Abstract. A study of the effective emissivity from clear skies shows significant differences between night- and day-time behaviours. These differences seem to be ...
DAY-NIGHT
DIFFERENCES
EMISSIVITY
FROM
L. ALADOS-ARBOLEDAS Dpto. Fisica Aplicada,
Facultad de Ciencias,
IN THE CLEAR
EFFECTIVE SKIES
and J. I. JIMENEZ
Universidad
de Granada,
E- 18071 Granada,
Spain
(Received in final form 22 April, 1988) Abstract. A study of the effective emissivity from clear skies shows significant differences between night- and day-time behaviours. These differences seem to be related to the different conditions aloft for the day and night periods. For this reason, estimation formulae that rely only on surface parameters do not provide accurate estimates on an hourly basis. A deviation correction in terms of the hour of the day is proposed. This term takes into account the differences in the daily cycle of effective emissivity for different seasons, and provides estimates accurate to within the experimental errors.
1. Introduction Knowledge of the thermal atmospheric radiation incoming at the earth surface is of fundamental importance both from the meteorological and the climatological points of view. Due to difficulties associated with its measurement, the thermal atmospheric radiation must be estimated from routinely collected meteorological data. There are detailed methods that require measurements of atmospheric variables at several levels (radiosonde data). These methods are based on numerical or graphical (radiation charts) solutions of Schwarzchild’s equation. Although these methods are very convenient, they require information that is not always available. That is why estimates of thermal atmospheric radiation often rely on meteorological variables measured routinely at surface level. This paper deals with the daily evolution of the well known effective emissivity, defined as E = L/uT4, where v is the Stefan-Boltzman constant, T is the screen air temperature (K) and L is the incoming thermal atmospheric radiation (W m-‘). Our purpose is to investigate the behaviour of the effective emissivity and its relations with other meteorological variables in their daily cycle. Such a study could indicate the successes and limitations of estimation methods based only on surface measurements. 2. Data Acquisition The data used in this study were collected in Granada (Spain) (37” 11’ N, 3” 35’ W, 680 m above MSL). The thermal atmospheric radiation was measured with an Eppley pyrgeometer (PIR). This radiometer has a silicon dome with an interference filter in its inner surface for the isolation of the longwave atmosBoundary-Layer Meteorology 45 (1988) 93-101. @ 1988 by Kfuwer Academic Publishers.
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pheric radiation flux (4-50 pm) that allows direct measurement of thermal atmospheric radiation during the day-time. Nevertheless, as pointed out by several authors (Alados et al., 1987b; Berdahl et al., 1982; Weiss, 1981) solar radiation heats the dome, which leads to anomalous measurements during the day-time. In this work, we used the following expression AL = -I .O + 0.036G (W m?)
obtained by Alados et ai. (1988b) for correcting the day-time pyrgeometer measurements, in terms of the solar global radiation G. For this purpose, the solar global radiation was measured with a pyranometer Kipp-Zonnen CM-5, located near the pyrgeometer. Standard meteorological observations (screen air temperature T (K), water vapor pressure e (mb) and cloud amount) were obtained from the Meteorological Office of Armilla Airport, located a few kilometers from the city. The thermal atmospheric radiation and solar global radiation are integrated on an hourly basis. The experimental errors associated with the measurements of solar global radiation were estimated to be about 5%. The measurements of thermal atmospheric radiation during night-time have an estimated experimental error of about 3% and the day-time errors are greater, around 5%, due to the necessary correction for solar heating of the dome, as indicated above. 3. Results and Discussion
For study of the daily cycle of effective emissivity, we utilized the hourly average for each hour of eighteen summer cloudless days and that of six winter cloudless days. Figures la and 2a show the daily evolution for summer and winter data, respectively. For both seasons, the effective emissivity shows similar behaviour, the day-time values being systematically lower than those at night. The maximum difference between day-night effective emissivity is of the same order for the two seasons, about 0.06, which means a 10% difference for winter and a slightly lower percentage, 9%, for summer. Another feature of Figures la and 2a is the different extension of the day-time plateau for each season. For the summer cycle, the decrease in effective emissivity begins shortly after dawn, reaching the day-time plateau a few hours later. The increase in effective emissivity begins a few hours before sunset, the night-time plateau being reached a few hours after sunset. In contrast, the winter decrease in effective emissivity begins a few hours after sunrise and reaches its minimum value close to noon. The effective emissivity increase in the afternoon has a pattern similar to that in the summer. Taking into account the weak dependence of effective emissivity on air temperature as indicated by the success of equations that rely only on water vapor pressure e (Brunt, 1932; Brutsaert, 1975) or dew point temperature Td
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Fig. 1. (a) Effective emissivity daily cycle and (b) water vapor e (mb) daily cycle for summer months.
