Real Atmosphere Research Articles

Advances in numerical simulation of sonic boom in realistic atmospheres

Efficient and accurate numerical simulation of sonic boom is a key issue for both the design of low boom aircraft and the definition of a standard on supersonic overland flights. Atmospheric turbulence is known since the 1960s to significantly alter the ideal N-wave boom waveform. Such random fluctuations cannot be reproduced by the standard ray tracing method. Neither can it simulate the lateral boom beyond the geometrical carpet edge. There occur many non-geometrical features such as creeping waves, wave guiding or scattering. To progress in the direction of boom simulation beyond the geometrical approximation, we developed the so-called FLHOWARD3D software. For accuracy, it can handle 3D temperature, density or wind heterogeneities, atmospheric absorption, and nonlinear propagation effects. For efficiency, a one-way approximation is performed, neglecting the backscattered field. Nevertheless, the forward field satisfies an accurate dispersion relation, even in moving atmospheres. Involved physical effects are handled separately by optimized algorithms, combined by a second-order split-step approach. The resulting software is parallelized using the MPI paradigm. The performances of the software will be illustrated by two cases: boom scattering by turbulence, and lateral boom propagation in case of temperature inversion. This last case will be compared with flight test data.

A numerical study of infrasound scattering from atmospheric inhomogeneities based on the 3-D unsteady compressible Navier-Stokes equations

A direct numerical simulation of the compressible unsteady Navier-Stokes equations is performed to investigate the 3-D nonlinear acoustic field generated by a high-amplitude infrasonic source placed at ground level in a realistic atmosphere. High-order finite differences and a Runge-Kutta time integration scheme originally developed for aeroacoustic applications are employed. The atmosphere is parametrized as a stationary and vertically stratified medium, constructed by specifying a speed of sound and a mean wind profiles which mimic the main trends observed during the Misty-Picture experiment. In the present talk, after a general description of the acoustic field observed up to 140 km altitude and 450 km range, the scattering from stratospheric inhomogeneities is investigated. The spectrum of the scattered wave recorded at ground level is more particularly discussed and its dependence on the spectral properties of the inhomogeneities is highlighted. A fast method for computing the scattered field, based on a wavelet representation of the temperature and wind fluctuations, is finally presented.

Toward realistic simulations of magneto-thermal winds from weakly-ionized protoplanetary disks

Protoplanetary disks (PPDs) accrete onto their central T Tauri star via magnetic stresses. When the effect of ambipolar diffusion (AD) is included, and in the presence of a vertical magnetic field, the disk remains laminar between 1-5 au, and a magnetocentrifugal disk wind forms that provides an important mechanism for removing angular momentum. We present global MHD simulations of PPDs that include Ohmic resistivity and AD, where the time-dependent gas-phase electron and ion fractions are computed under FUV and X-ray ionization with a simplified recombination chemistry. To investigate whether the mass loading of the wind is potentially affected by the limited vertical extent of our existing simulations, we attempt to develop a model of a realistic disk atmosphere. To this end, by accounting for stellar irradiation and diffuse reprocessing of radiation, we aim at improving our models towards more realistic thermodynamic properties.

Secondary organic aerosol formation from in situ OH, O<sub>3</sub>, and NO<sub>3</sub> oxidation of ambient forest air in an oxidation flow reactor

