Comparison of Surface Radiative Flux Parameterizations Part II

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 horizontal 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. 11 : e s 0 wsl 0.493 ,Ž. 11 T0 s y r where e00is estimated from e RH expŽ.Ž. 26.23 5416 T 0RH is relative humidity . The calculated wsl is then adjusted by an empirical correction formula, Eq.Ž. 12 , which Venalainen¨¨ Ž. 1994 derived using radio soundings from Jokioinen: s y w 0.71104wsl 0.032003.Ž. 12 The diffuse irradiance D in this scheme is presented as the sum of the three terms as shown in Eq.Ž. 13 : s q q D DRamD D ,13Ž. where DRais the Rayleigh-scattered and D is the aerosol-scattered diffuse irradiance, and Dm is the multiple-reflected irradianceŽ backward scattering of surface-reflected radiation.Ž see Iqbal, 1983 for more details . . The surface albedo, which is needed in the term Dm , was estimated by using the actual measured downwelling and upwelling hourly averaged SW fluxesŽ. see Section 4 for further discussion . S. Niemela¨ et al.rAtmospheric Research 58() 2001 141–154 145

3.2. The all-sky flux

The effects of clouds on the SW flux have typically been parameterized in the simpler schemes by multiplying the SW clear-sky flux by a cloud correction factor which depends on the total cloudiness c. Two previously suggested corrections are considered here. First, BerliandŽ. 1960 presented an all-sky flux parameterization linear on c as shown in Eq.Ž. 14 : xxs y q FSW,allŽ.1 c tc c F SW,clr ,14 Ž. s where tccis the cloud transmissivity. We assume t 0.48 as BennettŽ. 1982 did in sea ice experiments in the Arctic regions. Second, LaevastuŽ. 1960 assumed, based on data from midlatitude oceans, that the cloud factor was rather a cubic function of total cloudiness as indicated in Eq.Ž. 15 : x s y 3 x FSW,allŽ.1 0.6c F SW,clr .15 Ž. The previous parameterizations use only the total cloudiness as an input variable but sometimes there is more information available, for example the amount of low clouds. Therefore, we tested as the third alternative, a new parameterization derived using radiation and cloudiness data from Jokioinen, Finland, 1997. This scheme needs the total A B cloudiness c, the amount of low clouds clowand the amount of other clouds c oth s y A Ž.c clow as input variables. This parameterization is hereafter denoted as the low cloud schemeB described in Eq.Ž. 16 :

clow 4.7y2.24 q y3 Fx s 1yc c 10 q0.31c2.46q0.73cF 4.7 x .16Ž. SW,allž/ low oth SW,clr

3.3. Radiation schemes for NWP models

The downwelling surface clear-sky SW flux produced by the EC-OLD, DWD and HIRLAM schemes was evaluated in this study. A brief description of the main features of these schemes in the SW region is given below. More detailed documentation can be found in MorcretteŽ.Ž. 1991 EC-OLD , Ritter and Geleyn Ž.Ž. 1992 DWD and Savijarvi¨ Ž.1990 and Sass et al. Ž.Ž 1994 HIRLAM . . The SW radiation is calculated in the EC-OLD scheme and the DWD scheme using a d-two-stream approach. In the EC-OLD scheme, the SW part of the spectrum is divided into two intervals, whereas the DWD scheme has three intervals. Both schemes treat separately gas absorption by H23 O and O in the SW part of the spectrum. The uniformly A B mixed gasesŽ. CO22 , O , CH 42 , N O and CO are treated as a single hybrid gas in both schemes. Aerosols are divided into five AstandardB aerosol types both in the EC-OLD and DWD schemes; the continental type is assumed in the present study. The HIRLAM scheme differs considerably from EC-OLD and DWD. There is only one SW interval, and only H2 O is treated explicitly whereas other gases and aerosols are added using empirical coefficients. The HIRLAM scheme is much faster than the other NWP schemes, so it could be less accurate. 146 S. Niemela¨ et al.rAtmospheric Research 58() 2001 141–154

The EC-OLD and DWD schemes have formal wavelength limits of 0.25–4.0 and 0.25–4.64 mm. However, the top-of-the-atmosphere solar flux actually equals the Ž.season-corrected solar constant; this is also true for the HIRLAM scheme.

