The Role of Active Regions in the Generation of Torsional Oscillations

We present a model for torsional oscillations where the inhibiting effect of active region magnetic fields on turbulence locally reduces turbulent viscous torques, leading to a cycle- and latitude-dependent modulation of the differential rotation. The observed depth dependence of torsional oscillations as well as their phase relationship with the sunspot butterfly diagram are reproduced quite naturally in this model. The resulting oscillation amplitudes are significantly smaller than observed, though they depend rather sensitively on model details. Meridional circulation is found to have only a weak effect on the oscillation pattern.     

Asymmetric flux loops in active regions,II

We propose that magnetic flux loops in the subphotospheric layers of the Sun are seriously asymmetrical as a consequence of the drag force exerted on them because of the different rotational rate of the surrounding plasma. In numerical models of stationary slender flux loops in the plane parallel approximation we show that a serious tilt is both possible and probable. Observational facts (see van Driel-Gesztelyi and Petrovay, 1989; Paper I) strongly support the case for high asymmetry. The different stability of p and f spots may also be related to such an asymmetry.The tilts are very sensitive to the rotational profile and to the magnetic field structure. Nevertheless the characteristic maximal tilts can be tentatively estimated to be 20° for thin flux tubes and 5° for thick tubes.For two of the five observational consequences of such a tilt (described in detail in Paper I) order-of-magnitude estimates of the effects are given. The estimates are in reasonable accord with observations.We also explore the possibilities of an inverse treatment of the problem whereby subphotospheric rotation and/or flux tube shapes can be inferred from observations of velocities of photospheric spot motions. In particular we demonstrate how analytic inverse solutions can be obtained in special cases.     

The compatibility of erosion data at different temporal scales

Soil erosion processes have been studied intensively throughout the last decades and rates have been measured at the plot scale as well as at larger scales. However, the relevance of this knowledge for the modelling of long-term landscape evolution remains a topic of considerable debate. Some authors state that measurements of current rates are irrelevant to landscape evolution over a longer time span, as they are inconsistent with some fundamental characteristics of landscapes, such as the fact that the long-term sediment delivery ratio needs to be equal to 1 and that extrapolation of current rates would imply that all soils in Europe should have disappeared by now (e.g. Parsons, A.J., Wainwright, J., Brazier, R.E., Powell, D.M., 2006. Is sediment delivery a fallacy? Earth Surface Processes and Landforms 31, 1325–1328). In this study, we investigate if and to what extent estimates of long-term erosion rates are consistent with information obtained over much shorter time spans for the Loam Belt of Belgium.In a first step, observed short-term and long-term patterns in the Belgian loess area are compared statistically by classifying the study area into landscape element classes and comparing average erosion values per class. This analysis shows that the erosion intensities on the two temporal scales are of the same order of magnitude for each landscape element class. Next, the spatially distributed model WaTEM LT (Water and Tillage Erosion Model Long Term) is calibrated based on the available short-term data by optimising average erosion values for the same landscape element classes. Finally, the calibrated model is used to simulate long-term landform evolution, and is validated using long-term data based on soil profile truncation. We found that the model allows simulating landscape evolution on a millennial time scale using information derived from short-term erosion and deposition data. However, it is important that land use is taken into account for the calibration in order to obtain realistic patterns on a longer time scale. Our analysis shows that, at least for the study area considered, data obtained on erosion and deposition rates over various temporal scales have the same orders of magnitude, thereby demonstrating that measurements of current rates of processes can be highly relevant for interpreting long-term landscape evolution.     

On the validity of quasi-linear kinematic mean-field electrodynamics in astrophysical flows

Mean-field theory in its kinematic form with the quasi-linear approximation is widely used for the modelling of the transport of weak magnetic fields in turbulent media. The validity of this approach to real astrophysical flows is discussed. Numerically evaluating the turbulent electromotive force using Lagrangian analysis for a set of simple, prescribed 2D flow patterns with a wide range of parameters, we find that quasi-linear expressions for the turbulent diffusivities and for the pumping velocities are correct within a factor of 2 for a wide variety of flow types with order of unity (or even higher) effective Strouhal numbers. The degree of the non-linear quenching of turbulent transport by a weak magnetic field is also discussed. We argue that, owing to the intermittency and small filling factors of magnetic fields in realistic astrophysical media, diffusivity and pumping effects are not quenched to order of magnitude, while a more moderate quenching of order 10 per cent is still present.     

Making Sense of Sunspot Decay. I. Parabolic Decay Law and Gnevyshev–Waldmeier Relation

In a statistical study of the decay of individual sunspots based on DPR data we find that the mean instantaneous area decay rate is related to the spot radius r_o and the maximum radius r_o as D = C_D r/r_o, C_D = 32.0±0.26 MSH day ^-1. This implies that sunspots on the mean follow a parabolic decay law; the traditional linear decay law is excluded by the data. The validity of the Gnevyshev–Waldmeier relationship between the maximum area A ₀ and lifetime T of a spot group, A₀/T 10 MSH day^-1, is also demonstrated for individual sunspots. No evidence is found for a supposed supergranular quantization of sunspot areas. Our results strongly support the recent turbulent erosion model of sunspot decay while all other models are excluded.     

