Changes to Subaqueous Delta Bathymetry Following a High River Flow Event, Wax Lake Delta, USA

Abstract

The construction of the subaqueous delta front is foundational to deltaic land building and field data is needed to validate conceptual models of delta front evolution. The bathymetric change that occurred across the entire delta front (~ 75.9 km2) of the Wax Lake Delta (WLD) in coastal Louisiana was measured between February 2015 and July 2016. Sediment removal (− 9.85 × 106 m3) exceeded sediment accumulation (7.64 × 106 m3), making the delta front net-erosional (− 2.21 × 106 m3) despite the occurrence of a flood. These results factor in an estimated 4.28 cm of subsidence during the survey period. Deposition on the delta front was localized around channels and the northern and eastern flanks of the delta whereas erosion was more spatially uniform. This erosion coincides with an anomalously strong winter storm season that may have exported this sediment offshore and is consistent with a growing body of research that identifies winter storms as a significant mechanism for sediment removal from Atchafalaya Bay. Winter storm erosion is crucial to understanding and predicting volumetric growth of the WLD and has important implications to land building from sediment diversions. Future models of deltaic growth need to account for significant volume export and erosive episodes on the delta front.

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Data availability

Three bathymetric data sets used in this study are available for download in a digital data repository (https://figshare.com) using the supplied DOI: February 2015 (DEM) (https://doi.org/10.6084/m9.figshare.7674833), July 2016 DEM (https://doi.org/10.6084/m9.figshare.7674419), and DEM of Difference (DoD) from February 2015 and July 2016 (https://doi.org/10.6084/m9.figshare.7670813).

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Acknowledgments

The University of Arkansas faculty and students are gratefully acknowledged for their assistance in data collection and post-processing.

Funding

This study was funded through the Department of Energy grant (DESC0016163, which supported data collection) and Petroleum Research Fund grant (DNI-57764, which supported salary for Whaling) awarded to J.S.

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Correspondence to Amanda Whaling.

Additional information

Communicated by Mead Allison

Appendices

Appendix 1. Measurement Accuracy

Bathymetric surveying involves two primary measurements: horizontal position (xy-location), and the vertical position (depth below MLLW). The horizontal position accuracy is dependent on the instrument accuracy of the GPS and the cone area of the depth sounder. The integrated GPS measurements are WAAS (Wide Area Augmentation System) corrected which generates measurement accuracy of ± 4 m upper 95% confidence limit (WAAS Performance Standard, 2008). The cone area is dependent on the survey depth and the depth sounder’s beam angle; cone area increases with increasing depth and beam angle. For shallow depths (< 10 m), the component of horizontal accuracy affected by the Lowrance cone area is higher (± 1 m) than the WAAS-corrected measurement accuracy (Heyman et al. 2007). Since the survey area does not encompass depths > 10 m, we used the GPS instrument accuracy to choose a large cell size of 25 m for the DEMs. The vertical accuracy of the depth soundings is dependent on the instrument accuracy of the depth sounder and the speed of sound in water. Standard 200-kHz depth sounders are accurate to within ± 3 cm (Heyman et al. 2007). The depth soundings are corrected for temperature changes, but not salinity or depth. Salinity is assumed to be constant during the week of data acquisition since the survey area is located sufficiently landward of the salinity front which has a range of 25 psu in the mixing zone (Cobb et al. 2008). Even an unlikely 25-psu increase in salinity in the survey area would translate to a depth sounding < 2% deeper. Similarly, changes in the speed of sound due to depth will have a negligible effect on the depth sounding given that the speed increases linearly by ~ 0.02 m/s per meter increase in depth and the range in depth in the survey area is ~ 4 m below MLLW. As a result, we chose a contour interval of 20 cm, which is larger than the depth sounder instrument accuracy mentioned above.

Appendix 2. Error Analysis

In this section, we compute the bias of the DoD inherently introduced from the contouring method and interpolation methods used to create the 2015 and 2016 DEMs. Manual contouring was preferred over automated contouring techniques due to the density of survey transects and complexity of the delta front shape. At large, stream-wise distances between channel transects, most algorithms used to contour point data could not connect channel thalwegs and instead interpolate a topographic high between the thalwegs. This “bubbling effect” in the resultant DEM could potentially be avoided with more closely spaced transects; however, this is time-consuming and not cost-effective for repeat bathymetric surveys. The manual contouring method has the advantage of eliminating these interpolation errors; however, biases are inherently introduced.