4. Data and measurements

SYNOP observations, radio soundings and radiation measurements around 12 UTC XX XX collected from the JokioinenŽ 60849 N, 23830 E.Ž and Sodankyla¨ 67822 N, 26839 E. observatories, Finland, were used in the comparison. The Sodankyla¨ observation site was described in Part I. The climate conditions in Jokioinen are a little warmer; summers are temperateŽ. July mean temperature 15.88C and winters are fairly cold Ž.January mean temperature y7.58C . The annual mean precipitation amount in Jokioinen Ž.582 mm is slightly larger than in Sodankyla.¨ The area around the Jokioinen observa- tory consists mainly of field and forest terrain. The elevation is 103 m above the sea level and the area is basically flat. The comparison periods were from 1 January to 31 December 1997 and from 26 January to 13 November 1997 at Jokioinen and Sodankyla,¨ respectively. The data for Jokioinen included 26 clear-sky cases and 358 all-sky cases. The data for Sodankyla¨ included 27 clear-sky cases; cloudy conditions were not examined. x≠ The downwelling and upwelling SW fluxes ŽFSWand F SW . and diffuse SW flux x Ž DSW . were measured using a Moll–Gorczynski pyranometer with an estimated accuracy of "5%. The calculated SW fluxes were compared directly with the measured hourly averaged SW fluxes. The SYNOP observationsŽ. 12 UTC were made between 15 and 30 min, and the radio soundings were launched between 0 and 15 min of the same hour over which the radiation measurements were averaged. The SW parameterizations considered here use similar input variables as the LW schemes presented in Part I. In addition, the visually estimated amount of low clouds clow was collected for the SW all-sky calculations. The conditions were considered cloudless when the visually observed total cloudiness was zero or one octas. However, some of these cases were eliminated as possibly cloud-contaminated, based on a suspectibly large ratio of diffuse to total downwelling xxr SW radiation Ž DSWF SW . compared to clear cases with similar solar elevation. A total of 10 Jokioinen and 3 Sodankyla¨ cases were excluded. Temperature, pressure and humidity profiles from radio soundings were the input data for the EC-OLD, DWD and HIRLAM schemes. The ozone profiles and the vertical grid were the same as used in Part I. For the SW calculations, the vertically integrated optical thickness of aerosols at ls0.55 mm was set to a constant value 0.1 in the EC-OLD and DWD schemesŽ. continental aerosol assumed . The surface albedo for all schemes was given by the actual measured local albedo ≠ r x FSWF SW . It should be noted that this is another source of uncertainty: the effect of surface albedo on the downwelling fluxŽ due to the backward scattering of surface-reflected radiation. is not determined by the local albedo but by the AeffectiveB albedo of a larger area. The latter may differ substantially from the local albedo in horizontally heterogeneous conditions, especially in winter, when there are large albedo differences S. Niemela¨ et al.rAtmospheric Research 58() 2001 141–154 147

Fig. 1. Aerosol optical thickness in clear-sky 12 UTC cases in 1997. The solid line gives the constant value s taer 0.1 used in the standard set of calculations. The crosses connected by dashed line give taer estimated from visibility observations via Eq.Ž.Ž. 18 . a Jokioinen. Ž. b Sodankyla.¨ between open snowy areas and forest. A sensitivity test was made with the IqbalŽ. 1983 scheme in which the winter albedo was given a constant value 0.5Ž winter albedo x r 2 reduced on average by 0.25. . This reduced FSW on average by 2 W m only. Two sensitivity experiments were also made with the EC-OLD scheme. In the first test, a rather large uncertainty Ž."30% of the total ozone was assumed in all input x " r 2 profiles. The effect on FSW was only about 3W m , so the typical errors of the total ozone do not affect greatly the SW irradiance. In the second experiment, the aerosol optical thickness was estimated from local visibility observations assuming that the aerosol concentration decreases exponentially upward with a scale height Hs1 km. When JungeŽ. 1963 standard aerosol assumption was made, the aerosol volume extinc- tion coefficientw kmy1 x , shown in Eq.Ž. 17 , at height z wxkm is approximately 20 0.55 z b s0.2 exp y ,17Ž. aer ž/ž/V l ž/H where V is visibilitywx km and l is wavelength wmm x . The optical thickness of aerosols is then obtained by integrating baer over the air column as shown in Eq.Ž. 18 : ` 20 0.55 t s b s aerH aerd z 0.2 H.18Ž. 0 ž/ž/V l s Values of taer computed from Eq.Ž. 18 for l 0.55 mm Ž the reference wavelength used in the EC-OLD and DWD schemes for aerosols. are plotted in Fig. 1. The mean value is 0.10 for Jokioinen and 0.08 for Sodankyla,¨ indicating slightly cleaner air in the north.

