Improving transmission calculations for the Edwards Slingo radiation scheme using a correlated-k distribution method

Transcription

1 Quarterly Journal of the Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: , October 2011 B Improving transmission calculations for the Edwards Slingo radiation scheme using a correlated-k distribution method Zhian Sun* Centre for Weather and Climate Research, Australian Bureau of Meteorology, Melbourne, Victoria, Australia *Correspondence to: Z. Sun, Bureau of Meteorology, 700 Collins St, Melbourne, Victoria 3001, Australia. z.sun@bom.gov.au A new version of the Edwards Slingo (ES) radiation scheme is developed using the correlated-k distribution (CKD) method. The work is conducted based on the line-by-line radiative transfer scheme GENLN2. A dataset of new ozone absorption cross-section in the ultraviolet spectrum and new oxygen collisioninduced continuum data have been implemented in both the GENLN2 and new ES schemes. In order to improve the efficiency of the ES scheme, a new technique is proposed in this work to optimize the k distribution and a new method is used to deal with the gaseous overlapping absorption in a spectral band. The accuracy of the scheme is improved by replacing the scaling function used in the ES scheme with a pre-determined look-up table for consideration of the pressure and temperature dependency of the absorption oefficients. The number of spectral bands and number of absorbing species are both increased in the new scheme for better resolution of the spectral variation of absorbing species, aerosols and clouds. However, this does not increase the computational cost. Instead, it is reduced substantially compared with the previous version of the code. The treatment of transmission in the short-wave spectrum is improved by implementing the absorbing species of CH 4,N 2 OandO 2 collision-induced continuum absorption which are not included in the ES scheme. New O 3 absorption cross-section data in the ultraviolet spectrum measured by the European Space Agency are used to generate the CKD spectral data in the short-wave spectral bands. These data have a temperature dependency and better spectral resolution. The irradiance and heating rate determined by the new scheme are tested against the same variables determined by GENLN2. It has been shown that the new scheme produces results more accurate than the ES scheme. Copyright c 2011 Royal Meteorological Society Key Words: radiative transfer; GENLN2; heating rate; overlapping absorption Received 6 February 2011; Revised 30 May 2011; Accepted 5 June 2011; Published online in Wiley Online Library 2 August 2011 Citation: Sun Z Improving transmission calculations for the Edwards Slingo radiation scheme using a correlated-k distribution method. Q. J. R. Meteorol. Soc. 137: DOI: /qj Introduction The Edwards Slingo (ES) radiative transfer scheme was developed at the UK Met Office in the early 1990s (Edwards and Slingo, 1996). This scheme has a number of novel features that are not available in other radiation schemes. The most important one is that it was designed to suit applications both for a high-spectral-resolution narrow-band model for research purposes and a low-spectral-resolution broadband model for uses in numerical weather prediction (NWP) and climate models. For this reason, the code is designed to allow running radiative transfer calculations in a flexible spectral resolution. This is achieved using a spectral file containing the necessary spectral information such as spectral band limit, absorbing species, and spectral properties of atmospheric constituents required by the code. The spectral file can be pre-determined to suit the application needs and this enables users to have a full control of the Copyright c 2011 Royal Meteorological Society

2 Improvements for the Edwards Slingo radiation scheme 2139 spectral resolution of the code and the physical processes involved. Because of this feature, and also due to its comprehensive inclusion of the physical processes, this scheme has been used by many researchers in the community. The Australian Bureau of Meteorology adopted the ES scheme in It was implemented in the Bureau NWP and climate system for research and operational use. In the course of implementation, we took the advantage of the flexible spectral feature to establish a new version of the code for our purposes. We have also made many modifications to the ES original scheme to improve its accuracy and efficiency. For the purpose of convenient comparison and identification of our contribution to the scheme, the modified version was renamed as the Sun Edwards Slingo (SES) scheme. The modification of the scheme has undergone two versions. The first version (SES1) was described by Sun and Rikus (1999). This article describes the development of the second version (SES2). All the features of the ES scheme have been maintained in SES2. In addition, the SES2 utilizes a correlated-k distribution (CKD) method (Lacis and Oinas, 1991; Fu and Liou, 1992; Mlawer et al., 1997; Li and Barker, 2005) which is similar to the Exponential Sum Fit Transmission (ESFT) method used in the first version of ES and SES1. The correlated-k and ESFT methods both have the advantages of computational efficiency, direct adaptability to multiple-scattering calculations and ability to address quasisingle spectral line for improving heating rate calculations in the upper atmosphere. The main focus of developing CKD in this study is to try to use the minimum number of k terms in each band while maintaining the required accuracy for fluxes and heating rates. The SES2 development has been based on the general purpose line-by-line atmospheric transmittance and radiance model (GENLN2; Edwards, 1992), which provides the distributions for the relevant absorption coefficients k. The accuracy of these absorption coefficients has been tested by comparison of GENLN2 with other line-by-line models such as LBLRTM (Clough et al., 1992) and measurements from the Atmospheric Radiation Measurement (ARM) programme (Stokes and Schwartz, 1994). These validations show with high confidence that GENLN2 is accurate enough for use as the basis for development of a broadband radiation scheme. The article is arranged in the following sequence: section 2 describes the modifications of GENLN2 which are needed for the development and validation. Section 3 introduces a new technique used in the CKD method for generating an optimized k distribution. Section 4 deals with the gaseous overlapping absorption, and section 5 discusses the treatment of minor absorbing species. Section 6 presents a comparison of results and section 7 draws conclusions. 2. Modifications of GENLN2 and their validation Version 3.0 of the GENLN2 model is used in this study. GENLN2 allows users to calculate atmospheric radiances and transmittances and has been used to calculate gaseous transmissions required by the ES code (Edwards and Slingo, 1996). In order to use this model as a foundation and a reference to develop a broadband model and validate its accuracy, it is necessary to modify GENLN2 to allow the calculation of monochromatic fluxes and heating rates. The modifications for this purpose have been described in our earlier study (Sun and Rikus, 1999). The new modifications that make the code more useful are presented here Implementation of short-wave absorption cross-section data The high-resolution transmission molecular spectroscopic database, HITRAN (Rothman et al., 2003) is a major source of absorption coefficients for absorbing species included in radiative transfer models. However, the spectral data for ozone in the ultraviolet (UV) spectrum are not available in the HITRAN database and therefore other sources are required for treatment of the ozone absorption. The water vapour and oxygen continuum absorption data are also from other sources. The ozone absorption coefficients used in the original ES code were derived from data used in the radiance and transmittance model LOWTRAN (Kneizys et al., 1988), which has relatively low spectral resolution and is independent of temperature. Ozone is an important minor constituent of the Earth s atmosphere and is a strong absorber of the solar radiation in the UV and weak absorber in the visible wavelengths. Ozone absorption is a major heating source in the middle atmosphere, which provides energy for photochemical reactions (Chou and Lee, 1996). Therefore, the treatment of the solar radiation absorbed by ozone is important in providing accurate heating rates in the middle and upper atmosphere. In this study the ozone absorption cross-section data measured by Voigt et al. (2001) for the European Space Agency (ESA) remote-sensing program (Orphal, 2002) are adopted. This programme was assigned to retrieve trace gas distributions from space platforms. This requires absolute absorption cross-sections for all relevant gases as a function of optical frequency for appropriate physical conditions (e.g. pressure, temperature, mixing ratio) and appropriate instrument conditions (e.g. spectral coverage and resolution). Laboratory measurements of O 3,O 2,NO 2, SO 2 were made for specified physical and instrument conditions. The ozone cross-sections were measured at five different temperatures in the range K and two pressures in the spectral region nm with a spectral resolution of 5 cm 1. Therefore, the ESA data have the advantages of a better temperature dependence and higher spectral resolution. Following the treatment by Malicetet al. (1995), the temperature dependence of the ESA data was fitted to a polynomial function at each wavelength. The pressure dependence was found to be insignificant (Voigt et al., 2001) and therefore is not considered in this study; the ESA data at 1000 hpa are used. The ESA data were implemented into GENLN2 and used for generating k distributions of ozone for the SES2 code Molecular oxygen collision-induced continuum absorption Molecular oxygen has absorption bands throughout the spectrum from infrared (IR) to UV (Newnham and Ballard, 1998). Some of these absorptions appear as continuum features arising from dimmers or collision complexes of oxygen (e.g. O 2 O 2 ; O 2 N 2 ). The latter are described as collision-induced absorption. In the near-ir, these O 2 dimmers produce the (0,0) band centred near 7900 cm 1 (1.27 µm), the (1,0) band centred near 9400 cm 1 (1.06 µm),