(Berdahl ef al., 1982, 1983) and by the results of simplified integrations of Schwarzchild’s equation (Staley et al., 1972), we compare the daily cycle of emissivity with that of water vapor pressure shown in Figures lb and 2b for the summer and winter season, respectively. The summer evolution of water vapor pressure may indicate a negative feedback between emissivity and water vapor pressure, opposite to that predicted by theory and by the results of the empirical
96
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daily cycle and (b) water vapor e (mb) daily cycle for winter months.
studies mentioned above. Nevertheless, the behaviour of the winter cycle indicates that the day-time decrease in effective emissivity may not be related to the weak variations in water vapor pressure in this season. This fact leads us to consider another justification for the day-night differences in effective emissivity. The daily cycles of emissivity have some similarities with the daily variations of the vertical profiles of temperature. In this way, the winter delay in the start of the decrease may be related to the presence of a stronger night-time inversion
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that remains for several hours after sunrise, unlike summer inversions, which are shorter in duration and weaker. This indicates the importance of the vertical structure of the atmosphere on the effective emissivity and implies a limitation in the applicability of those formulae that rely only on surface information. Several authors (Paltridge, 1970; Idso, 1972, 1974; Arnfield, 1979) have inferred the existence of systematic deviations of the effective emissivity from the predictions of the empirical formulae of Swinbank (1963) and Idso-Jackson (1969), that rely only on air temperature. These deviations are explained by Idso (1974) in terms of the degree of correlation between surface vapor pressure and air temperature via a modified “opacity effect”. Figures 3 and 4 show the deviations (estimated minus measured) of the daily cycle for the estimation formulae of Idso (1981) and Brunt (1932). The former estimates the effective emissivity in terms of water vapor pressure e (mb) and air temperature T (K) as follows: E = 0.609 + 5.95 x IO-‘e exp(1500/T). The estimation formula of Brunt expresses the effective emissivity in terms of the water vapor pressure, and has the following form: E = 0.60 + 0.042e1’2. The coefficients utilized in the Idso equation are those originally proposed by the author except for the independent term that has been modified in the form indicated by Alados et al. (1987a). The empirical coefficients used in the Brunt equation are those of Boutaric (Brunt, 1932) that provide acceptable estimates in the Granada area (Alados et al., 1987a). Figures 3 and 4 show that both formulae produce day-time overestimation of effective emissivity with a daily cycle similar to that of the effective emissivity for each of the seasons analyzed. This result may be explained by the fact that the formulae are developed for night-time conditions and are biased towards night-time higher values. The magnitude of the daily overestimation reaches a maximum of about 12% for the Brunt formula for both seasons, and about 8% for the Idso modified formula. These results indicate that the empirical formulae based on surface vapor pressure and temperature do not provide good estimates on an hourly basis due to the influence of vertical atmospheric conditions. As indicated, they show a similar behaviour to those relying only on air temperature. Nevertheless, the explanation proposed by Idso (1974) in terms of a modified “opacity effect” seems not to be applicable to those formulae based on water vapor pressure. Perhaps the explanation may be the existence of a different correlation between surface humidity and conditions aloft for night-time and day-time. This implies that the use of a single formula for diurnal estimates of the effective emissivity need the inclusion of a dependence on atmospheric conditions aloft via a single
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parameter such as, for example, the lapse rate. However, a more simple approximation may be the use of a correction term based on the hour of the day. For the data used in this study, a very convenient correction term may be obtained as follows: Ar = Asin ~(((t-
t’)/t)-(f/At))
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DAY-NIGHT
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EMISSIVITY
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Fig. 4. Deviation of Idso formula (estimated minus measured effective emissivity) as a function of time of day, (a) for summer months (upper), (b) for winter months (lower).
