Algorithmen für q-holonome Funktionen und q-hypergeometrische Reihen

Die q-Analysis ist eine spezielle Diskretisierung der Analysis auf einem Gitter, welches eine geometrische Folge darstellt, und findet insbesondere in der Quantenphysik eine breite Anwendung, ist aber auch in der Theorie der q-orthogonalen Polynome und speziellen Funktionen von großer Bedeutung. Die betrachteten mathematischen Objekte aus der q-Welt weisen meist eine recht komplizierte Struktur auf und es liegt daher nahe, sie mit Computeralgebrasystemen zu behandeln. In der vorliegenden Dissertation werden Algorithmen für q-holonome Funktionen und q-hypergeometrische Reihen vorgestellt. Alle Algorithmen sind in dem Maple-Package qFPS, welches integraler Bestandteil der Arbeit ist, implementiert. Nachdem in den ersten beiden Kapiteln Grundlagen geschaffen werden, werden im dritten Kapitel Algorithmen präsentiert, mit denen man zu einer q-holonomen Funktion q-holonome Rekursionsgleichungen durch Kenntnis derer q-Shifts aufstellen kann. Operationen mit q-holonomen Rekursionen werden ebenfalls behandelt. Im vierten Kapitel werden effiziente Methoden zur Bestimmung polynomialer, rationaler und q-hypergeometrischer Lösungen von q-holonomen Rekursionen beschrieben. Das fünfte Kapitel beschäftigt sich mit q-hypergeometrischen Potenzreihen bzgl. spezieller Polynombasen. Wir formulieren einen neuen Algorithmus, der zu einer q-holonomen Rekursionsgleichung einer q-hypergeometrischen Reihe mit nichttrivialem Entwicklungspunkt die entsprechende q-holonome Rekursionsgleichung für die Koeffizienten ermittelt. Ferner können wir einen neuen Algorithmus angeben, der umgekehrt zu einer q-holonomen Rekursionsgleichung für die Koeffizienten eine q-holonome Rekursionsgleichung der Reihe bestimmt und der nützlich ist, um q-holonome Rekursionen für bestimmte verallgemeinerte q-hypergeometrische Funktionen aufzustellen. Mit Formulierung des q-Taylorsatzes haben wir schließlich alle Zutaten zusammen, um das Hauptergebnis dieser Arbeit, das q-Analogon des FPS-Algorithmus zu erhalten. Wolfram Koepfs FPS-Algorithmus aus dem Jahre 1992 bestimmt zu einer gegebenen holonomen Funktion die entsprechende hypergeometrische Reihe. Wir erweitern den Algorithmus dahingehend, dass sogar Linearkombinationen q-hypergeometrischer Potenzreihen bestimmt werden können. ________________________________________________________________________________________________________________

Atomistic-continuum modeling of ultrafast laser-induced melting of silicon targets

In this work, we present an atomistic-continuum model for simulations of ultrafast laser-induced melting processes in semiconductors on the example of silicon. The kinetics of transient non-equilibrium phase transition mechanisms is addressed with MD method on the atomic level, whereas the laser light absorption, strong generated electron-phonon nonequilibrium, fast heat conduction, and photo-excited free carrier diffusion are accounted for with a continuum TTM-like model (called nTTM). First, we independently consider the applications of nTTM and MD for the description of silicon, and then construct the combined MD-nTTM model. Its development and thorough testing is followed by a comprehensive computational study of fast nonequilibrium processes induced in silicon by an ultrashort laser irradiation. The new model allowed to investigate the effect of laser-induced pressure and temperature of the lattice on the melting kinetics. Two competing melting mechanisms, heterogeneous and homogeneous, were identified in our big-scale simulations. Apart from the classical heterogeneous melting mechanism, the nucleation of the liquid phase homogeneously inside the material significantly contributes to the melting process. The simulations showed, that due to the open diamond structure of the crystal, the laser-generated internal compressive stresses reduce the crystal stability against the homogeneous melting. Consequently, the latter can take a massive character within several picoseconds upon the laser heating. Due to the large negative volume of melting of silicon, the material contracts upon the phase transition, relaxes the compressive stresses, and the subsequent melting proceeds heterogeneously until the excess of thermal energy is consumed. A series of simulations for a range of absorbed fluences allowed us to find the threshold fluence value at which homogeneous liquid nucleation starts contributing to the classical heterogeneous propagation of the solid-liquid interface. A series of simulations for a range of the material thicknesses showed that the sample width we chosen in our simulations (800 nm) corresponds to a thick sample. Additionally, in order to support the main conclusions, the results were verified for a different interatomic potential. Possible improvements of the model to account for nonthermal effects are discussed and certain restrictions on the suitable interatomic potentials are found. As a first step towards the inclusion of these effects into MD-nTTM, we performed nanometer-scale MD simulations with a new interatomic potential, designed to reproduce ab initio calculations at the laser-induced electronic temperature of 18946 K. The simulations demonstrated that, similarly to thermal melting, nonthermal phase transition occurs through nucleation. A series of simulations showed that higher (lower) initial pressure reinforces (hinders) the creation and the growth of nonthermal liquid nuclei. For the example of Si, the laser melting kinetics of semiconductors was found to be noticeably different from that of metals with a face-centered cubic crystal structure. The results of this study, therefore, have important implications for interpretation of experimental data on the kinetics of melting process of semiconductors.

