Measuring Channel Planform Change From Image Time Series: A Generalizable, Spatially Distributed, Probabilistic Method for Quantifying Uncertainty

Abstract Channels change in response to natural or anthropogenic fluctuations in streamflow and/or sediment supply and measurements of channel change are critical to many river management applications. Whereas repeated field surveys are costly and time‐consuming, remote sensing can be used to detect channel change at multiple temporal and spatial scales. Repeat images have been widely used to measure long‐term channel change, but these measurements are only significant if the magnitude of change exceeds the uncertainty. Existing methods for characterizing uncertainty have two important limitations. First, while the use of a spatially variable image co‐registration error avoids the assumption that errors are spatially uniform, this type of error, as originally formulated, can only be applied to linear channel adjustments, which provide less information on channel change than polygons of erosion and deposition. Second, previous methods use a level‐of‐detection (LoD) threshold to remove non‐significant measurements, which is problematic because real changes that occurred but were smaller than the LoD threshold would be removed. In this study, we present a new method of quantifying uncertainty associated with channel change based on probabilistic, spatially varying estimates of co‐registration error and digitization uncertainty that obviates a LoD threshold. The spatially distributed probabilistic (SDP) method can be applied to both linear channel adjustments and polygons of erosion and deposition, making this the first uncertainty method generalizable to all metrics of channel change. Using a case study from the Yampa River, Colorado, we show that the SDP method reduced the magnitude of uncertainty and enabled us to detect smaller channel changes as significant. Additionally, the distributional information provided by the SDP method allowed us to report the magnitude of channel change with an appropriate level of confidence in cases where a simple LoD approach yielded an indeterminate result

Editorial for the Special Issue “Remote Sensing of Flow Velocity, Channel Bathymetry, and River Discharge”

River discharge is a fundamental hydrologic quantity that summarizes how a watershed transforms the input of precipitation into output as channelized streamflow [...

Characterizing the spatial structure of river morphology and hydraulics: Remote mapping and geostatistical modeling of dynamic fluvial systems

A river’smorphologic evolution reflects a complex suite of interactions between the form of the channel and the flow and sediment transport processes acting to modify that form. Efforts to better understand these interactions thus require an ability to measure river morphology and characterize its spatial structure. The primary objectives of this dissertation are to develop such a capacity and to apply these methods to the study of channel change. The feasibility of passive optical remote sensing of river bathymetry was examined via radiative transfer modeling, field spectroscopy, and image processing. These analyses indicated the robust performance of a simple, ratio-based depth retrieval algorithm; the conditions under which this technique is appropriate were defined by considering the relativemagnitudes of various radiance components. This physics-based approach allowed the utility of remotely sensed data to be evaluated with a forward image model, which highlighted the influence of both channel and sensor characteristics on depth retrieval accuracy and precision. The potential to obtain a more complete topographic representation of the fluvial environment by combining spectrally-based bathymetry with LiDAR data from bars and floodplains was also demonstrated. Remote sensing thus provides essentially continuous, high resolution data on river morphology, but improved, spatially explicit analytical methods are needed to fully capitalize on this information. This need is addressed by a geostatistical framework consisting of a channel-centered coordinate system and flexible modeling tools for describing reach-scale spatial patterns. Kriging-based spatial prediction techniques can yield geomorphic insight by revealing departures from an a priori expectation of channel form. Similarly, the spatial structure of river morphology and hydraulics can be quantified using a geostatistical metric called the variogram. Survey data from a recently restored channel and three reaches of a dynamic gravel-bed river in Yellowstone National Park documented various styles and degrees of channel change, and variogram models developed from these data were used to examine the relationship between geomorphic context, disturbance history, and the balance between sediment supply and transport capacity. Quantitatively characterizing the variability and spatial organization of channel form will advance our understanding of river morphodynamics

Depths Inferred from Velocities Estimated by Remote Sensing: A Flow Resistance Equation-Based Approach to Mapping Multiple River Attributes at the Reach Scale

Remote sensing of flow conditions in stream channels could facilitate hydrologic data collection, particularly in large, inaccessible rivers. Previous research has demonstrated the potential to estimate flow velocities in sediment-laden rivers via particle image velocimetry (PIV). In this study, we introduce a new framework for also obtaining bathymetric information: Depths Inferred from Velocities Estimated by Remote Sensing (DIVERS). This approach is based on a flow resistance equation and involves several assumptions: steady, uniform, one-dimensional flow and a direct proportionality between the velocity estimated at a given location and the local water depth, with no lateral transfer of mass or momentum. As an initial case study, we performed PIV and inferred depths from videos acquired from a helicopter hovering at multiple waypoints along a large river in central Alaska. The accuracy of PIV-derived velocities was assessed via comparison to field measurements and the performance of an optimization-based approach to DIVERS was quantified by comparing calculated depths to those observed in the field. We also examined the ability of two variants of DIVERS to reproduce the discharge recorded at a gaging station. This analysis indicated that the accuracy of PIV-based velocity estimates varied considerably from hover to hover along the reach, with observed vs. predicted R2 values ranging from 0.22 to 0.97 and a median of 0.57. Calculated depths were also reasonably accurate, with median normalized biases from −4% to 9.9% for the two versions of DIVERS, but tended to be under-predicted in meander bends. Discharges were reproduced to within 1% and 4% when applying the optimization-based technique to individual hovers or reach-aggregated data, respectively. The results of this investigation suggest that, in addition to the velocity field derived via PIV, DIVERS could provide a plausible, first-order approximation to the reach-scale bathymetry. This framework could be refined by incorporating hydraulic processes that were not represented in the initial iteration of the approach described herein

