Comments on “POTSOL: Model to predict extraterrestrial and clear sky solar radiation” and “Ground level solar radiation prediction model including cloud cover effects”

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  • Solar Energy Vol. 37, No. 4, pp. 319-321, 1986 0038-092X/86 $3.00 + .00 Printed in the U.S.A. 1986 Pergamon Journals Ltd.

    L E T T E R S T O T H E E D I T O R

    Comments on "POTSOL: Model to predict extraterrestrial and clear sky solar radiation" and "Ground level solar radiation prediction model including cloud

    cover effects"

    (Received 7 June 1985)

    Dear Sir: Two companion papers by Brinsfield et al. were re-

    cently published in Solar Energy[l, 2]. It appears that the models (POTSOL and ESR) proposed by these authors use extensively the algorithm first published by ASHRAE in 197113] and in a modified form in 197614].t The origi- nality of such a limited rephrasing of an old and well- known model appears to me questionable, inasmuch as this ASHRAE algorithm was found to have limitations[5], to perform poorly in Canada[6, 7] and to perform poorly in some U.S. stations[8, 9]. Of course, this model is per- fectible, as shown in [9], but some of the problems I point out below will address the questions whether or not the slight changes on the original algorithm proposed in [I, 2] are going in the right direction and whether or not the resulting model has a reliable background with regard to present knowledge.

    My specific comments are as follows: (1) In eqn (8) of [1], it appears that the clearness

    index, CN, has an exponent 1 on the denominator. This is surprising, as in [3] and [4], it has an exponent 2, while in the regular editions of the ASHRAE Handbook[10], it has an exponent 0. It might have been better if ASHRAE had decided from the beginning which exponent is the right one for this important equation. Maybe Brinsfield et al. (hereafter " the authors") chose a logical median way, but this should have been substantiated.

    (2) Equation (8) in [1] is based on the work of Ste- phenson[l l ] , stating that the diffuse component is pro- portional to the direct normal one (ld = Cla,). This result was deduced from the analysis of a limited set of data (20 clear days) for only one site (Toronto, Canada). As an attempt to verify the validity of this equation, I used three years (1973-75) of carefully recorded data of global and diffuse radiation in Montreal, Canada. I computed the ratio la/la, whenever clear sky conditions were estab- lished for the hour (i.e. zero cloud cover and 100% bright sunshine). The results show that the values of C provided by Stephenson and ASHRAE only pertain to low turbidity (i.e. high visibility) conditions. This was to be expected because Stephenson sought to determine "design values" of solar irradiation and selected only the clearest days for his analysis. During summer, high turbidity conditions (generally associated with maritime tropical air masses) are frequent in Montreal. At those times, the observed value of C may be as much as six times the proposed value. This high dependence of C on turbidity is consistent with results obtained with a physical radiation model[12]. As turbidity may vary greatly from one day to another and from one North American region to another for obvious climatological reasons, a more detailed study should be done in order to improve Stephenson's equation and make it really valid throughout the continent.

    (3) Concerning the diffuse sky radiation, the authors state on p. 486 [I] that: "The theory of radiation scattering is rather involved and currently no theoretical method for

    ? Note that this latter report was edited by T, Kusuda, not "Kusada" as systematically misspelled in [1, 2].

    determining diffuse sky radiation is known." The second part of this assertion is inexact, or at least incomplete and misleading. Highly sophisticated theoretical models exist (e.g. [13]), as well as a lot of more simple (nonspectral) physical ones (see, for example, the discussions in [12, 14, 15]).

    (4) Table 1 in [1] gives "statistical results comparing daily paired totals of potential radiation calculated with POTSOL with observed values." I cannot imagine how daily totals of extraterrestrial (or potential in the authors' words) radiation could have been measured in Ely (Ne- vada) during one year. A possible explanation is that these "observed values" are in fact precalculated--by means of standard equations--values of extraterrestrial irradia- tion, in which case Table I would be void of sense.

