect on the chip area and performance. The rectilinear embedding, which originates from graph theory, is widely employed in VLSI placement. In this paper, we set up a mathematical model for VLSI. Firstly, the issue of VLSI placement was converted to quadrangulation by using rectilinear embedding. Then we provided generating functions for two types of quadrangulations with graph multiple parameters. And the explicit formulae by employing Lagrangian inversion were obtained. Furthermore, we found the relation between outerplanar graph and Hamilton graph, so the counting result of Hamilton quadrangulation was derived. The quadrangulation calculation can be applied to the establishment of a computerized algorithm, which can be widely used for VLSI placement optimization.

Mathematical Models for VLSI Placement with Rectilinear Embedding

Based on the theory of functional equations in rectilinear embedding, a mathematical model of VLSI placement design was established in this paper. The cell on the plane is conceived as a point, while the wire links the cells is assumed as lines, then the VLSI placement is transformed into quadrangulation by using graph theory. First of all, we obtained generating functions for two types of quadrangulations (quartic graphs) with graph multiple parameters and secondly derived explicit formulae by employing Lagrangian inversion. Furthermore, we found a relation between outerplanar graph and Hamilton graph, and then got the counting result of Hamilton quadrangulation. The quadrangulation calculations could provide a theoretical foundation for computerized algorithm, which can be widely used for VLSI placement optimization.