Volume 9
Issue 4
Forestry
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Available Online: http://www.ejpau.media.pl/volume9/issue4/art28.html
MULTIANNUAL VARIATION OF THE EFFECTIVE SUNSHINE DURATION IN THE BESKID SADECKI MOUNTAINS
Grzegorz Durło
Chair of Forest Protection and Forest Climatology,
University of Agriculture in Cracow, Poland
A longterm variation of effective sunshine duration in the Beskid Sadecki Mountains during 1971–2005 is presented. It is based on measurement and observation data from six meteorological stations situated in this area, and representing the convex and concave terrain forms, situated at height 300–1100 m above sea level. The longterm mean annual sum of the effective sunshine duration was 1861 hours with deviation of 203 hours, which made 44% of the potential insolation in this part of the Carpathians. The highest longterm mean monthly sum of the effective sunshine duration in the Beskid Sadecki mountain range falls on August, amounting to 225 hours, and the lowest falls on December – 70 hours. General solar qualities of the Beskid Sadecki belong to very favorable ones. The comparison of results of this study with results of studies carried out during 1950–1970 indicated a visible improvement of solar conditions, especially in spring, i.e. April and May. On the basis of the forecast of the actual insolation in the Beskid Sadecki made on the basis of data for the period 1971–2005 no conclusion about a directional change of this element may be made with a required accuracy.
Key words: actual insolation, trend, Beskid Sadecki Mts.
INTRODUCTION
The longterm measurements series of the effective sunshine duration for the Polish Carpathians are rare. Very sporadic networks of actinometric stations in southern Poland, and a lack of synchronous measurement series, hinder a detailed elaboration of this element for a larger area [6,7,9,12]. On the other hand, the interest in solar energy in connection with observed and forecasted climatic changes in Europe becomes larger and larger. Apart from the obvious role played by the direct solar radiation in life of plants and man, there are possibilities of its utilization for the energetic purposes, alternatively to exploitation of natural resources. The increase of insolation, observed in last years, justifies the undertaking of research on the climatic potential of the Beskids in the aspect of utilization of solar energy in agriculture and forestry [9,16].
The aim of this study was to determine the variation of the effective sunshine duration in the Beskid Sadecki Mts. on the basis of the longterm measurements and observations conducted at meteorological stations situated in this area.
MATERIALS AND METHODS
The material for this study consisted of results of measurements of the effective sunshine duration gathered at the meteorological station of the Institute of Meteorology and Water Management in Nowy Sacz, as well as results of observations on the cloud cover carried out by the meteorological station of the Jaworzyna Krynicka, Muszyna, Piwniczna, Krynica Zdrój and phytoclimatological station of Agricultural University of Cracow, situated in Mochnaczka Wyżna. Detailed data concerning the location of these stations are in table 1.
Table 1. The characterisation of meteorological station localization in Beskid Sadecki Mts. region 
Station 
Altitude a.s.l. 
Latitude 
Longitude 
Landform 
Nowy Sacz 
293 
49° 27’ 
20° 42’ 
concave 
Jaworzyna Krynicka 
1113 
49° 41’ 
20° 89’ 
convex 
Muszyna 
445 
49° 21‘ 
20° 53‘ 
concave 
Piwniczna 
379 
49° 26‘ 
20° 42‘ 
concave 
Mochnaczka Wyżna 
720 
49° 27’ 
20° 58’ 
convex 
Krynica Zdrój 
582 
49° 25’ 
20° 58’ 
concave 
The measurements of the actual insolation were conducted at the station in Nowy Sacz during 1971 – 2005 using the CambellStokes heliograph placed 200 cm above the ground. The observations on the cloud cover were conducted at six stations in III climatological observation times, namely: 6:00, 12:00 and 18:00 (UTC). A longterm variation of the effective sunshine duration in the Beskid Sadecki Mountains, presented in this paper, was calculated on the basis of the 24hour sums of insolation obtained from the Nowy Sacz meteorological station, and mean 24hour values of the cloud cover from the six meteorological stations. To calculate the effective sunshine duration on the basis of daily values of the cloud cover the values of coefficients according to Kozmiński and Michalska [10] and formula (1) were used (tab. 2).
(1) 
where: U_{Rz} – effective sunshine duration; N – cloudiness; U_{M }– maximum potential sunshine duration.
