3.1. Flux Density Profiles
[11] Sediment flux density is generally expressed as the mass of sediment passing through a unit area perpendicular to the transport direction within a unit time. To establish the sediment flux density profiles, we converted the observed sediment masses in each observation into units of kg m^{−2} h^{−1}. Figure 4 shows some representative results for the variation in observed sediment flux density as a function of height (i.e., geometric mean height at the center of each sample chamber) in the three plots at different mean wind speeds.
[12] Regression analyses showed that for all three plots and all wind speeds, the flux density decays exponentially with height:
where q(z) is the flux density at height z, and a and b are regression coefficients. Table 1 indicates that all the correlations are statistically significant, in more than 85% of the cases, the correlation coefficient (r^{2}) was greater than 0.98. In only four cases, such as those at 8.72 ms^{−1} for the plot with enclosed shifting sand (nonfitted) and at 8.47, 8.72 and 9.10 ms^{−1} for the plot open shifting sand, the flux density profiles deviate significantly from the exponential decay law (with r^{2} < 0.8) because rippled sand accumulation about 30–40 mm tall formed about 0.5 m upwind the sampler.
Table 1. Results of the Regression Analyses for the Flux Density Profiles Above the Three Surfaces^{a}Plot  V (m s^{−1})  Q_{O} (kg m^{−1} h^{−1})  a  b  z_{a}  r^{2} 


Gravelcovered plot  5.29  3.6  132.6  0.028  0.028  0.999 
5.31  0.9  28.5  0.031  0.031  0.996 
5.33  3.9  136.8  0.029  0.029  0.994 
5.89  4.1  119.2  0.037  0.037  0.958 
5.93  4.6  189.1  0.026  0.026  0.999 
6.23  2.9  63.0  0.043  0.043  0.990 
6.55  4.7  199.2  0.024  0.024  1.000 
7.07  57.5  1250.7  0.045  0.045  0.996 
7.11  3.0  110.9  0.026  0.026  0.999 
7.18  67.6  1756.0  0.040  0.040  0.981 
7.19  3.7  62.1  0.058  0.058  0.989 
7.33  49.0  605.5  0.084  0.084  0.956 
7.70  12.6  428.2  0.029  0.029  0.999 
7.83  13.3  278.0  0.045  0.045  0.996 
8.34  28.7  486.4  0.054  0.054  0.973 
8.47  14.5  390.4  0.030  0.030  0.990 
8.54  38.9  486.1  0.078  0.078  0.994 
8.56  35.8  505.8  0.072  0.072  0.999 
8.72  14.5  419.2  0.032  0.032  0.997 
8.96  13.3  288.2  0.040  0.040  0.994 
9.10  30.6  599.4  0.038  0.038  0.979 
9.17  24.9  542.3  0.044  0.044  0.992 
11.3  74.8  889.6  0.077  0.077  0.934 

Plot with enclosed shifting sand  5.29  0.4  32.1  0.014  0.014  1.000 
5.31  1.5  91.3  0.017  0.017  1.000 
5.33  2.0  77.6  0.023  0.023  0.996 
5.89  4.5  229.8  0.020  0.020  0.999 
5.93  1.3  49.6  0.022  0.022  0.995 
6.23  4.0  197.6  0.019  0.019  0.997 
6.55  0.03  339.9  0.024  0.024  0.999 
7.07  55.0  2036.9  0.025  0.025  0.999 
7.11  4.6  163.1  0.028  0.028  1.000 
7.18  40.7  150.2  0.261  0.240  0.859 
7.19  12.0  410.7  0.029  0.029  0.999 
7.33  51.7  1578.9  0.032  0.032  1.000 
7.70  18.9  496.2  0.027  0.027  0.934 
7.83  18.6  542.5  0.033  0.033  0.992 
8.34  26.0  631.8  0.036  0.036  0.995 
8.47  22.2  702.8  0.029  0.029  0.998 
8.54  19.2  349.9  0.050  0.050  0.996 
8.56  22.4  414.7  0.056  0.056  0.991 
8.72  27.8  —  —  —  — 
8.96  18.3  641.6  0.026  0.026  0.998 
9.10  15.3  438.6  0.027  0.027  0.993 
9.17  45.1  1171.0  0.033  0.033  0.995 
11.30  97.5  1494.2  0.064  0.064  0.954 

Plot with open shifting sand  5.29  4.2  189.9  0.023  0.023  1.000 
5.31  1.3  82.0  0.016  0.016  1.000 
