JOURNAL OF CLIMATOLOGY, VOL. 1,255-272 (1981) UDC551.521.1:551.576.2 (489)

NET INCOMING RADIATION ESTIMATED FROM HOURLY GLOBAL RADIATION AND/OR CLOUD OBSERVATIONS

L. €I. NIELSEN*, L. P. PRAHM,t R. BERKOWICZ' AND K. CONRADSEN*

Danish Air Pollution Laboratory. National Agency of Environmentcl Rotcction, Risb Nationai Laboratory, 4000 Roskilde, Denmark

Receiued 7 November 1980 Raised 26 February 1981

ABSTRACT

From routine hourly observations reported during 5 years at one site in Denmark, empirical relations for net radiation over green grass are found. These relations give an estimate of the net radiation for the measuring site from the geographical position, local time, representative surface albedo, measured global radiation and/or total cloud cover in oktas. Cloud types are taken into account, if the reported clouds are mainly cirrus forms. This is a result of a classification of the net radiation according to cloud cover and type, i.e. a total of 90 classes. m e r e n t relations are found for different cloud covers,

The derived procedure is used on another site in Denmark with another representative surface albedo. From 112 years of data, consistency i s found for net radiation measurements at the two sites, allowing extrapolation of the derived net radiation procedure to other sites in Denmark. Data from the Wangara experiment (Clarke, 1971), covering 40 days, showed a similar refation for clear sky conditions, but revealed another general dependency of net radiation upon cloud cover than that found in Denmark. Therefore, relations of the kind found in this study are related to the weather and climate of the measuring site. Comparisons ktween net radiation estimated from the models and measurements from different sites is r* = 0.9.

KEY WORDS Net radiatioil Global radiation Energy balance Planetary Boundary Layer

INTRODUCTION

The turbulent state of the Planetary Boundary Layer (PBL) is of importance in many fields related to mankind, for example, weather forecasting, dispersion of gases and particulate matter in the atmos- phere and wind power prospecting.

The two predominating factors determining the turbulence characteristics of the PBL are the lateral pressure pattern as driving force for the mean wind, and the sensible heat flux at the ground. Both factors are fed by the radiation energy reaching the earth from the sun and are drained by radiative energy iosses to outer space. Most of the incoming and outgoing energy contributes to the energy balance at the earth's surface. Neglecting physical processes of minor importance for the surface energy balance, one obtains the well-known relation

R = H + L E + G , (1) where the net incoming radiation R during daytime hours contributes to the ground heat flux G, to the latent heat flux LE and to the sensible heat flux H. During night-time, the net incoming radiation is negative and is fed by the other three terms.

* Resent Affiliation: Department of Mathematical Statistics and Operations Research, Technical University of Denmark, 2800 Lyngbv, Denmark. t Addressee for correspondence.

0196-1748/81/030255-18$01.80 @ 1981 by the Royal Meteorological Society

256 L. B. NIELSEN ET AL..

The sensible heat flux, which is the key for the parameterization of the PBL, can be measured by correlating temperature and vertical eddy motion. A less sophisticated procedure is to measure temperature and wind profiles and combine these with empirical and theoretical knowledge of momentum and heat fluxes in the surface boundary layer. Often, none of these measurements are available, and it is necessary to give rough estimates by use of standard meteorological observations of clouds, temperature, humidity, precipitation and wind. At some locations, global radiation, i.e. incoming short-wave radiation, measurements are also available.

The present study concerns estimation of the net incoming radiation R on an hourly basis by use of the standard meteorological observations. A subsequent study will treat the latent heat flux and the soil heat flux, which finally will result in a procedure for estimation of the sensible heat flux H. We follow to a great extent the approach used by Smith and Blackall (1979), both for the estimation of R, and for the subsequent study of the remaining terms in the energy balance equation (1). Here, we are able to quantify R by using hourly measurements from a 10-year period of observation at two locations in Denmark.

Several authors have presented studies of relations between net incoming radiation and global radiation (e.g. Moore, 1976; Nkemdirim, 1972). The net incoming radiation has been of interest, for example, for agricultural studies where estimation of available energy for evaporation and soil humidity is of concern. However, in previous studies, the relations are usually not classified in detail according to cloud observations, as in the present study. The observations used in these previous studies were mainly performed under clear sky conditions.

