Atmospheric Energy Spectrum Research Articles

Spectral Budget of Rotational and Divergent Kinetic Energy in Global Analyses

Abstract To study the multiscale interactions between rotational and divergent components of atmospheric motion, a new formulation of spectral budget of rotational kinetic energy (RKE) and divergent kinetic energy (DKE) based on the primitive equations in the pressure coordinate is derived, with four main characteristics: 1) horizontal kinetic energy (HKE) spectral transfer is exactly divided into spectral transfer of RKE and DKE, 2) the exact spectral conversion term between DKE and RKE is constructed, 3) the Coriolis term is considered, and 4) both the baroclinic conversion from available potential energy (APE) and the vertical flux of HKE act only on DKE. With this new formulation, outputs from ERA5 global reanalysis are investigated. At planetary scales, HKE spectral transfer, mainly attributed to β effect, is dominated by downscale DKE transfer. At synoptic scales, it is dominated by an upscale transfer of RKE energized by conversion of DKE mainly due to the Coriolis effect. The ultimate source of DKE in the upper troposphere is conversion of APE, while in the stratosphere it is the vertical flux. At mesoscales, the spectral transfers of RKE and DKE are both downscale, and conversion from RKE to DKE exists at sub-800-km scales in the upper troposphere, which is mainly attributed to the contribution from relative vorticity. At different heights, the intersection scales of RKE and DKE spectra are affected by the scales of positive peaks of the local spectral conversion from DKE to RKE around total wavenumber 10. Significance Statement The purpose of this study is to explore more physical insights on the dynamics underlying the atmospheric energy spectra from the perspective of rotational and divergent components of motion. We derive a new formulation of the spectral rotational and divergent kinetic energy budget in the pressure coordinate for the global atmosphere, with application to ERA5 global reanalysis. Our results reveal the differences of spectral energy budget between rotational and divergent motions at different heights and scales. This new formulation provides a good tool for revealing the multiscale cascade and interaction between atmospheric rotational and divergent motions. Future work should investigate these dynamical processes with higher-resolution simulations and datasets.

Characteristics of Atmospheric Kinetic Energy Spectra during the Intensification of Typhoon Lekima (2019)

The intensification of Typhoon Lekima (2019) is simulated with the Weather Research and Forecasting model to study the atmospheric horizontal kinetic energy (HKE) spectra and corresponding spectral HKE budgets under the control of real tropical cyclone (TC). The results show that the TC has the ability to modify the canonical atmospheric energy spectrum during its evolution, which is dominated by its rotational mode. With the intensification of Lekima, the HKE spectrum in the troposphere swells over the central mesoscale and develops an arc-like shape. The stronger the TC, the more pronounced the arc-like shape is and the smaller scale it extends to. The roles various physical processes play at different heights and horizontal scales during the intensification of Lekima are investigated and the dependence of the effect of physical processes on scale and height is revealed. Meanwhile, the potential relationship between the intensification of TC, the activation of energy activity at smaller scales, and the downscale extension of the arc-like spectral shape is found.

Simulated research on displacement damage of gallium nitride radiated by different neutron sources

Gallium nitride (GaN), one of the third-generation wide-bandgap semiconductors, offers significant application for advanced electronic devices utilized in neutron irradiation environments, like the defense, space, and aerospace, etc. In these applications, neutron irradiation-induced defects affect the properties of GaN and eventually degrade the performance of devices. In this work, neutron transport process in GaN is simulated by using the Monte Carlo-based code, Geant4 toolkit under four different irradiation conditions, e.g. high flux isotope reactor, high temperature gas-cooled reactor, pressurized water reactor, and atmospheric neutron irradiation. The energy spectra of primary knock-on atoms (PKA) in GaN and the corresponding weighted spectra under those irradiation conditions are analyzed. It is found that there is one unusual “peak” at around 0.58 MeV in the Primary recoil spectrum, regardless of the irradiation conditions. This peak is attributed to the neutron reaction of hydrogen nucleus, i.e., (n, p). Because of the remarkable (n,p) reaction cross-section of low-energy neutron, the intensity of this peak is related to the ratio of low-energy neutron to the total neutron spectrum. By comparing these PKA energy spectra in GaN, we can see that the PKA energy spectrum created under atmospheric neutron irradiation is similar to that in the high flux isotopic reactor. Specifically, the energy distribution of PKA is wide, and the magnitude of energy is lower than those under fission neutron irradiation conditions. In combination with the effects of nuclear reaction products on electrical properties, the high flux isotopic reactor is more suitable for simulating the irradiation of GaN in an atmospheric neutron energy spectrum environment. These above results can provide not only some insights into the evaluation of the degradation of GaN-based electronic devices under neutron irradiation, but also dataset for the study of radiation damage effect of GaN in simulated neutron environment.

