The composite-tendency RAW filter in semi-implicit integrations

The time discretization in weather and climate models introduces truncation errors that limit the accuracy of the simulations. Recent work has yielded a method for reducing the amplitude errors in leapfrog integrations from first-order to fifth-order. This improvement is achieved by replacing the Robert--Asselin filter with the RAW filter and using a linear combination of the unfiltered and filtered states to compute the tendency term. The purpose of the present paper is to apply the composite-tendency RAW-filtered leapfrog scheme to semi-implicit integrations. A theoretical analysis shows that the stability and accuracy are unaffected by the introduction of the implicitly treated mode. The scheme is tested in semi-implicit numerical integrations in both a simple nonlinear stiff system and a medium-complexity atmospheric general circulation model, and yields substantial improvements in both cases. We conclude that the composite-tendency RAW-filtered leapfrog scheme is suitable for use in semi-implicit integrations.

Land use and climate change impacts on soil organic carbon stocks in semi-arid Spain

Purpose The sensitivity of soil organic carbon to global change drivers, according to the depth profile, is receiving increasing attention because of its importance in the global carbon cycle and its potential feedback to climate change. A better knowledge of the vertical distribution of SOC and its controlling factors—the aim of this study—will help scientists predict the consequences of global change. Materials and methods The study area was the Murcia Province (S.E. Spain) under semiarid Mediterranean conditions. The database used consists of 312 soil profiles collected in a systematic grid, each 12 km2 covering a total area of 11,004 km2. Statistical analysis to study the relationships between SOC concentration and control factors in different soil use scenarios was conducted at fixed depths of 0–20, 20–40, 40–60, and 60–100 cm. Results and discussion SOC concentration in the top 40 cm ranged between 6.1 and 31.5 g kg−1, with significant differences according to land use, soil type and lithology, while below this depth, no differences were observed (SOC concentration 2.1–6.8 g kg−1). The ANOVA showed that land use was the most important factor controlling SOC concentration in the 0–40 cm depth. Significant differences were found in the relative importance of environmental and textural factors according to land use and soil depth. In forestland, mean annual precipitation and texture were the main predictors of SOC, while in cropland and shrubland, the main predictors were mean annual temperature and lithology. Total SOC stored in the top 1 m in the region was about 79 Tg with a low mean density of 7.18 kg Cm−3. The vertical distribution of SOC was shallower in forestland and deeper in cropland. A reduction in rainfall would lead to SOC decrease in forestland and shrubland, and an increase of mean annual temperature would adversely affect SOC in croplands and shrubland. With increasing depth, the relative importance of climatic factors decreases and texture becomes more important in controlling SOC in all land uses. Conclusions Due to climate change, impacts will be much greater in surface SOC, the strategies for C sequestration should be focused on subsoil sequestration, which was hindered in forestland due to bedrock limitations to soil depth. In these conditions, sequestration in cropland through appropriate management practices is recommended.

The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

Interactive effect of floral abundance and semi-natural habitats on pollinators in field beans (Vicia faba)

Pollination services are economically important component of agricultural biodiversity which enhance the yield and quality of many crops. An understanding of the suitability of extant habitats for pollinating species is crucial for planning management actions to protect and manage these service providers. In a highly modified agricultural ecosystem, we tested the effect of different pollination treatments (open, autonomous self- and wind-pollination) on pod set, seed set, and seed weight in field beans (Vicia faba). We also investigated the effect of semi-natural habitats and flower abundance on pollinators of field beans. Pollinator sampling was undertaken in ten field bean fields along a gradient of habitat complexity; CORINE land cover classification was used to analyse the land use patterns between 500–3000 m around the sites. Total yield from open-pollination increased by 185% compared to autonomous self-pollination. There was positive interactive effect of local flower abundance and cover of semi-natural habitats on overall abundance of pollinators at 1500 and 2000 m, and abundance of bumblebees (Bombus spp.) at 1000–2000 m. In contrast, species richness of pollinators was only correlated with flower abundance and not with semi-natural habitats. We did not find a link between pod set from open-pollination and pollinator abundance, possibly due to variations in the growing conditions and pollinator communities between sites. We conclude that insect pollination is essential for optimal bean yields and therefore the maintenance of semi-natural habitats in agriculture-dominated landscapes should ensure stable and more efficient pollination services in field beans.

The elliptic sine-Gordon equation: a nonlinear elliptic integrable PDE

In this paper, we summarise this recent progress to underline the features specific to this nonlinear elliptic case, and we give a new classification of boundary conditions on the semistrip that satisfy a necessary condition for yielding a boundary value problem can be effectively linearised. This classification is based on formulation the equation in terms of an alternative Lax pair.