Many studies (e.g. Chrosicki, 1971; Nyberg, 1977; Lumb, 1964; Suckling and Hay, 1977) have been concerned with estimation of global radiation from cloud cover, which is of interest, for example, for technical solar energy installations or radiation potential for the photosynthesis of green vegetation.

When, as is often the case, radiation measurements are not available, it is necessary to rely on the relation between cloud cover and net radiation. Snch relations have previously been reported only by Smith and Blackall (1979), in a study which was based, however, on a relatively small amount of measurements compared with the amount available for the present study.

The present results are obtained over a grass surface. By use of known albedos for other surfaces, as summarized by Kondratyev (1969), extrapolation of the radiation relations can be made to surfaces where the surface energy budget is of interest, e.g. sugar fields, potato fields, corn fields and forests. Such an extrapolation is based on the assumption that the net long-wave radiation can be assumed nonvariable from one surface to another. Although this assumption is not completely fulfilled, the results can be useN in many applications.

MEASUREMENTS AND OBSERVATIONS

Measurements of radiation were made at the Climate and Water Balance Station on the experimental farm, Hgjbakkeghd, situated 20 km west of Copenhagen at 55"40'N and 12"18'E and at an elevation of 28m above sea level. The experimental site is 3Ox50m and the soil is covered by a dense, short clover-grass mixture. It is freely exposed and surrounded by ordinary agricultural fields.

Short-wave incoming and reflected radiation are recorded by Kipp and Zonen G-2 solarimeters. The solarimeter and its function are described by Bener (1951), Trickett et al. (1957), Aslyng and Friis-Nielsen (1960) and others. Net radiation is recorded from 1962 by polyethylene shielded net radiometers constructed at the Danish Royal Veterinary and Agricultural College (Jensen and Aslyng, 1967). All radiometers are placed one metre above the clover-grass covered ground.

The radiometers are calibrated once a year. The solarimeters are compared with the Angstram compensation pyrheliometer or with a newly calibrated solarimeter. The net radiometer is calibrated for short- and long-wave radiation in a special chamber (Jensen and Aslyng, 1967).

The solarimeters measure radiation between 0 . 3 ~ and 2.5~ while the net radiometer measures between 0.3~ and 100~. The outputs from the radiometers are sampled with digital equipment with a sampling time of 10 minutes in 1974-76 and 1 minute in 1977-78, and from the sample values hourly

INCOMING RADIATION ESTIMATES 257

Table I. Cloud types and associated heights

cirms cirrocumuls 1 High clouds Cirrostratus I Altocumuls Altostratus Nimbostratus Stratocumulus I

Medium-high clouds

Stratus Low clouds Cumulus Cumulonimbus

averaged radiation values are constructed. Studies show that hourly values from 10-minute sampling can give results that d8er as much as 20 per cent from hourly values constructed from one-minute sampling (Hansen and Jensen, 1980). If average values over longer periods are of interest, this uncertainty will diminish, and for statistical studies like the present study, it will be of no real concern. Errors in global radiation measurements are discussed by Stanhill et al. (1971). The net radiation measurements are generally correct to about 10 per cent (Hansen and Jensen, 1980).

The air screen temperature at 2 m above the grass is measured with a resistance thermometer, and the temperature is recorded with the same digital equipment as the radiation. Cloud observations are taken from the synoptic observation station at Vaerlrase Airport about 15km north of the radiation measuring site. The observations follow the WMO code (WMO, 1972, 1974) and are available on an hourly basis. We use total cloud cover in oktas, cloud type and base height of clouds in one or two heights. Two layers are reported, if the lowest layer covers less than and the highest covers more than $. The types reported are the basic ones listed in Table I. In the analysis, 5 years of data were used, since this was considered a representative period.

Several authors have published expressions from which the solar elevation can be calculated more or less accurately for a given time and geographical position. Here, we have used the formulae from Robertson and Russel (1968).

The Julian day number D in a year is found from the algorithm:

If month >2 then D = 31 (month- l)+day no. in month

D = D -integer part of (0.4 month+ 2.3) If leap year then D = D + l

ANG = 02~1365 S =0.3964+3.631 sin ANG-22.97 cos ANG

+Om03838 sin 2ANG - 0.3885 a s 2ANG + 0.07659 sin 3ANG - 0.1587 cos 3ANG + 0.07659 sin 3ANG- 0.1587 cos 3ANG -0*01021 cos 4ANG.

y =0*002733-7*343 sin ANG+O*5519 cos ANG - 9.470 sin 2ANG - 3.020 cos 2ANG -0.3289 sin 3ANG - 0.07581 cos 3ANG -0.1935 sin 4ANG-0.1245 cos 4ANG.

sin 8 = sin LAT sin S +cos LAT cos S +COS (CEST- 13*5+LON/15+7/60)

From equation (5) , sin 8 is calculated for the median of the observation hours.