In order to test whether the DoD provides an unbiased model of elevation change, we compare direct measurements of bed change (Δzobs) to DoD cell values (\( \Delta \hat{z}\Big) \). We assume that the bathymetric change at any point on the delta is parameterized by Δz which has a probability distribution for observed data, Δzobs, and an estimator \( \Delta \hat{z} \), the DoD cell values, based on the observed data such that

$$ {P}_{\Delta z}\left({\Delta z}_{\mathrm{obs}}\right)=P\left({\Delta z}_{\mathrm{obs}}|\Delta z\right). $$
(2)

In Eq. 2, Δzobs is the difference between the depth value at a cleaned data point from the 2016 survey that is located within 3 m radially from the coordinates of a cleaned data point from the 2015 survey, i.e.,

$$ {\Delta z}_{\mathrm{obs}}={\left({z}_{2016}\right)}_{x_b,{y}_b}-{\left({z}_{2015}\right)}_{x_a,{y}_a} $$
(3)

where xb = r cos(θ) and yb = r sin(θ); r is a distance between 0 and 3 m from the point (xa, ya) and θ is an angle between 0 and 360°. If we then take \( \Delta \hat{z} \) to be the difference values attained by differencing the 2016 and 2015 DEM depth values at the midpoint of (xa, ya) and (xb, yb), we can compute the bias of \( \Delta \hat{z} \) relative to Δz with Eq. 4:

$$ {\mathrm{Bias}}_{\Delta z}\left[\Delta \hat{z}\right]={E}_{{\Delta z}_{\mathrm{obs}}\mid \Delta z}\left[\Delta \hat{z}\right]-\Delta z={E}_{{\Delta z}_{\mathrm{obs}}\mid \Delta z}\left[\Delta \hat{z}-\Delta z\right] $$
(4)

where \( {E}_{{\Delta z}_{\mathrm{obs}}\mid \Delta z} \) denotes the expected value over the distribution Pzobs| Δz). An estimator is said to be unbiased if \( {\mathrm{Bias}}_{\Delta z}\left[\Delta \hat{z}\right]=0 \) for all values of parameter Δz. For a dataset of 927 observations, we find that \( {\mathrm{Bias}}_{\Delta z}\left[\Delta \hat{z}\right] \) = 0.0045 m (Fig. 7); therefore, the change in elevation estimated by the DoD is considered unbiased. The standard deviation of \( \Delta \hat{z} \), \( {\updelta}_{\Delta \hat{z}} \), was found to be ± 0.20 m.

Appendix 3. Uncertainty in Volume

Uncertainty estimates for volumetric change calculations provide bounds for the reliability of the magnitude of erosion and deposition on the WLD. The volume calculations are dependent on many random and systematic errors. Random errors, such as the sonar device’s measurement accuracy, are shown to be small in Appendix 1 and are therefore ignored here. Systematic errors are identifiable though difficult to model. Systematic errors, such as the interpolation of the tide value used to reference the depth measurements to MLLW, are also assumed to be negligible (Data Cleaning section). In order to determine the uncertainty in the volume (δVol), we only consider the error associated with the contouring method and interpolation methods used to create the 2015 and 2016 DEMs. Since the \( {\mathrm{Bias}}_{\Delta z}\left[\Delta \hat{z}\right]\approx 0 \) (Appendix 2), we can assume a constant variance, \( {\updelta_{\Delta \hat{z}}}^2 \), and δVol can then be computed with the semivariogram of \( \Delta \hat{z}-{\Delta z}_{\mathrm{obs}} \) as a function of x and y to model the spatially dependent errors. Using an exponential fit to the semivariogram, we found that r = 153.0 m and p = 0.037 m2 where r is the distance at which observations are no longer dependent and p is value that the semivariogram fit attains at r (Fig. 8). We then calculated the uncertainty in volume to account for spatial autocorrelation using the information provided by the semiovariogram.

Starting with a cell size of 25 × 25 m, we fit a 13 × 13-cell grid over a given cell, A, in the DoD that over-approximates the distance at which cells are spatially autocorrelated. The covariance between cell A and the cells outside the 13 × 13-cell grid is equal to zero. The semivariance value at every distance from cell A to the center of every cell within the 13 × 13-cell grid was extracted from the semivariogram fit above and these were subtracted from p in order to attain the covariance values. The total error in bathymetric change for cell A is then the sum of the variance of cell A, \( {\updelta A}^2={\updelta_{\Delta \hat{z}}}^2 \), and the covariance values between cell A and cell Xi, every other cell in the 13 × 13-cell grid. This sum is multiplied by cell area and the number of cells within the area for which the uncertainty in volume needs to be calculated (npix in Eq. 5). Thus, the uncertainty in volume accounting for spatial autocorrelation can be computed as follows in Eq. 5:

$$ \updelta \mathrm{Vol}=\mathrm{Cell}\ \mathrm{Area}\times \sqrt{\mathrm{npix}\left({\updelta A}^2+{\sum}_{i=1}^{13^2}\mathrm{COV}\left(A,{X}_i\right)\right)} $$
(5)

Table 3 summarizes the calculated VErosion, VDeposition, and δVol accounting for spatial autocorrelation for all volume calculations where \( {\sum}_{i=1}^{13^2}\mathrm{COV}\left(A,{X}_i\right) \) = 3.36 m in Eq. 5.

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Whaling, A., Shaw, J. Changes to Subaqueous Delta Bathymetry Following a High River Flow Event, Wax Lake Delta, USA. Estuaries and Coasts (2020). https://doi.org/10.1007/s12237-020-00727-y

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Keywords

  • River delta
  • Bathymetry
  • Delta morphology
  • Subaqueous delta growth
  • Subaqueous distributary channel
  • Winter storm