Category Archives: EuroSun2008-13

Young have developed a good, practical formula which is well suited for use with small solar elevation angles [8]

. _ ms ga а gtnv-i (2)

_ з tк* V 4 sin^V-t (S. ffiLGS 9&a ri tT V 4 GJGGCaca?

This equation approaches the simple expression 1/sin V asymptotically for angles greater than 250. (The reader may wish to try using the angle V = 900 in the Kasten-Young equation. Note that L = 1 with the sun directly overhead.

2.4 Enhanced global irradiance model

One would expect the diffuse contribution IF to the global irradiance to increase with increasing atmo­spheric turbidity (increasing values of a) and that these two quantities are related to one another and to the solar elevation angle. This connection has been examined in earlier work, and the graphical result is shown in Figure 3. The Linke turbidity factor TL enters the analysis in the term for the direct irradiance and is equal to unity for a pure Rayleigh atmosphere (no aerosols — only molecular scattering). The term aL is in this formulation replaced by:

a1 = «ф [-0.B662 ■ Тя ■ L ■ (3)

where Dr(L) is the Rayleigh optical depth as a function of the air mass L. A very useful empirical equation for 1/Dr has been developed by Louche, Peri and Iqbal and modified by Fritz Kasten [8]:

Подпись: Figure 3: The observed diffuse irradiance on a horizontal surface depends upon the value of the Linke turbidity factor TL and the solar elevation angle.

-7T = 6J&296+ 1.7 515 ■ L — 0.12Є2 ■ — (ШВ65 ■ £a — 0JD0Q13 ■ L4 <4)

The data of Figure 3 has been used to find an expression for the diffuse irradiance on a horizontal surface IF as a function of the elevation angle V and the turbidity factor TL:

£r = (4ВД4 ■ Г, — Ш2)- (1-ехр[аі — Г, — 0.P905- Y]’) (5)

2.5 Equation for finding TL from observations

In view of the foregoing remarks it is now possible to write an algorithm for the determination of the Linke turbidity factor from observations of the global solar irradiance on a horizontal surface and with knowledge of the solar elevation angle. The elevation angle is readily computed when the latitude, longitude and time of day are known.

tc = 2» ■ Щ — sinF ■ дС-азьи-*!. — l-вд + (4^4,^ _ 4^33) ■ (1 — (6)

IG is the global irradiance measured, and V can be found from the time and position data. Knowledge of V yields the air mass L which in turn permits the optical depth DR to be determined. The only unknown parameter in the equation is the Linke turbidity factor TL which can then be calculated. This program has been carried out for clear days at a wide range of locations during the voyage from the Arctic to the Antarctic.

2.6 Results

image006

For all of the good, clear days during the eight month expedition the Linke turbidity factor was computed using the algorithm described above. For these same days the mid day temperature and relative humidity were obtained by examination of the Galathea III database. From the temperature and humidity data it is straightforward to compute the amount of water present in a cubic meter of surface air. These calculations were performed with the data shown in Figure 4 as the result. The regression shows that a moisture content close to zero should yield a Linke turbidity factor near unity as expected. The value 1,19 may reflect the fact that some aerosols will typically be present in the maritime environments from which data is available in addition to water vapor.

This analysis permits the estimation of the Linke turbidity factor in maritime environments based upon knowledge of the temperature and relative humidity. Compute the water content of a cubic meter of surface air, and apply the equation shown in Figure 4 to find TL. With TL in hand a good prediction of the global irradiance on the horizontal on a clear day, including the distribution of direct and diffuse irradiance, can be made using Equation 6. As local temperature and relative humidity are standard meteorological parameters, no special equipment or data is needed to do the calculations. Visibility conditions are also derivable from knowledge of the turbidity factor as discussed elsewhere [7]. This method does not take account of other aerosol which may be present, but it can be applied in typical maritime conditions without a modest amount of dry atmospheric aerosol particles.

