Modeling canopy-induced turbulence in the Earth system: a unified parameterization of turbulent exchange within plant canopies and the roughness sublayer (CLM-ml v0)

Land surface models used in climate models neglect the roughness sublayer and parameterize within-canopy turbulence in an ad hoc manner. We implemented a roughness sublayer turbulence parameterization in a multilayer canopy model (CLM-ml v0) to test if this theory provides a tractable parameterization extending from the ground through the canopy and the roughness sublayer. We compared the canopy model with the Community Land Model (CLM4.5) at seven forest, two grassland, and three cropland AmeriFlux sites over a range of canopy heights, leaf area indexes, and climates. CLM4.5 has pronounced biases during summer months at forest sites in midday latent heat flux, sensible heat flux, gross primary production, nighttime friction velocity, and the radiative temperature diurnal range. The new canopy model reduces these biases by introducing new physics. Advances in modeling stomatal conductance and canopy physiology beyond what is in CLM4.5 substantially improve model performance at the forest sites. The signature of the roughness sublayer is most evident in nighttime friction velocity and the diurnal cycle of radiative temperature, but is also seen in sensible heat flux. Within-canopy temperature profiles are markedly different compared with profiles obtained using Monin–Obukhov similarity theory, and the roughness sublayer produces cooler daytime and warmer nighttime temperatures. The herbaceous sites also show model improvements, but the improvements are related less systematically to the roughness sublayer parameterization in these canopies. The multilayer canopy with the roughness sublayer turbulence improves simulations compared with CLM4.5 while also advancing the theoretical basis for surface flux parameterizations

Composition algebras and the two faces of G2G_{2}

We consider composition and division algebras over the real numbers: We note two r\^oles for the group $G_{2}$: as automorphism group of the octonions and as the isotropy group of a generic 3-form in 7 dimensions. We show why they are equivalent, by means of a regular metric. We express in some diagrams the relation between some pertinent groups, most of them related to the octonions. Some applications to physics are also discussed.Comment: 11 pages, 3 figure

Effects of white roofs on urban temperature in a global climate model

(c) American Geophysical Union. This article can be found on the publisher's website at http://dx.doi.org/10.1029/2009GL042194Increasing the albedo of urban surfaces has received attention as a strategy to mitigate urban heat islands. Here, the effects of globally installing white roofs are assessed using an urban canyon model coupled to a global climate model. Averaged over all urban areas, the annual mean heat island decreased by 33%. Urban daily maximum temperature decreased by 0.6°C and daily minimum temperature by 0.3°C. Spatial variability in the heat island response is caused by changes in absorbed solar radiation and specification of roof thermal admittance. At high latitudes in winter, the increase in roof albedo is less effective at reducing the heat island due to low incoming solar radiation, the high albedo of snow intercepted by roofs, and an increase in space heating that compensates for reduced solar heating. Global space heating increased more than air conditioning decreased, suggesting that end-use energy costs must be considered in evaluating the benefits of white roofs

A moving point approach to model shallow ice sheets: a study case with radially-symmetrical ice sheets

Predicting the evolution of ice sheets requires numerical models able to accurately track the migration of ice sheet continental margins or grounding lines. We introduce a physically based moving point approach for the flow of ice sheets based on the conservation of local masses. This allows the ice sheet margins to be tracked explicitly and the waiting time behaviours to be modelled efficiently. A finite difference moving point scheme is derived and applied in a simplified context (continental radially-symmetrical shallow ice approximation). The scheme, which is inexpensive, is validated by comparing the results with moving-margin exact solutions and steady states. In both cases the scheme is able to track the position of the ice sheet margin with high precision

Data assimilation for moving mesh methods with an application to ice sheet modelling

We develop data assimilation techniques for nonlinear dynamical systems modelled by moving mesh methods. Such techniques are valuable for explicitly tracking interfaces and boundaries in evolving systems. The unique aspect of these assimilation techniques is that both the states of the system and the positions of the mesh points are updated simultaneously using physical observations. Covariances between states and mesh points are generated either by a correlation structure function in a variational context or by ensemble methods. The application of the techniques is demonstrated on a one-dimensional model of a grounded shallow ice sheet. It is shown, using observations of surface elevation and/or surface ice velocities, that the techniques predict the evolution of the ice sheet margin and the ice thickness accurately and efficiently. This approach also allows the straightforward assimilation of observations of the position of the ice sheet margin

Constraining the date of a seasonally ice-free Arctic using a simple model

State-of-the-art climate models simulate a large spread in the projected decline of Arctic sea-ice area (SIA) over the 21st century. Here we diagnose causes of this intermodel spread using a model that approximates future SIA based on present SIA and the sensitivity of SIA to Arctic temperatures. This model accounts for 70-95% of the intermodel variance, with the majority of the spread arising from present-day biases. The remaining spread arises from model differences in Arctic warming, with some contribution from the local sea-ice sensitivity. Using observations to constrain the projections moves the probability of an ice-free Arctic forward by 10-35 years. Under a high-emissions scenario, an ice-free Arctic will likely (66% probability) occur in September around 2046 and from July-October around 2059. Under a medium-emissions scenario, this date occurs around 2051 in September and 2080 from July-October. These observation-based constraints imply ice-free Arctic summers are approaching faster than previously thought

