Measurement uncertainties in quantifying aeolian mass flux: evidence from wind tunnel and field site data

Measurement of sediment flux

Sediment flux was measured using the Modified Wilson and Cook sediment catchers (MWAC). These catchers are designed and used for capturing sediment ranging from dust to sand. This instrument has been extensively tested in numerous studies (e.g., Van Pelt, Peters & Visser, 2009; Sterk & Raats, 1996; Goossens, Offer & London, 2000; Poortinga et al., 2013a; Youssef et al., 2008), where efficiencies between 42% and 120% were reported. The original design (Wilson & Cooke, 1980) contained six plastic bottles with glass inlets and outlets, placed horizontally at six heights between 0.15 and 1.52 m. These bottles were mounted on a rotating pole with a wind vane. Later studies (e.g., Sterk & Raats, 1996) used the same principle, but placed the bottles vertically instead of horizontally (Fig. 2A). Under beach conditions, aeolian sediment transport is governed by saltation, which seldom reaches heights above 15–20 cm. A traditional MWAC sediment catcher would therefore only capture sediment in the lower two or three bottles. This generates significant uncertainty in the analysis, as sediment flux is calculated based solely upon the fitting of an exponential curve through only two or three data points. Therefore, three different designs based upon the traditional MWAC were introduced (Fig. 2), but with all bottles mounted below 25 cm. The first design, nicknamed the “Bug” (Fig. 2B), consists of two stacks of three bottles opposite each other, with their inlets at the same height. The bottles are fixed to a wooden plate with an iron thread to ensure the vertical distance between the two inlets is 5 cm. This design allows for the collection of more measurement points in case of any small horizontal variations in sediment flux, thereby reducing any uncertainty in flux calculations. The second design “Turtle” (Fig. 2C) consists of two bottles on each side, located at various heights. In this design, the bottles are fixed in the original clips, resulting in a larger vertical spacing of 8 cm. In both designs, the horizontal distance between the inlets is 22 cm. The “Tower” design (Fig. 2D) represents the more traditional setup with three or four bottles stacked above each other. The vertical spacing between the bottles is 5 cm, as the bottles are fixed to a wooden plate with iron thread instead of the conventional clips.

To evaluate the differences between the three new designs, they were placed in a 3 × 3 grid and separated by a distance of 3 m. After the first event, an additional array of MWACs was installed 8 m from the first array in order to obtain more measurements (Fig. 1B). To ensure careful monitoring of the experiment, this second array was only installed when environmental conditions were favourable. Each array contained three catchers of each type. They were placed in a relatively flat and homogeneous part of the beach to ensure that the measured sediment flux was uniformly distributed. The elevation of the bottles relative to ground level was measured to an accuracy of 1 mm in order to account for changes in base elevation due to ripples; this was done after installation and before removal of the bottles.

Weather data

A meteorological station with four anemometers was arranged as a vertical array on a tower, which included a wind vane, tipping bucket and two saltiphones (Spaan & van den Abeele, 1991), installed on the beach in the middle of the study area (Fig. 1B), recording every minute to a CR10 Campbell datalogger (Table 1) throughout the period of investigation. The on-site meteorological station contained 3 anemometers, measuring wind speed (ms^-1) at elevations of 0.54, 1.15 and 1.76 m. Pulses from the anemometer were averaged over the recording period and registered as average wind velocities per minute. Wind direction was measured using the wind vane at a height of 2.5 m, while the tipping bucket recorded rainfall to an accuracy of 0.2 mm.

In order to capture the temporal variability in transport intensity, two saltiphones were placed close to the surface at different locations in the experimental area (Fig. 1B). The saltiphones were also connected to a CR10 datalogger with a digital pulse output signal. For every second, the cumulative number of hits for that second were recorded.

Vertical distribution of aeolian mass flux

When using passive sediment traps, sediment is trapped in different compartments that are located at different elevations above the surface. Sediment from each compartment was weighed and then plotted against elevation from which a non-linear regression was calculated to estimate total sediment transport. Despite various thoughts on whether to use an exponential, power of five parameter regression curve, the recent literature (Ellis et al., 2009) suggests that an exponential decay function (Eq. (1)) is most appropriate to describe aeolian sediment transport. (1)${\displaystyle q_z=q_0{e}^{-\beta z}.}$

Curve fitting using Eq. (1) enables us to determine the coefficients q₀ and β, also referred to as the portion of creep (q₀) and decay (β), where z (m) represents the elevation and q_z (kg m^-2) the amount of sediment at elevation z. Regression coefficients q₀ and β can subsequently be used to calculate the total amount of sediment transport Q (kg m^-1). This is done by the integral of Eq. (1) over the height of the saltation layer (taken as 1 m). Sediment fluxes were expressed in kg m^-1 rather than kg m^-1s^-1, as transport was highly intermittent during some events.

