#### 3.1. Variation of ^{137}Cs Reference Inventory

The regional variability of

^{137}Cs reference inventories in China were mainly related to rainfall and climate, China’s nuclear test in Xinjiang, and the former Soviet Union’s nuclear test in Central Asia [

23]. Many studies have reported that

^{137}Cs reference inventories in Yunnan province are rather low; the main reasons could be that this region is far away from the nuclear test sites as they are separated by mountains. In addition, because of the influence of the southwest monsoon climate, water vapours mainly come from the low latitude Indian Ocean, where few nuclear tests were conducted.

The moisture-rich monsoon airflow from the Indian Ocean form precipitation when forced to rise upon encountering high mountains. As vertical gradients of elevation in the study area reach more than 1500 m, the precipitation increases with elevation, and the distribution of precipitation varies significantly because of the large fluctuation of terrain. The elevation gradients of the catchment selected in this study range from 1350 m to 2835 m along the valley to the summit. The precipitation in the past two years increased from 652.2 to 914.9 mm, increasing by 40.3% along the valley to the top of the mountain. The

^{137}Cs reference inventories increased by 23%, from 573.5 to 705.5 Bq/m

^{2} along a 1600–2600-m elevation. The vertical variability of

^{137}Cs reference inventories demonstrated that it was inaccurate to calculate the soil erosion modulus using only one mean value of reference inventories in the whole study area when the elevation and precipitation changed significantly in the vertical, when using the fallout radionuclide

^{137}Cs technique to estimate soil erosion or sediments deposition. In contrast, the design of multilocation and multi-reference inventories was a more reasonable sampling method (

Table 1).

American scientist Sutherland [

24] pointed out that the sampling method and sample size are primary factors that affect the experimental results of the fallout radionuclide

^{137}Cs technique. However, the sampling method and size of reference inventories are not described in detail in many studies that have applied this method. For reference areas with information on the number of control locations and the estimate of dispersion, the minimum number of samples (

n’) necessary to estimate the mean

^{137}Cs baseline inventory with an allowable error of 10% at a 90% confidence was determined using the following equation [

25]:

where

t is the Student’s

t-value for

a = 0.10 (90% confidence), with

n − 1 degrees of freedom. CV is the coefficient of variation (decimal fraction) and is defined as the standard deviation or arithmetic mean, and

AE is the allowable error 0.1.

Thus, the experimental results are not convincible if it lacks details of the sample method and size of reference inventories, as the estimation of the soil erosion was based on the average value of the reference inventories. Unscientific reference inventories would increase the deviation between the estimated results and the actual values of soil erosion or sediment deposition. Therefore, the dispersion degree of data at the sampling location is a prerequisite to calculate the CV value of the data. The minimum sample size n at a 90% confidence interval under the T test is calculated based on the CV value, and the sampling of reference inventories is unrepresentative when the number of samples (n) is less than n’. The variation coefficients of ^{137}Cs reference inventories at three vertical zones were all within the normal range in this study, with n > n’.

Figure 3 showed the depth distribution of

^{137}Cs reference inventories at the three sampling locations. The

^{137}Cs reference inventories obtained under the

Pinus yunnanensis forest at 2600 m, along a depth distribution, showed a significant variation in the exponential function because this site is covered with the Yunnan pine and is free from human interference due to its high elevation. The

^{137}Cs activities of surface soil were the highest and reached up to 13.2 Bq/kg. The

^{137}Cs activity values decreased exponentially with an increasing soil depth up to a 14-cm depth. The curve presented a typical depth variation of

^{137}Cs in uncultivated soil, which indicated that the sampling sites had not been disturbed by human activities in the past 50 years. The depth distribution of

^{137}Cs reference inventories obtained at 2200 m and 1600 m varied in a pattern typical of cultivated land. The

^{137}Cs activity values in the agricultural layer (approx. 15 cm) were uniform and decreased dramatically below the agricultural layer. It was confirmed that the two reference locations were old terraced fields that had not been changed artificially in the past 50 years; these locations were suitable as reference sites for

^{137}Cs at this elevation and were identified after inquiring with local farmers and investigations.

#### 3.2. Variability of Soil Erosion Modulus in Different Vertical Zones

The average annual soil erosion modulus was calculated by comparing the

^{137}Cs inventory values under different land use types and the

^{137}Cs reference inventory in the corresponding vertical zones. The greater the difference between the

^{137}Cs area activity density and the

^{137}Cs reference inventory value, the more intense the soil erosion of the slope soil was (

Figure 4). The average annual soil erosion modulus of a high-elevation forest (elevation > 2200 m) was 400.3 t/(km

^{2}·a), while that of a low-elevation sparse forest (elevation < 1600 m) was as high as 1756 t/(km

^{2}·a) with less annual rainfall. The average annual soil erosion modulus of a sloping farmland was 2771 t/(km

^{2}·a), which was mainly distributed between 1600 and 2200 m. Thus, the value of 632.7 Bq/m

^{2} was used as the reference inventory in the calculation process. The steep slope farmland (slope > 15°) had an intense soil erosion, with an average annual soil erosion modulus as high as 7282 t/(km

^{2}.a) (

Figure 5).

Many researchers have used different methods to study soil erosion in the Hengduan Mountains. For example, Wen [

26] obtained an average soil erosion modulus of 1668 t/(km

^{2}·a) in the upper reaches of Longchuan River, based on the relationship between the sediment transport modulus and catchment area. In this study area, the Liangshan Town catchment, the average soil erosion intensity of a sloping farmland, was 2771 t/(km

^{2}·a) over the recent decades, which belonged to moderate erosion intensity; the average soil erosion intensity of a sparse forestland was 1756 t/(km

^{2}·a), which belonged to a mild erosion intensity, indicating that the soil erosion situation in this area was not serious.

The soil erosion modulus of an entire catchment can be calculated using the following formula [

27]:

where

E_{w} is the erosion modulus for the entire catchment or area (t·km

^{−2}·a

^{−1});

n is the number of sampling units;

S_{i} is the surface area of the sampling units;

S_{tot} is the surface area of the entire catchment or area (km

^{2}); and

E_{i} is the average erosion modulus of the representative fields of the sampling unit

i (t·km

^{−2}·a

^{−1}). The average soil erosion modulus of the entire catchment was 1216.5 t/(km

^{2}·a), calculated using Equation (4), which was lower than the values obtained by other researchers in this region (

Table 2).