2.2 SOC and TN storage estimation and statistical analysis
SOC and TN storage were calculated using the FD and ESM methods
respectively. The lightest soil mass was referred as the equivalent soil
mass (Lee et al., 2009):
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ FDstock}_{\text{SOC\ or\ TN}}=\text{Con}_{\text{SOC\ or\ TN}}*\text{Soil}_{\text{BD}}*h*10^{-1}\)(1)
\(\text{\ \ \ \ \ \ \ \ \ ESMstock}_{\text{SOC\ or\ TN}}=\text{FDstock}_{\text{SOC\ or\ TN}}-M_{\text{ex}}*\frac{C_{\text{sn}}}{1000}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\)(2)\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ M}_{\text{ex}}=\sum_{1}^{n}\text{Soil}_{\text{BD}}*100-M_{\text{ref}}\)(3)
where \(\text{FDstock}_{\text{SOC\ or\ TN}}\) and\(\text{ESMstock}_{\text{SOC\ or\ TN}}\) represent the SOC or TN storage
estimated based on the FD and ESM methods, respectively;\(\text{Con}_{\text{SOC\ or\ TN}}\) indicates the concentration of SOC
or TN; \(\text{Soil}_{\text{BD}}\) and \(h\) represent soil bulk density
and sample depths, respectively; \(M_{\text{ref}}\ \)is the reference
soil mass (the lightest soil mass), and \(M_{\text{ex}}\ \)is the excess
soil mass. All the constants in Eqs.
(1)-(3) are unit conversion factors.
Due to unavailable soil BD data in some studies, the following
non-linear equations were used to estimate the BD (Song et al., 2005):
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{Soil}_{\text{BD}}=1.3770*Exp\left(-0.0048*\text{Con}_{\text{SOC}}\right)\text{\ \ \ }\)(4)
where BD is soil bulk density (Mg m-3) with a given concentration of SOC
(g kg-1). In addition, 1.3770 and -0.0048 are
empirical coefficients.
Different soil depths were sampled within this study (0-20, 20-30,
30-40, 40-60, 60-100 cm). In order to make comparable estimates of SOC
or TN changes to the same depth and to include more experimental results
from particular regions (southwest China), the storage changes with
irregular
sample depths (h, cm) were adjusted to those of the top 20 cm of the
soil sample using following equations (Yang et al., 2011):
\(Y=1-\beta^{h}\)(5)\(\backslash n\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ C}_{20}=\frac{1-\beta^{20}}{1-\beta^{h}}*C_{h}\)(6)
where \(Y\) is the cumulative proportion of the SOC or TN storage from
the surface to a specific depth h (cm); \(\beta\) is the relative rate
of decrease in the SOC or TN storage at specific depth (0.9786 for SOC
and 0.9831 for TN, respectively) (Jobbágy and Jackson, 2000; 2001).\(\text{\ \ C}_{20}\) is the expected SOC or TN storage adjusted to the
top 20 cm soil layer at a specific site; h is the sample depths
available in each study (cm); \(C_{h}\) is measured SOC or TN storage at
sample depth \(h\) (cm) at a specific site.
We used the mean (Mean), standard deviation (SD), sample size
(\(n\)), standard error (SE) and 95% confidence interval
(95%CI) to characterize the variations of selected datasets. The SE and
95%CI were calculated as follows:
\(SE=SD/\sqrt{n}\) (7)
If the SD data was missing, we would convert the coefficient
of variation of the entire database (Geisseler and Scow, 2014).
The natural logarithm of the response ratio (RR) was employed
to quantify the effect (Hedges et al., 1999):
\(\ \ \ \ \ \ \ \ \ \ lnRR=\ln{(\text{RR}_{d}}/\text{RR}_{c})=ln\text{RR}_{d}-lnRR_{C}\)(8)
where \(\text{RR}_{d}\) and \(\text{RR}_{c}\) are the values of the
control and experimental groups.
The statistical distribution of the lnRR calculated in this
way was found to be nearly normal, and only minor biases were detected
(Hedges et al., 1999). The variances (V) were calculated by:
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ V=\frac{\text{SD}_{d}^{2}}{n_{d}M_{d}^{2}}+\frac{\text{SD}_{c}^{2}}{n_{c}M_{c}^{2}}\)(9)
where \(\text{SD}_{d}\) and \(\text{SD}_{c}\) represent the standard
deviation of the control group and the experimental group, respectively.
In general, the land use pattern (native forest) with the least degree
of damage is the control group in deforestation, and the cropland with
the greatest intensity of activity disturbance is the land restoration
control group; nd and nc are the numbers
of control and experimental groups; \(M_{d}\) is the average of SOC or
TN storage in the control group, and \(M_{\text{c\ }}\)is the average of
the SOC or TN storage corresponding to the experimental group.
The reciprocal of the variance was used as the weight (W) for each lnRR:
\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ W=1/V\)(10)
The overall mean response ratio (lnRR++) and the SE of
lnRR++ were then calculated as:
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ lnRR}_{++}=\frac{\sum_{i=1}^{m}{\sum_{j=1}^{k}W_{\text{ij}R_{\text{ij}}}}}{\sum_{i=1}^{m}{\sum_{j=1}^{k}W_{\text{ij}}}}\)(11)\(\backslash n\ \ \ \ \ \ \ \ \ \ \ \ SE\left(\text{lnRR}_{++}\right)=1/\sqrt{\sum_{i=1}^{m}{\sum_{j=1}^{k}W_{\text{ij}}}}\)(12)
The lnRR++ and 95%CI can be converted by [EXP
(lnRR++) - 1] × 100%. We defined that if the 95%CI
is larger than zero, the effect of the treatment is considered as
significant.
Statistical analyses were performed with IBM SPSS 20.0 (SPSS Inc.,
Chicago, USA). The normality of the data was tested by using the
Shapiro-Wilk test (Stephens,1975). Because some datasets failed to meet
the assumptions underlying parametric statistical tests, nonparametric
procedures were applied to conduct further analysis. Correlation
analysis was applied to examine relationships of response change of SOC
and TN storage (only for cumulative SOC/TN storage on ESM basis) with
other impact factors: climate factors, and geographical factors, the
duration of LUCCs, and soil physicochemical properties. All differences
discussed are significant at the P < 0.05 probability
level unless otherwise stated.