    (5) In POTSOL[I], the diffuse radiation is treated as isotropically emanating from the sky. A more physically sound anisotropic method is used in the original algo- rithm[3, 4], taking into account the angle of incidence of la, on the surface. This procedure has an experimental background and it was verified to be very precise on clear sky condit ions[l@

    (6) In the cloudy part of the model[2], the authors argue (p. 495) that eqn (6)--first proposed in [17J--is gen- erally not utilizable in the United States, because detailed (layer by layer) cloud cover is only available at a limited number of sites. In fact, (6) was only provided in [17] in order to estimate TOCC (the total opaque cloud cover or "opaci ty") from TCA (the total cloud amount) whenever the former parameter is not available. Thus the authors finding that "TOCC provided a better estimation than TCA" was to be expected. The remaining question is why it is stated in [17] that opacity was not available in the United States, while Bennett[18] at the same time used this parameter and noted that it was a "neglected vari- able," though available together with total sky cover at 266 U.S. stations.

    (7) Equation (11) in [2] appears to use one set of coefficients that are the averages of the four sets provided in the original research [17]. These coefficients were them- selves obtained by regression from only four months of data in Ottawa, Canada, and their validity in other con- ditions is questionable. Averaging such empirical coeffi- cients may further degrade the precision of the model. Another surprising consequence of the use of (i 1) is that the cloud cover factor, CCF- - to be applied to the clear sky global radiation--is strictly superior to l for a cloud cover CC of 0 to 3 tenths. For the climate of Ottawa, such a finding may eventually be justified during summer, in the particular case when cumulus clouds are forming a "'tunneling" effect. But such an occurrence is rare during winter, so in this latter case we should have CCF < 1 for CC > 0. Looking back at the four sets of coefficients pro- vided in [17], it appears that the above-mentioned equation is combining the cloud cover attenuation and a climato- logical correction for other atmospheric effects (turbidity, water vapor). As pointed out in [5], this latter correction is rather in conflict with the clearness number. In other words, a further analysis should have been done by the


  • 320 Letters to

    ASHRAE or its followers before directly merging the con- cepts of a clearness number[19] and a cloud cover fac- tor[17] into a model that finally turns out to be rather hy- brid and difficult to interpret (see also comments (1) and (6)).

    Furthermore, it should be noted that the accuracy of any radiation model is directly related to the sophistication of the way it details cloud attenuation. For example, monthly and regional sets of coefficients are part of the Won's model[6, 20], and this is probably one main reason why it was shown to perform significantly better than the ASHRAE algorithm in Canada[6, 7].

    (8) On p. 497[2], the authors argue that the cloud observations at Salisbury, Maryland, "are made on a somewhat subjective basis." This unsubstantiated state- ment is surprising, as such a type of observation is sub- jective by nature. (Should we conclude that the observers at Salisbury are not doing their job properly?)

    (9) The authors chose to exclude the hourly values of radiation from the possible outputs of their ESR model[2]. Considering that the model needs hourly values of sky cover as input, this important restriction curiously is not explained. By comparison, the original ASHRAE algorithm is used to output hourly results as needed for engineering calculations and simulation programs. Radia- tion values for particular days are far less useful, unless a special application is considered, but such a case has not been mentioned by the authors.

    If only mean daily values (over one month or on a long- term basis) are needed, a lot of existing simpler models can give comparable results, without the trouble of using expensive data tapes and computer time.

    (10) No provision is made in the ESR model[2] to compute the cloudy radiation on tilted surfaces, though this is most important for solar applications. This is an omission with reference to the ASHRAE algorithm, but in this particular case, it is rather fortunate as a physical flaw has been discovered in it, leading to considerable overestimations during overcast conditions in winter[16, 211.

    ( l l ) The authors conclude on p. 497[2] that " the model ESR provides an excellent method for predicting solar radiation on a horizontal s u r f a c e . . . " and that " the model can serve as a valuable tool in assessing the fea- sibility of solar energy collection systems . . . . " In view of the comments above and below, these conclusions look incorrect or at least questionable.

    The term "excel lence" probably means "exception- ally reliable" and/or "more accurate than other models" in the authors' minds. The latter qualification has not been addressed at all in [l, 2], and the former one appears to me far from being established in view of the following points.

