3. Results
3.1. Correlation between surface runoff coefficient and the characteristic parameters of the spatial distribution of cypress and topography
The characteristic parameters of the spatial distribution of cypress and topography in each runoff plot were shown in Tab.2. When analyzing the coupling effects of multiple factors on surface runoff coefficient, it was necessary to assume that every single factor had a significant correlation with the surface runoff coefficient, so the irrelevant variables needed to be excluded in advance. Therefore, the Pearson correlation coefficient method was used to check the correlation between each characteristic parameter and the surface runoff coefficient, and the results were shown in Tab.3. The results of the correlation test showed that except for the surface cutting depth and L(d) index, other factors had significant correlations with the surface runoff coefficient. Besides, topographic relief and runoff path density were positively correlated with the surface runoff coefficient, while surface roughness, contagion index, and stand density of cypress were negatively correlated with the surface runoff coefficient.
3.2. Correlation between surface runoff coefficient and the characteristic parameters of the spatial distribution of cypress and topography
3.2.1. SEM construction
To construct an SEM to reflect the impact of the spatial distribution of cypress and topography on runoff coefficient, the first step was to clarify the independent and dependent variables, and the accuracy of the model depended on the significant differences of the correlation between the independent and dependent variables. According to Tab.3, three factors that characterizing topographical characteristics including topographic relief, surface roughness, and runoff path density, and two factors representing the spatial distribution of cypress including contagion index and stand density of cypress, were selected as independent variables, and surface runoff coefficient was used as the dependent variable for SEM construction.
In the construction of SEM, the relationship chains between variables were created in the form of a path diagram shown in Fig.2. The one-way arrow in the figure represented the effect of the independent variable on the dependent variable, and the two-way arrow represented the interaction between independent variables. The output results of the model included the fitness index of the model, the normalized path coefficient, and the corresponding significant differences between variables.
3.2.2. SEM simulation results
The simulation results of the model were presented in the form of a path diagram shown in Fig.3, the standardized path coefficients among the variables were shown in Tab.4, and the accuracy of the model was reflected in the form of the fitness index output by the model shown in Tab.5.
From Tab.5, the fit index values of the model were all within the acceptable range, indicating that the hypothetical structural model could simulate the coupling effects of the spatial distribution of cypress and topography on surface runoff coefficient in this study. The simulation results of the model showed that the five independent variables (topographic relief, surface roughness, runoff path density, contagion index, stand density of cypress) all had a significant impact on surface runoff coefficient, and the effects were 0.245, -0.272, 0.239, -0.311, -0.134, respectively. Among the five independent variables, there are significant interactions between stand density of cypress and surface roughness, between stand density of cypress and runoff path density, and between contagion index and topographic relief, and the interaction coefficients were 0.773, -0.491, -0.775, respectively.
3.3. Analysis of the coupling effects of the spatial distribution of cypress and topography on surface runoff coefficient
According to the output of SEM, the coupling effects of the spatial distribution of cypress and topography on surface runoff coefficient could be divided into three structures: The coupling effects of surface roughness, runoff path density, and stand density of cypress on surface runoff coefficient; The coupling effects of contagion index and topographic relief on surface runoff coefficient; and the coupling effects of all these five factors on surface runoff coefficient. The Response Surface Method (RSM) was used to analyze the response of surface runoff coefficient to each factor under three groups of structures.
3.3.1. Coupling effects of surface roughness, runoff path density and stand density of cypress on runoff coefficient
Runoff path density and surface roughness, as characteristic parameters of topography, had opposite effects on surface runoff coefficient. Taking the runoff path density/surface roughness as the composite index of surface roughness-runoff path density, the constructed nonlinear regression curve of the surface runoff coefficient to the composite index of surface roughness-runoff path density was shown in Fig.4. Fig.4 suggested that surface runoff coefficient had a positive correlation as well as exponential function relationship with the composite index of surface roughness-runoff path density (R2=0.623).
The nonlinear regression curve of the surface runoff coefficient to the stand density of cypress was shown in Fig.5. Fig.5 suggested that surface runoff coefficient had a negative correlation as well as quadratic function relationship with the stand density of cypress (R2=0.560).
The RSM was used to further analyze the response of the surface runoff coefficient to the coupling of stand density of cypress and the composite index of surface roughness-runoff path density. The response surface was shown in Fig.6, and the corresponding response surface regression equation was shown in Tab.7.
