mapping gravel bed river bathymetry from space

Mapping gravel bed river bathymetry from space

C. J. Legleiter1 and B. T. Overstreet1

Received 2 July 2012; revised 1 October 2012; accepted 5 October 2012; published 21 November 2012.

[1] Understanding river form and behavior requires an efficient means of measuringchannel morphology. This study evaluated the potential to map the bathymetry of twoclear-flowing, shallow (<3 m deep) gravel bed rivers <60 m wide from 2 m-pixelWorldView2 satellite images. Direct measurements of water column optical propertieswere used to quantify constraints on depth retrieval. The smallest detectable change indepth was 0.01–0.04 m and the maximum detectable depth was 5 m in green bands but<2 m in the near-infrared; lower sensor radiometric resolution yields less preciseestimates over a smaller range. An algorithm for calibrating a band ratio X to fieldmeasurements of depth d proved effective when applied to spectra extracted fromimages (R2 = 0.822 and 0.594 for the larger and smaller stream, respectively) ormeasured in the field (R2 = 0.769 and 0.452). This procedure also identified optimalwavelength combinations, but different bands were selected for each site. Accuracyassessment of bathymetric maps produced using various calibration approaches andimage types indicated that: 1) a linear d vs. X relation provided depth estimates nearlyas accurate as a quadratic formulation; 2) panchromatic and pan-sharpenedmultispectral images with smaller 0.5 m pixels did not yield more reliable depthestimates than the original images; and 3) depth retrieval was less reliable in pools dueto saturation of the radiance signal. This investigation thus demonstrated the feasibility,as well as the limitations, of measuring the bathymetry of clear, shallow gravel bedrivers from space.

Citation: Legleiter, C. J., and B. T. Overstreet (2012), Mapping gravel bed river bathymetry from space, J. Geophys. Res., 117,F04024, doi:10.1029/2012JF002539.

1. Introduction

[2] The form and behavior of gravel bed rivers reflectcomplex interactions among morphology, flow, and sedi-ment transport. Understanding connections between formand process is thus a principal objective of fluvial geomor-phology, but progress toward this goal is hindered by thedifficulty of collecting basic data on topography, flow con-ditions, and bed material properties. Moreover, the logisticalconstraints associated with traditional field methods formeasuring these attributes often limit investigations to short,isolated study reaches. Although recent advances in instru-mentation, such as total stations [Keim et al., 1999], real-time kinematic global positioning systems (RTK GPS)[Brasington et al., 2000], and terrestrial laser scanning[Hodge et al., 2009], have enabled more efficient data col-lection, most research continues to focus on scales rangingfrom a few to several tens of channel widths, often with littleconsideration of the broader watershed context for these

detailed surveys. A more synoptic perspective on fluvialsystems will require a different approach, and remote sens-ing is increasingly viewed as a viable alternative [Marcusand Fonstad, 2008, 2010]. Previous studies have demon-strated the feasibility of deriving various types of riverinformation from image data, ranging from measurements oflateral channel migration from historical air photos [e.g.,Micheli and Kirchner, 2002] to suspended sediment con-centrations inferred from Landsat scenes [Mertes et al.,1993; Kilham et al., 2012]. The most mature application ofremote sensing to rivers is retrieval of water depth frompassive optical images, primarily multi- or hyperspectral dataacquired from aerial platforms [e.g., Winterbottom andGilvear, 1997; Marcus et al., 2003; Lejot et al., 2007;Legleiter et al., 2009; Flener et al., 2012]. In this study, webuild upon these results by using field measurements andsatellite imagery to evaluate the potential for mapping thebathymetry of gravel bed rivers from space.[3] Knowledge of water depth is valuable for a number of

different purposes. For example, depth is an importantparameter for any hydrologic study that involves computingriver discharge and/or routing flows. From a geomorphicperspective, the depth, along with the water surface slope,exerts a primary control on the boundary shear stress that inturn drives bed material transport. In an ecological context,the thickness and optical properties of the water column

1Department of Geography, University of Wyoming, Laramie,Wyoming, USA.

Corresponding author: C. J. Legleiter, Department of Geography,University of Wyoming, Dept. 3371, 1000 E. University Ave., Laramie,WY 82071, USA.

©2012. American Geophysical Union. All Rights Reserved.0148-0227/12/2012JF002539

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, F04024, doi:10.1029/2012JF002539, 2012

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determine the amount of solar energy that propagates to thestreambed to fuel primary production by benthic algae. Formanagers interested in monitoring stream condition andchange, depth is one of the principal quantities used toassess habitat quality. In addition, when combined withinformation on water surface elevations, depth measure-ments can be used to obtain topographic input data fornumerical modeling of flow and sediment transport. Sim-ilarly, sequential observations of channel morphology canbe used to identify areas of erosion and deposition andhence to infer bed material transfer and storage [e.g.,Ashmore and Church, 1998; Ham and Church, 2000].A capacity to map river bathymetry efficiently, reliably,and over large extents would thus benefit the riverinesciences in many ways.[4] Remote sensing could provide such capability. The

potential of this approach has been confirmed first throughempirical case studies [e.g., Winterbottom and Gilvear,1997; Marcus et al., 2003] and more recently by consider-ing the underlying physics [Legleiter et al., 2004, 2009].Passive optical remote sensing of river bathymetry involvesmeasuring the amount of solar radiation reflected from thechannel, which depends not only on depth but also the tex-ture of the water surface, the concentration and compositionof sediment and organic materials within the water column,and the reflectance of the streambed. Moreover, all of thesequantities vary as a function of wavelength l. To gaininsight as to how the processes that govern the interaction oflight and water both enable and limit the remote sensing ofrivers, Legleiter et al. [2004] used a radiative transfermodel to isolate the effects of depth d, suspended sedimentconcentration, and bottom reflectance RB(l) on theupwelling spectral radiance L(l) recorded by a remotedetector. For conditions representative of a shallow, clear-flowing gravel bed river, this analysis indicated that depthwas the primary control on L(l) and that taking the loga-rithm of the ratio of two specific bands yielded an image-derived quantity X linearly related to d. Subsequently, weargued on theoretical grounds that spectrally-based depthretrieval would be feasible when d is small, the substrate ishighly reflective relative to the overlying water column,and attenuation of light is dominated by pure waterabsorption rather than scattering by suspended sediment.Radiative transfer modeling, field-based reflectance mea-surements, and bathymetric maps derived from hyper-spectral image data supported these conclusions andconfirmed the utility of a simple band ratio for remotemeasurement of water depths in certain types of rivers[Legleiter et al., 2009].[5] Although previous studies have shown that depth

information can be retrieved from aerial images, the feasi-bility of mapping river bathymetry from space has not beenassessed. In this study, we used field measurements andmultispectral image data to explore the possibility of mea-suring gravel bed river depths from a satellite platform. Ourresearch objectives were to: (1) characterize the inherentoptical properties of the water column by obtaining novel insitu measurements of absorption and attenuation in a pair ofclear-flowing gravel bed streams, (2) establish relationshipsbetween depth and reflectance based on field spectra fromthese rivers, and (3) evaluate different approaches for cali-brating image-derived quantities to flow depth and (4) assess

the accuracy of depth estimates produced from various typesof satellite imagery.

2. Methods

2.1. Study Area

[6] To evaluate the feasibility of mapping river bathyme-try from space, we examined two gravel bed streams in theRocky Mountains, USA: the Snake River in Grand TetonNational Park and Soda Butte Creek (SBC) in Yellow-stone National Park (Figure 1). Both watersheds aresnowmelt-dominated and generally exhibit clear waterconditions during late summer low flows. The two riversfeature wandering planforms with both sinuous, single-thread and more complex multi-thread segments. In addition,both streams are highly dynamic, with extensive morpho-logic change occurring during spring runoff in many years,including 2011. The steep, glaciated valley of SBC is com-posed of weak Eocene volcanic rock and provides an abun-dant sediment supply that drives channel change [Meyer,2001]. The Snake River is regulated at Jackson Lake, butsediment delivered from tributaries below the dam [Erwinet al., 2011], along with large woody debris, contribute tofrequent morphologic adjustments. We selected these riversfor study because the complexity and dynamism of thesechannels imply that remote sensing might be useful, if notnecessary, for characterizing their form, behavior, andevolution.[7] For the Snake River we focused on a meander called

Rusty Bend, shown in Figure 1c and described in Table 1.The channel curves smoothly to the right through this reachand has a relatively simple morphology consisting of a gravelbar along the inner (right, or north) bank and a vertical tosteeply sloping cutbank on the outside of the bend where theSnake River erodes into a high terrace. For the purposes ofthis investigation, the bar-pool topography of Rusty Bendwas attractive because of the broad range of depths encom-passed: very shallow over the bar and up to 2.77 m in the poolalong the outer bank. Also, a variety of substrates with dif-ferent reflectance characteristics were present within thisreach: clean gravel, bright green benthic algae, and blocks oflighter-colored bedrock (Figure 2b).[8] Soda Butte Creek has been the subject of previous

efforts to map river bathymetry from aerial platforms[Marcus et al., 2003; Legleiter et al., 2004, 2009; Legleiter,2012a] and thus provides a convenient opportunity to assesswhether similar information might be derived from satelliteimages. In this study, we focused on the Footbridge Reach,a site for which ground-based topographic surveys havebeen conducted each year since 2005 [Legleiter, 2012b].The reach comprises a sweeping meander and large pointbar, which is now being incised by a chute channel that hascaptured much of the stream’s flow and could soon cut offthe bend. Because the discharge is divided among multiplechannels and the image was acquired under base flow con-ditions, depths were generally quite shallow (Table 1) butdeeper pools were present in the middle of the chute chan-nel, along the west bank above the bend apex, and againstthe east bank at the lower end of the reach. The smaller sizeof SBC also implied that mixed pixels along channel mar-gins would be more extensive and potentially more prob-lematic than for the Snake River.