Abstract. Ambient pine forest air was oxidized by OH, O3, or NO3 radicals using an oxidation flow reactor (OFR) during the BEACHON-RoMBAS (Bio–hydro–atmosphere interactions of Energy, Aerosols, Carbon, H2O, Organics and Nitrogen – Rocky Mountain Biogenic Aerosol Study) campaign to study biogenic secondary organic aerosol (SOA) formation and organic aerosol (OA) aging. A wide range of equivalent atmospheric photochemical ages was sampled, from hours up to days (for O3 and NO3) or weeks (for OH). Ambient air processed by the OFR was typically sampled every 20–30 min, in order to determine how the availability of SOA precursor gases in ambient air changed with diurnal and synoptic conditions, for each of the three oxidants. More SOA was formed during nighttime than daytime for all three oxidants, indicating that SOA precursor concentrations were higher at night. At all times of day, OH oxidation led to approximately 4 times more SOA formation than either O3 or NO3 oxidation. This is likely because O3 and NO3 will only react with gases containing C = C bonds (e.g., terpenes) to form SOA but will not react appreciably with many of their oxidation products or any species in the gas phase that lacks a C = C bond (e.g., pinonic acid, alkanes). In contrast, OH can continue to react with compounds that lack C = C bonds to produce SOA. Closure was achieved between the amount of SOA formed from O3 and NO3 oxidation in the OFR and the SOA predicted to form from measured concentrations of ambient monoterpenes and sesquiterpenes using published chamber yields. This is in contrast to previous work at this site (Palm et al., 2016), which has shown that a source of SOA from semi- and intermediate-volatility organic compounds (S/IVOCs) 3.4 times larger than the source from measured VOCs is needed to explain the measured SOA formation from OH oxidation. This work suggests that those S/IVOCs typically do not contain C = C bonds. O3 and NO3 oxidation produced SOA with elemental O : C and H : C similar to the least-oxidized OA observed in local ambient air, and neither oxidant led to net mass loss at the highest exposures, in contrast to OH oxidation. An OH exposure in the OFR equivalent to several hours of atmospheric aging also produced SOA with O : C and H : C values similar to ambient OA, while higher aging (days–weeks) led to formation of SOA with progressively higher O : C and lower H : C (and net mass loss at the highest exposures). NO3 oxidation led to the production of particulate organic nitrates (pRONO2), while OH and O3 oxidation (under low NO) did not, as expected. These measurements of SOA formation provide the first direct comparison of SOA formation potential and chemical evolution from OH, O3, and NO3 oxidation in the real atmosphere and help to clarify the oxidation processes that lead to SOA formation from biogenic hydrocarbons.

NaCl-Induced High-Temperature Corrosion of β21S Ti Alloy

Titanium alloys are very interesting for aeronautics applications because of their low density, high mechanical resistance and good resistance to corrosion in aggressive environments. However, recent developments impose the use of these materials at higher temperatures than those initially envisaged (above 400 °C), revealing some uncertainties of their behavior. Depending on the operating conditions, the material can be exposed to variable humidity levels and, in some cases, can be in contact with silica or marine salt. This study aims to evaluate the influence of NaCl solid deposit on the behavior of β21S Ti alloy at 560 °C under realistic ambient atmospheres. The tests were carried out in laboratory air and in water vapor-enriched air, on uncoated samples and on samples with solid NaCl deposit. The reaction-product evolution (up to 600 h) was characterized by thermogravimetric analysis, SEM observations (surface and cross section), XRD and micro-hardness profiling on cross sections. An aggravation of the corrosion phenomena in the presence of NaCl solid deposit was observed, that was related to the presence of gaseous metal chlorides, leading to the establishment of an active corrosion process.

Adaptive covariance relaxation methods for ensemble data assimilation: experiments in the real atmosphere

Covariance inflation plays an important role in the ensemble Kalman filter because the ensemble‐based error variance is usually underestimated due to various factors such as the limited ensemble size and model imperfections. Manual tuning of the inflation parameters by trial and error is computationally expensive; therefore, several studies have proposed approaches to adaptive estimation of the inflation parameters. Among others, this study focuses on the covariance relaxation method which realizes spatially dependent inflation with a spatially homogeneous relaxation parameter. This study performs a series of experiments with the non‐hydrostatic icosahedral atmospheric model (NICAM) and the local ensemble transform Kalman filter (LETKF) assimilating the real‐world conventional observations and satellite radiances. Two adaptive covariance relaxation methods are implemented: relaxation to prior spread based on Ying and Zhang (adaptive‐RTPS), and relaxation to prior perturbation (adaptive‐RTPP). Both adaptive‐RTPS and adaptive‐RTPP generally improve the analysis compared to a baseline control experiment with an adaptive multiplicative inflation method. However, the adaptive‐RTPS and adaptive‐RTPP methods lead to an over‐dispersive (under‐dispersive) ensemble in the sparsely (densely) observed regions compared with the adaptive multiplicative inflation method. We find that the adaptive‐RTPS and adaptive‐RTPP methods are robust to a sudden change in the observing networks and observation error settings.