Acoustic loading beneath hypersonic transitional and turbulent boundary layers

This paper concerns a study of pressure fluctuations beneath hypersonic transitional and turbulent boundary layers and associated acoustic loading on a flat surface. We have employed high-order implicit large eddy simulations in conjunction with the atmospheric (von Kármán) multimode energy spectrum as initial condition, and conducted simulations at Mach 4, 6 and 8 and for different inflow turbulence intensities. The spectral analysis of the pressure fluctuations shows consistent results with the available theoretical, experimental and numerical data for fully turbulent boundary layers. In the transition region the spectrum roll-off diverges from the existing scaling predictions for incompressible, as well as fully-turbulent compressible flows. This study shows that the spectrum in the transition region is governed by different scaling laws. The Mach number has a direct impact on the spectrum for both transitional and fully turbulent flows, especially in the high-frequency region of the spectrum. Increasing the inlet turbulence intensity leads to higher amplitude pressure fluctuations in the mid-to-high-frequency region, faster transition to turbulence, and higher acoustic loading on the solid surface.

Direct Numerical Simulations to Investigate Energy Transfer between Meso- and Synoptic Scales

Abstract Understanding the development of the atmospheric energy spectrum across scales is necessary to elucidate atmospheric predictability. In this manuscript, the authors investigate energy transfer between the synoptic scale and the mesoscale using direct numerical simulations (DNSs) of two-dimensional (2D) turbulence transfer under forcing applied at different scales. First, DNS results forced by a single kinetic energy source at large scales show that the energy spectra slopes of the direct enstrophy cascade are steeper than the theoretically predicted −3 slope. Second, the presence of two inertial ranges in 2D turbulence at intermediate scales is investigated by introducing a second energy source in the meso-α-scale range. The energy spectra for the DNS with two kinetic energy sources exhibit flatter slopes that are closer to −3, consistent with the observed kinetic energy spectra of horizontal winds in the atmosphere at synoptic scales. Further, the results are independent of model resolution and scale separation between the two energy sources, with a robust transition region between the lower synoptic and the upper meso-α scales in agreement with classical observations in the upper troposphere. These results suggest the existence of a mesoscale feedback on synoptic-scale predictability that emerges from the concurrence of the direct (downscale) enstrophy transfer in the synoptic scales and the inverse (upscale) kinetic energy transfer from the mesoscale to the synoptic scale in the troposphere.

Testing of the EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 hadronic interaction models via help of the atmospheric vertical muon spectra

The recent results of the very precise measurements of the primary cosmic protons and helium nuclei energy spectra by AMS-02 and some rather accurate estimates of these energy spectra generated in SNR allow us to elaborate the new approximation of the pimary nucleon energy spectra. As the acuracy of this approximation is rather high we can use it to test various models of hadronic interactions with the help of atmospheric muon energy spectra. The atmospheric vertical muon energy spectra have been calcullated in terms of the EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 models in the energy range 102 ÷ 105 GeV with help of the CORSIKA package and this new approximation of the primary nucleon spectrum. The comparison of calculations with the muon spectra observed by collaborations L3+Cosmic, LVD and MACRO has shown that all models predict approximately two times lower intensity of the muon energy spectra. As these muons are products of decays of the most energetic π± and K± mesons in the atmosphere, we can conclude that production of these π± and K± mesons is underestimated by EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 models.

Energy Spectra and Inertia–Gravity Waves in Global Analyses

Abstract Several decades after E. Dewan predicted that the shallowing of the atmospheric energy spectrum in mesoscale is produced by the inertia–gravity (IG) waves, global analyses have reached the resolution at which the IG waves across many scales are resolved. The authors discuss the spatial filtering method based on the Hough harmonics that provides the temperature and wind perturbations associated with the IG waves in global analysis data. The method is applied to the ECMWF interim reanalysis and the operational 2014–16 analysis fields. The derived spectrum of IG wave energy is divided into three regimes: a part associated with the large-scale unbalanced circulations that has a slope close to −1 for zonal wavenumbers 1 ≤ k ≤ 6, a synoptic-scale range between 3000 and around 500 km (7 ≤ k ≲ 35) that is characterized by a nearly −5/3 slope, and a mesoscale range below 500 km where the slope of the IG energy spectrum in the 2015/16 analyses is steeper. In contrast, the energy spectrum of the Rossby waves has a −3 slope for all zonal wavenumbers k > 6. Presented results suggest that energy associated with the IG modes exceeds the level of energy associated with the Rossby waves around zonal wavenumber 35. The exact wavenumber depends on the season and considered atmospheric depth and it is suggested as a cutoff scale for studies of gravity waves.

