On the subdivision strategy in adaptive quadrature algorithms

AbstractThe subdivision procedure used in most available adaptive quadrature codes is a simple bisection of the chosen interval. Thus the interval is divided in two equally sized parts. In this paper we present a subdivision strategy which gives three nonequally sized parts. The subdivision points are found using only available information. The strategy has been implemented in the QUADPACK code DQAG and tested using the “performance profile” testing technique. We present test results showing a significant reduction in the number of function evaluations compared to the standard bisection procedure on most test families of integrands

Ozone formation during an episode over Europe: A 3-D chemical/transport model simulation

A 3-D regional photochemical tracer/transport model for Europe and the Eastern Atlantic has been developed based on the NASA/GISS CTM. The model resolution is 4x5 degrees latitude and longitude with 9 layers in the vertical (7 in the troposphere). Advective winds, convection statistics and other meteorological data from the NASA/GISS GCM are used. An extensive gas-phase chemical scheme based on the scheme used in our global 2D model has been incorporated in the 3D model. In this work ozone formation in the troposphere is studied with the 3D model during a 5 day period starting June 30. Extensive local ozone production is found and the relationship between the source regions and the downwind areas are discussed. Variations in local ozone formation as a function of total emission rate, as well as the composition of the emissions (HC/NO(x)) ratio and isoprene emissions) are elucidated. An important vertical transport process in the troposphere is by convective clouds. The 3D model includes an explicit parameterization of this process. It is shown that this process has significant influence on the calculated surface ozone concentrations

Implementing a sectional scheme for early aerosol growth from new particle formation in the Norwegian Earth System Model v2 : comparison to observations and climate impacts

Aerosol-cloud interactions contribute to a large portion of the spread in estimates of climate forcing, climate sensitivity and future projections. An important part of this uncertainty is how much new particle formation (NPF) contributes to cloud condensation nuclei (CCN) and, furthermore, how this changes with changes in anthropogenic emissions. Incorporating NPF and early growth in Earth system models (ESMs) is, however, challenging due to uncertain parameters (e.g. participating vapours), structural issues (numerical description of growth from similar to 1 to similar to 100 nm) and the large scale of an ESM grid compared to the NPF scale. A common approach in ESMs is to represent the particle size distribution by a certain number of log-normal modes. Sectional schemes, on the other hand, in which the size distribution is represented by bins, are considered closer to first principles because they do not make an a priori assumption about the size distribution. In order to improve the representation of early growth, we have implemented a sectional scheme for the smallest particles (5-39.6 nm diameter) in the Norwegian Earth System Model (NorESM), feeding particles into the original aerosol scheme. This is, to our knowledge, the first time such an approach has been tried. We find that including the sectional scheme for early growth improves the aerosol number concentration in the model when comparing against observations, particularly in the 50-100 nm diameter range. Furthermore, we find that the model with the sectional scheme produces much fewer particles than the original scheme in polluted regions, while it produces more in remote regions and the free troposphere, indicating a potential impact on the estimated aerosol forcing. Finally, we analyse the effect on cloud-aerosol interactions and find that the effect of changes in NPF efficiency on clouds is highly heterogeneous in space. While in remote regions, more efficient NPF leads to higher cloud droplet number concentration (CDNC), in polluted regions the opposite is in fact the case.Peer reviewe

