Download - Daytime net radiation parameterisation for Mexico City suburban areas

Ž .Atmospheric Research 50 1999 53–68

Daytime net radiation parameterisation for MexicoCity suburban areas

Roberto Sozzi a, Alejandro Salcido b, Ricardo Saldana Flores b,˜Teodoro Georgiadis c,)

a SerÕizi Territorio scrl, Õ. Garibaldi, 21, I-20126 Cinisello Balsamo, Italyb ( )IIE-Instituto de InÕestigaciones Electricas, 60490 Temixco Morelos , Mexico´

c C.N.R.-FISBAT, Physics and Chemistry of the Lower and Upper Atmosphere, Õ. Gobetti 101, I-40129Bologna, Italy

Received 14 October 1997; accepted 6 September 1998

Abstract

This study presents a simple parameterisation for forecasting daytime net radiation in a MexicoŽ .City suburban area Texcoco . The main characteristic of the parameterisation is that the only

input data are the global solar radiation and air temperature trends. Reliability of the model wasverified by measurements performed during two experimental campaigns carried out in 1992 and1993 under a contract sponsored by the European Community. The forecast and the experimentaldata were found to agree very well even in disturbed meteorological situations. q 1999 ElsevierScience B.V. All rights reserved.

Keywords: Daytime net radiation; Global solar radiation; Parameterisation of radiation trends

1. Introduction

The atmosphere obtains about 20% of its energy by direct absorption of incomingsolar radiation. About the 30% of this radiation is reflected or scattered to space. Therest of energy passes through the atmosphere and is absorbed by the surface.

Ž .In the lowest part of the atmosphere, called the Planetary Boundary Layer PBL orŽ .Atmospheric Boundary Layer ABL , the solar energy received at the surface undergoes

) C orresponding author. T el.: q 39-51-6399586; fax: q 39-51-6399652; e-m ail:[email protected]

0169-8095r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0169-8095 98 00088-X

( )R. Sozzi et al.rAtmospheric Research 50 1999 53–6854

partition processes of heat exchange between the ground and the atmosphere leading tothe development of fluxes of physical quantities.

Air flow in ABL has a turbulent character. Turbulent motion is understood to be anirregular condition of flow in which various quantities show random variation in timeand space. Turbulence is an essential part of the mechanism which disperses airpollutants resulting from anthropogenic activities and it is also crucial for the efficiencyof many natural processes, such as evaporation of water, dissipation of fog anddispersion of plant seed. The flows in ABL are controlled to a large extent by the diurnalcycle of surface energy balance, expressed as:

R qGqHqEs0n

Žwhere R is the flux of net radiation the global solar radiation received by the surfacen.plus atmospheric radiation minus terrestrial radiation , G is the vertical heat flux

between the surface and the soil and H and E are the sensible and latent heat fluxesbetween the surface and the atmosphere.

During the day, energy gained by the surface is transferred to the atmosphere, to thesoil and is absorbed in evaporation processes. This transfer of heat from the groundsurface to the air directly above can generate convection which redistributes heatthroughout the atmospheric boundary layer. The knowledge of net radiation is, thus, anecessary parameter to define surface processes.

This meteorological parameter is very often measured by meteorological stationseven though the measurements obtained with traditional instruments are not alwaysaccurate. In most practical situations the net radiation is inferred by parameterisations

Ž .from simple global solar radiation R measurements. The various mathematicalgŽparameterisations proposed e.g., Holtslag and Van Ulden, 1983; Van Ulden and

.Holtslag, 1985 are mostly semi-empiric containing many numerical coefficients ob-tained by fitting data taken under various experimental situations. In practice, beforeextensively using such a model in a specific geographical site, it is advisable to estimatethese coefficients by measurements obtained in experimental campaigns, even of limitedduration.

The aim of this paper is to report on a net radiation parameterisation scheme to beused during the daytime in Mexico City suburban areas. Utilising results obtained duringthe two experimental campaigns conducted in 1992 and 1993, it was possible to definean operative procedure for estimating net radiation based only on the measurement ofglobal solar radiation and air temperature. This paper outlines model details, methodolo-gies for estimating some of the numerical coefficients found in the model, and presentsresults obtained from comparison between measured and calculated values.

