EJPAU 2006. Durło G. MULTIANNUAL VARIATION OF THE EFFECTIVE SUNSHINE DURATION IN THE BESKID SADECKI MOUNTAINS

Electronic Journal of Polish Agricultural Universities (EJPAU) founded by all Polish Agriculture Universities presents original papers and review articles relevant to all aspects of agricultural sciences. It is target for persons working both in science and industry,regulatory agencies or teaching in agricultural sector. Covered by IFIS Publishing (Food Science and Technology Abstracts), ELSEVIER Science - Food Science and Technology Program, CAS USA (Chemical Abstracts), CABI Publishing UK and ALPSP (Association of Learned and Professional Society Publisher - full membership). Presented in the Master List of Thomson ISI.

2006
Volume 9
Issue 4

Topic:

Forestry

ELECTRONIC
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES

Durło G. 2006. MULTIANNUAL VARIATION OF THE EFFECTIVE SUNSHINE DURATION IN THE BESKID SADECKI MOUNTAINS, EJPAU 9(4), #28.
Available Online: http://www.ejpau.media.pl/volume9/issue4/art-28.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

ABSTRACT

A long-term 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 long-term 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 long-term 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 long-term 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 long-term 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 Cambell-Stokes 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 long-term variation of the effective sunshine duration in the Beskid Sadecki Mountains, presented in this paper, was calculated on the basis of the 24-hour sums of insolation obtained from the Nowy Sacz meteorological station, and mean 24-hour 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
Cloudiness	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 R²:

where: R² – 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:

H₀: ρ²=0 (lack of linear dependence),

H₁: ρ²>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 – F-Snedecor statistic; n – number of observations; R² – 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 β₁ (intersection) and β₀ (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(β₁) and D(β₀) – 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: β₁ and β₀ – model estimators; D(β₁ ) and D(β₀) – standard errors of model estimators

The statistics has Student’s t-distribution with the df freedom number. Testing of significance of the model parameters was accomplished on the basis of hypotheses:

H₀ = β₁= 0 (lack of linear dependence)

H₁ = β₁ 0 (linear dependence exist),

and

H₀ = β₀= 0 (lack of linear dependence)

H₁ = β₀ 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 H₁.

The last estimation of quality of the model fitting was the determination of confidence intervals for estimator’s β₁ and β₀, 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: β₁ and β₀ – model estimators, t_{(α, n-2)} – first order quartile 1- α/2 from Student’s distribution for n-2 freedom number; D(β₁) and D(β₀) – 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 long-term 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 long-term 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 1971-2005 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 1971-2005; t_min – lowest monthly sum of effective sunshine duration in years 1971-2005; – 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 1971-2005 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 1971-2005; t_min – lowest monthly average effective sunshine duration in years 1971-2005; – 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 long-term 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 a.s.l	Month
Altitude a.s.l	I	II	III	IV	V	VI	VII	VIII	IX	X	XI	XII
300-600	71	84	131	150	186	189	193	196	166	125	70	49
601-800	102	105	155	165	219	208	221	228	168	153	86	74
801-1100	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 1971-2005, Beskid Sadecki Mountains

Month	β₁	β₀	D(β₁)	D(β₁)	R²	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: β₁– parameter estimator (intersection); β₀ – parameter estimator (directional coefficient); D(β₁) – standard error of parameter β₁;
D(β₀) – standard terror of parameter β₀; R² – 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 1971-2005, Beskid Sadecki Mountains

Month	β₁	β₀	D(β₁)	D(β₁)	R²	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: β₁ – parameter estimator (intersection); β₀ – parameter estimator (directional coefficient); D(β₁) – standard error of parameter β₁; D(β₀) – standard terror of parameter β₀; R² – 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 1971-2005, Beskid Sadecki Mountains

A 10-year forecast for the period 2006 – 2015, made using the Winter’s method, on the basis of a 35-year 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 long-term trend. However, they do not provide the basis for conclusion about a steady insolation tendency in this part of the Beskids.

CONCLUSIONS

The highest long-term 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, 31-425 Cracow, Poland
Phone: +48126625142
email: rldurlo@cyf-kr.edu.pl

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