High tasting assessment of the fruit of sweet cherry is due to the favorable soluble solids content (SSC). The weather parameters and varietal features during the formation of fruit have the dominant influence on the accumulation of soluble solids. This issue has gained new relevance in the context of global climate change. The research aimed to develop a dependence of the accumulation of soluble solids of the various sorts of sweet cherries on the weather conditions of the South Steppe zone of Ukraine. Statistical analysis of the values of soluble solids in sweet cherry fruit was performed according to the average indicators of three groups of cultivars. To achieve this goal, the laboratory, factor, correlation, and regression analyses were carried out. The mathematical model was built with the application of factor and regression analysis methods, with the principal component analysis being used. The factor and regression analysis methods became the basis for the linear regression model of dependence of SSC fund accumulation on the influence of climatic parameters for the cultivar types of the three ripening terms. Based on the constructed regression models, we analyzed the degree of influence of the weather parameters on the SSC indicator by calculating the coefficients of Δ_{i} relative influence. The largest influence was set for the group of temperature and humidity parameters with the maximum share of Δ_{i} ≥9.50%. It was mathematically substantiated that the weather parameters of the last month of fruit formation had the greatest influence on the accumulation of SSC in the sweet cherry fruit, regardless of the period of ripening. For early and medium ripening sweet cherries, those were the weather parameters for May, and for those of lateterm of ripening June parameters were of the maximum value.
Sweet cherry is in demand in many countries of the world. The share of sweet cherry fertile plantations in the world is more than 3.1%, which makes about 12.5 thousand hectares. The majority of these plantations – 42.6% are concentrated in the Middle East and European countries (
The fruit of the sweet cherry cultivar, being the first to open the season, is a source of easily digestible monosaccharides and contains a powerful immunostimulatory complex of several valuable nutrients. This is the reason for their popularity not only in Ukraine but also in Hungary, Bulgaria, Turkey, etc. (
The ratios of soluble solids and insoluble solids according to Ukrainian and foreign researchers (
Several scientific research traditionally used regression and correlation analyses to assess the degree of influence of parameters on the experimental indicators. However, in conditions when the number of factors for analysis significantly exceeds the number of experimental research, it is not possible to apply a traditional least squares method to build a regression model. Therefore, it has been proposed to build a model using the method of factor analysis – principal component analysis (
Evaluation of climatic conditions during cultivation and selection of rational parameters for obtaining juice from cherry berries will increase the efficiency of the processing process and improve the method of determining the content of soluble solids in various fruit and berry raw materials, which in turn will intensify the process.
To determine the SSC, a sample was taken for each pomological cultivar which consisted of 100 fruit from 6 trees that came into full fruiting. Trees typical of a certain pomological cultivar, of the same age, with a medium intensity of fruiting, were selected for the research. The fruit was weighed and counted in the process of harvesting. The sweet cherries of each commercial cultivar were carefully harvested in the state of consumer ripeness. They were stored and transported to the laboratory provided that the fruit in the period of the indicator determination had the appearance and the taste inherent in the pomological cultivar.
Chemical reagents were not used for scientific research.
The study included sweet cherry fruit of 33 varieties, which were divided into three groups of ripening terms: Group1 – cultivars of the early termination of ripening – Sweet Erlise, Merchant, Bigaro Burlat, Rubinova Rannya (Figure
Photos of individual samples of cherries:
The agricultural background in the areas of the research within the whole period of the research met the requirements of agricultural technology. The accumulation of moisture in the soil mainly takes place in autumn, and partly in winter, and the early spring. The soils of the experimental plots for the cultivation of the crop are the light loamy black humus earth. The forest is the basis for soil formation. According to the aggregate size distribution, this type of soil has a high content of physical sand.
Horticultural farms of the region of research are located in the South Steppe subzone of Ukraine. The landscape of the territory is flat with the Atlanticcontinental climate and a hightemperature scenario. The range of average annual air temperature is 9.1 – 9.9 °С. The average monthly air temperature in the warmest months ranges from 20.5 – 2.1 °С. The sum of active temperatures above 10 °С from April to October is 33 to 16 °С. The average annual rainfall is 475 mm. In terms of rainfall, the region belongs to the area with insufficient moisturization. The average annual relative humidity is within 73%. The average annual wind speed is 3.7 m.s^{1}. The climate is arid with the dominance of dry east, northeast winds. The value of the hydrothermal coefficient is within the range of 0.22 – 0.77.
Refractometer (ABBE AR12, producer "InterSynthesis" Limited Liability Company, Ukraine).
Laboratory hydraulic press (LHP – 25, producer "Inter Synthesis" Limited Liability Company, Ukraine).
The meteorological data provided by the meteorological station at Melitopol.