On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy

In this paper, the available potential energy (APE) framework of Winters et al. (J. Fluid Mech., vol. 289, 1995, p. 115) is extended to the fully compressible Navier– Stokes equations, with the aims of clarifying (i) the nature of the energy conversions taking place in turbulent thermally stratified fluids; and (ii) the role of surface buoyancy fluxes in the Munk & Wunsch (Deep-Sea Res., vol. 45, 1998, p. 1977) constraint on the mechanical energy sources of stirring required to maintain diapycnal mixing in the oceans. The new framework reveals that the observed turbulent rate of increase in the background gravitational potential energy GPEr , commonly thought to occur at the expense of the diffusively dissipated APE, actually occurs at the expense of internal energy, as in the laminar case. The APE dissipated by molecular diffusion, on the other hand, is found to be converted into internal energy (IE), similar to the viscously dissipated kinetic energy KE. Turbulent stirring, therefore, does not introduce a new APE/GPEr mechanical-to-mechanical energy conversion, but simply enhances the existing IE/GPEr conversion rate, in addition to enhancing the viscous dissipation and the entropy production rates. This, in turn, implies that molecular diffusion contributes to the dissipation of the available mechanical energy ME =APE +KE, along with viscous dissipation. This result has important implications for the interpretation of the concepts of mixing efficiency γmixing and flux Richardson number Rf , for which new physically based definitions are proposed and contrasted with previous definitions. The new framework allows for a more rigorous and general re-derivation from the first principles of Munk & Wunsch (1998, hereafter MW98)’s constraint, also valid for a non-Boussinesq ocean: G(KE) ≈ 1 − ξ Rf ξ Rf Wr, forcing = 1 + (1 − ξ )γmixing ξ γmixing Wr, forcing , where G(KE) is the work rate done by the mechanical forcing, Wr, forcing is the rate of loss of GPEr due to high-latitude cooling and ξ is a nonlinearity parameter such that ξ =1 for a linear equation of state (as considered by MW98), but ξ <1 otherwise. The most important result is that G(APE), the work rate done by the surface buoyancy fluxes, must be numerically as large as Wr, forcing and, therefore, as important as the mechanical forcing in stirring and driving the oceans. As a consequence, the overall mixing efficiency of the oceans is likely to be larger than the value γmixing =0.2 presently used, thereby possibly eliminating the apparent shortfall in mechanical stirring energy that results from using γmixing =0.2 in the above formula.

Understanding mixing efficiency in the oceans. Do the nonlinearities of the equation of state matter?

There exist two central measures of turbulent mixing in turbulent stratified fluids that are both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy APE; 2) the turbulent rate of change Wr, turbulent of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPEr, owing to the well known exact equality D(APE)=Wr, turbulent for a Boussinesq fluid with a linear equation of state. Recently, however, Tailleux (2009) pointed out that the above equality no longer holds for a thermally-stratified compressible, with the ratio ξ=Wr, turbulent/D(APE) being generally lower than unity and sometimes even negative for water or seawater, and argued that D(APE) and Wr, turbulent actually represent two distinct types of energy conversion, respectively the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE0, and the conversion between GPEr and a different subcomponent of internal energy called "exergy" IEexergy. In this paper, the behaviour of the ratio ξ is examined for different stratifications having all the same buoyancy frequency N vertical profile, but different vertical profiles of the parameter Υ=α P/(ρCp), where α is the thermal expansion coefficient, P the hydrostatic pressure, ρ the density, and Cp the specific heat capacity at constant pressure, the equation of state being that for seawater for different particular constant values of salinity. It is found that ξ and Wr, turbulent depend critically on the sign and magnitude of dΥ/dz, in contrast with D(APE), which appears largely unaffected by the latter. These results have important consequences for how the mixing efficiency should be defined and measured in practice, which are discussed.

