Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Are the spatial patterns of weeds scale-invariant?

In previous empirical and modelling studies of rare species and weeds, evidence of fractal behaviour has been found. We propose that weeds in modern agricultural systems may be managed close to critical population dynamic thresholds, below which their rates of increase will be negative and where scale-invariance may be expected as a consequence. We collected detailed spatial data on five contrasting species over a period of three years in a primarily arable field. Counts in 20×20 cm contiguous quadrats, 225,000 in 1998 and 84,375 thereafter, could be re-structured into a wide range of larger quadrat sizes. These were analysed using three methods based on correlation sum, incidence and conditional incidence. We found non-trivial scale invariance for species occurring at low mean densities and where they were strongly aggregated. The fact that the scale-invariance was not found for widespread species occurring at higher densities suggests that the scaling in agricultural weed populations may, indeed, be related to critical phenomena.

An ASIFT-based local registration method for satellite imagery

Imagery registration is a fundamental step, which greatly affects later processes in image mosaic, multi-spectral image fusion, digital surface modelling, etc., where the final solution needs blending of pixel information from more than one images. It is highly desired to find a way to identify registration regions among input stereo image pairs with high accuracy, particularly in remote sensing applications in which ground control points (GCPs) are not always available, such as in selecting a landing zone on an outer space planet. In this paper, a framework for localization in image registration is developed. It strengthened the local registration accuracy from two aspects: less reprojection error and better feature point distribution. Affine scale-invariant feature transform (ASIFT) was used for acquiring feature points and correspondences on the input images. Then, a homography matrix was estimated as the transformation model by an improved random sample consensus (IM-RANSAC) algorithm. In order to identify a registration region with a better spatial distribution of feature points, the Euclidean distance between the feature points is applied (named the S criterion). Finally, the parameters of the homography matrix were optimized by the Levenberg–Marquardt (LM) algorithm with selective feature points from the chosen registration region. In the experiment section, the Chang’E-2 satellite remote sensing imagery was used for evaluating the performance of the proposed method. The experiment result demonstrates that the proposed method can automatically locate a specific region with high registration accuracy between input images by achieving lower root mean square error (RMSE) and better distribution of feature points.

The triggering of orographic rainbands by small-scale topography

The triggering of convective orographic rainbands by small-scale topographic features is investigated through observations of a banded precipitation event over the Oregon Coastal Range and simulations using a cloud-resolving numerical model. A quasi-idealized simulation of the observed event reproduces the bands in the radar observations, indicating the model’s ability to capture the physics of the band-formation process. Additional idealized simulations reinforce that the bands are triggered by lee waves past small-scale topographic obstacles just upstream of the nominal leading edge of the orographic cloud. Whether a topographic obstacle in this region is able to trigger a strong rainband depends on the phase of its lee wave at cloud entry. Convective growth only occurs downstream of obstacles that give rise to lee-wave-induced displacements that create positive vertical velocity anomalies w_c and nearly zero buoyancy anomalies b_c as air parcels undergo saturation. This relationship is quantified through a simple analytic condition involving w_c, b_c, and the static stability N_m^2 of the cloud mass. Once convection is triggered, horizontal buoyancy gradients in the cross-flow direction generate circulations that align the bands parallel to the flow direction.

Atmospheric factors governing banded orographic convection

Atmospheric factors Governing Banded Orographic Convection The three-dimensional structure of shallow orographic convection is investigated through simulations performed with a cloud-resolving numerical model. In moist flows that overcome a given topographic barrier to form statically unstable cap clouds, the organization of the convection depends on both the atmospheric structure and the mechanism by which the convection is initiated. Convection initiated by background thermal fluctuations embedded in the flow over a smooth mountain (without any small-scale topographic features) tends to be cellular and disorganized except that shear-parallel bands may form in flows with strong unidirectional vertical shear. The development of well-organized bands is favored when there is weak static instability inside the cloud and when the dry air surrounding the cloud is strongly stable. These bands move with the flow and distribute their cumulative precipitation evenly over the mountain upslope. Similar shear-parallel bands also develop in flows where convection is initiated by small-scale topographic noise superimposed onto the main mountain profile, but in this case stronger circulations are also triggered that create stationary rainbands parallel to the low-level flow. This second dominant mode, which is less sensitive to the atmospheric structure and the strength of forcing, is triggered by lee waves that form over small-scale topographic bumps near the upstream edge of the main orographic cloud. Due to their stationarity, these flow-parallel bands can produce locally heavy precipitation amounts.