3 2140 Z. Sun and the (0,1) band centred near cm 1 (1.58 µm). Currently, there is no theoretical solution to deal with these continuum absorptions. Mlawer et al. (1998) have proposed an empirical model based on difference analysis between the observed spectrum and line-by-line calculations of LBLRTM. They have shown that the LBLRTM residues have been greatly reduced using this scheme. However, the scheme has disadvantages in that it was not derived directly from the absorption cross-section measurements and does not have temperature dependency. As mentioned early, the absorption cross-sections of oxygen have been measured by Smith and Newnham (2000) at the Rutherford Appleton Laboratory for the ESA remotesensing programme. They have analyzed data to isolate the continuum cross-sections by removing the oxygen molecular line structure absorption. The continuum data for all three spectrum regions were generated for several temperatures and these data were implemented in GENLN2 for dealing with oxygen continuum absorptions. The optical depth for oxygen continuum absorption is determined by τ O2N2 = σ O2N2 ρ O2 ρ N2 z, (1) where σ O2N2 is the binary absorption cross-section due to collision of oxygen and nitrogen, and ρ represents the molecular density of oxygen or nitrogen. In the 1.59 µm band, the absorption is due to O 2 O 2 pair collision and therefore the index N2 in Eq. (1) is replaced by O2. In the 1.27 and 1.06 µm bands, the cross-section data for a concentration 21/79 of oxygen to nitrogen is used Comparison of spectral direct irradiance determined by GENLN2 with ARM observation Comparison of GENLN2 with other line-by-line models was reported in an earlier article (Sun and Rikus, 1999). In this study the validation was further conducted using the ARM observational data. The high-spectralresolution data measured by the Rotating Shadowband Spectroradiometer (RSS; Harrison et al., 1999) at the ARM research site at Southern Great Plains (SGP) for a clearsky condition are used for validation. The RSS provides spectrally resolved direct-normal, diffuse-horizontal, and total-horizontal irradiances. The data measured by the second-generation instrument with higher-performance charge-coupled device (CCD) arrays are used in this work. The data from the first-generation instrument have been usedby Mlaweret al. (2000) to validate LBLRTM. The data obtained at 1100 local time (solar zenith angle ) on 4 March 2000 were used. The pressure, temperature, and water vapour measurements from the radiosonde sounding form the basis of the atmospheric profile and are used as an input to the model. The water vapour profile has been scaled to match the total column value measured by a microwave radiometer which provides an accurate determination of total water vapour column. The midlatitude summer ozone profile is used and the values are scaled to agree with a total value of 323 Dobson Units which was obtained from the Total Ozone Mapping Spectrometer measurement nearest to the SGP site on that day. For a comparison with clear-sky measurements, the Rayleigh and aerosol scattering must be included in the calculations. The GENLN2 line-by-line model cannot handle scattering calculations. Therefore, some modifications to GENLN2 Figure 1. Comparison of measured (RSS) and calculated (GENLN2) solar spectral direct irradiances for clear-sky conditions at the ARM SGP site on 4 March shows the differences. are necessary to account for the effects of scattering. For simplicity, we consider only the scattering effect on the direct solar irradiance. In this case, both Rayleigh and aerosol effects can be accounted for by the Beer law. The Rayleigh scattering formula due to Edlen (1953) is implemented into GENLN2. Aerosol optical depths measured by collocated sun photometers at the SGP site on that day were interpolated onto the GENLN2 spectral grid and the downward direct irradiances at the surface were scaled by e τ to account for the attenuation by aerosols, where τ is the measured spectra aerosol optical depth. The RSS instrument (slit) response function was applied to the calculated irradiances, yielding a value of irradiance corresponding to each spectral channel of the instrument. Seven absorbing species (H 2 O, CO 2,O 3, O 2,N 2 O, CH 4,NO 2 ) are included in the calculations. The result is shown in Figure 1. It is seen that the modelled direct irradiance is in a good agreement with the observations. The differences between the measured and calculated irradiances, shown in Figure 1, are small across most of the measured spectrum. The total irradiance difference between the calculated result and the observation is 4 W m Improved correlated-k distribution for SES2 The development of the k distribution model has been well established. Any new work in this area should be focused on the issue of efficiency as this is critical to operational NWP applications. There are two issues in this method that affect the accuracy and efficiency. One is the method used to determine the sub-intervals in g space, where g is defined as an accumulative probability of the k distribution and represents a coordinate transformation from wavenumber grid to accumulative probability grid; the other is the method to determine a corresponding k value for each interval that may be representative for this interval. There is no unique method for identifying the optimal number of k terms. It is normally determined by the balance between accuracy and computing time. It is found from the author s experiences that the ESFT method may be superior at limiting the number of k terms to the methods which calculate the

