Atmospheric Solar Heating in Minor Absorption Bands

Solarradiationis theprimarysourceof energydrivingatmosphericandoceanic circulations.Concernedwith thehugecomputingtimerequiredfor computingradiative transferin weatherandclimatemodels,solarheatingin minorabsorptionbandshasoften beenneglected.Theindividualcontributionsof theseminorbandsto theatmospheric heatingis small,butcollectivelytheyarenotnegligible.Thesolarheatingin minorbands includestheabsorptiondueto watervaporin thephotosynthetically activeradiation(PAR) spectral regionfrom 14284cml to 25000cm_, theozoneabsorptionandRayleigh scatteringin thenearinfrared,aswell asthe 0 2 and CO 2 absorption in a number of weak bands. Detailed high spectraland angular-resolution calculations show that the total effect of these minor absorption is to enhance the atmospheric solar heating by 10%. Depending upon the strength of the absorption and the overlapping among gaseous absorption, different approaches are applied to parameterize these minor absorption. The parameterizations are accurate and require little extra time for computing radiative fluxes. They have been efficiently implemented in the various atmospheric models at NASA/Goddard Space Flight Center, including cloud ensemble, mesoscale, and climate models.


INTRODUCTION
The ultimate force driving the Earth's weather and climate is the solar radiation.

Satellite measurements
of the earth radiation budgets show that the Earth reflects -30% of the incoming solar radiation, and the rest is absorbed at the surface and in the atmosphere (Barkstrom, 1984, Kandel et al., 1998).Partitioning of the 70% of the solar heating between the surface and the atmosphere is very important to oceanic and atmospheric circulations; a larger solar heating at the surface will cause a higher surface temperature and an enhanced evaporation, leading to a more energetic atmospheric circulation.The broadband parameterizations for solar radiation used in weather and climate studies are mostly based on high spectral resolution calculations of gaseous absorption and detailed angular integration of particle scattering.
To enhance computing speed, the spectrum is divided into a small number of bands, and only important gaseous absorption and particle scattering are included.
Minor absorption and scattering due to gases or scatterers spread over a wide spectral range.They are almost always neglected in radial:_on models used in weather and climate studies in order to save computing time.Individug, y their effects are small, but the total effect may not be negligible.
As the capability of th_ computing system increases, more detailed physical processes are included and higher spatial and temporal resolutions are used in weather and climate models.
To be consist :_ with these improvements, radiative transfer calculations are required to be more accurate than the existing models.
Because calculations of radiative terms in weather and climate models require a large portion of the total computing time, it is essential that improvement in radiation parameterization should not have a large impact on computing speed.
There are a number of solar radiation schemes available for use in global climate models (cf.Fouquart et al., 1991).At NASA/Goddard Space Flight Center, a series of parameterizations for radiative transfer in the solar spectrum due to various absorbers and scatterers has been developed and applied to global and regional climate studies (Chou, 1986;Chou, 1992;Chou and Lee, 1996).The ozone absorption and Rayleigh scattering were included in the ultraviolet (UV) and visible regions with the wavenumber v>14285 cm _ (0.7 lam) but were neglected in the near infrared.
On the other hand, the absorption due to water vapor was included in the infrared with v<14285 cm l but were neglected in the photosynthetically active radiation (PAR) region between 14285 cm _ and 25000 cm _.
(0.4 p-m and 0.7 p.m). Oxygen and CO 2 also absorb solar radiation in the infrared.In additionto watervaporand03, oxygenandCO2alsoabsorbsolarradiation.small interval Av where the spectral variation of insolation is small, the integration of fluxes over wavenumbers can be replaced by that over the absorption coefficient.The mean transmission function of the interval Av can be written as where w' is the absorber amount, k v is the absorption coefficient at the wavenumber v, g is the k-distribution density function (cf.Arking and Grossman, 1972) such that the fraction of spectrum with the absorption coefficient in the between k -ldk and k + ldk 2 2 is g(k)dk, and a i (= g(ki)Ak i) is the k-distribution function.
It has been found (Chou and Lee, 1996) that the k-distribution method requires only -10 values of k (i.e.n-10) for accurate calculations of solar fluxes using the k-distribution method instead of > 106 s_ ,c_i points using the line-by-line method.
In the atmosphere where pressure and temperature change with height, the wavenumbers with a common absorption coefficient at a given height will not necess:, ily where Thus, the scaling of the absorption coefficient is reduced to the scaling of the absorber amount, and flux calculations are greatly simplified.
It is noted that the basis for the kdistribution method with the one-parameter pressure and temperature scaling is the same as the correlated k-distribution method (Goody et al., 1989;Lacis and Oinas, 1991;Fu and Liou, 1992), i.e. the dominant effect of line wings on the absorption.The accuracies of these two approaches are comparable, but the former is much simpler than the latter.