Moving towards a more mechanistic approach in the determination of soil heat flux from remote measurements - I. A universal approach to calculate thermal inertia

In this paper we pledge that physically based equations should be combined with remote sensing techniques to enable a more theoretically rigorous estimation of area-average soil heat flux, G. A standard physical equation (i.e. the analytical or exact method) for the estimation of G, in combination with a simple, but theoretically derived, equation for soil thermal inertia (F), provides the basis for a more transparent and readily interpretable method for the estimation of G; without the requirement for in situ instrumentation. Moreover, such an approach ensures a more universally applicable method than those derived from purely empirical studies (employing vegetation indices and albedo, for example). Hence, a new equation for the estimation of Gamma(for homogeneous soils) is discussed in this paper which only requires knowledge of soil type, which is readily obtainable from extant soil databases and surveys, in combination with a coarse estimate of moisture status. This approach can be used to obtain area-averaged estimates of Gamma(and thus G, as explained in paper II) which is important for large-scale energy balance studies that employ aircraft or satellite data. Furthermore, this method also relaxes the instrumental demand for studies at the plot and field scale (no requirement for in situ soil temperature sensors, soil heat flux plates and/or thermal conductivity sensors). In addition, this equation can be incorporated in soil-vegetation-atmosphere-transfer models that use the force restore method to update surface temperatures (such as the well-known ISBA model), to replace the thermal inertia coefficient.

Moving towards a more mechanistic approach in the determination of soil heat flux from remote measurements - II. Diurnal shape of soil heat flux

For vegetated surfaces, calculation of soil heat flux, G, with the Exact or Analytical method requires a harmonic analysis of below-canopy soil surface temperature, to obtain the shape of the diurnal course of G. When determining G with remote sensing methods, only composite (vegetation plus soil) radiometric brightness temperature is available. This paper presents a simple equation that relates the sum of the harmonic terms derived for the composite radiometric surface temperature to that of belowcanopy soil surface temperature. The thermal inertia, Gamma(,) for which a simple equation has been presented in a companion paper, paper I, is used to set the magnitude of G. To assess the success of the method proposed in this paper for the estimation of the diurnal shape of G, a comparison was made between 'remote' and in situ calculated values from described field sites. This indicated that the proposed method was suitable for the estimation of the shape of G for a variety of vegetation types and densities. The approach outlined in paper I, to obtain Gamma, was then combined with the estimated harmonic terms to predict estimates of G, which were compared to values predicted by empirical remote methods found in the literature. This indicated that the method proposed in the combination of papers I and II gave reliable estimates of G, which, in comparison to the other methods, resulted in more realistic predictions for vegetated surfaces. This set of equations can also be used for bare and sparsely vegetated soils, making it a universally applicable method. (C) 2007 Elsevier B.V. All rights reserved.