4 Improvements for the Edwards Slingo radiation scheme 2141 g i interval from physical principles. This method was also suggested by Cusack et al. (1999). Using the ESFT, the g i and values of k i at a reference pressure and temperature are determined simultaneously for a given fit accuracy. For a fixed accuracy, the number of k terms determined by the ESFT method depends on the reference pressure at which the transmissions are calculated. At low pressures, Doppler broadening dominates, and absorption coefficients are spread over a wide range of orders of magnitude, resulting in more k terms being needed in the ESFT fit than when a high pressure is chosen as a reference. Although the ESFT with a high reference pressure can lead to a reduction in the number of k terms, it cannot be used to develop a k distribution model as the accuracy of radiation in the upper atmosphere cannot be guaranteed. A lower reference pressure has to be chosen in the ESFT fit in order to accurately resolve the sharp variations of absorption coefficients for the g interval close to 1. It is almost impossible to obtain an accurate fit with only a few k terms (e.g. < 5) if a low reference pressure is used. To solve this problem, we sacrifice the fit accuracy by using a fixed number of k terms in ESFT to determine the values of the g interval. The loss of accuracy is then recovered by adjusting the k value in each g interval as discussed below. For each g interval, a representative k value can be determined by a number of methods. The simplest one is to obtain the representative k by a linear average of all k values across the g interval as suggested by Mlawer et al. (1997). The second is to use a k value corresponding to the middle point within the g interval. The third method is to calculate the average transmissions across the g interval for a set of absorber amounts and to fit the results to a grey exponential function to determine k. The fourth is to calculate a mean k value weighted by the transmission calculated at each g grid across the interval. We first use the ESFT to determine the number of g intervals for a reference pressure of 1 hpa and a temperature of 250 K. For an accuracy of 10 4 for the band average transmissions, ten exponential terms resulted from the ESFT fit. We then used the above methods to determine the k values in each g interval. In Figure 2, we show the k distributions determined using these methods for the water vapour line absorption in a spectral band cm 1.The solid curve in Figure 2 represents the line-by-line result and the symbols denote the k distributions determined using the different methods. The k values determined by ESFT are also shown in the figure. It is seen that there are no significant difference for the k values in the first seven g intervals (Figure 2) determined by the different methods. However, the difference becomes larger for g intervals close to 1 (Figure 2). Since the k values for g close to 1 dominate the radiative irradiance and heating rate in the upper atmosphere (Li and Barker, 2005), these differences must lead to large differences in the radiative transfer calculations. These methods are examined with the radiation code and it is found that if the number of k terms is large enough (e.g. 16 terms as used in Mlawer et al., 1997), the differences in radiative irradiance and heating rates determined using these methods are not significant. However, if only a few k terms are used (e.g. seven k terms), a large difference occurs. Figure 3 shows the downward irradiances above 100 hpa determined using these methods for the water vapour absorption in a spectral interval cm 1. One result is determined using 16 k terms and the rest are determined with seven k terms. The solid curve in the figure represents the reference result determined from GENLN2. For clarity, the results from the grey fit and transmission weighting methods are not shown, as these are worse than those shown in the figure. It is seen that for the results determined with seven k terms, the method of linear average generates the largest error for the downward irradiance. The irradiance profile determined using the method of a k value at the middle point within a g interval i is compatible with that using the 16 k terms. This comparison indicates that the k value at the middle g point may be a better representative if the number of g intervals within a band is small. It also has a theoretical basis as it is just the method of trapezoid integration. Although