LEGLEITER AND OVERSTREET: MAPPING RIVER BATHYMETRY FROM SPACE F04024F04024

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2.2. Field Data Collection

[9] On the Snake River, we surveyed channel bed topog-raphy using a high-precision (2–3 cm, both horizontal andvertical) real-time kinematic (RTK) GPS receiver. Eleva-tions were measured at points arranged along cross-sectionsthat traversed exposed bars and shallow areas of the wettedchannel. Depths were determined by subtracting the bedelevation for in-stream survey points from the elevationrecorded at the water’s edge along each transect [Legleiteret al., 2011a]. For areas that were too deep to wade safely,the GPS receiver was mounted on a cataraft and configuredto record water surface elevations while communicating withan echo sounder that measured flow depths. Measurements

Table 1. Channel Characteristics for Study Reaches

Snake RiverRusty Bend

Soda Butte CreekFootbridge Reach

Radius of curvature (m) 84 42Mean wetted width (m) 58 19Channel bed slope 0.0035 0.0065Mean �da � std. dev. (m) 1.23 � 0.57 0.22 � 0.15Maximum �d (m) 2.77 0.69nb 3276 655

aThe symbol �d denotes the pixel-scale mean depth determined from fieldmeasurements via ordinary block kriging.

bThe symbol n is the number of �d values for the reach.

Figure 1. (a) Map indicating the location of study sites in Grand Teton National Park (GTNP) and Yel-lowstone National Park (YNP), USA. WorldView2 images of the (b) Snake River and (d) Soda ButteCreek are shown, with insets highlighting (c) Rusty Bend and (e) the Footbridge Reach.


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were obtained along a series of transects across our RustyBend study reach as well as longitudinal profiles recorded asthe cataraft traveled downstream. Over 22 km of the SnakeRiver was surveyed in this manner during a 10-day period inAugust and September 2011, resulting in a total of 73,686echo sounder-based depth measurements. In addition, anacoustic Doppler current profiler (ADCP) deployed from akayak provided additional depth observations. To ensurethat the depth measurements obtained via the three methodswere consistent with one another, we compared echosounder and ADCP readings to the closest wading depth.This analysis indicated that in shallow areas where the datasets overlapped, the echo sounder depths were biased shal-low by 7 cm and the ADCP depths biased deep by 3 cmrelative to the wading depths. The mean differences betweenthe echo sounder and ADCP depths and the correspondingwading points were used to adjust the echo sounder andADCP data to match the wading depths. The resulting,combined bathymetric field data set was then used for cali-bration and validation of image-derived depth estimates.[10] For the smaller Soda Butte Creek, all field measure-

ments were obtained by wading, which allowed us to accessall but the deepest portions of the channel. Field data col-lection at the Footbridge Reach involved using the RTK GPSand a robotic total station to complete a detailed, terrain-sensitive survey that emphasized important breaks in slopesuch as the top and base of banks [e.g., Lane et al., 1994;Wheaton et al., 2010]. In addition, water surface elevationswere measured along channel margins and used to calculatedepths for in-stream points as the difference between watersurface and bed elevations. An earlier study confirmed thatdepths determined in this manner agreed closely withdepths measured directly with a ruler, which would havebeen a less efficient means of obtaining these data [Legleiter,2012c].

2.3. Geostatistical Analysis

[11] Before using the depth measurements describedabove to calibrate image-derived depth estimates and assesstheir accuracy, the original field data were processedusing geostatistical techniques. These analyses served two

important purposes: 1) up-scaling observations collected atpoints to the dimensions of an image pixel [Bailly et al.,2010]; and 2) producing continuous depth maps for com-parison with the remotely sensed bathymetry. To account forthe non-convex geometry of these meandering rivers, whichimplies that conventional Euclidean distances are not a validmetric [e.g., Little et al., 1997], data were transformed fromthe original Cartesian reference frame to an orthogonal cur-vilinear, channel-centered coordinate system defined by astreamwise axis s along the channel centerline and a cross-stream, or normal, n axis oriented perpendicular to the cen-terline [Smith and McLean, 1984; Legleiter and Kyriakidis,2006]. The spatial structure of each reach was then quanti-fied using anisotropic variograms, as described by Legleiter[2012d]. Briefly, variograms summarize the degree towhich observations are spatially correlated with one anotheras a function of the distance and direction (i.e., lag vector)between pairs of points and thus provide information onoverall variability as well as the length scales over which thisvariability is expressed along and across the channel. In thisstudy, de-trending was not necessary because we used depthmeasurements rather than bed elevations that would havebeen influenced by the overall slope of the channel. Samplevariograms were calculated for the s and n directions byrestricting the angular tolerances associated with each lagvector class. Variogram model parameters were estimatedfirst manually using an iterative graphical procedure and thenrefined using a weighted least squares algorithm thatemphasized shorter lag distances with larger numbers of pairs[Zhang et al., 1995; Pardo-Iguzquiza, 1999].[12] Although field measurements were collected at dis-

crete points, depth estimates derived from satellite imagespertain to larger areas of space, represented by image pixels.To account for this difference in scale, or change of support[e.g., Atkinson and Curran, 1995], we employed a geosta-tistical algorithm known as ordinary block kriging (OBK),described in general by Goovaerts [1997] and in a remotesensing context by Bailly et al. [2010]. Here, we brieflysummarize the rationale for and implementation of thisprocedure. Essentially, we used OBK to upscale pointobservations to the dimensions of an image pixel and obtain

Figure 2. (a) Field measurements of flow depth and spectral reflectance were obtained from a cataraft;the spectroradiometer extends out over the water from the rear of the cataraft (right in this photo).(b) Blocks of light-colored bedrock present along Rusty Bend. (c) Underwater photograph of the scissor liftapparatus used to measure downwelling radiant energy at different depths within the water column.


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spatially distributed estimates of the pixel-scale mean depth.Also, because some pixels contained multiple points, thisanalysis served to avoid the redundancy that would haveoccurred if the original field measurements were paireddirectly with specific image pixels. Instead, the OBK algo-rithm yielded a single estimate of the average depth withineach pixel, regardless of the number of points present withinthat area. To compute OBK estimates, we first created a fine-scale grid of discretization points for each reach, consistingof 16 points per pixel, and transformed these predictionlocations to the same channel-centered coordinate system asthe field data. A depth estimate for each discretization pointwas then calculated using an ordinary kriging algorithm thatincorporated the anisotropic variogram models describedabove [Legleiter and Kyriakidis, 2008]. Taking the averageof the ordinary kriging estimates for the 16 points withineach pixel yielded the block kriging estimate of the pixel-scale mean depth [Goovaerts, 1997, p. 152]. For purposes ofcalibration and validation, OBK depth estimates were com-puted only for those pixels containing one or more pointmeasurements. In addition, to examine spatial patterns ofdepth retrieval accuracy, continuous field-based bathymetricmaps were generated by estimating via OBK the mean depthfor all pixels within each reach.