(3)

(4)

258 L. B. NIELSEN ET AL.

PARAMETERIZATION OF THE COMPOhiENTS OF THE NET RADIATION

The net radiation at the surface is divided into its downwards and upwards, short-wave and long-wave components

R = s d + Ld- Su-L 6) Sd, the global radiation, is the direct and dilluse radiation from the sun that reaches the surface of the earth. The irradiance from the sun that reaches the atmosphere is the sun constant, 1,353 W/m*. In this study, the sun-earth distance is assumed constant, due to the minor importance of its variation for the derived relations. Within a year, the distance has a variation of 3.5 per cent and this effect can be included by use of a formula from Robertson and Russel0 (1968). The global radiation at the surface is a reduced part of the sun constant due to reflection back to space and absorption by clouds, water vapour, ozone, aerosols and air molecules. Of these effects, the ones due to clouds are the primary, and considering the uncertainty in cloud observations, variations in water vapour, aerosols and omne can be disregarded in simple models. A brief investigation of the global radiation for different wind directions toward north-westerly clean air regions, did reveal that the variation h s d due to a polluted atmosphere compared with a clear atmosphere is not significant in Denmark.

Following Paltridge and Platt (1976) and Petersen (1980), variations in global radiation due to variations in water vapour and aerosols are likely to be of the magnitude 3-5 per cent.

S, is the reflected short-wave radiation from the ground. Using the reflection coefficient, the albedo ag, equation (6) can be written

where a, is a representative surface albedo. In simple models, a, can be taken as a constant for a given surface (e.g. Paltridge and Platt, 1976), though it is dependent on solar elevation and spectrum of the radiation.

Ld is the downward heat flux mainly from clouds, water vapour, COz and omne to the ground. The water vapour content of the atmosphere absorbs nearly all of the spectrum of L, that lies outside the atmospheric window, 8 p - 14p. The long-wave radiation exchange between the atmosphere-earth system and space mainly takes place in the atmospheric window. Thus, because only about 30 per cent of the radiation from a black body at terrestrial temperature lies in the atmospheric window, Ld is always about 70 per cent of L, or greater. For clear skies, Swinbank (Amfield, 1979) has developed an empirical formula

where d = 5.31 . lo-” K-6W/mZ. This formula is derived for clear skies at night. Paltridge and Platt (1976) and Arnfield (1979) have

verified the formula and tried to extrapolate its validity to daytime and even cloudy skies. For clear skies, Swinbank’s formula is able to estimate Ld with an accuracy of 20W/m2 (Paltridge and Platt, 1976).

R =(l-ag)Sd+Ld-L, (7)

Ld = d P , (8)

L, the upward heat flux from the ground, is given by

where E , accounts for the fact that the surface does not absorb and emit long-wave radiation exactly like a black body.

RESULTS

From 5 years of data, empirical relations are derived for net radiation from global radiation and cloud observations. Diverse relations are found in the literature at Merent sites based on a rather limited amount of data. Here, we have hourly values measured on a routine basis for 14 years, out of which we have chosen data from the latest 5 years, which is thought to be the most representative, and which is sufficient to give the studied relations a statistical significance.

INCOMING RADIATION ESTIUATES 259

CLOUD COVER = 4 OKTRS RLBEDO C . 4

0 100 200 399 400 59e 600 709 800 900 1000 CLOPRL R R D I R T I O N I W/M2

Figure 1. Scatter plots of net radiation against global radiation for a cloud cover of 4 oktas. Ob$ervations with snow on the ground are excluded

Daytime net radiation from global radiation and cloud observations

Net radiation can be estimated with reasonable accuracy from global radiation alone, but a better accuracy can be achieved, if cloud observations are included. Figures I and 2 show net radiation against global radiation for different cloud cover. It is found that with a good approximation, R can be written