References:

[1] Galathea 3 Expedition portal in English: http://galathea3.emu. dk/eng/index. html

[2] Frank Bason; Solar Irradiance Measurements from the Danish Galathea 3 Expedition, ISES Solar World Conference Beijing 2007, Proceedings.

[3] Pierre Ineichen, Richard Perez; A new airmass independent formulation for the Linke turbidity coef­

ficient, Solar Energy 73, no. 3, pp 151-157, 2002.

[4] Linke, F.; Transmissions-Koeffizient und Trubungsfaktor, Beitr. Phys. fr. Atmos. 10, 91-103 (1922).

[5] Frank Bason; Solar Radiation Measurements from Greenland to Antarctica — Optics Table Data from the Danish Galathea III Expedition (2006-2007) , North Sun Conference 2007, Riga,

Latvia, May 2007

[6] John Duffie, William Beckman, Solar Engineering of Thermal Processes, Wiley & Sons, New York, 1991.

[7] Frank Bason; Diffuse Solar Irradiance and Atmospheric Turbidity, EuroSun 2004 Conference

Proceedings, Freiburg, Germany, June 2004.

[8] F. Kasten, A. T. Young; Revised optical air mass tables and approximation formula, Applied Optics,

28, no. 22, pp 4735-4738, 15 Nov 1989.

Materials and Methods

The meteorological and climatic features of Galicia are monitored by a network made up by 93 weather stations, located all over the region covering the usual meteorological parameters. Ten — minute averaged data were collected for both monitoring and climatic studies. The network is managed by MeteoGalicia, the Galician weather service (www. meteogalicia. es). Currently, 25 stations provide the solar radiation measurements with Ph Schenk first class pyranometers (Philipp Schenk GmbH Wien & Co KG, Wien, Austria) and Kipp & Zonen sunshine duration sensors (Kipp & Zonen, Delft, The Netherlands) located in the most representative sites of Galicia. Moreover, 40 silicon cell sensor pyranometres (Skye Instruments LTD, UK), are installed in as many stations. These sensors are periodically cleaned and calibrated by specialized crew, following the manufacturer’s recommendations. Data are collected by dataloggers, sent to a central data server and stored in a database specifically designed for environmental data sets. Here, several filters are applied to ensure the data quality [10, 11].

image059

Fig. 1: Names and locations of the meteorological stations considered in this work, and location of the two pyranometers (at A Coruna and Vigo) used by Vazquez et al. [7].

As a part of the Solar Radiation subject’s programme, each student was required to choose one station between the 65 equipped with pyranometers and to analyse data between September 2006 and August 2007. The main features of these stations are listed on Table 1.

Data proceeding from every selected meteorological station have been processed to obtain monthly-averaged daily values of global irradiation, sunshine duration and clearness index. Measurements of precipitation, temperature and relative humidity have also been processed in order to complete the dataset for analysis.

Table 1: Main features of the meteorological stations applied in the analysis.

Code

Station

Latitude

Longitude

Altitude (m)