The cumulative transport function (CTF) of an aeolian mass flux (q_c) can be described by Eq. (2), using coefficient β from Eq. (1). Figure 3 illustrates the relative sediment flux (black line) and the CTF (green line). When studying the characteristics of aeolian sediment flux, the CTF is preferred to the relative sediment flux, as this function is independent of the number of measurement points. Moreover, only coefficient β is used in the calculation, and therefore, the shape of the CTF is determined by the specific mass distribution between the different compartments and not by their elevation above the ground. (2)${\displaystyle q_c=1-e^{-\beta z}.}$

Coefficient β (Eq. (1)) can also be used to determine the mean (Eq. (3)), median (Eq. (4)), and lower (Eq. (5)) and upper quartile (Eq. (6)). Figure 3 shows the distribution function as a box-plot (top) and also for the relative sediment flux and CTF (bottom). The difference between the mean (brown line) and median (blue line) is the mean is calculated by the integral and the median by the point where the integral is 0.5. The median splits the CTF into two equal parts, whereas the mean describes the point where the CTF would balance. As the median is less sensitive to outliers compared to the mean, we make use of the median. (3)${\displaystyle \overline{q_z}=\frac{1}{\beta }}$ (4)${\displaystyle q_{z_{50}}=\frac{ln\left(2\right)}{\beta }}$ (5)${\displaystyle q_{z_{25}}=\frac{ln\left(\frac{4}{3}\right)}{\beta }}$ (6)${\displaystyle q_{z_{75}}=\frac{ln\left(4\right)}{\beta }.}$

Dong et al. (2003) performed a series of wind tunnel experiments to investigate the flux profile of wind-blown sand. They determined the cumulative mass distribution from the measured data. Moreover, they used the equation q_z = q₀e^−b/z, where the regression coefficient β (here given as b) is divided by elevation (Eq. (1)). Regression parameter β (as in Eq. (1)) can be calculated by β = 1/b. The q_z50 for the different sediment size fractions and wind velocities, using β, is shown in Fig. 4.

Figure 4 shows the variation in q_z50 for the various sediment size fractions over a range of wind speeds, especially where coarser sediments are transported at higher elevations, with q_z50 increasing with wind velocity.

Uncertainties in estimation of aeolian mass flux

Ellis et al. (2009) identified three common methodological inconsistencies and thus sources of uncertainty in measuring aeolian sediment transport using passive traps. These include: (1) inconsistent representation of sediment trap elevations; (2) erroneous or sub-optimal regression analysis; and (3) inadequate or ambiguous bed elevation measurements.

In addition, the number of trapping compartments and location of the lowest sediment trap are also important considerations. Results from Dong & Qian (2007) (Table 1) were used to illustrate how base elevation and number of traps affects sediment flux estimation. They made use of a WITSEG sampler (Dong, Sun & Zhao, 2004), which is a vertically integrated wedge-shaped trap with 60 different compartments, where the lowest orifice can be aligned with the surface. The high data density of the WITSEG is advantageous when interested in a detailed description of the vertical mass distribution.

Dong & Qian (2007) determined the relative sediment flux (using Eq. (7)), where the relative sediment flux (qr_z) at height (z) is calculated by dividing the measured sediment flux (qz) by the total amount of sediment (Q) collected within all compartments. The dimensionless relative height (Zr) was calculated by dividing the actual height (z) by the maximum height (Z; 0.6 m in their study). After fitting a non-linear regression (Eq. (1)) through the relative sediment flux data, they found a linear correlation between the regression coefficients q₀ (portion of creep) and β (decay function). (7)${\displaystyle q{r}_z=\frac{qz}{Q},Zr=\frac{z}{Z}.}$

Figure 5 displays the dimensionless regression coefficients q₀ and β. Using elevation data of the different compartments, we calculated the relative regression coefficient q₀ for a sequence of β’s, while changing the elevation from the base (lines with different colors), but using the same distribution of compartments. Measurements using the WITSEG were taken between 0 and 1 cm, which is in agreement with the experiments. Here, it is important to note the difference in shape between the different base elevation lines. When measurements are taken close to the surface, the correlation between q₀ and β is almost linear, for the domain under consideration. However, when moving further away from the surface, the relationship becomes log-linear (Fig. 5), which has major implications in terms of generating uncertainty in the estimation of q₀. Where measurements are taken further away from the surface, a small error in the calculation of β has even greater impacts upon estimating q₀ compared to measurements taken closer to the surface. An under- or overestimation in the q₀ regression parameter can have a significant effect on determining the total mass flux.