5. Results

Similar to the LW comparisons in Part I, the quality of the SW flux parameterizations is estimated by considering the mean difference to observationsŽ. bias , the standard 148 S. Niemela¨ et al.rAtmospheric Research 58() 2001 141–154 deviation around the mean difference, and the RMS difference. As pointed out in Part I, these differences are not only caused by model inaccuracy, but also by inaccuracy in the input dataŽ. screen-level observations and radio soundings used, and by errors in the measured radiative fluxes used for validation.

5.1. Clear-sky results

x The differences of the parameterized downwelling SW fluxes FSW,clr in clear-sky situations are shown in Fig. 2. The bias, standard deviation and RMS difference of the parameterized fluxes for Jokioinen and Sodankyla¨ are given in Table 1. Most of the schemes overestimate the SW flux in Jokioinen, whereas all schemes underestimate the SW flux in Sodankyla.¨ This difference is discussed further below. The most accurate parameterization was Iqbal’sŽ. 1983 scheme; its bias, RMS difference and standard deviation were the lowest of all schemes in Jokioinen. The HIRLAM scheme had the lowest bias in Sodankyla,¨ while the DWD scheme and Iqbal’sŽ. 1983 scheme had the smallest standard deviations. Surprisingly, the parameterization used by IqbalŽ. 1983 was slightly better than the EC-OLD, DWD and HIRLAM schemes. The DWD and HIRLAM schemes had almost the same values of the standard deviation, whereas for the EC-OLD scheme the standard deviation was about 5–6 Wrm2 higher. The HIRLAM scheme was more transparent than the DWD and EC-OLD schemes. The results of the simplest schemes contained much more scatter. Bennett’sŽ. 1982 scheme performed surprisingly well in Jokioinen, while Shine’sŽ. 1984 scheme was good in Sodankyla.¨ The good performance of Iqbal’sŽ. 1983 scheme could be due to the modifications by Venalainen¨¨ Ž. 1994 , which were based on data from the same stations. The next step was to remove these adjustments from Iqbal’s scheme and recalculate the fluxes using cloudless data from Jokioinen. Thus, the empirical Eq.Ž. 10 for transmittance by aerosols was modified so that the vertical optical thickness of aerosols was set to constant 0.1

Table 1 Results of the SW comparison in cloudless situations. The average measured SW flux values were 378 Wrm2 for Jokioinen and 356 Wrm2 for Sodankyla¨ Schemes Jokioinen 1997 Sodankyla¨ 1997 Bias SD RMS Bias SD RMS Paltridge and PlattŽ. 1976 y16.1 29.7 33.8 y41.1 21.5 46.4 MoritzŽ. 1978 y13.8 42.7 44.8 y38.1 30.3 48.7 BennettŽ. 1982 y5.2 20.7 21.3 y26.2 26.1 37.0 ZillmanŽ. 1972 11.7 37.0 38.8 y15.4 27.5 31.5 ShineŽ. 1984 15.7 23.4 28.2 y10.5 17.8 20.7 IqbalŽ. 1983 y1.1 12.4 12.4 y19.9 8.3 21.5 EC-OLD 5.9 19.7 20.6 y16.3 14.1 21.5 DWD 2.9 13.7 14.0 y17.2 8.0 19.0 HIRLAM 13.6 13.1 18.9 y6.0 9.9 11.5