2. Modelling net radiation

The net radiation consists of four radiation components: the incoming short-waveŽ . Ž .solar radiation global solar radiation, R , the outgoing reflected solar radiation K ,g y

( )R. Sozzi et al.rAtmospheric Research 50 1999 53–68 55

Ž .the incoming longwave radiation from the atmosphere L and the outgoing longwaveqŽ .radiation L ; thus:y

R sR qK qL qLn g y q y

Ž .It is possible to split radiation into only two wavelength bands short and longwavebecause the peak in the solar spectrum is in the visible wavelengths, while theearthratmosphere system is emitting infrared radiation characteristic of its absolute

Žtemperature in the range of 280 K at the surface to about 245 K at the top of the.atmosphere .

2.1. Incoming shortwaÕe radiation

The intensity of incoming solar radiation at the top of the atmosphere is called thesolar constant. It is only approximately constant, ranging from about 1360 to 1380

y2 Ž .Wm Stull, 1989, 1995 . Some of this radiation is attenuated by scattering, absorptionŽ .and reflection from clouds on the way down to the surface sky transmissivity . When

the Sun is low in the sky, the radiation will also be attenuated by its longer path throughthe atmosphere enroute to the surface.

Ž .Therefore, the solar elevation angle c , defined as:

p tUTCsincssinfPsind ycoswPcosd Pcos yls s ež /12

Ž . Ž .where f and l are the latitude positive north and longitude positive west , d ise sŽ .the solar declination angle angle of the Sun above the equator and t is theUTC

Coordinated Universal Time.The solar declination angle is defined as:

2p dydŽ .rd sf coss r dy

Ž .where f is the latitude of the Tropic of Cancer 23.458 , d is the Julian day, d is ther rŽ .day of the summer solstice 173 and d is the average number of days per yeary

Ž .365.25 .Many synthetic parameterisations have been proposed for forecasting R and all areg

Žformally congruent with the physical principles mentioned. The most utilised and. Ž . Žsimplest is the model proposed by Kasten and Czeplak 1979 , defined without

.considering cloud cover as:

R sa sin c ya 1Ž . Ž .g 0 1 2

Ž .where sin c is the solar elevation angle, a and a are two coefficients expressed in1 2y2 ŽWm derived from experimental observations and depend on the local situation sea

. Ž y2 .level, atmospheric turbidity, etc. and R is Wm . Table 1 indicates some valuesg0Ž .found in the literature Kasten and Czeplak, 1979; Holtslag and Van Ulden, 1983 for

these coefficients.


Table 1Ž .Empirical coefficients of Eq. 1 proposed in literature

2 2Ž . Ž .a Wrm a Wrm Location1 2

Ž .910 y30 Hamburg 1980Ž .1100 y50 North Atlantic 1964

Ž .1098 y65 Boston 1945Ž .1041 y69 De Bilt 1983

As can be seen, variations in the coefficients obtained in different geographical placescannot be overlooked. These variations are due mostly to different altitudes above sealevel, atmospheric turbulence and atmospheric pollution of the various localities. If thismodel were to be applied to Mexico City, different coefficients would be obtained dueto the altitude as well as for the air turbidity caused by the notable atmospheric pollutionof this area. In principle, it is possible to infer the contribution of atmospheric pollutants

Žmodelling the radiation transfer through the whole troposphere Davies, 1995; Chou and.Lee, 1995; Pfeilsticker et al., 1997 but the information required are often difficult to

Ž .found, so, in practice, it is convenient to adopt simple relationships as 1 . Mexico Cityair pollution is only slightly variable during the course of the year so a time-limiteddata-set can be utilised for practical purposes as for the determination of sensible heat

Ž .flux reported by Van Ulden and Holtslag 1985 .Ž .Another interesting parameterisation is due by Haurwitz 1945 defined as:

R ya sin c exp ya rsin c 2Ž . Ž . Ž .g 0 0 1

Ž 2 . Ž 2 .where proposed values for a is 1098 Wrm and a is y0.059 Wrm . These0 1

numerical values were obtained from an analysis of data from Boston. An extension ofthis parameterisation is:

a1R sa sin c exp ya rsin c 3Ž . Ž . Ž .g 0 0 2

Ž . Ž . Ž .The relation between 2 and 3 appears more interesting than 1 from a physicalŽ .point of view. The part of Eq. 3 preceding the exponential represents the global solar

energy available. This depends on the solar elevation and the altitude above the sea levelof the site under consideration. The exponential represents the reducing factor derivedfrom local atmospheric turbulence conditions.