2.4. Spectral Characteristics of Gravel Bed Rivers:Field Measurements and Data Analysis

[13] One of our long-term research objectives is to build amore thorough database on the spectral characteristics offluvial environments, where only a few quantitative obser-vations of water column optical properties and bottomreflectance have been made [Legleiter et al., 2009, 2011b].In this study, we began the process of compiling a spectrallibrary for rivers by collecting field spectra and measuringthe apparent and inherent optical properties of the watercolumn in a pair of clear-flowing gravel bed streams.[14] Reflectance spectra were recorded from above the

water surface using an Analytical Spectral Devices (ASD)FieldSpec3 spectroradiometer that measured wavelengthsfrom 350–1025 nm with a 1 nm sampling interval; only the400–850 nm region was considered here due to noise at bothends of the spectrum. A 100% reflectant Spectralon cali-bration panel was used to establish a white reference prior toeach round of measurements. For data collection along theSnake River, the ASD was mounted on a rod extending fromthe rear of the cataraft and configured to record spectra onceeach second as we traversed a series of transects acrossRusty Bend (Figure 2a). Flow depths were recorded simul-taneously using the survey instrumentation described above,providing the paired observations of depth and reflectanceneeded to develop bathymetric mapping algorithms. More-over, these data extended the range of river conditions underwhich spectra have been measured from shallow, wadeablestreams [Legleiter et al., 2009] to a deeper, larger channelwith diverse bottom types (Figure 2b). For SBC, fieldspectra were recorded at points accessed by wading anddepths measured with a ruler. Additional detail on theacquisition and processing of reflectance data were providedby Legleiter et al. [2011b].[15] Because water column optical properties influence the

feasibility of inferring depth from image data, we directlymeasured several attributes of the water within our study

streams. Attenuation of light was characterized by measur-ing the total amount of incident solar radiation, referred to asthe downwelling spectral irradiance Ed(l), at various depthswithin the water column. These irradiance profiles werecollected by connecting the ASD to an upward-facing cosineresponse detector that integrated radiant energy arrivingfrom all directions within the upper hemisphere to obtainEd(l); the fore-optic was attached to a waterproof cable andmounted on an adjustable scissor lift to position the sensor atdifferent depths (Figure 2c). These measurements were usedto calculate the diffuse attenuation coefficient Kd(l), anapparent optical property that quantifies the rate at whichlight is attenuated with distance traveled through the watercolumn, following the procedure outlined by Mishra et al.[2005] and applied to the Platte River by Legleiter et al.[2011b]. In addition, we used a WET Labs ac-9 to directlymeasure two inherent optical properties of the water column,the absorption and attenuation coefficients, a and c. Theseoptical data were collected on several dates along the SnakeRiver and SBC. Ancillary data in support of these mea-surements included water samples analyzed for suspendedsediment concentration and turbidity readings made with aEureka Environmental Manta2 multiprobe.[16] Measuring water column optical properties allowed

us to examine two important constraints on remote sensingof river bathymetry: the precision of spectrally-based depthestimates and the maximum depth detectable by an imagingsystem. This analysis was based on the early work of Philpot[1989], which was revisited in a fluvial context by Legleiterand Roberts [2009]. The original publications provideadditional detail, but only the key results relevant to thisinvestigation are highlighted herein. Values of Kd(l) deter-mined from our field measurements were used to calculatebathymetric precision as

Dd lð Þ ¼ �1

2Kd lð Þ ln 1�DLN lð ÞLB lð Þ exp 2Kd lð Þd0f g

� �ð1Þ

where Dd(l) is the smallest detectable difference in depth atan initial depth d0, DLN(l) is the sensor’s noise-equivalentdelta radiance (essentially the smallest change in brightnessthe system can resolve), and LB(l) is that portion of the totalradiance signal that has interacted with the bottom and isthus related to depth. Because DLN(l) and LB(l) are bothspectral radiance values, the units cancel and only the ratioDLN(l)/LB(l) is significant in equation (1). This ratio servesas a convenient index of the detectability of the bottom for agiven river and sensor configuration. In this study, we cal-culated Dd(l) values by specifying DLN(l)/LB(l) = 0.01,based on prior radiative transfer modeling [Legleiter andRoberts, 2009], and using 2Kd(l) as an effective attenua-tion coefficient, following Philpot [1989] and Maritorenaet al. [1994]. Similarly, the maximum detectable depthoccurs when the difference between the at-sensor radianceand the radiance from a hypothetical infinitely deep watercolumn is equivalent to the sensor’s DLN(l) and was calcu-lated as

dmax lð Þ ¼ �1

2Kd lð Þ lnDLN lð ÞLB lð Þ

� �: ð2Þ

In this case, we used DLN(l)/LB(l) values of 0.1, 0.01,0.001, and 0.0001 to illustrate the effects of a greater bottom


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contrast between the substrate and water column and/or amore sensitive detector, either or both of which would cor-respond to smaller values of DLN(l)/LB(l).

2.5. Image Data Acquisition and Processing

[17] To evaluate the feasibility of mapping gravel bedriver bathymetry from space, this study used satellite imagesacquired by the WorldView-2 (WV2) sensor. This imagingsystem became operational in January 2010 and features aunique combination of high spatial resolution (pixel sizes of0.5 and 2 m for panchromatic and multiband images,respectively) and multispectral measurement capabilities,with eight bands spanning visible and near-infrared (NIR)wavelengths. In addition to the standard blue, green, red, andNIR bands, WV2 also includes coastal (400–450 nm), yel-low (585–625 nm), and red edge (705–745 nm) bandspotentially useful for depth retrieval from shallow streams aswell as a longer-wavelength NIR band (860–1040 nm) thatcould be used to discriminate land from water. This satellitealso features advanced pointing technology that allows foroff-nadir viewing, reduced revisit times, and precise geo-metric positioning, with nominal geo-referencing accuracieson the order of 4 m (Digital Globe, data available at http://worldview2.digitalglobe.com/about/, 2012).[18] WV2 images of the Snake River and SBC were

acquired on 13 September 2011 (Figure 1). Deliverablesincluded geo-referenced multispectral and panchromaticdata sets and supporting metadata. In addition to the originalimages, which were not radiometrically calibrated andconsisted of raw digital numbers, we received atmospherically-corrected data processed to units of apparent surface reflec-tance in-house by DigitalGlobe. Depth retrieval performancewas evaluated for the multispectral reflectance images aswell as the higher spatial resolution panchromatic data sets.In addition, we considered hybrid, pan-sharpened images thatconsisted of eight spectral bands, like the original multi-spectral images, but had a smaller 0.5 m pixel size equivalentto the panchromatic images; these images were generatedusing the Gram-Schmidt spectral sharpening tool in theENVI software. The three different types of images (multi-spectral, panchromatic, and pan-sharpened) allowed us toassess the relative significance of spatial and spectral reso-lution for remote sensing of river depths.[19] Geo-referencing of the WorldView-2 image for the

Snake River was highly accurate, with stream banks andother distinctive features in the image closely aligned withour field maps; no further geometric correction of this dataset was needed. For SBC, however, the spatial referencing ofthe original image was not as reliable, with many of thepoints at which depths were measured plotting outsidethe wetted channel when overlain on the image. Given thesmaller size of this stream and the abrupt variations indepth over the scale of a single, 2 m image pixel, improvedgeo-referencing was required. The necessary refinementwas achieved by digitizing a wetted channel polygon onthe image and comparing this feature to a polygon createdfrom water surface elevation points surveyed in the field.The parameters of an affine transformation were theniteratively adjusted so as to maximize the area of overlapbetween the image- and field-based channel polygons andthe original image transformed using the optimal para-meters [Legleiter, 2012a]. This algorithm greatly improved

agreement between field and image data, with depth pointslocated within the wetted channel on the transformedimage.[20] An important pre-processing step was the definition

of in-stream masks for each image. These masks served toisolate active channels and thus highlight variations inreflectance within the water portion of each scene. In thisstudy, binary, water-only masks were produced by display-ing the longest wavelength NIR band as a gray scale image,inspecting the histogram of pixel values, and interactivelyadjusting the contrast stretch to determine a NIR reflectancethreshold that effectively distinguished dark water frombrighter terrestrial features. Pixels with NIR reflectancevalues below this threshold were included in an initial watermask that was refined using image processing operations:morphological opening to remove isolated pixels, interactivesegmentation to select in-stream image objects, and mor-phological closing to fuse small gaps [Legleiter et al.,2011a]. The resulting raster masks then were converted tovector representations that enabled manual editing to removepersistent shadows along steep cut banks, for example. Thevector masks were rasterized and applied to the originalimages. Finally, the resulting in-stream images were spa-tially filtered using a 3 � 3 pixel Wiener smoothing filterthat has been shown to improve depth retrieval performance[Legleiter, 2012c].

2.6. Spectrally-Based Depth Retrieval

[21] Mapping river bathymetry from satellite imagesrequires a quantitative relationship between water depth dand reflectance R(l) in one or more spectral bands; radianceor raw digital numbers also could be used for this purpose.Efforts to establish such relationships are complicated,however, by the influence exerted on the remotely sensedsignal by several other factors, including variations in bottomreflectance, water column optical characteristics, water sur-face roughness, and atmospheric conditions. The availabilityof multiple spectral bands provides some leverage for iso-lating the effect of depth, and Legleiter et al. [2009] showedthat under appropriate circumstances and for certain combi-nations of wavelengths, the image-derived quantity

X ¼ lnR l1ð ÞR l2ð Þ

� �ð3Þ

is linearly related to depth. The physical basis for ratio-baseddepth retrieval was examined in detail by Legleiter et al.[2004, 2009] and is only summarized herein. The upwellingspectral radiance from a clear-flowing, shallow streamchannel is primarily a function of depth and bottom albedo.Whereas the reflectances of various substrates tend to bewithin a few percent of one another at a given wavelengthand thus have similar band ratio values, the absorptioncoefficient of pure water increases by an order of magnitudefrom the blue into the NIR portion of the spectrum. As aresult, the reflectance in the longer wavelength band withstronger absorption, l2, decreases more rapidly as depthincreases than does R(l1) and the ratio X increases with depthwhile remaining relatively insensitive to differences in bot-tom type. Taking the logarithm of the band ratio accounts forthe exponential attenuation of light by the water column.