BiasŽ Wrm2 .sparameterizedymeasured. SDŽ Wrm2 .sstandard deviation. RMSŽ Wrm2 .sroot-mean-square difference. S. Niemela¨ et al.rAtmospheric Research 58() 2001 141–154 149

Fig. 2. DifferencesŽ. Diff sparameterizationymeasurement in downwelling SW flux in cloud-free conditions. Ž.a Paltridge and Platt Ž 1976 . . Ž. b Moritz Ž 1978 . . Ž. c Bennett Ž 1982 . . Ž. d Zillman Ž 1972 . . Ž. e Shine Ž 1984 . . Ž. f IqbalŽ 1983 . . Ž. g EC-OLD scheme. Ž. h DWD scheme. Ž. i HIRLAM scheme. Jokioinen Žq .and Sodankyla¨ Ž.= . 150 S. Niemela¨ et al.rAtmospheric Research 58() 2001 141–154

s y r ŽŽta exp 0.1 cosu ..as for the other schemes. The correction of the precipitable waterŽŽ.. Eq. 12 was also removed. The surface albedo was given constant values; in summerŽ. May–Oct 0.21 and in winter Ž. Nov–Apr 0.71. This AstrippedB Iqbal’s scheme still outperformed the other schemes as regards with standard deviation. The bias was y3.2 Wrm22 and the standard deviation became 12.7 WrmŽ. cf. Table 1 . When aerosol optical thickness from Eq.Ž. 18 was used in the EC-OLD scheme, the bias and standard deviation for Jokioinen were 8.5 and 19.0 Wrm2, whereas those for Sodankyla¨ were y12.6 and 14.9 Wrm2 . Thus, the biases were slightlyŽ about 3 Wrm2 . more positive than in the AstandardB set of calculations, in which a constant value s taer 0.1 was assumed. The differences in standard deviation were small. Thus, even if the use of Eq.Ž. 18 brings visibility-dependent variation into the aerosol optical thickness, this did not greatly improve the calculated SW fluxes. The above test also suggests that differences in atmospheric transparency cannot explain the main part of the systematic difference in biases between the Jokioinen and Sodankyla¨ results. Evidently, systematic measurement errors at one or both stations contribute to this difference. When using constant taer , a value of 0.14 was needed to eliminate the bias of the EC-OLD scheme in Jokioinen, whereas the corresponding value was only 0.03 for Sodankyla.¨ This difference is substantially greater than that suggested in Fig. 1.

5.2. All-sky results

The differences of the calculated SW all-sky fluxes are shown in Fig. 3Ž for Jokioinen, 1997. . The bias, standard deviation and RMS difference of the parameterized

Fig. 3. DifferencesŽ. Diff sparameterizationymeasurement in downwelling SW flux in all cases in Jokioinen, x 1997. FSW ,clr is calculated by Iqbal’sŽ 1983 . scheme. Ž. a No cloud correction. Ž. b Berliand Ž 1960 . . Ž. c LaevastuŽ.Ž. 1960 . d ALow cloud scheme.B S. Niemela¨ et al.rAtmospheric Research 58() 2001 141–154 151

Table 2 Results of the SW comparison in all-sky situations. The average measured SW flux value was 288 Wrm2. x FSW,clr is calculated using Iqbal’sŽ. 1983 scheme Schemes Jokioinen 1997 BiasŽ. WrmSDW22 Ž.rm RMS Ž. Wrm 2 No correction 149.7 155.5 215.8 BerliandŽ. 1960 y6.9 96.7 97.0 LaevastuŽ. 1960 19.0 84.4 86.5 ALow cloud schemeB y9.5 85.2 85.7