where t’ is the approximate hour of sunrise in solar time, At is the maximum length of day and f is a term that takes into account the delay of the effective emissivity cycle in relation to the solar cycle. For summer data, the appropriate values are AE = 0.060 sin Ir(((t - 5)/14) - (l/14))
(1)
100
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as a function
24 of
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above with the Idso formula. One can see that the magnitude of the day-time deviation is close to that of the night-time. The results for the Brunt formula are slightly worse, but the deviations are within the magnitude of the experimental errors. Nevertheless, if that formula is adjusted for Granada conditions, and the appropriate coefficients are obtained, the final results will presumably be improved. Acknowledgements This research was supported by a grant from the CAICYT, Institution of the Spanish Education and Science Ministry. Valuable comments in the translation of this manuscript were provided by Dr. A. Delgado. References Alados-Arboledas, L., Jimenez, J. I., and Castro-Diez, Y.: 1987a, ‘Thermal Radiation from Cloudless Skies in Granada’, Theor. Appl. Climatol. 37, 84-89. Alados-Arboledas, L., Vida, J., and Jimenez, J. I.: 1988, ‘Effects of Solar Radiation on the Performance of Pyrgeometers with Silicon Domes’, .I. Atmos. Oceanic Tech. (in press). Amfield, A. J.: 1979, ‘Evaluation of Empirical Expressions for the Estimation of Hourly and Daily Totals of Atmospheric Longwave Emission under all Sky Conditions’, Quart. J. R. Meteorol. Sot. 105, 1041-1052. Berdahl, P. and Fromberg, R.: 1982, ‘The Thermal Radiance of Clear Skies’, Solar Energy 29, 299-3 14. Berdahl, P. and Martin, M.: 1984, ‘Emissivity of Clear Skies’, Solar Energy 32, 663-664. Brunt, D.: 1932, ‘Notes on Radiation in the Atmosphere’, Quart. J. R. Meteorol. Sot. 58, 389-420. Brutsaert, W.: 1975, ‘On a Derivable Formula for Longwave Radiation from Clear Skies’, Water Resources Res. 11, 742-744. Eppley Laboratory, Inc.: 1975, Instrumentation for the Measurements of Components of Solar and Terrestrial Radiation, Unpublished document of the Eppley Laboratory, Newport. Idso, S. B.: 1972, ‘Systematic Deviations of Clear Sky Atmospheric Thermal Radiation from Predictions of Empirical Formulae’, Quart. J. R. Meteorol. Sot. 98, 399-401. Idso, S. B.: 1974, ‘On the Use of Equations to Estimate Atmospheric Thermal Radiation’, Arch. Met. Geoph. Biokl.,
Ser B 22, 287-299.
Idso, S. B.: 1981, ‘A Set of Equations for full Spectrum and 8-14 Micron and 10.5-12.5 Micron Thermal Radiation from Cloudless Skies’, Water Resources Res. 17, 295-304. Idso, S. B. and Jackson, R. D.: 1969, ‘Thermal Radiation from the Atmosphere’, .I. Geophys. Res. 74,5397-5403. Paltridge, G. W.: 1970, ‘Day-time Long-wave Radiation from the Sky’, Quart. J. R. Meteorol. Sot. 96, 645-653. Staley, D. 0. and Jurica G. M.: 1972, ‘Effective Atmospheric Emissivity under Clear Skies’, J. Appl. Meteorol. 11, 349-356. Swinbank, W. C.: 1963, ‘Long-wave Radiation from Clear Skies’, Quart. J. R. Meteorol. &c. 89, 339-348. Weiss, A.: 1981, ‘On the Performance of Pyrgeometers with Silicon Domes’, J. Appl. Meteorol. 20, 962-965.
