Recursive formulas for the motivic Milnor basis

We give recursive formulas for the generating elements in the Milnor basis of the mod 2 motivic Steenrod algebra.Comment: 10 page

Technical note: The libRadtran software package for radiative transfer calculations - description and examples of use

The libRadtran software package is a suite of tools for radiative transfer calculations in the Earth's atmosphere. Its main tool is the uvspec program. It may be used to compute radiances, irradiances and actinic fluxes in the solar and terrestrial part of the spectrum. The design of uvspec allows simple problems to be easily solved using defaults and included data, hence making it suitable for educational purposes. At the same time the flexibility in how and what input may be specified makes it a powerful and versatile tool for research tasks. The uvspec tool and additional tools included with libRadtran are described and realistic examples of their use are given. The libRadtran software package is available from http://www.libradtran.org

Radiation transport in cloudy and aerosol loaded atmospheres

Thesis (Ph.D.) University of Alaska Fairbanks, 1992The equation for radiation transport in vertical inhomogeneous absorbing, scattering, and emitting atmospheres is derived from first principles. It is cast in a form amenable to solution, and solved using the discrete ordinate method. Based on the discrete ordinate solution a new computationally efficient and stable two-stream algorithm which accounts for spherical geometry is developed. The absorption and scattering properties of atmospheric molecules and particulate matter is discussed. The absorption cross sections of the principal absorbers in the atmosphere, H\sb2O, CO\sb2 and O\sb3, vary erratically and rapidly with wavelength. To account for this variation, the correlated-k distribution method is employed to simplify the integration over wavelength necessary for calculation of warming/cooling rates. The radiation model, utilizing appropriate absorption and scattering cross sections, is compared with ultraviolet radiation measurements. The comparison suggests that further experiments are required. Ultraviolet (UV) and photosynthetically active radiation (PAR) is computed for high and low latitudes for clear and cloudy skies under different ozone concentrations. An ozone depletion increases UV-B radiation detrimental to life. Water clouds diminish UV-B, UV-A and PAR for low surface albedos and increase them for high albedos. The relative amount of harmful UV-B increases on overcast days. The daily radiation doses exhibit small monthly variations at low latitudes but vary by a factor of 3 at high latitudes. Photodissociation and warming/cooling rates are calculated for clear skies, aerosol loaded atmospheres, and atmospheres with cirrus and water clouds. After major volcanic explosions aerosols change O\sb3 and NO\sb2 photodissociation rates by 20%. Both aged aerosols and cirrus clouds have little effect on photodissociation rates. Water clouds increase $(\sim$100%) photodissociation rates that are sensitive to visible radiation above the cloud. Solar warming rates vary by 50% in the stratosphere due to changing surface albedo. Water clouds have a similar effect. The net effect of cirrus clouds is to warm the troposphere and the stratosphere. Only extreme volcanic aerosol loadings affect the terrestrial warming rate, causing warming below the aerosol layer and cooling above it. Aerosols give increased solar warming above the aerosol layer and cooling below it

A model sensitivity study of the impact of clouds on satellite detection and retrieval of volcanic ash

Volcanic ash is commonly observed by infrared detectors on board Earth-orbiting satellites. In the presence of ice and/or liquid-water clouds, the detected volcanic ash signature may be altered. In this paper the sensitivity of detection and retrieval of volcanic ash to the presence of ice and liquid-water clouds was quantified by simulating synthetic equivalents to satellite infrared images with a 3-D radiative transfer model. The sensitivity study was made for the two recent eruptions of Eyjafjallajokull (2010) and Grimsvotn (2011) using realistic water and ice clouds and volcanic ash clouds. The water and ice clouds were taken from European Centre for Medium-RangeWeather Forecast (ECMWF) analysis data and the volcanic ash cloud fields from simulations by the Lagrangian particle dispersion model FLEXPART. The radiative transfer simulations were made both with and without ice and liquid-water clouds for the geometry and channels of the Spinning Enhanced Visible and Infrared Imager (SEVIRI). The synthetic SEVIRI images were used as input to standard reverse absorption ash detection and retrieval methods. Ice and liquid-water clouds were on average found to reduce the number of detected ash-affected pixels by 6-12 %. However, the effect was highly variable and for individual scenes up to 40% of pixels with mass loading > 0 : 2 gm 2 could not be detected due to the presence of water and ice clouds. For coincident pixels, i. e. pixels where ash was both present in the FLEXPART (hereafter referred to as "Flexpart") simulation and detected by the algorithm, the presence of clouds overall increased the retrieved mean mass loading for the Eyjafjallajokull (2010) eruption by about 13 %,while for the Grimsvotn (2011) eruption ash-mass loadings the effect was a 4% decrease of the retrieved ash-mass loading. However, larger differences were seen between scenes (standard deviations of +/- 30 and +/- 20% for Eyjafjallajokull and Grimsvotn, respectively) and even larger ones within scenes. The impact of ice and liquid-water clouds on the detection and retrieval of volcanic ash, implies that to fully appreciate the location and amount of ash, hyperspectral and spectral band measurements by satellite instruments should be combined with ash dispersion modelling