عنوان مقاله [English]
Occurrence of extreme climatic phenomena such as Frost causes damage to agricultural sectors. Investigating the occurrence of this phenomenon in terms of the impact of climate change and its management can be useful in reducing potential damage. In this study, an attempt was made to evaluate of Late Spring Frost (LSF), Early Fall Frost (EAF), and the Frost Free Period (FFP) with different intensities in different climates of Iran in the long-term climatic period of 1960-2019. Then, investigated and evaluated the probabilities of LSF, EAF and FFP based on the large-scale atmospheric indices ( El Nino Southern Oscillation index (ENSO). Finally, the trend of the LSF, EAF and FFP were determined by modified modified Mann-Kendall and the Sen’s slope estimator (Gilbert, 1987).
Materials and methods
After providing frost dates for climate sample stations, it was necessary to change those into a form that we could analyzed statistically. For this purpose Julian days were used. Number 1 was given to the 1st of January and 2 to the 2nd of January and for next days of January, the next numbers were devoted. For the month of February we used numbers 32 to 60 and for other months the same method was followed. The frost free period is the time between the date of the last spring frost and the first fall frost. Frost days (the number of days the temperature is 0°C during the year) of each station also were extracted. The number of frost days is always less than frost free periods. The trend of each frost series including date of last spring and first fall frost and also the length of the frost-free season were calculated.
The classification of freeze temperatures is based on WMO:
Light freeze: 0° to -1.1° C
Moderate freeze: -1.1° to -2.2°C
Severe freeze: -2.2> and colder
The Mann-Kendall Test is used to determine whether a time series has a monotonic upward or downward trend. It does not require that the data be normally distributed or linear. It does require that there is no autocorrelation. The null hypothesis for this test is that there is no trend, and the alternative hypothesis is that there is a trend in the two-sided test or that there is an upward trend (or downward trend) in the one-sided test. For the time series x1, .., xn, the MK Test uses the following statistic:
Note that if S > 0 then later observations in the time series tend to be larger than those that appear earlier in the time series, while the reverse is true if S < 0.
The variance of S is given by
where t varies over the set of tied ranks and ft is the number of times (i.e. frequency) that the rank t appears.
The MK Test uses the following test statistic:
where se = the square root of var. If there is no monotonic trend (the null hypothesis), then for time series with more than 10 elements, z ∼ N(0, 1), i.e. z has a standard normal distribution.
The usual method for estimating the slope of a regression line that fits a set of (x, y) data elements is based on a least squares estimate. This approach is not valid when the data elements don’t fit a straight line; it is also sensitive to outliers.
We now describe an alternative, more robust, nonparametric estimate of the slope, called Sen’s slope, for the set of pairs (i, xi) where xi is a time series. Sen’s slope is defined as
A 1–α confidence interval for Sen’s slope can be calculated as (lower, upper) where
Here, N = the number of pairs of time series elements (xi, xj) where i < j and se = the standard error for the Mann-Kendall Test.
El Niño is characterized by unusually warm ocean temperatures in the Equatorial Pacific, as opposed to La Niña, which characterized by unusually cold ocean temperatures in the Equatorial Pacific. ENSO (El Nino Southern Oscillation) is an oscillation of coupled response between ocean and atmosphere circulations over the tropical Pacific and the ocean-atmosphere coupled system in the tropical Pacific having important consequences for weather around the globe. (Krishna Kumar et al. 2005, Wang et al. 2005, Kug et al. 2008).
The results showed that the earliest and latest spring frosts occurred at Tehran and Saghez stations at 51 to 64 and 94 to 109 Julian day; latest and earliest fall frosts at Tehran and Saghez stations are 346 to 361 and 297 to 308 Julian days, respectively. The maximum and minimum FFP with different intensities occurred in Tehran station (with arid climate) and Saghez (Mediterranean climate) are 281 to 310 and 188 to 214 day/year, respectively. Also, the results showed that the probability of occurrence of LSF, EAF and FFP in different phases of ENSO compared to long-term period is associated with precedence or latency, which varies depending on the Frost intensity and type of climate. Therefore, due to the predictability of different phases of ENSO, it can be used as decision support system in the management of LSF, EAS and FFP. Trend analysis also shows that the occurrence of the LSF, EAS and FFP vary depending on the climate and the intensity of frost in the 60-year period, so that it occurred earlier in spring and later in fall. As a result, the trend of FFP were increasing in Tehran and Mashhad and decreasing in Isfahan and Saghez stations, respectively.