Parameterization of global and longwave incoming radiation for the Greenland Ice Sheet

GLOBALANDPLANETARY CHANGE ELSEVIER

Global and Planetary Change 9 (1994) 143-164

Parameterization of global and longwave incoming radiation for the Greenland Ice Sheet Thomas Konzelmann a, Roderik S.W. van de Wal b W o u t e r Greuell b, Richard Bintanja b, Edwin A.C. H e n n e k e n c, Ayako Abe-Ouchi a " Department of Geography, Swiss Federal Institute of Technology (ETH), Winterthurerstrasse 190, (21t-8057 Zurich, Switzerland b Institute for Marine and Atmospheric Research, Utrecht University, Princetonplein 5, NL-3584 CC Utrecht, The Netherlands c Faculty of Earth Sciences, Free University of Amsterdam, De Boelelaan 1085, NL-I081 HVAmsterdam, The Netherlands

(Received November 10, 1992; revised and accepted August 16, 1993)

Abstract

Meteorological measurements from various projects on West Greenland are used to parameterize the global and long-wave incoming radiation during summer months for the Greenland Ice Sheet. The parameterizations are based on the independent variables, air temperature, vapour pressure, surface albedo, cloud amount and elevation and can be used to improve results from numerical surface energy-balance models. The parameterization for global radiation contains all of the independent variables. The uncertainty for the various locations is 3% for clear skies and 6 to 7% on average for all cloud conditions. The longwave incoming radiation can be estimated from two equations. One is valid for instantaneous values and one for daily means. The uncertainty is 4% (instantaneous values) and 3% (daily means) for clear skies, and 6% (instantaneous values) and 5% (daily means) on average for all cloud conditions.

I. Introduction With the recognition of the importance of the Greenland Ice Sheet for a possible sea level rise as a consequence of the anticipated anthropogenic greenhouse warming (Warrick and Oerlemans, 1990), extensive scientific activities took place on the ice sheet in 1990 and 1991. The general aim of these studies was to investigate and to model mass- and energy-flux processes as a necessary prerequisite for the understanding of the ice-sheet climate. Simulating the response of the Greenland Ice Sheet to changing climatic conditions is attempted by thermomechanic ice-sheet models (Huybrechts et al., 1991; Abe-Ouchi et al., 1994).

The surface mass balance is a necessary boundary condition and until now it was modelled with a d e g r e e - d a y model (Reeh, 1989) or with a prescribed mass balance as a function of height (Abe-Ouchi et al., 1994), although in nature it is determined by the energy balance at the surface. In future, the ice-sheet model results can be improved by using surface energy-balance models, because they are more realistic. The success of this coupling will depend on the quality of the energy-balance models. Up to now only simple surface energy-balance models have existed for the entire ice sheet (Oerlemans, 1991; Van de Wal and Oerlemans, 1994). A more detailed model was developed by Greuell and Konzelmann (1994) but it was ap-

0921-8181/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0921-81 81(94)E0073-8

144

T. Konzelmann et al. / Global and Planetary Change 9 (1994) 143-164

plied to only one specific location. Parameterizations of the various processes described by these numerical surface energy-balance models can be derived from meteorological measurements at specific sites. The meteorological studies carried out in 1990 and 1991 offer the opportunity to improve the existing parameterization schemes. Once new parameterization schemes are developed, sensitivity studies can be performed to gain insight into the relative importance of relevant variables determining the radiative and turbulent fluxes. Above all simulations for different climatic conditions can be performed. The short- and long-wave radiative fluxes play an important role in the energy balance on the Greenland Ice Sheet. For a location close to the equilibrium line altitude (Camp IV; Fig. 1), Ambach (1963) shows that the energy gain in summer at the surface is mainly caused by the radiative fluxes because the sensible and latent heat flux almost cancel each other. Here, we present parameterizations for the global and longwave incoming radiation to be used in numerical surface energy-balance models for the Greenland Ice Sheet. The parameterizations contain the following independent variables: screen-level air temperature, screen-level vapour pressure, surface albedo, cloud amount and elevation. For evaluating the global radiation in numerical surface energy-balance models of the Greenland Ice Sheet, parameterizations derived from measurements in the Alps (e.g. Sauberer, 1955) have been used until now. For the development of the parameterization developed here, equations from the existing literature (Kasten, 1983) were taken for the clear-sky radiation. Measurements from several locations in West Greenland were used to optimize a parameterization describing the cloud transmission. Parameterizations for longwave incoming radiation have been proposed by Idso (1981) and Kimball et al. (1982), but for locations outside Greenland. The parameterization of the longwave incoming radiation is based on the measurements during the ETH experiments in 1990 and 1991. These measurements were compared with LOWTRAN7 (a numerical radiative band model)

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Fig. 1. Locations of meteorological measurements in 1990 and 1991 on the Greenland Ice Sheet with Summit (3230 m), ETH Camp (1155 m) and the GIMEx transect with GIMEx-IMAU (340-1028 m) at the left side and GIMEx (1520 m) at the right side. Measurements at Camp IV (1004 m) were carried out in 1959 and at Carrefour (1850 m) in 1967, respectively (Ambach, 1963, 1977 and Ambach and Markl, 1983).

calculations. The parameterization was tested by using an independent data set (Ambach, 1963, 1977; Ambach and Markl, 1983). Additionally, an

T. Konzelmann et al. / Global and Planetary Change 9 (1994) 143-164

expression containing cloud amount due to low clouds and cloud amount due to middle clouds as independent variables instead of total cloud amount is presented in Appendix B for instantaneous values.

2. Set up and instrumentation

Data obtained during the following expeditions were used for the present study: (a) E T H Camp, (b) Summit (GRIP), (c) GIMEx-IMAU and (d) GIMEx-FUA (Fig. 1). Relevant parts of the set up and instrumentation will be described below. These expeditions were all held during the summers 1990 and 1991. In addition, data from Camp IV (1959) and Carrefour (1967), as presented by Ambach (1963, 1977) and Ambach and Markl (1983), were used. 2.1. M e a s u r e m e n t s on G r e e n l a n d ETH Camp

The E T H Camp is located 69°34'N, 49°17'W at 1155 m a.s.1, near the average equilibrium line altitude. During the periods June 6 to September 1, 1990 and May 9 to August 30, 1991, meteorological measurements, including air temperature, relative humidity, wind speed, wind direction, radiative and turbulent fluxes, upper air sounding and synoptic observations were carried out. A detailed description of the E T H expeditions is given in Ohmura et al. (1991, 1992). Global radiation, diffuse sky radiation, shortwave reflected radiation and allwave sky radiation (diffuse sky radiation and longwave incoming radiation) were measured directly with Swissteco SS-25 pyranometers and a Swissteco ST-25 pyrradiometer. The longwave incoming radiation was then calculated as the difference between the allwave sky radiation and the diffuse sky radiation and compensated for by the emission loss of the instrument (~rTi4), where ~r is the StefanBoltzmann constant ( = 5.67 x 10 -8 W m -2 K -4) and T~ the temperature of the pyrradiometer in Kelvin. The signals of the radiometers were recorded every 15 seconds. This time interval was

