Simulation of atmospheric effects on the emergent radiation over a checkerboard type of terrain

To evalute the effect of the non-uniform surface on the radiation field, the upwelling radiation at the top of the atmosphere bounded by the checkerboard type of terrain is computed using the modified doubling method. The terrain is composed of the square Lambert surfaces with two different albedoes. The dimension of the each square is assumed to be 0.5–6 km. The radiance of the terrain is discussed with respect to the atmospheric effect. The observational site is located at altitude 30 km. The corresponding projected point on the ground is located at the center of a square. The solar and observational direction is located in the plane parallel to the checkerboard squares. The atmosphere is assumed to be homogeneous, which is composed of aerosol and molecules, where the model aerosol is of the oceanic or the water soluble types.Numerical simulation exhibits the extraordinary effect near the edge of each squares. The radiance of the terrain depends upon the difference of albedoes and size of squares. It increases with the increase of the dimension of the square. It decreases with the optical thickness. At large optical thickness, the variation of radiation with zenith direction depends upon the aerosol characteristics. It shows little dependence on the solar zenith angle if less than 20°.     

Atmospheric effect on the upwelling radiation at the top of the atmosphere over a stream

A new version is adopted for the evaluation of the upwelling radiation from atmosphere bounded by the surface, where the surface is composed of two half semi-infinite Lambert surfaces and a stream is inserted between them. The contrast of the stream is discussed with respect to the atmospheric effect. The width of the stream is considered to be 0.5, 1, and 3km; The solar and observational direction is located in the normal plane to the stream. The observational site is located at altitude 30km. The horizontal distance of observational site to the stream is fixed to 6.28 . The atmosphere is assumed to be homogeneous, which is composed of aerosol and molecules, where the model aerosol is of the oceanic type.In the computational procedure, a probability of radiation interacting with respective half surfaces and the stream are calculated based on the assumption of single scattering in the atmosphere, where isotropic scattering is undertaken. By use of this probability, the emergent radiation at the top of the atmosphere is calculated approximately by considering the radiative interactions between atmosphere and surfaces up to twice. The numerical simulation exhibits the extraordinary effect near the stream. The contrast of the stream depends upon the albedo of the surrounding surfaces. It increases with the increase of the stream width and decreases with the optical thickness.     

Emergent radiation from the atmosphere bounded by the two halves of the Lambert surface with different albedos

For the evaluation of the effect of the nonuniform surface albedo to the emergent radiation from the atmosphere, the emergent radiation from the atmosphere bounded by the two-halves of the Lambert surface with different albedos is computed. The principal plane is assumed to be perpendicular to the boundary of surfaces. The atmosphere is assumed to be homogeneous, which is composed of aerosol, molecules, and absorbent gases. Their optical thicknesses are 0.25, 0.23, and 0.02, respectively. The model aerosol is of the oceanic and water soluble types.In the computational procedure, the emergent radiation is approximated by the contributions due to the multiple scattering in the atmosphere, directly attenuated radiation, and radiation due to single scattering in the atmosphere which is reflected by the Lambert surface (up to 4 interactive radiative modes between atmosphere and surface). For quantitative analysis, results are compared with those of the atmosphere-uniform surface model, where the multiple scattering is considered. The numerical simulation exhibits the extraordinary effect near the surface boundary of different albedos. The effect decreases exponentially with the distance from the boundary. It is a function of the observational position, difference of surface albedos, optical thickness and aerosol type.The upward radiance would simply be evaluated using the present scattering approximation method if the atmosphere is in clear condition. Whereas in hazy condition, the effect of multiple scattering in the atmosphere should be considered more precisely, since the upward radiance exhibit a strong dependence on observational nadir angles due to multiple scattering in the atmosphere. Furthermore, it depends on the optical characteristics of aerosols.     

