Introduction

Heat waves are one of the most dangerous climate threats associated with global warming, affecting society, economy and environment (Kogenhof et al., 2015: 930). We can say that the first step to control or at least reduce the damage caused by climatic hazards, including heat waves, is to define, detect and identify their characteristics using scientific methods (Abbasnia et al., 2016: 25). Therefore the purpose of this study is Simulation and prediction of maximum temperature and heat waves Southwest of Iran (Case study: Ahvaz and Ilam cities)

Methodology

In the present study to identify heat waves, Maximum daily temperature data of each studied stations, from 1961 to 2005, were obtained from the Meteorological Organization and SDSM software and CanESM2 model and three RCP scenarios (2.6, 4.5 and 8.5) were used. Then using error measurement indicators the lowest risk scenario was selected for each city and the maximum temperature was predicted based on that scenario and using the Fumiaki index and through programming in MATLAB software, Days that had temperatures above +2 standard deviation or above average (NTD) and these conditions lasted for at least two days, were identified and selected as the day with heat waves. The Fumiaki index is obtained by relation 1:

(1 (T(i,j) ) ̅=∑_(n=2020)^2050▒〖T(i,j,n)÷N〗

Where T (i, j, n) temperature of day i th from month j th in year n th, (T (i,j)) ̅ the average temperature of day i from month j. To eliminate the noise in the mean, a 9-day moving average filter was performed on these data three times and calculated by the following equation (Fujibi et al., 2007; Ismail Nejad et al. 2014).

(2 ∆T=(i,j,n)=T(i,j,n)-T(I,J)

Where ∆T= (i, j, n) absolute deviation of temperature from the average on day j th of the month i th, in year n th compared to the average temperature of the same day. In order to the values of temperature deviation of different times and places to be comparable at a certain time and place, it is necessary to standardize these absolute values of temperature deviation by means of temperature diffraction. Like day-to-day changes, diffuse T∆ at 31 days for each day is calculated by the following equation:

(3 (σ^2(i,j) ) ̅=∑_(n=2021)^2050▒〖 ∑_(j-31)^(j+31)▒〖[∆T(i,j^',n)-(∆T(i,j^',n) ) ̅ ]^2÷31N 〗〗

The value (T (i,j)) ̅ is the average temperature deviation in 31 days that is calculated by the following equation:

(∆T*(i,j)) ̅=∑_(n=2020)^2050▒∑_(j=j-31)^(j+31)▒〖T(i,j^',n)÷31N 〗 (4

Finally, (NTD) is calculated by the following equation:



(5 (i,j,n)=∆T(i,j,n)÷(σ(i,j)) ̅ x



Where .Then days with temperatures +2 above average (NTD) and lasting at least two days, were selected as the day with the HW. (Ismail Nejad et al, 2014). Equation 6:

(6 2 ≥ NTD (i+p) NTD (i+p-1) ≥ 2, NTD (i-1), NTD (i+1)… NTD (i),



To evaluate the ability of CanESM2 model scenarios to predict the average maximum temperature for the next 31 years, the outputs of each scenario are averaged by the absolute error values (MAD), mean square error (MSE), root mean square error (RMSE) were compared and the most accurate and least error scenario was selected. Equation 7-9.

(7 MAD= (∑_(t=1)^n▒〖〖|A〗_t-F_t |〗)/n

(8 MSE= (∑_(t=1)^n▒〖〖(A_t-F_t)〗^2 |〗)/n

(9 RMSE=√((∑_(t=1)^n▒〖(A_t-F_t)〗^2 )/n)

Results and discussion

According to the results, during the next 31 years (2020-2020) there will be an increasing trend in the average maximum temperature in both Ahvaz and Ilam stations, which will be the most increasing trend in Ahvaz. Results also showed during the years 2050-2020, the heat waves of these two cities were identified and divided into two categories: short -term and Long-term waves. (Heat waves lasting between 2 to 5 days as short-term heat waves and waves lasting 6 days or more, long-term heat waves). According to the results, in both cities, 2-day heat waves will have the highest frequency, which is predicted to be higher in Ahvaz than in Ilam. But three-day waves in Ilam more than Ahvaz and 4-day heat wave in Ahvaz more and 5-day heat wave in both Ahvaz and Ilam only one case is predicted. The highest frequency of 2-day heat waves in Ahvaz cities in the months related to spring was predicted in Ilam in summer. The 3-day heat waves in both cities will be in the fall. Ahvaz four-day heat waves in autumn, in Ilam in summer. Five-day heat waves, one of which was forecast in the fall at both stations. The highest frequency of this hazard in both stations was related to 2-day warm waves, which were predicted more in Ahvaz than in Ilam, and in terms of time of occurrence in Ahvaz in late winter and early spring, and in Ilam in late summer and early autumn. Most heat waves will be experienced. In general, the occurrence of heat waves in the predicted period in both cities will often occur in the cold seasons of the year.



Conclusion

The purpose of this study was to use the CanESM2 model in simulating and predicting the maximum temperature and heat waves of Ahvaz and Ilam cities as selected cities in southwest of Iran. Based on the results of simulation of maximum temperature and forecast of heat waves during the years 2020-2050. The maximum temperature in both stations will have an increasing trend, which will be the highest increasing trend in Ahvaz. The maximum continuity of heat waves in both stations will be 5 days and therefore short-term, and the 2-day heat wave will have the highest frequency. The trend of two-day heat waves in Ahvaz will be increasing and decreasing in Ilam, but the 3-day, 4, and 5-day waves did not show special trend in any of the stations. Over the next 31 years, heat waves will be less continuous and often occur in the cold months of the year.