Parsing autogenic and allogenic processes in aeolian stratigraphy

I am beyond excited to present highly collaborative work that begins to parse records of autogenic processes and allogenic forcings preserved within set-scale aeolian architecture in two companion articles: (1) numerical experiments (preprint) and (2) the scour-fill dominated Jurassic Page Sandstone, Arizona (preprint).

synStrat
Set-scale aeolian architecture from a numerical model of dynamic dune topography driven by steady allogenic boundary conditions. Color represents time of deposition.

In the first companion article, a reduced complexity model of aeolian dune strata-formation is developed and applied to explore the roles of autogenic processes on the preservation of allogenic sourced from three sets of external environmental forcing. In each scenario, rapid dune growth is found to completely cannibalize early dune deposits, thus shredding any records of early allogenic or autogenic signals. However, later dune deposits are found to contain commingled autogenic and allogenic signals. This theoretical work frames five working hypotheses surrounding the nature of aeolian dune deposits for future workers to explore and discuss! The source code (Matlab) will reproduce all figures in this article is available here. A Python version is planned.

cardenasJSR2018
Page Sandstone. Early dune deposits (smaller sets in B,D) are preferentially preserved in antecedent lows in paleotopography.

In the companion article, collaborator Benjamin Cardenas leads interpretation of set-scale aeolian architecture within multiple exposures of the Page Sandstone (Jurassic) near Page Arizona, USA. This work interprets the set-scale architecture of the Page Sandstone to record multiple transgressions of the Carmel Sea. Drying, and associated decreases in base-level between transgressions liberates significant quantities of sand.  After drying, dune growth and scour are interpreted to cannibalize early dune deposits, except for those created in antecedent lows in paleotopography. Ongoing dune motion in the dry sand sea creates scour and fill architecture which is thought to characterize autogenic dune behavior. Eventually, the Carmel Sea completely transgresses the sand accumulation, and shuts down the aeolian system at the end of the Page (pun intended).

Exploring the completeness of the aeolian record within synthetic stratigraphy

synStrat

To be submitted soon! 

Abstract: A reduced complexity model aeolian dune stratification model is developed and applied to explore the role of dune morphodynamics in the creation of synthetic sections of aeolian stratigraphy and shredding of environmental signals originating from three sets of environmental forcing: 1) steady transport capacity, 2) steady bed aggradation and variable transport capacity, and 3) steady transport capacity and bed aggradation. In each scenario, the forward motion of initial, highly disorganized dunes generates a significant record exclusively containing autogenic signals that arise from early dune growth, deformation, and merger. However, continued dune growth scours deeply, and shreds all records of early dunes. Afterward, dunes self-organize into groups of dunes. Forward motion of dune groups create, truncate, and amalgamate sets and co-sets of cross-strata, quickly forming a second, significantly more robust stratigraphic record, which preserves a comingling of signals sourced from ongoing autogenic processes and each scenario’s specific set of environmental forcings. Although the importance of self-organization on modeled aeolian stratification is clear in the few presented scenarios, self-organization maybe throttled via variability within environmental forcings. Therefore, additional work is warranted as this numerical experiment only begins to sample possible sets of environmental forcing, boundary conditions, and initial conditions, geomorphic responses, and consequential preservation.

Here’s a sneak peak of the simulations:

The videos below so the co-evolution of dune topography and stratigraphy for three different model scenarios. In each video, bedform stratigraphy is vertically exaggerated 100x. Additionally, bedform topography is reduced 20x.  η* and x* are non-dimensional vertical and horizontal scales, respectively. η* represents the fraction of equilibrium dune height, and similarly, x* represents the number of equilibrium dune wavelengths. Enjoy!