As shown in Fig.6, higher surface runoff coefficient (M>0.5) corresponded to lower stand density of cypress (T<53 ind/100m2) and higher composite index of surface roughness-runoff path density (Q>7.64), while lower surface runoff coefficient (M<0.3) corresponded to lower composite index of surface roughness-runoff path density (Q<6.44). According to Fig.6 and Tab.7, any value of Q in its value range always made ∂M/∂Q>0, indicating that the surface runoff coefficient increased with the increase of Q value, and the increase rate gradually became flat. The surface runoff coefficient increased first and decreased later with the increase of T value, and the critical point of trend change appeared at ∂M/∂T=0. The critical value of T that made ∂M/∂T=0 decreased as the Q value gradually increased.
3.3.2. Coupling effects of contagion index and topographic relief on surface runoff coefficient
The nonlinear regression curve of the surface runoff coefficient to contagion index was shown in Fig.7. Fig.7 suggested that surface runoff coefficient had a negative correlation as well as exponential function relationship with contagion index (R2=0.702).
The nonlinear regression curve of the surface runoff coefficient to topographic relief was shown in Fig.8. Fig.8 suggested that surface runoff coefficient had a positive correlation as well as exponential function relationship with topographic relief (R2=0.493).
The RSM was used to further analyze the response of the surface runoff coefficient to the coupling of the contagion index and topographic relief. The response surface was shown in Fig.9, and the corresponding response surface regression equation was shown in Tab.9.
As shown in Fig.9, higher surface runoff coefficient (M>0.54) corresponded to lower contagion index (W<0.43) and higher topographic relief (S>1.48), while lower surface runoff coefficient (M<0.3) corresponded to higher contagion index (W>0.54). According to Fig.9 and Tab.9, any value of W in its value range always made ∂M/∂W<0, indicating that the surface runoff coefficient decreased with the increase of W value. Any value of S in its value range always made ∂M/∂S>0, indicating that the surface runoff coefficient increased with the increase of S value.
3.3.3. Coupling effects of five factors on surface runoff coefficient
Among the factors that characterize topographic features, the effect directions of runoff path density and topographic relief on runoff coefficient were opposite to that of surface roughness. Taking the topographic relief *runoff path density/surface roughness as the composite index of topography, the constructed nonlinear regression curve of the surface runoff coefficient to the composite index of topography was shown in Fig.10. Fig.10 suggested that surface runoff coefficient had a positive correlation as well as exponential function relationship with the composite index of topography (R2=0.717).
Among the factors that characterized the spatial distribution of cypress, the effect direction of stand density of cypress and contagion index on runoff coefficient was the same. Taking the stand density of cypress* contagion index as the composite index of the spatial distribution of cypress, the constructed nonlinear regression curve of the surface runoff coefficient to the composite index of the spatial distribution of cypress was shown in Fig.11. Fig.11 suggested that surface runoff coefficient had a negative correlation as well as quadratic function relationship with the composite index of the spatial distribution of cypress (R2=0.565).
The RSM was used to further analyze the response of the surface runoff coefficient to the coupling of the composite index of the spatial distribution of cypress and the composite index of topography. The response surface was shown in Fig.12, and the corresponding response surface regression equation and standardization effect of arrangement diagram were shown in Tab.11 and Fig.13.
As shown in Fig.12, higher surface runoff coefficient (M>0.6) corresponded to higher composite index of topography (U>11.4), while lower runoff coefficient (M<0.3) corresponded to lower composite index of topography (U<9.0). According to Fig.12 and Tab.11, any value of U in its value range always made ∂M/∂U>0, indicating that the surface runoff coefficient increased with the increase of U value, and the increase rate gradually became steeper. The surface runoff coefficient increased first and decreased later with the increase of V value, and the critical point of trend change appeared at ∂M/∂V=0. The critical value of V that made ∂M/∂T=0 increased as the U value gradually increased. Fig.23 further illustrated the effect of each parameter in the regression equation on surface runoff coefficient. The parameters U and V2 had a dominant effect on surface runoff coefficient, making the surface runoff coefficient increase monotonically with the change of U value, and change parabolic with the increase of V value, which was consistent with the nonlinear relationship shown in Fig.10 and Fig.11. According to Tab.11, the coefficient of VU was opposite to the coefficient of V2, but the same as the coefficient of U, indicating that the interaction between the spatial distribution of cypress and the topography enhanced the influence of topography on the surface runoff coefficient, with an enhancement rate of 25.05%, and weakened the influence of the spatial distribution of cypress on the surface runoff coefficient, with a weakening rate of 40.74%.