R = (l-aJ/(l+B)Sd+Lno(W, (10) where L, is a constant for given total cloud cover N. B is the heating coefficient equal to -dL,JdR (Monteith and Szeicz, 1961). Estimated values of (1 -aJ/( l+B) and L,(W from linear regressions are shown in Table II and the regression lines are shown in Figure 3. (1 - ad/( 1 + 0) is only slightly variable with cloud cover, while L,, varies with cloud cover and is nearly zero for 8 oktas cloud cover. Estimation

HOEJBRKKEGRRRD VfiERLOESE 74-78 E CLOUD COVER = . 8 OKTAS T

0 190 280 308 400 500 600 709 000 900 1000

CLODRL RIIBIRTION I U/M2 )

Figure 2. As figure 1, for cloud cover 8 oktas

260 L. B. NIELSEN ET AL.

Table 11. Linear regression between net radiation and global radia- tion for dderent total cloud cover N. Intercept is L,, (1 - a3/(1+

0) is the slope and s is the standard error of estimated R

~

0 1 2 3 4 5 6 7 8

ALL

-95.0 -89.2 -78.2 -674 -57.1 -45.7 -33.2 -16.5 -4.3 -28.4

0.73 0-72 0.72 0.72 0-72 0.70 0.70 0.69 0.69 0.65

~ ~

31.5 0.98 30.7 0.99 31.6 0.99 35.2 0.98 33.6 0.98 32.5 0.98 28.2 0.98 21.3 0.98. 11.6 0.97 37.3 0.94

~~

759 2,874 1,7 34 1,869 1,570 1,791 .2,043 3,494 4,332 20.466

of p from Table II cannot be made with great statistical significance, but nevertheless, extrapolation can be made to other surfaces using the estimated ( l -ab/( l+p) values and assuming constant p. The inferred values are in agreement with other investigations (Nkemdirim, 1972; Stanhill et al., 1966; Gay, 1971). Several authors have reported that the heating coefficient is as much dependent on atmospheric properties as upon the surface conditions (Idso et al., 1969; Moore, 1976). However, the values generally found are small compared with 1.

The albedo

The dependence of ag on the solar elevation is shown in Figure 4 for the seasons known to be without snow. Figure 4 reveals that a, is only slightly dependent on solar elevation for all cloud conditions, which is to be expected over a grass surface, and a representative ap can be found to be 0-25, which is in agreement with a, values generally found (Kondratyev, 1969). No information on snow cover at the experimental site was available, but a test for snow on the ground was chosen as a, greater than 0.4. The albedo of snow is dependent on the age of the snow and the content of impurities. A survey of

-200 1 1 1 1 1 1 I I I 1 1 1 1 1 I 1 1 1 1 0 200 400 600 800 1000

QLOBAL RADIATION ( W/mz 1 Figure 3. Regression lines for the relation between R and S,. for dierent total cloud covers in oktas. Mjbakkeghd data

INCOMING RADIATION ESTIMATES 26 1

1 . e I I

1 .9 1 HOEJBAKKEGRRRD 7 6 , JAN,FEB,MRR RND DEC EXCLUDED

e .e . l .2 .3 .4 .5 .6 .7 .8 .9

SINE OF SOLAR ELEVATION

Figure 4. Scatter plots of albedo against sin 8. The albedo is calculated as the ratio between hourly mean values of S, and S,

albedo values for representative land and city areas excluding and including snow cover is made by Kung et al. (1964). The referred albedo values are representative average values. A more detailed evaluation of the albedo may take into account the dependence on solar elevation and radiation spectrum.

Night-time net radiation from cloud observations

During night-time, R is equal to L,, and during daytime, L,, can be deduced from R, S, and S,. In the stable boundary layer at night, net radiation is dependent on the surface wind speed. At the measuring site, measurements of wind speed at 2 m were available. This is not a standard meteorologi- cal parameter, but it is included here for the purpose of showing the physical importance of the surface wind speed.

With equations (8) and (9) and Figure 5 in mind, a regression analysis was performed for separate cloud conditions at night with

For clear skies and scattered clouds, wind speed describes a part of the variation in net radiation. For overcast conditions, there is no correlation between wind speed and net radiation. This follows from the well-known fact that the surface of the ground becomes significantly cooler than the overlying air in situations with low wind speeds. Furthermore, the measured relative humidity at 2 m is weakly negative-correlated with wind speed, but this is not used here.

