http://www.nonlin-processes-geophys.net/Nonlinear Processes in Geophysics Latest Articleshttp://www.nonlin-processes-geophys.net/17/395/2010/<b>The use of artificial neural networks to analyze and predict alongshore sediment transport</b><br /><br />Nonlinear Processes in Geophysics, 17, 395-404, 2010<br /><br />Author(s): B. van Maanen, G. Coco, K. R. Bryan, and B. G. Ruessink<br /><br />An artificial neural network (ANN) was developed to predict the depth-integrated alongshore suspended sediment transport rate using 4 input variables (water depth, wave height and period, and alongshore velocity). The ANN was trained and validated using a dataset obtained on the intertidal beach of Egmond aan Zee, the Netherlands. Root-mean-square deviation between observations and predictions was calculated to show that, for this specific dataset, the ANN (&epsilon;_rms=0.43) outperforms the commonly used Bailard (1981) formula (&epsilon;_rms=1.63), even when this formula is calibrated (&epsilon;_rms=0.66). Because of correlations between input variables, the predictive quality of the ANN can be improved further by considering only 3 out of the 4 available input variables (&epsilon;_rms=0.39). Finally, we use the partial derivatives method to "open and lighten" the generated ANNs with the purpose of showing that, although specific to the dataset in question, they are not "black-box" type models and can be used to analyze the physical processes associated with alongshore sediment transport. In this case, the alongshore component of the velocity, by itself or in combination with other input variables, has the largest explanatory power. Moreover, the behaviour of the ANN indicates that predictions can be unphysical and therefore unreliable when the input lies outside the parameter space over which the ANN has been developed. Our approach of combining the strong predictive power of ANNs with "lightening" the black box and testing its sensitivity, demonstrates that the use of an ANN approach can result in the development of generalized models of suspended sediment transport.2010-09-02T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/383/2010/<b>Wave vector analysis methods using multi-point measurements</b><br /><br />Nonlinear Processes in Geophysics, 17, 383-394, 2010<br /><br />Author(s): Y. Narita, K.-H. Glassmeier, and U. Motschmann<br /><br />Recent developments of multi-point measurements in space provide a means to analyze spacecraft data directly in the wave vector domain. For turbulence study this means that we are able to estimate energy, helicity, and higher order moments in the wave vector domain without assuming Taylor's hypothesis or axisymmetry around the mean magnetic field. The methods of the wave vector analysis are presented and applied to four-point data of Cluster in the solar wind.2010-09-01T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/371/2010/<b>Spatial structures and directionalities in Monsoonal precipitation over South Asia</b><br /><br />Nonlinear Processes in Geophysics, 17, 371-381, 2010<br /><br />Author(s): N. Malik, N. Marwan, and J. Kurths<br /><br />Precipitation during the monsoon season over the Indian subcontinent occurs in form of enormously complex spatiotemporal patterns due to the underlying dynamics of atmospheric circulation and varying topography. Employing methods from nonlinear time series analysis, we study spatial structures of the rainfall field during the summer monsoon and identify principle regions where the dynamics of monsoonal rainfall is more coherent or homogenous. Moreover, we estimate the time delay patterns of rain events. Here we present an analysis of two separate high resolution gridded data sets of daily rainfall covering the Indian subcontinent. Using the method of event synchronization (ES), we estimate regions where heavy rain events during monsoon happen in some lag synchronised form. Further using the delay behaviour of rainfall events, we estimate the directionalities related to the progress of such type of rainfall events. The Active (break) phase of a monsoon is characterised by an increase(decrease) of rainfall over certain regions of the Indian subcontinent. We show that our method is able to identify regions of such coherent rainfall activity.2010-09-01T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/361/2010/<b>Image-model coupling: application to an ionospheric storm</b><br /><br />Nonlinear Processes in Geophysics, 17, 361-369, 2010<br /><br />Author(s): N. D. Smith, D. Pokhotelov, C. N. Mitchell, and C. J. Budd<br /><br />Techniques such as tomographic reconstruction may be used to provide images of electron content in the ionosphere. Models are also available which attempt to describe the dominant physical processes operating in the ionosphere, or the statistical relationships between ionospheric variables. It is sensible to try and couple model output to tomographic images with the aim of inferring the values of driver variables which best replicate some description of electron content imaged in the ionosphere, according to some criterion. This is a challenging task. The following describes an