The SSC was determined by the refractometric method. The essence of the method is based on determining the mass fraction of SSC with the help of a refractive index. The refractive index of the solution under analysis was measured at the temperature of 20.0 ±0.5 °С on the ABBE AR12 refractometer. In the process of sampling, care was taken to ensure that the sample received for the research was representative and was not subject to spoilage during the transportation and storage. The juice was squeezed from the selected average sample with the help of a press. The resulting juice was used for determination. The mass fraction of soluble solids was determined by direct readout of the instrument scale in percent. In case of temperature deviation in the process of measurement, the values of temperature corrections were taken into account. The quality assessment of each pomological cultivar was performed five times (
As it is known, the analysis of matching correlation coefficients is an initial but rather rough estimate of the degree of influence of a single factor on the indicator under research. Other instruments of statistical analysis, such as regression and factor analysis, the principal component analysis, should be used to further investigate the issue (
However, since the number of considered factors x_{j,j} = 1.25 in this case, significantly exceeds the number of observations (Y_1i,Y_2i,Y_3i, where i = 1 – 12 years of research) it is not possible to apply the classical pattern of regression analysis. Moreover, the factors themselves are strongly correlated with each other, as many interfactor matching correlation coefficients are close to ±1. This indicates the presence of multicollinearity effect.
Therefore, it is proposed to conduct the research of the degree of influence of each of the factors and identify the most significant ones using the method of principal component analysis (PCA). The principal component analysis method allows reducing a large number of variables by constructing artificial factors (principal components – (
The main components are a linear combination of the original factors x_{i} and do not correlate with each other. At the same time, a set of such principal components is distinguished, which extracts the maximum variance from the variables (
Description of the Experiment. The research was conducted during 12 consecutive vegetation periods from 2008 to 2019. During the experiment, we used the meteorological data provided by the meteorological station at Melitopol, Ukraine.
The construction of models of sweet cherry SSC dependence on weather parameters was carried out following the following pattern:
1. Determination of SSC using the above method.
2. Systematization of information and creation of a database of weather conditions in the years of research. At this stage, the following indicators were selected: average minimum air temperatures, average air temperatures, average maximum air temperatures, absolute minimum air temperatures, absolute maximum air temperatures, precipitation total, average relative humidity, minimum relative humidity, absolute minimum relative humidity.
3. Based on the indicators selected above, the following indicators were calculated: hydrothermal coefficient, temperature differences for certain periods, sums of active temperatures, sums of effective temperatures.
4. Based on the correlation analysis, the weather factors that significantly affect the accumulation of SSC for the sweet cherry of the early, medium, and lateripening terms were identified.
5. Analysis of the factors defined in Paragraph 4 by methods of factor and regression analysis to determine the degree of influence of each factor on the SSC for the cultivar groups of 3 ripening terms (
The following pattern of statistical data analysis is proposed:
1. Using the principal component analysis of the given factors (parameters
2. Using the leastsquares method, the regression dependence of the indicators
3. The expressions of the principal components through the initial values of the weather factors (
Where:
4. The constructed regressions are analyzed and the degree of influence of each of the factors on the resulting indicators are evaluated. The analysis of the constructed regression is performed based on Δ_{i} coefficients. These coefficients characterize the relative degree of influence of each of the considered factors (
Where:
To perform the statistical analysis, the instruments of a modern Data Mining computer technology with RStudio v. 1.3.959 software environment was used.
The level of soluble solids accumulation can change under the influence of soil and weather conditions, yield, and the degree of fruit ripeness. In the south of Ukraine, the fruit of the best cultivars of sweet cherry contain 12.1 – 19.9% of soluble solids, whereas in the central part of the country this indication is only 11.3 – 12.8% (
Year, treatment, and their interaction had significant effects on fruit size, thickness, and weight. Fruit height, the height: width ratio and SSC were not influenced by year and treatment, though the interaction of these factors significantly affected SSC (
The difference between daytime and nighttime temperatures positively influenced the accumulation of dry solids and sugar content in sweet cherry fruits, whereas the amount of precipitation had a negative impact, forming fissures (
Low temperatures during the blooming cause reduction of the yield capacity, but winter frosts and relatively low temperatures during the pollination might also negatively affect yields (
The SSC (consisting mostly of sugars) varies between 11 and 25 °Brix in sweet cherry (
The results of twelve years of research suggest that the average content of CPP in cherries grown in the analyzed region was at the level of 16.7%. The average content of CPP in the fruits of cherries of the early maturing varieties was at the level of 15.3% (Table
Dry matter content in cherries cultivars of the early termination of ripening, % (2008 – 2019 yy.),
Pomological variety  Average contentSSC, %  min content SSC, %  max content SSC, %  Variation by years,V_{p}, % 