Heat tolerance in groundnut

Tolerance to high soil and air temperature during the reproductive phase is an important component of adaptation to and and semi-arid cropping environments in groundnut. Between 10 and 22 genotypes were screened for tolerance to high air and soil temperature in controlled environments. To assess tolerance to high soil temperature, 10 genotypes were grown from start of podding to harvest at ambient (28 degrees) and high (38 degreesC) soil temperatures, and crop growth rate (CGR), pod growth rate (PGR) and partitioning (ratio PGR:CGR) measured. To assess tolerance to high air temperature during two key stages-microsporogenesis (3-6 days before flowering, DBF) and flowering, fruit-set was measured in two experiments. In the first experiment, 12 genotypes were exposed to short (3-6 days) episodes of high (38 degreesC) day air temperature at 6 DBF and at flowering. In the second experiment, 22 genotypes were exposed to 40 degreesC day air temperature for I day at 6 DBF, 3 DBF or at flowering. Cellular membrane thermostability (relative injury, RI) was also measured in these 22 genotypes. There was considerable variation among genotypes in response to high temperature, whether assessed by growth rates, fruit-set or RI. Pod weight at high soil temperature was associated with variation in CGR rather than partitioning. Flowering was more sensitive to high air temperature than microsporogenesis. Genotypes tolerant to high air temperature at microsporogenesis were not necessarily tolerant at flowering, and nor was tolerance correlated with RI. Six genotypes (796, 55-437, ICG 1236, ICGV 86021, lCGV 87281 and ICGV 92121) were identified as heat tolerant based on their performance in all tests. These experiments have shown that groundnut genotypes can be easily screened for reproductive tolerance to high air and soil temperature and that several sources of heat tolerance are available in groundnut germplasm. (C) 2003 Elsevier Science B.V. All rights reserved.

Phenotyping parents of mapping populations of rice for heat tolerance during anthesis

Seed set of rice (Oryza sativa L.) is highly sensitive to short episodes of high temperature at anthesis events that are likely to be more frequent in future climates. Breeding for tolerance is therefore an essential component of adaptation to climate variability and change. Experiments were conducted in 2003 and 2004 at optimum (30 degrees C daytime) and high (35 and 38 degrees C) air temperature using parents of some prominent mapping populations (i) to determine whether there were differences in the daily flowering pattern and hence a potential heat avoidance mechanism, and (ii) to identify rice genotypes having true heat tolerance during anthesis, that is, high seed set in spikelets exposed to high temperature. Rice cultivar CG14 (O. glaberrima) reached peak anthesis earlier in the morning (1.5 h after dawn) under both control (30 degrees C) and high (38 degrees C) temperature conditions than O. sativa genotypes (>= 3 h after dawn). Exposure to high temperature (centered on the time of peak anthesis) for 6 h reduced spikelet fertility more than exposure for 2 h, and fertility was lower at 38 degrees C than at 35 degrees C. Genotypic ranking for spikelet fertility at 35 and 38 degrees C was highly correlated in both 2003 and 2004. Fertility was also highly correlated across years, suggesting a consistent and reproducible response of spikelet fertility to temperature. The check cultivar N22 was the most heat tolerant genotype (64-86% fertility at 38 degrees C) and cultivars Azucena and Moroberekan the most susceptible (<8%).

Physiological and proteomic approaches to address heat tolerance during anthesis in rice (Oryza sativa L.)

Episodes of high temperature at anthesis, which in rice is the most sensitive stage to temperature, are expected to occur more frequently in future climates. The morphology of the reproductive organs and pollen number, and changes in anther protein expression, were studied in response to high temperature at anthesis in three rice (Oryza sativa L.) genotypes. Plants were exposed to 6 h of high (38 °C) and control (29 °C) temperature at anthesis and spikelets collected for morphological and proteomic analysis. Moroberekan was the most heat-sensitive genotype (18% spikelet fertility at 38 °C), while IR64 (48%) and N22 (71%) were moderately and highly heat tolerant, respectively. There were significant differences among the genotypes in anther length and width, apical and basal pore lengths, apical pore area, and stigma and pistil length. Temperature also affected some of these traits, increasing anther pore size and reducing stigma length. Nonetheless, variation in the number of pollen on the stigma could not be related to measured morphological traits. Variation in spikelet fertility was highly correlated (r=0.97, n=6) with the proportion of spikelets with ≥20 germinated pollen grains on the stigma. A 2D-gel electrophoresis showed 46 protein spots changing in abundance, of which 13 differentially expressed protein spots were analysed by MS/MALDI-TOF. A cold and a heat shock protein were found significantly up-regulated in N22, and this may have contributed to the greater heat tolerance of N22. The role of differentially expressed proteins and morphology during anther dehiscence and pollination in shaping heat tolerance and susceptibility is discussed.