it is superior to the other methods, the result is not as good as that from using 16 k terms. Therefore, an alternative approach is needed. Li and Barker (2005) have mathematically demonstrated that the linear average method generally overestimates the absorptions. A factor α should be used to scale the linear averaged k values, where α (0 α 1) can be determined by a numerical fitting. As shown in Figure 3, the downward irradiance from averaged k values is overestimated if seven k terms are used. This result supports Li and Barker s study. After checking the irradiances from all seven g intervals, we found that it is just the last k term that causes the significant flux departures from the reference values. We then follow the suggestion by Li and Barker to apply the following function to scale the k values in the last g interval for pressure less than 100 hpa: k 7 = k 7(p/p 0 ) α, (2) where p 0 =1013 hpa, and the parameter α is determined by minimizing an error equation defined by ɛ i = l(p=0.001) l(p=100) (f ref i l f i l )2. (3) f ref represents the net radiative irradiances determined by GENLN2 and f i denotes the net irradiances from the CKD method. The result determined using this scaling function is also shown in Figure 3 which has almost the same accuracy as that from using the 16 k terms. The long-wave heating comparison for this band is shown in Figure 4. Again, the accuracy of the heating rate determined using the seven k terms with the scaling Eq. (2) is compatible with that from using the 16 k terms. The above exercise indicates that, for a smaller number of g intervals, the representative k values may be better determined by a numerical fit as recommended by Li and Barker. The numerical fit approach is just what the ESFT does. The difference between the ESFT method and the above approach is that the ESFT adjusts all k values and width of g intervals to get an overall better result by gradually increasing the number of k terms until satisfactory accuracy is achieved while our approach is to adjust the last k term only because it is responsible for the large error in radiation calculations in the upper levels of the atmosphere. This means that the numerical fit may be better performed for each g interval separately to obtain a best representative k value in that interval. This will require line-by-line calculations using the re-ordered absorption

5 2142 Z. Sun Figure 2. Absorption coefficients for water vapour line only in each g interval determined using the five methods. The solid curve represents the values at the line-by-line grids and the symbols denote those using ten g points. shows the results in the g intervals between 0 and 0.9 on a linear scale, and is for an interval between 0.9 and 1.0 on a logarithmic scale. The corresponding spectral region is cm 1. Heating rate (K day 1 ) Figure 3. Downward long-wave irradiances above 100 hpa in a spectral region between 0 and 250 cm 1 determined using LBL and SES2 with four methods of determination of absorption coefficients. The calculations were performed using 60 levels of a middle latitude summer atmosphere for a case of water vapour line absorption. The legend ps means a pressure scaling was applied for the last k term. coefficients so that the irradiance profiles for each interval can be obtained and used as reference for the fit. This procedure is possible but too expensive. Alternatively, we propose the following procedures to achieve this goal. For each band, we generate a reference CKD code using 145 k terms as suggested by Fu and Liou (1992). The accuracy of the radiation calculation determined using such a large number of k terms in the g space can be safely guaranteed. We then use the ESFT to determine the weights for a fixed number of intervals. The representative k value in each interval is determined by minimizing the error function given by l=m2 ɛ i = (fl 145i l=m1 f i l )2, (4) Figure 4. As Figure 3, but for long-wave heating rates and heating errors determined using LBL and SES2 with the four methods of determination of the absorption coefficients. where f 145i is the net irradiances in an ith interval of the g space determined by the reference code with 145 k terms, and f i is the irradiances in this interval determined by the code with single k profile. We start this process with one interval and gradually increase the number of intervals until a satisfactory result is obtained. The k values corresponding to the middle point in the interval are used as initial values. The summation in Eq. (4) is from reference pressure level m1 to m2, where m1 and m2 are determined by examining the irradiance and heating rate profiles for each g interval. Therefore, only the k values within these two reference pressure levels are fitted. In general, the values of m1 and m2 shift from a high reference pressure regime to a low pressure regime as the g interval moves close to 1. Using this approach, we can limit the number of k values in each band to a minimum at 1 and a maximum at 7 while the accuracies of irradiance and heating rate are well maintained. The number of k terms obtained for each of the SES2 bands