SNR and transmission error rate for remote laser communication system in real atmosphere channel

Performance of remote laser communication system fluctuates greatly due to influence by atmospheric turbulence, it is difficult to assess its system error performance effectively. On the basis of the atmospheric attenuation channel and atmospheric turbulence channel, this paper establishes the integrated computation signal-to-noise ratio(SNR) function and transmission error rate function under the condition of atmospheric attenuation and the atmospheric turbulence, analyzes the affecting factors of the transmission error rate under two kinds of channel in remote transmission, calculates the relation between atmospheric attenuation coefficient and haze particle size under different visibility in atmospheric attenuation channel, as well as the relationship between the optimal threshold and intensity fluctuation under different transmitting powers in atmospheric turbulence channel. Through the test in atmospheric turbulence channel, results show that light intensity fluctuation is the main factor causing low system performance within a certain range of background noise, the new calculation method of SNR makes the variation between the actual system bit error rate and the achievable minimum bit error rate in theory several orders of magnitude. The models can effectively assess the performance of laser communication system under atmospheric attenuation and atmospheric turbulence, and provide a reference for relevant researches.

Numerical non-LTE 3D radiative transfer using a multigrid method

3D non-LTE radiative transfer problems are computationally demanding, and this sets limits on the size of the problems that can be solved. So far Multilevel Accelerated Lambda Iteration (MALI) has been to the method of choice to perform high-resolution computations in multidimensional problems. The disadvantage of MALI is that its computing time scales as $\mathcal{O}(n^2)$, with $n$ the number of grid points. When the grid gets finer, the computational cost increases quadratically. We aim to develop a 3D non-LTE radiative transfer code that is more efficient than MALI. We implement a non-linear multigrid, fast approximation storage scheme, into the existing Multi3D radiative transfer code. We verify our multigrid implementation by comparing with MALI computations. We show that multigrid can be employed in realistic problems with snapshots from 3D radiative-MHD simulations as input atmospheres. With multigrid, we obtain a factor 3.3-4.5 speedup compared to MALI. With full-multigrid the speed-up increases to a factor 6. The speedup is expected to increase for input atmospheres with more grid points and finer grid spacing. Solving 3D non-LTE radiative transfer problems using non-linear multigrid methods can be applied to realistic atmospheres with a substantial speed-up.

Modification of the Gravity Wave Parameterization in the Whole Atmosphere Community Climate Model: Motivation and Results

Abstract The current standard version of the Whole Atmosphere Community Climate Model (WACCM) simulates Southern Hemisphere winter and spring temperatures that are too cold compared with observations. This “cold-pole bias” leads to unrealistically low ozone column amounts in Antarctic spring. Here, the cold-pole problem is addressed by introducing additional mechanical forcing of the circulation via parameterized gravity waves. Insofar as observational guidance is ambiguous regarding the gravity waves that might be important in the Southern Hemisphere stratosphere, the impact of increasing the forcing by orographic gravity waves was investigated. This reduces the strength of the Antarctic polar vortex in WACCM, bringing it into closer agreement with observations, and accelerates the Brewer–Dobson circulation in the polar stratosphere, which warms the polar cap and improves substantially the simulation of Antarctic temperature. These improvements are achieved without degrading the performance of the model in the Northern Hemisphere stratosphere or in the mesosphere and lower thermosphere of either hemisphere. It is shown, finally, that other approaches that enhance gravity wave forcing can also reduce the cold-pole bias such that careful examination of observational evidence and model performance will be required to establish which gravity wave sources are dominant in the real atmosphere. This is especially important because a “downward control” analysis of these results suggests that the improvement of the cold-pole bias itself is not very sensitive to the details of how gravity wave drag is altered.

Effect of atmosphere parameter oscillation at high altitude in the northern hemisphere for near space hypersonic flight aerothermodynamic prediction