16.8±3.9  11.7  22.6  23.3  
16.5±3.7  11.4  21.2  22.7  
16.2±3.3  11.7  21.2  20.4  
14.0±2.7  11.5  18.7  19.3  
14.8±3.4  10.1  20.5  22.8  
13.5±2.7  10.3  18.9  19.6  
14.9±2.7  11.4  21.0  18.4  
15.3±3.3  10.1  22.6  21.9  
0.416       
In the fruits of cherries of groups of varieties of medium and late maturity, the average content of SSC exceeded the average varietal value by 1.8 and 7.2%, respectively (Tables
Dry matter content in cherries cultivars of the mediumterm of ripening, % (2008 – 2019 yy.),

Average content SSC, %  min content SSC, %  max content SSC, %  Variation by years,V_{p}, % 



16.8±3.4  10.9  21.7  20.0  
16.7±3.5  10.5  21.1  21.1  
17.4±3.1  12.1  22.3  17.6  
15.3±3.0  12.3  22.1  19.9  
18.5±2.9  15.1  23.2  16.1  
17.8±3.3  12.5  22.5  18.3  
17.2±3.8  12.3  22.4  21.4  
16.6±2.6  12.0  20.0  15.9  
16.3±3.2  11.8  20.2  19.5  
17.6±3.8  12.0  22.8  21.5  
17.3±3.3  11.9  22.1  19.0  
18.5±2.6  15.1  23.3  14.0  
15.7±4.6  10.0  22.0  29.0  
17.0±3.3  10.0  23.3  19.6  
0.455       
Dry matter content in cherries cultivars of the lateterm of ripening, % (2008 – 2019 pp.),
Pomological variety  Average content SSC, %  min content SSC, %  max content SSC, %  Variation by years, V_{p}, % 