6 Improvements for the Edwards Slingo radiation scheme Treatment of gaseous overlapping absorption In some spectral bands, more than one significant absorbing species must be considered. The overlapping absorption by these species is treated in the same way as in the SES1 scheme (Sun and Rikus, 1999) with some modifications necessary for the CKD model. For two absorbing species, the spectral optical depth is calculated from τ = k 1 u 1 + k 2 u 2, (5) where u 1 and u 2 represent the molecular absorber amounts for each species. In order to treat the two absorbing species as a single pseudo-species, we express the above optical depth by τ = k m u m, (6) Figure 5. Comparison of net short-wave irradiances in each g interval due to the absorption by ozone in a spectral region of cm 1 determined using five k terms (bold lines) with those using 145 k terms (thin lines). shows results determined using method of ESFT and gives the results from the fitting method. The curve on the right in each panel shows the band total irradiance. using this method is listed in Table I. The total number of k terms for SES2 is only 58. The same numbers in SES1 and original ES are 109 and 121, respectively. As a result, SES2 should be more efficient than the SES1 and ES schemes. Figure 5 shows the net irradiance profiles in each g interval for the short-wave spectral band cm 1 determined by the reference code using 145 k terms and the code with five k terms determined by ESFT with k values taken at the middle point in each interval (Figure 5) and by the fit method (Figure 5). The absorption by ozone is included in the calculations. The biases between reference and ESFT occur in all g intervals, but the values of bias in the second g interval are relatively larger in this case. These biases are all reduced using the fit method, leading the total band irradiances to be in a good agreement with the reference results. Figure 6 shows the downward irradiance due to absorption by the water vapour in a long-wave spectral band cm 1. The fit method with only four k terms generates a result that is almost the same as that from using 145 k terms. The above method is used to generate the CKD spectral data for both long-wave and short-wave spectral bands listed in Table I. The absorption coefficients in these bands are determined for 59 reference pressure levels ranging from 1050 to 0.01 hpa with an equal spacing in log pressure as suggested by Mlawer et al. (1997). For each reference pressure, k values for five reference temperatures (T ref,t ref ± 15 K, T ref ± 30 K) are calculated, where T ref is the temperature corresponding to this pressure in the midlatitude summer atmospheric profile. These reference values roughly cover the full atmospheric conditions and are used in the SES2 scheme to determine the absorption coefficients by a linear interpolation. The absorption coefficients due to water vapour, carbon dioxide, ozone, methane, nitrous oxide, oxygen, CFC11, CFC12, CFC113, and CFC114 are included in the reference table. where k m represents the effective absorption coefficient for a binary species and u m is a binary absorber amount defined by u m = u 1 + fu 2, (7) where f is a tunable parameter that scales the contribution to the optical depth from u 2 to be of the same order of magnitude as that from u 1 (Sun and Rikus, 1999). Therefore, f can be simply defined as a ratio of the maximum absorber amounts of the two species, i.e. f = umax 1 u max 2. (8) The effective absorption coefficient k m can then be determined by k m = k 1u 1 + k 2 u 2 u 1 + u 2. (9) The dependence of k m on the binary absorber amounts is determined by a linear interpolation of a binary parameter η defined by Mlawer et al. (1997): η = u 1 u 1 + fu 2. (10) For a fixed η value, this equation sets up a constraint that ensures that the absorber amount u 1 is fully correlated with u 2.Theu m in Eq. (7) is then determined using this relationship to ensure that it is equivalent to a single species. Substituting Eq. (10) into (9), we can see that From this equation we obtain that 1 η k m = k 1 η + k 2. (11) f τ m = k 1 u 1 if u 2 = 0, (12) τ m = k 2 u 2 if u 1 = 0. (13) These equations clearly show the relationship between k m and η and also indicate that the treatment for the binary species overlapping absorption meets the optical depth calculation for either single gas. The values k m for nine η values equally spaced as 0, 1/8, 2/8, 3/8,, 1 as suggested

7 2144 Z. Sun Table I. Division of spectral bands, absorbing species and number of k terms in each band. SW Species No. of band (µm) k terms O O O 3,H 2 O O 3,H 2 O, O O 3,H 2 O, O H 2 O H 2 O, CO 2,O H 2 O, CO 2,CH 4,N 2 O H 2 O, CO 2,CH 4,N 2 O 5 LW band (cm 1 ) H 2 O H 2 O H 2 O, CO 2,O 3,N 2 O H 2 O, CO 2, CFC11, 2 CFC12, CFC113, CFC H 2 O, CO 2,O 3, CFC11, 3 CFC12, CFC113, CFC H 2 O, CH 4,N 2 O H 2 O, N 2 O H 2 O, CO 2,CH 4,N 2 O 3 Total number 58 Figure 6. Long-wave irradiance profile due to the absorption by water vapour in the spectrum cm 1 determined by GENLN2, and the difference from of two CKD models, one using 145 k terms and one using four k terms.