145

chosen because the response time of the instruments is about 5 seconds and to avoid a statistical error due to the discrete sampling of a quantity displaying a large and fast variability. Every 30 minutes the average was computed. The maintenance conditions of the instruments were checked several times a day. The uncertainties of the pyranometers and the pyrradiometer are 2% and 2.5%, respectively. The first number is derived by absolute and relative calibrations and the second one is given by the manufacturer. The uncertainty of the longwave incoming radiation using the shading method is set at + 10 W m -2 according to an instrument intercomparison performed by De Luisi et al. (1993). Due to the fact that direct solar radiation is known the cosine error of the up facing pyranometers was corrected accordingly. For the locations mentioned below this correction could not be done (missing direct solar radiation), but there is only a small effect on daily mean global radiation because of low intensities at low solar elevations. Air temperature and relative humidity were measured at screen-level height (2 m) and the signals were recorded every 15 seconds, averaged over a 10 minutes period and stored on a data logger. In 1990, air temperature and relative humidity were measured with Aanderaa 2775 and Vaisala HMP l13Y sensors, respectively. The instruments were not ventilated, though shielded from radiation by an Aanderaa radiation shield. From the analysis of the data it was concluded that temperature and humidity data should be discarded if global radiation exceeds 200 W m-2 and wind speed is less than 2.5 m s- ~ at the same time (Ohmura et al., 1991). The uncertainty of the humidity sensor was estimated to be 3% up to 90% relative humidity and 5% above 90%. In 1991, the humidity sensor was replaced by a Vaisala H M P 35A. Temperature and humidity sensors were ventilated and radiation shielded. The accuracy for temperature is 0.2 K at 20°C and is less for values closer to 0°C due to instrument specification and calibrations made with a w a t e r / i c e mixture (0°C) in 1990 and 1991. The accuracy for humidity is 2% up to 90% relative humidity and 3% above 90% at 20°C with a temperature dependency of +0.04% R H / ° C .

T. Konzelmann et aL / Global and Planetary Change 9 (1994) 143 - 164

146

Radio sondes were launched once a day (00 UTC) in 1990 and twice a day (00 and 12 UTC) in 1991. The portable rawinsonde system Vaisala MW (Marwin) 12 was used. The radio sondes measured pressure, temperature and relative humidity up to altitudes of 25 kilometres. The uncertainty of the measurements of the radio sonde are described in Section 4.1. Cloud observations, including amount and type, were made seven times a day, by several persons during the two field seasons.

Summit (GRIP Camp) Summit (GRIP Camp) is located 72°35'N, 37°38'W at 3230 m a.s.1, in the accumulation area. During the period June 11 to June 27, 1991, measurements of air temperature, relative humidity, radiative fluxes and synoptic observations were carried out as a contribution to the Greenland Icecore Project (GRIP), a European Science Foundation programme with eight nations collaborating to drill through the central Greenland Ice Sheet. Global radiation and shortwave reflected radiation were measured with pyranometers of the Davos type (PD-4). The signals were recorded every 15 seconds and averaged for 30 minutes. The accuracy of the pyranometers given by the manufacturer is 2.5%. Measurements obtained when riming occurred on the radiometers were corrected afterwards. Air temperature and relative humidity were measured with Aanderaa 3145 and Aanderaa 2820, respectively, by an automatic weather station of the Danish Meteorological Institute. The

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instruments were not ventilated, though shielded from radiation. The uncertainties of unventilated temperature and humidity measurements are assumed to be equal to those derived at the E T H camp. Cloud observations (amount and type) were made three times a day, by one person.

GIMEx-IMA U The Institute for Marine and Atmospheric Research, Utrecht University, carried out a meteorological field e x p e r i m e n t in the S0ndre Str0mfjord area. During the periods July 18 to August 17, 1990, and June 10 to July 31, 1991, meteorological measurements, including air temperature, relative humidity, wind speed, wind direction, radiative fluxes and synoptic observations were carried out. Seven meteorological masts (in 1990 six) were erected along a line perpendicular to the ice edge, see Fig. 2. Site 9 was operated by the Free University of Amsterdam (FUA), see Section below. Masts on the ice sheet were standing freely on the surface. They consisted of a standard aluminium mast, with four long legs at the base, making an angle (10 °) with the surface. The height of the instruments above the surface is kept constant with this system in spite of an ablation of approximately 2 m ice near the ice margin during the measuring period. Masts were checked once a week and no adjustments were necessary during period of measurements. A telemetric data acquisition system was used to enable continuous measurements at the unmanned masts. Data were initially stored locally at the masts, and after some time they were sent in packets to the receiving station at the base camp.

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T. Konzelmann et al. /Global and Planetary Change 9 (1994) 143-164

A detailed description of the individual masts during the G I M E x expeditions is given by Bintanja et al. (1991) and by Boot et al. (1991). Global radiation and shortwave reflected radiation were measured simultaneously with Kipp CM14 pyranometers. The sample interval of the instruments was 2 minutes. This time interval was chosen for consistency with the other meteorological measurements. However, it should be noted that this relatively short sampling interval does not influence the daily mean radiative fluxes as was proved during the intercomparison of pyranometers (Section 2.2). No condensation on the instruments occurred because of the relatively high temperatures in the area during the field experiment (mean temperature at 2 m on site 4 equals 4.7°C). Furthermore, it is estimated that the tilt of the site is less than 2 ° over the entire period. This means that the tilt has a negligible effect on the daily means of the shortwave radiative fluxes (Mannstein, 1985). The accuracy of the up- and down facing pyranometers is 2%. Air temperature was measured with Aanderaa 2775 sensors and Rotronic YA-100 instruments. All instruments were ventilated and shielded from radiation. The sampling rate was 2 minutes. The accuracy for temperature (Rotronic YA-100) is 0.2°C in the range - 30 ° to + 130°C. The Rotronic YA-100 sensors were also used to measure the relative humidity. The accuracy of the relative humidity sensors is 2% up to 100% relative humidity. Cloud observations (amount and type) were only made in the base camp, seven times a day by several persons. GIMEx-FUA

During the period June 26 to July 25, 1991, intensive meteorological measurements, including air temperature, relative humidity, wind speed, w i n d direction, radiative and turbulent fluxes, and synoptic observations were carried out. The camp of G I M E x - F U A was located 67°02'N, 48°07'W at 1520 m a.s.l, at a distance of 90 km from the ice margin (site 9; Fig. 2). Global radiation and shortwave reflected radiation were measured with a KIPP CM7 albedometer consisting of two pyranometers which are selected on equal sensitivity (maximal discrepancy

147

0.5%). The accuracy of the up- and down-facing pyranometers is 2%. Samples were taken every 15 seconds. Every 30 minutes, averages and standard deviations were stored. Air t e m p e r a t u r e and relative humidity were measured with Rotronic YA-100 sensors as described in the Section above. The data handling was the same as for the radiation measurements. The instruments were not ventilated, though shielded from radiation. From the analysis of the data it was concluded that the air temperature had to be corrected according to an empirical formula which contains global radiation and wind speed as variables. Cloud observations (amount and type) were made at least four times a day, by one person. 2.2. Intercomparison o f pyranometers

To be able to compare the different data sets of shortwave radiative fluxes, an intercomparison of the pyranometers as described in section 2.1 was made in Cabauw (51°57'N, 4°55'E), the Netherlands, in M a r c h / A p r i l 1992. All instruments were installed above a pasture, using the same calibration coefficients, data acquisition system, cables and software as during the field experiment in Greenland. A Kipp & Zonen, CC10, solar integrator (analogue sensor) was used as reference instrument. Before the experiment this instrument was calibrated by the Royal Netherlands Meteorological Institute (KNMI). Table 1 lists the mean global radiation for the instruments used in Cabauw, during a period of 14 days. The observed relative deviation for the I M A U instruments (site 4-6) is considerably larger than for the other instruments. This is probably due to an error in the original calibration procedure. Of course, one can argue whether the results of such an experiment can be applied to recalibrate instruments used in another area during another period of the year. But we think it is justified because the results of the intercomparison are independent of the absolute value of the global radiation and because an identical set up was used in Greenland. The original global radiation measurements at

T. Konzelmann et al. /Global and Planetary Change 9 (1994) 143-164

148

Table 1 Results of an intercomparison experiment in Cabauw in M a r c h / A p r i l 1992. T h e m e a n global radiation is the average over a period of 14 days. The standard deviation of the relative deviation is calculated for daily m e a n values Site at which instrument was used in Greenland

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Camp IV and Carrefour (Ambach, 1963, 1977; Ambach and Markl, 1983) are published in the International Pyrheliometric Scale (IPS 1956). To enable a comparison of these data with the measurements in 1990 and 1991, the data were adapted to the World Radiometric Reference (WRR) with the ratio W R R / I P S 1956 = 1.022 (Fr6hlich and London, 1986).

