A comparative analysis of analytical hierarchy process and machine learning techniques to determine the fractional importance of various moisture sources for Iran’s precipitation

: Iran is a semi-arid and arid region in southwest Asia. Hence, studying the moisture sources of precipitation in this country has great importance. Iran ’s moisture sources have been determined for dry (May-October) and wet (November to April) periods. Understanding the importance of each moisture source influencing Iran has great application in climatological models. In this study, the fractional importance of various water bodies providing moisture for Iran has been determined for 35 years (1981-2015) by various machine learning as well as Analytical Hierarchy Process (AHP) and Fuzzy AHP models. Finally, the accuracy of developed models was valdiated by Coefficient of determination (R 2 ) and Mean Squared Error (MSE).


Introduction
Iran is a semi-arid and arid country in the Middle East region with an annual precipitation average of 252 mm which has faced a water shortage crisis from early times.
Hence, various elements of the hydrological cycle should be studied deeply and accurately in this country. The hydrological year in Iran is divided into dry (May to October) and wet (November to April) periods [1,2]. Iran's climate is under the influence of various air masses such as continental polar (cP) from the north, maritime polar (mP) from the northwest, Mediterranean (MedT) from the west, continental tropical (cT) from the southwest, all belong to wet and cold periods. However during hot and dry periods, only a maritime tropical (mT) air mass from the southeast direction influences Iran [1,2]. This is due to the high pressure Azores which expands over large parts of Iran and prevents air masses and moisture from entering the country [1,2]. These various air masses bring the moisture from the nearby water bodies. Numerous studies have been [12]. The FLEXPART divides the atmosphere in to 2 million particles with an equal mass and then moves these particles by time in three (one vertical and two horizontal) dimensional wind field [13,14]. In each particle trajectory, the specific humidity in particle can be estimated considering the content of evaporation (e) and precipitation (p) in the particle using the equation 1 [10,11].
(e-p) = m (dq/dt) (1) In this equation, considering the mass of each particle (m) constant may cause a small error. However, according to Stohl and James [11], particles mass changes are so slight through the removal or addition of water. Finally, resolving the above equation for all the particle residing over the area (A) will result in the calculation of the surface freshwater flux (being the difference of area evaporation (E) and area precipitation (P)) by equation 2.
For each parcel backward trajectory, the (E-P)>0 values indicate a region where evaporation exceeds precipitation. However, the region with (E-P)<0 indicates higher precipitation compared to evaporation. Finally, the moisture uptake from each water body has been calculated by masking each nearby water body area from the (E-P)>0 maps ( Figure 1) developed using the FLEXPART model. The results of FLEXPART model outputs also show that the Arabian Sea with a share of 28.3% of total moisture uptake ( Figure-2) is the dominant source for Iran moisture during wet periods, followed by the Persian Gulf with a share of 21.5% and the Mediterranean Sea with a share of 17.3%. However, during dry periods, the Red Sea plays the dominant role with a contribution of 52.2% followed by the Caspian Sea with a contribution of 16.7% [9]. In the Karimi and Farajzadeh study [15], they believed that the Arabian Sea and the Mediterranean Sea with a share of 39% and 38% are the main moisture providers for Iran precipitation. There is an important difference between their study and Heydarizad et al. study [9].  Although obtaining the contribution of each moisture source compared to total moisture uptake is extremely important, it is also needed to understand the fractional importance of each moisture source influencing precipitation amounts across Iran. To study the fractional importance of each moisture source influencing precipitation amount various methods including Analytical Hierarchy Process (AHP), and machine learning techniques can be applied. The application of AHP methods to organize and analyze complicated scenarios has been conducted in numerous studies since Thomas L.Saaty has developed this method in the 1970s [16]. In addition to AHP, artificial intelligence and machine learning techniques can also be applied to investigate the fractional importance of each moisture source affecting precipitation in Iran. The application of machine learning models in different aspects of the sciences has been increased dominantly during the last few years.
The aim of the following survey is to determine the fractional importance of various moisture sources influencing Iran during wet and dry periods using AHP and machine learning techniques.

Materials and Methods
To determine the fractional importance of various moisture sources influencing Iran, the (E-P) values for each nearby water bodies has been calculated and used as input to the Where N is the number of data points, fi the value simulated by the model and yi the actual value for data point i.

Results and Discussions
To study the fractional importance of various water bodies (including the Caspian Sea, The Mediterranean Sea, the Black Sea, The Arabian Sea, the Red Sea, the Oman Sea, the Persian Gulf, and the Indian Sea) which provide moisture for Iran, firstly (E-P) values for each water bodies for the period 1981 till 2015 by the FLEXPART model has been used from the pervious study [2,9]. The (E-P) values have been entered as input in various machine learning models to simulate the precipitation amount across Iran and the results are shown in Figure 3. It can be seen that during wet periods when in most parts of Iran  Red Sea and to a lower extent from the Persian Gulf is extremely significant due to high air temperatures during dry periods, their influence on Iran's precipitation amount is scarce. This is because of a significant role of atmospheric stability that exists in this region, which prevents moisture from turning into precipitation. In contrast to the Red Sea, the contribution of the moisture uptake from the Arabian Sea, the Black Sea, and the Indian Ocean is so scarce (with a share of 1.5%, 1.9%, and 0.7%, respectively), but their influence on precipitation amount across Iran is stronger ( fractional importance of 24.3%, 13.6%, and 11.7%, respectively). Regarding the Black and Arabian Seas, the elevation in which these water bodies moisture is transferred to Iran and the local situation is appropriate for precipitation to take place. For the Indian Ocean, moisture originating from this water body is transferred via maritime tropical (mT) air mass and causes intense monsoon precipitation in the southeast part of Iran.
Studying the performance of the developed models according to the R 2 and MSE shows that none of the developed models are reliable and applicable during dry periods (Table-1). This is because the small amount of precipitation which occurs during dry periods in Iran is mainly under the influence of the local moisture sources and small scale climatology processes. During dry periods, although the amount of evaporation and (E-P) values are high, the parameters which are responsible for precipitation are not strong and active enough to cause precipitation to take place. The main reason which prevents precipitation from occuring during dry periods in large parts of Iran is atmospheric stability [9]. In stable atmospheric conditions, if an air parcel is lifted over a mountain or blown upward by an updraft, the lifted air parcel will sink down to the earth due to the fact that this air parcel is cooler than air particles around it. This phenomenon will prevent precipitation from taking place during dry periods in Iran [8]. In October (the beginning of cold and wet periods), the air temperature reduces which able the ascending motion of air parcels results in instability of the atmosphere and helps precipitation to take place.
During wet periods, the ANN model had the best performance among the developed models, while the DNN model was the second best model. However, the Decision tree model performance was the worst among the studied models (Table-1).

Conclusion
The results of this study show that the contribution percentage of moisture uptake from the various sources does not totally match the fractional importance of various moisture sources influencing the precipitation amount in Iran. This mainly occurs during dry and hot periods when the local phenomena dominantly control precipitation amount across this country.