attempt to couple an ionospheric model to a tomographic reconstruction of the geomagnetic storm of 20 November 2003, along a latitudal line segment above north America. A simple model was chosen to reduce the number of input drivers that were varied. The investigation illustrates some of the issues involved in image-model coupling. The ability to make scientific deductions depends on the accuracy of the assumptions in the ionospheric model and the accuracy of the tomographic reconstruction. An ensemble technique was used to help assess confidence in the reconstruction.2010-08-20T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/345/2010/<b>Energy transformations and dissipation of nonlinear internal waves over New Jersey's continental shelf</b><br /><br />Nonlinear Processes in Geophysics, 17, 345-360, 2010<br /><br />Author(s): E. L. Shroyer, J. N. Moum, and J. D. Nash<br /><br />The energetics of large amplitude, high-frequency nonlinear internal waves (NLIWs) observed over the New Jersey continental shelf are summarized from ship and mooring data acquired in August 2006. NLIW energy was typically on the order of 10⁵ Jm⁻¹, and the wave dissipative loss was near 50 W m⁻¹. However, wave energies (dissipations) were ~10 (~2) times greater than these values during a particular week-long period. In general, the leading waves in a packet grew in energy across the outer shelf, reached peak values near 40 km inshore of the shelf break, and then lost energy to turbulent mixing. Wave growth was attributed to the bore-like nature of the internal tide, as wave groups that exhibited larger long-term (lasting for a few hours) displacements of the pycnocline offshore typically had greater energy inshore. For ship-observed NLIWs, the average dissipative loss over the region of decay scaled with the peak energy in waves; extending this scaling to mooring data produces estimates of NLIW dissipative loss consistent with those made using the flux divergence of wave energy. The decay time scale of the NLIWs was approximately 12 h corresponding to a length scale of 35 km (<i>O</i>(100) wavelengths). Imposed on these larger scale energetic trends, were short, rapid exchanges associated with wave interactions and shoaling on a localized topographic rise. Both of these events resulted in the onset of shear instabilities and large energy loss to turbulent mixing.2010-08-03T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/339/2010/<b>Self-organized criticality in solar flares: a cellular automata approach</b><br /><br />Nonlinear Processes in Geophysics, 17, 339-344, 2010<br /><br />Author(s): L. F. Morales and P. Charbonneau<br /><br />We give an overview of a novel lattice-based avalanche model that reproduces well a number of observed statistical properties of solar flares. The anisotropic lattice is defined as a network of vertically-connected nodes subjected to horizontal random displacements mimicking the kinks introduced by random motions of the photospheric footpoints of magnetic fieldlines forming a coronal loop. We focus here on asymmetrical driving displacements, which under our geometrical interpretation of the lattice correspond to a net direction of twist of the magnetic fieldlines about the loop axis. We show that a net vertical electrical current density does build up in our lattice, as one would expect from systematic twisting of a loop-like magnetic structure, and that the presence of this net current has a profound impact on avalanche dynamics. The presence of an additional energy reservoir tends to increase the mean energy released by avalanches, and yield a probability distribution of released energy in better agreement with observational inferences than in its absence. Symmetrical driving displacements are in better conceptual agreement with a random shuffling of photospheric footpoint, and yield a power-law distribution of energy release with exponent larger than 2, as required in Parker's nanoflare model of coronal heating. On the other hand, moderate asymmetrical driving generate energy distribution exponents that are similar to those obtained from SOHO EUV observations.2010-07-22T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/329/2010/<b>Spatio-temporal error growth in the multi-scale Lorenz'96 model</b><br /><br />Nonlinear Processes in Geophysics, 17, 329-337, 2010<br /><br />Author(s): S. Herrera, J. Fernández, M. A. Rodríguez, and J. M. Gutiérrez<br /><br />The influence of multiple spatio-temporal scales on the error growth and predictability of atmospheric flows is analyzed throughout the paper. To this aim, we consider the two-scale Lorenz'96 model and study the interplay of the slow and fast variables on the error growth dynamics. It is shown that when the coupling between slow and fast variables is weak the slow variables dominate the evolution of fluctuations whereas in the case of strong coupling the fast variables impose a non-trivial complex error growth pattern on the slow variables with two different regimes, before and after saturation of fast variables. This complex behavior is analyzed using the recently introduced Mean-Variance Logarithmic (MVL) diagram.2010-07-22T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/319/2010/<b>Assessing microstructures of pyrrhotites in basalts by multifractal analysis</b><br /><br />Nonlinear Processes in Geophysics, 17, 319-327, 2010<br /><br />Author(s): S. Xie, Q. Cheng, S. Zhang, and K. Huang<br /><br />Understanding and describing spatial arrangements of mineral particles and determining the mineral distribution structure are important to model the rock-forming process. Geometric properties of individual mineral particles can be estimated from thin sections, and different models have been proposed to quantify the spatial complexity of mineral arrangement. The Gejiu tin-polymetallic ore-forming district, located in Yunnan province, southwestern China, is chosen as the study area. The aim of this paper is to apply fractal and multifractal analysis to quantify distribution patterns of pyrrhotite particles from twenty-eight binary images obtained from seven basalt segments and then to discern the possible petrological formation environments of the basalts based on concentrations of trace elements. The areas and perimeters of pyrrhotite particles were measured for each image. Perimeter-area fractal analysis shows that the perimeter and area of pyrrhotite particles follow a power-law relationship, which implies the scale-invariance of the shapes of the pyrrhotites. Furthermore, the spatial variation of the pyrrhotite particles in space was characterized by multifractal analysis using the method of moments. The results show that the average values of the area-perimeter exponent (<i>D_AP</i>), the width of the multifractal spectra (&Delta;(<i>D(0)&minus;D(2)</i>) and &Delta;(<i>D(q</i>_min)&minus;<i>D(q</i>_max))) and the multifractality index (&tau;"(1)) for the pyrrhotite particles reach their minimum in the second basalt segment, which implies that the spatial arrangement of pyrrhotite particles in Segment 2 is less heterogeneous. Geochemical trace element analysis results distinguish the second basalt segment sample from other basalt samples. In this aspect, the fractal and multifractal analysis may provide new insights into the quantitative assessment of mineral microstructures which may be closely associated with the petrogenesis as shown by the bulk-rock geochemical analysis.2010-07-19T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/303/2010/<b>A model for large-amplitude internal solitary waves with trapped cores</b><br /><br />Nonlinear Processes in Geophysics, 17, 303-318, 2010<br /><br />Author(s): K. R. Helfrich and B. L. White<br /><br />Large-amplitude internal solitary waves in continuously stratified systems can be found by solution of the Dubreil-Jacotin-Long (DJL) equation. For finite ambient density gradients at the surface (bottom) for waves of depression (elevation) these solutions may develop recirculating cores for wave speeds above a critical value. As typically modeled, these recirculating cores contain densities outside the ambient range, may be statically unstable, and thus are physically questionable. To address these issues the problem for trapped-core solitary waves is reformulated. A finite core of homogeneous density and velocity, but unknown shape, is assumed. The core density is arbitrary, but generally set equal to the ambient density on the streamline bounding the core. The flow outside the core satisfies the DJL equation. The flow in the core is given by a vorticity-streamfunction relation that may be arbitrarily specified. For simplicity, the simplest choice of a stagnant, zero vorticity core in the frame of the wave is assumed. A pressure matching condition is imposed along the core boundary. Simultaneous numerical solution of the DJL equation and the core condition gives the exterior flow and the core shape. Numerical solutions of time-dependent non-hydrostatic equations initiated with the new stagnant-core DJL solutions show that for the ambient stratification considered, the waves are stable up to a critical amplitude above which shear instability destroys the initial wave. Steadily propagating trapped-core waves formed by lock-release initial conditions also agree well with the theoretical wave properties despite the presence of a "leaky" core region that contains vorticity of opposite sign from the ambient flow.2010-07-15T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/293/2010/<b>A simple metric to quantify seismicity clustering</b><br /><br />Nonlinear Processes in Geophysics, 17, 293-302, 2010<br /><br />Author(s): N. F. Cho, K. F. Tiampo, S. D. Mckinnon, J. A. Vallejos, W. Klein, and R. Dominguez<br /><br />The Thirulamai-Mountain (TM) metric was first developed to study ergodicity in fluids and glasses (Thirumalai and Mountain, 1993) using the concept of effective ergodicity, where a large but finite time interval is considered. Tiampo et al. (2007) employed the TM metric to earthquake systems to search for effective ergodic periods, which are considered to be metastable equilibrium states that are disrupted by large events. The physical meaning of the TM metric for seismicity is addressed here in terms of the clustering of earthquakes in both time and space for different sets of data. It is shown that the TM metric is highly dependent not only on spatial/temporal seismicity clustering, but on the past seismic activity of the region and the time intervals considered as well, and that saturation occurs over time, resulting in a lower sensitivity to local clustering. These results confirm that the TM metric can be used to quantify seismicity clustering from both spatial and temporal perspectives, in which the disruption of effective ergodic periods are caused by the agglomeration of events.2010-07-02T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/287/2010/<b>Is current disruption associated with an inverse cascade?