18.5±2.5  13.9  22.5  13.4  
18.2±3.8  12.4  23.1  20.9  
17.1±3.2  12.9  22.8  18.7  
18.2±3.5  12.8  23.0  19.3  
18.6±3.5  12.8  22.8  18.5  
17.0±2.5  12.9  19.7  14.8  
17.9±3.4  13.0  23.0  19.0  
17.8±3.8  11.9  23.0  21.5  
17.7±2.9  12.7  21.3  16.3  
16.8±2.3  11.9  19.5  13.7  
17.6±3.8  10.3  21.5  21.6  
18.3±3.4  11.2  21.5  18.7  
18.4±2.9  11.0  22.3  15.9  
17.9±3.2  10.3  23.1  17.7  
0.635       
The variety of early maturity, which according to the results of twelve years of research was characterized by the largest mass fraction of SSC was Rubinov early, and the smallest – Merchant (Table
Among the varieties of the group of medium maturity, the maximum average content of CPP was recorded in the fruits of the varieties Talisman and Dachnytsia, and the groups of the late group  in the fruits of the variety Udivitelna.
These research results indicate significant variability in the content of SSC over the years of research in the group of varieties of early maturity. The greatest influence of abiotic factors on the content of CPP in the fruits of this group was found for varieties Kazka and Valeriy Chkalov with coefficients of variation of 22.8 and 22.7%, respectively. The most stable in terms of SSC are varieties Zabuta, Merchant, Bigaro Burlat, as evidenced by the corresponding coefficients of variation of 18.4, 19.3, and 19.6%. The variability of these varieties under the influence of weather factors is considered average.
The variability of the SSC content over the years of research in the fruits of cherries of the groups of varieties of medium and late maturity was average (
Thus, in terms of dry matter content and variability of their formation under the influence of weather factors in the analyzed region, the most promising from a technological point of view were varieties Dachnytsia, medium ripening, and largeripening varieties Krupnoplidna. These varieties differed in the high content of SSC, and their low variability over the years of research. Among the group of varieties of early maturity of the most promising variety is not identified. All studied varieties with a high content of CPP were characterized by high variability. Varieties Zabuta, Merchant, Bigaro Burlat, in which the variability of SSC content over the years of research was average, were characterized by their low content.
The average cultivar content of SSC in the sweet cherry of 33 researched cultivars grown in the South Steppe subzone of Ukraine was at the level of 16.7%. In the group of cultivars of early ripening, the maximum average SSC is recorded in the fruit of Rubinova Rannya sweet cherries. It was at the level of 16.8%.
Among the cultivars of the other two groups, the fruit of Talisman and Dachnytsia, Krupnoplidna, and Udivitelna cultivars were characterized by the highest average SSC. They accumulated 18.5 – 18.6% of SSC. The fruits of cultivars Prostir and Anons, collected in 2015, were characterized by the lowest quantity of dry solutes. The quantity of the dry solutes was lower than the average cultivar value, by 59.8 and 61.7% accordingly. The highest mass fraction of the dry solutes was recorded in fruits of the Dachnytsia and Karina cultivars, collected in 2012 (
To establish the share of the influence of the weather parameters and cultivar characteristics on the formation of SSC of sweet cherry fruit, a twofactor analysis of variance was performed. Its results showed that for all groups of cultivars, regardless of ripeness, the weather parameters of the year of research has the dominant influence on the formation of SSC fund with the share of influence for the cultivars of early ripening being 74.5%, for those of medium ripening – 61.9% and for the groups of lateripening – 69.4%.
The influence of the characteristics of the cultivar was less significant. The results of the study are presented in more detail in the research of
Thus, the results obtained earlier proved the feasibility of predicting the SSC in sweet cherries following the average values for the certain group of cultivars, and not separately for each pomological cultivar. Medium dependence was found between the fruit weight and the fruit SSC (correlation coefficient 0.53 – 0.59) (
For these factors the presence of the weak, medium, and strong linear correlations, as evidenced by the values of matching correlation coefficients between values of each factor and the resulting rate
Thus medium ripening cultivars, we identified 17 and, for early and the lateripening cultivars, there were 16 weather parameters, for which a strong or medium linear correlation dependence with the analyzed indicator (SSC) was established. Further research was carried out according to the pattern given above.
1. Five main components were identified by the principal components method (
2. Regression models of the dependence of the soluble solids index for each group of cultivars on the selected main components (
3. After the transition to the initial factors, we obtain a regression model of the form (2). This regression model characterizes the dependence of the SSC index (for
Matching correlation coefficients and meanings of relative share of influence (∆_{i})for weather parameters (X_{i}) and soluble solids content (SSC) in the fruit of sweet cherry of Early (
Conventional Sign of a Parameter (X 
Matching Correlation Coefficients 