3. Parameterization of the global radiation A parameterization of the global radiation on the Greenland Ice Sheet was developed containing screen-level temperature (Ta), screen-level

vapour pressure (ea), surface albedo (as), cloud amount (n) and elevation (h) as independent variables. Data from seven meteorological experiments were used, see Fig. 1. The main characteristics of the data sets are listed in Table 2. The parameterization consists of two parts, the first describing radiative transfer for clear skies, the second describing cloud transmission.

3.1. A simple radiative transfer model for clear skies There exists a wealth of radiation models with varying degree of accuracy and detail (Stephens, 1984). The purpose of this study is to provide a parameterization which can be used in energy balance models for the Greenland Ice Sheet. Therefore, we make no distinction between direct solar and diffuse radiation. The model has also no spectral resolution. The model is a variant of the Kasten model (Kasten, 1983) where the cloudless sky transfer is given by: Gcalc

S

- y exp(--/3~'Lmr)

(1)

where S is the radiation at the top of the atmosphere on a horizontal plane. The solar radiation at the top of the atmosphere can be calculated using the position of the sun and the variation of the solar constant in time (e.g. Walraven, 1978). Gcalc is the calculated global radiation at the surface, m r is the relative optical air mass, ~'L is the Linke turbidity factor and 3' and /3 are con-

Table 2 The characteristics of the seven data sets used in the parameterization of the global radiation. T h e topographical locations are presented in Fig. 1. Values for air temperature, vapour pressure, cloud amount, global radiation and surface albedo are mean values over the entire measuring period together with standard deviations of daily m e a n values Period

GIMEx-IMAU 4 Camp IV ETHg0 ETH91 GIMEx-FUA Carrefour Summit

1 0 / 6 - 3 1 / 7 91 2 6 / 5 - 8 / 8 59 6/6-1/990 11/5-27/891 2 / 7 - 2 8 / 7 91 1 6 / 5 - 2 7 / 7 67 1 1 / 6 - 2 7 / 6 91

Length (days) 52 75 88 109 27 70 17

Elevation (masl)

Air temperature (°C)

Vapour pressure (Pa)

Cloud amount (%)

Global radiation ( W / m 2)

Albedo

340 1013 1155 1155 1520 1849 3230

4.7 + 1.2 0.2 _+ 2.3 -0.6+2.0 -2.4-+4.3 0.1 -+ 1.0 - 6.7 -+ 3.7 - 13.4 + 3.7

590 + 55 515 -+ 90 402-+ 40 452-+128 505 -+ 55 330 -+ 105 213 -+ 63

46 -+ 32 55 + 36 51-+32 60+31 50 -+ 32 48 _+ 34 65 -+ 31

261 + 73 286 + 68 284-+91 296-+75 319 -+ 53 349 -+ 41 357 -+ 30

55 ± 2 57 + 15 72-+ 8 80-+ 7 71 -+ 7 82 _+ 4 91 _+ 3

(%)

T. Konzelmann et aL / Global and Planetary Change 9 (1994) 143-164

stants having the values of 0.84 and 0.027, respectively, based on analysis of G e r m a n data. The turbidity factor represents radiative transfer associated with scattering and absorption by air molecules, aerosols, ozone, and water vapour. Note that the transmission coefficient for clouds is not included in the turbidity factor. A detailed description of the parameterization of the turbidity factor is presented in Appendix A. Here, it is sufficient to know that the input parameters are air temperature, vapour pressure, zenith angle and elevation. Although this model is used here for the calculation of daily-mean values of the transmission, it is also capable to calculate hourly values of the transmission. Multiple reflection is considered because the model is applied to the Greenland Ice Sheet, where considerable variation in albedo in space and time occurs (Van de Wal and Oerlemans, 1994). As will be demonstrated later on, high albedos introduce a significant increase in the global radiation compared to areas with low albedo. Therefore, the surface albedo is added as input parameter. The multiple reflection term is written as:

For simplicity, the albedo of the air (oqi r) is taken to be constant in time and space (0.075), representing a clean atmosphere (Iqbal, 1983). The surface albedo equals the daily mean measured albedo at the specific site for which the radiation is calculated. To test the model all clear sky days were selected from the seven data sets. Measurements were also taken from the G I M E x - I M A U experiment at site 5 and site 6, where no cloud observation were made. The complete group of 29 days covers a period from May 27 until August 16 and a height interval from 340 to 3230 m a.s.l. Fig. 3 presents calculated as a function of measured global radiation. The m e a n value of the measured divided by the calculated radiation for these 29 days is 1.015 + 0.032 which, in view of the simplicity of the model, is satisfying. It may also be noted that no significant shortcomings of the model were observed when the calculated divided

149

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by the measured radiation was plotted as a function of daily mean zenith angle. However, this might be due to the limited time interval covered (81 days) or the limited geographical distribution of the sites (67°N to 72°N), together resulting in a daily mean zenith angle ranging from 66 ° to 76 ° . To test the model sensitivity, a reference calculation was performed. The transmission was calculated for G I M E x - I M A U site 4 (h = 340 m a.s.l., 67.05°N) at June 15 (daily mean vapour pressure equal to 516 Pa and daily mean albedo equal to 0.59 and n = 0). The reference experiment was used to normalize the calculated variation in transmission as a function of vapour pressure, surface albedo and elevation. The results of this sensitivity analysis are presented in Fig. 4. The range in transmission as a result of the albedo variations from 0.1 to 0.9 is approximately 6.5% which is due to variations in the multiple reflection term. The transmission increases with approximately 4% for an increase in height from sea level to 3500 m a.s.l, due to the decreasing relative optical air mass. Increasing the vapour pressure from 300 to 700 Pa yields a decrease of approximately 1% in the transmission due to increased absorption by water vapour. It may be noted that these model sensitivity experiments are only valid for clear-sky situations. This is particularly true for the sensitivity to albedo variations. Clouds reflect much more shortwave radiation than clear skies, leading to a considerable

7". Konzelmann et al. / Global and Planetary Change 9 (1994) 143-164

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increase of the multiple reflection term and therefore to an increase in the sensitivity to albedo variations with cloud amount. However, a thorough description of this subject is outside the scope of this paper. 3.2. T r a n s m i s s i o n by c l o u d s