</b><br /><br />Nonlinear Processes in Geophysics, 17, 287-292, 2010<br /><br />Author(s): Z. Vörös, A. Runov, M. P. Leubner, W. Baumjohann, and M. Volwerk<br /><br />Current disruption (CD) and the related kinetic instabilities in the near-Earth magnetosphere represent physical mechanisms which can trigger multi-scale substorm activity including global reorganizations of the magnetosphere. Lui et al. (2008) proposed a CD scenario in which the kinetic scale linear modes grow and reach the typical dipolarization scales through an inverse cascade. The experimental verification of the inverse nonlinear cascade is based on wavelet analysis. In this paper the Hilbert-Huang transform is used which is suitable for nonlinear systems and allows to reconstruct the time-frequency representation of empirical decomposed modes in an adaptive manner. It was found that, in the Lui et al. (2008) event, the modes evolve globally from high-frequencies to low-frequencies. However, there are also local frequency evolution trends oriented towards high-frequencies, indicating that the underlying processes involve multi-scale physics and non-stationary fluctuations for which the simple inverse cascade scenario is not correct.2010-06-16T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/283/2010/<b><i>Preface</i> "Nonlinear processes in oceanic and atmospheric flows"</b><br /><br />Nonlinear Processes in Geophysics, 17, 283-285, 2010<br /><br />Author(s): A. M. Mancho, S. Wiggins, A. Turiel, E. Hernández-García, C. López, and E. García-Ladona<br /><br />Nonlinear phenomena are essential ingredients in many oceanic and atmospheric processes, and successful understanding of them benefits from multidisciplinary collaboration between oceanographers, meteorologists, physicists and mathematicians. The present Special Issue on "Nonlinear Processes in Oceanic and Atmospheric Flows" contains selected contributions from attendants to the workshop which, in the above spirit, was held in Castro Urdiales, Spain, in July 2008. Here we summarize the Special Issue contributions, which include papers on the characterization of ocean transport in the Lagrangian and in the Eulerian frameworks, generation and variability of jets and waves, interactions of fluid flow with plankton dynamics or heavy drops, scaling in meteorological fields, and statistical properties of El Niño Southern Oscillation.2010-05-31T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/273/2010/<b>FEM and ANN combined approach for predicting pressure source parameters at Etna volcano</b><br /><br />Nonlinear Processes in Geophysics, 17, 273-282, 2010<br /><br />Author(s): A. Di Stefano, G. Currenti, C. Del Negro, L. Fortuna, and G. Nunnari<br /><br />A hybrid approach for forward and inverse geophysical modeling, based on Artificial Neural Networks (ANN) and Finite Element Method (FEM), is proposed in order to properly identify the parameters of volcanic pressure sources from geophysical observations at ground surface. The neural network is trained and tested with a set of patterns obtained by the solutions of numerical models based on FEM. The geophysical changes caused by magmatic pressure sources were computed developing a 3-D FEM model with the aim to include the effects of topography and medium heterogeneities at Etna volcano. ANNs are used to interpolate the complex non linear relation between geophysical observations and source parameters both for forward and inverse modeling. The results show that the combination of neural networks and FEM is a powerful tool for a straightforward and accurate estimation of source parameters in volcanic regions.2010-05-20T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/269/2010/<b><i>Brief communication</i> "A statistical validation for the cycles found in air temperature data using a Morlet wavelet-based method"</b><br /><br />Nonlinear Processes in Geophysics, 17, 269-272, 2010<br /><br />Author(s): S. Nicolay, G. Mabille, X. Fettweis, and M. Erpicum<br /><br />Recently, new cycles, associated with periods of 30 and 43 months, respectively, have been observed by the authors in surface air temperature time series, using a wavelet-based methodology. Although many evidences attest the validity of this method applied to climatic data, no systematic study of its efficiency has been carried out. Here, we estimate confidence levels for this approach and show that the observed cycles are significant. Taking