In general, the presence of clouds reduces the incoming solar radiation. In order toŽ .take into account cloud effects, Kasten and Czeplak 1979 proposed the relationship:

R sR 1qb N b2 , 4Ž .Ž .g g 0 1

Ž .where N is the total cloud cover in 8ths or 10ths and b and b are empirical1 2

coefficients, which may depend on the climate of a specific site. From 10 years ofobservations at Hamburg,

b sy0.75 b s3.41 2


Ž . Ž .Eq. 4 can be used to estimate total and effective cloud cover starting from a Rg

measure, according to:1rb21 R g

Ns y1 5Ž .ž /b R1 g 0

2.2. The outgoing shortwaÕe radiation

Ž .The albedo r is defined as the fraction of incoming shortwave radiation that isreflected by Earth’s surface. The albedo varies from about 0.95 over fresh snow, to 0.4over light-coloured dry soil, to 0.2 over grass and many agricultural crops, to 0.1 over

Žconiferous forests, to 0.05 over dark wet soil Brutsaert, 1982; Stull, 1989; Garratt,.1992 . The outgoing shortwave radiation is thus:

K syrPR 6Ž .y g

The albedo is a function of solar elevation. All the typical albedo values reported inliterature were obtained for solar elevation angles greater than 308. For such angles thealbedo variation can be considered negligible. A suitable parameterisation which takes

Ž .into account albedo variations due to low solar elevation angles is Iqbal, 1983 :X1yr

X Xr c sr q 1yr exp y0.1cy 7Ž . Ž . Ž .2

where rX is the albedo coefficient at maximum solar elevation and c is the solarelevation angle in degrees.

2.3. Incoming longwaÕe radiation

A very simple parameterization of the incoming longwave radiation in the absence ofŽ . Ž .clouds L was proposed by Swinbank 1963 . He related L to the air temperature0q 0q

Ž .T K at a screen height by:

L sc T 6 ,0q 1

y13 Ž y2 y6.where c s5.31 10 Wm K is an empirical constant.1Ž .Arnfield 1979 tested this relation for several locations. The results indicated a

difference between measured and modelled values of no greater than 5%; so this relationcan be adopted for clear skies. To account for cloud cover, we employ the linear

Ž .correction by Paltridge and Platt 1976 :

L sc T 6 qc N 8Ž .q 1 2

Ž y2 .where c s60 Wm is appropriate for mid-latitudes.2

2.4. Outgoing longwaÕe radiation

The outgoing longwave radiation from surface arises from Stefan–Boltzmann law:

L ss T 4y s


Ž .where Earth’s surface is assumed to be a black body and T K is the surface radiations

temperature. In reality, Earth’s surface has the characteristics of a grey body with aŽlong-wave emissivity ranging from 0.9, snow-surfaces, to 0.98, semi-arid soils Garratt,

.1992 . In the present case, the approximation of the emissivity value to unity does notproduce significant errors. Since the surface radiation temperature is not normallyavailable, we approximate L with a Taylor expansion byy

L ss T 4 q4s T 3 T yT ,Ž .y s

where T is the air temperature and T the soil temperature.s

During unstable conditions, the surface radiation temperature T exceeds the airs3Ž .temperature T. To obtain a suitable description of correction term 4s T T yT , ans

extensive examination of a large set of experimental data was done. The results obtainedled to the relationship:

4s T 3 T yT sc PRŽ .s 3 n

which is an implicit relation between the outgoing longwave radiation and the netradiation. In this relation c s0.12 agrees with the experimental data and can be3

regarded as a heating coefficient for the surface. Finally L can be approximated by:y

L ss T 4 qc PR 9Ž .y 3 n

2.5. The net radiation parameterisation

According to the relations describing the four energy components, a suitable parame-terisation of the net radiation is:

1yr R qc T 6 ys T 4 qc NŽ . g 1 2R s 10Ž .n 1qc3

This parameterisation, utilised in the analysis of the present data, requires theknowledge of the global radiation, the cloud cover and the albedo coefficient.

3. Experimental data set

Two experimental campaigns were conducted in the Northeast suburb of Mexico CityŽ .Texcoco area , a region characterised by semi-arid soil with short and patchy vegeta-tion.