Heat balance in Titan's atmosphere

The recent measurements of the vertical distribution and optical properties of haze aerosols as well as of the absorption coefficients for methane at long paths and cold temperatures by the Huygens entry probe of Titan permit the computation of the solar heating rate on Titan with greater certainty than heretofore. We use the haze model derived from the Descent Imager/Spectral Radiometer (DISR) instrument on the Huygens probe [Tomasko, M.G., Doose, L., Engel, S., Dafoe, L.E., West, R., Lemmon, M., Karkoschka, E., See, C., 2008a. A model of Titan's aerosols based on measurements made inside the atmosphere. Planet. Space Sci., this issue, doi:10.1016/j.pss.2007.11.019] to evaluate the variation in solar heating rate with altitude and solar zenith angle in Titan's atmosphere. We find the disk-averaged solar energy deposition profile to be in remarkably good agreement with earlier estimates using very different aerosol distributions and optical properties. We also evaluated the radiative cooling rate using measurements of the thermal emission spectrum by the Cassini Composite Infrared Spectrometer (CIRS) around the latitude of the Huygens site. The thermal flux was calculated as a function of altitude using temperature, gas, and haze profiles derived from Huygens and Cassini/CIRS data. We find that the cooling rate profile is in good agreement with the solar heating profile averaged over the planet if the haze structure is assumed the same at all latitudes. We also computed the solar energy deposition profile at the 10°S latitude of the probe-landing site averaged over one Titan day. We find that some 80% of the sunlight that strikes the top of the atmosphere at this latitude is absorbed in all, with 60% of the incident solar energy absorbed below 150 km, 40% below 80 km, and 11% at the surface at the time of the Huygens landing near the beginning of summer in the southern hemisphere. We compare the radiative cooling rate with the solar heating rate near the Huygens landing site averaging over all longitudes. At this location, we find that the solar heating rate exceeds the radiative cooling rate by a maximum of 0.5 K/Titan day near 120 km altitude and decreases strongly above and below this altitude. Since there is no evidence that the temperature structure at this latitude is changing, the general circulation must redistribute this heat to higher latitudes.     

Emergent radiation from the atmosphere bounded by the two half Lambert surfaces composed of different albedo,II

For the evaluation of the effect of the non-uniform surface albedo on the emergent radiation from the atmosphere, the emergent radiation from the atmosphere bounded by the two half Lambert surfaces composed of different albedo is computed. This paper is the improved version of the previous paper (Takashima and Masuda, 1991). The atmosphere is assumed to be homogeneous, which is composed of aerosol, molecules, and absorbent gases. Their optical thicknesses are (1) 0.25, 0.23, and 0.02, and (2) 0.75, 0.23, and 0.02, respectively. The model aerosol is of the oceanic and water soluble types.In the computational procedure, the emergent radiation is calculated approximately by the contributions due to the multiple scattering in the atmosphere, and due to the diffusely or directly transmitted radiation through the atmosphere which is reflected by the surfaces once (4 interactive radiative modes between atmosphere and surface). Furthermore, to perform the hemispherical integration processing the radiative interaction, the transmission function based on the single scattering in the atmosphere is introduced and then the transmission function is averaged over the hemisphere with weighting function. The numerical simulation exhibits the extraordinary effect near the two half surface boundary of different albedoes. The effect decreases exponentially with the distance from the boundary. The effect depends on the atmospheric aerosol type, optical thickness, and surface albedo. The present version enables us to quantitatively discuss the radiative transfer trend near the boundary of two half surfaces. The upward radiance would simply be evaluated using the present scattering approximation method if the surface albedo is less than 0.3. The present method is thought of as a first step extending the one-dimensional radiative transfer model to two-dimensional using the doubling-adding method.     

Turbulence in the troposphere of Venus: Refined characteristics and new estimates

Based on spaceborne experimental data, characteristics of turbulence are calculated for the Venusian troposphere under conditions corresponding to the planet-averaged flux of solar radiation, which is equal to its value at a solar zenith angle of 66°. Additionally, given experimental data on radiation fluxes and their numerical calculations, turbulence characteristics were calculated for a solar zenith angle of 45°. The turbulence pattern is significantly different for small and large solar zenith angles. At large solar zenith angles, there exist an anomalous downward turbulent heat flux above 7–10 km and a normal upward flux at lower heights. At small zenith angles, the turbulent flux is normal throughout the entire troposphere. The dissipation of turbulent energy contributes significantly to the atmospheric heating in a wide range of altitudes. The spectrum of the time and space scales of dissipative processes in the troposphere is very wide and changes with height.Translated from Astronomicheskii Vestnik, Vol. 39, No. 1, 2005, pp. 38–50.Original Russian Text Copyright © 2005 by Izakov.     