Biassparameterizedymeasured. all-sky fluxes are given in Table 2. The all-sky fluxes were produced by multiplying the clear-sky flux by cloud-correction factorsŽŽ.Ž.. Eqs. 14 – 16 . The clear-sky fluxes were calculated using Iqbal’sŽ. 1983 scheme. The bias of Iqbal’s scheme was very low Žy1.1 Wrm2 . in Jokioinen so most of the biases in the all-sky calculations are caused by the cloud correction factors. If a greatly biased clear-sky scheme was used, the conclusions regarding the cloud corrections would also be erroneous. The all-sky SW flux is of course heavily overestimated if no cloud correction is used Ž.Fig. 3a . The corrections improve the results but the scatter still remains very large. The low cloud scheme gave the best overall results. The standard deviation was smallest

xxr Fig. 4. Shortwave cloud correction coefficient ŽFSW,allF SW,clr . as a function of total cloudiness. The triangles xx represent the measured FSW,alldivided by the calculated clear-sky flux F SW,clr Ž.Iqbal, 1983 . The lines are for the referred all-sky schemes. The lines Alow cloudsB and Aother cloudsB are both related to the Alow cloud schemeB: the former gives the correction in cases in which the whole visible cloud cover consists of low clouds while the latter represents cases with middle andror high clouds only. 152 S. Niemela¨ et al.rAtmospheric Research 58() 2001 141–154 using Laevastu’sŽ. 1960 scheme but its bias is quite large Ž 19.0 Wrm2 . . Although the bias was smallest for Berliand’sŽ. 1960 scheme, the performance of this method is poor because of the large standard deviationŽ 96.7 Wrm.2 . In Fig. 4, the different cloud corrections are compared with observations as a function of total cloudiness. AMeasuredB correction over unity implies reflections from cloud sides; this strong three-dimensional radiative transfer effect of the inhomogeneous sky is seen to occur occasionally at almost all cloud amounts. Berliand’sŽ. 1960 linear scheme underestimates the all-sky flux for almost all values of the total cloudiness. The curves of the low cloud scheme and Laevastu’sŽ. 1960 scheme follow the mean of the AmeasuredB values much better. A major problem with the cloud corrections is the uncertainty in cloud optical properties, the optical thickness being the most important of these. The low cloud scheme accounts implicitly for the fact that low clouds tend to be optically thicker than higher clouds. This brings some advantage over the other schemes although the improvement is limited: physically, it is indeed the cloud optical thickness rather than the cloud height that is important for the downwelling solar flux.

6. Conclusions

The goals of this study were to evaluate the performance of several simple and some more complex radiation schemes in computing the downwelling SW radiative fluxes, and to find the optimum simple SW parameterization in both clear and cloudy conditions. The calculated fluxes were compared to hourly averaged radiation observations made at the Jokioinen and Sodankyla¨ observatories in southern and northern Finland in 1997 at 12 UTC. All the simpler parameterization schemes were empirical methods, whose input variables were screen level weather observationsŽ e.g. water vapour pressure. along with the solar zenith angle. Comparisons were also made with three different radiation schemes used for NWP. Input to these was provided by radio soundings. As these schemes also need cloud water profiles, which are not observed, their comparisons were restricted to clear-sky cases only. The SW clear-sky fluxes were estimated most accurately using the modified Ž.Venalainen,¨¨ 1994 parameterization of Iqbal Ž. 1983 . It was anticipated that this scheme would outperform all the simpler schemes. Surprisingly, it was also better than the NWP schemes, which used atmospheric sounding profiles as input. The DWD and HIRLAM schemes gave the next best results. The clear-sky results of the EC-OLD scheme did not improve significantly when we used varying aerosol optical thickness values estimated from local visibility observations instead of the constant value 0.1. On the average, the atmospheric SW transmissivity was a bit larger when using optical thickness deduced from visibility. The all-sky fluxes were calculated using simple cloud correction factors, which depend mainly on total cloudiness. These cloud factors were used together with Iqbal’s Ž.1983 scheme. The SW all-sky fluxes were produced most accurately using the new Alow cloudB scheme introduced in this articleŽŽ.. Eq. 16 . Laevastu’s Ž 1960 . scheme was nearly as good. However, the new scheme may be site specific due to fact that it was S. Niemela¨ et al.rAtmospheric Research 58() 2001 141–154 153 derived using data from Jokioinen only. The accuracy of the SW all-sky schemes was generally poor because of the large scatter in the results. A major limitation of the present study is that it was made using data from two stations only. Thus, the results cannot be generalized to climatic conditions significantly different from Jokioinen and Sodankyla.¨ For obtaining better geographic coverage, the comparisons should be made for a larger set of stations. It could also be interesting to compare the results with ECMWF ReanalysisŽ. ERA, Gibson et al., 1997 or National Center for Environmental PredictionŽ. NCEP, Kalnay et al., 1996 reanalysis data sets, although it should be noted that reanalysed radiative fluxes are naturally model-dependent.

