Research ArticleEARTH SCIENCES

Wind-invariant saltation heights imply linear scaling of aeolian saltation flux with shear stress

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Science Advances  07 Jun 2017:
Vol. 3, no. 6, e1602569
DOI: 10.1126/sciadv.1602569
  • Fig. 1 Measurements of saltation layer heights.

    (A) Characteristic saltation layer heights zq versus shear velocities u*, acquired over 30-min intervals, grouped into u* bins. Bars represent uncertainties in zq for each bin. Methods for computing zq from field data of Greeley et al. (57), Namikas (58), and Farrell et al. (59) are described in the Supplementary Materials. (B) Slope parameter b for linear fit to zq = a + bu* versus d50. Data are plotted separately for Farrell et al. (59), who did not report d50. Bars represent uncertainties in b for each site. (C) Mean dimensionless saltation layer height 〈zq〉/d50 versus particle diameter d50. Bars represent uncertainties in 〈zq〉/d50 for each site. Dimensionless saltation layer heights from wind tunnel experiments (30, 39, 40) are shown for comparison.

  • Fig. 2 Saltation mass flux Q versus wind shear stress τ at the three field sites.

    The plotted data correspond to values computed over 30-min intervals and combined into τ bins, with error bars denoting uncertainties in the binned values. Solid lines show linear fits to Eq. 12, whereas dashed lines show nonlinear 3/2 fits to Eq. 13. Fit lines have been extended to demonstrate differences between linear and 3/2 flux law predictions for large τ. The specific parameter values for these fits are listed in Table 2.

  • Fig. 3 Normalized saltation mass flux Embedded Image versus excess shear stress τex.

    Normalized saltation mass flux Embedded Image is computed using Eq. 14, and excess shear stress τex is calculated by Eq. 2. Data are grouped into τex bins, with bars denoting uncertainties for each bin. Dashed lines indicate expected Embedded Image for best-fit values of CQ for each site (Oceano and Rancho Guadalupe values are almost identical), and the solid black line denotes the expected Embedded Image for the uncertainty-weighted mean of CQ across all sites. The values of CQ for each site are also listed in Table 1.

  • Table 1 Grain size, saltation profile, and flux law fit values.

    d50 is the median grain diameter for surface samples. Full grain-size distributions for field sites can be found in the study of Martin et al. (83). Farrell et al. (59) did not report a surface grain size, and Greeley et al. (57) and Namikas (58) did not report associated uncertainties. 〈zq〉 is mean saltation layer height. 〈zq〉/d50 is the ratio of saltation height to grain size. τit and u*,it are best-fit saltation impact threshold shear stress and shear velocity, respectively, for the linear flux law. CQ is the best-fit scaling parameter for Eq. 10 for each site. Included uncertainties here and elsewhere represent 1 SD.

    Location/studyd50 (mm)zq〉 (m)zq〉/d50τit (Pa)u*,it (m s−1)CQ
    Jericoacoara0.53 ± 0.040.097 ± 0.005184 ± 100.135 ± 0.0150.341 ± 0.0197.3 ± 0.9
    Rancho Guadalupe0.53 ± 0.030.107 ± 0.005202 ± 100.110 ± 0.0210.300 ± 0.0285.8 ± 0.5
    Oceano0.40 ± 0.070.055 ± 0.004138 ± 90.094 ± 0.0060.277 ± 0.0095.9 ± 1.0
    Greeley et al. (57)0.230.050 ± 0.006218 ± 26
    Namikas (58)0.250.049 ± 0.003197 ± 11
    Farrell et al. (59)0.081 ± 0.008
  • Table 2 Comparison of linear and nonlinear 3/2 flux law fit values for the three field sites.

    Uncertainties for fit values—scaling parameter C and impact threshold shear stress τit—are expressed as ±1 SD. d50 is the median grain diameter for surface samples, and Embedded Image is the normalized mean-squared difference between best-fit and observed values of saltation flux Q.

    Sited50
    (mm)
    Linear: Q = C(τ − τit)Nonlinear 3/2: Q = Cu*(τ − τit)
    C
    (s × 103)
    τit
    (Pa)
    Embedded ImageC
    (m−1s2 × 103)
    τit
    (Pa)
    Embedded Image
    Jericoacoara0.53 ± 0.04259 ± 160.135 ± 0.0152.59480 ± 430.119 ± 0.0113.56
    Rancho Guadalupe0.53 ± 0.03178 ± 140.110 ± 0.0210.51303 ± 350.080 ± 0.0250.44
    Oceano0.40 ± 0.07165 ± 60.094 ± 0.0062.04359 ± 190.084 ± 0.0052.62

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/6/e1602569/DC1

    Supplementary Text

    fig. S1. Wind angle θ versus shear stress τ over individual 30-min intervals at the three field sites.

    fig. S2. Stability parameter Formula versus shear stress τ over individual 30-min intervals at the three field sites.

    fig. S3. Typical 30-min vertical profile of saltation flux.

    fig. S4. Thirty-minute values of saltation layer height zq versus shear velocity u* at the three field sites.

    fig. S5. Thirty-minute values of saltation mass flux Q versus wind shear stress τ at the three field sites.

    fig. S6. SD of saltation flux values within individual stress bins i, SDQi, versus bin-averaged saltation fluxes, Qi.

    data file S1. Excel spreadsheet (.xlsx) containing unbinned 30-min values for shear velocity u*, shear stress τ, wind direction θ, stability parameter z/L, saltation layer height zq, total saltation flux Q, saltation detection frequency fQ, and associated uncertainties for all of these values (except θ, z/L, and fQ) for each field site.

    data file S2. Excel spreadsheet (.xlsx) containing binned 30-min values for shear velocity u*, shear stress τ, excess shear stress τex, saltation layer height zq, total saltation flux Q, normalized saltation flux Formula, saltation detection frequency fQ, and associated uncertainties for all of these values.

    References (8792)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • fig. S1. Wind angle θ versus shear stress τ over individual 30-min intervals at the three field sites.
    • fig. S2. Stability parameter z/L versus shear stress τ over individual 30-min intervals at the three field sites.
    • fig. S3. Typical 30-min vertical profile of saltation flux.
    • fig. S4. Thirty-minute values of saltation layer height zq versus shear velocity u* at the three field sites.
    • fig. S5. Thirty-minute values of saltation mass flux Q versus wind shear stress τ at the three field sites.
    • fig. S6. SD of saltation flux values within individual stress bins i, SDQi, versus bin-averaged saltation fluxes, Qi.
    • Legends for data files S1 and S2
    • References (87–92)

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    Other Supplementary Material for this manuscript includes the following:

    • data file S1(Microsoft Excel format). Excel spreadsheet (.xlsx) containing unbinned 30-min values for shear velocity u*, shear stress τ, wind direction θ, stability parameter z/L, saltation layer height zq, total saltation flux Q, saltation detection frequency fQ, and associated uncertainties for all of these values (except θ, z/L, and fQ) for each field site.
    • data file S2 (Microsoft Excel format). Excel spreadsheet (.xlsx) containing binned 30-min values for shear velocity u*, shear stress τ, excess shear stress τex, saltation layer height zq, total saltation flux Q, normalized saltation flux ˆQ , saltation
      detection frequency fQ, and associated uncertainties for all of these values.

    Files in this Data Supplement:

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