Table 2. The relative sunshine duration for 10 gradual scale of cloudiness [8] 
Cloudiness 
Relative sunshine duration 

0.0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 

1 
0.945 
0.939 
0.933 
0.927 
0.921 
0.915 
0.908 
0.901 
0.894 
0.887 
2 
0.880 
0.873 
0.866 
0.859 
0.852 
0.845 
0.837 
0.829 
0.821 
0.813 
3 
0.805 
0.797 
0.789 
0.781 
0.773 
0.765 
0.756 
0.747 
0.738 
0.729 
4 
0.720 
0.711 
0.702 
0.693 
0.684 
0.675 
0.665 
0.655 
0.645 
0.635 
5 
0.625 
0.615 
0.606 
0.595 
0.585 
0.575 
0.564 
0.553 
0.542 
0.531 
6 
0.520 
0.509 
0.498 
0.487 
0.476 
0.465 
0.453 
0.441 
0.429 
0.417 
7 
0.405 
0.393 
0.381 
0.369 
0.357 
0.345 
0.332 
0.319 
0.306 
0.293 
8 
0.280 
0.267 
0.254 
0.241 
0.228 
0.215 
0.201 
0.187 
0.173 
0.159 
9 
0.114 
0.129 
0.114 
0.099 
0.084 
0.069 
0.051 
0.039 
0.024 
0.008 
In order to determine a multiannual variation of heliographic conditions the index values for monthly, seasonal, and annual periods were utilized. For calculated indexes the trends, representing a general direction of changes of insolation during the period 1971 – 2005, were worked out. The trend testing was based on the model of linear regression, using a variant of the classic least squares method 1 MNK. The estimation of quality of the model fitting was accomplished on the basis of the following characteristics:
1. Coefficient of determination R^{2}:
where: R^{2} – coeficient of determination; n – sample size; y_{i} – value of next observation i of y variable; ŷ_{i} – value of regression function for x_{i},
2. The F statistic, estimate of linear dependence between variables, testing on the basis of hypotheses:
H_{0}: ρ^{2}=0 (lack of linear dependence),
H_{1}: ρ^{2}>0 (linear dependence exist)
where: ρ – coefficient of correlation between x and y variables.
For verification of hypothesis using the F_{Stat} statistic:
where: F_{Stat} – FSnedecor statistic; n – number of observations; R^{2} – coeficient of determination.
3. Residual standard deviation:
where: n – sample size; y_{i} – y value from sample; ŷ_{i} – theoretical value.
4. Ratio of expressiveness w:
where: Se – residual standard deviation; – arithmetic average of y variable.
It was assumed that the dependent variable is predictable when the value of the index of sharpness w assumes the value from the interval 0.01 – 0.09.
To estimate the significance of regression coefficients the values of standard errors of parameter estimators were used. Values of the estimator’s β_{1} (intersection) and β_{0} (coefficient of direction) and their errors were determined on the basis of the following formulae:
and
where: x – independent variable (time); y – dependent variable.
where: Se – residua standard deviation; D(β_{1}) and D(β_{0}) – standard errors of model estimators
The significance of model parameters were tested on the basis of the statistics t_{Stat} determined by the formulae:
and
where: β_{1} and β_{0} – model estimators; D(β_{1} ) and D(β_{0}) – standard errors of model estimators
The statistics has Student’s tdistribution with the df freedom number. Testing of significance of the model parameters was accomplished on the basis of hypotheses:
H_{0} = β_{1 }= 0 (lack of linear dependence)
H_{1} = β_{1 } 0 (linear dependence exist),
and
H_{0} = β_{0 }= 0 (lack of linear dependence)
H_{1} = β_{0 } 0 (linear dependence exist),
The calculated value was compared with the critical value determined from Student’s distribution of the assumed level of significance α = 0.05, and the number of degrees of freedom equal to df. A zero hypothesis was rejected if t_{α}<t_{Stat} (p<α), thus accepting correctness of the hypothesis H_{1}.
The last estimation of quality of the model fitting was the determination of confidence intervals for estimator’s β_{1} and β_{0}, and comparison of results obtained with values of lower and upper limits of intervals. Confidence intervals were determined according to the following formulae:
and
where: β_{1} and β_{0} – model estimators, t_{(α, n2)} – first order quartile 1 α/2 from Student’s distribution for n2 freedom number; D(β_{1}) and D(β_{0}) – standard errors of model estimators
Besides the estimation of development tendencies the decomposition of time series was made on the basis of mean monthly sums of the effective sunshine duration from the period 1971 – 2005, using the Winter’s additive model, taking into account linear trends, seasonal components, and a random component. The estimation of fitting of the model exponential smoothing was based on the mean percent absolute error expressed by the formula:
where: x_{t} – value of time series in t moment; P_{t} – calculate forecast in t moment; n – number of elements in time series.