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[22] This approach to retrieving water depth fromremotely sensed data requires: 1) selecting a suitable pair ofwavelengths; and 2) calibrating a linear relation between dand X. Both of these objectives can be achieved by OptimalBand Ratio Analysis, or OBRA [Legleiter et al., 2009].Given paired observations of depth and reflectance, thisalgorithm performs regressions of d on X for all possiblecombinations of numerator (l1) and denominator (l2)wavelengths and identifies the optimal band ratio as thatwhich yields the highest coefficient of determination R2; thecorresponding regression equation provides a calibrated dvs. X relation. Because depth is regressed against X valuesdefined by all possible band combinations, OBRA also isuseful for examining spectral variations in the nature andstrength of the relationship between d and X, which can bevisualized by plotting the matrix of R2(l1,l2) values as amatrix.[23] In this study, we performed OBRA of both field

spectra collected along the Snake River and SBC and imagespectra extracted from WV2 images of these streams.Analysis of the field spectra made use of the collocateddepths measured with the echo sounder or by wading,whereas OBRA of image spectra used pixel-scale meandepths estimated via OBK. For the larger and deeper SnakeRiver, we also performed a modified version of OBRA thatincluded not only a linear X term but also an X2 term in eachregression, based on the finding of Dierssen et al. [2003]that a quadratic equation improved bathymetric retrievalsin areas of greater depth.[24] To assess whether d vs. X relations derived from field

spectra could be used to infer depth from remotely senseddata, we convolved the original field spectra, which wererecorded with a sampling interval of 1 nm (Figure 3a), to thespecific band passes of the WV2 sensor. The convolvedspectra shown in Figure 3b thus had a similar, though lesswell-resolved, shape as the original measurements, but theconvolved field spectra differed from the image spectra inabsolute magnitude due to residual atmospheric effects(Figure 3c). To account for this difference, we subtracted themean reflectance of the image spectra from that of the field

spectra for each band and then added this correction factor tothe image spectra to force a closer agreement between thefield measurements and remotely sensed data (Figure 3d).OBRA was then performed for the convolved field spectraand the resulting d vs. X relation applied to both the originalimage and the image corrected to better match the fieldspectra. This analysis thus allowed us to evaluate the per-formance of bathymetric mapping algorithms calibrated viafield spectroscopy.[25] Although OBRA exploits the spectral information

available from multiband data sets, this procedure is notapplicable to panchromatic images that achieve a higherspatial resolution by integrating electromagnetic energyfrom across the spectrum. To assess whether this additionalspatial detail might enable reliable depth retrieval withoutrequiring spectral information, we evaluated the bathymetricmapping capabilities of the 0.5 m-pixel panchromatic WV2images of the Snake River and SBC. Rather than relating dto X as for the multispectral data, we used the linear trans-form, or Lyzenga [1981] algorithm, a more traditionalapproach to depth retrieval in rivers [e.g., Winterbottom andGilvear, 1997; Fonstad and Marcus, 2005; Flener et al.,2012]. In this case, the image-derived quantity related todepth is given by

Y ¼ ln R� R∞½ � ≈ ln DN � min DNð Þ þ 1½ � ð4Þ

where R represents the reflectance integrated over the WV2sensor’s panchromatic band and R∞ is the reflectance from ahypothetical, infinitely deep water column that encompassesthe contributions from the water column, water surface, andatmosphere but which lacks any signal from the bottom; thelatter term is thus known as the deep-water correction.Computationally, we implemented this algorithm using theraw digital numbers (DN) from each gray scale image andused the minimum pixel value from the in-stream portion ofthe scene as an estimate of R∞; the last term on the right isadded to avoid taking the logarithm of zero. Pixel-scalemean depths estimated from the original field measurementsvia OBK were then regressed against Y values for the

Figure 3. (a) Field spectra recorded at Rusty Bend of the Snake River; the median and interquartile rangeof n = 904 samples are plotted. (b) Field spectra convolved to the spectral band passes of the WorldView-2(WV2) sensor. (c) Image spectra from the WV2 image of Rusty Bend, extracted from the unique pixels atwhich flow depths were measured in the field (n = 1638). (d) Image spectra corrected to better match theconvolved field spectra by adding the mean difference between the field and image spectra to the originalimage spectra.


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corresponding locations to establish d vs. Y calibrationrelations.[26] Calibration relationships obtained via OBRA or the

linear transform were based on randomly selected subsets(50%) of the pixel-scale mean depths derived from theoriginal field measurements. The remaining d values werereserved and used to validate image-derived depth estimates;accuracy assessment involved calculating mean errors (anindication of bias) and root mean square errors (RMSE), asdescribed by Legleiter et al. [2011a], and examining residualmaps. In addition, we performed regressions of observed(pixel-scale mean depths obtained via OBK) versus pre-dicted (derived from the image) depths [Pineiro et al., 2008].We conducted this type of analysis for Rusty Bend and theFootbridge Reach and considered several different calibra-tion approaches and image data types: 1) linear vs. quadraticOBRA for the Snake River; 2) OBRA of convolved fieldspectra, with or without a correction applied to the image toforce better agreement with the field spectra; and 3) pan-chromatic vs. pan-sharpened WV2 images.

3. Results

3.1. Optical Characteristics of Gravel Bed Rivers

3.1.1. Water Column Optical Properties[27] Ancillary data collected along the Snake River and

SBC confirmed our visual impression of exceptional waterclarity. Turbidity values were consistently low (2–3 Neph-elometric Turbidity Units, or NTU) and suspended sedimentconcentrations were minimal: 2 mg/L for each of three watersamples from the Snake River and one sample from SBC.We characterized the interaction of solar energy with the

water column by measuring vertical profiles of downwellingspectral irradiance and calculating values of the diffuseattenuation coefficient Kd(l) (Figure 4). Data sets from sixdifferent dates resulted in similar Kd(l) spectra that variedlittle with wavelength through the visible but increasedabruptly at 700 nm due to a sharp rise in the absorptioncoefficient of pure water, denoted by aw(l), in the NIR.Similarly, the dip in Kd(l) around 810 nm is associated witha decrease in aw(l) at this wavelength. Because thesestreams had only small amounts of suspended sediment ordissolved organic matter, their optical properties were dic-tated primarily by those of pure water. To illustrate thecontrast between these clear-flowing gravel bed rivers and amore turbid sand-bed channel, a Kd(l) spectrum from thePlatte River was added to Figure 4 [Legleiter et al., 2011b].The higher turbidity (49.5 NTU) and suspended sedimentconcentration (161 mg/L) of the Platte River lead to Kd(l)values 2–5 times greater than those observed in our studyarea throughout the visible, with the greatest differenceoccurring in shorter blue-green wavelengths more suscepti-ble to scattering by suspended sediment. In the NIR, whereoptical properties were driven primarily by pure waterabsorption, the Kd(l) spectra for the three rivers convergedbut remained higher for the Platte.[28] The diffuse attenuation coefficient is an apparent

optical property influenced by variations in the ambient lightfield, in addition to the spectral characteristics of the wateritself. To isolate the effects of the water on the interaction oflight with the river, we made direct measurements of inher-ent optical properties with an ac-9. In situ observations of theattenuation a(l) and absorption c(l) coefficients quantita-tively verified the clarity of both streams (Figure 5). Again,

Figure 4. Diffuse attenuation coefficient spectra Kd(l) calculated from field measurements of the down-welling spectral irradiance Ed(l) at various depths within the water column. For each irradiance profileEd(l) was measured at 10–12 different depths from just beneath the water surface to 0.6 m. Data were col-lected from the clear-flowing Snake River (SR) and Soda Butte Creek (SBC) on the indicated dates in2011, and from the more turbid Platte River (PR) in Nebraska in 2010 [Legleiter et al., 2011b].