Genetic analysis of heat tolerance at anthesis in rice

Genetic analysis of heat tolerance will help breeders produce rice (Oryza sativa L.) varieties adapted to future climates. An F6 population of 181 recombinant inbred lines of Bala (tolerant) × Azucena (susceptible) was screened for heat tolerance at anthesis by measuring spikelet fertility at 30°C (control) and 38°C (high temperature) in experiments conducted in the Philippines and the United Kingdom. The parents varied significantly for absolute spikelet fertility under control (79–87%) and at high temperature (2.9–47.1%), and for relative spikelet fertility (high temperature/control) at high temperature (3.7–54.9%). There was no correlation between spikelet fertility in control and high-temperature conditions and no common quantitative trait loci (QTLs) were identified. Two QTLs for spikelet fertility under control conditions were identified on chromosomes 2 and 4. Eight QTLs for spikelet fertility under high-temperature conditions were identified on chromosomes 1, 2, 3, 8, 10, and 11. The most significant heat-responsive QTL, contributed by Bala and explaining up to 18% of the phenotypic variation, was identified on chromosome 1 (38.35 mega base pairs on the rice physical genome map). This QTL was also found to influence plant height, explaining 36.6% of the phenotypic variation. A comparison with other studies of abiotic (drought, cold, salinity) stresses showed QTLs at similar positions on chromosomes 1, 3, 8, and 10, suggesting common underlying stress-responsive regions of the genome.

Numerical study of a M-cycle cross-flow heat exchanger for indirect evaporative cooling

In this paper, numerical analyses of the thermal performance of an indirect evaporative air cooler incorporating a M-cycle cross-flow heat exchanger has been carried out. The numerical model was established from solving the coupled governing equations for heat and mass transfer between the product and working air, using the finite-element method. The model was developed using the EES (Engineering Equation Solver) environment and validated by published experimental data. Correlation between the cooling (wet-bulb) effectiveness, system COP and a number of air flow/exchanger parameters was developed. It is found that lower channel air velocity, lower inlet air relative humidity, and higher working-to-product air ratio yielded higher cooling effectiveness. The recommended average air velocities in dry and wet channels should not be greater than 1.77 m/s and 0.7 m/s, respectively. The optimum flow ratio of working-to-product air for this cooler is 50%. The channel geometric sizes, i.e. channel length and height, also impose significant impact to system performance. Longer channel length and smaller channel height contribute to increase of the system cooling effectiveness but lead to reduced system COP. The recommend channel height is 4 mm and the dimensionless channel length, i.e., ratio of the channel length to height, should be in the range 100 to 300. Numerical study results indicated that this new type of M-cycle heat and mass exchanger can achieve 16.7% higher cooling effectiveness compared with the conventional cross-flow heat and mass exchanger for the indirect evaporative cooler. The model of this kind is new and not yet reported in literatures. The results of the study help with design and performance analyses of such a new type of indirect evaporative air cooler, and in further, help increasing market rating of the technology within building air conditioning sector, which is currently dominated by the conventional compression refrigeration technology.

Infrared dynamics of decaying two-dimensional turbulence governed by the Charney-Hasegawa-Mima equation

The low wave number range of decaying turbulence governed by the Charney-Hasegawa-Mima (CHM) equation is examined theoretically and by direct numerical simulation. Here, the low wave number range is defined as values of the wave number k below the wave number kE corresponding to the peak of the energy spectrum, or alternatively the centroid wave number of the energy spectrum. The energy spectrum in the low wave number range in the infrared regime (k →0) is theoretically derived to be E(k) ∼k5, using a quasinormal Markovianized model of the CHM equation. This result is verified by direct numerical simulation of the CHM equation. The wave number triads (k,p,q) responsible for the formation of the low wave number spectrum are also examined. It is found that the energy flux Π(k) for k< kE can be entirely expressed by Π(-)(k), which is the total net input of energy to wave numbers k. Furthermore, the contribution of nonlocal triad interactions to the energy flux is found to be predominant in the range log (k/kE)<-0.5, where the nonlocal interactions are defined to be those triad interactions for which the ratio of the largest leg of the triad to the smallest leg is larger than four. ©2001 The Physical Society of Japan

Multi-scale sensible heat fluxes in the urban environment from large aperture scintillometry and eddy covariance