Calculations of basic statistical measures, estimation of significance of regression models, and the procedure Census 1 for time series were made in the program STATISTICA 7.1 PL [15].
RESULTS
The longterm mean annual sum of the actual insolation in the Beskid Sadecki was 1861 hours with deviation of 203 hours. August and December were the months with the highest and the lowest mean sum of insolation hours: 225 hours with deviation of 44 hours, and 70 hours with deviation of 26 hours respectively (tab. 3). The lowest monthly sum of the actual insolation occurred in December 1988, amounting to only 23 hours, while the highest one occurred in August 2003 – 318 hours, which made 71.5% of the maximum potential insolation. March, May, and June were characterized by the greatest values of the mean deviations, while November and December by the smallest ones (Fig. 1). The mean sum of the effective sunshine duration in individual seasons was also quite variable (tab. 4). During the summer season it was twice as great as in autumn. The sum of the effective sunshine duration in summer was 613 hours with deviation of 86 hours. The greatest seasonal sum of the effective sunshine duration occurred in spring 2000 amounting to 831 hours, at the seasonal average of 588 hours. This is 40% more than the average in this part of the year. Also the sunshine amplitudes indicated a great diversification of this element within individual seasons. In spring they amounted to over 400 hours, in summer and winter 340 hours, while in autumn a little above 200 hours (tab. 4). Proportion of the effective sunshine duration in autumn in respect of the annual sum was 16.4%, and it was the lowest among all seasons (Fig. 2). Autumn is also the season during which the deviation and amplitude were reaching the smallest values (tab. 4). The longterm mean sum of the effective sunshine duration during the growing season was 1349 hours, which made 45% of the maximum potential sunshine. The highest sum of the effective sunshine duration during the growing season occurred in 2000, amounting to 1615 hours (tab. 4). During 35 years only in two cases, i.e. in 1978 and 1980, the annual sum of the effective sunshine duration was lower than 1000 hours, coming close to 30% of the potential astronomic insolation.
Table 3. Climatologically indexes of effective sunshine duration and its statistical coefficients in years 19712005 in Beskid Sadecki Mountains 
Month 
t_{max} 
t_{min} 
σ 
σ_{x} 
m_{e} 
z_{t} 
v_{x} 

January 
187 
45 
95.5 
29.9 
5.06 
95 
142 
31 
February 
166 
39 
104.5 
28.6 
4.8 
108 
127 
28 
March 
292 
100 
156.1 
46.5 
7.9 
146 
192 
30 
April 
238 
116 
164 
36.8 
6.2 
162 
123 
22 
May 
312 
118 
215.4 
49.0 
8.3 
219 
194 
312 
June 
306 
104 
208.8 
50.8 
8.6 
207 
202 
306 
July 
312 
121 
216.8 
52.3 
8.8 
209 
191 
24 
August 
318 
132 
225.3 
44.2 
7.5 
224 
186 
20 
September 
252 
78 
169.4 
44.1 
7.6 
177 
174 
26 
October 
221 
84 
148.0 
39.4 
6.7 
146 
137 
27 
November 
136 
23 
86.6 
26.8 
4.5 
85 
113 
31 
December 
143 
23 
70.3 
26.0 
4.4 
64 
120 
37 
Year 
2199 
1433 
1861.6 
202.9 
34.3 
1849 
766 
11 
where: t_{max} – highest monthly sum of effective sunshine duration in years 19712005; t_{min} – lowest monthly sum of effective sunshine duration in years 19712005; – multiannual average of effective sunshine duration sum; σ – standard deviation; σ_{x} – standard error; m_{e} – median; z_{t} – range; v_{x} – differentiation coefficient (%).. 
Table 4. Climatologically indexes of effective sunshine duration and its statistical coefficients of seasons in years 19712005 in Beskid Sadecki Mountains 
Month 
t_{max} 
t_{min} 
σ 
σ_{x} 
m_{e} 
z_{t} 
v_{x} 

Spring 
831 
414 
588.2 
99.8 
16.9 
580.0 
417 
31 
Summer 
799 
456 
613.4 
86.4 
14.6 
605.0 
344 
14 
Autumn 
425 
218 
304.9 
54.9 
9.3 
297.2 
207 
18 
Winter 
567 
237 
355.1 
71.2 
12.0 
346.5 
330 
31 
MOW 
1615 
983 
1349.6 
170.9 
28.9 
1362.1 
632 
13 
where: t_{max} – highest monthly average of effective sunshine duration in years 19712005; t_{min} – lowest monthly average effective sunshine duration in years 19712005; – multiannual average of effective sunshine duration; σ – standard deviation; σ_{x} – standard error; m_{e} – median; z_{t} – range; v_{x} – differentiation coefficient (%); MOW – meteorological vegetation period. 