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the data sets agreed closely with one another, with highervalues of a(l) and c(l) in the shortest- and longest-wavelength bands and the weakest absorption and attenua-tion in the green at 555 nm, implying that penetration ofsolar energy through the river was most efficient at thiswavelength. Also included in Figure 5 are the absorptioncoefficients of pure water and suspended sediment, based ona specified concentration of 2 mg/L (= 2 g/m3) and an opticalcross-section included with the HydroLight radiative transfermodel [Mobley and Sundman, 2001]. These data are con-sistent with our measurements of a(l) for l > 600 nm, wheresediment has little influence on overall water columnabsorption. For shorter wavelengths more strongly absorbedby suspended mineral matter, the sum of the pure waterand suspended sediment absorption coefficients agrees wellwith our field data, implying that a simple two-componentoptical model might be a sufficient description of thesestreams. The difference between the absorption and attenu-ation coefficients is due to the effects of scattering, primarilyby suspended sediment [Legleiter et al., 2011b]. Overall,the relatively simple optical characteristics and great clarityof the Snake River and SBC implied that these channelswould be amenable to spectrally-based depth retrieval.[29] Our measurements of water column optical properties

also allowed us to quantify some of the limitations associ-ated with remote sensing of river bathymetry. Becauseimaging systems have a finite capacity to detect smallchanges in the amount of upwelling spectral radiance, trulycontinuous depth maps cannot be derived from digital imagedata. Instead, the smallest change in depth a particular sensorcan resolve depends on the rate at which light is attenuatedby the water column, the amount of radiance reflected from

the streambed LB(l), and the sensor’s noise-equivalent deltaradiance DLN(l) [Philpot, 1989; Legleiter et al., 2004;Legleiter and Roberts, 2009]. To explore the implications ofthis important concept, we inserted observed values of Kd(l)into equation (1) and calculated the smallest detectablechange in depth Dd(l) at a range of initial depths d0; theratio DLN(l)/LB(l) was held constant at 0.01 [e.g., Philpot,1989]. The results of this analysis are illustrated inFigure 6a, based on an irradiance profile from the SnakeRiver; Dd(l) values for other sites and dates were nearlyidentical because Kd(l) values for the various data sets wereso similar. For this example, at a wavelength of 700 nm adifference in depth of 0.01 m or less would be detectable atdepths up to 0.4 m, and even at a depth of 1 m Dd(l)remained less than 0.04 m. These calculations imply that ifthe imaging system is sufficiently sensitive and the bottom iswell-illuminated and highly reflective, precise depth esti-mates could be derived from remotely sensed data. Note,however, that less sensitive instrumentation (i.e., largerDLN(l)), less reflective substrates, and/or smaller amountsof incident radiation (i.e., smaller LB(l)), would lead tolarger Dd(l) and less precise depth estimates. For example,images acquired at greater solar zenith angles (e.g., early orlate in the day, or during the spring or fall) and/or encom-passing darker streambed materials (e.g., basalt) will havesmaller values of LB(l) and hence larger values of Dd(l) fora given sensor.[30] The finite sensitivity of imaging systems also dictates

that river bathymetry can only be mapped up to some max-imum detectable depth. Again, dmax(l) depends on theoptical properties of the water column, summarized in termsof an effective attenuation coefficient 2Kd(l), and the ratio

Figure 5. Inherent optical properties of the water column measured with an ac-9 on the indicated dateson the Snake River (SR) and Soda Butte Creek (SBC). The blue lines represent the attenuation coefficientc and the black lines the absorption coefficient a. Also included are the absorption coefficients of purewater and suspended sediment with a concentration of 2 g/m3, based on data included with the HydroLightradiative transfer model [Mobley and Sundman, 2001].


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DLN(l)/LB(l), where in this case DLN(l), the smallest dif-ference in radiance the imaging system can resolve, is setequal to the difference between the at-sensor radiance andthe radiance from optically deep water [Philpot, 1989;Legleiter et al., 2004]. Maximum detectable depths werecalculated via equation (2) for a range of DLN(l)/LB(l)values; the results of this analysis, based on a Kd(l) spec-trum from the Snake River, are summarized in Figure 6b.For DLN(l)/LB(l) = 0.0001 (i.e., a highly sensitive instru-ment), dmax(l) was 10.9 m in the green wavelengths wherewater column attenuation was weakest. As pure waterabsorption increased through the red and NIR, dmax(l)decreased to less than 2 m for l > 730 nm. For a system witha lower radiometric resolution, corresponding to a two-orderof magnitude decrease in DLN(l)/LB(l) to 0.01 (the valueused to calculate the Dd(l) values in Figure 6a), depths upto 5.45 m could be detected at 560 nm, but dmax(l) = 0.67 inthe NIR at 760 nm. These results implied that a sensorcapable of resolving small changes in radiance would becrucial to mapping bathymetry across a broad range ofdepths. Similarly, multispectral data would allow for selec-tion of bands well-suited for depth retrieval across thisrange. The maximum detectable depth also would be influ-enced by the nature of the fluvial environment itself. For agiven imaging system (i.e., a fixed DLN(l)), dmax(l)depends on the bottom contrast between the substrate andwater column, implying that highly reflective substrates and/or clear water would favor depth retrieval from deeperchannels. Also note that the absolute magnitude of LB(l) issignificant, such that images acquired under less well-illu-minated conditions (i.e., early or late in the day, or at highlatitudes) would result in smaller values of dmax(l). In anycase, our field measurements of water column optical prop-erties, together with the analytical framework represented byequations (1) and (2), implied that bathymetry could be

mapped remotely with a high degree of precision across therange of depths, typically less than 2.5 m, observed in manygravel bed rivers.3.1.2. Field Spectroscopy and Relationships BetweenReflectance and Water Depth[31] A primary objective of this study was to establish

quantitative relationships between reflectance and waterdepth for the two streams we examined. Field spectra mea-sured from above the water surface on the Snake River andSBC were processed following Legleiter et al. [2011b]. Eachset of field spectra, together with the corresponding depthmeasurements, was then used as input to the OBRA algo-rithm described in Section 2.6. This procedure identifiedcombinations of wavelengths that were sensitive to varia-tions in depth but robust to other factors that might influencereflectance, such as substrate heterogeneity or sun glint fromthe water surface. The results of this analysis are summa-rized in Figure 7 using OBRA matrices that represent thestrength of the linear relation between d and X for all pos-sible band combinations. Figure 7a indicates that for RustyBend, where depths reached up to 3 m, a strong (R2 = 0.887)relation between d and X was obtained for a green numeratorband and red denominator band. Moreover, the OBRAmatrix shows that a broader range of wavelengths wouldhave resulted in d vs. X relations nearly as strong: numeratorbands less than 550 nm resulted in R2 > 0.8 for575 < l2 < 720 nm. For this relatively deep reach, the NIRportion of the spectrum was not useful because strongabsorption by pure water lead to saturation of the reflectancesignal in pools. Similarly, the decrease in predictive power atl2 = 675 nm was due to chlorophyll absorption by benthicalgae present on the streambed; the reduced bottom albedoresulted in a smaller reflectance and a somewhat weakerrelation between d and X in this band.

Figure 6. Example calculations of the precision of image-derived depth estimates Dd(l) and maximumdetectable depth dmax(l) based on Kd(l) values from the Snake River collected on 9 September 2011(Figure 4). (a) The Dd values calculated for a wavelength of l = 700 nm for a range of initial depthsd0 and a DLN/LB ratio of 0.01 using equation (1). (b) The dmax(l) spectra calculated for the DLN(l)/LB(l) values indicated in the legend using equation (2).


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[32] Results from SBC were similar, but the optimal bandratio produced an even higher regression R2 (0.975) for apair of longer wavelengths, and a number of other bandswould have yielded d vs. X relations nearly as strong(Figure 7b). In contrast to Rusty Bend, NIR wavelengthswere effective denominator bands for any numeratorl1 < 730 nm. In this case, the NIR was more useful due toshallower depths along the Footbridge Reach. Strongabsorption by pure water at these wavelengths implied thatsmall changes in depth would produce in large changes inreflectance, resulting in very strong d versus X relations.Because depths were so shallow, the saturation that limitedthe utility of the NIR on the Snake River was less of an issueon SBC. In general, stronger d vs. X relations at longer NIRwavelengths could be expected for shallower streams.Low concentrations of suspended sediment and dissolvedorganic matter and highly reflective substrates also favorremote bathymetric mapping [Legleiter et al., 2009]. Bothrivers examined in this study satisfied these criteria, andanalysis of field spectra showed that spectrally-baseddepth retrieval would not only be feasible but potentiallyhighly accurate.[33] An example of this capability is given in Figure 8,

which shows data collected on a transect across Rusty Bend.Depths measured by the echo sounder agreed closely withdepths calculated from the field spectra using the OBRArelation from Figure 7a. Correspondence between theobserved and predicted profiles was best over the shallowbar surface on the right side of the channel (Figure 8, left).Through the middle of the stream, the OBRA relationresulted in slight over-predictions of depth, and the spec-trally-based estimates were shallower than the echo sounderdata in the pool along the outer bank. These discrepancies