Calculating vertical atmospheric muon energy spectra for energies ranging from 102 to 105 GeV

New calculations of the atmospheric vertical muon energy spectra for energies ranging from 102 to 105 GeV are performed using an original approach and the CORSIKA 7.4 software package. The intensity of the atmospheric muon flux calculated using the SIBYLL 2.1 and QGSJET II-03 models for muon energies of ~(103–105) GeV is 1.7 times lower than the intensity predicted by L3+Cosmic, MARO and LVD collaborations on the basis of experimental data. For the energy range of ~(102–103) GeV, this reduction is as high as ~2.2 for the QGSJET II-03 model; for the SIBYLL 2.1 model, it falls to 2.1. If we assume that the first generation of charged π± and K ± mesons makes the greatest contribution to the most energetic muon flux, the generation of mesons is underestimated by 1.7 times in the abovementioned models.

Fast simulation of atmospheric turbulence phase screen based on non-uniform sampling

The generation of atmosphere turbulence wave-front is important for studying the light propagation and imaging through the atmosphere, and correcting the atmosphere turbulence, such as the adaptive optics system. The power spectral density method generates phase screens quickly for using the fast Fourier transform (FFT). The main drawback to this approach is that lower order aberrations such as tilt are often under represented. The reason is that the low frequency is sampled inadequately. Since the low order aberrations include a major percentage of the atmospheric energy spectrum, the error of simulated phase screens makes this method less desirable to use. To overcome this shortcoming, a non-uniform sampling method is proposed to generate phase screens accurately. Unfortunately, when the sampling is nonuniform, the FFT does not apply directly. Generating such a phase screen is computation intensive which greatly reduces simulation speed. In this paper, we develop a fast, more accurate method to generate atmospheric turbulence phase screens, according to non-uniforming sampling. The nonequispaced fast Fourier transform (NUFFT) arises in a variety of application areas, ranging from medical imaging to radio astronomy to the numerical solution of partial differential equations. Speeding up the simulation of atmospheric turbulence phase screens is possible by using the non-uniform fast Fourier transform. In this paper, the atmospheric turbulence phase screen is decomposed into a series of harmonics. Then the non-uniform distributed harmonics are projected onto over-sampled uniform grid by using the Gaussian kernel function. Atmospheric turbulence phase screen will be generated using the standard fast Fourier transform on the over-sampled uniform grid. The atmospheric turbulence phase screens can be generated quickly. Using Kolmogorov spectrum model in this paper, the phase screens can be generated quickly. The performances of generated phase screens are analyzed through their phase structure functions. The statistical results are in very good agreement with the theoretical values. The relative error curve of simulation phase screens is calculated and analyzed. The more the oversampling grid, the more the relative error is. Compared with the result from the direct harmonics summation method, the error here mainly concentrates in high-frequency region where the sampling frequency points are sparse. However, the atmosphere turbulence phase screen is simulated in high accuracy on the whole. Compared with the time cost of the harmonics summation, the time using NUFFT is decreased to about 800 times. The simulated phase screens indicate that non-uniform fast Fourier transform is able to generate atmospheric turbulence phase screen with high accuracy and fast speed.

Transition from geostrophic turbulence to inertia-gravity waves in the atmospheric energy spectrum.

Midlatitude fluctuations of the atmospheric winds on scales of thousands of kilometers, the most energetic of such fluctuations, are strongly constrained by the Earth's rotation and the atmosphere's stratification. As a result of these constraints, the flow is quasi-2D and energy is trapped at large scales—nonlinear turbulent interactions transfer energy to larger scales, but not to smaller scales. Aircraft observations of wind and temperature near the tropopause indicate that fluctuations at horizontal scales smaller than about 500 km are more energetic than expected from these quasi-2D dynamics. We present an analysis of the observations that indicates that these smaller-scale motions are due to approximately linear inertia-gravity waves, contrary to recent claims that these scales are strongly turbulent. Specifically, the aircraft velocity and temperature measurements are separated into two components: one due to the quasi-2D dynamics and one due to linear inertia-gravity waves. Quasi-2D dynamics dominate at scales larger than 500 km; inertia-gravity waves dominate at scales smaller than 500 km.