Figure 1. The longterm monthly mean sum of the effective sunshine duration in the Beskid Sadecki with standard deviations 
Figure 2. The annual sum of the effective sunshine duration in the Beskid Sadecki Mountains 
During the period investigated, 1997 was the most sunny year, when the total time of a direct solar radiation was 2199 hours. The least sunny year was 1980, when the actual insolation was 1433 hours (Fig. 2).
Within individual altitudinal climatic zones, in which measuring posts were located (tab. 5), the effective sunshine duration was considerably diversified. The lowest sunshine values occurred at the bottoms of valleys oriented meridionally and on slopes of the northern and northwestern exposures at the height of 300 – 600 m above sea level. In these areas the annual sum of effective sunshine duration was 1600 hours (tab. 5). Considerably better conditions prevailed in the Poprad River Valley which have a more favorable orientation (1700 hours), and on sites situated between 600 and 800 m where annual sums reached 1880 hours. The best solar conditions prevailed on ridges and mountain summits, where the annual sum of the effective sunshine duration was over 2000 hours (tab. 5).
Table 5. The multiannual average of effective sunshine duration in consequence months in Beskid Sadecki Mts. according to altitude localization 
Altitude 
Month 

I 
II 
III 
IV 
V 
VI 
VII 
VIII 
IX 
X 
XI 
XII 

300600 
71 
84 
131 
150 
186 
189 
193 
196 
166 
125 
70 
49 
601800 
102 
105 
155 
165 
219 
208 
221 
228 
168 
153 
86 
74 
8011100 
112 
119 
176 
179 
227 
229 
236 
250 
183 
165 
101 
89 
Characteristics of linear trends, calculated on the basis of data from the period 1971 – 2005, indicated a significant increasing trend of the effective sunshine duration in January, but a low value of the sharpness index indicated that forecasting on the basis of the development equation is uncertain (tab. 6). In the remaining cases (months and seasons) the trend equations yielded results statistically insignificant (tab. 6, 7). A general annual trend of the effective sunshine duration in the Beskid Sadecki Mountains is positive, but statistically insignificant. The analysis of time series carried out using the Census 1 method, and based on the centered moving averages indicated a positive increasing trend of the effective sunshine duration in the Beskid Sadecki, but its statistical estimation is insignificant (Fig. 3).
Table 6. Results of regression analysis (trend line) for effective sunshine duration in years 19712005, Beskid Sadecki Mountains 
Month 
β_{1} 
β_{0} 
D(β_{1}) 
D(β_{1}) 
R^{2} 
Se 
F_{stat} 
df 
w 
SSR 
SSE 
January* 
1.340 
119.606 
0.452 
9.338 
0.210 
27.033 
8.778 
33 
0.28 
6414.85 
24116.14 
February 
0.062 
102.402 
0.486 
10.040 
0.000 
29.064 
0.016 
33 
0.28 
13.66 
27876.48 
March 
1.126 
176.379 
0.765 
15.792 
0.062 
45.715 
2.166 
33 
0.29 
4526.72 
68966.52 
April 
1.124 
143.676 
0.592 
12.221 
0.098 
35.378 
3.606 
33 
0.22 
4512.66 
41302.44 
May 
1.548 
187.571 
0.788 
16.274 
0.105 
47.110 
3.856 
33 
0.22 
8558.49 
73238.81 
June 
0.826 
194.015 
0.851 
17.563 
0.028 
50.844 
0.941 
33 
0.24 
2433.03 
85307.05 
July 
0.373 
210.095 
0.887 
18.305 
0.005 
52.992 
0.176 
33 
0.24 
495.57 
92667.45 
August 
0.595 
214.581 
0.744 
15.365 
0.019 
44.479 
0.640 
33 
0.20 
1265.60 
65287.25 
September 
0.197 
167.708 
0.761 
15.703 
0.002 
45.457 
0.067 
33 
0.27 
138.65 
68188.65 
October 
0.418 
140.480 
0.666 
13.747 
0.012 
39.796 
0.393 
33 
0.27 
623.07 
52262.47 
November 
0.267 
81.825 
0.452 
9.335 
0.010 
27.022 
0.348 
33 
0.31 
253.75 
24096.98 
December 
0.007 
70.403 
0.442 
9.125 
0.000 
26.415 
0.000 
33 
0.38 
0.20 
23026.65 
Year 
2.936 
1808.742 
3.409 
70.369 
0.022 
203.708 
0.741 
33 
0.11 
30763.58 
1369403.77 
where: β_{1 }– parameter estimator (intersection); β_{0} – parameter estimator (directional coefficient); D(β_{1}) – standard error of parameter β_{1}; D(β_{0}) – standard terror of parameter β_{0}; R^{2} – determination coefficient; Se – residue standard error (error of estimation); F_{stat} – value of F statistic (qualify of linear ); df – degrees of freedom; w – ratio of expressiveness; SSR – regression sum of squares; SSE – error sum of squares; * – significance on level p=0.01. 