For real atmosphere parameter fluctuates from the standard atmosphere model according the time and geography with stochastic atmospheric wave, it is important to predict the deviation effect on the aerothermodynamics environment for gliding hypersonic vehicle. However, according to the experts at NASA Johnson Space Center, at present neither the standard atmosphere model or the reference atmospheric model is able to describe the complex real atmosphere accurately. Especially, above 70 km altitude, the atmosphere parameter varies complicatedly, and deviates from standard atmosphere model intensely. The measurement results of atmosphere parameter from SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) on TIMED satellite, launched at 2001, are testified widely with data from other sources. In this paper, based on measurement results between 2002 and 2010 from SABER on TIMED satellite, the atmosphere parameter statistics characters for 85 km altitude in typical months (January, April, July and October) and typical northern latitudes (0°, 20°, 40°, 60°, 80°) are obtained. In every research case, over 5000 stochastic samples are produced, which are satisfied with Max-Min distributing or normal distributing for the atmosphere model. The heating transfer on stagnation for stochastic sample in the on-the-spot survey parameter has been also studied. Then the statistics characteristics of the heating transfer on stagnation can be obtained and compared with the results based on U.S.1976 standard atmosphere, which shows the atmosphere oscillation statistics effect. The effect for latitudes and seasons on aerothermodynamics prediction has been investigated. It is shown that fluctuation for the atmosphere parameter plays an important role on the aerothermodynamics environment in near space flight. In the high altitude zone, season factor has a notable effect on the heating distribution. However, close to the equator, season factor has a little effect. At the same reason, heating transfer in higher altitude zone is usually greater than that from the standard model; on the contrary, heating transfer in lower altitude zone is general lower than that from the standard model. In summer (July), the higher latitude zone locates, the higher heating distribution it gets. The maximum heating transfer appears in July on 80° latitude. In extreme case, the maximum stagnation heating exceeds the result from the standard atmosphere model about 40%. At the same altitude, the maximum heating transfer appears in April or July. In the future work, the affection about the difference between Northern and Southern Hemisphere, between ocean and land and atmosphere parameter relativity will be researched.

Moisture‐radiative cooling instability

AbstractRadiative‐convective equilibrium (RCE)—the statistical equilibrium state of the atmosphere where convection and radiation interact in the absence of lateral transport—is widely used as a basic‐state model of the tropical atmosphere. The possibility that RCE may be unstable to development of large‐scale circulation has been raised by recent modeling, theoretical, and observational studies, and could have profound consequences for our understanding of tropical meteorology and climate. Here, we study the interaction between moisture and radiative cooling as a contributor to instability of RCE. We focus on whether the total atmospheric radiative cooling decreases with column water vapor; this condition, which we call moisture‐radiative cooling instability (MRCI), provides the potential for unstable growth of moist or dry perturbations. Analytic solutions to the gray‐gas radiative transfer equations show that MRCI is satisfied when the total column optical depth—linked to column water vapor—exceeds a critical threshold. Both the threshold and the growth rate of the instability depend strongly on the shape of the water vapor perturbation. Calculations with a realistic radiative transfer model confirm the existence of MRCI for typical tropical values of column water vapor, but show even stronger dependence on the vertical structure of water vapor perturbation. Finally, we analyze the sensitivity of atmospheric radiative cooling to variability in column water vapor in observed tropical soundings. We find that clear‐sky MRCI is satisfied across a range of locations and seasons in the real tropical atmosphere, with a partial growth rate of ∼1 month.

Simultaneously Photoacoustic Measurement of Carbon Dioxide and Nitrous Oxide Using a Quantum Cascade Laser

In this paper a photoacoustic senor for carbon dioxide and nitrous oxide detection is described which uses a quantum cascade laser. The sensor relies on a 4.43 μm continuous-wave room temperature quantum-cascade laser source and a homemade photoacoustic cell based on a cylindrical acoustic resonator. Primary laboratory tests have been performed for estimation of the achievable detection limits and possible applications for in situ and real time atmosphere measurements. It is demonstrated that the minimum detectable concentration of 13CO2 and N2O under laboratory conditions is 8 ppbv and 0.45 ppbv, respectively.

High molecular weight organic compounds (HMW-OCs) in severe winter haze: Direct observation and insights on the formation mechanism

High molecular weight organic compounds (HMW-OCs), formed as secondary organic aerosols (SOA), have been reported in many laboratory studies. However, little evidence of HMW-OCs formation, in particular during winter season in the real atmosphere, has been reported. In January 2013, Beijing faced historically severe haze pollution, in which the hourly PM2.5 concentration reached as high as 974 μg m−3. Four typical haze events (HE1 to HE4) were identified, and HE2 (Jan. 9–16) was the most serious of these. Based on the hourly observed chemical composition of PM2.5 and the daily organic composition analyzed by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS), we found that abundant ion peaks in m/z 200–850 appeared on heavy haze days, whereas these were negligible on a clear day, indicating the existence of HMW-OCs in the wintertime haze. A negative nonlinear correlation between HMW-OCs and O3 suggested that gas oxidation was not likely to be the dominant mechanism for HMW-OCs formation. During the heavy haze events, the relative humidity and mass ratio of H2O/PM2.5 reached as high as 80% and 0.2, respectively. The high water content and its good positive correlation with HMW-OCs indicated that an aqueous-phase process may be a significant pathway in wintertime. The evidence that acidity was much higher during HE2 (0.37 μg m−3) than on other days, as well as its strong correlation with HMW-OCs, indicated that acid-catalyzed reactions likely resulted in HMW-OCs formation during the heavy winter haze in Beijing.