Environment

Manufacturer

C1

CIS Ferrol

43.49° N

8.2°

W

34

Suburban, Coastal

Schenk

C2

Sergude

42.82° N

8.46°

W

230

Rural, Inland

N. A.

C3

Rio do Sol

43.1° N

8.69°

W

540

Rural, Inland

Skye

C4

Marco Curra

43.34° N

7.89°

W

649

Rural, Inland

Schenk

C5

EOAS Santiago

42.87° N

8.57°

W

255

Urban, Inland

Schenk

C6

Olas

43.13° N

8.28°

W

401

Rural, Inland

Skye

C7

Serra Faladoira

43.59° N

7.79°

W

576

Rural, Coastal

Skye

C8

Fontecada

42.97° N

8.87°

W

369

Rural, Inland

Schenk

C9

Malpica

43.34° N

8.82°

W

161

Rural, Coastal

Schenk

L1

Courel

42.6° N

7.19°

W

777

Rural, Inland

Skye

L2

Foz

43.56° N

7.28°

W

73

Rural, Inland

Skye

L3

Penedo Galo

43.66° N

7.56°

W

545

Rural, Coastal

Schenk

L4

Burela

43.65° N

7.37°

W

421

Rural, Coastal

Skye

L5

Ancares

42.82° N

6.92°

W

1364

Rural, Inland

Schenk

L6

Boveda

42.65° N

7.47°

W

432

Rural, Inland

Schenk

L7

Pedro Murias

43.54° N

7.08°

W

51

Rural, Coastal

Schenk

L8

Abradelo

42.75° N

7.25°

W

826

Rural, Inland

Skye

L9

Portomarin

41.81° N

7.62°

W

447

Rural, Inland

Skye

P1

Cies

42.22° N

8.9°

W

25

Rural, Coastal

Skye

P10

Queimadelos

42.23° N

8.43°

W

371

Rural, Inland

Schenk

P11

Corrubedo

42.56° N

9.03°

W

30

Rural, Coastal

Schenk

P2

Coron

42.58° N

8.8°

W

14

Rural, Coastal

Schenk

P3

Pereira

42.63° N

8.32°

W

717

Rural, Inland

Skye

P4

Monte Aloia

42.08° N

8.68°

W

484

Rural, Inland

Schenk

P6

Lourizan

42.41° N

О

SO

SO

00

W

57

Urban, Coastal

Schenk

P7

Castro Vicaludo

42° N

8.86°

W

473

Rural, Coastal

Skye

P8

Serra do Faro

42.58° N

7.93°

W

991

Rural, Inland

Skye

P9

Rebordelo

42.47° N

8.5°

W

367

Rural, Inland

N. A.

R1

Baltar

41.95° N

7.71°

W

807

Rural, Inland

Skye

R2

Ourense

42.35° N

7.85°

W

167

Urban, Inland

Skye

R3

Invernadeiro

42.12° N

7.34°

W

1026

Rural, Inland

Schenk

R4

Monte Medo

42.23° N

7.63°

W

608

Rural, Inland

Skye

R5

Amiudal

42.42° N

8.24°

W

553

Rural, Inland

N. A.

R6

Xures

41.9° N

7.9°

W

1059

Rural, Inland

Schenk

Finally, monthly and yearly values of global solar irradiation measured in the meteorological stations have been compared with the results obtained by Vazquez et al. [7].

The clearness index, KT, has been evaluated by the ratio G/G0, where G is the ground measured irradiation and G0 is the extraterrestrial irradiation. For this purpose, a solar constant value of

Подпись: C9 Подпись: C3 image062 Подпись: P3 Подпись: C7, Подпись: -7.5 Подпись: R3 Подпись: I

1376 Wm-2 was adopted, as recommended by Davies [12]. Astronomical relationships were obtained following Iqbal [13].

image068 Подпись: 3100 3000 2900 2800 2700 2600 2500 2400 2300 2200 2100 2000 1900 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800 700 600 500 image070 Подпись: -9 image072 image073 Подпись: -7.5 Подпись: -7 Подпись: 7 3

Fig. 2: Annual mean values of daily global solar irradiation (kJm-2) distribution over the region. Squares show the locations of the stations selected by the students and applied in this analysis.

image077image078Fig. 3: Annual values of (a) precipitation (mm) and (b) mean relative humidity (%) over the region.

Data for every station were collected, joined together and interpolated using Kriging technique, in order to get appropriate maps for analysis. Software package SURFER (http://www. ssg- surfer. com/) provided graphical representation of these results.

2. Results

Discussion of the results, conclusions and future activities

As shown in figures 3 to 5 the presented MOS model improves considerably the output of the ARPS model simulation. Small amount of performance improvement may be obtained by the single convolution of each data block, instead of chaining, to avoid the boundary uncertainties at the borders of each of the data block on the training set (se section 4). However, to evaluate the operation of the statistical correction, the uncertainties under continuous boundary conditions have to be evaluated (see sections 3.2 and 5).