these cycles into consideration should prove helpful in increasing the accuracy of the climate model projections of climate change and weather forecast.2010-05-20T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/245/2010/<b>Lower-hybrid (LH) oscillitons evolved from ion-acoustic (IA)/ion-cyclotron (IC) solitary waves: effect of electron inertia</b><br /><br />Nonlinear Processes in Geophysics, 17, 245-268, 2010<br /><br />Author(s): J. Z. G. Ma and A. Hirose<br /><br />Lower-hybrid (LH) oscillitons reveal one aspect of geocomplexities. They have been observed by rockets and satellites in various regions in geospace. They are extraordinary solitary waves the envelop of which has a relatively longer period, while the amplitude is modulated violently by embedded oscillations of much shorter periods. We employ a two-fluid (electron-ion) slab model in a Cartesian geometry to expose the excitation of LH oscillitons. Relying on a set of self-similar equations, we first produce, as a reference, the well-known three shapes (sinusoidal, sawtooth, and spiky or bipolar) of parallel-propagating ion-acoustic (IA) solitary structures in the absence of electron inertia, along with their Fast Fourier Transform (FFT) power spectra. The study is then expanded to illustrate distorted structures of the IA modes by taking into account all the three components of variables. In this case, the ion-cyclotron (IC) mode comes into play. Furthermore, the electron inertia is incorporated in the equations. It is found that the inertia modulates the coupled IA/IC envelops to produce LH oscillitons. The newly excited structures are characterized by a normal low-frequency IC solitary envelop embedded by high-frequency, small-amplitude LH oscillations which are superimposed upon by higher-frequency but smaller-amplitude IA ingredients. The oscillitons are shown to be sensitive to several input parameters (e.g., the Mach number, the electron-ion mass/temperature ratios, and the electron thermal speed). Interestingly, whenever a LH oscilliton is triggered, there occurs a density cavity the depth of which can reach up to 20% of the background density, along with density humps on both sides of the cavity. Unexpectedly, a mode at much lower frequencies is also found beyond the IC band. Future studies are finally highlighted. The appendices give a general dispersion relation and specific ones of linear modes relevant to all the nonlinear modes encountered in the text.2010-05-07T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/237/2010/<b>Kernel estimation and display of a five-dimensional conditional intensity function</b><br /><br />Nonlinear Processes in Geophysics, 17, 237-244, 2010<br /><br />Author(s): G. Adelfio<br /><br />The aim of this paper is to find a convenient and effective method of displaying some second order properties in a neighbourhood of a selected point of the process. The used techniques are based on very general high-dimensional nonparametric smoothing developed to define a more general version of the conditional intensity function introduced in earlier earthquake studies by Vere-Jones (1978).2010-04-22T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/221/2010/<b>The effect of volatile bubble growth rate on the periodic dynamics of shallow volcanic systems</b><br /><br />Nonlinear Processes in Geophysics, 17, 221-235, 2010<br /><br />Author(s): I. L'Heureux<br /><br />Many volcanic eruptions exhibit periodic behavior. For instance, periodic ground inflations and deflations in proximity to a volcano are the consequences of periodic overpressure variations in the magma conduit and periodic magma flow rate. The period varies from a few hours to many years, depending on the volcano parameters. On the other hand, volatile components exsolve from an ascending magma by forming bubbles. The strong dependence of the melt viscosity with the volatile concentration generates a positive feedback on the magma flow. We consider here the effect of the growth of volatile bubbles on the dynamics of a magmatic flow in a shallow volcanic system. Various expressions for the bubble growth rate are treated, thus generalizing previous work. In particular, a growth rate law derived from a recent many-bubble theory is considered. It is seen that, for a range of flow rate values at the base of the magma conduit, the system undergoes a Hopf bifurcation. Periodic solutions compatible with the observations are generated. This work shows that measurements of volcanic activity have the potential to test various bubble growth models in magmatic systems.2010-04-20T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/211/2010/<b>An extension of conditional nonlinear optimal perturbation approach and its applications</b><br /><br />Nonlinear Processes in Geophysics, 17, 211-220, 2010<br /><br />Author(s): M. Mu, W. Duan, Q. Wang, and R. Zhang<br /><br />The approach of conditional nonlinear optimal perturbation (CNOP) was previously proposed to find the optimal initial perturbation (CNOP-I) in a given constraint. In this paper, we extend the CNOP approach to search for the optimal combined mode of initial