High resolution observations of the 6300 Å oxygen line in the day airglow

Ground based high resolution (R ～ 120,000) spectra of the zenith day sky near 6300 Å were obtained with a PEPSIOS. When compared with the solar spectrum taken with the same spectrometer, the 6300.3 Å line of atomic oxygen was clearly present in emission. The apparent emission rate averaged 6 to 8 kR for solar zenith angles of 50 to 60 deg and decreased smoothly to about 1 kR as the solar zenith angle increased to 95 deg. The average emission line is somewhat different in width than the thermal line width expected with the Jacchia (1971) model for a 250 km altitude.     

The interpretation of velocity filtergrams

The paper describes a numerical experiment in which the effect of an assumed velocity distribution in the solar atmosphere on the intensity difference between a blue- and a red-wing filter-gram is derived. This results in the effective optical depth at which the velocity is measured. It is shown that this _eff strongly depends on the assumed velocity distribution.     

Distribution of HCN in Titan’s upper atmosphere from Cassini/VIMS observations at 3 μm

Cassini/VIMS limb observations have been used to retrieve vertical profiles of hydrogen cyanide (HCN) from its 3 μm emission in the region from 600 to 1100 km altitude at daytime. While the daytime emission is large up to about 1100 km, it vanishes at nighttime at very low altitudes, suggesting that the daytime emission originates under non-LTE conditions. The spectrally integrated radiances around 3.0 μm shows a monotonically decrease with tangent altitude, and a slight increase with solar zenith angle in the 40-80° interval around 800 km.A sophisticated non-LTE model of HCN energy levels has been developed in order to retrieve the HCN abundance. The population of the HCN 0 0⁰ 1 energy level, that contributes mostly to the 3.0 μm limb radiance, has been shown to change significantly with the solar zenith angle (SZA) and HCN abundance. Also its population varies with the collisional rate coefficients, whose uncertainties induced errors in the retrieved HCN of about 10% at 600-800 km and about 5% above. HCN concentrations have been retrieved from a set of spectra profiles, covering a wide range of latitudes and solar zenith angles, by applying a line-by-line inversion code. The results show a significant atmospheric variability above ∼800 km with larger values for weaker solar illumination. The HCN shows a very good correlation with solar zenith angles, irrespective of latitude and local time, suggesting that HCN at these high altitudes is in or close to photochemical equilibrium. A comparison with UVS and UVIS measurements show that these are close to the lower limit (smaller SZAs) of the VIMS observations above 750 km. However, they are in reasonable agreement when combining the rather large UV measurement errors and the atmospheric variability observed in VIMS. A comparison of the mean profile derived here with the widely used profile reported by Yelle and Griffith (Yelle R.V., Griffith, C.A. [2003]. Icarus 166, 107-115) shows a good agreement for altitudes ranging from 850 to 1050 km, while below these altitudes our result exhibits higher concentrations.     

Daytime ionosphere of Venus as studied with Veneras 9 and 10 dual-frequency radio occultation experiments

We present results of the dual-frequency radio sounding of the Venusian ionosphere carried out by the Venera 9 and 10 satellites in 1975. Thirteen height profiles of electron density for different solar zenith angles varying from 10 to 87° have been obtained by analyzing the refraction bending of radiorays in the sounded ionssphere. The main maximum of electron density at a height of 140–150 km depends on the solar zenith angle and is 1.4 to 5 × 10⁵ cm^?3. The lower maximum is determined definitely to be at ～130 km high. In the main and lower maxima the electron density variations with solar zenith angle are in good agreement with the Chapman layer theory. For the first time it is found that the height of the upper boundary for the daytime ionosphere (h_i) depends regularly on the solar zenith angle. At Z_⊙ < 60°, h_i does not exceed 300 km while at Z_⊙ > 60°, it increases with Z_⊙ and comes up to ～ 600 km at Z_⊙ ～ 80°.     

Variation of Spectral Radiance of the Zenith Sky During the Annular Eclipse on May 21, 2012

The absolute brightness of the zenith sky was measured using a simple calibrated spectrometer during the annular solar eclipse event on May 21, 2012 in Fujioka City, Japan (36.2924°N, 139.0823°E). The sensitivity of the spectrometer was calibrated as a function of wavelength between 400 and 700 nm with an integral sphere. The brightness of the sky decreased to 6 % of its usual condition at the maximum magnitude of the annular eclipse of 0.95 for all wavelengths. The curve describing the variation of sky brightness accords well with the total luminosity of the solar disk estimated by a simple model that accounts for the limb darkening effect. This study provides zenith sky radiance as a function of wavelength and solar elevation angle, which is useful for the investigation of new optical instruments for atmospheric studies.     