The measured global radiation can be divided by the global radiation for clear-sky conditions as calculated with the model described in the previous section. This results in the transmission due

to the presence of clouds. Fig. 5 present the cloud transmission as a function of the cloud amount for the various data sets available. In the lower left corner the correlation coefficient ( r ) and the residual standard deviation for a second order regression equation ((r) are shown. The residual standard deviation varies between 3 and 7%. Clearly the scatter of the data around the regression equations increases with cloud amount. To test whether the residual standard deviation could be reduced, cloud types were introduced as variables in the regression analysis. A subdivision into low, middle and high clouds for the ETH-91 data set revealed a residual standard deviation of 6.1% after multiple linear regression whereas the non-linear regression in Fig. 5 with total cloud amount as the only independent variable revealed a residual standard deviation of 5.6%. This means that the introduction of cloud types does not improve the statistical results. Because not all data sets give information concerning cloud type and because the introduction of cloud type does not improve the statistical result, total cloud amount is used as the only variable for the cloud transmission. Fig. 6 presents the regression equations for the different sites. Obviously, the largest decrease in transmission with increasing cloud amount is found at the lowest elevation (GIMEx-IMAU). The smallest decrease in transmission with increasing cloud amount can be observed at the higher elevations (Carrefour and Summit). This means that, on average, the optical depth of the clouds decreases with elevation. The large variation of up to 50% for constant cloud amount also shows that a more detailed radiative transfer model for clear skies is useless since the sensitivity of the model for variations in albedo, vapour pressure and elevation is considerably smaller (5%) as presented in Fig. 4. To combine the dependence of the cloud transmission on cloud amount and elevation the following expression was chosen: tel = 1 - a n 2 e x p ( - b h )

(3)

where rc~ is the cloud transmission, n cloud amount (n = 1 for a completely overcast sky), h elevation in m, and a and b are constants. This

T. Konzelmann et aL /Global and Planetary Change 9 (1994) 143-164

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Xx Xx

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~=o.o3

o=0.06 L ~ , I ~ L ~ I L ~ L I ~ ~ J I ~ h 0.2

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0.8

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4 i

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t

i

I

L

0.4

J

h

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1

cloud tunount p

i

,

,

i

'

'

r

I

r

,

,

I

'

'

'

I

'

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X X

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0.8 ~a

0.6 0.4 Sumnlit 0.2

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0.4

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0.8

cloud alnoul]t F i g . 5. M e a s u r e d

daily mean

(Gcalc) for the various

data

global

radiation

sets as a function

(G)

divided

of cloud

by the calculated

amount.

daily mean

global

radiation

under

clear-sky

conditions

152

T. Konzelmann et al. / Global and Planetary Change 9 (1994) 143-164

lw~

, ~_~.~,,_r-'''

I ' ' ' I '

---~ -- Camp IV - -o - ETH Camp 1990 -x - ETHcamp 1991 + Gimex-FUA - - ~ Canefour • - Summit

0.4 0.2

' 4

~a..

~

-

i

0 t)

0.2

i

]_i

~

0.8

1).4 (1.6 cloud amount

i

1 1

Fig. 6. The regression equations as presented in Fig. 5 for the various locations. Note the increasing transmission for increasing elevation.

m e a n s that the t r a n s m i s s i o n is 1 if the cloud a m o u n t is zero, i n d e p e n d e n t l y of h. F u r t h e r m o r e , the t r a n s m i s s i o n a p p r o a c h e s 1 for h increasing to infinity. A n o p t i m a l fit was o b t a i n e d by setting a = 0.78 a n d b = 0.00085. T h e residual s t a n d a r d deviation for the c o m p l e t e data set (seven sites, t o g e t h e r 436 days) is t h e n 6.5% which is only

slightly higher t h a n the residual s t a n d a r d deviation for the regression e q u a t i o n s p r e s e n t e d in Fig. 5 for the different sites. This m e a n s that the scatter of the m e a s u r e m e n t s a r o u n d the fit is d o m i n a t e d by the variations in optical thickness of the clouds for c o n s t a n t cloud a m o u n t . T h e p a r a m e t c r i z a t i o n resulting from Eq. 3 with a = 0.78 a n d b -- 0.00085 is p r e s e n t e d in Fig. 7 for a height interval from 0 to 3500 m a.s.1, a n d cloud a m o u n t r a n g i n g from 0 to 1. T h e data o n which the p a r a m e t e r i z a t i o n is b a s e d cover the r a n g e 340 to 3230 m a.s.1, as can be seen in T a b l e 2. T h e extremely high t r a n s m i s s i o n for high cloud a m o u n t s at high elevations is p r o b a b l y an artefact resulting from the limited n u m b e r of m e a s u r e m e n t s in the S u m m i t data set. This p a r a m e t e r i z a t i o n can be c o m p a r e d with the p a r a m e t e r i z a t i o n p r e s e n t e d by S a u b e r e r (1955) which reads: ~- = 1.0 - (0.41 - 0 . 0 0 0 0 6 5 h ) n - 0.37n 2

(4)

This p a r a m e t e r i z a t i o n is b a s e d o n m e a s u r e m e n t s in the Alps b u t is used in some of the existing e n e r g y - b a l a n c e models for the G r e e n l a n d Ice Sheet ( O e r l e m a n s , 1991, a n d V a n de W a l a n d

0oo 200 5°0

t

L

1000

--

5O0

i 0.00

0.10

0.20

0..30

0.40 0.50 0.60 cloud omoun(

0.70

0.80

0.90

.00

Fig. 7. The cloud transmission (Eq. 3) as a function of cloud amount (n) and elevation (h) with the optimal values of 0.78 for a and 0.00085 for b.

T. Konzelmann et al. / Global and Planetary Change 9 (1994) 143-164

Oerlemans, 1994). Fig. 8 shows a contour diagram with the differences between Eqs.3 and 4 as a function of cloud amount and height. The figure shows that the differences between both parameterizations are considerable, especially for higher cloud amounts. It can be observed in Fig. 8 that, at similar elevation, the transmission is larger in Greenland than in the/kips. The rectangle in Fig. 8 indicates a typical ablation zone of the Greenland Ice Sheet, with the elevation ranging between 200 and 800 m a.s.1., and a mean cloud amount of approximately 0.6. In this zone the transmission based on the Greenland data (Eq. 3) is typically 18% higher than the transmission based on the data from the Alps (Eq. 4).

4. Parameterization of the long-wave incoming radiation A parameterization of the long-wave incoming radiation ( L $) on the Greenland Ice Sheet was developed, containing screen-level temperature (Ta), screen-level vapour pressure (e a) and cloud amount (n) as independent variables. Many pa-

/

3500

3000

2500

-

2000

-

1500

--

1ooo

-

500

-

I

I

153

rameterizations of this kind, but for other locations, have been proposed in the literature, see, for example, Idso (1981) and Kimball et al. (1982). Generally, the equations take the form: (5)

L $ = ecsO-T4F(n)

where ecs is full-spectrum, clear-sky emittance and the "cloud factor" F ( n ) describes the increase in radiation due to clouds. The clear-sky emittance is an empirically determined function of Ta a n d / o r e a and the "cloud factor" depends on cloud amount only. Thus, in this equation L $ is a function of temperature and humidity at screen level only, although, in principle, the entire vertical profiles of temperature and humidity affect the surface flux. Nevertheless, expressions of this kind work reasonably well, because most of the radiation received at the surface is emitted in the lowest atmospheric layers (Geiger, 1966; Keding, 1989). The effect of the shape of the profiles is then somehow represented by the values of the constants in the expression for ecs (see, for instance, Eq. 6). Because, on average, the shape of the profiles over the Greenland Ice Sheet with its inversion is different from the

Io

q o E

o

0.00

J8 0.10

0.20

0.,50

0.40 0.50 0.60 cloud omount

0.70

0.80

0.90

.00

Fig. 8. A contour diagram showing the difference in the cloud transmission derived in this paper (Eq. 3) and in Sauberer (1955). The differences are expressed as a function of cloud a m o u n t (n) and elevation (h).