Flux calculations
For a spectral band with a width Av, the direct solar flux at a given pressure level p can be written as f -kvw,,, This approach is applied to computing fluxes due to water vapor absorption in the infrared.
For the case that either the range of k or the value of k itself is small within a spectral band, the transmission can be approximated by r( w ) =e --_w ( 16) where L-is the mean absorption coefficient of a spectral band.This approach is applied to computing fluxes due to 03 absorption.16).
To derive k, the mean transmission function z'(w) given by ( 7) is first computed using the line-by-line method for w ranging from 5 g cm 2 to 20 g cm 2. For each w, an effective absorption coefficient is computed from _:(w) = -lln r(w) (23) w The value of k at pr=300 hPa and Tr=240 K is found to range from 0.00065 to 0.00080 gl cm 2, and a mean value of 0.00075 gJ cm z is adopted in the broadband flux calculations.
For the midlatitude summer atmosphere, the vertical-integrated scaled water vapor amount in the direction 60 °from the zenith is 14 g cm z, and the absorptance in the PAR spectral region is -0.01.With a fraction of 0.391 of the extraterrestrial solar radiation contained in the PAR, it corresponds to an atmosphere solar heating of -2.6 W m 2. so that the absorption of solar radiation due to 03 in the near infrared is correctly computed, where w' is the ozone amount, and AV 1 and Av 2 are the widths of Bands 8 and 9, respectively.
It is noted that the absorption due to ozone is nearly independent of pressure and temperature, it is not necessary to scale the ozone amount given by ( 5).For a wide range of w' found in the atmosphere, the value of Ak ranges between 0.0032 and 0.0033 (cm-atm)sw _.Therefore, the ozone absorption coefficient in Band 8 is enhanced by 0.0033 (cm-atm)svo _ to take into account the absorption by ozone in the infrared.This approach to computing the ozone absorption in the near infrared requires no extra computing time.For the midlatitude summer atmosphere, the column ozone amount is 0.318 (cm-atm)sv e.It can be easily shown that the solar heating of the atmospheric column is enhanced by 0.56 W m z, which is independent of the solar zenith angle due to the opposite impacts of the solar zenith angle on the insolation and the ozone pathlength.Table 3 shows that the surface flux reduction in the near infrared due to 03 is 0.54 W m 2 as computed from the parameterization, which is very close to that computed with a high spectral resolution.

Oxygen absorption
As shown in Figure 3, the absorption due to Oz occurs in narrow spectral intervals, but is not necessary weak near band centers.
To includetheabsorption in all thosebands,the meantransmissionfunctionof 02 at pr=300 hPa and Tr=240 K in the spectral regions 7600-8050, 12850-13190, 14310-14590, and 15730-15930 cm t is computed from (7) using the line-by-line method, and the effective mean absorption coefficient k is computed from The value of k is between 0.000135 (cm-atm)sTP _a and 0.000155 (cm-atm)s_ l_z for a large range of w encountered in the atmosphere, and a mean value of 0.000145 (cmatm)sav _r2 is adopted to compute the flux reduction due to O z from (18).The insolation, S, in the spectral regions 7600-8050, 12850-13190, 14310-14590, and 15730-15930 cm 1 is 86.53 W m z or 6.33% of the total solar flux at the top of the atmosphere.Table 3 shows that, for a solar zenith angle of 60 °, the surface flux reduction due to O z is 4.29 W m z from line-by-line calculations and 4.18 W m 2 from the parameterization.