Furthermore, as the presented results are only based on simulated reanalysis data, they have to be still compared with the statistical corrections of ARPS simulations based on data of analysis, and forecast global simulations. The former is important to verify the performance loss for the analysis data. The latter is important to verify the statistical correction of both the analysis and the forecast uncertainties, since they appear in a combined form within the forecast results. Furthermore, actualizations of the NWP model may lead to additional uncertainties in the analysis and forecast corrections. With a forecast based on the reanalysis data, also named reforecast, these actualizations are avoided [12]. Additional performance improvement may be obtained by the inclusion of time series of other variables forecasted by the NWP [36]. Comparable to the MOS in [12], the presented MOS method DWT-ANN is only able to improve the forecasts at sites where measurements of the simulated variable are available. A solution for this problem is proposed in [36] with a site unspecific time series MOS, based on a wavelet model. This model may be applied with low uncertainties for the NWP output corrections of a limited region, as e. g. a city, where CSDHWS installations can be find in different locations.

Acknowledgements

The authors are indebted to the CAPES — Coordenagao de Aperfeigoamento de Pessoal de Nivel Superior for support to the present work and to Dr. Reinaldo Haas to place at disposal the simulated data using the ARPS model.

References

[1] Eletrobras, Programa National de Conservagao de Energia Eletrica (PROCEL) apresenta pesquisa sobre posse e uso de equipamentos eletricos. 2007, Noticias da Eletrobras, 18. 04. 2007 ,http://www. eletrobras. com. br/elb/portal/main. asp.

[2] Salazar, J. P., Economia de energia e redugao do pico da curva de demanda para consumidores de baixa renda por agregagao de energia solar termica, Dissertagao. Departamento de Engenharia Mecanica, Laboratorio de Energia Solar. 2004, Florianopolis: Universidade Federal de Santa Catarina.

[3] Colle, S., Glitz, K., Salazar, J. P., and S. L. Abreu. Cost Optimization of Low-Cost Solar Domestic Hot Water Systems Assisted by Electric Energy. in ISES Solar World Congress 2003. Goteburg, Sweden: ISES — International Solar Energy Society.

[4] Colle, S., Abreu, S. L., Glitz, K., and F. Colle. Optimization of the auxiliary heating and water storage insulation of a low cost domestic hot water heating system with an electric shower. in ISES — Solar World Congress. 2001. Adelaide — Australia.

[5] Salazar, J. P., Abreu S. L., Borges T. P. F, Colle S. Optimization of a compact solar domestic hot water system for low-income families with peak demand and total cost constraints. in Solar World Congress 2003. Goteborg, Sweden: ISES — International Solar Energy Society.

[6] Duffie, J. A. and W. A. Beckman, Solar engineering of thermal processes. 3rd ed. 2006, Hoboken, N. J.: Wiley Interscience, New York. 908.

[7] Mellit, A., M. Benghanem, and S. A. Kalogirou, An adaptive wavelet-network model for forecasting daily total solar-radiation. J. Applied Energy, 2006. 83(7): p. 705-722.

[8] Cao, J. and L. Xingchun, Study of hourly and daily solar irradiation forecast using diagonal recurrent wavelet neural networks. Energy & Conversion Management, 2008. 49: p. 1396-1406.

[9] Cao, S. and Cao J., Forecast of solar irradiance using recurrent neural networks combined with wavelet analysis. Applied Thermal Engineering, 2004. 25: p. 161-172.

[10] Lorenz, E., Methoden zur Beschreibung der Wolkenentwicklung in Satellitenbildern und ihre Anwendung zur Solarstrahlungsvorhersage, Ph. D. thesis. 2004, Carl von Ossietzky University, Faculty of Mathematics and Natural Sciences: Oldenburg, Germany. p. 111.