154

T. Konzelmann et al. /Global and Planetary Change 9 (1994) 143-164

shape elsewhere, specific values for the constants had to be derived. This was done exclusively with the measurements from the E T H camp, while the measurements carried out by Ambach (1963, 1977) and Ambach and Markl (1983) were used as an independent data set in order to test the parameterizations. 4.1. Comparison o f the measurements with numerical calculations

As a kind of quality control, measurements from the E T H camp were compared with calculations made with LoWrRAN7, a numerical radiative band model (Kneizys et al., 1988). With LOWT ~ N 7 the radiation received from a single zenith angle may be calculated. In the case of infrared radiation, temperature, pressure and the concentration of greenhouse gases must be prescribed along the atmospheric path in the given direction. For this purpose, upper air sounding profiles can be used. LOWrl~AN7 has a maximum spectral resolution of 20 cm-1 and contains band-model parameters for twelve radiatively active gases, among which H 2 0 , CO2, 03, N 2 0 and CH 4. Continuum absorption by water vapour is taken into account and the effect of aerosols and clouds can be computed. From the upper air sounding profiles of pressure, temperature and humidity, 32 levels were selected with a resolution of 10 m near the surface changing to 2 km at the maximum height of 11 km above the surface. Sensitivity experiments showed that such a high resolution near the surface is necessary because most of the longwave radiation received at the surface is emitted in the lowest atmospheric layers. Atmospheric concentrations of greenhouse gases other than H 2 0 were specified according to Watson et al. (1990). As in the case of global radiation (Section 3), the atmosphere was assumed to be free of aerosols. This is justified by the virtually unlimited visibility on the ice sheet, unless clouds obscure the horizon. For computational speed, the calculations made during this study were performed with frequency increments of 100 cm-1. Sensitivity experiments showed that, as compared to taking smaller frequency increments, this choice had a negligible

effect. Radiances were computed for 10 zenith angles (0, 10, 2 0 , . . . , 80 and 89.9 degrees) and integration over the hemisphere was accomplished assuming azimuthal symmetry. No computations were done for partly overcast skies because in those cases it is difficult to estimate cloud amount, and longwave incoming radiation and cloud amount may vary quickly. Hence, only clear skies and skies that were completely overcast by low clouds (mostly stratus) were considered. In the latter case, cloud-base elevation was estimated from the sounding profiles of relative humidity and, following Kimball et al. (1982), the cloud base was assumed to radiate as a black body with the temperature of the cloud base. Extensive sensitivity experiments were performed in order to estimate the uncertainty in the computed longwave incoming radiation. Dominant contributions to the uncertainty for clear skies arise from: - - t h e uncertainty in the upper air sounding of relative humidity ( + 5 % ) : +2.5 W m -2, - - t h e uncertainty in the upper air sounding of temperature ( + 0.5°C): + 2 W m - 2, - - t h e assumption of an aerosol-free atmosphere. The magnitude of the extra radiation due to aerosols can be estimated with LOWTRAN7. The user can specify the type of profile, for instance rural, maritime or urban, and the visibility. Setting the visibility equal to 50 km, the maritime profile yielded the greatest increase of the flux: + 1.5 W m -2. Because visibility usually seemed to be greater than 50 kin, the error should be in the range between 0 and 1.5 W m-2, - - a n d the uncertainties in the radiative-transfer calculation itself, e.g. uncertainties in band parameters derived from spectroscopic data. Many radiation codes, including line-by-line, narrow-band and wide-band models, were compared by Ellingson et al. (1991). LOWTX~AN7(a narrowband model) was not considered by these authors, but they list some of their test profiles and results obtained with them. This offered the opportunity to test LOWrRANT. The A F G L reference mid-latitude summer profile was used as test profile. The Lowrr~AN7 calculation yielded a long-wave incoming radiation of 339 W m -2. This value was

T. Konzelmann et al. / Global and Planetary Change 9 (1994) 143-164

band parameters have a negligible influence. The accuracy of the cloud-base temperature is determined by the accuracy of the radio sonde temperature measurement (+0.5°C, giving + 2 W m -2) and the accuracy of the estimate of the cloud-base elevation. Cloud-base elevation was estimated from upper air sounding profiles of relative humidity. Two criteria were used and differences in cloud-base elevation could be up to 300 m. However, due to the generally small lapse rate near the cloud base, differences in longwave incoming radiation were small (1 W m -2, on average). Therefore, the total uncertainty for completely overcast skies is estimated to be + 3 W m-2. The LOWTRAN7 calculations are instantaneous values. They are compared with half-hourly means of the measurements. In addition to the uncertainties in the measurements and calculations discussed above, this results in some random scatter, since the longwave incoming radiation may vary by a few W m-2 during half an hour. Differences between measurements and calculations are depicted in Fig. 9. The most obvious characteristic is a clear separation between clear-sky and overcast results. Except for one case, measurements are always greater than calculations for clear-sky conditions (on average by 10 _+ 4 W m -z) and always smaller for completely overcast skies (on average by - 8 _ 5 W m--Z). It was tested whether the difference between measurements and calculations was related to global radiation, longwave incoming radiation itself, or any other meteoro-

compared to the result (342 W m -2) obtained with the Fels-Schwarzkopf line-by-line calculation. It should be noted that line-by-line models are the most accurate radiation codes since they have the greatest spectral resolution. As other results of surface fluxes are not given by Ellingson et al. (1991), this is the only comparison made. The difference might be greater for other profiles but it is assumed that the uncertainty is not greater than 2%, or 4 W m -2, for typical clear-sky fluxes of 200-240 W m -2. Note, however, that line-by-line model results cannot be used as an absolute reference, due to uncertainties about line shape and absorption continua (Ellingson et al., 1991). Measurements of the longwave incoming flux that are more accurate than presently possible are required in order to validate line-by-line models. Assuming that these uncertainties are independent, the total uncertainty in the computed longwave incoming radiation amounts to +_6 W m -2 for clear skies. However, in view of the unknown accuracy of line-by-line model calculations, this should be considered as the lower limit. When the sky is completely overcast by low clouds, the uncertainty in the calculated longwave incoming radiation is determined mostly by the uncertainty in the cloud-base temperature. Uncertainties in conditions in the atmospheric layer between cloud and surface have a negligible influence. This also means that uncertainties in

\ 3:

5ur~ue r 1991

ETH Camp, 1155 m Summer 199D

%

oo o 2O

20

t" "4

o

clear sky

A

overcast

oo 0 00

'

5

%°

O0

o°2g o

~

OO

OO O O

0

O" o

o

155

o

~o

u

O

O

&

u i

& &

tn

A

A

©

z -20

..............

17.6

I ..............

2.7

~..............

17,7

~..............

1.8

i .........

15.8

-20

..............

13.5

, ..............

28.5

i ..............

12.5

I ..............

27.5

I ..............

12.7

i ..............

27.7

i ~ .......

11.8

Fig. 9. Measured values of longwave incoming radiation minus values calculated with LOWTRAN7for 1990 (June 17 to August 28, 45 samples) and 1991 (May 13 to August 22, 98 samples).

