2.1. Site Description
The Qinling Mountains (32°30′–34°45′ N, 104°30′–112°45′ E) in central China constitute a substantial physical obstacle for northward and southward movement of air masses, because of their high elevation and east-to-west arrangement. Therefore, these mountains are critical in stabilizing the distribution of climate and life zones in eastern China [
21]. The pine-oak mixed stand is extensive in the middle of the altitudinal gradient of the Qinling Mountains and it plays important ecological roles in water purification and carbon sequestration.
Experiments were conducted at the Qinling National Forest Ecosystem Research Station (QNFERS), located on the southern slope of the Qinling Mountains, in Huoditang, Ningshan County, Shaanxi Province (32°18′ N, 108°20′ E). The altitude of the study area is from 1500–2500 m above sea level. The area experiences a subtropical climate, with annual mean temperatures around 8–10 °C, annual mean precipitation around 900–1200 mm, and annual mean evaporation around 800–950 mm. The main soil type is mountain brown soil, developed from granite material, with depths ranging from 30 to 50 cm. The total forest area is 2037 hectares in the station. Natural forest occupies 93% of the total forest area in QNFERS, with various vegetation types distributed in this region along the altitudinal gradient, such as evergreen deciduous mixed forest (pine-oak mixed forest), deciduous broad-leaved forest (oak, red birch), temperate coniferous forest (Chinese red pine, Armand pine) and cold temperate coniferous forest (spruce, fir). The most dominant forest type is pine-oak mixed forest with an average stand age of the stands of 42 years and an average height of 9.2 m. Common tree species include Pinus tabulaeformis, Pinus armandii, and Quercusaliena var. acuteserrata. The understory species are abundant.
2.2. Experimental Design
Our experimental plots were located on steep slopes (average slope gradient 30°) with thin soil depth (<50 cm), and in fragmented terrain. These characteristics make it extremely difficult to obtain the amount of replications for a randomized block design or orthogonal experiment design.
The Central Composite design (CCD) is the most popular of the many response surface methodology (RSM) classes, and is widely used for estimating second-order response surfaces [
22]. The application of these statistical techniques in experiments has the advantages of requiring fewer resources (time, numbers of duplication, and amount of experimentation), but can also reduce process variability [
23]. RSM is a collection of statistical and mathematical techniques useful for developing, improving, and optimizing processes [
24]. These techniques relate a response variable to predictors that have multiple levels. The coded levels and the actual levels of the independent variables were calculated according to Equations (1)–(3):
where
Xj is the real value of the independent variable,
X0 is the real value of an independent variable at the center point, ∆
j is the step change value, and
xj is the coded value of an independent variable [
25].
The CCD consists of 2
k full or 2
k−1 half-replicate (
k = number of independent variables) factorial points (±1, ±1, …, ±1); 2
k axial or star points of the form (±α, 0, …, 0), (0, ±α, …, 0); and a center point (0, 0, …, 0). The axial points are replicated one and two times, and allow for the efficient estimation of pure quadratic terms. The center points are replicated one and three times, and provide information about the existence of curvature. The number of center runs can be altered, providing flexibility to improve error estimates and power. Finally, the factorial points allow estimation of the first-order and interaction terms. The CCD can be summarized with the following equation (Equation (4)):
where
N is the total number of experimental runs,
f is the number of factorial points, 2
k is the axial point, α is the number of times the axial point is replicated, and
n0 is the center point. The axial distance, α is chosen based on the region of interest. Selecting the appropriate values of α specifies the CCD type, with
being a spherical CCD [
22].
The relationship between response and predictor levels can be approximated with a second-order response surface mode [
22] (see Equation (5)):
where
y is the measured response; β
0, β
i, β
j, β
ii, and β
ij are parameter coefficients;
xi,
xj are the input variables; and ε
ij is an error term.
Analysis of Variance (ANOVA) is used to optimize Equation (5) and analyze the interaction effect of the input variables on measured response and the single effect of input variables on measured response by differentiating variable
j on variable
i and vice versa [
25].
The contributions of the controlled variables to the dependent variable, as
F > 1 were estimated following the method of Tang [
25] (see Equations (6) and (7)).
where Δ
j is the contribution of controlled variable
j to the dependent variable;
Sj is the linear term for the controlled variable
j;
Sij is the interaction term for the controlled variables
i and
j;
Sjj is the quadratic term for the controlled variable
j;
F is the
F-value in the ANOVA.
Our experiment was based on CCD, generated using Data Processing System (DPS) version 14.50 [
25].