Table 7. Results of regression analysis (trend line) for effective sunshine duration in years 19712005, Beskid Sadecki Mountains 
Month 
β_{1} 
β_{0} 
D(β_{1}) 
D(β_{1}) 
R^{2} 
Se 
F_{stat} 
df 
w 
SSR 
SSE 
Spring 
3.498 
525.263 
1.583 
32.677 
0.129 
94.595 
4.882 
33.000 
0.16 
43686.94 
295293.97 
Summer 
1.165 
592.384 
1.454 
30.017 
0.019 
86.896 
0.642 
33.000 
0.14 
4845.78 
249180.71 
Autumn 
0.677 
292.708 
0.925 
19.099 
0.016 
55.290 
0.535 
33.000 
0.18 
1636.00 
100880.27 
Winter 
2.405 
398.388 
1.135 
23.420 
0.120 
67.798 
4.491 
33.000 
0.19 
20643.34 
151685.61 
MOW 
5.081 
1258.12 
2.765 
57.075 
0.093 
165.225 
3.376 
33.000 
0.12 
92165.22 
900881.65 
where: β_{1 } – parameter estimator (intersection); β_{0} – parameter estimator (directional coefficient); D(β_{1}) – standard error of parameter β_{1}; D(β_{0}) – standard terror of parameter β_{0}; R^{2} – determination coefficient; Se – residue standard error (error of estimation); F_{stat} – value of F statistic (qualify of linear ); df – degrees of freedom; w – ratio of expressiveness; SSR – regression sum of squares; SSE – error sum of squares; * – significance on level p=0,01. 
Figure 3. Results of regression analysis (trend line) for effective sunshine duration in seasons, in years 19712005, Beskid Sadecki Mountains 
A 10year forecast for the period 2006 – 2015, made using the Winter’s method, on the basis of a 35year series of data, showed a growing trend. However, the additive Winter’s model, along with a linear trend and seasonal as well as random fluctuations, did not fit to empirical data with a required accuracy. The mean absolute error was 28%, and this indicated a low accuracy of the forecast.
DISCUSSION
The effective sunshine duration in the investigated area is characterized by a high variation in respect of time and space. This character results in the first place from a strong relationship between the duration of a direct solar radiation and the cloud cover as well as the orographic conditions [3]. In temperate warm climatic zone including areas situated on slopes, and on mountain ridges the diversification of insolation in individual months was reaching as much as even 50 hours. This fact has great weight to plant community formation, growth and evolution [5,13,14].
The annual sum of insolation varied from about 1600 hours at the bottoms of valleys to over 2000 hours on summits. The largest difference was appear when the bottoms of valleys are oriented meridionally.
General solar qualities of the Beskid Sadecki Mountains belong to very favorable ones. The comparison of results of this study with results of studies carried out during 1950 – 1970 indicated a visible improvement of solar conditions, especially in spring, i.e. April and May [1,2,4]. High annual sums of insolation in 2000 and 2003 affected the value of the coefficient of direction of the longterm trend. However, they do not provide the basis for conclusion about a steady insolation tendency in this part of the Beskids.
CONCLUSIONS
The highest longterm mean monthly sum of the effective sunshine duration in the Beskid Sadecki mountain range falls on August, amounting to 225 hours, and the lowest falls on December – 70 hours.
The highest sums of insolation occurred on summits and mountain ridges in temperate cool climatic zone, and they reached 2070 hours.
In comparison with measurement series of insolation for the period 1950 – 1979 an improvement of solar conditions may be observed, especially in the temperate warm climatic zone at 600 – 800 m in elevation.
On the basis of the forecast of the effective sunshine duration in the Beskid Sadecki Mountains made on the basis of data for the period 1971 – 2005 no conclusion about a directional change of this element may be made with a required accuracy.
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Accepted for print: 22.11.2006
Grzegorz Durło
Chair of Forest Protection and Forest Climatology,
University of Agriculture in Cracow, Poland
29 Listopada Av., No. 46, 31425 Cracow, Poland
Phone: +48126625142
email: rldurlo@cyfkr.edu.pl
Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.