These campaigns were part of a project sponsored by the European Communityaimed at acquiring experimental data for defining the micrometeorology of the suburbanareas of the Valle de Mexico. The first campaign was carried out from May 20 to 28,1992. The campaign site was located at approximately 2280 msl, within the perimeter ofthe Valle de Mexico Thermal Power Plant located in the North East suburbs of MexicoCity. The second experimental campaign was carried out from September 13 to 22, 1993at a site located about 2 km from the 1992 experimental site.


The meteorological conditions encountered during the experiments were typical forValle de Mexico for part of the year, with the exception of the brief rainy period whichis typical of tropical latitudes. Consequently, in spite of the short duration of the

Ž .Fig. 1. Data collected during the first experimental campaign 1992 .


experimental campaigns, the collected data can be considered representative of most ofthe climatic situations of the investigated area.

Measurements of global radiation, net radiation and temperature were conducted atŽ .the two sites Figs. 1 and 2 . Global radiation was measured by means of Li-200 sensor

Ž .Fig. 2. Data collected during the second experimental campaign 1993 .


Ž . Ž .Li-Cor, USA , net radiation by a Q6 radiometer Reps, Australia and temperature by aŽ .HPM35A sensor Vaisala, Finland . Data were taken every minute and stored on a CR10

Ž .data-logger Campbell Sci., USA , then averaged every 15 min. Radiosoundings wereperformed from 6:00 in morning to 18:00 in the evening every 2 h by means of an AIR

Ž .system USA .In the first campaign, during the radiosounds, cloud cover was visually estimated as

normal WMO standard methodology. These estimates were, in general, not veryaccurate, with their reliability decreasing as cloud cover increased. As will be seen, itwas important to have cloud cover observations available in order to distinguish whichof the monitored situations was characterised by clear skies.

4. The Mexico City suburbs net radiation parameterisation

The proposed daytime net radiation parameterisation requires knowledge of theglobal solar radiation and the total cloud cover. The aim was to develop a parameterisa-tion permitting to a common meteorological station to effect daytime estimates of netradiation with only automatically measured and processed meteorological data. Thesesituations do not commonly provide for the acquisition of cloud cover data. Dataindicating cloud cover were available for only limited periods of time during thecampaign. Therefore, the following steps were used to overcome this problem.

First it was necessary to verify which of the proposed models for describing globalsolar radiation was the most suitable in obtaining data during the campaign. This wasdone by:

Ø Extracting data from those available that certainly corresponded to cloud cover lessthan 2r8;

Ž . Ž .Ø R can be described with one of the three Eqs. 1 – 3 under these sky conditions;gŽ .Ø Using 1 and R data measured in these sky conditions during the first campaign,g

Ž .it was possible to estimate values with common Linear Regression methods of the twocoefficients a and a , as well as the standard deviation s from measured values and1 2

those estimated by the model. Results obtained are:

a s1087 Wrm2 a2 s209 Wrm2 ss"53 Wrm2Ž . Ž . Ž .1

Ž .Ø Using 2 and R data measured in these sky conditions during the first campaign,gŽit is possible to estimate values with non-linear parameter estimation methods Mc

.Keown, 1980; Press et al., 1992 , of the two coefficients a and a and the standard0 1

deviation s from measured values and those estimated by the model. Results obtainedare:

a s1486 Wrm2 a s0.46 ss"43 Wrm2Ž . Ž .0 1

Ž .Ø Using 3 and measured Rg data in these sky conditions during the first campaign,it was possible also in this case to estimate values of the three coefficients a , a and a0 1 2


as well as the standard deviation s from values measured and those estimated by themodel. Results obtained are:

a s1356 Wrm2 a s1.17 a s0.36 ss"42 Wrm2Ž . Ž .0 1 2

As can be seen from results obtained, all parameterisations considered seem torepresent well the available measurements and all are characterised by a Pearsoncorrelating coefficient over 0.99.

Ž .In the case of model 1 , the value obtained for coefficient a is comparable to those1

reported in literature, while coefficient a resulted 3–4 times higher. Because of the role2

covered by this latter coefficient, this discrepancy should be ascribable to the high levelof atmospheric pollution of Mexico City.

Ž .As far as concerns model 2 , a comparison with the coefficient obtained by HaurwitzŽ .1945 in Boston showed that our results are markedly higher.

Ž .Hereafter the model obtained with Eq. 3 will be used. The scatter plot withŽ . Ž .measured R R and calculated R values are indicated in Fig. 3.g gm gt

The Fig. 4 indicates the estimated solar radiation trend from the parameterisation withsolar elevation and experimental data available under clear sky conditions. Note the verygood agreement between model and experimental data.