Acknowledgements

We thank the Finnish Meteorological Institute for providing all the data used in this study. Comprehensive comments made by an anonymous reviewer who helped to improve the original manuscript significantly. Sami Niemela¨¨¨ and Petri Raisanen have been financed by the Academy of FinlandŽ. Project 40544 .

References

Bennett, T.J., 1982. A coupled atmosphere–sea ice model study of the role of sea ice in climatic predictability. J. Atmos. Sci. 39, 1456–1465. Berliand, T.C., 1960. Method of climatological estimation of global radiation. Meteorol. Gidrol. 6, 9–12. Gibson, J.K., Kallberg,˚ P., Uppala, S., Hernandez, A., Nomura, A., Serrano, E., 1997. ERA description. ECMWF Re-Analysis Project Rep. Ser. 1, European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom, 66 pp. Iqbal, M., 1983. An Introduction to Solar Radiation. Academic Press, 390 pp. Junge, C.E., 1963. Air Chemistry and Radioactivity. Academic Press, 382 pp. Kalnay, E., Kanamitsu, M., Kistler, R. et al., 1996. The NCEPrNCAR 40-year reanalysis project. Bull. Am. Meteorol. Soc. 77, 437–471. Laevastu, T., 1960. Factors affecting the temperature of the surface layer of the sea. Commentat. Phys.-Math., 25. Lumb, F.E., 1964. The influence of cloud on hourly amounts of total solar radiation at the sea surface. Q. J. R. Meteorol. Soc. 90, 43–56. Morcrette, J.J., 1991. Radiation and cloud radiative properties in the European Centre for Medium-Range Weather Forecasts forecasting system. J. Geophys. Res. 96Ž. D5 , 9121–9132. Moritz, R.E., 1978. A model for estimating global solar radiation. Energy budget studies in relation to fast-ice breakup processes in Davis Strait. Occas. Pap.- Univ. Colorado, Inst. Arct. Alps Res. 26, 121–142. Niemela,¨¨¨ S., Raisanen, P., Savijarvi, ¨ H., 2001. Comparison of surface radiative flux parameterizations: Part I. Longwave radiation. Atmos. Res 58, 1–18. Paltridge, G.W., Platt, C.M.R., 1976. Radiative Processes in Meteorology and Climatology. Elsevier, Amsterdam, 318 pp. Ritter, B., Geleyn, J.-F., 1992. A comprehensive radiation scheme for numerical weather prediction models with potential applications in climate simulations. Mon. Weather Rev. 120, 303–325. Sass, B.H., Rontu, L., Raisanen,¨¨ P., 1994. HIRLAM-2 radiation scheme: Documentation and tests. HIRLAM technical report 16, SMHI, Norrkoping,¨ Sweden, 43 pp. Savijarvi,¨ H., 1990. Fast radiation parameterization schemes for mesoscale and short-range forecast models. J. Appl. Meteorol. 29, 437–447. 154 S. Niemela¨ et al.rAtmospheric Research 58() 2001 141–154

Shine, K.P., 1984. Parametrization of the shortwave flux over high albedo surfaces as a function of cloud thickness and surface albedo. Q. J. R. Meteorol. Soc. 110, 747–764. Venalainen,¨¨ A., 1994. The spatial variation of mean monthly global radiation in Finland. Ph. lic. thesis, Department of Meteorology, University of Helsinki, 47 pp. Zillman, J.W., 1972. A study of some aspects of the radiation and heat budgets of the southern hemisphere oceans. Meteorological Study, vol. 26, Bur. of Meteorol., Dep. of the Inter., Canberra, Australia.