    (12) The authors generally quantify the performance of the ESR model in terms of the correlation coefficient between calculated and measured data. However, a very high degree of correlation may be obtained if calculated results are s t rongly--but systematically--either overes- timated or underestimated. More significant--though sim- p le -s ta t i s t ica l tests would have been the mean bias error and the RMS error, thus permitting quantitive compari- sons with published results of other models.

    (13) Only two sites have been retained for validation purpose in [1, 2]. One of them (Ely, Nevada) has a par- ticularly uncloudy climate. This situation is withdrawing the main cause of inaccuracy in the radiation prediction. So any model should perform well in such conditions. With this in mind, the scattering of data points which is apparent in Fig. 2[2] looks too important and should at least be explained.

    (14) Only the global daily irradiation received by a horizontal plane, as calculated by ESR, is subjected to a l imited--see the two comments above--validation effort. This looks rather insufficient for most solar energy appli-

    the Editor

    cations, where direct and diffuse components have to be known independently and precisely on horizontal as well as inclined planes.

    At this point, I have a strong doubt that POTSOL and ESR may bring any substantial improvement over the ex- isting models of the same type. The solar scientific com- munity do need state-of-the-art radiation models that may effectively be appreciated as "excellent" and "valuable tools." However, it is my opinion that such a result cannot be obtained without a preliminary systematic scrutiny of the basic equations used for their derivation.

    Hello-Science 1215 Preston Avenue Sillery, Quebec, Canada G1S 4L1



    1. R. Brinsfield et al., POTSOL: Modv: .o predict ex- traterrestrial and clear sky solar ra~itation. Solar En- ergy 33, 485-492 (1984).

    2. R. Brinsfield et al., Ground level solar radiation pre- diction model including cloud cover effects. Solar En- ergy 33, 493-499 (1984).

    3. M. Lockmanhekim (ed.), Procedures for Determining Heating and Cooling Loads for Computerized Energy Calculations. ASHRAE, New York (1971).

    4. T. Kusuda (ed.), Procedure for Determining Heating and Cooling Loads for Computerized Energy Calcu- lations. ASHRAE, New York (1975). See also: T. Ku- suda, NBSLD, the computer program for heating and cooling loads in buildings. NBS Rep. BSS69, National Bureau of Standards, Washington, DC (1976).

    5. E. F. Sowell, The use and limitations of ASHRAE solar algorithms in solar energy utilization studies. ASHRAE Trans. 84, 77-93 (1978).

    6. F. C. Hooper et al., Define, develop and establish a merged solar and meteorological computer data base. Canadian Climate Centre Rep. 80-8, AES, Downs- view, Ontario (1980).

    7. C. Gueymard et al., lnventaire et validation des mo- dules de calcul du rayonnement solaire au Quebec en rue des applications 6nerg~tiques. Ministry of Energy and Resources, Quebec (1983).

    8. G. L. Powell, A comparative evaluation of hourly solar global irradiation models. Ph.D. thesis, Arizona State University (1980).

    9. G. L. Powell, The ASHRAE clear sky model - -An evaluation. ASHRAE J. 11, 32-34 (1982).

    10. ASHRAE, Handbook of Fundamentals. American Society of Heating, Refrigerating and Air Condition- ing Engineers, New York (1972, 1977, 1981).

    11. D. G. Stephenson, Equations for solar heat gain through windows. Solar Energy 9, 81-86 (1965).

    12. C. Gueymard, Modrlisation physique du rayonne- ment solaire basre sur les donnres mrt~orologiques horaires. Proc. AFME Conference Meteorology and Renewable Energies, Valbonne, France (1984).

    13. N. Braslau and J. V. Dave, Effect of aerosols on the transfer of solar energy through realistic model at- mospheres. J. Appl. Met. 30, 601-619 (1973).

    14. C. Gueymard and N. Galanis, Sur le calcul du ra- yonnement solaire au Quebec. I. Mrthode de classi- fication des modules. Proe. SESCI Conference, Mon- treal, pp. 358-363 (1981).

    15. J. A. Davies et al., Estimating solar irradiation on hor- izontal surfaces. Int. J. Solar Energy 2, 405-424 (1984).

    16. C. Gueymard, Radiation on tilted planes: A physical model adaptable to any computational time-step. In lntersol 85 Congress of ISES, Montreal, Pergamon Press, Elmsford, NY (1985).