Sensible heat fluxes (QH) are determined using scintillometry and eddy covariance over a suburban area. Two large aperture scintillometers provide spatially integrated fluxes across path lengths of 2.8 km and 5.5 km over Swindon, UK. The shorter scintillometer path spans newly built residential areas and has an approximate source area of 2-4 km2, whilst the long path extends from the rural outskirts to the town centre and has a source area of around 5-10 km2. These large-scale heat fluxes are compared with local-scale eddy covariance measurements. Clear seasonal trends are revealed by the long duration of this dataset and variability in monthly QH is related to the meteorological conditions. At shorter time scales the response of QH to solar radiation often gives rise to close agreement between the measurements, but during times of rapidly changing cloud cover spatial differences in the net radiation (Q*) coincide with greater differences between heat fluxes. For clear days QH lags Q*, thus the ratio of QH to Q* increases throughout the day. In summer the observed energy partitioning is related to the vegetation fraction through use of a footprint model. The results demonstrate the value of scintillometry for integrating surface heterogeneity and offer improved understanding of the influence of anthropogenic materials on surface-atmosphere interactions.

Urban microclimates and urban heat island in Chongqing, China

Chongqing is the largest directly-controlled municipality in China, which is now undergoing a rapid urbanization. The urbanization rate increased from 35.6% in 2000 to 48.3% in 2007, and it is estimated to reach at least 70% by 2020. The question remains open: What are the consequences of such rapid urbanization in Chongqing in terms of urban microclimate? Furthermore, Chongqing is located within the Three Gorges Reservoir (TGR) region and the upper Yangtze River, where the Three Gorges Reservoir (TGR) project started in 1993 and was completed in 2010. As one of the biggest construction projects in the world with a rising water level of 175m and water storage capacity of about 39.3 billion m3, it would be interesting to investigate how such a gigantic project impacts the surrounding micro-environment, especially in Chongqing. Different research approaches are adopted in the study. Our literature review indicates present studies on the urban climate in Chongqing are mainly confined within the historical trend analysis of several weather stations operated by the Chongqing government, little is known about the spatial distribution of urban air temperature and how the local land cover influences the air temperature, especially when there are rivers running through the Chongqing urban area. To contribute to the present knowledge, a series of field measurement campaigns and numerical simulations were carried out. Two complementary types of field measurements are included: fixed weather stations and mobile transverse measurement. Numerical simulations using a house-developed program are able to predict the urban air temperature in Chongqing.

Anthropogenic heat in the city of So Paulo, Brazil

The main goal of this work is to describe the anthropogenic energy flux (Q (F)) in the city of So Paulo, Brazil. The hourly, monthly, and annual values of the anthropogenic energy flux are estimated using the inventory method, and the contributions of vehicular, stationary, and human metabolism sources from 2004 to 2007 are considered. The vehicular and stationary sources are evaluated using the primary consumption of energy based on fossil fuel, bio fuel, and electricity usage by the population. The diurnal evolution of the anthropogenic energy flux shows three relative maxima, with the largest maxima occurring early in the morning (similar to 19.9 Wm(-2)) and in the late afternoon (similar to 20.3 Wm(-2)). The relative maximum that occurs around noontime (similar to 19.6 Wm(-2)) reflects the diurnal pattern of vehicle traffic that seems to be specific to So Paulo. With respect to diurnal evolution, the energy flux released by vehicular sources (Q (FV)) contributes approximately 50% of the total anthropogenic energy flux. Stationary sources (Q (FS)) and human metabolism (Q (FM)) represent about 41% and 9% of the anthropogenic energy flux, respectively. For 2007, the monthly values of Q (FV), Q (FS), Q (FM), and Q (F) are, respectively, 16.8 +/- 0.25, 14.3 +/- 0.16, 3.5 +/- 0.03, and 34.6 +/- 0.41 MJ m(-2) month(-1). The seasonal evolution monthly values of Q (FV), Q (FS), Q (FM), and Q (F) show a relative minimum during the summer and winter vacations and a systematic and progressive increase associated with the seasonal evolution of the economic activity in So Paulo. The annual evolution of Q (F) indicates that the city of So Paulo released 355.2 MJ m(-2) year(-1) in 2004 and 415.5 MJ m(-2) year(-1) in 2007 in association with an annual rate of increase of 19.6 MJ m(-2) year(-1) (from 2004 to 2006) and 30.5 MJ m(-2) year(-1) (from 2006 to 2007). The anthropogenic energy flux corresponds to about 9% of the net radiation at the surface in the summer and 15% in the winter. The amplitude of seasonal variation of the maximum hourly value of the diurnal variation increases exponentially with latitude.