According to the Environmental Quality Standards for Surface Water (GB 3838-2002), the critical concentration of chromium in water is 10 μg/L. The concentration of chromium in water of the research area was from 0.1059 to 1.2883 μg/L. However, previous studies indicated that low concentration of chromium might also cause serious harm to humans and organisms after its accumulation (Wimalawansa, 2016) . Therefore, it is necessary to take effective measures to control chromium pollution for ensuring ecological safety and human health of local residents. According to variance analysis, the concentrations of chromium in water showed significant difference at different sampling stations (P = 0.000 < 0.01). Therefore, the different control measures should be adopted for controlling chromium pollution at different sampling stations. For example, reducing chromium pollution caused by the heavy industrial areas of Fushun City is the main measure to reduce chromium pollution near H1. However, reducing chromium pollution caused by industrial and agricultural production along the Dongzhou River is an important measure to control chromium pollution near H2. The highest concentration of chromium in water of the research area appeared at H53 (Figure 2), which was mainly attributed to electroplating, metal processing and agriculture along the Guchengzi River (Wang, Cao, Li, & Zhang, 2017) . In addition, the average concentrations of chromium in water at H1, H2 and H5 were much higher than those at other sampling stations (Figure 2). However, the concentrations of chromium in water decreased sharply from H5 to H6 (Figure 2). It was reasonable to speculate that chromium at H5 migrated to sediment and organisms of the Hun River in various ways (Zhao, Chang, Liu, Zhang, & Ma, 2018) . Therefore, the concentration of chromium in water at H5 failed to form the relatively heavily polluted area based on the concentrations of chromium from H4 to H6. Therefore, the measured data showed that the relatively heavily polluted area of chromium was from H1 to H2 (Figure 2).

The concentrations of chromium in water at H51, H52 and H53 might be omitted by using descriptive statistics (Figure 3). The results indicated that the removal of the concentration of chromium in water at H5 did not affect the study of the regional coordinate of the relatively heavily polluted area of chromium in water. Of course, the sources and control measures of chromium in water near H5 need to be further studied for fully understanding the current situation and development trend of chromium pollution in water. Field research indicated that the length and breadth of the research area were approximately 72 km and 0.6 km, respectively. In order to simplify the calculation, the horizontal coordinate 0 km < x < 72 km was converted into 1 km ≤ x ≤ 11 km, and the vertical coordinate 0 km ≤ y ≤ 0.6 km was converted into 1 km ≤ y ≤ 3 km by using data

standardization. By using a curve-fitting tool in Matlab, the concentrations of chromium in water at sampling points were fitted on the premise of ensuring the fitting accuracy. Therefore, the static concentration function θ ( x , y ) of chromium was obtained by

θ ( x , y ) = 15.28 x e − 2.241 x − 0.4456 y 2 + 0.0001491 x 2 y 3 − 0.001826 x 2 y 2     + 0.1365 x + 0.09998 (3)

R 2 = 0.9323 .

The average absolute error between the static concentration function in Formula (1) and the measured data was 0.0441 μg/L. Therefore, the static concentration function of chromium in Formula (3) has high fitting accuracy and may be used for subsequent research. It is clear that the static concentration function of chromium in Formula (3) can effectively investigate the concentration of chromium at discrete sampling point. In addition, the static concentration function perfectly reveals the change regulations between the concentration of chromium with spatial coordinate. By Formula (3), it was clear that the static concentration function θ ( x , y ) was continuous function on the research area D = { ( x , y ) | 1 ≤ x ≤ 11 , 1 ≤ y ≤ 3 } . The continuity of the static concentration function θ ( x , y ) theoretically guaranteed the existence of double integral, which provided a theoretical premise for subsequent research. Therefore, the static concentration function of chromium in Formula (3) plays an irreplaceable role for obtaining the relatively heavily polluted area of chromium.

It is well known that the migration regulation of heavy metal pollution in water may be affected by many influencing factors such as velocity of water flow, temperature and pH and so on (Kanai & Kawahara, 2012) . In addition, the diffusion coefficient also has important influence on the distribution and accumulation characteristics of heavy metal pollution in water ( Wu & Wu, 2018). By using barycenter coordinate formula and diffusion coefficients of chromium in Formulas (3) and (2), the regional coordinate ( x ¯ , y ¯ ) of the relatively heavily polluted area of chromium was defined by

x ¯ = ∬ D θ ( x , y ) d x d y ∬ D x 2 θ ( x , y ) d x d y ( ∬ D x θ ( x , y ) d x d y ) 2 (4)

and

y ¯ = ∬ D θ ( x , y ) d x d y ∬ D y 2 θ ( x , y ) d x d y ( ∬ D y θ ( x , y ) d x d y ) 2 . (5)

By Formulas (1)-(5), it was easy to obtain that

x ¯ = ∬ D θ ( x , y ) d x d y ∬ D x 2 θ ( x , y ) d x d y ( ∬ D x θ ( x , y ) d x d y ) 2 = 1.1806 (6)

and

y ¯ = ∬ D θ ( x , y ) d x d y ∬ D y 2 θ ( x , y ) d x d y ( ∬ D y θ ( x , y ) d x d y ) 2 = 1.0897 . (7)

By Formulas (6) and (7), the relatively heavily polluted area of chromium was from H1 to H2, which was the same as the measured data (Figure 2). Field research indicated that industry and agriculture along the Zhangdang and Dongzhou Rivers contributed large amounts of chromium to water of the Hun River near H1 and H2 (Zhang, Sun, & Zhao, 2012) . In fact, Formulas (6) and (7) also indicated that the concentration of chromium at H1 was higher than that at H2, which was the same as the measured data (Figure 2). In addition, Formulas (6) and (7) also indicated that the highest concentration of chromium appeared at H11 except for the concentration of chromium at H53, which was the same as the measured data (Figure 2). According to different pollution characteristics of chromium at different sampling stations, local government should take different measures to control chromium pollution along the Zhangdang and Dongzhou Rivers to reduce chromium pollution near H1 and H2. For example, the abuse of fertilizer and industrial sewage along the Zhangdang River should be avoided to reduce chromium pollution near H1. However, chromium pollution caused by industrial sewage, livestock and poultry industry and agriculture should be avoided to reduce chromium pollution near H2. In addition, the results showed that the main tributaries of the research area contributed large amounts of chromium to the mainstream of the Hun River. Therefore, the treatment of chromium pollution in main tributaries of the Hun River is the current urgent task. It is clear that the regional coordinate of the relatively heavily polluted area of chromium provides quantitative tool for studying the distribution and accumulation characteristics of chromium.