Atmospheric Research 58Ž. 2001 141–154 www.elsevier.comrlocateratmos Comparison of surface radiative flux parameterizations Part II. Shortwave radiation Sami Niemela¨¨¨¨), Petri Raisanen, Hannu Savijarvi Department of Meteorology, UniÕersity of Helsinki, PO Box 64, FIN-00014 Helsinki, Finland Received 16 January 2001; accepted 25 April 2001 Abstract This paper presents a comparison of several shortwaveŽ. SW downwelling radiative flux parameterizations with hourly averaged pointwise surface radiation observations made at Jokioinen and Sodankyla,¨ Finland, in 1997. Both clear and cloudy conditions are considered. The clear-sky comparisons included six simple SW parameterizations, which use screen level input data, and three radiation schemes from numerical weather predictionŽ. NWP models: the former European Centre for Medium-Range Weather ForecastŽ. ECMWF scheme, the Deutscher WetterdienstŽ. DWD scheme, and the High Resolution Limited Area Model Ž HIRLAM . scheme. Atmospheric-sounding profiles were used as input for the NWP schemes. For the cases with clouds, three simple cloud correction methodsŽ. mainly dependent on the total cloud cover were tested. In the SW clear-sky comparisons, the relatively simple scheme by Iqbal provided the best results, surprisingly outperforming even the NWP radiation models. Simple cloud corrections performed poorly in the SW region. Out of these schemes, a new cloud correction method developed using the present data provided the best results. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Shortwave radiation; Surface radiative flux; Empirical formulas; Cloud corrections 1. Introduction Downwelling fluxes of longwaveŽ.Ž LW, 4.0–100 mm and shortwave SW, 0.3–4.0 mm. radiation are key terms of the surface energy budget and are vitally important for ) Corresponding author. Fax: q358-9-191-50860. E-mail addresses: [email protected]Ž. S. Niemela¨¨¨ , [email protected] Ž P. Raisanen . , [email protected]Ž. H. Savijarvi¨ . 0169-8095r01r$ - see front matter q2001 Elsevier Science B.V. All rights reserved. PII: S0169-8095Ž. 01 00085-0 142 S. Niemela¨ et al.rAtmospheric Research 58() 2001 141–154 climate studies and many applications such as agricultural meteorology and air–sea–ice interaction studies. In Niemela¨ et al.Ž. 2001 , hereafter Part I, we compared several simple parameterization formulas and radiation codes from numerical weather prediction Ž.NWP models with LW flux observations in Finland. This paper presents a similar SW comparison. The performance of six simple SW clear-sky radiation parameterization schemes and three cloud correction methods is evaluated using data from Jokioinen and Sodankyla,¨ Finland. In addition to the simple parameterizations, three NWP radiation codes are included in the clear-sky intercomparison: the former radiation scheme from the European Centre for Medium-Range Weather ForecastŽ.Ž ECMWF model hereafter EC-OLD; Morcrette, 1991.Ž , the Deutscher Wetterdienst DWD; Ritter and Geleyn, 1992.Ž. scheme and the High Resolution Limited Area Model HIRLAM; Savijarvi,¨ 1990 scheme. 2. Physical background The downwelling shortwave flux at the surface may be written as shown in Eq.Ž. 1 : x s s FSWtScosu teS 0 cosu ,1Ž. s where S eS0 is the incident solar radiation at the top of the atmosphere on a surface s r 2 s perpendicular to the solar beam ŽS0 1367 W m is the solar constant and e 0.967– 1.033 accounts for the seasonal variations of the Earth–Sun distance. , u is the solar zenith angle, and t is a broadband atmospheric transmissivity. The transmissivity can be writtenŽ. neglecting atmospheric refraction and the curvature of Earth as shown in Eq. Ž.2: 1 ` s yt r u q l t H S0,llexpŽ.cos t l,DIF d .2 Ž. S0 0 Here, l is wavelength, tl is the monochromatic optical thickness, the first term within the wavelength integral represents the contribution by the direct solar beam, and the second term represents diffuse solar radiation. It is evident from Eqs.Ž. 1 and Ž. 2 that the solar elevation has a very strong effect on the downwelling flux at the surface. The top-of-the atmosphere insolation on a horizon- tal surface is directly proportional to cosu, and the atmospheric transmissivity, particu- larly its direct beam component, decreases with decreasing cosu as the slant path lengths become larger. The factors contributing to atmospheric attenuation of solar radiation include gaseous absorptionŽ. most importantly, by water vapour and ozone , Rayleigh scattering by air molecules, and scattering and absorption by cloud droplets, ice crystals and aerosols. The total optical thickness tl needed in the computation of direct beam transmission is obtained simply as the sum of the