Impact of historic grazing on steppe soils on the northern Tibetan Plateau

Abstract

Aims

Few studies have focused on changes in the physical and chemical properties of soils that are induced by grazing at high altitudes. Our aim was to identify potential responses of soil to grazing pressure on the semiarid steppe of the northern Tibetan Plateau and their probable causes.

Methods

Fractal geometry to describe soil structure, soil dynamics, and physical processes within soil is becoming an increasingly useful tool that allows a better understanding of the performance of soil systems. In this study, we sampled four experimental areas in the northern part of the Tibetan Plateau under different grazing intensities: ungrazed, lightly grazed, moderately grazed and heavily grazed plots. Fractal methods were applied to characterise particle-size distributions and pore patterns of soils under different grazing intensities.

Results

Our results reveal a highly significant decrease in the fractal dimensions of particle size distributions (D ₁ ) and the fractal dimensions of all pores (D ₂ ) with increasing grazing intensity. Soil organic carbon (SOC), total N and total P concentrations increased significantly with decreasing grazing intensity. We did not find differences in soil pH in response to grazing.

Conclusions

Grazing induced a significant deterioration of the physical and chemical topsoil properties in the semiarid steppe of the northern Tibetan Plateau. Fractal dimensions can be a useful parameter for quantifying soil degradation due to human activities.

Appendix

Equation 2 was derived from a modified number-based method for estimating fractal dimensions of soils. The following algorithm was extracted from Kozak et al. (1996).

As suggested by Mandelbrot (1982), the fractal dimension, D, is defined as

$$ N(x > {x_{{\min }}}) = kx_{{\min }}^D $$

(A1)

where x _min is a linear size, N (x > x _min ) is the number of objects with linear sizes, x, greater than x _min and k is a constant.

According to Eq. A1, the number of soil particles greater than x _n is calculated as

$$ N(x > {x_n}) = \sum\limits_{{i = 1}}^n {\frac{{M({x_{{i - 1}}} > x > {x_i})}}{{{c_i}{\rho_i}\bar{x}_i^3}}} $$

(A2)

where M is a set of relative masses of soil particles and n is the total number of classes. The symbol ρ _i designates the particle density, and c _i is the constant related to the particle shape. In a fraction of sizes x _i-1 > x > x _i , the number of particles, N (x _i-1 > x > x _i ), is related to the mass of this fraction, M (x _i-1 > x > x _i ), as

$$ N({x_{{i - 1}}} > x > {x_i}) = \frac{{M({x_{{i - 1}}} > x > {x_i})}}{{{c_i}{\rho_i}\bar{x}_i^3}} $$

(A3)

where ${\bar{x}_i}$ is a characteristic particle size. A common assumption is that

$$ {\bar{x}_i} = \frac{{{x_{{i - 1}}} + > {x_i}}}{2} $$

(A4)

If we treat the mass of the ith fraction, M (x _i-1 > x > x _i ) as a sum of the masses of the P subfractions,

$$ M({x_{{i - 1}}} > x > {x_i}) = \sum\limits_{{j = 1}}^p {M({y_{{j - 1}}} > y > {y_j})} $$

(A5)

where

$$ {y_0} = {x_{{i - 1}}},{y_j} = {x_{{i - 1}}} + ({x_i} - {x_{{i - 1}}})\frac{j}{p},{y_p} = {x_i},j = 1,2, \ldots, p $$

(A6)

If the particle size distribution satisfies Eq. A1, the number of particles of sizes y _j-1  > y > y _j is equal to

$$ N({y_{{j - 1}}} > y > {y_j}) = k\left( {y_j^{{ - D}} - y_{{j - 1}}^{{ - D}}} \right) $$

(A7)

Substituting the above into Eq. A3, we have

$$ M({y_{{j - 1}}} > y > {y_j}) = k{c_j}{\rho_j}\bar{y}_j^3\left( {y_j^{{ - D}} - y_{{j - 1}}^{{ - D}}} \right) $$

(A8)

We assume that within a given fraction i, c _j and ρ _j are constants equal to c _i and ρ _i . Then, as the value of subfraction p approaches infinity, we derive the following from Eqs. A4 and A8 applied to the right-hand side of Eq. A5:

$$ \frac{{M({x_{{i - 1}}} > x > {x_i})}}{{{c_i}{\rho_i}k}} = \mathop{{\lim }}\limits_{{p \to \infty }} \sum\limits_{{j = 1}}^p {\left( {y_j^{{ - D}} - y_{{j - 1}}^{{ - D}}} \right)\bar{y}_j^3} $$

(A9)

Using Taylor’s expansion, we derive

$$ \mathop{{\lim }}\limits_{{p \to \infty }} \sum\limits_{{j = 1}}^p {\left( {y_j^{{ - D}} - y_{{j - 1}}^{{ - D}}} \right)\bar{y}_j^3} = D\int {_x^{{{x_{{i - 1}}}}}} {y^{{2 - D}}}dy $$

(A10)

Integration in Eq. A10 yields Eq. 2:

$$ \frac{{M({x_{{i - 1}}} > x > {x_i})}}{{{c_i}{p_i}k}} = \left\{ {\begin{array}{*{20}{c}} {\frac{D}{{3 - D}}\left( {x_{{i - 1}}^{{3 - D}} - x_i^{{3 - D}}} \right),\quad D \ne 3} \\ {3\ln (\frac{{{x_{{i - 1}}}}}{{{x_i}}}),\quad D = 3} \\ \end{array} } \right. $$