Latitudinal variations in Titan’s methane and haze from Cassini VIMS observations

We analyze observations taken with Cassini’s Visual and Infrared Mapping Spectrometer (VIMS), to determine the current methane and haze latitudinal distribution between 60°S and 40°N. The methane variation was measured primarily from its absorption band at 0.61 μm, which is optically thin enough to be sensitive to the methane abundance at 20-50 km altitude. Haze characteristics were determined from Titan’s 0.4-1.6 μm spectra, which sample Titan’s atmosphere from the surface to 200 km altitude. Radiative transfer models based on the haze properties and methane absorption profiles at the Huygens site reproduced the observed VIMS spectra and allowed us to retrieve latitude variations in the methane abundance and haze. We find the haze variations can be reproduced by varying only the density and single scattering albedo above 80 km altitude. There is an ambiguity between methane abundance and haze optical depth, because higher haze optical depth causes shallower methane bands; thus a family of solutions is allowed by the data. We find that haze variations alone, with a constant methane abundance, can reproduce the spatial variation in the methane bands if the haze density increases by 60% between 20°S and 10°S (roughly the sub-solar latitude) and single scattering absorption increases by 20% between 60°S and 40°N. On the other hand, a higher abundance of methane between 20 and 50 km in the summer hemisphere, as much as two times that of the winter hemisphere, is also possible, if the haze variations are minimized. The range of possible methane variations between 27°S and 19°N is consistent with condensation as a result of temperature variations of 0-1.5 K at 20-30 km. Our analysis indicates that the latitudinal variations in Titan’s visible to near-IR albedo, the north/south asymmetry (NSA), result primarily from variations in the thickness of the darker haze layer, detected by Huygens DISR, above 80 km altitude. If we assume little to no latitudinal methane variations we can reproduce the NSA wavelength signatures with the derived haze characteristics. We calculate the solar heating rate as a function of latitude and derive variations of ∼10-15% near the sub-solar latitude resulting from the NSA. Most of the latitudinal variations in the heating rate stem from changes in solar zenith angle rather than compositional variations.     

Upper thermal boundary layer of planetary atmosphere: An attempt of developing a general model

In any planetary atmosphere there is an uppermost layer in which the molecular thermal conduction is a significant mechanism of forming the thermal structure of the atmosphere. In this paper, the similarity approach is first used to develop the 1-D general model of aforementioned layer. The main concepts of the model are (i) the radiative equilibrium condition at the lower boundary of the layer and (ii) taking into account a single rovibrational band for radiative cooling of the layer. Five dimensionless parameters of the model characterize both “strengths” and altitudinal distributions of heat sources and sinks in the layer, including an effect of the atmosphere under the layer. By fitting the modeled temperature profile to the mean empirical profile, both the magnitudes of the parameters and the relations between them have been determined for the Earth and Mars. Distinctions between these planets in both the parameter magnitudes and relationships can be accounted for by distinction in composition of their atmospheres. For both planets the model shows weak sensitivity of the modeled temperature profile to significant changes in the state of the underlying atmosphere. The model demonstrates some prognostic capabilities. Namely, the fitting reveals presence of O in the martian thermosphere. (However, the fractional O abundance is overestimated.) From drag deceleration of the MGS orbiter the mean temperature profile of the martian thermosphere between 115 and 170 km has been derived for the solar zenith angle of 45°-70°, the solar longitude of 30°-80°, and the latitude range from −10° to 60°at a moderate level of solar activity.     

The troposphere-stratosphere radiation field at twilight: A spherical model

Time-dependent calculations of trace constituent distributions require as input the dissociating radiation field as a function of altitude and solar zenith angle. An isotropic, spherical, multiple scattering model of the radiation field has been developed to determine the radiation field at twilight. Comparison of the spherical model with a plane parallel model at twilight shows that: (1) for solar zenith angles less than 92°, plane parallel solutions for the source function are suitable if the initial deposition of solar energy is calculated for a spherical atmosphere; (2) for solar zenith angles greater than 92°, the plane parallel radiation field can be several orders of magnitude smaller than that calculated with the spherical model; (3) at altitudes above 40 km and at all solar zenith angles, the spherical model predicts 10–20% less radiation than the radiation field calculated with the plane parallel model. Calculations of the rate of photodissociation of NO₂ in the troposphere and stratosphere show that the spherical model yields significantly higher values at solar zenith angles greater than 92°.     