Waveform inversion of acoustic waves for explosion yield estimation

AbstractWe present a new waveform inversion technique to estimate the energy of near‐surface explosions using atmospheric acoustic waves. Conventional methods often employ air blast models based on a homogeneous atmosphere, where the acoustic wave propagation effects (e.g., refraction and diffraction) are not taken into account, and therefore, their accuracy decreases with increasing source‐receiver distance. In this study, three‐dimensional acoustic simulations are performed with a finite difference method in realistic atmospheres and topography, and the modeled acoustic Green's functions are incorporated into the waveform inversion for the acoustic source time functions. The strength of the acoustic source is related to explosion yield based on a standard air blast model. The technique was applied to local explosions (<10 km) and provided reasonable yield estimates (<∼30% error) in the presence of realistic topography and atmospheric structure. The presented method can be extended to explosions recorded at far distance provided proper meteorological specifications.

A numerical study of nonlinear infrasound propagation in a windy atmosphere.

Direct numerical simulations of the two-dimensional unsteady compressible Navier-Stokes equations are performed to study the acoustic field generated by an infrasonic source in a realistic atmosphere. Some of the main phenomena affecting the propagation of infrasonic waves at large distances from the source are investigated. The effects of thermal and wind-related refraction on the signals recorded at ground level are highlighted, with particular emphasis on the phase shift induced by the presence of caustics in the acoustic field. Nonlinear waveform steepening associated with harmonic generation, and period lengthening, both of which are typical of large source amplitudes, are illustrated, and the importance of thermoviscous absorption in the upper atmosphere is clearly demonstrated. The role of diffraction in the shadow zone, around caustics and at stratospheric altitudes is also pointed out. The Navier-Stokes equations are solved using high-order finite-differences and a Runge-Kutta time integration method both originally developed for aeroacoustic applications, along with an adaptive shock-capturing algorithm which allows high-intensity acoustic fields to be examined. An improvement to the shock detection procedure is also proposed in order to meet the specificities of nonlinear propagation at long range. The modeling as well as the numerical results are reported in detail and discussed.

Rb and Zr abundances in massive Galactic AGB stars revisited

We report new abundances of Rb and Zr in a sample of massive Galactic asymptotic giant branch (AGB) stars that were previously studied with hydrostatic models by using more realistic dynamical model atmospheres. We use a modified version of the spectral synthesis code Turbospectrum, and consider the presence of a circumstellar envelope and a radial wind in the modelling of these Galactic AGB stars. The Rb and Zr are determined from the 7800 Å Rb I resonant line and the 6474 Å ZrO bandhead, respectively, and they are compared with the AGB nucleosynthesis theoretical predictions. The derived Rb abundances are much lower (∼⃒1-2 dex) with the new dynamical models, while the Zr abundances, however, are closer to the hydrostatic values. The new model atmospheres can help to resolve the problem of the mismatch between the observations and the nucleosynthesis theoretical predictions of massive AGB stars.

Analytical Model of an Asymmetric Sunspot with a Steady Plasma Flow in its Penumbra

A new exact analytical solution to the stationary problem of ideal magnetohydrodynamics is derived for an unipolar asymmetric sunspot immersed in a realistic solar atmosphere. The radial and vertical profiles of pressure, plasma density, and temperature in the visible layers of the sunspot are calculated. The reduction in plasma density in the magnetic funnel of the sunspot, corresponding to the Wilson depression, is also obtained. The magnetic structure of the sunspot is given analytically in a realistic way: a part of the magnetic flux of the sunspot approaches the surrounding photosphere at the outer edge of the penumbra. The magnetic field of the sunspot is not assumed to be axially symmetric. For the first time, the angular dependence of the physical variables in this model allows us to simulate not only a deviation from the circular shape of the sunspot, but also a fine filamentary structure of the sunspot penumbra. The Alfven Mach number (the ratio of the plasma speed to the Alfven speed) is zero at the center of the sunspot and rises slowly toward the periphery of the sunspot; this corresponds to the structure of the Evershed flow in the penumbra. The Evershed flow in our model is mainly concentrated in dark penumbral filaments, as is observed.