T. Konzelmann et al. / Global and Planetary Change 9 (1994) 143-164

156

logical element, in order to possibly obtain a clue for explaining these characteristics, but no clear correlation was found.

.8

rO J

!

.7

4.2. The clear-sky emittance

An overview of parameterizations of the clearsky emittance is given by Idso (1981). These parameterizations contain Ta, e a o r ea/T a as independent variable. In order to determine which type of expression is the most appropriate one, LOWTRAN7 is used again. First, a kind of "standard clear-sky atmosphere" was computed in terms of temperature, humidity and pressure by averaging all 127 upper air sounding profiles obtained during clear-sky conditions at the E T H camp in 1990 and 1991. Then, test profiles were produced by changing the temperature at all levels by the same amount (giving 12 temperature profiles) and by multiplying the relative humidity at all levels by the same factor (giving 7 humidity profiles, one representing a completely dry atmosphere). Next, all possible combinations of temperature and humidity profiles (84, in total) were made. For each of them the longwave incoming radiation was computed with LOWTRAN7. Then, the calculated clear-sky emittance was plotted against Ta (Fig. 10) and ea/T a (Fig. 11). Values of the clear-sky emittance for completely dry atmospheres (12 different temperature profiles) are not shown in the figures. They ranged between 0.22 and 0.24. At this stage it should be noted that the use of e a (expressed in Pa) as independent variable yielded qualitatively the same results as the use of e a / T a. This is due to the fact that in the ratio ea/T a, Z~ is expressed in Kelvin so that its range is small compared to its absolute value. Hence, Ta is almost a constant so that ea/T ~ is almost proportional to ea. Obviously, e~ can quite well be described as a function of ea/T ~ (or e~) alone. Such an equation was proposed by Brutsaert (1975):

e,, ) 1/7 eCs = b ' ( - ~

(6)

in ) l. r~ (9

×x

! ! x x

QJ

The type of the equation

× × ~ × ~ x ×

(D

!

.6

×

x x

× xx .5

Perturbed

profiles

for

ETH

Camp

n=72

× I -40

I -30

I -2D

I -10

Temperature

I 0

I 10

20

in °C

Fig. 10. Clear-sky emittance (ecs = L , l , / o T 4 ) as calculated with LOWTRAN7 as a function of the screen-level temperature. The input for LOWTRAN7 was given by test profiles derived from the clear-sky m e a n profiles of temperature and humidity. Values of the clear-sky emittance for completely dry atmospheres with different screen-level temperatures range between 0.22 and 0.24 and are not shown here.

where b' is a constant. Brutsaert derived this equation analytically by integrating Schwarzschild's transfer equation for simple atmospheric profiles of temperature and vapour pressure, and

.8

r0

0J

in i

.G

rD (9

Camp n=72 .5

Vapour

I

I

1

I

I

1

2

3

4

5

pressure

/

Lemperature

in Pa/K

Fig. 11. Clear-sky emittance (Ecs = L $ / o - Z 4) as calculated with LOWrRAN7 as a function of the ratio of screen-level vapour pressure and screen-level temperature. The input for L o w r R a s 7 was given by test profiles derived from the clear-sky m e a n profiles of temperature and humidity. Values of the clear-sky e m i n a n c e for completely dry atmospheres (e a / Ta = 0) with different screen-level temperatures range between 0.22 and 0.24 and are not shown here. The curve represents the optimal fit of Eq. 7 to the points shown in the figure.

T. Konzelmann et aL / Global and Planetary Change 9 (1994) 143-164

prescribing a simple dependency of the emissivity on the amount of water vapour. A limitation of this expression is that the wrong asymptotic behaviour is predicted, namely Ecs(ea = 0 ) = 0, due to the neglect of greenhouse gases other than water vapour. In order to take the effect of greenhouse gases other than water vapour into account, the equation was somewhat modified here:

157

0.85 o • •

0.75

¢.~

>~

• ,"

•

"

'

"

~'e * . t

u.TM- "

" " ,

2

•

#

w;

• Nml~,•

"

~

~

I °e

0.65

2 ,"

612 samples

/

0.55 I

,

19~X) 1991

0.45 0.0

where 0.23 is clear-sky emittance of a completely dry atmosphere as calculated by LOWrRAN7, and b and m are constants. Absorption bands of water vapour and other gases overlap. Therefore, Ecs increases more slowly with e a than if greenhouse gases other than water vapour are neglected. Hence, m is expected to be greater or equal to 7. An optimal fit (see Fig. 11) was obtained by setting b = 0.443 and m = 8 (only integer values were allowed). Indeed, m appears to be greater than 7. The values of the coefficients Having established the type of the expression for the clear-sky emittance (Eq. 7), an optimal fit to the available data was made. These data consisted of the measurements from the E T H camp for both 1990 and 1991. The data set was limited by the number of cloud observations, which were usually made seven times per day. Total cloud amounts, which are instantaneous values, were associated with hourly means, centred around the cloud observation, of longwave incoming radiation, air temperature and vapour pressure. The total number of samples was equal to 1239. For the study of the clear-sky emittance, samples were selected whenever cloud amount due to low and middle clouds was less or equal to one eighth. High clouds were neglected because sensitivity experiments with LOWTRAN7 showed that they have a negligible effect on longwave incoming radiation at the surface. For the selected data set of 612 samples, E c s = L $ / ( r T 4 was computed. The resulting values are plotted against ea/T~, in Fig. 12. For fitting Eq. 7, m was set

0.5 1.0 1.5 2,0 Vapour pressure / temperature in P'MK

2.5

Fig. 12. Clear-sky emittance (ecs = L $ / ~ r T 4) as calculated from measured half-hourly values of the longwave incoming radiation as a function of the ratio of screen-level vapour pressure and screen-level temperature. The curve represents the parameterization of the clear-sky emittance optimized by m e a n s of these data (Eq. 10 with cloud amount equal to 0). Broken lines represent an uncertainty of 10 W / m 2, assuming a relative humidity of 70%.

equal to 8. A minimum standard deviation of the residuals (9 W m -2, approx. 4%) was found for b = 0.484 and the corresponding curve is shown in the figure. For daily means (51 samples) a minimum standard deviation of the residuals (7 W m -z, approx. 3%) was found for b = 0.483. Apparently (Fig. 12), Eq. 7 is not confirmed by the data, which only justify a clear-sky emittance that is independent of e a / T a. Nevertheless, Eq. 7 was preferred above a constant clear-sky emittance because it is physically based (see Brutsaert, 1975, and the short description of LOWTRAN7 in Section 4.1). Hence, Eq. 7 is more likely to yield correct results whenever it is used for values of e a / T a outside the range covered by the data set used here and when sensitivity studies are performed. The large discrepancy between the data and Eq. 7 for small e a / T a might be due to the measurements. The instruments were calibrated in the field in a down-facing position above a melting surface. Therefore, measurements performed around 0°C (right half of the figure) may be expected to be more precise than measurements

T. Konzelmann et al. /Global and Planetary Change 9 (1994) 143-164

158

350

performed at much lower temperatures (left half of the figure).

I

I

4.3. The cloud factor

•,

dL~

275

The type of the equation A common way (see, for instance, Kimball et al., 1982) to parameterize the "cloud factor" is F ( n ) = 1 q-bc nm~

m

.=.