contributions by all of these components. The computation of the diffuse transmissivity tl,DIF is not simple. Physically, diffuse radiation is produced by all atmospheric scattering processes. The diffuse radiation reaching the ground also depends on the surface albedo via atmospheric re-reflection of surface-reflected radiation. S. Niemela¨ et al.rAtmospheric Research 58() 2001 141–154 143 3. Parameterization schemes The simple parameterization schemes presented below in Sections 3.1 and 3.2 are based on empirical relationships derived from observed radiation fluxes. The simplest schemes depend only on the solar zenith angle u while others also use screen level input wx variables such as water vapour pressure e0 hPa . Cloud correctionsŽ. all-sky methods use mainly total cloudiness observations. The NWP SW radiation parameterization schemes are briefly described in Section 3.3. 3.1. The clear-sky flux Six formulasŽŽ.Ž.. Eqs. 3 – 8 are considered for the calculation of the downwelling SW flux in clear-sky conditions. In the first threeŽŽ.Ž.. Eqs. 3 – 5 , only the cosine of the solar zenith angleŽ. cosu is used. Ž.1 The scheme by Bennett Ž 1982 . is the simplest of all. It is based on the assumption that knowledge of the atmospheric mean transmissivity is sufficient for calculating the monthly mean fluxes. Bennett used this scheme shown in Eq.Ž. 3 as: x s FSW,clr0.72S 0 cosu ,3Ž. r 2 where S0 is the solar constantŽ 1367 W m. Here, as in all the following formulas, the unit of the flux is Wrm2 . Eq.Ž. 3 does not take into account the decrease of atmospheric transmissivity with increasing solar zenith angleŽ. i.e. increasing slant path lengths , so it might not be very appropriate for the calculation of hourly values. Ž.2 The method of Paltridge and Platt Ž 1976 . was derived using a long-time series of hourly averaged values of measured SW flux from Aspendale, Australia and is described in Eq.Ž. 4 as: x s q y FSW,clr 10 1411 cosu 310' cosu .4Ž. Ž.3 The formula by Moritz Ž 1978 . , shown in Eq. Ž. 5 , is based on the scheme by Lumb Ž.1964 , which was intended for hourly as well as daily and monthly mean calculations. However, Lumb’s coefficients are very sensitive to local conditions so Moritz derived new coefficients to fit measured data from Baffin Bay, Canada: x s q FSW,clrS 0 cosu Ž.0.47 0.47cosu .5 Ž. wx The next formulasŽŽ.Ž.. Eqs. 6 – 7 add the screen level water vapour pressure e0 hPa as an extra input parameter. The short-time variability of the near-surface humidity is thus taken into account, which should make these formulas better suited for the calculation of instantaneous fluxes than the three previous formulasŽŽ.Ž.. Eqs. 3 – 5 . Ž.4 Zillman Ž 1972 . used radiation data from islands of the Indian Ocean for deriving his scheme shown in Eq.Ž. 6 : 2 S0 cos u Fx s .6 SW,clr q q = y3 q Ž. 1.085cosu e0 Ž.2.7 cosu 10 0.10 Ž.5 Shine Ž 1984 . improved the scheme of Zillman Ž 1972 . by adjusting its coefficients to give better results in arctic winter conditions. Shine noticed that Zillman’s equation 144 S. Niemela¨ et al.rAtmospheric Research 58() 2001 141–154 underestimates the SW fluxes especially in the Arctic regions. Shine’s version of Eq.Ž. 6 is shown as Eq.Ž. 7 : 2 S0 cos u Fx s .7 SW,clr q q = y3 q Ž. 1.2cosu e0 Ž.1.0 cosu 10 0.0455 Ž.6 All the previous schemes are rough approximations; they even ignore the fact that the top-of-the-atmosphere insolation S varies with season due to the elliptical orbit of the Earth. The sixth parameterizationŽ. Iqbal, 1983 is somewhat more detailed than the previous ones. IqbalŽ. 1983 presented a parameterization as shown in Eq. Ž. 8 : x s q FSW,clrS dir D,8Ž. where Sdir is the direct solar radiation on a horizontal surface and D is the diffuse irradiance. The direct radiation is calculated as shown in Eq.Ž. 9 : s Sdir0.9751SŽ.cosu ttttt R g w a o ,9 Ž. where S is the broadband solar radiation at the top of the atmosphere, tR is the transmittance by Rayleigh scattering, tg is the transmittance by uniformly mixed gases, twaois the transmittance by water vapour, t is the transmittance by aerosols and t is the transmittance by ozone. More detailed documentation can be found in IqbalŽ. 1983 . The version used in this paper is based on Venalainen¨¨ Ž. 1994 . Eq. Ž. 10 shows his derived empirical function for the calculation of ta using SW radiation measurements from Jokioinen and Sodankyla:¨ s q y = y4 2 ta 0.59 0.012u 1.336 10 u .10Ž. Moreover, the estimation of the precipitable water content w wxcm , which is used in the calculation of tw , was modified. The precipitable water is originally estimated using wx w x screen levelŽ. sl temperature T00K and water vapour pressure e Pa via Eq.Ž.