Reduced space optimal interpolation of daily rain gauge precipitation in Switzerland

The coarse spacing of automatic rain gauges complicates near-real- time spatial analyses of precipitation. We test the possibility of improving such analyses by considering, in addition to the in situ measurements, the spatial covariance structure inferred from past observations with a denser network. To this end, a statistical reconstruction technique, reduced space optimal interpolation (RSOI), is applied over Switzerland, a region of complex topography. RSOI consists of two main parts. First, principal component analysis (PCA) is applied to obtain a reduced space representation of gridded high- resolution precipitation fields available for a multiyear calibration period in the past. Second, sparse real-time rain gauge observations are used to estimate the principal component scores and to reconstruct the precipitation field. In this way, climatological information at higher resolution than the near-real-time measurements is incorporated into the spatial analysis. PCA is found to efficiently reduce the dimensionality of the calibration fields, and RSOI is successful despite the difficulties associated with the statistical distribution of daily precipitation (skewness, dry days). Examples and a systematic evaluation show substantial added value over a simple interpolation technique that uses near-real-time observations only. The benefit is particularly strong for larger- scale precipitation and prominent topographic effects. Small-scale precipitation features are reconstructed at a skill comparable to that of the simple technique. Stratifying the reconstruction method by the types of weather type classifications yields little added skill. Apart from application in near real time, RSOI may also be valuable for enhancing instrumental precipitation analyses for the historic past when direct observations were sparse.

Theoretical insights into bacterial chemotaxis

Research into understanding bacterial chemotactic systems has become a paradigm for Systems Biology. Experimental and theoretical researchers have worked hand-in-hand for over 40 years to understand the intricate behavior driving bacterial species, in particular how such small creatures, usually not more than 5 µm in length, detect and respond to small changes in their extracellular environment. In this review we highlight the importance that theoretical modeling has played in providing new insight and understanding into bacterial chemotaxis. We begin with an overview of the bacterial chemotaxis sensory response, before reviewing the role of theoretical modeling in understanding elements of the system on the single cell scale and features underpinning multiscale extensions to population models. WIREs Syst Biol Med 2012 doi: 10.1002/wsbm.1168 For further resources related to this article, please visit the WIREs website.

Determination of eddy-diffusivity in the lowermost stratosphere

We present a 2D-advection-diffusion model that simulates the main transport pathways influencing tracer distributions in the lowermost stratosphere (LMS). The model describes slow diabatic descent of aged stratospheric air, vertical (cross-isentropic) and horizontal (along isentropes) diffusion within the LMS and across the tropopause using equivalent latitude and potential temperature coordinates. Eddy diffusion coefficients parameterize the integral effect of dynamical processes leading to small scale turbulence and mixing. They were specified by matching model simulations to observed CO distributions. Interestingly, the model suggests mixing across isentropes to be more important than horizontal mixing across surfaces of constant equivalent latitude, shining new light on the interplay between various transport mechanisms in the LMS. The model achieves a good description of the small scale tracer features at the tropopause with squared correlation coefficients R2 = 0.72…0.94.

The biogeophysical climatic impacts of anthropogenic land use change during the Holocene

The first agricultural societies were established around 10 ka BP and had spread across much of Europe and southern Asia by 5.5 ka BP with resultant anthropogenic deforestation for crop and pasture land. Various studies (e.g. Joos et al., 2004; Kaplan et al., 2011; Mitchell et al., 2013) have attempted to assess the biogeochemical implications for Holocene climate in terms of increased carbon dioxide and methane emissions. However, less work has been done to examine the biogeophysical impacts of this early land use change. In this study, global climate model simulations with Hadley Centre Coupled Model version 3 (HadCM3) were used to examine the biogeophysical effects of Holocene land cover change on climate, both globally and regionally, from the early Holocene (8 ka BP) to the early industrial era (1850 CE). Two experiments were performed with alternative descriptions of past vegetation: (i) one in which potential natural vegetation was simulated by Top-down Representation of Interactive Foliage and Flora Including Dynamics (TRIFFID) but without land use changes and (ii) one where the anthropogenic land use model Kaplan and Krumhardt 2010 (KK10; Kaplan et al., 2009, 2011) was used to set the HadCM3 crop regions. Snapshot simulations were run at 1000-year intervals to examine when the first signature of anthropogenic climate change can be detected both regionally, in the areas of land use change, and globally. Results from our model simulations indicate that in regions of early land disturbance such as Europe and south-east Asia detectable temperature changes, outside the normal range of variability, are encountered in the model as early as 7 ka BP in the June–July–August (JJA) season and throughout the entire annual cycle by 2–3 ka BP. Areas outside the regions of land disturbance are also affected, with virtually the whole globe experiencing significant temperature changes (predominantly cooling) by the early industrial period. The global annual mean temperature anomalies found in our single model simulations were −0.22 at 1850 CE, −0.11 at 2 ka BP, and −0.03 °C at 7 ka BP. Regionally, the largest temperature changes were in Europe with anomalies of −0.83 at 1850 CE, −0.58 at 2 ka BP, and −0.24 °C at 7 ka BP. Large-scale precipitation features such as the Indian monsoon, the Intertropical Convergence Zone (ITCZ), and the North Atlantic storm track are also impacted by local land use and remote teleconnections. We investigated how advection by surface winds, mean sea level pressure (MSLP) anomalies, and tropospheric stationary wave train disturbances in the mid- to high latitudes led to remote teleconnections.