A spatially confined long-lived stream of solar particles

The intensities of low-energy solar-interplanetary electrons and ions at 1 AU occasionally change in a square-wave fashion. The changes may be increases or decreases and they have duration of a few hours. In one such example following a solar flare, particles flow away from the Sun in a well-defined channel 2.5 × 10⁶ km in width for twenty hours or longer. We believe that the interplanetary magnetic lines defined by this channel connect to an active region at 16° N solar latitude. At this time the Earth was located at a solar latitude of 2° S. Evidently the particle channel connects to a region of the solar atmosphere which supplies particles over these long times either via storage of the flare accelerated particles or else by continuous acceleration. Arguments are given against the latter possibility. We discuss a model for coronal storage which is consistent with the observations.Also Physics Department.     

The interpretation of velocity filtergrams

From simultaneous filtergrams taken in opposite wings of the 6569.2 solar absorption line we derive the velocity profile of an average solar granule. We definitely established the existence of the horizontal outflow in a granule in addition to the vertical upflow at the granule center. The magnitude of this outflow is strongly dependent on the influence of instrumental and atmospheric smoothing and on the effective height in the solar atmosphere at which the velocity is measured. The maximum upflow (at the granule center) equals 0.4 km/sec, the maximum outflow (500 km from the granule center) equals 0.25 km/sec.Part of the research reported here was carried out while the author was at the High Altitude Observatory, Boulder, Colorado.     

A model of Titan's aerosols based on measurements made inside the atmosphere

The descent imager/spectral radiometer (DISR) instrument aboard the Huygens probe into the atmosphere of Titan measured the brightness of sunlight using a complement of spectrometers, photometers, and cameras that covered the spectral range from 350 to 1600 nm, looked both upward and downward, and made measurements at altitudes from 150 km to the surface. Measurements from the upward-looking visible and infrared spectrometers are described in Tomasko et al. [2008a. Measurements of methane absorption by the descent imager/spectral radiometer (DISR) during its descent through Titan's atmosphere. Planet. Space Sci., this volume]. Here, we very briefly review the measurements by the violet photometers, the downward-looking visible and infrared spectrometers, and the upward-looking solar aureole (SA) camera. Taken together, the DISR measurements constrain the vertical distribution and wavelength dependence of opacity, single-scattering albedo, and phase function of the aerosols in Titan's atmosphere.Comparison of the inferred aerosol properties with computations of scattering from fractal aggregate particles indicates the size and shape of the aerosols. We find that the aggregates require monomers of radius 0.05 μm or smaller and that the number of monomers in the loose aggregates is roughly 3000 above 60 km. The single-scattering albedo of the aerosols above 140 km altitude is similar to that predicted for some tholins measured in laboratory experiments, although we find that the single-scattering albedo of the aerosols increases with depth into the atmosphere between 140 and 80 km altitude, possibly due to condensation of other gases on the haze particles. The number density of aerosols is about 5/cm³ at 80 km altitude, and decreases with a scale height of 65 km to higher altitudes. The aerosol opacity above 80 km varies as the wavelength to the −2.34 power between 350 and 1600 nm.Between 80 and 30 km the cumulative aerosol opacity increases linearly with increasing depth in the atmosphere. The total aerosol opacity in this altitude range varies as the wavelength to the −1.41 power. The single-scattering phase function of the aerosols in this region is also consistent with the fractal particles found above 60 km.In the lower 30 km of the atmosphere, the wavelength dependence of the aerosol opacity varies as the wavelength to the −0.97 power, much less than at higher altitudes. This suggests that the aerosols here grow to still larger sizes, possibly by incorporation of methane into the aerosols. Here the cumulative opacity also increases linearly with depth, but at some wavelengths the rate is slightly different than above 30 km altitude.For purely fractal particles in the lowest few km, the intensity looking upward opposite to the azimuth of the sun decreases with increasing zenith angle faster than the observations in red light if the single-scattering albedo is assumed constant with altitude at these low altitudes. This discrepancy can be decreased if the single-scattering albedo decreases with altitude in this region. A possible explanation is that the brightest aerosols near 30 km altitude contain significant amounts of methane, and that the decreasing albedo at lower altitudes may reflect the evaporation of some of the methane as the aerosols fall into dryer layers of the atmosphere. An alternative explanation is that there may be spherical particles in the bottom few kilometers of the atmosphere.     