I

I

w I

m~m

,-3

(8)

where bc and m~ are coefficients depending on mean cloud characteristics. However, this parameterization yields an equation for the longwave incoming radiation that is physically unsatisfactory for large cloud amounts. For skies that are completely overcast by low clouds, L $ is primarily determined by the temperature of the cloud base while conditions in the atmospheric layer between cloud and surface are less important. Hence, for completely overcast skies the parameterization of L $ should not contain the clear-sky emittance. This condition is satisfied by the following equation which describes the emittance as the weighted mean of the clear-sky emittance (given in Eq. 7) and the emittance of a completely overcast sky (eoc): L $ = [,cs(1 - n p) + EocnP]orT4

(9)

whereby the coefficients eo~ and p are determined by mean cloud characteristics.

The values of the coefficients Next, the data were used to determine optimal values for eoc and p. Using the entire data set of instantaneous cloud observations and hourly mean values of longwave incoming radiation, air temperature and vapour pressure, the following values were found: eoc = 0.952 and p - - 4 (only integer values of p were allowed), with a standard deviation of the residuals of 16 W m -2 (approx. 6%), see Fig. 13. The total equation for instantaneous values thus reads:

,,,i

X ( 1 -- n 4) + 0 . 9 5 2 n 4 [ o ' T 4

J

(10)

200

~1~N

t

•

ETH Camp, 1155 m 1239 samples

•

•

1990 1991 1:1 line

•

- 125

I

I

L

125

,

k

200

i 275

350

Measured L$ in W/m2 Fig. 13. Longwave incoming radiation as calculated with Eq. 10 against measured longwave incoming radiation. Each cross represents one cloud observation and hourly means (around the moment of the cloud observation) of longwave incoming radiation, air temperature and vapour pressure.

The high power ( p = 4) reflects a characteristic of the cloud climatology of the E T H camp. In most cases low cloud amounts were caused by high clouds while high cloud amounts were caused by low clouds (stratus and stratocumulus). Due to this non-linearity, the expression changes if daily means of the variables are used: eo~ = 0.963 and p = 3, with a standard deviation of the residuals of 12 W m -2 (approx. 5%), see Fig. 14. Hence, the total equation for daily means reads:

, q

X ( 1 -- n 3) +

0.963n31trT.4

(11)

An expression containing cloud amount due to low clouds and cloud amount due to middle clouds as independent variables instead of total cloud amount is presented in Appendix B for instantaneous values.

T. Konzelmann et aL / Global and Planetary Change 9 (1994) 143-164

159

350

4.4. Test with an independent data set

13(, daily means

Finally, the expression for daily means (Eq. 11) was tested with the measurements made at C a m p IV (Ambach, 1963, 1977) and Carrefour (Ambach and Markl, 1983). Fig. 1 shows where these sites were located. At both sites the short- and longwave radiative fluxes were determined with Moll-Gorczynski p y r a n o m e t e r s and Schulze pyrradiometers. As at the E T H camp, the components of the longwave radiative fluxes were calculated as the differences of the allwave and the shortwave fluxes, but, unlike at the E T H camp, Ambach did not use shading rings or discs. Since Ambach used a value for Stefan-Boltzmann's constant that was 1.25% greater than the currently accepted value ( = 5 . 6 7 × 10 -8 W m -2 K - a ) , his measurements were divided by a factor 1.0125. Calculated daily mean values obtained with Eq. 11 are compared with measured values in Fig. 15. On average, measured values are 0.4 W m -2 (or 0.16%) greater than calculated values, with a standard deviation of 14 W m -2 (or 6%). The mean difference is negligible. Apparently,

o x - '~

Camp IV, 1004 m Carrefour, 1850 m 1:1 line

/ ~9~-o o o°ff¢"~ ~ Oo~°.~x~ ~ _ ^

275

'

Oo

__-) X

x :-'

200

x

125

125

2(X)

275

350

Measured L,[, in W / m 2 Fig. 15. Measured daily mean values of the longwave incoming radiation against values calculated with Eq. 11 for C a m p IV and Carrefour.

the data from Camp IV and Carrefour confirm the parameterization.

5. Discussion and conclusions 350

'

'

I

'

'

J

ETH Camp, 1155 m 177 daily means o . x - -

275

1990 1991 1:1 line

r

/ , /

o A

O 0 ~ "'O xx _ v ~ t ~ x x

.=. ,.d

¢9

200

/

125

x

~ 125

,

I 200

,

I 275

, 350

Measm~edL$ in W/m2 Fig. 14. Longwave incoming radiation as calculated with Eq. 11 against measured longwave incoming radiation for daily means.

A simple radiative transfer model (Section 3.1) is presented which in combination with a parameterization for the cloud transmission (Section 3.2) can be used to estimate the global radiation at the surface of the Greenland Ice Sheet as a function of screen-level vapour pressure, screenlevel temperature, surface albedo, cloud amount and elevation. The cloud transmission increases with height. The reason probably is the gradual change in cloud type and cloud thickness. Above the tundra convection forms cumulus clouds whereas no convection occurs higher on the ice sheet where cirrus clouds dominate. The uncertainty in the computed global radiation is remarkably low, only 3% for clear skies. The uncertainty is somewhat larger ( 6 - 7 % ) on average for all cloud conditions. It is important to realize that the parameterization based on measurements in Greenland (Eq. 3) yields a higher transmission for clouds compared to the parame-

160

T. Konzelmann et al. /Global and Planetary Change 9 (1994) 143-164

terization based on measurements in the Alps (Eq. 4). The difference is due to a smaller optical depth of clouds in Greenland than in the Alps. For energy-balance models the higher transmission means an increase of the shortwave radiation fluxes compared to the turbulent heat flux, yielding a lower sensitivity of energy-balance models to temperature variations. Two equations are presented from which longwave incoming radiation at the surface of the Greenland Ice Sheet can be estimated as a function of screen-level temperature, screen-level vapour pressure and cloud amount. One is valid for instantaneous values (Eq. 10) and one for daily means (Eq. 11). A modified version of Brutsaert's equation (Eq. 6) appeared to be the most appropriate type of the expression for the clearsky emittance. Individual values computed with Eqs. 10 (and 11) have an uncertainty of approx. 4% (and 3%) for clear skies, but the uncertainty increases to 6% (and 5%) on average for all cloud conditions. Hence, both for global and longwave incoming radiation the scatter increases with cloud amount. This is caused by several factors. Firstly, the same cloud amount may be due to different types of clouds, which have different effects on the radiative fluxes. Secondly, cloud observations are subjective. Different observers estimate cloud amount differently under the same conditions. Finally, the number of cloud observations is rather limited (3-7 per day), so that the calculated daily mean cloud amount can have a large error. Upper air sounding profiles measured during clear-sky conditions or when the sky was completely overcast with low clouds were used for the calculation of the longwave incoming radiation with LOWTRANT, a numerical radiative band model. Sensitivity studies show that the uncertainty in the calculations is _+6 W m -2 for clear skies and + 3 W m -z for completely overcast skies. Note that the uncertainty in the clear-sky calculations cannot be estimated conclusively as long as the accuracy of line-by-line model calculations is unknown. The uncertainty in the measurements amounts to _+10 W m -2. In fact, it increases with the amount of diffuse sky radiation.