early  medium  late  



∆_{i}, % 

∆_{i}, % 

∆_{i}, %  


X_{1}  0.965  14.71  0.958  13.02  0.615  1.87 
X_{2}  0.401*  **  0.464*  **  0.864  13.85 
X_{3}  0.746  5.00  0.811  8.17  0.683  2.98 
X_{4}  0.772  14.23  0.730  0.86  0.342*  ** 
X_{5}  0.402*  **  0.472*  **  0.831  8.02 
X_{6}  0.568  1.26  0.656  9.62  0.531*  1.47 
X_{7}  0.950  16.06  0.958  5.45  0.604  2.83 
X_{8}  0.504*  **  0.540  **  0.823  13.98 
X_{9}  0.934  15.94  0.901  14.18  0.701  3.11 
X_{10}  0.375*  **  0.371*  **  0.713  9.49 
X_{11}  0.769  4.58  0.818  12.92  0.477*  ** 
X_{12}  0.304*  **  0.440*  **  0.630  4.56 
X_{13}  0.621  0.53  0.705  3.84  0.192*  ** 
X_{14}  0.714  3.48  0.743  0.83  0.414*  ** 
X_{15}  0.557  0.87  0.492*  3.22  0.225*  ** 
X_{16}  0.785  2.83  0.851  2.18  0.546  ** 
X_{17}  0.581  **  0.653  **  0.589  3.85 
X_{18}  0.624  0.12  0.638  1.07  0.480*  0.84 
X_{19}  0.507*  0.83  0.590  0.53  0.068*  ** 
X_{20}  0.296*  **  0.366*  **  0.571  6.99 
X_{21}  0.606  9.54  0.638  12.16  0.155*  ** 
X_{22}  0.551  0.57  0.555  2.73  0.229*  ** 
X_{23}  0.300*  6.84  0.380*  8.00  0.763  11.48 
X_{24}  0.658  **  0.720  **  0.685  7.94 
X_{25}  0.588  1.15  0.637  1.33  0.729  9.69 
Note: * Insignificant matching correlation coefficients (
Main regression characteristics of the ssc index from the main components.
Coefficients of Regression  Adjusted Rsquared 















11.9533  0.5675  0.23137  0.4717  0.50313  0.17735  0.9498  0.0001224 

12.85308  0.5177  0.15739  0.1426  0.28085  0.41546  0.9305  0.000342 

13.1096  0.6491  0.27885  0.1925  0.27026  0.01668  0.8854  0.00862 
Based on the constructed models, the coefficients Δ_{i}, (
For the cultivars of early and medium ripening terms Δ_{i} varies within 0.12 – 16.06% (Table
The first group includes the factors that have a strong influence on the accumulation of SSC with the value of Δ_{i} ≥ 9.50%. For the cultivars of early ripening sweet cherries, these include the average monthly, absolute maximum, average maximum, and minimum air temperature in May and absolute minimum relative humidity in May. For the fruit of the medium ripening group, these are the average monthly and average minimum air temperatures in May, the average maximum temperature in April, the sum of annual effective temperatures above 15 °C, and the absolute minimum relative humidity in May. For the fruit of lateripening, the average monthly, average maximum, and average minimum temperature on June, the absolute minimum, and the average relative humidity in the period of blossom. The second group includes the factors that have an average influence on the accumulation of SSC on the sweet cherry fruit with the meaning of Δ_{i} from 2.00 – 9.48% (Table
As a result, the weather conditions of the last month of fruit formation have the greatest influence on the accumulation of SSC in sweet cherry fruit, regardless of the ripening term. For the sweet cherry cultivars of early and medium ripening, these are the weather conditions of May, for the lateripening cultivars it is June.
1. A correlation analysis was performed among 25 weather factors (Х
2. Based on the methods of factor and regression analysis, linear regression models of the dependence of SSC fund accumulation on the influence of weather factors on the groups of cultivars of the early, medium, and lateripening terms.
3. Based on the constructed regression models, the analysis of the degree of influence of weather factors on the SSC indicator was performed by calculating the coefficients of relative influence Δ_{i},%. The greatest influence is established for the group of temperature and humidity indicators with the maximum share of participation Δ_{i} ≥ 9.50%.
4. It was mathematically substantiated that the weather conditions of the last month of fruit formation have the greatest influence on the accumulation of SSC in the sweet cherry fruit, regardless of the ripening term. For the sweet cherry cultivars of early and medium ripening, these are the weather conditions of May, for the lateripening cultivars it is June.
5. It is established that in terms of dry matter content and variability of their formation in regions with climatic conditions of the Southern steppe subzone of Ukraine the most promising from the technological point of view were varieties Dachnytsia, medium maturity, and variety Krupnoplidna, late maturity. These varieties differed in the high content of dry soluble substances and their low variability over the years of research.