Atmospheric muons: experimental aspects

Abstract. We present a review of atmospheric muon flux and energy spectrum measurements over almost six decades of muon momentum. Sea level and underground/water/ice experiments are considered. Possible sources of systematic errors in the measurements are examined. The characteristics of underground/water muons (muons in bundle, lateral distribution, energy spectrum) are discussed. The connection between the atmospheric muon and neutrino measurements are also reported.

Measurement of the atmospheric neutrino energy spectrum from 100 GeV to 400 TeV with IceCube

A measurement of the atmospheric muon neutrino energy spectrum from 100 GeV to 400 TeV was performed using a data sample of about 18,000 up-going atmospheric muon neutrino events in IceCube. Boosted decision trees were used for event selection to reject mis-reconstructed atmospheric muons and obtain a sample of up-going muon neutrino events. Background contamination in the final event sample is less than one percent. This is the first measurement of atmospheric neutrinos up to 400 TeV, and is fundamental to understanding the impact of this neutrino background on astrophysical neutrino observations with IceCube. The measured spectrum is consistent with predictions for the atmospheric muon neutrino plus muon antineutrino flux.

Comment on "Reinterpreting aircraft measurement in anisotropic scaling turbulence" by Lovejoy et al. (2009)

Abstract. Recently, Lovejoy et al. (2009) argued that the steep ~k−3 atmospheric kinetic energy spectrum at synoptic scales (≥1000 km) observed by aircraft is a spurious artefact of aircraft following isobars instead of isoheights. Without taking into account the earth's rotation they hypothesise that the horizontal atmospheric energy spectrum should scale as k−5/3 at all scales. We point out that the approximate k−3-spectrum at synoptic scales has been observed by a number of non-aircraft means since the 1960s and that general circulation models and other current models have successfully produced this spectrum. We also argue that the vertical movements of the aircraft are far too small to cause any strong effect on the measured spectrum at synoptic scales.

Monte Carlo calculation of the atmospheric antinucleon flux

The atmospheric antiproton and antineutron energy spectra are calculated at float altitude using the CORSIKA package in a three-dimensional Monte Carlo simulation. The hadronic interaction is treated by the FLUKA code below 80 GeV/nucleon and NEXUS elsewhere. The solar modulation which is described by the force field theory and the geomagnetic effects are taken into account. The numerical results are compared with the BESS-2001 experimental data.

Muons in IceCube

The IceCube detector allows for the first time a measurement of atmospheric muon and neutrino energy spectra from tens of GeV up to the PeV range. The lepton flux in the highest energy region depends on both the primary cosmic ray composition around the “knee” and the contribution from prompt decays of mostly charmed hadrons produced in air showers. It is demonstrated here that a direct measurement of the atmospheric muon spectrum in the region above 100 TeV is feasible using data that is already available.

Uncertainties of Estimates of Inertia–Gravity Energy in the Atmosphere. Part I: Intercomparison of Four Analysis Systems

Abstract This paper presents the application of the normal-mode functions to diagnose the atmospheric energy spectra in terms of balanced and inertia–gravity (IG) contributions. A set of three-dimensional orthogonal normal modes is applied to four analysis datasets from July 2007. The datasets are the operational analysis systems of NCEP and ECMWF, the NCEP–NCAR reanalyses, and the Data Assimilation Research Testbed–Community Atmospheric Model (DART–CAM), an ensemble analysis system developed at NCAR. The differences between the datasets can be considered as a measure of uncertainty of the IG contribution to the global energetics. The results show that the percentage of IG motion in the present NCEP, ECMWF, and DART–CAM analysis systems is between 1% and 2% of the total energy field. In the wave part of the flow (zonal wavenumber k ≠ 0), the IG energy contribution is between 9% and 15%. On the contrary, the NCEP–NCAR reanalyses contain more IG motion, especially in the Southern Hemisphere extratropics. Each analysis contains more energy in the eastward IG motion than in its westward counterpart. The difference is about 2%–3% of the total wave energy and it is associated with the motions projected onto the Kelvin wave in the tropics. The selected truncation parameters of the expansion (zonal, meridional, and vertical truncation) ensure that the projection provides the optimal fit to the input data on model levels. This approach is different from previous applications of the normal modes and under the linearity assumption it allows the application of the inverse projection to obtain details of circulation associated with a selected type of motion. The bulk of the IG motion is confined to the tropics. For the successful reproduction of three-dimensional circulations by the normal modes it is important that the expansion includes a number of vertical modes.