5.33  2.5  113.9  0.022  0.022  1.000 
5.89  4.4  176.1  0.023  0.023  0.998 
5.93  2.6  151.2  0.018  0.018  0.999 
6.23  3.5  143.8  0.025  0.025  1.000 
6.55  5.9  258.3  0.022  0.022  0.999 
7.07  74.0  2913.5  0.024  0.024  0.999 
7.11  5.6  194.0  0.027  0.027  0.997 
7.18  89.6  1403.9  0.060  0.060  0.985 
7.19  7.8  312.9  0.024  0.024  0.999 
7.33  67.4  2355.8  0.029  0.029  0.993 
7.70  12.8  401.7  0.023  0.023  0.983 
7.83  14.5  484.2  0.030  0.030  0.999 
8.34  17.4  458.9  0.035  0.035  0.989 
8.47  18.5  105.1  0.093  0.093  0.629 
8.54  24.2  792.1  0.024  0.024  0.989 
8.56  23.1  806.7  0.025  0.025  0.997 
8.72  33.5  602.2  0.022  0.022  0.725 
8.96  17.5  450.0  0.031  0.031  0.991 
9.10  38.2  390.0  0.094  0.094  0.798 
9.17  90.3  1106.5  0.068  0.068  0.964 
11.30  110.8  391.1  0.294  0.260  0.951 
[13] Integration of the flux density profile function for height yields the calculated transport rate (Q_{c}) that is defined as the mass passing through a unit width perpendicular to the transport direction within a unit time. An ideal flux density profile function should also be a good predictor of the transport rate.
[14] To confirm the goodness of fit of equation (1), we compared the transport rate calculated using equation (2) with the actual observed transport rate obtained by summing up the observed mass flux at all heights (Figure 5). The fit was strong and statistically significant (r^{2} = 0.98, significance level p < 0.05). Therefore, equation (1) provides an adequate description of the aeolian flux density profiles in the three plots. This may be because the particlesize distribution (Figure 3) in the study plots is predominantly within the range for saltation [Pye and Tsoar, 1990]. It is now widely accepted that the mass flux density of suspended sediment decays with increasing height following a power function [Zingg, 1953; Liu, 1960; Nickling, 1978; Takeuchi, 1980; Fryrear, 1987; Ni et al., 2003], while the mass flux density of saltating sediments decays with increasing height following an exponential decay function such as equation (1) [Kawamura, 1951; Horikawa and Shen, 1960; Williams, 1964; Nalpanis, 1985; Nalpanis et al., 1993; Dong et al., 2003b; Ellis et al., 2009]. Our results confirm this belief.
[15] The regression coefficients in equation (1) can be defined as a function of the surface treatment, wind speed, and aeolian transport rate. Equation (2) indicates that coefficient a should be proportional to the transport rate. This is supported by the relationship between coefficient a and observed transport rate Q_{o} in Figure 6. Although regression analysis can yield various empirical relationship between coefficient a and Q_{o}, equation (3) in which coefficient a is proportional to Q_{o} is also proven to be a reasonable good descriptor with a little reduced correlation coefficient (Figure 6).
where Q_{o} is the observed transport rate (kg m^{−1} h^{−1}), k is a regression coefficient that equaled 18.0 for the gravel surface (r^{2} = 0.77, p < 0.05), 23.4 for the enclosed shifting sand (r^{2} = 0.73, p < 0.05), and 25.0 for the open shifting sand (r^{2} = 0.64, p < 0.05). The relationships for the enclosed shifting sand and open shifting sand were similar, but both differed greatly from that for the gravel surface. Difference in coefficient k implies the influence of surface treatment on aeolian transport, which will be discussed in section 3.2.
