2.1 Study area

The Gavkhouni wetland sub-basin, located in Central Iran (31º 51’-32º 45’ N, 52º 31’-53º 21’ E), has an area of 3616 km² (Fig. 1a). The average altitude of this sub-basin is 1549 m. The international Gavkhouni wetland occupies about 472 km² of the basin area and is located in the outermost part of the Zayandeh Roud river in the southeastern part of Isfahan city. Based on the Koppen classification, this region has a dry climate. Average annual precipitation is about 60 mm and the mean precipitation during the sampling period in autumn, winter, spring and summer was 18.2, 31.8, 9.1, and 1.1 mm, respectively. The average annual temperature is 18.6 ºC and the mean temperature during sampling periods in autumn, winter, spring and summer was 8.8, 8.9, 27.7, and 29.3 ºC, respectively. Figure 2 shows wind roses of the atmospheric dust sampling periods, which were plotted using the WR View 7.0.0 software.

Fig. 1 The location of Gavkhouni wetland sub-basin. (a) Atmospheric dust and (b) surface soil sampling sites. 

Fig. 2 Wind roses showing the direction and speed of wind during atmospheric dust sampling periods in (a) autumn, (b) winter, (c) spring, and (d) summer, as well as (e) annual in the study area. 

2.2 Sampling method

A set of 124 atmospheric dust samples was collected from a flat surface with an area of 1 m² (Fig. 3). This method has been widely used in previous studies (^{Menéndez et al., 2007}; ^{Hojati et al., 2012}; ^{Norouzi et et al., 2015}). The sampling surface consisted of a glass plate (1 × 1 m) covered with a PVC net (2 mm mesh opening) in order to trap atmospheric dust particles. In each sampling site, a glass tray was placed on a roof of a one-floor building about 3-4 m above the ground level. Dust samples were collected from 31 sampling sites (Fig. 1b) from autumn 2013 to summer 2014. The last two months (60 days) of each four seasons were considered as a dust-sampling period.

Fig. 3 Glass tray (1 × 1 m) covered with a 2 mm PVC net mesh used for atmospheric dust collection. 

Atmospheric dust samples trapped on glass trays were collected and transferred to the laboratory in plastic sealed containers. At the end of each sampling period, glass trays were washed with distilled water. DDR was calculated according to Eq. 1 (^{Hojati et al., 2012}):

In addition, a particle size distribution analysis of atmospheric dust was carried out. Dust sand particles (0.05-2 mm) were separated by sieving through a 270-mesh US standard sieve. Dust silt particles (0.002-0.05 mm) were also separated from dust clay particles (< 0.002 mm) by centrifuge, according to the Stokes law (^{Burt, 2004}).

Surface soil samplings (0-10 cm) from the Gavkhouni sub-basin were carried out by the method of random sampling within blocks at the beginning of the atmospheric dust sampling, in autumn 2013. According to the Gavkhouni sub-basin area (i.e., 3616 km²), the region was divided into 96 blocks with an area of 6 × 6 km and surface soil samples were collected randomly in each block from a depth of 0-10 cm (Fig. 1b). Soil samples were passed through a 2 mm sieve after air-drying. Gravel content was determined using the volumetric method. Other soil analyses included electrical conductivity (EC) and soil pH (^{Page et al., 1986}), soil organic matter (^{Walkley and Black, 1934}), dissolved sodium concentration (^{Chapman, 1965}), concentrations of dissolved calcium and magnesium (^{Burt, 2014}), calcium carbonate equivalent (CCE) (^{Allison and Moodie 1965}), gypsum (^{Artieda et al., 2006}) and clay, silt and sand percentages (^{Gee and Bauder, 1986}).

2.3 Statistical descriptions

SPSS 23 software was used to determine the statistical characteristics of data including maximum, minimum, mean, skewness, kurtosis and coefficient of variation (CV), as well as investigating the correlation of DDR and soil properties. Distribution of variables was investigated using the Kolmogorov-Smirnov test (^{Massey, 1951}).

2.4 Multiple linear regression

Linear regressions are simple modeling methods that can be used to predict one or more response variable (dependent) values from a set of predictors (independent). Linear regressions may be used for bivariate and/or multiple regressions. In bivariate regressions, there are one independent variable and one dependent variable, while in multiple regression analysis there are one dependent variable and two or more independent variables. Eq. (2) is an example of an overall multiple linear regression:

Where Y is the dependent variable, X is the independent variable, and β_i is the regression coefficient of variable X _i (^{Schneider et al., 2010}).

2.5 CHAID algorithm method

The CHAID method was originally proposed by ^{Kass (1980)} and was then further developed by ^{Magidson (1993)}. CHAID is considered one of the main decision-tree methods. In order to build a decision tree, this method splits the data into similar number of subsets until each subset of data covers a given number of samples. The CHAID algorithm can produce a decision tree that, in some cases, acts as non-binary. In fact, it uses multiple separate methods instead of binary separation means that can be divided into more than 90 parents. This algorithm uses the chi-square test to decide in each division for specifying child nodes. Tree branches are then pruned to fulfill the stop criteria or reach the required level of complexity.

In other words, the CHAID algorithm first finds the differences between each sample and the other samples to produce a tree. The pruning of the tree is done by finding the differences (^{Chattamvelli, 2011}). In CHAID trees, the homogeneity of the groups that generated the tree is evaluated by a Bonferroni corrected P-value obtained from the chi-square statistic applied to two-way classification tables with K splits and C classes for each tree node (^{Maroco et al., 2011}):

where n̂ _ck refers to the observed frequencies of the cell ck and n̂ _ck is an expected frequency under the null hypothesis of two-way homogeneity. In the CHAID analysis, the epsilon parameter for convergence and the maximum number of runs for convergence were set at 0.001 and 100, respectively. The Pearson method was used for the chi-square of the categorical target. The variable selection using CHAID was carried out using Clementine 15 software.

It should be noted that the temporal variability studies (both CHAID and MLR) were performed with the assumption that the physical and chemical characteristics of surface soil did not have a notable temporal variability in the area during the short study period, thus soil samples were collected only once.

3.1 Statistical description of the studied properties

Table I shows annual and seasonal DDR statistics and also some measured physical and chemical parameters of surface soil in the study area. The maximum and minimum DDR were 4.8 and 3.0 t km^-2 month^-1 corresponding to summer and autumn, respectively. Furthermore, the maximum and minimum coefficients of variation for DDR were found in summer and spring, respectively. ^{Norouzi (2016)} also studied DDR in Isfahan province and reported that summer and autumn had the highest and lowest DDR, respectively, in this region. ^{Ta et al. (2004)} studied DDR in Gansu province, China and found that the highest and lowest DDR may happen in spring and autumn. ^{Javed et al. (2015)} reported that concentrations of all size fractions were lowest during the monsoon sampling period at all sites in Faisalabad, Pakistan.

^{Al-Harbi (2015)} investigated the monthly total amount of dust fall in Shuwaikh city, Kuwait and reported that the highest DDR in the study area was observed during the summer. It appears that dryness, and lack of moisture and rainfall in summer are the main reasons for increased DDR as well as a high coefficient of variation (CV) during this season.

The adhesion of dust particles is probably increased by the increase in rainfall and relative humidity, which leads to reduced dust generation in the source area and ultimately to reduced DDR in the deposition area. On the other hand, precipitation affects soil moisture and vegetation, which are the two most important factors controlling dust, and reduces the amount of dust produced (^{Ta et al., 2004}). ^{Kutiel and Furman (2003)} reported that rainfall and the presence of vegetation significantly reduced the amount of dust because of their impacts on wind speed and particle sizes. Among the surface soil properties in the study area, gypsum, EC and sodium adsorption ratio (SAR) with a CV > 100% (^{Nielsen and Wendroth, 2003}) had a strong variation and pH with a CV < 10% showed a weak variation. The reason for the observed changes in parameters of gypsum, EC and SAR might be the salty wetland in the region and large variations of soluble salts in soil from the wetland. The minimum CV value belonged to pH, since pH is the logarithm of H⁺ concentration in soil solution and if this parameter is reflected directly by proton concentration, it could show more changes. Other researchers have also observed less variation in soil pH than other soil parameters (^{Tesfahunegn et al., 2011}; ^{Mousavifard et al., 2013}).

To determine the relationship between annual and seasonal DDR and surface soil properties in the study area, correlation coefficients were calculated (Table II). The results showed that annual and seasonal DDR (except for summer) are negatively correlated with soil pH. DDR in winter showed a significant positive correlation with CCE, EC, and SAR. However, no significant correlation was observed between the annual and seasonal DDR and other soil parameters.