1) Steady transport capacity

2) Steady bed aggradation and time-varying transport capacity

3) Steady bed aggradation and transport capacity

Fitting PDFs with constraints

Occasionally, data are published in the limiting form of a few values and corresponding cumulative percentiles. For example, grain size data are frequently published in terms of the 10th, 50th, and 90th cumulative percentiles. However, sometimes it’s nice to have an approximation of what a model distribution would look like if constrained to fit these points. Based on the solution given by Matt Tearle, here’s a short function below that gives an approximation of the mean and standard deviation of a log-normal distribution given at least two value-percentile pairs:

function m = prc2dist(p,q,guess)
%fit a log normal distribution to given p (percentiles), q (value) pairs,
%and a guess vector where guess=[guessMean guessStd].
%Output: m is a vector with elements, m(1) = mean,
%                                 and m(2) = standard deviation,
%                                 of the fitted distribution.
% see: help logninv for more information.
% Example:
% p = [0.1, 0.8]; %percentiles (cumulative probability)
% q = [1, 100]; %values
% guess = [1, 1]; %initial guess of mean and stdev, respectively.
% m = prc2dist(p,q,guess) % returns mean and standard dev of log-normal distribution

%regularize input
p = p(:);
q = q(:);
guess = guess(:)';
%validate input
if length(p) ~= length(q)
      fprintf('value and percentile vectors must be the same length.\n');
      m = nan(1,2);
      return
elseif length(p) < 2
     fprintf('value and percentile vectors must be > 2 elements in length.\n');
     m = nan(1,2);
     return
else
     g = @(p,b,q) logninv(p,b(1),b(2))-q;%distance between guess and input
     f = @(b) norm(g(p,b,q));%calculate l2 norm of distance vector
     m = fminsearch(f,guess);
end

download a zipped archive containing prc2dist.m

A new surface model for aeolian dune topography

MatGeoPaper2016Aeolian dune topography arises from a highly non-linear interaction between sediment transport,  topography, and boundary shear stress.  To explore the growth of aeolian dunes under a variety of boundary conditions, a new surface model for aeolian bedform topography is adapted from a surface model of subaqueous bedform topography (Jerolmack and Mohrig, 2005)[1]. The resulting modeling framework approximates the dynamic motions of aeolian bedform topography driven by bedform field boundary conditions; namely, different distributions of sediment transport direction and investigating bedform growth with and without the constraint of a fixed sediment source area (modeled as a fixed elevation boundary). The rates at which modeled aeolian bedforms grow and morphologically mature are found to be highly sensitive to the chosen boundary conditions. Click on the image of the manuscript header to visit the journal’s website and read more about this study.

The videos below show four permutations of two boundary conditions: uni- and bi-modal distributions of sediment transport direction are used to grow bedform topography with and without the constraint of a sediment source area. In these videos hot colors indicate higher topography and cooler colors indicate lower topography.

Uni-modal distribution of sediment transport direction with periodic boundaries

Uni-modal distribution of sediment transport moving sediment from a fixed source

Bi-modal distribution of sediment transport direction with periodic boundaries

Bi-modally distributed sediment transport moving sediment from a fixed source

The aeolian bedform surface model code is malleable and readily modified for exploratory study of bedform topography that inherits morphological traits from aeolian bedform field boundary conditions. A version of the source code for these simulations is available from MATGEO. However, a newer version of this software will be made available via a public repository on GitHub, shortly.

[1] Jerolmack DJ, Mohrig D (2005) A unified model for subaqueous bed form dynamics. Water Resour Res 41(12):W12421. doi:10.1029/2005WR004329 (PDF link)

Ex-Stream: a program for calculating vertical fluid flux in porous media based on temperature profiles

CAGS2011Temperature is a useful environmental tracer for quantifying movement and exchange of water and heat through and near sediment–water interfaces (SWI). Heat tracing involves analyzing temperature time series or profiles from temperature probes deployed in sediments. Ex-Stream is a MATLAB program that brings together two transient and two steady one-dimensional coupled heat and fluid flux analytical models. The program includes a graphical user interface, a detailed user manual, a practice data set from Swanson and Cardenas (2010)[1], and postprocessing capabilities that enable users to extract fluid fluxes from time-series temperature observations. CAGS2011cProgram output is written to comma-separated values files, displayed within the MATLAB command window, and may be optionally plotted. The models that are integrated into Ex-Stream can be run collectively, allowing for direct comparison, or individually.

 

Download Ex-Stream software

[1] Swanson, T., and M. Cardenas, 2010, Diel heat transport within the hyporheic zone of a pool-riffle-pool sequence of a losing stream and evaluation of models for fluid flux estimation using heat: Limnology and oceanography, v. 55, p. 1741-1754.