Evaluating the impact of soil redistribution on the in situ mineralization of soil organic carbon

Soil erosion, transport and deposition by water drastically affect the distribution of soil organic carbon (SOC) within a landscape. Moreover, soil redistribution may have a large impact on the exchange of carbon (C) between the pedosphere and the atmosphere. One of the large information gaps within this research domain, concerns the fate of SOC after erosion by water. According to different (mainly laboratory) studies, soil redistribution leads to aggregate breakdown, thereby exposing the contained SOC to mineralization. Our study aims to quantify the extent to which such increased mineralization occurs in a real field situation. Carbon dioxide (CO₂)‐efflux was measured in the field after an important erosion event for a continuous period of 112 days. The specific situation on the field ensured that almost none of eroded SOC was exported from the field. Measurements of CO₂‐efflux were done in areas with sediment deposition, as well as in comparable areas without sedimentation. Comparison of these measurements allowed the net effect of soil deposition on CO₂‐efflux to be assessed. Field data were complemented by measurements on incubated, undisturbed soil core samples, in order to disentangle the contribution of environmental factors (moisture, temperature) from any erosional effect on CO₂‐efflux. Results of these measurements on the field showed that CO₂‐efflux was regulated by a complex interplay of different factors (mostly soil porosity, soil moisture and soil temperature). In combination with the incubation measurements, it could be concluded that the processes of erosion and transport indeed led to an increased mineralization of SOC, as a result of aggregate breakdown and exposure of previously encapsulated SOC. This effect was, however, much smaller than observed in previous laboratory studies. Moreover, it was only important in the first weeks, immediately after the erosion event. The calculated net erosional effect on CO₂‐efflux represented a mere 1·6% of total SOC, originally present in the soil. Copyright © 2010 John Wiley & Sons, Ltd.     

Matching INSPIRE Quality of Service Requirements with Hybrid Clouds

A lot of effort has been invested in Spatial Data Infrastructures (SDIs) during the last decade regarding interoperable standards for services and data. But still the scalability and performance of SDI services is reported to be crucial especially if they are accessed concurrently by a high number of users. Furthermore, laws and provisions such as the INSPIRE directive specify challenging requirements regarding the performance, availability and scalability of SDI services. This article presents a Hybrid Cloud architecture for matching INSPIRE‐related Quality of Service (QoS) requirements, without investing in rarely used hardware in advance, by occupying external third‐party resources on a pay‐as‐you‐go basis. The presented Hybrid Cloud is a composition of a local IT‐infrastructure (Private Cloud) and the computational resources of third‐party vendors (Public Cloud). The local infrastructure is laid out to handle the average main load of a service and in lasting peak times additional resources of external providers are allocated and integrated on demand into the local infrastructure to provide sufficient service quality automatically. A proof‐of‐concept implementation of the proposed Hybrid Cloud approach is evaluated and benchmarked with respect to INSPIRE‐related QoS requirements.     

On the Compatibility of a Flux Transport Dynamo with a Fast Tachocline Scenario

The compatibility of the fast-tachocline scenario with a flux-transport dynamo model is explored. We employ a flux-transport dynamo model coupled with simple feedback formulae relating the thickness of the tachocline to the amplitude of the magnetic field or to the Maxwell stress. The dynamo model is found to be robust against the nonlinearity introduced by this simplified fast-tachocline mechanism. Solar-like butterfly diagrams are found to persist and, even without any parameter fitting, the overall thickness of the tachocline is well within the range admitted by helioseismic constraints. In the most realistic case of a time- and latitude-dependent tachocline thickness linked to the value of the Maxwell stress, both the thickness and its latitudinal dependence are in excellent agreement with seismic results. In nonparametric models, cycle-related temporal variations in tachocline thickness are somewhat larger than admitted by helioseismic constraints; we find, however, that introducing a further parameter into our feedback formula readily allows further fine tuning of the thickness variations.     

Making sense of sunspot decay – II. Deviations from the Mean Law and Plage Effects

In a statistical analysis of Debrecen Photoheliographic Results sunspot area data we find that the logarithmic deviation (logD) of the area decay rate D from the parabolic mean decay law (derived in the first paper in this series) follows a Gaussian probability distribution. As a consequence, the actual decay rate D and the time-averaged decay rate are also characterized by approximately lognormal distributions, as found in an earlier work. The correlation time of (logD) is about 3 days. We find a significant physical anticorrelation between (logD) and the amount of plage magnetic flux of the same polarity in an annulus around the spot on Kitt Peak magnetograms. The anticorrelation is interpreted in terms of a generalization of the turbulent erosion model of sunspot decay to the case when the flux tube is embedded in a preexisting homogeneous plage field. The decay rate is found to depend inversely on the value of this plage field, the relation being very close to logarithmic, i.e., the plage field acts as multiplicative noise in the decay process. A Gaussian probability distribution of the field strength in the surrounding plage will then naturally lead to a lognormal distribution of the decay rates, as observed. It is thus suggested that, beside other multiplicative noise sources, the environmental effect of surrounding plage fields is a major factor in the origin of lognormally distributed large random deviations from the mean law in the sunspot decay rates.     

On the possibility of a bimodal solar dynamo

A simple way to couple an interface dynamo model to a fast tachocline model is presented, under the assumption that the dynamo saturation is due to a quadratic process and that the effect of finite shear layer thickness on the dynamo wave frequency is analogous to the effect of finite water depth on surface gravity waves. The model contains one free parameter which is fixed by the requirement that a solution should reproduce the helioseismically determined thickness of the tachocline. In this case it is found that, in addition to this solution, another steady solution exists, characterized by a four times thicker tachocline and 4–5 times weaker magnetic fields. It is tempting to relate the existence of this second solution to the occurrence of grand minima in solar activity. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)