were small, however, on the order of 0.2–0.4 m, and thiscross-section illustrated the robust performance of theOBRA relation across a range of depths up to 2.75 m. Thislevel of accuracy was noteworthy due to the pronounceddifferences in bottom reflectance along this transect(Figure 2c). Whereas most of the cross-section consisted of agravel substrate with some degree of algal coating, severallarge blocks of clay bedrock were located near the outerbank. This cohesive material was noticeably lighter-coloredthan the surrounding gravel and resulted in large spikes inreflectance in this part of the channel, as shown in Figure 8for the OBRA denominator band. The OBRA-based depthestimates were shallower at these locations but not to thedegree that the abrupt increases in reflectance might seem todictate. These results thus confirmed that OBRA enabledeffective depth retrieval in the presence of highly heteroge-neous substrates, cited by Legleiter and Roberts [2005] asone of the primary advantages of this technique. This studysupported this conclusion in the context of a deeper riverwith more variable bottom reflectance than had been con-sidered previously.[34] These results, though encouraging, were derived from

field spectra that provided essentially continuous reflectancedata with a 1 nm sampling interval. To assess whether strongrelations between d and X could be derived from image datathat integrate reflectance over a smaller number of broaderbands, we convolved the original field spectra to match theWV2 sensor response function, as described in Section 2.6and illustrated in Figures 3a and 3b. The convolved spectraconsisted of eight discrete bands and were subjected toOBRA to quantify the extent to which reduced spectralresolution might compromise the ability to retrievebathymetry from satellite images. The results of this analysis

Figure 7. Optimal band ratio analysis (OBRA) of field spectra from (a) Rusty Bend and (b) the Foot-bridge Reach. The color scale represents the coefficient of determination (R2) value for regressions of don X, where X is an image-derived quantity defined via equation (3), for all possible band combinations.The numerator, l1, and denominator, l2, wavelengths defining the optimal band ratio are listed in the insetof each panel, along with the corresponding regression equation, R2 value, and standard error.


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are summarized in Figure 9a, which indicates only a slightdecrease in the OBRA R2 to 0.839. For the convolvedspectra, the optimal WV2 band combination was a greennumerator and yellow denominator, essentially the samewavelengths as for the original field spectra. The OBRAmatrix also indicated that the blue band would have been aneffective numerator with either the yellow or red band as adenominator. These results implied that the sensor’s broaderbands contained sufficient spectral information for inferringdepth and provided further evidence of the feasibility ofmapping river bathymetry from space.

3.2. Mapping River Bathymetry From SatelliteImage Data

[35] Our in situ measurements of water column opticalproperties, together with visual inspection of WV2 images,implied that flow depths could be inferred from satellitedata. In this section, we report depth retrieval results fromthe Snake River and SBC, with a focus on accuracy assess-ment of depth estimates obtained using various calibrationapproaches and image data types.3.2.1. Snake River3.2.1.1. Depth Retrieval Calibration Approaches[36] The most direct means of mapping bathymetry from

remotely sensed data involved extracting image spectra fromthe locations of field-based depth measurements and usingthese data to calibrate a relationship between d and theimage-derived quantity X defined by equation (3). The

Snake River posed a challenging test of this approachbecause flow depths ranged up to 3 m, far greater than theshallow streams that have been the subject of our priorremote sensing investigations [Legleiter et al., 2009, 2011a].In larger gravel bed rivers, saturation of the radiance signalmight lead to a non-linear relationship between d and X andcould preclude depth retrieval from pools. To account forthis possibility we performed both linear OBRA, with asingle X term in the regression against field measurements ofd, and a quadratic OBRA in which an X2 term also wasincluded in the regression, based on a similar study byDierssen et al. [2003]. The resulting OBRA matrices arepresented in Figures 9b and 9c, which indicate that the sameband combination, a blue numerator with a yellow denomi-nator, was optimal for both linear and quadratic formula-tions. The simple d vs. X regression yielded a strong(R2 = 0.827) linear relationship between depth and the bandratio, but adding an X2 term only slightly increased predic-tive power (R2 = 0.864). Closer inspection of the OBRAmatrices indicated similar spectral patterns, but the NIRbands became more useful when the X2 term was included.To an extent, allowing for a non-linear d vs. X relationaccounted for saturation of the radiance signal in deeperwater in the NIR. Nevertheless, the marginal improvementprovided by the quadratic term implied that the additionalcomplexity of this approach was not justified.[37] Bathymetric maps generated from the WV2 satellite

image of Rusty Bend using linear and quadratic OBRA

Figure 8. Cross-section of observed depths and image-derived estimates from a transect of Rusty Bendare plotted on the right axes. On the left axes is the reflectance at 607 nm, the denominator wavelength forthe optimal band ratio for this reach, recorded as the cataraft traversed the cross-section.


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relations are shown in Figures 10a and 10b, respectively.The maps were very similar to one another, with the linearformulation yielding slightly shallower depth estimates inthe pool along the outer bank and over the bar surface on theright (north) side of the channel, relative to the quadraticOBRA. Both techniques produced realistic depictions of thegross morphology, with an asymmetric cross-sectional shapeextending from above the apex through the middle of thebend before the thalweg shifted toward the right at the lowerend of the reach. Depth retrieval accuracy was assessed viacomparison with pixel-scale mean depths obtained by OBKof the field survey data. The resulting residual maps areshown in Figures 11a and 11b, where negative residuals(bright red tones) represent over-predictions of depth andpositive residuals (darker blue tones) represent under-predictions of depth. Again, spatial patterns for the twoversions of OBRA were similar, with the linear d vs. Xrelation leading to more extensive underestimates of depthalong the outer bank in the upper end of the reach and agreater number of overestimates along the left bank past thebend apex. Most depth retrieval residuals were on the orderof 0.25 m but locally ranged as high as 0.6 m, nearly half themean depth of 1.23 m, in the thalweg above the apex and onthe outer bank through the lower portion of Rusty Bend.[38] For the most part, depth estimates from both linear

and quadratic OBRA were reliable, as indicated by high R2

values for observed vs. predicted (OP) regressions based onfield measurements set aside for validation (Figure 12 andTable 2). Moreover, small mean errors and OP intercept andslope values near 0 and 1, respectively, implied that depthestimates were unbiased on average. The OP regression plotin Figure 12a revealed a curved trend for linear OBRA,however, with systematic under-prediction of depth in bothshallow and deep water. This trend arose from the non-lin-earity of the relationship between d and X and was effec-tively removed by including an X2 term in the OBRAregression (Figure 12b). Nevertheless, the depth retrievalRMSE and OP regression standard errors were only slightlyless for the quadratic vs. linear OBRA, and a typical error of0.22 m would be less than 20% of the reach-averaged meandepth. Because the quadratic formulation did not signifi-cantly improve accuracy, the standard linear OBRA appearedto be well-suited for bathymetric mapping in larger, deepergravel bed rivers such as the Snake, although an X2 termcould prove useful in streams with greater depths.[39] An alternative strategy for remote mapping of river

bathymetry would involve making direct measurements ofdepth and reflectance and using field spectra to develop dversus X relations that could then be applied to remotelysensed data. If the spectral response function of the sensorwere known, the field spectra could be convolved to matchthe instrument’s band passes, as shown in Figures 3a and 3bfor the WV2 satellite. Ideally, OBRA of the convolved fieldspectra would result in a calibrated relationship between dand X that could be applied directly to images of the river

Figure 9. Optimal band ratio analysis (OBRA) from RustyBend of the Snake River: (a) field spectra convolved tomatch the band passes of the WorldView-2 (WV2) sensor;(b) linear OBRA of WV2 satellite image spectra; and(c) quadratic OBRA of WV2 satellite image spectra.


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from which the field spectra were collected and potentiallyother streams as well. To assess the feasibility of thisapproach, we measured depth and reflectance on transectsacross Rusty Bend, convolved the spectra to the WV2bands, and performed OBRA. This analysis is summarizedin Figure 9a, which indicated a strong linear relation(R2 = 0.839) between d and X, defined as the logarithm ofthe ratio of the green and red bands. This R2 value was nearlyas high as that associated with the original field spectra(Figure 7a) and slightly better than that associated with thelinear OBRA of image spectra (Figure 9b). Applying theOBRA relation from Figure 9a to the WV2 image resulted inthe bathymetric map in Figure 10c, which has the same colorscaling as the maps produced via OBRA of image spectra.A comparison of these maps indicated that the pool along the

outer bank was not well-resolved by depth estimates basedon convolved field spectra, and depths on the shallow barsurface tended to be over-predicted. This pattern was evidentin the residual map in Figure 11c, which featured under-estimates on the order of 0.6 m in the pool above the bendapex and overestimates of similar magnitude at the lower endof the reach. The OP regression for these depth estimatesyielded a lower R2 value of 0.75, a large negative interceptterm, and a slope much greater than 1 (Figure 12c), implyingthat predictions based on convolved field spectra werebiased.[40] In an effort to account for this bias, we adjusted the

image data to better match the field spectra as described inSection 2.6 and illustrated in Figure 3. This adjustment,which could be considered a simple means of radiometric

Figure 10. Image-derived depth maps for Rusty Bend of the Snake River produced using various calibra-tion approaches and image data types. All maps have a common color scale shown at the bottom. Flow isfrom right to left.