The term with Tim was found insignificant on a 5 per cent level for all cloud conditions, while the term with T;, was found insignificant for clear skies and 1 okta total cloud cover. The results from the regression are tabulated in Tables 111, IV and V. Some of the r2 values are very low, but significant because of the great number of observations. Table IV shows the simple average values found at night for cloud cover greater than 1 okta. The most significant feature from this table is that the long-wave net radiation at night is greater, when the cloud base is high, compared to a medium high or low cloud base. As a simple system for predicting L,, at night, information on total cloud cover and height of dominating clouds is used, and a modified cloud cover N, is defined from the algorithm:

R = a, + a, u2, + a&, + a3 c,,, + a4Gm (11)

N < 3 --* N, = N If dominating cloud cover is high then N = 3 + N, = 2

N > 3 + N, = N - 2

N e t

i n c e

m 0

Figure 5. btter plot of net radiation against wind speed for clear skies at night

I

Hoejbakkqaard Yaerlorrc 74-78 Night t i be

Clear rkyes . D w , Jan and f rb cxcludQd

I 1 . . . '

Table 111. Regression coefficients for L,, = R = ao+ alub + azwf,+a3fi,,, during night-time. s is the standard error of

estimated L,, ~~ ~ ~ ~

a. 41 az a 3 . 10'' S N W/m2 Wslm3 Wsz/m4 W/mzk6 rz WlmZ

0 -96.1 -16.4 1.35 100 0.48 15.7 1 -101.5 -12.6 0.99 104 0.42 15.1 2 -76.1 -13.0 1.16 66 0.26 17.3 3 -80.1 -9.8 0.90 72 0.16 18.8

Table IV. Estimated constant L , values of L , = R and standard error s during night-time for ditlerent cloud heights.

Hi& clouds Medium-high clouds Low clouds

4 -65.4 17.2 117 -51.5 17.7 198 -52.5 21.7 627 5 -60.2, 20.0 206 -43.5 20.8 232 -44.9 21.6 608 6 -56.9 18.9 265 -36.2 15.6 426 -35.3 20.8 773 7 -47.7 18.6 230 -28.5 14.4 732 -21.1 16.6 2,188 8 -33.6 18.1 73 -20.7 12.4 695 -8-6 9.4 5,886

Table V. Estimated constant L, values of L t = R and standard error s during night-time for mod-

ified cloud cover classification N,

S N, 62 W/mz n

4 -53.5 20.5 1,104 5 -45.3 20.9 1,088 6 -35.5 19.1 1,283 7 -23.0 16.5 2,929 8 -9.9 10.5 6,638

INCOMING RADIATION ESTIMATES 263

Daytime net radiation from cloud observations

During daytime, a relation betieen net radiation, solar elevation and cloud cover is sought, following Smith and Blackall (1979).

The influence of clouds on net radiation is classified according to the available observations. This is limited information, because information on the position of the clouds in the sky, the depth af the clouds and information on precipitation are lacking. These deficiencies cause severe limitations for the prediction of the net radiation at a given time and geographical site.

In order to evaluate the influence on R from the obsened cloud types, observations with only one cloud type apparent were selected, if the difference betwen the cover of the reported cloud layer and the total cloud cover was less than 8. This data set was classified according to total cloud cover (9 classes) and cloud type (10 classes), a total of 90 classes. For each class, scatter plots of net radiation against sine of solar elevation were drawn. By a subjective judgement, it was concluded that the 90 classes could be clustered into 2 classes, high clouds and lower clouds. Physically, this is a classification between clouds of ice crystals and clouds of water droplets. To extrapolate this classification to all observations, it was decided to perform the classification on the dominating cloud layer, i.e. the layer with the largest horizontal extent. Scatter plots for three cloud types are shown in Figures 6, 7 and 8. The regression lines on these figures are estimated using data for all cloud types. It is seen that only cirrus clouds differentiate significantly from the regression. These high cIouds cause larger R than average clouds.

Scatter plots of net radiation against sine of solar elevation are shown in Figures 9, 10 and 11. The clusters in the figures are caused by a combination of the yearly variation of the declination, which behaves approximately like a harmonic wave with a relatively flat maximum and minimum, and by the fixed hours for the measurements every day throughout the years. These plots are for a grass surface, because snow is exclilded. Plots for all cloud covers show a distinguished difTerence in net radiation for different N. An empirical relationship of the form

(13) was used for each N. The nonlinear terms account for physical effects like refraction for low solar elevations, diflerent radiation pathways through the atmosphere and the albedo dependency of solar

R = ao+al sin 8 +a2 sin2 8 +a3 sin3 8

- n-?

