Exactly Solvable Balanced Tenable Urns with Random Entries via the Analytic Methodology

This paper develops an analytic theory for the study of some Polya urns with random rules. The idea is to extend the isomorphism theorem in Flajolet et al. (2006), which connects deterministic balanced urns to a differential system for the generating function. The methodology is based upon adaptation of operators and use of a weighted probability generating function. Systems of differential equations are developed, and when they can be solved, they lead to characterization of the exact distributions underlying the urn evolution. We give a few illustrative examples.Comment: 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), Montreal : Canada (2012

Exactly Solvable Balanced Tenable Urns with Random Entries via the Analytic Methodology

This paper develops an analytic theory for the study of some Pólya urns with random rules. The idea is to extend the isomorphism theorem in Flajolet et al. (2006), which connects deterministic balanced urns to a differential system for the generating function. The methodology is based upon adaptation of operators and use of a weighted probability generating function. Systems of differential equations are developed, and when they can be solved, they lead to characterization of the exact distributions underlying the urn evolution. We give a few illustrative examples

Modulation of precipitation by conditional symmetric instability release

Although many theoretical and observational studies have investigated the mechanism of conditional symmetric instability (CSI) release and associated it with mesoscale atmospheric phenomena such as frontal precipitation bands, cloud heads in rapidly developing extratropical cyclones and sting jets, its climatology and contribution to precipitation have not been extensively documented. The aim of this paper is to quantify the contribution of CSI release, yielding slantwise convection, to climatological precipitation accumulations for the North Atlantic and western Europe. Case studies reveal that CSI release could be common along cold fronts of mature extratropical cyclones and the North Atlantic storm track is found to be a region with large CSI according to two independent CSI metrics. Correlations of CSI with accumulated precipitation are also large in this region and CSI release is inferred to be occurring about 20% of the total time over depths of over 1km. We conclude that the inability of current global weather forecast and climate prediction models to represent CSI release (due to insufficient resolution yet lack of subgrid parametrization schemes) may lead to errors in precipitation distributions, particularly in the region of the North Atlantic storm track

Impact of an improved shortwave radiation scheme in the MAECHAM5 General Circulation Model

International audienceIn order to improve the representation of ozone absorption in the stratosphere of the MAECHAM5 general circulation model, the spectral resolution of the shortwave radiation parameterization used in the model has been increased from 4 to 6 bands. Two 20-years simulations with the general circulation model have been performed, one with the standard and the other with the newly introduced parameterization respectively, to evaluate the temperature and dynamical changes arising from the two different representations of the shortwave radiative transfer. In the simulation with the increased spectral resolution in the radiation parameterization, a significant warming of almost the entire model domain is reported. At the summer stratopause the temperature increase is about 6 K and alleviates the cold bias present in the model when the standard radiation scheme is used. These general circulation model results are consistent both with previous validation of the radiation scheme and with the offline clear-sky comparison performed in the current work with a discrete ordinate 4 stream scattering line by line radiative transfer model. The offline validation shows a substantial reduction of the daily averaged shortwave heating rate bias (1?2 K/day cooling) that occurs for the standard radiation parameterization in the upper stratosphere, present under a range of atmospheric conditions. Therefore, the 6 band shortwave radiation parameterization is considered to be better suited for the representation of the ozone absorption in the stratosphere than the 4 band parameterization. Concerning the dynamical response in the general circulation model, it is found that the reported warming at the summer stratopause induces stronger zonal mean zonal winds in the middle atmosphere. These stronger zonal mean zonal winds thereafter appear to produce a dynamical feedback that results in a dynamical warming (cooling) of the polar winter (summer) mesosphere, caused by an increased downward (upward) circulation in the winter (summer) hemisphere. In addition, the comparison of the two simulations performed with the general circulation model shows that the increase in the spectral resolution of the shortwave radiation and the associated changes in the cloud optical properties result in a warming (0.5?1 K) and moistening (3%?12%) of the upper tropical troposphere. By comparing these modeled differences with previous works, it appears that the reported changes in the solar radiation scheme contribute to improve the model mean temperature also in the troposphere

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

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

The surprising role of orography in the initiation of an isolated thunderstorm in southern England