8 Improvements for the Edwards Slingo radiation scheme 2145 (c) (d) Figure 7. the long-wave cooling rates for the three atmospheres determined by the LBL scheme and the errors of SES2 relative to GENLN2. (c) shows the corresponding short-wave heating rates and (d) the the errors of SES2 relative to LBL. The short-wave calculations assume a solar zenith angle of 30 and a surface albedo of 0.2. by Mlawer et al. (1997) are determined for all 59 reference pressures and five temperatures at each level and the results are stored as a look-up table for interpolation. To calculate the optical depth for a mixture of the two species in a broadband model, η is determined from Eq. (10) and k m is determined by linear interpolation from the stored values at reference η. The above method is applied to the cases in which both absorbing species have significant absorption in a band, e.g. CO 2 band in 15 µmwithh 2 O, and O 3 band in 9.6 µmwith H 2 O. These strong absorbing species are referred to as the key species. Species that have a weak absorption effect are defined as minor species. The treatment of the minor species is described in the next section. 5. Treatments of other quantities in the CKD model 5.1. Minor species The overlapping absorptions due to minor species are treated in a less precise way. Following the method used in Mlaweret al. (1997), the k values for these minor species are sorted in g space according to the position of the key species sorted at the reference pressures and temperatures. Thus, the spectral correlation between the key species and minor species is maintained. The overlapping transmission by minor species is then accounted for in terms of a monochromatic transmission m T mix = i=1 { ( w i exp τ key i )} + τi minor. (14) The results of radiative irradiances and heating rates are examined against the reference values after adding these minor species. If the differences are not acceptable, then the k values for these species are adjusted using the same fitting procedures as for the key species Water vapour continuum The water vapour continuum scheme of MT CKD (Mlawer, personal communication) is used in both GENLN2 and SES2. As is usual practice, the effect of the foreign broadening continuum absorption is included in the treatment of the water vapour line absorption. The self-continuum is treated separately. The absorption coefficients of the self-continuum component are calculated for 21 reference water vapour pressures ranged from 0 to 50 hpa in 2.5 hpa increments and five temperatures (180, 215, 250, 285, 320 K) for each reference vapour pressure. The results are used to determine the absorption coefficient corresponding to the real water vapour pressure and temperature by linear interpolation. Its contribution to the transmission is also treated using Eq. (14) with k values sorted according to the position of the sorted water vapour line spectrum.

9 2146 Z. Sun Figure 8. Comparison of the long-wave results determined by LBL, SES2 and the ES schemes for a midlatitude summer atmosphere. Panels on the right show differences from the LBL scheme Planck function The Planck function in the ES scheme is determined by fitting the temperature dependence of the band average Planck function in terms of a polynomial function. In SES2, the band average Planck functions are pre-determined for 161 temperatures ranging from 180 to 340 K with 1 K increments. The value of the Planck function at the real temperature is then determined by linear interpolation using these reference values. The results have been compared with those determined by the polynomial function used in the ES model and they are in good agreement. However, using the interpolation approach may be more efficient Oxygen collision-induced continuum The oxygen collision-induced continuum absorption crosssection data were introduced in the previous section. To implement this contribution to the SES2 model, the binary cross-section absorption data at the 1.27 µm band are derived using GENLN2 for three temperatures (200, 250, and 300 K). These data are sorted according to the position of the sorted spectrum for the key species in the band. The effect on the radiative transfer calculations is then considered in the same way as for the minor species. Again, a linear interpolation is used to determine the temperature-dependent cross-sections in the model. The same procedure is applied to the other two spectral bands, but they have no temperature dependence Treatment of overlapping absorption of the solar and IR The solar spectrum is traditionally defined as a region cm 1, and the IR spectrum as cm 1. Any spectral overlap between the solar and IR is usually ignored because the fraction of solar irradiance in this region is small and its effect is not important (Liou, 1980). Such a division makes it possible to treat the radiative transfer and source functions separately for the two spectral regions and therefore to simplify the solution. In the ES code, this fraction of the solar energy is added to the last near-ir band. This only makes the input total solar irradiance right at the top of the atmosphere. Since the absorption of solar energy is spectrally dependent, adding this part of the energy to another spectral region may produce absorption errors. The solar irradiance in the overlapping region cm 1 is about 12 W m 2, which is about 1% of the total solar energy. This issue has been discussed by Li et al. (2010), where the effect of the solar energy in this region is treated by imposing an additional solar irradiance in cm 1 onto the downward irradiance for the appropriate IR bands. This treatment is simple and natural and therefore adopted in the SES2.

