Morphodynamic Analysis and Statistical Synthesis of Geomorphic Data: Application to a Flume Experiment

Abstract

Many Earth surface processes are studied using field, experimental, or numerical modeling data sets that represent a small subset of possible outcomes observed in nature. Based on these data, deterministic models can be built that describe the “average” evolution of a system. However, these models commonly cannot account for the complex variability of many processes or present a quantitative statement of uncertainty. To assess such uncertainty, stochastic models are needed that can mimic spatial as well as temporal variability. A common limitation for applying stochastic models to Earth surface processes is a lack of data and methods that allow constraining the full spatiotemporal variability of these models. In this paper, we propose a Bayesian framework for calibrating input parameters to stochastic models of morphodynamic systems using time series of image data from the field, or from numerical and laboratory experiments. The framework consists of generating synthetic time series of images using the stochastic model and rejecting those time series that do not reproduce key morphodynamic statistics of the available data sets. The calibrated stochastic model allows us to quantify both the spatial and temporal uncertainty about the evolution of the morphodynamic systems of interest. For demonstration purposes, we apply the framework to a single flume experiment of braided river channels evolving under steady water and sediment discharges, but it can be used more generally to quantify spatiotemporal uncertainty for any time series of morphodynamic data for which key statistics can be defined.

Remote sensing of laboratory rivers

“…Care must be taken to ensure that dye concentration and lighting conditions remain constant during an experiment so that a single threshold can be used throughout. Although channel mapping was done manually for some earlier studies (e.g., Ashworth et al., 2007; Egozi & Ashmore, 2008; Whipple et al., 1998; Zarn & Davies, 1994), automated channel identification algorithms have been applied widely, to quantify lateral mobility and avulsion (Bufe et al., 2016, 2019; Cazanacli et al., 2002; Hoffimann et al., 2019; Sapozhnikov & Foufoula‐Georgiou, 1997; Tal & Paola, 2007, 2010; Wickert et al 20132021; Carlson et al., 2018; Chadwick et al., 2022; Esposito et al., 2018; Jarriel et al., 2019; Leenman & Eaton, 2021; Leenman et al., 2022; Lentsch et al., 2018; Miller et al., 2019; Martin et al., 2009; Nicholas et al., 2009; Piliouras et al., 2017; Piliouras & Kim, 2019a, 2019b; Reitz & Jerolmack, 2012; Reitz et al., 2010), to monitor bifurcation dynamics (Daniller‐Varghese et al., 2020), to track simulated Martian valley evolution (Marra et al., 2014) and to highlight the construction of stratigraphy (Sheets et al., 2002; Terwisscha van Scheltinga et al., 2020).…”

Mapping high-resolution basal topography of West Antarctica from radar data using non-stationary multiple-point geostatistics (MPS-BedMappingV1)

“…MPS approaches use the training images (TIs) as explicit prior models to generate realistic topographical models and quantify spatial uncertainty. The simulation of nonstationary and morphologically complex topography can also be achieved with MPS (Hoffimann et al, 2017(Hoffimann et al, , 2019Mariethoz and Caers, 2014). Compared to alternative machine learning or deep learning approaches (Laloy et al, 2018;Mo et al, 2020), MPS has a flexible conditioning capability and can accommodate sparse and non-uniform sampling in space.…”

“…This is particularly important as the MPS modelling relies on the spatial information provided by the training images. In the third option, Hoffimann et al (2019) introduced an approach to generate time-series training images to model the spatial and temporal evolutions of geomorphology, which is similar to Pirot et al (2014Pirot et al ( , 2015. A training image transitional model in time was proposed to reproduce the non-stationary geomorphologic evolutions.…”

Mapping high-resolution basal topography of West Antarctica from radar data using non-stationary multiple-point geostatistics (MPS-BedMappingV1)

“…MPS approaches use the training images (TIs) as explicit prior models to generate realistic topographical models and quantify spatial uncertainty. The simulation of non-stationary and morphologically complex topography can also be achieved with MPS (Hoffimann et al, 2017a(Hoffimann et al, , 2019Mariethoz and Caers, 2014). Compared to alternative machine learning or deep learning approaches (Laloy et al, 2018;Mo et al, 2020), MPS has a flexible conditioning capability and can accommodate sparse and non-uniform sampling in space.…”

“…This is particularly important as the MPS modeling relies on the spatial information provided by the training images. Hoffimann et al (2019) introduced an approach to generate time-series training images to model the spatial and temporal evolutions of geomorphology. A training image transitional model in time was proposed to reproduce the nonstationary geomorphologic evolutions.…”