BVOC-aerosol-climate feedbacks investigated using NorESM

Both higher temperatures and increased CO2 concentrations are (separately) expected to increase the emissions of biogenic volatile organic compounds (BVOCs). This has been proposed to initiate negative climate feedback mechanisms through increased formation of secondary organic aerosol (SOA). More SOA can make the clouds more reflective, which can provide a cooling. Furthermore, the increase in SOA formation has also been proposed to lead to increased aerosol scattering, resulting in an increase in diffuse radiation. This could boost gross primary production (GPP) and further increase BVOC emissions. In this study, we have used the Norwegian Earth System Model (NorESM) to investigate both these feedback mechanisms. Three sets of experiments were set up to quantify the feedback with respect to (1) doubling the CO2, (2) increasing temperatures corresponding to a doubling of CO2 and (3) the combined effect of both doubling CO2 and a warmer climate. For each of these experiments, we ran two simulations, with identical setups, except for the BVOC emissions. One simulation was run with interactive BVOC emissions, allowing the BVOC emissions to respond to changes in CO2 and/or climate. In the other simulation, the BVOC emissions were fixed at present-day conditions, essentially turning the feedback off. The comparison of these two simulations enables us to investigate each step along the feedback as well as estimate their overall relevance for the future climate. We find that the BVOC feedback can have a significant impact on the climate. The annual global BVOC emissions are up to 63 % higher when the feedback is turned on compared to when the feedback is turned off, with the largest response when both CO2 and climate are changed. The higher BVOC levels lead to the formation of more SOA mass (max 53 %) and result in more particles through increased new particle formation as well as larger particles through increased condensation. The corresponding changes in the cloud properties lead to a -0.43 W m(-2) stronger net cloud forcing. This effect becomes about 50 % stronger when the model is run with reduced anthropogenic aerosol emissions, indicating that the feedback will become even more important as we decrease aerosol and precursor emissions. We do not find a boost in GPP due to increased aerosol scattering on a global scale. Instead, the fate of the GPP seems to be controlled by the BVOC effects on the clouds. However, the higher aerosol scattering associated with the higher BVOC emissions is found to also contribute with a potentially important enhanced negative direct forcing (-0.06 W m(-2)). The global total aerosol forcing associated with the feedback is -0.49 W m(-2), indicating that it has the potential to offset about 13 % of the forcing associated with a doubling of CO2.Peer reviewe

Black carbon in the atmosphere and snow, from pre-industrial times until present

The distribution of black carbon (BC) in the atmosphere and the deposition of BC on snow surfaces since pre-industrial time until present are modelled with the Oslo CTM2 model. The model results are compared with observations including recent measurements of BC in snow in the Arctic. The global mean burden of BC from fossil fuel and biofuel sources increased during two periods. The first period, until 1920, is related to increases in emissions in North America and Europe, and the last period after 1970 are related mainly to increasing emissions in East Asia. Although the global burden of BC from fossil fuel and biofuel increases, in the Arctic the maximum atmospheric BC burden as well as in the snow was reached in 1960s, with a slight reduction thereafter. The global mean burden of BC from open biomass burning sources has not changed significantly since 1900. With current inventories of emissions from open biomass sources, the modelled burden of BC in snow and in the atmosphere north of 65° N is small compared to the BC burden of fossil fuel and biofuel origin. From the concentration changes radiative forcing time series due to the direct aerosol effect as well as the snow-albedo effect is calculated for BC from fossil fuel and biofuel. The calculated radiative forcing in 2000 for the direct aerosol effect is 0.35 W m<sup>−2</sup> and for the snow-albedo effect 0.016 W m<sup>−2</sup> in this study. Due to a southward shift in the emissions there is an increase in the lifetime of BC as well as an increase in normalized radiative forcing, giving a change in forcing per unit of emissions of 26 % since 1950

Metrics for Aggregating the Climate Effect of Different Emissions: A Unifying Framework. ESRI WP257, September 2008

Multi-gas approaches to climate change policies require a metric establishing “equivalences” among emissions of various species. Climate scientists and economists have proposed four classes of such metrics and debated their relative merits. We present a unifying framework that clarifies the relationships among them. We show that the Global Warming Potential, used in international law to compare greenhouse gases, is a special case of the Global Damage Potential, assuming (1) a finite time horizon, (2) a zero discount rate, (3) constant atmospheric concentrations, and (4) impacts that are proportional to radiactive forcing. We show that the Global Temperature change Potential is a special case of the Global Cost Potential, assuming (1) no induced technological change, and (2) a short-lived capital stock. We also show that the Global Cost Potential is a special case of the Global Damage Potential, assuming (1) zero damages below a threshold and (2) infinite damage after a threshold. The UN Framework Convention on Climate Change uses the Global Warming Potential, a simplified cost-benefit concept, even though the UNFCCC frames climate policy as a cost-effectiveness problem and should therefore use the Global Cost Potential or its simplification, the Global Temperature Potential