A model analysis of climate and CO2 controls on tree growth in a semi-arid woodland

We used a light-use efficiency model of photosynthesis coupled with a dynamic carbon allocation and tree-growth model to simulate annual growth of the gymnosperm Callitris columellaris in the semi-arid Great Western Woodlands, Western Australia, over the past 100 years. Parameter values were derived from independent observations except for sapwood specific respiration rate, fine-root turnover time, fine-root specific respiration rate and the ratio of fine-root mass to foliage area, which were estimated by Bayesian optimization. The model reproduced the general pattern of interannual variability in radial growth (tree-ring width), including the response to the shift in precipitation regimes that occurred in the 1960s. Simulated and observed responses to climate were consistent. Both showed a significant positive response of tree-ring width to total photosynthetically active radiation received and to the ratio of modeled actual to equilibrium evapotranspiration, and a significant negative response to vapour pressure deficit. However, the simulations showed an enhancement of radial growth in response to increasing atmospheric CO2 concentration (ppm) ([CO2]) during recent decades that is not present in the observations. The discrepancy disappeared when the model was recalibrated on successive 30-year windows. Then the ratio of fine-root mass to foliage area increases by 14% (from 0.127 to 0.144 kg C m-2) as [CO2] increased while the other three estimated parameters remained constant. The absence of a signal of increasing [CO2] has been noted in many tree-ring records, despite the enhancement of photosynthetic rates and water-use efficiency resulting from increasing [CO2]. Our simulations suggest that this behaviour could be explained as a consequence of a shift towards below-ground carbon allocation.

The composite-tendency Robert-Asselin-Williams (RAW) filter in semi-implicit integrations

Timediscretization in weatherandclimate modelsintroduces truncation errors that limit the accuracy of the simulations. Recent work has yielded a method for reducing the amplitude errors in leap-frog integrations from first-order to fifth-order.This improvement is achieved by replacing the Robert–Asselin filter with the Robert–Asselin–Williams (RAW) filter and using a linear combination of unfiltered and filtered states to compute the tendency term. The purpose of the present article is to apply the composite-tendency RAW-filtered leapfrog scheme to semi-implicit integrations. A theoretical analysis shows that the stability and accuracy are unaffected by the introduction of the implicitly treated mode. The scheme is tested in semi-implicit numerical integrations in both a simple nonlinear stiff system and a medium-complexity atmospheric general circulation model and yields substantial improvements in both cases. We conclude that the composite-tendency RAW-filtered leap-frog scheme is suitable for use in semi-implicit integrations.

Just add water and salt: the optimisation of petrogenic hydrocarbon biodegradation in soils from semi-arid Barrow Island, Western Australia

We investigated the potential of soil moisture and nutrient amendments to enhance the biodegradation of oil in the soils from an ecologically unique semi-arid island. This was achieved using a series of controlled laboratory incubations where moisture or nutrient levels were experimentally manipulated. Respired CO2 increased sharply with moisture amendment reflecting the severe moisture limitation of these porous and semi-arid soils. The greatest levels of CO2 respiration were generally obtained with a soil pore water saturation of 50–70%. Biodegradation in these nutrient poor soils was also promoted by the moderate addition of a nitrogen fertiliser. Increased biodegradation was greater at the lowest amendment rate (100 mg N kg−1 soil) than the higher levels (500 or 1,000 mg N kg−1 soil), suggesting the higher application rates may introduce N toxicity. Addition of phosphorous alone had little effect, but a combined 500 mg N and 200 mg P kg−1 soil amendment led to a synergistic increase in CO2 respiration (3.0×), suggesting P can limit the biodegradation of hydrocarbons following exogenous N amendment.

Transcendental Brauer groups of products of CM elliptic curves

Let L be a number field and let E/L be an elliptic curve with complex multiplication by the ring of integers O_K of an imaginary quadratic field K. We use class field theory and results of Skorobogatov and Zarhin to compute the transcendental part of the Brauer group of the abelian surface ExE. The results for the odd order torsion also apply to the Brauer group of the K3 surface Kum(ExE). We describe explicitly the elliptic curves E/Q with complex multiplication by O_K such that the Brauer group of ExE contains a transcendental element of odd order. We show that such an element gives rise to a Brauer-Manin obstruction to weak approximation on Kum(ExE), while there is no obstruction coming from the algebraic part of the Brauer group.

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Shadow lines in the arithmetic of elliptic curves

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)\otimes Qp. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples.