Ice in the Environment: Proceedings of the 16th IAHR International Symposium on Ice Dunedin, New Zealand, 2nd 6th December 22 International Association of Hydraulic Engineering and Research ON THE SHORTWAVE RADIATION PARAMETERIZATION IN THERMODYNAMIC SEA ICE MODELS IN THE BALTIC SEA Jens Ehn 1, Kai Rasmus 1, Matti Leppäranta 1 and Kunio Shirasawa 2 ABSTRACT An ice research station was established in autumn 1999 in Santala Bay near 6 N on the coast of Finland, and data collection based on weekly winter-time sampling and an automatic station has been ongoing until the end of spring 22. This work included automatic irradiance sensors above and in the ice, as well as spectral data collection of the downwelling shortwave irradiance. The first results of the irradiance time series from year 2 are presented. The collected data is used to perform tests on the commonly used empirical downwelling radiative flux parameterizations by Zillman, Shine and Iqbal for clear sky fluxes, and Reed and Bennett for all-sky fluxes. For all-sky fluxes during the ice covered period, the best results were derived from the schemes by Shine in combination with Reed. INTRODUCTION Locally during a cloud-free day the downwelling shortwave irradiance (SW ) mainly depends on the solar zenith angle. Most of the simple radiative flux parameterizations are based on experiments comparing the zenith angle to radiative flux (irradiance). Results between different areas are, however, highly dependent on the structure and composition of the atmosphere; parameterizations based on measurement in the Indian Ocean (Zillman, 1972) might not be suitable for the calculation of the fluxes above sea ice in the Baltic Sea. This paper presents downwelling shortwave irradiance measurement results covering the first of three years of measurements made on the coast of the Baltic Sea. These measurement results are then compared to three different parameterizations for downwelling shortwave radiative flux during clear skies and two schemes to account for clouds. The Zillman (1972) empirical formulation for the downwelling flux takes into account the attenuation of shortwave radiation in the atmosphere due to water vapour. The effect 1 Division of Geophysics, Department of Physical Sciences, P.O.Box 64, FIN-14 University of Helsinki, Finland. 2 Sea Ice Research Laboratory, Hokkaido University, 6-4-1 Minamigaoka, Mombetsu, Hokkaido 94-13 Japan.
of the water vapour is parameterized using the two-meter water vapour pressure e. This scheme was developed for use in marine regions in the Southern hemisphere. SW = S cos 2 θ z 1.85 cos θ z + e (2.7 + cos θ z ) 1 3 +.1 (1) where S is the solar constant, e is the two-meter water vapour and θ z is the solar zenith angle. Shine (1984) varied the coefficients in Eq. 1 to make the scheme better suited for the northern hemisphere above surfaces with a high albedo: SW = S cos 2 θ z 1.2 cos θ z + e (1. + cos θ z ) 1 3 +.455 (2) This parameterization has recently been used by Cheng (22) for Baltic Sea ice thermodynamic modelling (see also Launiainen and Cheng, 1998). Key et al. (1996) found Eq 2 to be the most suitable for use in sea ice modelling at high latitudes. Another recent sea ice thermodynamic model by Saloranta (1998) used the parameterization presented by Iqbal (1983). In the Iqbal model the shortwave radiative flux depends on the solar constant S, the eccentricity of the Earth orbit E, the solar zenith angle, θ z, atmospheric turbidity, T. The formula is: SW = T S E cos θ z (3) where E and θ z are calculated through experimentally obtained polynomials. In this work T =.8 according to Haapala and Leppäranta (1993). In Saloranta (1998) the additional cloud insulation was estimated using the approximation suggested by Reed (1977): SW c = SW [1 ].632 N +.19 θ z (4) where N is the cloud fraction with values between and 1. In Cheng (22) the all-sky shortwave radiation flux was estimated according to Bennett (1982): SW c = SW [1.52 N ] (5) MEASUREMENTS A three-winter experiment, Hanko99-1, was performed in 1999-21, with an additional winter in 22, by sea ice groups from the University of Helsinki and Hokkaido University. The measurement was in the fast ice zone in Santala Bay (59 55 N, 23 5 E) near the Hanko Peninsula in the Gulf of Finland. A pilot study in Santala Bay was performed in 1998 by Rasmus et al. (22). A Small light sensor (MDS-L, Alec Instruments) measuring downwelling shortwave irradiance was installed on a floating ice-station in Santala Bay. The sensor was set up to log instantaneous values of irradiance in µes 1 m 2 at 1 minute intervals. The data was converted to Wm 2 using spectral irradiance data for clear skies obtained with a LI-18UW
75 29.3. 5 25 8: 1: 12: 14: 16: 18: 75 75 15.3. 5 25 17.3. 5 25 8: 1: 12: 14: 16: 18: 8: 1: 12: 14: 16: 18: Figure 1: Comparison between three instruments used for measuring the incident irradiance; LI-1SA (black), MDS-L (gray) and Solar13 (+ sign). The stars indicate PAR irradiances integrated from LI-18UW spectra. spectroradiometer (LI-COR, Inc.). The global incident irradiance was additionally measured with 1-hour averaging from the ice-station using a Solar13 (Haenni, Germany). During field work in year 2 a LI-2SA pyranometer (LI-COR, Inc.), mounted on a tripod that was standing on the ice, was used for measuring the global downwelling irradiance during weekly sampling sessions. These measurements were conducted with 1-minute intervals for a few hours at a time. IN SITU DATA COMPARISON In Fig. 1 the results from the LI-2SA, MDS-L and Solar13 instruments are shown for a few days with different sky-conditions during March 2; the top panel shows results from March 29 with clear sky-conditions, while the two bottom panels show results from March 15 and 17 with variable sky-conditions. The Solar13 shows lower values, while the MDS-L is variable during morning hours as both instruments were shadowed or in other ways influenced by the ice-station structure. This will affect the daily mean values. The stars denote irradiance values integrated between 4-7 nm (PAR) from LI-18UW spectra and are about 4% of the incoming global radiation measured with the LI-2SA. The irradiance data from the MDS-L and the Solar13, averaged into daily mean values, is shown in Fig. 2 along with the theoretical estimates obtained using the three clear sky SW schemes, i.e. the Zillman (1972), Shine (1984) and Iqbal (1983). The data is in good agreement (see table 1) except for the MDS-L giving higher values during clear days up to around day 93. Often these peak values are higher than what the three clear sky schemes would predict. After day 93 the MDS-L peak values start levelling of, giving
4 35 3 Shine (1984) Zillman (1972) Iqbal (1983) MDS L Solar13 daily mean irradiance [Wm 2 ] 25 2 15 1 5 2 4 6 8 1 12 14 16 18 Figure 2: Comparison between the daily mean irradiances calculated from the Zillman (1972), Shine (1984) and Iqbal (1983) schemes for the clear skies and data measured with the MDS-L and the Solar13 during year 2. lower values compared to the Solar13. This might be an error in the response of the MDS-L instrument, as irradiances never seem to exceed 5 Wm 2. SHORTWAVE FLUX SCHEME COMPARISONS The three clear sky schemes seen in Fig. 2 are in good agreement, with Zillman (1972) giving slightly lower and Iqbal (1983) slightly higher daily mean irradiances compared to Shine (1984) (see table 1). The values obtained during the separate hours of the day are slightly different using the Zillman and Shine schemes; the values at noon are differing by approximately 2 Wm 2 at Julian day 31 and by 1 Wm 2 at Julian day 111, with Shine showing higher values at day 31 but lower values at day 111 than Zillman, even though the daily mean values are larger in Shine. Because these three schemes were in good agreement, the Shine scheme is used in comparisons with the measurements. Cloud fraction data was obtained from Russarö weather station (Finnish Meteorological Institute) with 3-hour intervals from January 1 to March 19 (8 days in all). Russarö is located about 16 km south-west of Santala Bay. The reduction due to the cloud cover is calculated using the cloudiness data in the cloud factors by Reed (1977) and Bennett (1982), together with the clear sky scheme by Shine (1984). Fig. 3 shows the daily mean values of these estimates together with the in situ data measured with the Solar13. The parameterized shortwave flux errors for all-sky conditions are shown in Fig. 4. The top panels show the errors from the daily mean values. The bottom panels show the errors of the data plotted against the solar angle, while using all available cloud fraction data, i.e. with 3-hour intervals. The corresponding statistics are given in table 1. The most
18 8 16 14 daily mean irradiance [Wm 2 ] 12 1 8 6 Cloudiness Shine (clear sky) Solar13 Shine + Reed Shine + Bennett 4 2 1 2 3 4 5 6 7 8 Figure 3: Calculated and measured daily mean irradiances from January 1 to March 19, 2. The cloudiness is shown on the top of the figure on a scale from (clear) to 8 (totally overcast). 4 Reed (1977), daily mean 8 Bennett (1982), daily mean 2 6 2 4 4 2 6 2 8 2 4 6 8 4 2 4 6 8 4 Reed (1977), 3 h interval 4 Bennett (1982), 3 h interval 2 2 2 2 4 1 2 3 solar altitude 4 1 2 3 solar altitude Figure 4: The all-sky shortwave flux error for two parameterizations between January 1 and March 19, 2, in Santala Bay (black dots are estimated Solar13 data, grey dots are estimated MDS-L data).
accurately parameterized fluxes are those using Reed (1977). Table 1: Statistics of the errors in parametrized and measured all-sky incident shortwave fluxes. mean max min std corr no Daily mean: Shine Zillman 4.2 7.4.4 2.5.999 18 Shine Iqbal -1.1-3.8-14.8 3.5.999 18 MDS-L Solar13.2 4.6-53.3 18.9.972 138 Shine/Reed Solar13.35 3.9-34.8 22.4.91 8 Shine/Reed MDS-L -9. 28.7-64.6 22.4.856 8 Shine/Bennett Solar13 14.4 54.7-16.1 29..868 8 Shine/Bennett MDS-L 5. 52.6-47.3 29..791 8 3-hour interval: Shine/Reed Solar13 3.7 218.4-262.1 44..786 623 Shine/Bennett Solar13 11.3 235. -222.4 48.5.781 623 Shine/none Solar13 36.9 423.1-16.3 84.6.713 623 values in watts per square meter. CONCLUSIONS The objective of this study was to evaluate the collected incident irradiance data and use it to study the suitability of downwelling shortwave radiative flux parameterizations for the Baltic Sea. The correlation of the daily mean values between the two instruments measuring incident irradiance, i.e. the MDS-L and the Solar13, is about.97 and the mean error.2 Wm 2. Altough the correlation is so high, the errors for individual days may exceed 5 Wm 2. Even though the MDS-L data follows the Solar13 data quite well, it should be mentioned that it does not seem capable of measuring irradiances larger than 5 Wm 2. This could be seen during clear days later in the season as the irradiances tended to flatten out around mid-day. One obvious source of error is the shading of the structure on the ice-station. This can be seen on the morning hours during clear days (see Fig. 1), and might cause the higher peak values seen for the MDS-L in Fig. 2. The measured irradiance, seen in Fig. 2, follow the calculated quite well until around day 9-1, after which it starts to flatten out. This date coincides quite near with the ice break-up, and might thus reflect the change of surface conditions from highly reflecting ice to open water. For all-sky fluxes, the most accurate estimates were given by the schemes of Shine (clear sky) and Reed (cloud factor). However, there are a number of schemes not tested in this work, e.g. Shine (cloud factor), which would include the albedo and the cloud optical thickness. More work is needed to include the years 21-2 in the time-series analyzes and to decide which parameterization scheme best accounts also for the daily variations.
ACKNOWLEDGEMENT The authors would like to thank M. A. Granskog for helpful comments while preparing the manuscript and A. Lindfors for his efforts in the fieldwork. This work is a part of the project Ice Climatology of the Okhotsk and Baltic Seas, financed by the Japanese- Finnish Bilateral Programs with the Japan Society for the Promotion of Science and the Academy of Finland. Jens Ehn is supported by the Walter and Andrée de Nottbeck foundation. REFERENCES Bennett, T.J. A coupled atmosphere-sea-ice model study of the role of sea-ice in climate predictability. J. Atmos. Sci. 39: 1456 1465 (1982). Cheng, B. On the Modelling of Sea Ice Thermodynamics and Air-Ice Coupling in the Bohai Sea and the Baltic Sea. PhD thesis, Finnish Institute of Marine Research, Helsinki, Finland (22). Haapala, J. and Leppäranta, M. Data Programme for Baltic Sea Ice Climate Modelling. Report Series in Geophysics, No 27, University of Helsinki, Finland (1993). Iqbal, M. Introduction to Solar Radiation. Academic Press Canada, Ontario (1983). Key, J.R., Silcox, R.A. and Stone, R.S. Evaluation of surface radiative flux parameterizations for use in sea ice model. J. Geophys. Res. 11(C2): 3839 3849 (1996). Launiainen, J. and Cheng, B. On the modelling of ice thermodynamics in natural water bodies. Cold Regions Science and Technology 27: 153 178 (1998). Rasmus, K., Ehn, J., Reinart, A., Granskog, M., Kärkäs, E., Leppäranta, M., Lindfors, A., Pelkonen, A. and Rasmus, S. Optical measurements of sea ice in the Gulf of Finland. Nordic Hydrology 33(2/3): 27 226 (22). Reed, R.K. On estimating insolation over the ocean. J. Phys. Oceanogr. 7: 482 485 (1977). Saloranta, T.M. Snow and Ice in Sea Ice Thermodynamic Modeling. Master s thesis, Department of Geophysics, University of Helsinki, Finland (1998). Shine, K. Parameterization of short wave flux over high albedo surfaces as a function of cloud thickness and surface albedo. Q. J. R. Meteorol. Soc. 11: 747 764 (1984). Zillman, J.W. Study of Some Aspects of the Radiation and Heat Budgets of the Southern Hemisphere Oceans. Meteorol. Stud. Rep. 26, Bur. of Meteorol., Dep. of Inter., Canberra, ACT (1972).