OH radical’ s solar resonance fluorescence is the excited emergent light by solar radiation around 309 nm. A²Σ ⁺ is the excited state and X²Π is the ground state in A²Σ ⁺-X²Π (0, 0) transition. Due to Hund’ s cases (a) and (b) and Λ doubling of X²Π ^[11], these two levels split. Following selection rules for this transition, some rotational transitions are allowed in Figure 4^[12].

Fig.4

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	Fig.4 A2Σ +-X2Π (0, 0) allowed transitions

Rotational emission rate factor g measures the emission efficiency of a molecule, which means when being excited by solar radiation, how many photons can emit per second per molecule. Suppose that in mesosphere with thin optical depth, the observed intensity 4π I_v'v″ can be related to the g factor^[13],

4πIv'v″(z)=η(z)gv'v″(T, z)(1)

where η (z) is the column abundance along the viewing path and can be calculated by SCIATRAN. The g factor is a function of temperature T and tangent altitude z.

Rotational emission rate factor g may be calculated by the expression,

gg'g″(T)=S(J'J″)2J'+1ωv'v″πe2mc2fv'0×∑J=Λ+Σ∞λJ'J2πFJ'JS(J'J)2J+1NJ(T)(2)

Where the values of following parameters are the same as that in Stevens and Conway’ s paper.is the vibrational band branching ratio and f_v'0 is the band oscillator strength. S is Hö nl-London factors, The branching ratiois ω ₀₀=A₀₀/Σ A_0v″ taken to be 1.00. The constant πe2mc2=8.829× 10^-20 cm²· nm^-1 and the absorption oscillator strength f₀₀=1.04× 10^-3. λ is the wavelength of the absorption transitions. π F(photons/cm²/s/nm) used in [Stevens and Conway 1999] is the unattenuated solar irradiance at the top of the atmosphere. We modify it by considering the extinction from the sun to the tangent point, though the optical thickness is relatively small between 45km-85km. The extinction process is calculated by SCIATRAN.

There are other parameters need to be calculated using molecular spectroscopy theory, HITRAN databases^[14], energy level information J', J″ and low energy E₀. N_J(T) is the relative population in rotational level J at temperature T. It could be calculated by Boltzmann distribution.

If the hydroxyl molecules in the atmosphere are in thermal equilibrium, the rotational population distribution can be described by the Maxwell-Boltzmann distribution law^{[6, 15, 16]}.

N(v, v', J, J', T)=(2J+1)exp(-hcE(J)/kT)Q(T)(3)

where h is Plank’ s constant, c is the speed of light, E(J) (cm^-1) is the energy of the X²Π state, k is the Boltzmann constant, T is the equilibrium temperature in K, and Q(T) is the partition function. The partition function Q(T)=Q_vQ_r, where the vibrationalpartition function Q_v is

Qv=(1-exp[-hcωe/kT])-1(4)

ω _e is the first order vibrational constant which is equal to 3 737.761 cm^-1. Because of this large energy separation between vibrational levels, Q_v≈ 1 at middle atmospheric temperatures.

The rotational partition function Q_r is

Qr=∑J″, Σ″(2J″+1)exp(-hcE(J″, Ω″)/kT)(5)

Thus, N_J(T) is worked out as is showed in Figure 5.

Fig.5

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	Fig.5 Calculated relative population of the ground rotational states of OH

Solar irradiance showed in Figure 6 with a high spectral resolution of 3.5× 10^-4 nm in this band (308.2~309.8 nm) used in this calculation is from NSO (National Solar Observatory)^[17] and it has already been modified so that it’ s the direct irradiance at the observation point.

Fig.6

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	Fig.6 Solar irradiance used in calculation of g factors

The g factors results compared with Stevens and Conway’ s work is shown in Figure 7. We choose the temperature 200K because the previous works have published a result at this temperature which is nearly the temperature at 70 km in mesosphere. We can tell that our results are about 60% larger because of the larger solar irradiance. And change of HITRAN databases of OH molecule in these years may cause different relative intensity.

Fig.7

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	Fig.7 g factors calculation comparison with previous work at 200 K

We use the profiles of OH, O₃ and other trace gases in SCIATRAN B2D profiles databases to match the forward model algorithm of SCIATRAN. In forward model simulation, we calculate 45 km to 85 km in 1 km step.

Slant column is the column abundance along the viewing path, which could be calculated by the absorption of OH along the LOS. Thus the final signal may include the OH abundance information which can be retrieved from formula (1).

The limb mode has a long viewing path which leads to a relatively large slant column. Under optically thin condition, the emission energy may transfer from the observation point to the instrument without attenuation. The slant column in 70 km tangent point calculated by SCIATRAN with parameter settings listed in Table 1 is showed in Figure 8. Each wavelength has different value because the algorithm used in slant column calculation depends on the absorption characteristics of OH. This may mean that stronger absorption line corresponds to relatively larger slant column and the integration over the band should be equalthe to column abundance in unit molecules· cm^-2. The spectral band we choose is 308.2~309.8 nm which meets the need of our spatial heterodyne spectrometer that intends to detect mesospheric OH radicals. At the same time, we calculate solar direct radiance at each tangent point.

