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

Combination of mesoscale and synoptic mechanisms for triggering an isolated thunderstorm: Observational case study of CSIP IOP 1

Copyright @ 2007 AMSAn isolated thunderstorm formed in the southern United Kingdom on 15 June 2005 and moved through the area where a large number of observational instruments were deployed as part of the Convective Storm Initiation Project. Earlier, a convergence line had formed downstream of Devon in the southwest of the United Kingdom in a southwesterly airflow, along which a series of light showers had formed. The depth of these showers was limited by a capping inversion, or lid, at around 2.5 km. The deep thunderstorm convection developed from one of these showers when the convection broke through the lid and ascended up to the next inversion, associated with a tropopause fold at around 6 km. A series of clear-air reflectivity RHIs are used to map the height of the capping inversion and its lifting resulting from the ascent along the convergence line. The origins of the lid are tracked back to some descent from the midtroposphere along dry adiabats. The strength of the lid was weaker along a northwest-to-southeast-oriented region located behind an overrunning upper cold front. The transition from shallow to deep convection occurred where this region with a weaker lid intersected the region with a raised lid, oriented southwest to northeast, downstream of Devon. A very high resolution forecast model that is being developed by the Met Office predicted the isolated thunderstorm successfully. This success depended on the accurate representation of the following two scales: the synoptic-scale and the surface-forced mesoscale convergence line. The interaction between these scales localized the convection sufficiently in space and time for the initiation and subsequent development to be highly predictable despite the relatively poor representation in the model of processes at the cloud scale.This work was funded from the Natural Environment Research Council and the Met Office National Meteorology Programme

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

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

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

Trace gas/aerosol boundary concentrations and their impacts on continental-scale AQMEII modeling domains

Copyright 2011 Elsevier B.V., All rights reserved.Over twenty modeling groups are participating in the Air Quality Model Evaluation International Initiative (AQMEII) in which a variety of mesoscale photochemical and aerosol air quality modeling systems are being applied to continental-scale domains in North America and Europe for 2006 full-year simulations for model inter-comparisons and evaluations. To better understand the reasons for differences in model results among these participating groups, each group was asked to use the same source of emissions and boundary concentration data for their simulations. This paper describes the development and application of the boundary concentration data for this AQMEII modeling exercise. The European project known as GEMS (Global and regional Earth-system Monitoring using Satellite and in-situ data) has produced global-scale re-analyses of air quality for several years, including 2006 (http://gems.ecmwf.int). The GEMS trace gas and aerosol data were made available at 3-hourly intervals on a regular latitude/longitude grid of approximately 1.9° resolution within 2 "cut-outs" from the global model domain. One cut-out was centered over North America and the other over Europe, covering sufficient spatial domain for each modeling group to extract the necessary time- and space-varying (horizontal and vertical) concentrations for their mesoscale model boundaries. Examples of the impact of these boundary concentrations on the AQMEII continental simulations are presented to quantify the sensitivity of the simulations to boundary concentrations. In addition, some participating groups were not able to use the GEMS data and instead relied upon other sources for their boundary concentration specifications. These are noted, and the contrasting impacts of other data sources for boundary data are presented. How one specifies four-dimensional boundary concentrations for mesoscale air quality simulations can have a profound impact on the model results, and hence, this aspect of data preparation must be performed with considerable care.Peer reviewedFinal Accepted Versio

A ‘warm path’ for Gulf Stream–troposphere interactions

Warm advection by the Gulf Stream creates a characteristic ‘tongue’ of warm water leaving a strong imprint on the sea surface temperature (SST) distribution in the western North Atlantic. This study aims at quantifying the climatological impact of this feature on cyclones travelling across this region in winter using a combination of reanalysis data and numerical experiments. It is suggested that the Gulf Stream ‘warm tongue’ is conducive to enhanced upward motion in cyclones because (i) it helps maintain a high equivalent potential temperature of air parcels at low levels which favors deep ascent in the warm conveyor belt of cyclones and (ii) because the large SST gradients to the north of the warm tongue drive a thermally direct circulation reinforcing and, possibly, destabilizing, the transverse circulation embedded in cyclones. This hypothesis is confirmed by comparing simulations at 12 km resolution from the Met Office Unified Model forced with realistic SST distribution to simulations with an SST distribution from which the Gulf Stream warm tongue was artificially removed or made colder by . It is also supported by a dynamical diagnostic applied to the ERA interim data-set over the wintertime period (1979–2012). The mechanism of oceanic forcing highlighted in this study is associated with near thermal equilibration of low level air masses with SST in the warm sector of cyclones passing over the Gulf Stream warm tongue, which is in sharp contrast to what occurs in their cold sector. It is suggested that this ‘warm path’ for the climatic impact of the Gulf Stream on the North Atlantic storm-track is not currently represented in climate models because of their coarse horizontal resolution

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

Combined CloudSat-CALIPSO-MODIS retrievals of the properties of ice clouds

In this paper, data from spaceborne radar, lidar and infrared radiometers on the “A-Train” of satellites are combined in a variational algorithm to retrieve ice cloud properties. The method allows a seamless retrieval between regions where both radar and lidar are sensitive to the regions where one detects the cloud. We first implement a cloud phase identification method, including identification of supercooled water layers using the lidar signal and temperature to discriminate ice from liquid. We also include rigorous calculation of errors assigned in the variational scheme. We estimate the impact of the microphysical assumptions on the algorithm when radiances are not assimilated by evaluating the impact of the change in the area-diameter and the density-diameter relationships in the retrieval of cloud properties. We show that changes to these assumptions affect the radar-only and lidar-only retrieval more than the radar-lidar retrieval, although the lidar-only extinction retrieval is only weakly affected. We also show that making use of the molecular lidar signal beyond the cloud as a constraint on optical depth, when ice clouds are sufficiently thin to allow the lidar signal to penetrate them entirely, improves the retrieved extinction. When infrared radiances are available, they provide an extra constraint and allow the extinction-to-backscatter ratio to vary linearly with height instead of being constant, which improves the vertical distribution of retrieved cloud properties