High altitude haze: Influence of monomer particles on Titan’s temperature profile

The present study investigates the role of high altitude monomer particles in the energy balance of Titan’s upper atmosphere above an assumed low and high aggregate formation altitude of 385 km and 535 km. A ‘single particle approach’ was applied, where the starting point is the energy balance of an individual aerosol. In our analysis 0.01–0.06 μm radius aerosol particles were chosen for the proposed monomer formation regions. These particles absorb solar radiation, emit in the infrared, and are energetically linked to the surrounding gas by thermal conduction. To compute the monomer particle heating effect, the aerosols are assumed to radiate directly to space. We found that high altitude monomers may affect the profile of Titan’s thermosphere from 2 to 20 K depending on the formation altitude of fluffy non-spherical aggregates, the monomer size and distribution. The actual Titan temperature profile in this altitude range including all heating effects will be measured by the HASI instrument during the descent of the Huygens probe.     

Optical Response of the Atmosphere During the Caribbean Total Solar Eclipses of 26 February 1998 and of 3 February 1916 at Falcón state,Venezuela

An investigation of the optical response of the atmosphere before, during, and afterthe total solar eclipse of 26 February 1998 at the Caribbean Peninsula of Paraguaná (Falcón State) in Venezuela, was made by measuring photometrically the intensity of the sky brightness in three strategic directions: zenith, horizon anti-parallel or opposite the umbra path, and horizon perpendicular to this path. From these measurements, and by applying in an inverse way an empirical photometric model, very rough estimations of theextinction coefficient, and also of the average optical depth, were obtained in one of these particular directions. However based on meteorological measurements such as those of relative humidity and temperature, and applying a different model, a better estimation in the visual of the total global extinction coefficient of the sky (except the horizon), were made considering the contribution of each component: atmospheric aerosol, water vapour, ozone and Rayleigh scattering. It is shown that this global coefficient is mostly dependent upon aerosol extinction. In spite of the strong reduction of sky brightness photometrically observed during the totality, the results show that the sky was not dark. This is confirmed by the results obtained for the total global extinction coefficient. Additionally it is estimated that the total solar eclipse that took place also in Falcón State, Venezuela, at the beginning of the last century on 3 February 1916, was 30% darker that the 1998 eclipse, and that atmospheric aerosol played a relevant and similar role in the scattering of sunlight during the totality as it was for 1998's. Visual observations made during each event, which show that at length only one or two bright stars could be seen in the sky, support the results obtained for both eclipses.     

Model of photoelectron impact ionization within the high latitude ionosphere at Mars: Comparison of calculated and measured electron density

The production rate, ion density and electron density are calculated between longitudes 0° and 360° E due to incident radiation of wavelength range 1-102.57 nm in the dayside atmosphere of Mars. These calculations are made by using global analytical yield spectrum (AYS) model at solar zenith angle 80° between latitudes 50° and 70° N for spring equinox and medium solar activity condition. These conditions are appropriate for Mars Global Surveyor (MGS) Phase 2 aerobraking period during which both the accelerometer and the radio occultation data are used. The calculated results are compared with MGS radio occultation measurements carried out at different latitudes (64.7°-67.3° N) and longitudes (0°-360° E) in December 1998 between solar zenith angle 78° and 81°. This measurement shows primary and secondary ionization peaks, which are varying with longitudes. Our calculation suggests that first peak is produced by photoionization and photoelectron impact ionization processes due to absorption of solar EUV radiation (9-102.57 nm). The second peak is produced by photoelectron impact ionization of soft X-ray photon (1-9 nm). There is a good agreement between our calculation and measurement as far as the maximum and the minimum values of primary peak altitude/peak density of electrons are concerned. However, the calculated values of secondary peak density and peak altitude are higher than the measured values by a factor of 1.5-2.0 and 1.1, respectively. The secondary peak is brought into agreement with the measurement using low X-ray flux by a factor of 2 to 3 below 9 nm. The longitudinal distribution of calculated and measured peak density and peak altitude are fitted by least-square method with 0.95 confidence limits.