In a preliminary investigation conducted over the 15–25 August 2012, we selected 13 plots (20 m × 20 m) with similar slope gradients, canopy cover, tree species composition, and soil depths (
Table 1) for the current experiment. For each plot, we surveyed the soil depth, as well as the height (m), diameter at breast height (DBH, cm), and canopy cover (%) of the tree species. The intensity of selective thinning (
ST, %) and thinning residual removal rate (
TRR, %) were calculated using Equations (8) and (9), respectively:
where
Af,
AT,
Qi, and
Qt are the basal area of logged trees, total basal area of trees, fresh weight of removed residue, and fresh weight of total residue in all plots.
The design consisted of two independent variables (
X1 = thinning and
X2 = thinning residual removal), each with five intensity/rate gradients (
Table 2). For the controlled factor (independent variable) in the current study, the value α was
= 1.414. We set the +α and −α level thinning intensity to 25% and 5% respectively according to the Regulation for Tending of Forest [
26], and 100% and 0% for the residual removal rate. To explore the effects of the thinning operation on NEP, zero-treatment of thinning intensity was excluded.
For a central composite design with two independent, five-level variables, 13 experimental runs are required, with four factorial points from treatment I to treatment IV, four axial points from treatment to treatment VIII, and five center points treatment IX (
Table 3). The factorial points were a combination of controlled variables at ±1 levels (a thinning intensity at ±1 level represent 22.07% and 7.93% respectively; a thinning residual removal rate at ±1 levels represent 85.36% and 14.64% respectively) in our study. Similarly, the star points were a combination of controlled variables at ±α and 0 levels (a thinning intensity at ±α and 0 levels represented 25%, 5%, and 15% respectively; a thinning residual removal rate at ±α and 0 levels represented 100%, 0%, and 50% respectively). The center point was a combination of controlled variables at 0 levels. Different thinning factors were applied in each plot, except for the plots categorized as center points (
Table 3).
The dependent variable in this study was the average of NEP in 2013 and in 2014 in post-treatments. The experimental results were fitted to a second-order polynomial model, and the regression coefficients were determined. The quadratic model for predicting the optimal combination of thinning intensity and removal rate to reach the highest value of NEP (
Yk) is described by Equation (10):
where
bk0,
bki,
bkii, and
bkij are the constant regression coefficients of the model, and
xi,
xj are codes of the independent variables (
xi = thinning intensity and
xj = thinning residual removal rate).
2.6. Data Processing and Analysis
Ratio of tree species (
Ri) was calculated as Equation (11).
where
bi and
B is basal area of the tree species
i and total basal area of tree species in an identical treatment.
Composition of tree species is the proportion Ri: Rm: Rn.
Where Ri, Rm and Rn is ratio of tree species i, m and n respectively.
Diameter classes were used to describe the DBH dynamics of tree species (
Table 4). DBH ratio of tree species (
Dij) was calculated as follows:
where
nij is number of tree species
i in diameter calss
j and
Ni is number of total tree species in all diameter classes of 13 plots.
Chemical compound groups (ESC, WSC, ASC, and NSC) of litterfall were calculated by mass weighted average of tree species. We inputted the quality of litterfall from each post-treatment, the measured chemical compound groups of tree species, and the data of annual precipitation and air temperature from QNFERS into the Yasso07 model to estimate soil CO
2 efflux (
Rs) [
28].
Based on monitoring DBH and the height of remaining trees in the thirteen plots in 2013 and 2014, living biomass (Mg·ha
−1) of whole remaining trees was estimated as Equations (13)–(15) [
36].
Q. aliena var.
acutesserata:
where
Y is the living biomass of trees and
x is the stand growing stock (m
3·ha
−1).
The stand growing stock was calculated by the stems and volume of each tree. The volume of a single tree was calculated as follows [
37] (see Equations (16)–(18)):
Q. aliena var.
acutessera:
where V (m
3), D (cm), and H (m) are volume, DBH, and height of a tree respectively.
Net primary productivity (NPP) of the current forest was the living tree biomass increment in two consecutive years multiplied by the carbon ration in plants (0.50 in this study).
NEP was calculated as following.
Figures were plotted using Origin8.0 (OriginLab Corporation, Northampton, MA, USA) software. DPS v14.50 software (Zhejiang University, Hangzhou, China) was used to fit models, analyze the data, determine the effects of a single independent variable and the interaction of independent variables on NEP and optimize the combination of thinning intensity and residual removal rate for the highest NEP.