Depths Inferred from Velocities Estimated by Remote Sensing: A Flow Resistance Equation-Based Approach to Mapping Multiple River Attributes at the Reach Scale

Remote sensing of flow conditions in stream channels could facilitate hydrologic data collection, particularly in large, inaccessible rivers. Previous research has demonstrated the potential to estimate flow velocities in sediment-laden rivers via particle image velocimetry (PIV). In this study, we introduce a new framework for also obtaining bathymetric information: Depths Inferred from Velocities Estimated by Remote Sensing (DIVERS). This approach is based on a flow resistance equation and involves several assumptions: steady, uniform, one-dimensional flow and a direct proportionality between the velocity estimated at a given location and the local water depth, with no lateral transfer of mass or momentum. As an initial case study, we performed PIV and inferred depths from videos acquired from a helicopter hovering at multiple waypoints along a large river in central Alaska. The accuracy of PIV-derived velocities was assessed via comparison to field measurements and the performance of an optimization-based approach to DIVERS was quantified by comparing calculated depths to those observed in the field. We also examined the ability of two variants of DIVERS to reproduce the discharge recorded at a gaging station. This analysis indicated that the accuracy of PIV-based velocity estimates varied considerably from hover to hover along the reach, with observed vs. predicted R2 values ranging from 0.22 to 0.97 and a median of 0.57. Calculated depths were also reasonably accurate, with median normalized biases from −4% to 9.9% for the two versions of DIVERS, but tended to be under-predicted in meander bends. Discharges were reproduced to within 1% and 4% when applying the optimization-based technique to individual hovers or reach-aggregated data, respectively. The results of this investigation suggest that, in addition to the velocity field derived via PIV, DIVERS could provide a plausible, first-order approximation to the reach-scale bathymetry. This framework could be refined by incorporating hydraulic processes that were not represented in the initial iteration of the approach described herein

sUAS-Based Remote Sensing of River Discharge Using Thermal Particle Image Velocimetry and Bathymetric Lidar

This paper describes a non-contact methodology for computing river discharge based on data collected from small Unmanned Aerial Systems (sUAS). The approach is complete in that both surface velocity and channel geometry are measured directly under field conditions. The technique does not require introducing artificial tracer particles for computing surface velocity, nor does it rely upon the presence of naturally occurring floating material. Moreover, no prior knowledge of river bathymetry is necessary. Due to the weight of the sensors and limited payload capacities of the commercially available sUAS used in the study, two sUAS were required. The first sUAS included mid-wave thermal infrared and visible cameras. For the field evaluation described herein, a thermal image time series was acquired and a particle image velocimetry (PIV) algorithm used to track the motion of structures expressed at the water surface as small differences in temperature. The ability to detect these thermal features was significant because the water surface lacked floating material (e.g., foam, debris) that could have been detected with a visible camera and used to perform conventional Large-Scale Particle Image Velocimetry (LSPIV). The second sUAS was devoted to measuring bathymetry with a novel scanning polarizing lidar. We collected field measurements along two channel transects to assess the accuracy of the remotely sensed velocities, depths, and discharges. Thermal PIV provided velocities that agreed closely ( R 2 = 0.82 and 0.64) with in situ velocity measurements from an acoustic Doppler current profiler (ADCP). Depths inferred from the lidar closely matched those surveyed by wading in the shallower of the two cross sections ( R 2 = 0.95), but the agreement was not as strong for the transect with greater depths ( R 2 = 0.61). Incremental discharges computed with the remotely sensed velocities and depths were greater than corresponding ADCP measurements by 22% at the first cross section and <1% at the second

Spatial prediction of river channel topography by Kriging

Topographic information is fundamental to geomorphic inquiry, and spatial prediction of bed elevation from irregular survey data is an important component of many reach-scale studies. Kriging is a geostatistical technique for obtaining these predictions along with measures of their reliability, and this paper outlines a specialized framework intended for application to river channels. Our modular approach includes an algorithm for transforming the coordinates of data and prediction locations to a channel-centered coordinate system, several different methods of representing the trend component of topographic variation and search strategies that incorporate geomorphic information to determine which survey data are used to make a prediction at a specific location. For example, a relationship between curvature and the lateral position of maximum depth can be used to include cross-sectional asymmetry in a two-dimensional trend surface model, and topographic breaklines can be used to restrict which data are retained in a local neighborhood around each prediction location. Using survey data from a restored gravel-bed river, we demonstrate how transformation to the channel-centered coordinate system facilitates interpretation of the variogram, a statistical model of reach-scale spatial structure used in kriging, and how the choice of a trend model affects the variogram of the residuals from that trend. Similarly, we show how decomposing kriging predictions into their trend and residual components can yield useful information on channel morphology. Cross-validation analyses involving different data configurations and kriging variants indicate that kriging is quite robust and that survey density is the primary control on the accuracy of bed elevation predictions. The root mean-square error of these predictions is directly proportional to the spacing between surveyed cross-sections, even in a reconfigured channel with a relatively simple morphology; sophisticated methods of spatial prediction are no substitute for field data