Spatial covariation of Azotobacter abundance and soil properties: A case study using the wavelet transform

The soil microflora is very heterogeneous in its spatial distribution. The origins of this heterogeneity and its significance for soil function are not well understood. A problem for understanding spatial variation better is the assumption of statistical stationarity that is made in most of the statistical methods used to assess it. These assumptions are made explicit in geostatistical methods that have been increasingly used by soil biologists in recent years. Geostatistical methods are powerful, particularly for local prediction, but they require the assumption that the variability of a property of interest is spatially uniform, which is not always plausible given what is known about the complexity of the soil microflora and the soil environment. We have used the wavelet transform, a relatively new innovation in mathematical analysis, to investigate the spatial variation of abundance of Azotobacter in the soil of a typical agricultural landscape. The wavelet transform entails no assumptions of stationarity and is well suited to the analysis of variables that show intermittent or transient features at different spatial scales. In this study, we computed cross-variograms of Azotobacter abundance with the pH, water content and loss on ignition of the soil. These revealed scale-dependent covariation in all cases. The wavelet transform also showed that the correlation of Azotobacter abundance with all three soil properties depended on spatial scale, the correlation generally increased with spatial scale and was only significantly different from zero at some scales. However, the wavelet analysis also allowed us to show how the correlation changed across the landscape. For example, at one scale Azotobacter abundance was strongly correlated with pH in part of the transect, and not with soil water content, but this was reversed elsewhere on the transect. The results show how scale-dependent variation of potentially limiting environmental factors can induce a complex spatial pattern of abundance in a soil organism. The geostatistical methods that we used here make assumptions that are not consistent with the spatial changes in the covariation of these properties that our wavelet analysis has shown. This suggests that the wavelet transform is a powerful tool for future investigation of the spatial structure and function of soil biota. (c) 2006 Elsevier Ltd. All rights reserved.

Results of PMIP2 coupled simulations of the mid-Holocene and Last Glacial Maximum, Part 1: experiments and large-scale features

A set of coupled ocean-atmosphere simulations using state of the art climate models is now available for the Last Glacial Maximum and the Mid-Holocene through the second phase of the Paleoclimate Modeling Intercomparison Project (PMIP2). This study presents the large-scale features of the simulated climates and compares the new model results to those of the atmospheric models from the first phase of the PMIP, for which sea surface temperature was prescribed or computed using simple slab ocean formulations. We consider the large-scale features of the climate change, pointing out some of the major differences between the different sets of experiments. We show in particular that systematic differences between PMIP1 and PMIP2 simulations are due to the interactive ocean, such as the amplification of the African monsoon at the Mid-Holocene or the change in precipitation in mid-latitudes at the LGM. Also the PMIP2 simulations are in general in better agreement with data than PMIP1 simulations.

Climate response to basin-scale warming and cooling of the North Atlantic Ocean

Using experiments with an atmospheric general circulation model, the climate impacts of a basin-scale warming or cooling of the North Atlantic Ocean are investigated. Multidecadal fluctuations with this pattern were observed during the twentieth century, and similar variations--but with larger amplitude--are believed to have occurred in the more distant past. It is found that in all seasons the response to warming the North Atlantic is strongest, in the sense of highest signal-to-noise ratio, in the Tropics. However there is a large seasonal cycle in the climate impacts. The strongest response is found in boreal summer and is associated with suppressed precipitation and elevated temperatures over the lower-latitude parts of North and South America. In August­-September-­October there is a significant reduction in the vertical shear in the main development region for Atlantic hurricanes. In winter and spring, temperature anomalies over land in the extratropics are governed by dynamical changes in circulation rather than simply reflecting a thermodynamic response to the warming or cooling of the ocean. The tropical climate response is primarily forced by the tropical SST anomalies, and the major features are in line with simple models of the tropical circulation response to diabatic heating anomalies. The extratropical climate response is influenced both by tropical and higher-latitude SST anomalies and exhibits nonlinear sensitivity to the sign of the SST forcing. Comparisons with multidecadal changes in sea level pressure observed in the twentieth century support the conclusion that the impact of North Atlantic SST change is most important in summer, but also suggest a significant influence in lower latitudes in autumn and winter. Significant climate impacts are not restricted to the Atlantic basin, implying that the Atlantic Ocean could be an important driver of global decadal variability. The strongest remote impacts are found to occur in the tropical Pacific region in June­-August and September­-November. Surface anomalies in this region have the potential to excite coupled ocean­atmosphere feedbacks, which are likely to play an important role in shaping the ultimate climate response.