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calibration and atmospheric correction, served to modify theimage so that the d vs. X relation derived from the convolvedfield spectra (Figure 9a) could be applied directly to theWV2 scene. The resulting bathymetric map, shown inFigure 9d, featured greater depth estimates than did theoriginal, uncorrected image but still failed to resolve the fulldepth of the pool along the outer bank. On the opposite sideof the channel, depths tended to be under-predicted,including some negative estimates. The spatial pattern ofthese errors is illustrated in Figure 11d, which shows thateven after modifying the image data to better match theconvolved field spectra, pool depths were underestimated by0.5 m or more throughout much of the bend; overestimatesof 0.5 m or more occurred at the lower end of the reach.

Accuracy assessment using the validation subset of the fieldsurvey resulted in OP regression intercept and slope valuescloser to 0 and 1, respectively, implying that the imagecorrection was effective in removing the bias associated withcalibration based on field spectra, but the OP R2 improvedonly marginally, from 0.75 to 0.77. The RMSE and OPregression standard errors for both depth retrieval methodsbased on convolved field spectra were greater than those forOBRA of image spectra; typical errors on the order of 0.3 mwould be approximately 25% of the mean depth for thereach. These results imply that calibration via field spec-troscopy was a plausible strategy, especially when the imagewas corrected to better match the field spectra, but thisapproach was less reliable than OBRA of image spectra.

Figure 11. Maps of depth retrieval residuals, defined as the difference between the field-based depthmap and the image-derived depth estimates, for Rusty Bend of the Snake River produced using variouscalibration approaches and image data types. All maps have a common color scale shown at the bottom.Flow is from right to left.


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Figure 12. Depth retrieval validation for Rusty Bend of the Snake River for the various calibrationapproaches and image data types labeled for each plot. Each plot represents the results of an observedversus predicted (OP) regression as well as the one-to-one line of perfect agreement for comparison.


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3.2.1.2. Image Data Types[41] Although depth retrieval via OBRA requires multiple

spectral bands, bathymetric maps also can be generated fromsingle-band or panchromatic gray scale images using thelinear transform algorithm introduced by Lyzenga [1981].In the context of satellite imagery, this capability is poten-tially significant because many spaceborne sensors feature apanchromatic band with a greater spatial resolution than theindividual multispectral bands; for the WV2 system, thepixel sizes for the panchromatic and multispectral images are0.5 m and 2 m, respectively. If spectral information is notessential for accurate depth retrieval, application of the lineartransform (equation (4)) might enable more effective map-ping of smaller streams and enhanced spatial detail in largerrivers. If spectral information does prove critical, a hybridapproach based on a pan-sharpened image that features thehigh spatial resolution of the panchromatic image but alsoincorporates the multispectral data could prove to be mostuseful.[42] We explored this possibility and evaluated the rela-

tive significance of spectral and spatial resolution by pro-ducing bathymetric maps from 0.5 m-pixel panchromaticand pan-sharpened WV2 images of the Snake River. Thesemaps are included in Figures 10e and 10f, along with thebathymetry inferred from the original, 2 m-pixel multispec-tral images. For the panchromatic scene, depth retrieval viathe linear transform algorithm captured the general mor-phology of the reach but the map had a grainy appearancedue to high-frequency noise that persisted despite theapplication of a smoothing filter. The area of deeper flowalong the outer bank was narrower in the bathymetric mapderived from the panchromatic data than in the map based onthe original multispectral image (Figure 10a), suggestingthat spectral information was needed to resolve greaterdepths. The corresponding residual map (Figure 11e) high-lighted this pattern, with depth underestimates on the orderof 0.6 m extending across a greater fraction of the channelwidth over the upper half of the reach. Past the bend apex,depths were over-predicted in a large area along the left sideof the channel. Accuracy assessment of the linear transform-

derived depths indicated a weaker, but still fairly strongagreement between observations and predictions (R2 = 0.67),and the OP regression equation did not imply any systematicbias. Closer examination of Figure 12e revealed that thisagreement deteriorated considerably in deeper water, withthe image-derived estimates failing to increase as rapidly asthe field-surveyed depths for d > 1 m.[43] The bathymetric map derived from the pan-sharpened

image (Figure 10f) included a broader area of deep wateralong the outer bank than did the map produced from thepanchromatic image, suggesting that the additional spectralinformation resulted in a more accurate representation of thethalweg. The grainy texture of the panchromatic imagepersisted in the pan-sharpened data, however, and appearedto be even more pronounced over the point bar on the rightside of the channel at the lower end of the reach. Theresidual map in Figure 11f was similar to that associatedwith the panchromatic image, but the large underestimates inthe upper portion of the bend were less extensive. Accuracyassessment of depth estimates from the pan-sharpened mul-tispectral image, which had a pixel edge dimension fourtimes smaller than the original multispectral data, yielded anOP regression R2 of 0.80 (Figure 12f), which was a signifi-cant improvement over the panchromatic image but was lessthan that associated with the 2 m-pixel multispectral image.This result implied that greater spectral information contentwas more important than enhanced spatial detail for depthretrieval from this relatively large gravel bed river. The noiseintroduced by fusing the panchromatic image with the mul-tispectral data also might have contributed to the greaterdepth retrieval errors associated with the pan-sharpenedimage. In any case, our analysis suggested that the additionalimage processing required to generate the pan-sharpenedimage was not justified and that depth retrieval from theoriginal multispectral images might be both simpler andmore accurate in this setting.3.2.2. Soda Butte Creek3.2.2.1. Depth Retrieval Calibration Approaches[44] The Footbridge Reach presented a different type of

challenge for remote sensing of river bathymetry: for this

Table 2. Depth Retrieval Accuracy Assessment for Various Calibration Methods and Image Types

Reach Method OBRAaR2Num.b

(nm)Den.c

(nm)Mean

Error (m)RMSE(m) OPdR2

OP Std.Error (m)

OPSlope

OP Intercept(m)

Rusty Lineare 0.827 480 605 �0.004 0.238 0.822 0.238 0.993 0.005Quadratice 0.864 480 605 �0.003 0.212 0.859 0.212 0.977 0.026Fieldf 0.839 545 605 �0.056 0.305 0.753 0.280 1.326 �0.476Field + imageg 0.839 545 605 0.058 0.271 0.769 0.271 1.005 0.052Panh N/A N/A N/A �0.032 0.327 0.666 0.327 0.952 0.027Pan-sharpi 0.794 480 605 �0.009 0.254 0.801 0.254 0.992 0.001

Footbridge Lineare 0.585 545 725 0.001 0.094 0.594 0.110 0.987 0.004Fieldf 0.962 660 725 0.026 0.195 0.452 0.110 0.380 0.157Panh N/A N/A N/A 0.003 0.115 0.414 0.115 0.928 0.020Pan sharpi 0.578 545 725 0.003 0.110 0.504 0.110 0.969 0.011

aOptimal Band Ratio Analysis.bNumerator wavelength for optimal band ratio.cDenominator wavelength for optimal band ratio.dObserved versus predicted regression.eLinear and quadratic refer to linear and quadratic OBRA of image spectra.fField refers to OBRA of field spectra convolved to match WorldView-2 sensor band passes.gField + image is similar but refers to application of the OBRA relation from convolved field spectra to an image corrected to better match the field

spectra.hPan refers to depth retrieval via the linear transform algorithm applied to the panchromatic image.iPan-sharp refers to linear OBRA of image spectra from a pan-sharpened multispectral image.