Carbon dioxide absorption
The absorption of solar radiation due to CO 2 spreads over the middle infrared from 2000 to 7000 cm 1.It overlaps substantially with the absorption due to water vapor in some spectral regions.Line-by line calculations show that, for a solar zenith angle of 60 °and a CO 2 concentration of 350 ppmv, the atmosphere heating due to CO 2 alone is 8.73 W m 2 but reduces to 3.30 W m z when overlaps with water vapor absorption in the midlatitude summer atmosphere.
Because of this strong overlapping, the CO z transmission function cannot be computed independently of water vapor.
flux reduction due to CO 2 only for the spectral bands centered at -3700 cm _ and 5000 _n '_.
To include the CO 2 absorption in the minor bands, the flux reduction AF(w,u) is recomputed in this study to cover the entire solar spectrum which includes the strong b7 " :_:: 2480 cm _ and the weak bands at 6300 cm 1 and 7000 cm 1. Line-by-line calculations show that, for the mid-latitude summer atmosphere, a solar zenith angle of 60 °, and a CO 2 concentration of 350 ppmv, the surface flux reduction due to CO 2 increases by 1.21 W m z when the minor absorption is included.
Table 3 shows that the flux reduction computed from the parameterization is 3.60 W m 2 which is slightly larger than that from line-by-line calculations.

where
solar zenith angle, k is the absorption coefficient, and w is the scaled absorber amount above the pressure level p in the direction of the solar beam.The t_ _.qn transmission of a band is given by a spectral band into m small intervals and apply the k -Sj is the mean flux density in the interval Avj, ai, j is the klayer are first computed for each value of k.The two -stream adding method (cf.Chou, 1992)  is then used to compute the fluxes components F i associated with ki, i= 1, 2 ..... n.The total flux of a band is the sum of F i weighted by the k-distribution function, n F(w)= EhiVi(w) (15) i=I computed the mean transmission function in the O z A and B bands centered at 13150 cm 1 and 14510 cm _ and fit the transmission function by (17).The absorption in the weak bands centered at 7890 cm _ and 15870 cm _ was not included.Line-by-line calculations show that the total atmospheric heating due to 02 is 4.29 W m 2 for a sol_,: zenith angle of 60 °.The O 2 A and B bands contribute 3.70 W m 2 to the total absorpt?cn.

FIGURECAPTIONSFigure1.
FIGURECAPTIONSFigure1.Spectral distributionof theozonetransmission functionof the entire atmospheric column in the vertical direction averaged over 10 cm t.

Figure 2 .
Figure 2. Same as Fig. 1 except for the water vapor transmission function.

Figure 3 .
Figure 3. Same as Fig. 1 except for the 02 transmission function.

Figure 4 .
Figure 4. Same as Fig. 1 except for the CO 2 transmission function.

Table 1
shows the spectral bands of the solar radiation model used at NASA/Goddard Band 8 of our radiation model.Because the absorption due to water vapor is weak in this spectral region, it can be represented by a single effective absorption coefficient k in (

Table 3 .
Rayleigh scattering in the near infrared near infrared amount to ~5.0 W m 2. Raleigh scattering in the near infrared reduces the surface solar heating by -3 W m -2.The sum of these heating is -10% of the total solar heating of the Earth's surface, which is not negligible.Effects of minor absorption and scattering on the solar heating of the surface from detailed high spectral-resolution calculations and parameterizations.