Two Comments on the Surface Quasigeostrophic Model for the Atmospheric Energy Spectrum

Abstract The horizontal wavenumber spectra of wind and temperature in the upper troposphere and lower stratosphere display a narrow k−3 range at scales on the order of 1000 km and a broad k−5/3 range at mesoscales on the order of 1 to 500 km. Recently, Tulloch and Smith suggested that a surface quasigeostrophic (SQG) turbulence model can explain the observed spectra. Here, it is first argued that the mesoscale spectra are not likely to be explained by any quasigeostrophic model because the Rossby number corresponding to the mesoscale dynamics is on the order of unity or larger. Then it is argued that the SQG model in particular cannot explain the observations because its mesoscale spectrum displays a k−5/3 dependence only in a very thin layer just below the tropopause. The thickness of this layer can be estimated to be of the order of 10 m, whereas aircraft measurements are typically performed several hundred meters away from the tropopause.

Quasigeostrophic Turbulence with Explicit Surface Dynamics: Application to the Atmospheric Energy Spectrum

Abstract The horizontal wavenumber spectra of wind and temperature near the tropopause have a steep −3 slope at synoptic scales and a shallower −5/3 slope at mesoscales, with a transition between the two regimes at a wavelength of about 450 km. Here it is demonstrated that a quasigeostrophic model driven by baroclinic instability exhibits such a transition near its upper boundary (analogous to the tropopause) when surface temperature advection at that boundary is properly resolved and forced. To accurately represent surface advection at the upper and lower boundaries, the vertical structure of the model streamfunction is decomposed into four parts, representing the interior flow with the first two neutral modes, and each surface with its Green’s function solution, resulting in a system with four prognostic equations. Mean temperature gradients are applied at each surface, and a mean potential vorticity gradient consisting both of β and vertical shear is applied in the interior. The system exhibits three fundamental types of baroclinic instability: interactions between the upper and lower surfaces (Eady type), interactions between one surface and the interior (Charney type), and interactions between the barotropic and baroclinic interior modes (Phillips type). The turbulent steady states that result from each of these instabilities are distinct, and those of the former two types yield shallow kinetic energy spectra at small scales along those boundaries where mean temperature gradients are present. When both mean interior and surface gradients are present, the surface spectrum reflects a superposition of the interior-dominated −3 slope cascade at large scales, and the surface-dominated −5/3 slope cascade at small scales. The transition wavenumber depends linearly on the ratio of the interior potential vorticity gradient to the surface temperature gradient, and scales with the inverse of the deformation scale when β = 0.

An Analysis of the 3-D Atmospheric Energy Spectra and Interactions Using Analytical Vertical Structure Functions and Two Reanalyses

In this study, the energy spectrum and the energy interactions of the atmospheric general circulation are analyzed, using the expansion in three dimensional normal mode functions for JRA-25 and ERA-40. The analytical solutions of the vertical structure equation are used for the expansion in the vertical direction. The problem of aliasing associated with the numerical solution is avoided by the present approach. According to the result of the energy spectrum, using the analytical vertical structure functions, it is found that the energy spectrum indicates a clear peak in the middle vertical modes, and the spectrum decreases monotonically at the higher order vertical modes. The energy interactions for lower order vertical modes are consistent with that by Tanaka and Kung (1988). It is found from the analysis of the energy interactions that there is another energy source region in the higher order vertical modes in the zonal field. It is also found from the energy flux analysis in the vertical domain that the atmospheric energy is converted from baroclinic component to barotropic component.

A theory for the atmospheric energy spectrum: Depth-limited temperature anomalies at the tropopause

The horizontal spectra of atmospheric wind and temperature at the tropopause have a steep -3 slope at synoptic scales, but transition to -5/3 at wavelengths of the order of 500-1,000 km [Nastrom, G. D. & Gage, K. S. (1985) J. Atmos. Sci. 42, 950-960]. Here we demonstrate that a model that assumes zero potential vorticity and constant stratification N over a finite-depth H in the troposphere exhibits the same type of spectra. In this model, temperature perturbations generated at the planetary scale excite a direct cascade of energy with a slope of -3 at large scales, -5/3 at small scales, and a transition near horizontal wavenumber k(t) = f/NH, where f is the Coriolis parameter. Ballpark atmospheric estimates for N, f, and H give a transition wavenumber near that observed, and numerical simulations of the previously undescribed model verify the expected behavior. Despite its simplicity, the model is consistent with a number of perplexing features in the observations and demonstrates that a complete theory for mesoscale dynamics must take temperature advection at boundaries into account.