The vertical cumulative mass distribution of the aeolian mass flux was investigated for each of the previous studies as well as for the newly collected dataset. The spatial variability for q_z50 and Q was also investigated for this newly acquired dataset. Due to the relative limited number of datapoints and the desire to maintain the original values in the interpolated maps, we used a simple inverse-distance weighting algorithm, with a minimum of three and a maximum of eight neighbours for spatial interpolation.

The field experiment

New data were collected for six different events (Fig. 14). The duration of the experiments varied from a few hours to two days, whereas saltation was measured for several hours. The averaged shear velocity during these saltation periods varied between 0.30 ms⁻¹ for event 1 and 0.41 ms⁻¹ for event 3. Wind directions predominantly came from the E-NE while only event 3 had variable wind conditions (Fig. 14). During events 2, 3 and 4, rainfall was recorded. Saltiphone data were also included as an indication of the degree of saltation activity.

Of the three catchers (Turtle, Bug and Tower) used in the experiments, two of them contained compartments on both sides of the catchers. The impact of this horizontal variation on sediment flux was investigated by evaluating R² as a non-linear regression (Eq. (1)) was applied to all measurements with at least four data-points. For the bug sampler, a non-linear regression was applied to both sides of the catcher, where the middle bottle of the opposite side was included. The results (Fig. 15A) show that the Tower has the best correlation, followed by the Turtle. The Bug has the poorest performance but contains more measurements. Disturbance of the airflow might have caused the decrease in performance. In general, most measurements have a very high correlation, indicating only minor impacts of horizontal variability. However, to exclude the effect of horizontal variability and other sources of uncertainty, only measurements with an R² > 0.98 were included for further analysis.

The q_z50 values are shown in Fig. 15B. Values for event 6 are higher compared to other events, which is most likely caused by the frozen surface. During events experiencing rainfall, sediment was generally transported over higher elevations. However, the configuration of the traps on the catcher were also found to have an impact. Figure 15C shows that the the Turtle design gives generally higher values for q_z50 compared to the other two designs. This is caused by point density being close to the surface. For the Bug and Tower designs, regression coefficient β is based on one point close to the surface, whereas the Turtle has two data points. The range in q_z50 is larger for the Tower compared to the Bug, as the Bug has two data points at approximately the same elevation, with the measurement being refuted when these points do not match. Measured base elevation was in good agreement with the calculated base elevation, with an average difference of 0.7 mm and a maximum of 5 mm; with the Turtle displaying the largest variation, followed by the Bug and the Tower.

An Inverse Distance Weighting (IDW) algorithm was used to investigate the spatial variability of q_z50 and Q (Fig. 16). We selected events 2, 3, 5 and 6, as during these experiments, two arrays of catchers were used. For all events, the lower-located array has lower values for q_z50 compared to the higher array. Based on our observations, we can confirm that the surface of the upper array was generally wetter than the lower array. This is in line with other findings by Nield & Wiggs (2011). Farrell et al. (2012) also found that sediment is transported over higher elevations on wet surfaces. The spatial variability in saltation height (and thus surface characteristics) shows no alignment with the total transported sediment. Furthermore, the large variability in sediment flux between the different events, suggests there is also large variability in total sediment transport within individual events. Peak values are eight times higher than the lowest values within measurement plots. In general, there is good agreement in measured sediment flux between points located close to each other. However, within meters of these measurements we can see major differences in total sediment flux. Besides the limiting effect of surface moisture on aeolian sediment transport (Namikas & Sherman, 1995; Cornelis & Gabriels, 2003; Neuman, 2003), the variability in sediment flux can be attributed to the presence of aeolian streamers (Baas & Sherman, 2005; Baas, 2008) and/or fetch length (Davidson-Arnott, MacQuarrie & Aagaard, 2005; Bauer et al., 2009; Delgado-Fernandez, 2010).

Differences in vertical sediment flux as found in the wind tunnel studies have limited validity for field studies, as surface conditions were found to have an important impact on saltation. Wet, frozen or crusted surfaces increase saltation height, as particles retain a higher proportion of their impact energy (Farrell et al., 2012). This effect was regarded as localized due to the spatial variability of the surface. Moreover, saltation trajectories have a scattered pattern between impact and fluid threshold. This may impact results from the field, as during some events, transport was highly intermittent due to fluctuations in wind speed (Davidson-Arnott & Bauer, 2009; Stout & Zobeck, 1997). However, additional rapidly-acquired field data are necessary to study this phenomena in more detail.