-280 e .e . 1 .2 . 3 .4 .6 .6 .7 .8 .Y

S I N E O f SOLAR ELEVflTION

Figure 6. Scatter plot of net radiation against sin 0 for observed Cirms clouds covering 4 oktas. l k iine is the regnssion line for N,, = 4 and all cloud conditions. See figure 14

264 L. B. NIELSEN ET AL.

N E T

1 N C 0 H I N C

R A D I A T I 0 N

600

600

400

300

200

100

e

600

HOEJBAKKECAARD VAERLOESE 74-78 ALBEDO < .4 AND DAYTIME CLOUD COVER = 4 OKTAS CLOUD = ALTOCUMULUS

400 - 300 -

200 - 100 -

e

-108 -

-200 0 .0 .1 .2 .3 .4 .S .6 .7 .8 .9

S I N E OF SOLAR ELEVATION

-108 ' -200 I

0 .0 .1 .2 .3 .4 .S .6 .7 .8 .9

S I N E OF SOLAR ELEVATION

Figure 7. As Figure 6, for altocumulus clouds

elevation. For a given measuring equipment, the higher order terms will also take into account nonlinearity in the equipment. The coefficients of equation (13) were found from a weighted regression analysis where the weights were the empirical variances for given sin 8. The regressions were first performed with a classification according to total cloud cover and height of dominating cloud layer. Results for N = 5 and N = 7 are shown on Figures 12 and 13. A detailed investigation for all N revealed that a classification could be made in the same way as during night-time, with a modified N called N,, when a simple procedure is sought.

With a classification on N,, a regression analysis was performed to determine the constants in equation (13). The term with sin3 8 was insignificant on a 5 per cent level and was excluded. The results are shown in Table VI. A test was made with another regression, including terms with 7'&, and T&, for a better description of the long-wave part of R, but this did not reduce the standard error. An attempt

6 0 8 I 1 I . 8 .

HOEJBAKKECAARD VAERLOESE 74-78 ALBEDO < a 4 AND DRYTINE CLOUD COVER = 4 OKTRS CLOUD = CUMULUS

I 400 - 0 w 300 - I

200 -

u -100 - n2

-200 0 .0 .1 .2 .3 .4 .6 .6 .? .a .9

S I N E OF SOLAR ELEVATION

Figure 8. As Figure 6, for cumulus clouds

INCOMING RADIATION ESTJh4ATJS 265

-200' . . I 0 . 8 . l . 2 . 3 .4 .5 .6 .7 .8 .9

SINE OF SOLRR ELEVATION

Figure 9. Scatter plot of net radiation against sin 8 for cloud cover of 1 okta

to include the observed synoptic sight, W, did not improve the model description either. The resulting regression curves are shown in Figure 14. Parts of these curves, for low solar elevations, are below the R estimates for night-time, due to the estimation procedure, and this feature is thought to be nonphysical, because R does not decrease when the sun is rising, and does not increase when the sun is setting. Therefore, the night-time R estimates are used during daytime hours, if they are larger than the daytime estimates of R for the same N,. It might be noted that during daytime the net radiation for N = 1 okta is slightly larger than for N = 0 oktas under average conditions.

Model test

As a control of the derived model for R, the cumulative distributions of measured and estimated net radiation are shown in Figure 15. From this figure, it is seen that there is an overall agreement between

600

HOEJBRKKECAARD VAERLOESE 74-78 E 5e0 CJLBEDO < .4 AND DAYTIME

1 CLOUD COVER= 5 4

I 488 H C 0 n 3e.e I N c R A

200

iee

I e A 1

N

-100 - M2

-200 8.8 .2 .3 .4 .5 .6 .7 .8 .9

SINE OF SOLAR ELEVATION

Figure 10. As Figure 9, for cloud cover of 5 oktas

266 L. B. W E N ET Ai,

I - I .. 1 --- I

w -ieeC 1

e .e .1 . 2 .3 .4 .6 .6 .7 .8 .9 SINE OF SOLAR ELEVATION

Figure 11. As Figure 9, for cloud cover of 8 oktas

the measured and estimated cumulative distributions of net radiation. This appears, because the regressions for the dserent classes are unbiased. The most severe limitations of the model formulation are the nonability for the model to predict the extreme net radiations, and the discretization of the net values at night. Nevertheless, these limitations are not critical for the heat budget estimation where spatial and time averages are of concern.