    17. K. Kimura and D. G. Stephenson, Solar radiation on cloudy days. ASHRAE Trans. 75, 227-233 (1969).

  • Letters to the Editor 321

    18. 1. Bennett, Correlation of daily insolation with daily total sky cover, opaque sky cover and percentage of possible sunshine. Solar Energy 12, 391-393 (1969).

    19. J. L. Threlkeld and R. C. Jordan, Direct solar radia- tion available on clear days. ASHRAE Trans. 64, 45- 68 (1958).

    20. T. K. Won, The simulation of hourly global radiation from hourly reported meteorological parameters--

    Canadian prairie area. Paper E40-M, Proc. Third SESCI Conference, Edmonton, Alia (1977).

    21. C. Gueymard, Utilisation des donn6es m6t6orolo- giques horaires pour le calcul du rayonnement solaire sur des surfaces inclin6es. Applications/i la simulation thermique des b~timents solaires passifs (with English abstract). Ph. D. thesis, University of Montreal (1983).

    Reply to "Comments on POTSOL: Model to predict extraterrestrial and clear sky solar radiation and ground level solar radiation prediction model including

    cloud cover effects"

    Dear Sir: We welcome the comments and questions of Christian

    Gueymard concerning the recently published papers in Solar Energy[l, 2]. Although the models propose limited changes to the original algorithm, the use of our versions has been widely accepted.

    The following are specific responses to selected com- ments by Christian Gueymard. In response to comment (1), eqn (8) of [1] was developed by Imamura, et al.[3] as follows:

    ld = C I ( c r ) / C N 2,


    Itcr) = CNlp e x p [ - ~ sec (0o)].


    la = C[CNIv e x p [ - , sec (Oo)]/CN 2

    o r

    Id = (C/CN)lp e x p [ - x sec (0o)].

    In response to comment (2), we agree that a more detailed study should be implemented to improve on the work of Stephenson, but such a study was beyond the scope of these papers. In response to comment (4), the "calculated values" were part of a data tape obtained from the Na- tional Climatic Center. Table 1 of [1] was included simply to show that the results for the site using our model agreed with the precalculated values.

    In response to comment (7), justification in using av- erage values for eqn (11) in [2] is supported by Imamura, et al.[3], Appendix A, p. 18: "Test runs were made using both seasonal P, Q and R's and the average P, Q and R's. In terms of yearly integrated solar irradiance, the differ- ence between the results was insignificant,"

    In response to comment (8), an interesting fact about

    the Salisbury data is the low number of observations in- dicating 10% covered skies and 90% covered skies. The authors believe that the low number of observations in classes next to the two extremes of the data range is due to observational bias. An interview with the observers at Salisbury airport, where the cloud cover data were col- lected, reveals that observers may tend to enter 90% cov- ered skies as totally overcasted (100% covered), since from a pilot's viewpoint a cloud cover of 9 or 10 is basically the same. Similarly, the observers may enter 10% covered skies as totally clear. For a more detailed analysis, see Yaramanoglu, et al. [4].

    In response to comment (9), the model is fully capable of providing hourly outputs. Daily totals were reported simply because that data base was available for both Sal- isbury and Ely.

    Department o f Agricultural Engineering University o f Maryland RUSSELL BRINSFIELD Queenstown, MD 21658 U.S.A.

    Department of Agricultural Engineering University o f Maryland MELIH YARAMANOGLU College Park, MD 20740 FREDRICK WHEATON U.S.A.


    1. R. Brinsfield, et al., POTSOL: Model to predict ex- traterrestrial and clear sky solar radiation. Solar En- ergy 33, 485-492 (1984).

    2. R. Brinsfield, et al., Ground level solar radiation pre- diction model including cloud cover effects. Solar En- ergy 33, 493-499 (1984).

    3. M.S. Imamura, et al., Definition Study for photovoltaic residential prototype system. U,S. Department of Commerce Report No. N77-13533 (1976).

    4. M. Yaramanoglu, et al., Estimation of solar radiation using stochastically generated cloud cover data. Energy Agriculture 4, 227-242 (1985).


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