perturbations and model parameter perturbations. This optimal combined mode, also named CNOP, has two special cases: one is CNOP-I that only links with initial perturbations and has the largest nonlinear evolution at a prediction time; while the other is merely related to the parameter perturbations and is called CNOP-P, which causes the largest departure from a given reference state at a prediction time. The CNOP approach allows us to explore not only the first kind of predictability related to initial errors, but also the second kind of predictability associated with model parameter errors, moreover, the predictability problems of the coexistence of initial errors and parameter errors. With the CNOP approach, we study the ENSO predictability by a theoretical ENSO model. The results demonstrate that the prediction errors caused by the CNOP errors are only slightly larger than those yielded by the CNOP-I errors and then the model parameter errors may play a minor role in producing significant uncertainties for ENSO predictions. Thus, it is clear that the CNOP errors and their resultant prediction errors illustrate the combined effect on predictability of initial errors and model parameter errors and can be used to explore the relative importance of initial errors and parameter errors in yielding considerable prediction errors, which helps identify the dominant source of the errors that cause prediction uncertainties. It is finally expected that more realistic models will be adopted to investigate this use of CNOP.2010-04-13T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/201/2010/<b>The effect of shear on the generation of gravity waves</b><br /><br />Nonlinear Processes in Geophysics, 17, 201-210, 2010<br /><br />Author(s): M. Humi<br /><br />Previous research regarding the solutions of Long's equation always presumed that the flow far upstream is without shear. In this paper we derive the proper form of this equation when shear is present. We then apply a sequence of transformations to this equation which make it possible to linearize it while preserving its physical contents. We then derive conditions under which the solutions of this linear equation admit the existence (or creation) of gravity waves. We present also a solution of this model equation when the presence of shear in the overall flow is "small".2010-04-12T00:00:00+02:00http://www.nonlin-processes-geophys.net/17/187/2010/<b>Estimating the diffusive heat flux across a stable interface forced by convective motions</b><br /><br />Nonlinear Processes in Geophysics, 17, 187-200, 2010<br /><br />Author(s): C. Chemel, C. Staquet, and J.-P. Chollet<br /><br />Entrainment at the top of the convectively-driven boundary layer (CBL) is revisited using data from a high-resolution large-eddy simulation (LES). In the range of values of the bulk Richardson number <I>Ri</I>_B studied here (about 15&ndash;25), the entrainment process is mainly driven by the scouring of the interfacial layer (IL) by convective cells. We estimate the length and time scales associated with these convective cells by computing one-dimensional wavenumber and frequency kinetic energy spectra. Using a Taylor assumption, based upon transport by the convective cells, we show that the frequency and wavenumber spectra follow the Kolmogorov law in the inertial range, with the multiplicative constant being in good agreement with previous measurements in the atmosphere. We next focus on the heat flux at the top of the CBL, <IMG WIDTH="12" HEIGHT="22" ALIGN="MIDDLE" BORDER="0" SRC="npg-17-187-2010-2.gif" ALT="$\mathcal{F}_i$">, which is parameterized in classical closure models for the entrainment rate <I>w</I>_e at the interface. We show that <IMG WIDTH="12" HEIGHT="22" ALIGN="MIDDLE" BORDER="0" SRC="npg-17-187-2010-2.gif" ALT="$\mathcal{F}_i$"> can be computed exactly using the method proposed by Winters et al. (1995), from which the values of a turbulent diffusivity <IMG WIDTH="9" HEIGHT="9" ALIGN="BOTTOM" BORDER="0" SRC="npg-17-187-2010-4.gif" ALT="$\mathcal{K}$"> across the IL can be inferred. These values are recovered by tracking particles within the IL using a Lagrangian stochastic model coupled with the LES. The relative difference between the Eulerian and Lagrangian values of <IMG WIDTH="9" HEIGHT="9" ALIGN="BOTTOM" BORDER="0" SRC="npg-17-187-2010-4.gif" ALT="$\mathcal{K}$"> is found to be lower than 10%. A simple expression of <I>w</I>_e as a function of <IMG WIDTH="9" HEIGHT="9" ALIGN="BOTTOM" BORDER="0" SRC="npg-17-187-2010-4.gif" ALT="$\mathcal{K}$"> is also proposed. Our results are finally used to assess the validity of the classical "first-order'' model for <I>w</I>_e. We find that, when <I>Ri</I>_B is varied, the values for <I>w</I>_e derived from the "first-order'' model with the exact computation of <IMG WIDTH="12" HEIGHT="22" ALIGN="MIDDLE" BORDER="0" SRC="npg-17-187-2010-2.gif" ALT="$\mathcal{F}_i$"> agree to better than 10% with those computed directly from the LES (using its definition). The simple expression we propose appears to provide a reliable estimate of <I>w</I>_e for the largest values of <I>Ri</I>_B only.2010-04-08T00:00:00+02:00