Table 1

Table 1

Table 1 Main input parameters settings in SCIATRAN Input parameters Value Spectral segment information/nm 308.2~309.8, 0.001 Trace gases BrO, NO3, OCLO, O3, NO2, SO2, CLO, HCHO, OH, HF, HCl Tangent height/km 45~85 Solar zenith angle/(° ) 50 Solar azimuth angle/(° ) 120 Surface settings Lambertian: soil Aerosol settings LOWTRAN aerosol

Table 1 Main input parameters settings in SCIATRAN

Fig.8

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	Fig.8 Calculated slant column at 70 km for each wavelength

Figure 9 shows simulated background spectrum in 70 km with the same settings in slant column calculation. The shape is almost like the solar irradiance because it consists of Rayleigh scattering, extinction of OH itself, aerosols and other trace gases without OH emissions, whose value depends on atmospheric condition including solar irradiance, aerosol, cloud, trace gases, surface and observation geometry. In this case, we don’ t consider cloud due to its ignorable disturbance in mesospheric limb mode.

Fig.9

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	Fig.9 Calculated background signal

We add the product of g factors and slant column to the background signal, then do a convolution with the instrument line shape function which is a Gaussian function with a FWHM of 0.015 nm. This FWHM value corresponds to the spectral resolution of our spatial heterodyne spectrometer.

Using this forward model, we also simulate OH emission signals at different altitudes between 45 and 85 km. The OH intensity increases as the height goes down, but combining Figure 10 and Figure 11, we can tell that at 40 km, OH signal is difficult to be distinguished from the total signal because of rapid increasing of Rayleigh scattering signal in lower altitudes.

Fig.10

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	Fig.10 Simulated results at 45 and 70 km. In upper two panels are the synthetic signal, background signal and the OH emission signal at 70 km. In lower two panels are ones at a different tangent height of 45 km

Fig.11

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	Fig.11 OH emission intensity in different tangent height

Figure 12 shows OH density and radiance profiles between 60 and 85 km. We choose this altitude range for analyzing because our forward model is more applicable and accurate in this area and previous research such as SHIMMER has a reliable result only in this range. From this result we can tell that the intensity of OH emission signal is related to the density at different tangent heights. The shape of the OH radiance profile is similar to that of density profile.

Fig.12

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	Fig.12 Input OH density profile and simulated OH radiance

Fig.13

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	Fig.13 Observation radiance with different solar zenith angles and azimuth angles

In the mesosphere, land surface parameters are relatively small, so the most important factors in limb observation mode is the geometry parameters including solar zenith angle, solar azimuth angle and tangent point position. These three parameters determine the position of the observation point.

The parameter of “ Azimuth angles” here defines the values of the relative azimuth angles of line-of-sight with respect to the sun. The value of 0° means instrument is pointed into the solar direction. The intensity decreases rapidly with increasing SZA near 90° because in this position, the observation geometry is going into twilight mode like in Figure 14(b). In azimuth angles sensitivity analysis, when SAA=180° , the sun and the instrument are in a line by two sides, so more transmitted and scattered solar radiation are transferred into the instrument.

Fig.14

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	Fig.14 Geometry in (a) nontwilight (b) twilight

The sum of the aerosol scattering coefficient and the aerosol absorption coefficient yields the aerosol extinction coefficient for each aerosol type. These three coefficients have the unit of an inverse length (km^-1).

We use user-define aerosol settings and set AOT in range of 0 to 5 by the step of 0.05 with reference wavelength of 308 nm. For mesospheric aerosol, scattering coefficient is much larger than absorption coefficient^[6]. Therefore, larger AOT brings out larger limb-scattered radiation. Figure 15 proved this statement.

Fig.15

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	Fig.15 Limb-scattered radiance at 70 km with different AOT

We do a 10% perturbation to OH concentration by step of 1 km and simulate limb-scattered radiance in 41 tangent heights between 44 to 84 km.

The relationship between limb-scattered radiance and OH concentration could be described by a parameter called “ Weighting Functions” . It’ s a matrix usually used in retrieval, whose element could be expressed as

Kjk=∂Ij∂nk=ΔIjΔnk

Where I_j is the limb-scattered radiance and n_k is the OH concentration in the tangent height j, Δ is the difference before and after perturbation.

From Figure 16, we can tell the sensitive tangent height range for OH is above 70 km. That is to say, it’ s more effective and would have higher accuracy of OH’ s retrieval in this height. The weighting function has different maximum intensity in different wavelength due to relative intensity of OH emission line.

Fig.16

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	Fig.16 OH Weighting functions in different wavelength