An Urban Parameterization for a Global Climate Model. Part II: Sensitivity to Input Parameters and the Simulated Urban Heat Island in Offline Simulations

© 2008 American Meteorological SocietyIn a companion paper, the authors presented a formulation and evaluation of an urban parameterization designed to represent the urban energy balance in the Community Land Model. Here the robustness of the model is tested through sensitivity studies and the model’s ability to simulate urban heat islands in different environments is evaluated. Findings show that heat storage and sensible heat flux are most sensitive to uncertainties in the input parameters within the atmospheric and surface conditions considered here. The sensitivity studies suggest that attention should be paid not only to characterizing accurately the structure of the urban area (e.g., height-to-width ratio) but also to ensuring that the input data reflect the thermal admittance properties of each of the city surfaces. Simulations of the urban heat island show that the urban model is able to capture typical observed characteristics of urban climates qualitatively. In particular, the model produces a significant heat island that increases with height-to-width ratio. In urban areas, daily minimum temperatures increase more than daily maximum temperatures, resulting in a reduced diurnal temperature range relative to equivalent rural environments. The magnitude and timing of the heat island vary tremendously depending on the prevailing meteorological conditions and the characteristics of surrounding rural environments. The model also correctly increases the Bowen ratio and canopy air temperatures of urban systems as impervious fraction increases. In general, these findings are in agreement with those observed for real urban ecosystems. Thus, the model appears to be a useful tool for examining the nature of the urban climate within the framework of global climate models

Moduli spaces of G2 manifolds

This paper is a review of current developments in the study of moduli spaces of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional holonomy group G2. Although they are odd-dimensional, in many ways they can be considered as an analogue of Calabi-Yau manifolds in 7 dimensions. They play an important role in physics as natural candidates for supersymmetric vacuum solutions of M-theory compactifications. Despite the physical motivation, many of the results are of purely mathematical interest. Here we cover the basics of G2 manifolds, local deformation theory of G2 structures and the local geometry of the moduli spaces of G2 structures.Comment: 31 pages, 2 figure

On linearly related sequences of derivatives of orthogonal polynomials

We discuss an inverse problem in the theory of (standard) orthogonal polynomials involving two orthogonal polynomial families (Pn)n and (Qn)n whose derivatives of higher orders m and k (resp.) are connected by a linear algebraic structure relation such as for all n=0,1,2,..., where M and N are fixed nonnegative integer numbers, and ri,n and si,n are given complex parameters satisfying some natural conditions. Let u and v be the moment regular functionals associated with (Pn)n and (Qn)n (resp.). Assuming 0[less-than-or-equals, slant]m[less-than-or-equals, slant]k, we prove the existence of four polynomials [Phi]M+m+i and [Psi]N+k+i, of degrees M+m+i and N+k+i (resp.), such that the (k-m)th-derivative, as well as the left-product of a functional by a polynomial, being defined in the usual sense of the theory of distributions. If k=m, then u and v are connected by a rational modification. If k=m+1, then both u and v are semiclassical linear functionals, which are also connected by a rational modification. When k>m, the Stieltjes transform associated with u satisfies a non-homogeneous linear ordinary differential equation of order k-m with polynomial coefficients.http://www.sciencedirect.com/science/article/B6WK2-4SSNDCC-2/1/2844d686d4f273e5ddf7b4d7146c9ee

An examination of urban heat island characteristics in a global climate model

This is the publisher's version, also available electronically from http://onlinelibrary.wiley.com/doi/10.1002/joc.2201/abstract;jsessionid=8D053A7D1E2894F4658DDA991ACAB056.f04t03.A parameterization for urban surfaces has been incorporated into the Community Land Model as part of the Community Climate System Model. The parameterization allows global simulation of the urban environment, in particular the temperature of cities and thus the urban heat island. Here, the results from climate simulations for the AR4 A2 emissions scenario are presented. Present-day annual mean urban air temperatures are up to 4 °C warmer than surrounding rural areas. Averaged over all urban areas resolved in the model, the heat island is 1.1 °C, which is 46% of the simulated mid-century warming over global land due to greenhouse gases. Heat islands are generally largest at night as evidenced by a larger urban warming in minimum than maximum temperature, resulting in a smaller diurnal temperature range compared to rural areas. Spatial and seasonal variability in the heat island is caused by urban to rural contrasts in energy balance and the different responses of these surfaces to the seasonal cycle of climate. Under simulation constraints of no urban growth and identical urban/rural atmospheric forcing, the urban to rural contrast decreases slightly by the end of the century. This is primarily a different response of rural and urban areas to increased long-wave radiation from a warmer atmosphere. The larger storage capacity of urban areas buffers the increase in long-wave radiation such that urban night-time temperatures warm less than rural. Space heating and air conditioning processes add about 0.01 W m−2 of heat distributed globally, which results in a small increase in the heat island. The significant differences between urban and rural surfaces demonstrated here imply that climate models need to account for urban surfaces to more realistically evaluate the impact of climate change on people in the environment where they live. Copyright © 2010 Royal Meteorological Societ