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%.