10 Improvements for the Edwards Slingo radiation scheme 2147 Figure 9. As Figure 8, but for the short-wave results. The calculations use a solar zenith angle of 30 and surface albedo of Comparisons of SES2 with the GENLN2 and ES schemes The radiative irradiances and heating rates determined using the SES2 radiation scheme are compared with the reference results determined using the GENLN2 and the ES schemes. Figure 7 shows a comparison of long-wave cooling and short-wave heating rates determined by SES2 and LBL. The calculations were performed for three atmospheres (midlatitude summer, tropical and subarctic winter). In the short-wave calculations, a solar zenith angle of 30 and a surface albedo of 0.2 are used. The absorptions due to H 2 O, CO 2,O 3,CH 4,N 2 O, O 2, and the water vapour continuum are included in the calculations. The Kurucz (1992) solar source function is employed. In the long-wave calculations, the absorptions due to CFC11, CFC12, CFC113 and CFC114 are also included. Figure 7 shows that SES2 produces more accurate heating/cooling rates for pressure levels below 10 hpa with the errors being less than 0.5 K d 1. The errors of less than 1 K d 1 occur above 10 hpa for the midlatitude summer and tropical atmospheres. Errors at upper levels for the subarctic winter atmosphere are slightly larger than about 2Kd 1. This reveals a possible problem when using Eq. (4) to determine the representative k values in each interval based on the calculations for the midlatitude summer atmosphere only. A further investigation will be needed to find out why the errors for the cold atmosphere are relatively large. Nevertheless, the results are still considered accurate at this pressure level because the absolute heating/cooling rates are very large here and therefore the relative errors are still very small. The results determined by SES2 are further compared with those from the ES scheme. In these comparisons, only H 2 O, CO 2 and O 3 are included in the short-wave calculations as the other species are not available in the ES scheme. The water vapour continuum absorption is also not included in the short-wave. Figure 8 shows the long-wave results. It is seen that the downward irradiance at the surface generated by the ES scheme is close to that from the GENLN2 but the result around 450 hpa is about 4 W m 2 higher than that determined by the GENLN2. The upward irradiance at the top of the atmosphere from the ES scheme is also overestimated by about 4 W m 2. The maximum long-wave heating error of 1.5 K d 1 from the ES scheme occurs around 1 hpa. The short-wave results are shown in Figure 9. Both the downward irradiance at the surface and upward irradiance at the top of the atmosphere from the ES scheme are compatible with those from the GENLN2, but the downward irradiance around 100 hpa is overestimated by about 4 W m 2.The heating rate around 1 hpa is underestimated by about 5Kd Conclusions This paper has described work to improve the transmission calculations for the ES radiation scheme. This includes the modifications of the GENLN2 line-by-line radiation model

11 2148 Z. Sun and the development of SES2, a new version of the ES scheme. The important outcome from the SES2 scheme is its ability to produce accurate results for most NWP and climate applications. This is particularly true due to the inclusions of absorption of the solar radiation by CH 4 and N 2 O. The short-wave absorptions due to these two species have been absent from all the short-wave radiation schemes contributing to the Intergovernmental Panel on Climate Change (IPCC) AR4 assessment and it has been suggested that they should be included in the IPCC fifth assessment (Collins et al., 2006). The short-wave effects of these two species have been thoroughly investigated by Li et al. (2010). The results support the Collins suggestion. The GENLN2 model has been modified by incorporating ozone short-wave absorption cross-section data and oxygen continuum absorption data. These implementations have strengthened the foundation of GENLN2 and made it more accurate and safer to be used as a tool and benchmark for development of broadband radiation schemes. A new approach based on the correlated-k distribution method has been developed for the SES2 radiation scheme. It has been shown that this method is successful in the reduction of computational cost while maintaining calculation accuracy. Using this technique, the total number of monochromatic radiative transfer calculations in each radiation call in a model integration is reduced to 58 in the SES2 which is significantly less than that used in the ES scheme, indicating its improved efficiency. SES2 has been tested against the GENLN2 line-by-line code and compared with the original ES scheme. The results show that both irradiance and heating rates determined by the ES scheme have been improved in SES2. Acknowledgements The author wishes to thank S. Voigt and J. 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