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Comments on paper by Gordon, Govaer and Zarmi
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LETTERS TO THE EDITOR Comments on Paper by Gordon, Govaer and Zarmi Dear Sir, In the paper entitled "The Utilizability Method with Hourly vs Daily Insolation Data" (Solar Energy 27, 99-102), the authors conclude that the application of the Liu and Jordan (Ref. [2]) generalized utilizability method with daily rather than hourly, radiation data can lead to a significant error in the predicted useful energy collection. They imply that the Liu and Jordan utilizability curves are in error since they were developed from daily data. The authors' conclusion has resulted from a misuse of the Liu and Jordan method. The following points should be noted. 1. Although the Liu and Jordan utilizability curves were developed from daily data, they were intended to be used only on an hourly basis. The authors' definition of X~ in the introduction as "the threshold (radiation level) divided by the average insolation over the period under consideration (e.g. month, year, etc.)" is incorrect. For proper application of the Liu and Jordan utilizability method, Xc must be defined as the threshold radiation level divided by the monthly-average hourly solar radiation for the hour in question. To obtain the monthly-average daily utilizable radiation, it is necessary to sum the hourly contributions. (Reference[3] describes a method to determine the monthly-average daily utilizable radiation with a single calculation.)
2. Although the Liu and Jordan method must be applied on a monthly-average hourly basis, it is not necessary to have hourly data. In Fig. 3 of their 1963 paper, Liu and Jordan provide a graph of the ratio of monthly-average hourly to daily radiation versus the number of hours from sunrise to sunset and the number of hours from solar noon. The information in this graph was later fit with an analytical expression by Collares-Pereira and Rabl (Solar Energy 22, 155-164). 3. All of the figures in the paper show annual results. In addition, values of the clearness index Kr, are given only for the year. It appears as if the authors have applied the Liu and Jordan method once to obtain annual results rather than summing the 12 monthly results. Because of the geometry factors which need to be evaluated, both the Liu and Jordan method and the method in Ref. [3] should be used on a monthly basis only.
Solar Energy Laboratory University of Wisconsin-Madison U.S.A.
S. A. KLEIN
*References appear in original paper.
Reply to S. A. Klein's Comments Dear Sir, Re S. A. Klein's letter commenting on "The Utilizability Method With Hourly vs Daily Insolation Data", Solar Energy 27, 99 (1981). The main point of our paper was to indicate and explain the significant differences in utilizability curves calculated on a daily as opposed to an hourly basis. The results and conclusions we presented are correct. Klein is correct of course in the points made in his letter. Although l.Ju and Jordan developed their correlations from daily data (Ref. [1, 2]), those correlations were intended to be used on an hourly basis only. We regret that our presentation may lead the reader to conclude that Liu and Jordan calculated utilizability curves incorrectly.
We simply took advantage of the correlations developed by Liu and Jordan (Refs.[l,2D and by Bendt et al. (Ref.[5]) for daily insolation to generate daily utilizability curves. As pointed out in our paper, these daily utilizability curves are not the correct way to calculate the utilizable energy delivered by a solar collector, and the quantitative differences relative to the correct hourly calculation are presented therein.
Applied Solar Calculations Unit Blaustein Institute for Desert Research Ben-Gurion University of the Negev Sede Boqer Campus Israel
87
J. M. GORDON D. GOVAER Y. ZARMI
O038-092Xlg210700~7-Ol$03.0010
Printed in/3reat gr~ta;n.
Pergamon Press Lid.
LETTERS TO THE EDITOR Comments on Paper by Gordon, Govaer and Zarmi Dear Sir, In the paper entitled "The Utilizability Method with Hourly vs Daily Insolation Data" (Solar Energy 27, 99-102), the authors conclude that the application of the Liu and Jordan (Ref. [2]) generalized utilizability method with daily rather than hourly, radiation data can lead to a significant error in the predicted useful energy collection. They imply that the Liu and Jordan utilizability curves are in error since they were developed from daily data. The authors' conclusion has resulted from a misuse of the Liu and Jordan method. The following points should be noted. 1. Although the Liu and Jordan utilizability curves were developed from daily data, they were intended to be used only on an hourly basis. The authors' definition of X~ in the introduction as "the threshold (radiation level) divided by the average insolation over the period under consideration (e.g. month, year, etc.)" is incorrect. For proper application of the Liu and Jordan utilizability method, Xc must be defined as the threshold radiation level divided by the monthly-average hourly solar radiation for the hour in question. To obtain the monthly-average daily utilizable radiation, it is necessary to sum the hourly contributions. (Reference[3] describes a method to determine the monthly-average daily utilizable radiation with a single calculation.)
2. Although the Liu and Jordan method must be applied on a monthly-average hourly basis, it is not necessary to have hourly data. In Fig. 3 of their 1963 paper, Liu and Jordan provide a graph of the ratio of monthly-average hourly to daily radiation versus the number of hours from sunrise to sunset and the number of hours from solar noon. The information in this graph was later fit with an analytical expression by Collares-Pereira and Rabl (Solar Energy 22, 155-164). 3. All of the figures in the paper show annual results. In addition, values of the clearness index Kr, are given only for the year. It appears as if the authors have applied the Liu and Jordan method once to obtain annual results rather than summing the 12 monthly results. Because of the geometry factors which need to be evaluated, both the Liu and Jordan method and the method in Ref. [3] should be used on a monthly basis only.
Solar Energy Laboratory University of Wisconsin-Madison U.S.A.
S. A. KLEIN
*References appear in original paper.
Reply to S. A. Klein's Comments Dear Sir, Re S. A. Klein's letter commenting on "The Utilizability Method With Hourly vs Daily Insolation Data", Solar Energy 27, 99 (1981). The main point of our paper was to indicate and explain the significant differences in utilizability curves calculated on a daily as opposed to an hourly basis. The results and conclusions we presented are correct. Klein is correct of course in the points made in his letter. Although l.Ju and Jordan developed their correlations from daily data (Ref. [1, 2]), those correlations were intended to be used on an hourly basis only. We regret that our presentation may lead the reader to conclude that Liu and Jordan calculated utilizability curves incorrectly.
We simply took advantage of the correlations developed by Liu and Jordan (Refs.[l,2D and by Bendt et al. (Ref.[5]) for daily insolation to generate daily utilizability curves. As pointed out in our paper, these daily utilizability curves are not the correct way to calculate the utilizable energy delivered by a solar collector, and the quantitative differences relative to the correct hourly calculation are presented therein.
Applied Solar Calculations Unit Blaustein Institute for Desert Research Ben-Gurion University of the Negev Sede Boqer Campus Israel
87
J. M. GORDON D. GOVAER Y. ZARMI