[11] Girodo, M., ed. Solarstrahlungsvorhersage auf der Basis numerischer Wettermodelle, Ph. D. thesis. ed. E. a.S. R.L. Faculty of Mathematics and Natural Sciences. 2006, Carl von Ossietzky University:

Oldenburg, Germany. 159 p.

[12] Hamill, T. M., Whitaker, J. S., Mullen S. L., Reforecasts, an important data set for improving weather predictions. Bulletin of the American Meteorological Society, 2005: p. 43.

[13] Guarnieri, R. A., Emprego de Redes Neurais Artificials e Regressao Linear Mhltipla no Refinamento das Previsoes de Radiagao Solar do Modelo Eta, Dissertagao. CPTEC-INPE. 2006, Sao Jose dos Campos (SP).

[14] Wilks, D. S., Statistical methods in the atmospheric sciences, in International Geophysics Series, Dep. of Earth and Atmospheric Sciences. 2006, Academic Press: Cornell University. p. 179-548.

[15] Libonati R., Trigo I., and C. C. DaCamara, Correction of 2 m-temperature forecasts using Kalman Filtering technique. Atmospheric Research, 2008. 87: p. 183-197.

[16] Julier, S. J., Uhlmann, J. K., A new extension of the Kalman Filter to nonlinear systems, in The Robotics Research Grou, Department of Engineering Science. 1997, University of Oxford: Oxford U. K.

[17] DeCruyenaere J. P. and H. M. Hafez. A comparison between Kalman filters and recurrent neural networks. in Neural Networks — IJCNN conference. 1992. Baltimore, MD, USA.

[18] Todini, E., Using phase-state modeling for inferring forecasting uncertainty in nonlinear stochastic decision schemes. J. Hydroinformatics, 1999. 1(2): p. 75-82.

[19] Addison, P. S., The illustrated wavelet transform handbook: Introductory theory and applications in science, engineering, medicine and finance. 2002, Institute of Physics Publ.: Bristol U. S.A. p. 353.

[20] Nanavati, S. P., Panigrahi, P. K., Wavelet transform: A new mathematical microscope. J. Resonance, 2004. 9(3): p. 50-64.

[20]Cohen, A., I. Daubechies, and J. C. Feauveau, Biorthogonal bases of compactly supported wavelets. J. Communications on Pure and Applied Mathematics, 1992. 55: p. 458-560.

[22] Souza, E. M., et al., Comparagao das Bases de Wavelets Ortonormais e Biortogonais: Implementagao, Vantagens e Desvantagens no Posicionamento com GPS. J. Mat. Apl. Comput., 2007. 8(1): p. 149-158.

[23] Renaud, O., J. C. Starck, and Murtagh F., Wavelet-based combined signal filtering and prediction. J. IEEE — Transactions on Systems, MAN and Cybernetics, 2005. 36(6): p. 1241-1251.

[24] Xia, X., D. Huang, and Jin Y. Nonlinear adaptive predictive control based on orthogonal wavelet networks. in Proceedings of the 4th World Congress on Intelligeut Control and Automation. 2002. Shanghai, China IEEE.

[25] Goswami, J. C. and C. A. K., Fundamentals of Wavelets ed. I. John Wiley & Sons. 1999, New York. 319.

[26] Daubechies, I. Ten lectures on wavelets. 1992. Philadelphia,: Regional Conferences Series in Applied Mathematics SIAM.

[27] Alsberg, B. K., et al., Variable selection in wavelet regression models. Analytica Chimica Acta, 1998. 368(1): p. 29-44.

[28] Tsay, R. S., Analysis of financial time series — Financial econometrics. 2002, John Wiley & Sons, INC. p. 457p.

[29] Kratzenberg, M. G. and C. S. Selegao da transformada de wavelet para a corregao estatistica da previsao da radiagao sola. in II Congresso Brasileiro de Energia Solar e III Conferencia Regional Latino- Americana da ISES. 2008 b. Florianopolis — Brazil.