COMPARISON WITH OTHER MEASUREMENTS

-200 I I I I I I I I I I I I I I 1 I 0.0 0.2 0.4 0.6 0.8

SINE OF SOLAR ELEVATION

Figure 12. Regression lines for high (H). medium-higb (M) and low (L) clouds for cloud cover of 5 oktas. HBjbakkegArd data

SINE OF SOLAR ELEVATION Figure 13. As Figure 12, for cloud cover of 7 oktas

Table VI. Regression coe5cierits for R = ao+ aI sin 8 +a3 sin3 8, s is the standard error on estimated values of R

-- 0 1 2 3 4 5 6 7 8

ALL

-112.6 -112.6 -107.3 -97.8 -85.1 -77.1 -71.2 -31.8 -13.7

-- 653.2 686.5 650.2 608.3 552.0 511.3 4954 287.5 154.2

~~

174.0 120.9 127.1 110.6 106.3 58.5 -37.9 94.0 64.9

~

37.5 0.95 40.1 0.94 57.4 0.87 72.0 0.78 75.6 0.72 80.1 0.65 78.3 0.60 74.2 0-54 52.9 043

759 2,874 2,042 3,103 2,944 1,660 1,645 3,193 4,246

2 1,466

(Wm2) OKTAS

268 L. B. NIELSEN ET AL

MEASURED VALUES

***** ESTIMATED VALUES

-

1 6 1 I I I I I I I 1 I -

-100 0 100 100 300 400 y)(1

NET INCOMING RADIATION (Wh’ l

Figure 15. Accumulated distribution of estimated and measured net radiation

with the same type of instruments as for HBjbakkegArd. Instantaneous values are recorded every 10 minutes for all 10 years. Measurements are performed over a grass field, where the grass has not fully covered the ground. Synoptic cloud observations are performed routinely every hour at Karup Airport, 10 km away from the experimental site.

Results are shown in Tables VII and VIII and Figure 16. It is seen that the net radiation for a given insolation for Karup data is about 5 per cent higher than for the Hgjbakkegkd data, which is due to the

Table VII. As Table 11, but for the Karup site

n

-77.3 -79-7 -65.6 -54-9 -45.9 -37.5 -28.4 - 14.3 -3.0

0.78 0-79 0.80 0.79 0.79 0.79 0.79 0-77 0.78

36.9 0.96 34.5 0.97 38.1 0.96 39.1 0.96 37.3 0.95 35.3 0.95 32.8 0.95 23.8 0.95 13.4 0.95

1,494 4,945 2,545 2,664 2,008 2,615 3,396 5,951 7,600

ALL -22.2 0.72 38.3 0-94 33,218 ~ ~ ~~ ~~ ~~~

Table VIII. As Table VI, but for the Karup site

0 -112.9 1 -113.2 2 -116.4 3 -109.5 4 -93.1 5 -85.6 6 -53.4 7 -42.1 8 -18.7

792.0 800.8 784.1 730-2 661.2 596-4 480.4 378-2 199.8

46.6 0.93 57.5 0.89 70.3 0.82 83.3 0-72 89.2 0.66 90.0 0.62 87-2 0.53 73.8 0.55 54.6 042

1,495 4,946 2,948 3,046 2,945 2,871 2,475 5,063 7,581

ALL 33,218

INCOMING RADIATION ESTEMATES 269

688

600

400

300

200

108

8

/ 5

....... *.- 6 ........

3 7 ........ 7: .......

......... ./ -. .-.- - ....... ./I-.-

___-----

- ......... ./.- //--

- - .I.- _--- 8 - __----- - - -

- -

- - . l ~ l . 1 . 1 I 1 , 1 . 1 . 1 ,

- U R N G R R R DATR CLOUD COVER = 0 OKTRS

-

- -

- 1

‘0.. ’. .,*

I I I 1 I I 1 I I 1 I I I I I L 1

-200d.o 0.2 0.4 0.6 0.0 ’

SINE OF SOLAR ELEVATION

w -100

tl2 -

Figure 16. As Figure 14, for Karup data

-/

lower albedo for the more sparse grass at Karup. The reason why the coefficient for (l-cw,J/(l+@) shown in Table VII does not vary for different N, as is the case for the H&bakkeg&rd values, may be explained by dif€erent responses by the measuring equipment, see Stanhill et al. (1971). The same explanation may also apply for the linear dependency of net radiation upon sin 8 at the Karup site. The variation of net radiation for diflerent N is seen to be qualitatively similar for Karup and H6jbakkegh-d.