Many factors, both mesoscale and larger scale, often come together in order for a particular convective initiation to take place. The authors describe a modeling study of a case from the Convective Storms Initiation Project (CSIP) in which a single thunderstorm formed behind a front in the southern United Kingdom. The key features of the case were a tongue of low-level high θw air associated with a forward-sloping split front (overrunning lower θw air above), a convergence line, and a “lid” of high static stability air, which the shower was initially constrained below but later broke through. In this paper, the authors analyze the initiation of the storm, which can be traced back to a region of high ground (Dartmoor) at around 0700 UTC, in more detail using model sensitivity studies with the Met Office Unified Model (MetUM). It is established that the convergence line was initially caused by roughness effects but had a significant thermal component later. Dartmoor had a key role in the development of the thunderstorm. A period of asymmetric flow over the high ground, with stronger low-level descent in the lee, led to a hole in a layer of low-level clouds downstream. The surface solar heating through this hole, in combination with the tongue of low-level high θw air associated with the front, caused the shower to initiate with sufficient lifting to enable it later to break through the lid

Cloud optical depth retrievals from the Aerosol Robotic Network (AERONET) cloud mode observations

Cloud optical depth is one of the most poorly observed climate variables. The new “cloud mode” capability in the Aerosol Robotic Network (AERONET) will inexpensively yet dramatically increase cloud optical depth observations in both number and accuracy. Cloud mode optical depth retrievals from AERONET were evaluated at the Atmospheric Radiation Measurement program’s Oklahoma site in sky conditions ranging from broken clouds to overcast. For overcast cases, the 1.5 min average AERONET cloud mode optical depths agreed to within 15% of those from a standard ground‐based flux method. For broken cloud cases, AERONET retrievals also captured rapid variations detected by the microwave radiometer. For 3 year climatology derived from all nonprecipitating clouds, AERONET monthly mean cloud optical depths are generally larger than cloud radar retrievals because of the current cloud mode observation strategy that is biased toward measurements of optically thick clouds. This study has demonstrated a new way to enhance the existing AERONET infrastructure to observe cloud optical properties on a global scale

Aerosol analysis and forecast in the European Centre for Medium-Range Weather Forecasts Integrated Forecast System: 2. Data assimilation

This study presents the new aerosol assimilation system, developed at the European Centre for Medium-Range Weather Forecasts, for the Global and regional Earth-system Monitoring using Satellite and in-situ data (GEMS) project. The aerosol modeling and analysis system is fully integrated in the operational four-dimensional assimilation apparatus. Its purpose is to produce aerosol forecasts and reanalyses of aerosol fields using optical depth data from satellite sensors. This paper is the second of a series which describes the GEMS aerosol effort. It focuses on the theoretical architecture and practical implementation of the aerosol assimilation system. It also provides a discussion of the background errors and observations errors for the aerosol fields, and presents a subset of results from the 2-year reanalysis which has been run for 2003 and 2004 using data from the Moderate Resolution Imaging Spectroradiometer on the Aqua and Terra satellites. Independent data sets are used to show that despite some compromises that have been made for feasibility reasons in regards to the choice of control variable and error characteristics, the analysis is very skillful in drawing to the observations and in improving the forecasts of aerosol optical depth

Direct observation of active material concentration gradients and crystallinity breakdown in LiFePO4 electrodes during charge/discharge cycling of lithium batteries

The phase changes that occur during discharge of an electrode comprised of LiFePO4, carbon, and PTFE binder have been studied in lithium half cells by using X-ray diffraction measurements in reflection geometry. Differences in the state of charge between the front and the back of LiFePO4 electrodes have been visualized. By modifying the X-ray incident angle the depth of penetration of the X-ray beam into the electrode was altered, allowing for the examination of any concentration gradients that were present within the electrode. At high rates of discharge the electrode side facing the current collector underwent limited lithium insertion while the electrode as a whole underwent greater than 50% of discharge. This behavior is consistent with depletion at high rate of the lithium content of the electrolyte contained in the electrode pores. Increases in the diffraction peak widths indicated a breakdown of crystallinity within the active material during cycling even during the relatively short duration of these experiments, which can also be linked to cycling at high rate