[30] Haykin, S. S., Neural networks: A comprehensive foundation. 1994, New York, Toronto: Maxwell Macmillan International. xix, 696 p.

[31] Kipp&Zonen, Instruction manual — CM11 pyranometer. 1999, Delft, Holland. 63.

[32] Younes, S., R. Claywell, and T. Muneer, Quality control of solar radiation data: Present status and proposed new approaches. J. Energy, 2005. 30(9): p. 1533-1549.

[33] Abreu, S. L., Colle, S., and A. P. Almeida, Mantelli, S. L.N. Qualificagao e recuperagao de dados de radiagao solar medidos em Florianopolis — SC. in ENCIT — VIII, Encontro Nacional de Ciencias Termicas. 2000. Porto Alegre, Brazil.

[34] Kaastra, I. and M. Boyd, Designing a Neural Network for Forecasting, Financial and Economic Time Series. Neurocomputing, 1996. 10: p. 215-236.

[35] Mantelli, S. L.N., E. B. Pereira, and C. Thomaz. J. C. J., S. Sistema de Organizagao Nacional de Dados Ambientais para o setor de energia. in SNPTEE Seminario Nacional de Produgao e Transmissao de Energia Eletrica, Grupo de estudo de impactos ambientais. 2007. Rio de Janeiro, Brazil.

[36] Kratzenberg, M. G., Corregao estatistica a base da transformada wavelet para previsao de energia solar atraves de modelo numerico meteorologico, Exame de Qualificacgao de Doutorado, D. d.E. M. Universidade Federal de Santa Catarina, Editor. 2008 a: Florianopolis. p. 69.

Ordinary kriging model evaluation

Подпись: Fig. 3. June and October H maps based on the ordinary kriging method on a 1 km x 1 km grid.

Validation dataset results showed, overall, that the ordinary kriging is able to provide fair estimates. Error values present a seasonal pattern: the summer months shows the lowest RMSE values (in percentage) and the winter months the highest ones. For instance, in October RMSE is 1.44 MJ m-2day-1 (11.21%) and for June RMSE is 1.63 MJ m-2day-1 (6.20%). The MAE values ranges from 0.26 MJ m-2day-1 (2.6%) in February to 0.78 MJ m-2day-1 (6%) in October. Additionally, the ordinary kriging estimates shows scarce bias, being the ME values almost negligible for almost all the months. Only for November, a slight overestimation is found. Values of R2 range from 0.9 in December to 0.96 in June. Figure 3 shows the estimated H maps of June and October based on the ordinary kriging procedure.

Reference values for cloud reflectivity

The cloud reflectivity pc also depends on the sun-satellite geometry. Therefore, different values of pc are calculated using histograms of reflectivity values for classes with similar geometric configurations. Fig. 2 illustrates the approach to assign the cloud reflectivity to each class: The measured histogram is fitted by a superposition of two functions, the first is representing the ground reflectivity distribution fitground and the second the cloud reflectivity distribution fitcioud. As cloud reflectivity we chose a value close to the reflection point (Pdoud , a*max(fitcioud)).

Methods for analysis and results

1.1. Atmospheric gases

Firstly, one calculates Ig0 which is the SSI for a clear atmosphere containing none of the six gases nor aerosol. Attenuation in this case is due to the rest of molecules in the atmosphere, which is called background Mbg. Secondly, one computes the clearness index KT0 which is the ratio of Ig0 to the extraterrestrial irradiance I0. Then, one varies the amount of a molecule M in the atmosphere and maintains to zero the other quantities. M will be successively H2O, O3, CO2, O2, CH4, and N2O, thus leading to SSI IgM. The ratio of IgM to I0 gives the clearness index KTM+ for the molecule Mplus Mbg. Since the transmittance of several gases is obtained by multiplying the transmittances of each gas, the clearness index due to the single molecule M is given by:

Подпись:KTM = KTM+ / KT0

Подпись: 0 Подпись: 0 Подпись: 4 image137

We observe an important variation of the transmittance with molecule and wavelength. Changes in quantities of O2, CO2, CH4, and N2O create a variation of transmittance of the atmospheric column less than 1 / 10000 for all wavelengths. We can thus conclude that changes in these quantities have a negligible effect on radiation. The transmittance of O3 is almost zero for wavelengths less than 0.3 pm. Its change is large in the region [0.31 pm, 0.33 pm] (more than 0.2) and is about 0.02 in the region [0.52 pm, 0.68 pm]. Regarding water vapour, the variation of transmittance which change in content is important in the region [0.57 pm, 4 pm] (Fig. 1 left). In addition, the influence of the atmosphere profile on the range of variation is significant ; the errors committed on the SSI if one does not take the right atmospheric profile are shown in Fig. 1 right.

Figure 1. Spectral transmittance of H2O (on left) for different water content (in kg m-2) and relative error due to
atmosphere profile (on right); the reference model is afglus. Calculations for Kato bands.

1.2. Aerosols

For assessing the deviation on the SSI induced by deviation of the properties of aerosols, one computes the SSI of reference Iaref with the aerosol optical thickness at 550 nm Taer 550 set to 0.1, a to 1.5 and the aerosol types to haze 1 and vulcan 1 and season 1. Then these parameters are changed and one computes the absolute deviation of the SSI to the reference case.

image138
image139

Fig. 2 (left) shows the influence of aerosol optical thickness on the SSI. The deviation due to a is large (up to 20% of deviation on the SSI for a = 2) and decreases as the wavelength increases. As a increases, the SSI decreases. The influence of aerosol optical thickness at 550 nm is similar. Then, aerosol type is changed from haze 1 to haze 4, haze 5 and haze 6, vulcan 1 to vulcan 2, vulcan 3 and vulcan 4 and season 1 to season 2. The influences of the models vulcan and season are very low: the absolute deviations on the SSI are below 0.5%. Fig. 2 (right) shows the influence of the aerosol types on the SSI. The deviation due to model haze (on right) is less important than that due to the aerosol optical thickness and reaches 3 %.

Figure 2. Absolute deviation on spectral irradiance in comparison to the reference case. Solar zenith angle
(30°), water content (15 kg m-2), ozone amount (300 DU) and ground albedo (0). haze 1, 4, 5 and 6 respectively
means rural, marine, urban and tropospheric aerosol type from 0 km to 2 km altitude.

1.3. Cloud

We compute the spectral transmittance of clouds in the same way than the gas transmittances (Fig. 3). An increase in tc leads to a large decrease in cloud transmittance and consequently in the SSI. This decrease is wavelength-dependent. For tc greater than 15, cloud transmittance is very small or null for wavelengths greater than 2 pm. For the same tc, attenuation of radiation is stronger for water cloud than for ice cloud. The decrease in direct SSI is more marked than that in diffuse SSI; the direct SSI normal to sun rays reaches zero for tc around 7.

image140

1st International Congress on Heating, Cooling, and Buildings — 7th to 10th October, Lisbon — Portugal /

Figure 3. Change in spectral transmittance of clouds with tc. Water cloud, ztop = 5 km, zbot = 2 km, ref = 10 pm.

To assess the influence of ztop and zbot on the SSI, we use the typical values given by Liou (1976) for different types of clouds. Fig. 4 shows the variation of cloud transmittance with ztop and zbot as the function of tc. All curves are superimposed: the maximum difference in transmittance is equal to 0.01 for albedo 0. The influence of ztop and zbot on the SSI is negligible; this is true for other albedos. Similar results are obtained with the ice cloud. Our results are similar to those of Kuhleman and Betcke (1995).

Подпись:zbot=0, ztop=1 zbot=2, ztop=3 zbot=3, ztop=8 zbot=4, ztop=7 zbot=1, ztop=4 zbot=2, ztop=6 zbot=1, ztop=7 zbot=2, ztop=10