Spatial analysis of temporal and spatial distribution of the start and end of frost period In Yazd province

Introduction
One of the climatic factors that occur during the cold period of the year in most parts of the country is the phenomenon of cold and glacial. Glacial begins when the temperature decreases and falls to a certain critical threshold, and with the effects it has on the earth's surface, it affects human life as well as construction activities and the yield of horticultural crops. This complication occurs on fruit trees in winter or early spring and causes a lot of damage. The glacial phenomenon not only endangers the natural life of all living things but also plays an important and decisive role in economic, environmental, and development matters such as roads, dams, and bridges. Glacial is very important in different stages of growth of agricultural and horticultural crops. Because if happen, it leads to production constraints. Glacial means zero temperatures or less than zero. Likewise in terms of technology for agriculture, in the event of thin ice crystals formation on the surfaces with sub-zero temperatures, the temperature of the surface air layer is reached above the dew point. In terms of farming meteorology, glacial is related to the low-temperature alteration which causes damage to the tissues of the plant. Glacials can be classified based on the severity, duration, and timing of occurrence. The classification based on the severity is the power of energy distribution components, which usually are measured based on average temperature, minimum, and average of zero and sub-zero and the lowest temperature of the minimums. The beginning and end dates of the glacial period are important from an agricultural point of view. The first glacial that occurs at the beginning of the glacial age is called early autumn glacial. In the autumn, glacial earlier than normal damage to actively growing branches. The last glacial that occurs at the end of the glacial period is called the late spring glacial. Fruit trees are increasingly susceptible to glacial damage from the time flower buds open, during flowering to the stage of small green fruit. To minimize glacial damage in susceptible areas, full knowledge of the frequency, persistence, and timing of glacial events is essential. To measure the risk of glacial, the recorded data of the minimum air temperature in meteorological stations are used. From a meteorological point of view, glacial occurs when the surface temperature and vegetation on it decrease to less than zero degrees Celsius.
Materials and Methods
In the current study, the minimum daily temperature statistics of 10 meteorological stations during a period of 17 years (2001-2018) have been used. To analyze the frequency of glacial occurrences for each year, the time of occurrence of the first early autumn glacial and the last late spring glacial was obtained. To convert the data into processable numbers based on the Julian days, each date is assigned a number. Based on this, the September 23 (1st of Mehr) was considered No. 1 and August 23 (31^st of Shahrivar) in normal crop years was considered 365, and based on this, the number of the first glacial (early autumn cold) and the last glacial (late spring cold) were identified separately based on the stations during each crop year. Days, when the temperature was less than zero degrees Celsius, were extracted as glacial day and glacial at 5 weak temperature thresholds (temperature between zero to -1.9 degrees Celsius), mild (temperature between -1.9 to -3.9 ° C), moderate (temperature -4 to -5.9 ° C), severe (temperature between -6 to -9.9 ° C) and very severe (temperature -10 ° C and Less) was studied (adapted from Qalehri, 2018: 16). Using SPSS software, the best statistical sequence was obtained to calculate the start and end dates of glacial at different probability levels. The results indicated that most of the selected statistical series have a normal distribution. ArcGIS software was used to zoning the time of onset and end of glacial and to prepare many maps of glacial occurrence.