[17] Thus, regression coefficient b in equation (1) characterizes the relative decay rate of flux density with increasing height. The greater the b value, the more gently the flux density decays with height. Figure 7 shows that the relative decay rate depends on both the surface treatment and the wind speed, and that it increases with increasing wind speed. The enclosed shifting sand and open shifting sand plots had similar relative decay rates, but the relative decay rate above the gravelcovered plot was much larger (i.e., the rate of decay was smaller). This can be explained if saltation is more intense over the gravelcovered plot (i.e., because the collisions between saltating particles and the gravel are more elastic) and if saltation height increases as the wind speed increases. Previous wind tunnel tests reached the same conclusions [Dong et al., 2003b, 2004].
[18] The relative intensity of saltation can be represented by the average saltation height:
where z_{a} (m) is the average saltation height. In the present study, we calculated the average saltation height using the following equation:
[19] Table 1 indicates that the average saltation height equaled the corresponding value of b. This is because the value of b in the present study was so small that the value of e^{−1/b} in equation (6) was almost negligible. In that case:
[20] It is worth noting that b will become significantly greater when saltation increases in intensity, and that z_{a} will then differ increasingly from coefficient b. This analysis suggests that the relative decay rate and the average saltation height are two aspects of the same physical phenomenon, and that a greater saltation height corresponds to a lower relative decay rate.
[21] These results indicate that the flux density profiles for the three surface treatments are adequately described by the coefficients a and b in equation (1). Figures 6 and 7 indicate that the flux density profiles for the enclosed and open shifting sand plots were very similar, but that both differed greatly from that for the gravelcovered plot. The characteristics of surface cover that influences saltation of particles is therefore an important variable that influence the flux density profile.
3.2. Transport Rate
[22] Most previous research revealed that aeolian transport rate was proportional to the cube of wind speed (Dong et al., 2003a). Although the field observed data in Figure 8 is scattered, trend lines that relate transport rate linearly with the cube of both the mean wind speed (Figure 8a) and the maximum wind speed (Figure 8b) can be found. This is because the wind speed fluctuated during the observation period, but the stronger winds, including the maximum wind speed, were more significant in determining the transport rate.
[23] The drift potential parameter proposed by Fryberger [1979] that is calculated by equation (8) is commonly used by aeolian researchers to characterize the transport potential of a wind. We used our data to describe the relationship between the observed transport rate (Q_{o}) and the drift potential (D_{P}). We found that the transport rate was more strongly correlated with drift potential (Figure 8c) than with the mean and maximum wind speeds.
where D_{p} is drift potential, V is wind velocity at 10 m height, V_{t} is the threshold wind velocity at 10 m height, t is time wind blew, expressed as a percentage on N summary.
[24] We obtained the following empirical relationship between transport rate and drift potential by regression analysis:
where D_{p} is the drift potential (in vector units, VU) and A is a regression coefficient, which equaled 2967.6 for the gravelcovered plot (r^{2} = 0.93, p < 0.05), 2891.4 for the plot with enclosed shifting sand (r^{2} = 0.76, p < 0.05), and 3996.5 for the plot with open shifting sand (r^{2} = 0.80, p < 0.05). The transport rates for the gravelcovered plot and the plot with enclosed shifting sand were similar, and both were much smaller than the value for the plot with open shifting sand. This is because the gravelcovered plot tends to trap passing sand particles, whereas the aeolian transport above the plot with enclosed shifting sand does not become saturated because of the limited fetch length.