Ž .Fig. 3. Measured global radiation versus calculated utilising Eq. 3 .


Fig. 4. Estimated solar radiation as a function of solar elevation angle c .

Data available from both experimental campaigns did not permit the verification ofŽ .the correctness of Eq. 4 which also considers cloud cover situations. Therefore it was

necessary to utilise the equation proposed with coefficients found in literature.Ž .Eq. 5 permits the estimating of effectiÕe cloud coÕer starting from only Rg

measurement. This leads to a more extensive verification of the global radiation modelused proceeding as follows:

Ž Ž ..Ø effective cloud cover using 5 was evaluated for all data obtained;Ø the global radiation value was estimated in all experimental situations;

Ž . Ž .Ø estimated R and measured R data were compared.gt gm

Results of this verification are synthetically described in the Fig. 5 scatter plot. Sincethe Pearson correlated coefficient is 0.88 and the standard deviation between measured

Ž y2 .and calculated values is about 170 Wm , it can be concluded that the measurementsagree with the model. In this figure are also evident some clusters of data highlyscattered which prevalently lead to an underestimation of the calculated global radiationvalues. It appears to be ascribable to complex atmospheric situations where the modelpresents a lack of confidendence in their representation.

Knowledge of albedo at the measuring stations is fundamental when using a netradiation model. Based on available data, it was possible to define the albedo coefficient

Ž .for the two measuring stations by means of the following methodology. Eq. 10 puts net


Ž .Fig. 5. Measured global radiation versus calculated utilising Eq. 5 .

Ž .radiation in relation to R . Cloud cover is present in 10 which can be directlygŽ .estimated by R as described in the previous paragraph. The albedo r is present in 10g

which is obtained with the following equation:

1qc R yc T 6 qs T 4 yc NŽ .3 n 1 2rs1y 11Ž .

Rg

To obtain an average albedo coefficient weakly influenced by solar elevation, it isŽ .advisable to only consider those situations with sin c )0.9. Elaboration of this data

supplies the average albedo coefficient value for both campaign sites. Results are: forthe first site rs0.15, and for the second rs0.23. The corresponding standarddeviations for both sites resulted ss"0.03.

The estimation of net radiation evolution starts from knowledge of a typical albedo ofŽ .a measuring site and the global radiation trend is completely described in Eq. 10 ,

where parameters assume values indicated in previous paragraphs. The model is appliedas follows:Ø first a typical albedo of the site under study is estimated;

Ž .Ø effective cloud cover is estimated using 5 for each Rg and air temperaturemeasurement;

Ž .Ø it is then possible to estimate net radiation using 10 .

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Fig. 6. Comparison between measured and calculated net radiation during the first experimental campaign.

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Fig. 7. Comparison between measured and calculated net radiation during the second experimental campaign.


Ž .Fig. 8. Scatter plot of measured vs. calculated net radiation 1992 and 1993 data .

Fig. 6 indicates the comparison between trends measured during the first experimen-tal campaign and those calculated with the model while Fig. 7 indicates a similarcomparison relative to the second campaign. It is interesting to note that the standarddeviation between measured and calculated values is about 23 Wrm2 for the firstcampaign and about 32 for the second, indicating for the test the validity of the schemeutilised to estimate the model parameters. This is further confirmed in Fig. 8 scatter plotwhere all data obtained during both experimental campaigns are shown. The figureshows three points, all obtained during the second campaign, markedly scattered; as faras net radiation is concern, these data must be attributed to bad runs of the model.

5. Conclusions

A parameterisation scheme for estimating daytime net radiation has been presented inthis study. The applied model requests global radiation and air temperature trends asinput data. This meteorological data is that most easily measured and available fromusual meteorological stations.

Meteorological data obtained in Mexico City suburban areas during the 1992 and1993 campaigns have supplied experimental data for the estimating of parameters which


have a key role in the proposed model. This, in turns allows to a detailed definition of adaytime net radiation pattern.

Acknowledgements

The authors are grateful to the management of the Instituto de InvestigacionesŽ .Electricas IIE for permission to use experimental data obtained during the two´

Ž .meteorological campaigns and to Dr. D. Fraternali Servizi Territorio, Italy for hisassistance. Thanks are also extended to all IIE technicians and researchers who invarious ways contributed to the satisfactory outcome of the two experimental campaigns.

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