ZK-Burgers equation for three-dimensional Rossby solitary waves and its solutions as well as chirp effect

Two-dimensional Rossby solitary waves propagating in a line have attracted much attention in the past decade, whereas there is few research on three-dimensional Rossby solitary waves. But as is well known, three-dimensional Rossby solitary waves are more suitable for real ocean and atmosphere conditions. In this paper, using multiscale and perturbation expansion method, a new Zakharov-Kuznetsov (ZK)-Burgers equation is derived to describe three-dimensional Rossby solitary waves that propagate in a plane. By analyzing the equation we obtain the conservation laws of three-dimensional Rossby solitary waves. Based on the sine-cosine method, we give the classical solitary wave solutions of the ZK equation; on the other hand, by the Hirota method we also obtain the rational solutions, which are similar to the solutions of the Benjamin-Ono (BO) equation, the solutions of which can describe the algebraic solitary waves. The rational solutions of the ZK equations are worth of attention. Finally, with the help of the classical solitary wave solutions, similar to the fiber soliton communication, we discuss the dissipation and chirp effect of three-dimensional Rossby solitary waves.

A Four-Dimensional Incremental Analysis Update for the Ensemble Kalman Filter

Abstract The analysis produced by the ensemble Kalman filter (EnKF) may be dynamically inconsistent and contain unbalanced gravity waves that are absent in the real atmosphere. These imbalances can be exacerbated by covariance localization and inflation. One strategy to combat the imbalance in the analyses is the incremental analysis update (IAU), which uses the dynamic model to distribute the analyses increments over a time window. The IAU has been widely used in atmospheric and oceanic applications. However, the analysis increment that is gradually introduced during a model integration is often computed once and assumed to be constant for an assimilation window, which can be seen as a three-dimensional IAU (3DIAU). Thus, the propagation of the analysis increment in the assimilation window is neglected, yet this propagation may be important, especially for moving weather systems. To take into account the propagation of the analysis increment during an assimilation window, a four-dimensional IAU (4DIAU) used with the EnKF is presented. It constructs time-varying analysis increments by applying all observations in an assimilation window to state variables at different times during the assimilation window. It then gradually applies these time-varying analysis increments through the assimilation window. Results from a dry two-layer primitive equation model and the NCEP GFS show that EnKF with 4DIAU (EnKF-4DIAU) and 3DIAU (EnKF-3DIAU) reduce imbalances in the analysis compared to EnKF without initialization (EnKF-RAW). EnKF-4DIAU retains the time-varying information in the analysis increments better than EnKF-3DIAU, and produces better analysis and forecast than either EnKF-RAW or EnKF-3DIAU.

Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit

Context. This paper presents a numerical application of a self-consistent theory of partial redistribution in nonlocal thermodynamical equilibrium conditions, developed in previous papers of the series.Aims. The code was described in IV of this series. However, in that previous paper, the numerical results were unrealistic. The present paper presents an approximation able to restore the reliability of the outgoing polarization profiles.Methods. The convergence of the results is also proved. It is demonstrated that the step increment decreases like 1/N α , with α > 1.Results. Thanks to these additions, the results series behaves like a Riemann series, which is absolutely convergent. However, convergence is not fully reached in line wings within the allocated computing time. Development of efficient acceleration methods would be desirable for future work.Conclusions. Agreement between the computed and observed linear polarization profiles remains qualitative only. The discrepancy is assigned to the plane parallel atmosphere model, which is insufficient to describe the chromosphere, where these lines are formed. As all the integrals are numerical in the code, it could probably be adapted to more realistic and higher dimensional model atmospheres. However, this is time consuming for lines with a hyperfine structure, as in the Na I D lines. The net linear polarization observed in Na I D1 with the Zurich Imaging Polarimeter ZIMPOL mounted on the McMath-Pierce telescope at Kitt Peak is not confirmed by the present calculations and could be an artefact of instrumental polarization. The presence of instrumental polarization could be confirmed by the higher linear polarization degree observed by this instrument in the Na I D2 line center with respect to the present calculation result where the magnetic field is not accounted for. At this precise point, the Hanle effect acts as a depolarizing effect in the second solar spectrum. The observed linear polarization excess is found to be of the same order of magnitude in both line centers, namely 0.1%, which is also comparable to the instrumental polarization compensation level of this experiment.