Result and discussion
The spatial distribution of the beginning of the glacial in the province follows the topographic state of the region and begins earlier in the southern and southeastern parts of the province. In some parts of the southern and southeastern regions, due to the high altitude of the region and being located in the mountainous areas, early autumn glacial occurs earlier, such as Garizat station, and occurs from November 6 to 12 (Aban 15 to 21). At Bafgh station, the beginning of autumn glacial occurs from November 13 to 19 (Aban 22 to 28). At Marvast, Meybod, and Abarkooh stations, the starting date of glacial is from November 20 to 25 (Aban 29 to Azar 4). The date of occurrence of early autumn glacial in Herat and Robat stations is November 26 to December 2 (5 to 11 Azar). The beginning date of glacial in Mehriz, Yazd, and Aqda stations is from December 3 to 9 (12-18 Azar). The beginning date of glacial based on different probabilities in Garizat stations with a probability of 30%, is November 3 (12 Aban), with a probability of 50% is November 6 (15 Aban), with a probability of 70%, November 9 (18 Aban), and with a probability of 90%, November 14 (Aban 23), as the earliest start date of autumn glacial. At Yazd station, with a probability of 30%, the first glacial has occurred on November 23 (2 Azar), with a probability of 50%, December 4 (Azar 13), with a probability of 70%, December 8 (Azar 17) and with a probability of 90% on December 24[Ma1]  (3 Dey). The glacial at Bafgh station will end sooner on January 8 -17 (18-27 Bahman). Glacial in central and southern areas such as Mehriz, Yazd, Aqda, and Herat will end on February 18 to February 26 (Bahman 28 to Esfand 7). At Meybod, Abarkooh, and Robat Posht Badam stations, the end date of the glacial is February 27 to March 9 (Esfand 8-18). At Marvast station, the end of the glacial occurred on March 9-19 (Esfand 18-28). In the highlands, including Garizat station, the glacial starts earlier and ends later, so the glacial season is longer in these areas and the growing season is shorter, March 20-30 (Esfand 29 to Farvardin 10). The end date of glacial at Bafgh station with a probability of 30%, occurs at January 23 (Bahman 3), with a probability of 50%, February 12 (Bahman 23), with a probability of 70%, February 25 (Esfand 6) and with a probability of 90%, March 5 (Esfand 14). At Garizat station, the last glacial occurs with a probability of 30% on March 26, (Farvardin 6), with a probability of 50%, on March 29 (Farvardin 9), with a probability of 70% on March 31 (Farvardin 11), and with a probability of 90% on April 8 (Farvardin 19).
The spatial distribution of the number of glacial days on the threshold zero shows that southeast areas including Garizat station have the most frosty days (1685 days) and Bafgh (483 days), Mehriz (484 days), Robate Posht Badam (518 days), Yazd (463 days) and Aqda (362 days) have the lowest number of glacial days during the statistical period (2001-2018). Spatial distribution of glacial occurrence at temperature thresholds of (0 and -1.9) have the highest number of glacials and the central and northern regions have the lowest number of glacials. Therefore, the Garizat station (467 days) has the highest amount of glacial, and Bafgh and Aqda stations have the lowest amount of glacial at this threshold. Likewise, on the threshold (-2 to -3.9), the southeastern and northwestern regions have the highest number of glacial and the northern and central regions have the lowest number of glacial. So, Garizat, Abarkooh, and Meybod stations have the highest amount of glacial and Mehriz, Yazd, Bafgh, Robat-e Posht Badam and Aqda stations have the lowest amount of glacial at this threshold.
Conclusion
Studies conducted between the start and end dates of glacial and the height of selected stations showed that there is a significant relationship between altitude and the date of occurrence of early autumn glacials. As altitude increases, glacial begins sooner. This fact designates that early autumn glacials happen earlier in the mountains than in the plains. The glacial onset map shows that in the plains of the province, the time of the first glacial is about a month later than the highlands of the province. In late spring glacials, the relationship between altitude and the end of the glacial is direct and by increasing the altitude, the date of the last spring glacial is delayed. This indicates that in the plains, the glacial period begins later and ends earlier, in other words, the glacial season in these areas is shorter and the growing season is longer. Conversely, in the highlands, the length of the glacial increases, and the length of growth decreases. This is significant from an agricultural point of view. Besides, the frequency of glacial in the southern and southeastern regions is higher than in the northern and northeastern regions, which has a significant relationship with altitude. The results of the analyzes showed that the Garizat station has the most glacial at all thresholds in the studied period. The lowest amount of glacial days is related to Bafgh, Aqda, and Mehriz stations in the temperature threshold (less than -10). The spatial distribution of the occurrence of glacial at different temperature thresholds also showed that in general, the southern and southeastern regions of the province have the highest frequency of this phenomenon, and as we move to the north of the province, the frequency of glacial decreases.