Measurements and calculations are compared in Fig. 9. Measurements are always greater than calculations for clear-sky conditions (on average by 10 + 4 W m -2) and always smaller for completely overcast skies (on average by - 8 + 5 W m-2). In view of the uncertainties in the measurements and the calculations, these discrepancies are acceptable. No explanation was found for the fact that the difference between measurements and calculations depends on cloud amount. A comparison between measurements and calculations as performed here seems to be useful. However, calculations cannot replace measurements because they are restricted to those moments when upper air soundings are made. Moreover, calculations become less accurate for partly overcast skies or when it is difficult to estimate the cloud-base elevation. Energy-balance calculations for the Greenland Ice Sheet can be significantly improved by using the global and long-wave radiation parameterization schemes as proposed in this paper. Data used for the parameterization of global radiation were measured at many locations, covering a considerable part of West Greenland, whereas the parameterization of longwave incoming radiation was developed with data from the E T H camp and successfully validated with data from Camp IV and Carrefour (Fig. 15). Hence, both parameterizations are based on data from West Greenland only. As a result the uncertainty of calculated radiative fluxes will be greater on application of the parameterizations to other parts of the ice sheet due to, for instance, different cloud characteristics. Nevertheless, they are certainly more realistic than the parameterizations based on measurements outside Greenland. Another drawback of the data sets used here is that they were all collected during the summer season only. High-quality measurements in other parts of the ice sheet and other seasons, as well as satellite measurements, could certainly provide useful new data for confirmation or improvement of the proposed parameterizations. In most of the parameterizations proposed here, clouds are described by total cloud amount only because observations of other cloud characteristics were absent in many of the data sets

T. Konzelmann et aL / Global and Planetary Change 9 (1994) 143-164

used. In Appendix B it is shown that an equation containing cloud amount due to low clouds and cloud amount due to middle clouds as independent variables provides better predictions of the longwave incoming radiation. Therefore, it is desirable that during future expeditions cloud amounts due to different cloud types are recorded.

161

Tjemkes for helpful discussions and J. Kipfstuhl for his support in the field on Summit. The authors are extremely grateful to the above organisations and individuals for the successful completion of the field work and to all the people joining the ETH and GIMEx expeditions.

7. Appendix A 6. Acknowledgements The ETH Greenland Expedition was financed by the Swiss Federal Institute of Technology (ETH), Zurich (Grant No. 0-20-013-90 and 0-40040-90) and the Swiss National Foundation for Scientific Research (Grant No. 21-27449-89 and 20-32649-91). The Danish Polar Centre, the Danish Communication Office and the Danish Ministry of Justice provided the necessary legal arrangements. People from the Geological Survey of Greenland (GGU) helped with logistics. We would like to thank the GRIP Steering Committee, the Alfred Wegener Institute for Polar and Marine Research (AWI) in Bremerhaven and the Danish Meteorological Institute in Kopenhagen for their generous support on Summit. Financial support for the GIMEx experiments were provided by the Netherlands Organisation for Scientific Research (NWO) and the Dutch National Research Programme on Global Air Pollution and Climate Change (Grant No. 276/91-NOP). Additional support was obtained from the Climate Programme of the European Commission, under Grant No. EVUC-0053-NL (GDF). We are very grateful for all the support we received from the local people, especially the staff of the Danish Meteorological Institute in Sondre Stromfjord. We are also grateful to Kipp&Zonen for providing the solar integrator, and to the calibration division of the KNMI for calibrating this instrument. The people working at the Cabauw mast of the KNMI are acknowledged for their co-operative attitude during the intercomparison experiment. We like to thank J. Oerlemans, A. Ohmura, H.F. Vugts, H. Blatter, P. Duynkerke and S.

In this appendix we describe the equations used to calculate the optical air mass and the turbidity factor as used in Eq. 1 in Section 3.1. A synopsis of parameterizations used for radiative transfer is given by Iqbal (1983). The relative optical air mass (m r) is written as:

cos( +_015 1' mr =

(93.885 - Z ) 1"253 ]

(A1)

in which Z is the zenith angle in degrees. This formula is an approximation of the tables presented by Kasten (1966). Eq. A1 is applicable to a standard pressure (Po) of 1013.25 mbar at sea level. Here, we employ the following approximation to obtain the relative optical air mass at a specific height (ma): m~ = mr

(12)

Here is P the local pressure in millibars. In this model the pressure is calculated with the following equation (Lunde, 1980): P (P00) = exp( - 0.0001184h)

(13)

where h is the elevation in metres. The turbidity factor (~'e) is written as: r E= 1 +

(Ao3+AH2o)

(1 --Tr)

(A4)

in which Ao3 is the absorption by ozone, AH2o the absorption by water vapour and % the transmission due to Rayleigh scattering. The absorption of shortwave radiation by aerosols is neglected because we apply the model to the

162

T. Konzelmann et aL / Global and Planetary Change 9 (1994) 143-164

Greenland Ice Sheet where the amount of aerosols is assumed to be small. The ozone absorption is given by Lacis and Hansen (1974): 0.02118U 3 A°3

= 1 + 0.042U 3 + 3.23 × 10-4U 2 1.082U 3

+

(1 + 138.6U3) °8°5 0.0658U 3

+

(AS)

1 + (103.6U3) 3 U3 is the ozone relative optical path length given by:

where l o is the vertical ozone amount which is assumed to be a constant equal to 0.30 cm. For the absorption of water vapour we used an equation presented by Lacis and Hansen (1974) based on a study by Y a m a m o t o (1962): =

2.90U 1 (1 + 141.5U1) °'635 + 5.925U 1

(A7)

where U~ is the pressure corrected relative optical path length of precipitable water given by: O 1 = wm a

One may anticipate that calculations of the longwave incoming radiation improve when observations of cloud amounts of different cloud types and an appropriate equation are available. In this appendix such an equation is presented using the cloud amount due to low clouds (n l) and the cloud amount due to middle clouds (n m) as independent variables. High clouds (cirrus) were not considered since LOWTRAN7 experiments showed that they have a negligible effect on the longwave incoming radiation at the surface. The equation reads: L $ = [%s(1 - n I - nm) + elF/I + •rnnm]trT:

(A6)

U 3 = lom r

AH20

8. Appendix B

(A8)

where w is the reduced precipitable water in centimetres which can be expressed in terms of screen-level vapour pressure (e a) and screen-level temperature (Ta) in Kelvin (Leckner, 1978):

(B1) where e I and ~?m are the e , d t t a n c e s of skies overcast by low and middle clouds, respectively. Note that here, in contrast to Eqs. 10 and 11, the contributions of the different cloud types are assumed to be linear in the respective cloud amounts. Optimal values of e I and e m were found by means of the E T H camp data using the leastsquares criterion. For instantaneous values El = 0.956 and Em 0.893 so that the total equation reads: =

L$ =

0.23+0.484

ea g ~ (1-nL-nm)

+ 0.956n, + 0.853nm] rJ

(B2)

1 The transmission due to Rayleigh scattering is an algebraic expression (M~ichler, 1983) of a table presented by Hoyt (1978): r r = 0.615958 + 0.375566 e x p ( - 0.221185ma) (A10) The complete set of equations (A1-A10) can be solved if screen-level temperature, screen-level vapour pressure, elevation and zenith angle are specified.

The amount of data was not sufficient for the derivation of an equation for daily means. Using Eq. B2, the standard deviation of the residuals (14 W m -2) is somewhat smaller than if the equation (Eq. 10) containing total cloud amount as independent variable is used (16 W m - e ) while the number of unknowns was the same in both cases. Thus, if observations of cloud amounts due to low and middle clouds are available, Eq. B2 should be preferred.

T. Konzelmann et al. / Global and Planetary Change 9 (1994) 143-164

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