3.2 Linear relationships between physical and chemical properties of soil and DDR (MLR model results)

The characteristics influencing DDR in the study area were determined with the linear method (i.e., the MLR); the results are depicted in Figure 4. Based on the obtained results, the effective parameters of DDR in the study area using the MLR method in autumn, winter, spring and summer were SAR (Fig. 4a), pH (Fig. 4b), clay (Fig. 4c) and gravel (Fig. 4d), respectively. Moreover, the parameter influencing annual DDR in the study area was SAR (Fig. 4e).

Fig. 4 Importance coefficient (IC) values of surface soil physical and chemical parameters in the Gavkhouni sub-basin affecting DDR in (a) autumn, (b) winter, (c) spring, and (d) summer, as well as (e) annual DDR using the MLR method. 

3.3 Non-linear relationships between physical and chemical properties of soil and DDR (CHAID algorithm results)

Figure 5 presents the characteristics influencing DDR in the study area, which were determined by using the non-linear decision tree CHAID method. Determinant parameters in autumn in order of importance coefficients (IC) were organic matter (IC = 0.34), sand (IC = 0.28), silt (IC = 0.25), and gravel (IC = 0.14) (Fig. 5a), whereas the most effective parameters in winter were gypsum (IC = 0.42), sand (IC = 0.38), clay (IC = 0.14), and soil organic matter (IC = 0.06) (Fig. 5b).

Fig. 5 Importance coefficient (IC) values of surface soil physical and chemical parameters in the Gavkhouni sub-basin affecting DDR in (a) autumn, (b) winter, (c) spring, and (d) summer, as well as (e) annual DDR using the CHAID method. 

In spring, soil texture was introduced as a determinant parameter influencing the DDR within the area where sand content was the most important feature (IC = 0.39) and silt percentage (IC = 0.26) had the minimal effect (Fig. 5c). Prevailing westerly wind in spring (Fig. 2) and sand dunes in the west of the study region, which could lead to release of sand in the area, might be the most important factors explaining the importance of sand content. In summer, five variables including silt, sand, organic matter, gypsum and soil pH had a greater influence on DDR in the study area. Among these parameters, silt had the highest importance coefficient (IC = 0.31), whereas pH and gypsum had the lowest IC (0.15) (Fig. 5d). Determinant parameters influencing annual DDR in the study area were sand, soil organic matter, silt, CCE, clay and pH, being sand the most important feature (IC = 0.23) and pH (IC = 0.04) the least significant (Fig. 5e).

3.4 Comparing MLR and CHAID model results

Based on the results obtained from the MLR model, only one parameter was introduced as determinant factor affecting DDR in the study area. However, several parameters were determined as affecting factors in each sampling period with the non-linear CHAID algorithm method. In addition, according to the results obtained with the CHAID analysis, it appears that among the measured parameters, surface soil sand content in the Gavkhouni wetland had the greatest impact on DDR during the sampling periods, where similar particle size distribution of surface soil and atmospheric dust were found (see Table III).

Therefore, it can be concluded that the accuracy of MLR is unacceptable as compared with the non-linear CHAID algorithm to determine parameters influencing DDR in the Gavkhounisub-basin. Since the results of CHAID algorithm are more acceptable and much more similar to ground measurements and natural conditions of the study area, most soil physical and chemical properties seem to have non-linear relationships with DDR in the study area. ^{Abbaszadeh Afshar et al. (2016)} found that the CHAID algorithm had a greater ability to determine clay content with higher accuracy by comparing it with the MLR method for estimating clay. ^{Besalatpour et al. (2015)} used the MLR method to model aggregate stability and reported its non-acceptable accuracy for estimating and modeling the aggregate geometric mean diameter in the northern Karun Basin. ^{Tóth et al. (2012)} developed some transitional relations based on the CHAID classification tree and used them as input data; they concluded that classification tree methods (regression trees and CHAID) are useful and effective to model complex relationships between soil water retention and soil properties in salt affected soils. In general, the CHAID algorithm has extreme flexibility and high performance to detect complex nonlinear relationships between input and output data. On the other hand, training based methods in comparison with regression-based models have much more ability to recognize relationships between inputs and target variables. Therefore, it seems that in areas with high ecological complexity and complex nonlinear relationships among input and output data, nonlinear methods such as the CHAID algorithm are superior to linear methods such as MLR.