Net radiation data and cloud observations were obtained as a part of the Wangara experiment (Clarke, 1971), where data for a period of 40 days were gathered. Scatter plots of net radiation against sin of solar elevation were produced for different total cloud covers. The results for clear skies are in agreement with the Danish data, see Figure 17, considering the albedo for sparse grass, whereas the

N E T 1 N C 0 II I N C

R R D I R T I 0 N

Figure 17. !Scatter plot of net radiation against sine for Wangara data with clear skies. The line is the regression line for HBjbawEegHrd data

270 L. B. NIELSEN ET AL.

Wangara results for cloud cover 2, 3, 4 and 5 oktas are very much the same as for clear skies, in disagreement with the Danish data. This feature may be explained by the difTerent climate over the Australian inland site at Hay during the experimental season from the one found in Denmark under average conditions. This underlines the statement of Nkemdirim (1972) that empirical expressions for R are to be sought for the geographical sites where they are to be used.?

CONCIJJSION

A procedure for estimation of the net radiation is derived for use in heat budget calculations at the surface of the earth. The relations for the estimation require the following information:

(a) geographical position and time (b) global radiation measurements and/or cloud observations (c) ground surface albedo and heating coefficient

The cloud observations should contain information on total cloud cover in oktas and on whether clouds of cirrus form are the dominating cloud type. The model for estimation of the net radiation R consists of regression curves for R as a function of global radiation or sun height. For each okta, separate regression curves are computed. A procedure for correction in the case of cirrus-form clouds is defined for use in computation of net radiation from solar elevation, because cirrus-type clouds reflect and absorb less incoming radiation than medium high and low clouds.

The net radiation varies from about -125 W/m2 during night-time to a maximum of 550 W/m2 during daytime in June. During night-time, the standard error on the estimated net radiations is between 10 W/m2 and 20 W/m2. From global radiation measurements and cloud observations, net radiation during the daytime can be estimated with a standard error between 10 W/m2 for a cloud cover of 8 oktas, and 35 W/m2 for a cloud cover of 3 oktas. Jf only cloud observations are used, the uncertainty of estimated net radiations is larger than if global radiation measurements are used, and the uncertainty is about proportional to R. On the average, the standard error on estimated net radiations is smallest for clear skies, about 37 W/m2, and largest for 5 oktas, about 80 W/m2.

The Danish measurements used are taken over dense irrigated grass, but extrapolation can be done to other natural surfaces using representative albedo values and assuming the same heating coefficient. With greater uncertainty, extrapolation can be done to e.g. urban areas from representative albedo values and heating coefficients inferred from other studies. Comparison of the Danish data with data from the Wangara experiment shows good agreement for clear skies, but the results under cloudy conditions must be considered dependent upon the climate of the measuring station.

ACKNOWLEDGEMENTS

We wish to thank Sv. E. Jensen and S. Hansen from the Hydrotechnical Laboratory, the Royal Veterinary and Agricultural College, Copenhagen, Denmark for kindly making their data available for us, and for our many valuable discussions. Sv. E. Jeiisen has been in charge of the radiation measurement programme and S. Hansen has conducted the quality control of the gathered radiation data. The synoptic data were supplied by the Danish Meteorological Institute, and we appreciate their collaboration. We also wish to thank F. B. Smith, of the British Meteorological otfice, for inspiring discussions. Marie Bille typed the manuscript and her linguistic proficiency has been helpful.

APPENDIX: NOMENCLATURE

ANG Julian day angle CEST Central European Standard Time D Julian day number

t The net radiation model based on cloud cover observations has now been compared with measurements from both Sweden and from the Netherlands. The agreement is excellent with correlations rz 10.9. These results well be reported elsewhere.

INCOMING RADIATION ESTIMATES 27 1

solar constant downward long-wave radiation (terrestrial) net long-wave radiation at the ground estimated constant L,, for given cloud layer upward long-wave radiation (terrestrial) latitude longitude fractional cloud cover modified fractional cloud cover number of observations net incoming radiation squared correlation coefficient standard deviation downward short-wave radiation (terrestrial) upward short-wave radiation (terrestrial) absolute ground temperature absolute air temperature at 2 m surface albedo heating coefficient solar time correction factor solar declination ground emissivity solar elevation

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