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small gravel bed stream, the pixel size was a significantfraction of the mean channel width, particularly under thelow-flow conditions when the WV2 image was acquired.Moreover, at this discharge, SBC split into two separatechannels, each of which was further divided by mid-channelbars. As a result, the flow was quite shallow (Table 1) andderiving information on channel form thus required animaging system capable of resolving subtle variations indepth. Based on the results for the Snake River, and becauseSBC was so much shallower, we focused on the standardlinear formulation of the OBRA algorithm and did not pur-sue the quadratic alternative. Similarly, because our analysisof convolved field spectra from the Snake River indicatedthat depth estimates would be biased unless the image datawere adjusted to match the field spectra, we considered onlythe latter approach for SBC.[45] OBRA results obtained using spectra extracted from

the WV2 image or measured directly in the field are shownin Figures 13a and 13b, respectively. For the image spectra,the highest d vs. X regression R2 occurred for a greennumerator and NIR numerator (the sensor’s ‘red edge’ band)but was only 0.585, significantly less than the 0.827 R2 onthe Snake River. The OBRA matrix in Figure 13a indicatedthat this NIR band was by far the most useful denominatorwavelength with any visible numerator; other denominatorbands produced much weaker d vs. X relations. For theconvolved field spectra, the OBRA results were moreencouraging, with an optimal R2 value of 0.962 for a rednumerator band and the same 725 nm denominator as for theimage spectra. Unlike the image spectra, however, a broaderrange of bands produced strong, linear relationships betweend and X, including longer NIR wavelengths. This result wasexpected because strong absorption by pure water in the NIRcaused small changes in depth to be expressed as relativelylarge changes in reflectance; because depths in this reachwere so shallow, saturation of the NIR reflectance signal wasless of an issue than along the deeper Snake River. OBRA of

the two Footbridge Reach data sets suggested that bathy-metric mapping based on field spectra might be moreeffective than extracting spectra directly from an image.Whereas many of the image spectra were from mixed pixelscontaminated by radiance from adjacent terrestrial features,each of the field spectra sampled a smaller area entirelywithin the wetted channel. Atmospheric effects present inthe satellite image data but absent from the field measure-ments also might have contributed to the inferior OBRAresults for the image spectra.[46] Bathymetric maps produced using these two calibra-

tion methods are presented in Figures 14a and 14b, both ofwhich have a common color scale with an upper limit set tothe maximum depth observed in the field. In general, bothmaps captured the gross morphology of the reach, withdeeper flow along the left (east) bank at the upper end of ourstudy area, in a pool on the far right channel near theentrance to the bend, in the lower half of the left chutechannel, and at the bottom of the reach where the channelsconverge and the stream enters a curve to the right. Asidefrom these areas, depths were very shallow, on the order of0.2 m. Although both OBRA of image spectra and applica-tion of a d vs. X calibration relation derived from fieldspectra to the corrected WV2 image produced reasonablespatial patterns, the absolute magnitudes of the depth esti-mates were less reliable, especially for calibration based onfield spectra. The bathymetric map shown in Figure 14bexceeded the specified color limits at both the shallow anddeep ends of the spectrum, resulting in the dark red tonesmost notable over the point bar near the apex and the darkblue tones at the upper and lower ends of the reach. Depthsestimated from image spectra, in contrast, fell within therange of observed depths and were more accurate.[47] Differences between the two approaches also were

highlighted by the residual maps shown in Figures 15a and15b. For the image-based algorithm, most of the residualswere near zero, with a tendency to over-predict depth in

Figure 13. Optimal band ratio analysis (OBRA) from the Footbridge Reach of Soda Butte Creek:(a) OBRA of image spectra; and (b) field spectra convolved to match the WorldView-2 sensor bands.


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shallow areas and under-predict in pools. When the OBRArelation from the field spectra was applied to the correctedimage, the overestimates of depth in shallow riffles and barswere more pronounced, as was the under-prediction in theleft chute channel and along the outer banks at both theupper and lower ends of the reach. Large positive residualsnear steep cutbanks suggested that the presence of bothbright terrestrial features and deep water within mixed pixelsmight have lead to unreliable depth estimates along channelmargins and that sensor spatial resolution might have been a

limiting factor for this small stream. Similarly, the inabilityof either method to detect the deep pool in the middle of theleft chute channel, evident as a dark blue area on the residualmaps, also implied that the 2 m pixel size might not havebeen adequate for mapping SBC under low-flow conditions.[48] The accuracy assessment summarized in Figures 16a

and 16b yielded further insight regarding discrepanciesbetween bathymetric maps produced from field vs. imagespectra. Regression of observed vs. predicted depths yieldeda stronger correlation (R2 = 0.59) for depth retrieval based on

Figure 14. Image-derived depth maps for the Footbridge Reach of Soda Butte Creek produced usingvarious calibration approaches and image data types. All maps have a common color scale shown atthe bottom. Flow is from top to bottom.

Figure 15. Maps of depth retrieval residuals, defined as the difference between the field-based depthmap and the image-derived depth estimates, for the Footbridge Reach of Soda Butte Creek produced usingvarious calibration approaches and image data types. All maps have a common color scale shown at thebottom. Flow is from top to bottom.


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image spectra than when using the convolved field spectrafor calibration, which resulted in an R2 of only 0.45. Moreimportantly, however, the image-based estimates wereunbiased, with an OP regression intercept near 0 and slopenear 1. In contrast, depth estimates derived using the cali-bration relation for the convolved field spectra resulted in apositive intercept term nearly as large as the mean depth forthe reach and a much smaller slope, implying biased esti-mates. This bias lead to over-predictions of depth in shallowareas and under-predictions in deep areas and persisteddespite the correction applied to the image to force closeragreement with the field spectra. Although the simple imageadjustment outlined in Section 2.6 allowed for reasonablyaccurate depth retrieval for the Snake River, this techniquewas not effective on SBC, implying that more sophisticatedradiometric calibration and atmospheric correction mightbe required before relationships derived from field spectracan be applied to remotely sensed images. Another factorthat might have contributed to biased estimates was the

use of a near-infrared band that might have been morestrongly affected by residual atmospheric effects not fullyaccounted for in the reflectance retrieval algorithm used byDigitalGlobe.3.2.2.2. Image Data Types[49] Given the small size of SBC and the modest depth

retrieval performance of the 2 m-pixel WV2 data, we eval-uated whether images with greater spatial resolution mightprove more useful for bathymetric mapping. Depth mapsproduced from 0.5 m-pixel panchromatic and pan-sharpenedimages are shown in Figures 14c and 14d, with the samecolor scaling as used for the maps generated from thecoarser-resolution data. Overall spatial patterns were similar,but the smaller pixel size revealed some details of the mor-phology that were not evident in Figures 14a and 14b. Forexample, the depth map generated by applying the lineartransform to the panchromatic image captured shoaling ofthe flow onto the point bar in the middle of the three chan-nels present at the bend apex, a feature that was not resolved

Figure 16. Depth retrieval validation for the Footbridge Reach of Soda Butte Creek for the various cal-ibration approaches and image data types labeled for each panel. Each plot represents the results of anobserved versus predicted (OP) regression as well as the one-to-one line of perfect agreement for compar-ison. Note that Figure 16b has different axis limits than the other plots.


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by any of the other image types. The linear transform failedto detect the full depth of pools located in the left chutechannel and at the lower end of the reach, however. The pan-sharpened multispectral image did not provide quite as muchdetail but yielded greater depth estimates in the pools thandid the panchromatic data. The residual maps in Figure 15indicated that depth retrieval errors from the higher resolu-tion images were of a similar magnitude as those associatedwith the original multispectral image. Over-predictions ofdepth in the riffle at the upper end of the reach andapproaching the bar at the bend apex and under-predictionsof depth throughout the lower portion of the reach weresalient in the residual maps for both the panchromatic andpan-sharpened images. The accuracy assessment summa-rized in Figures 16c and 16d indicated that depth estimateswere unbiased in both cases but were more reliable for thepan-sharpened than for the panchromatic image. OP regres-sion R2 values of 0.50 and 0.41, respectively, were signifi-cantly less than the 0.59 obtained using image spectra fromthe original multispectral scene. Typical errors of 0.11 mwere half the mean flow depth for the reach. These resultsimply that even in a smaller stream such as SBC, the addi-tional spatial detail provided by the panchromatic image didnot translate into improved depth retrieval performance.Instead, spectral information was essential for reliablebathymetric mapping.

4. Discussion

[50] Efforts to characterize the complex interactionsamong flow, morphology, and sediment transport that shapealluvial river channels have often been compromised by thedifficulty of acquiring basic measurements of channel form.As a result, field studies typically have examined only shortreaches in isolation. Important, increasingly interdisciplin-ary research opportunities thus exist at larger segment andwatershed scales [e.g., Fausch et al., 2002; Carbonneauet al., 2011]. For example, geomorphologists might seekto examine how the detailed process mechanics documentedthrough reach-scale studies self-organize within a catchmentto create emergent patterns in channels and landscapes thathave tended to be described only in conceptual or theoreticalterms [e.g., Church, 2002; Benda et al., 2004]. Similarly,greater insight on the distribution of in-stream habitat withina watershed would help biologists to understand the move-ment of fish throughout their life histories [e.g., Ganio et al.,2005]. In an applied context, a more synoptic perspective onfluvial systems would help to provide a holistic, integratedcontext for the planning, implementation, and monitoring ofriver restoration projects [e.g., Beechie et al., 2010; Downset al., 2011]. For all of these purposes, the lack of an efficientmeans of mapping river morphology has impeded progressand the development of new techniques could thus stimulatesignificant advances in each of these fields [Fonstad andMarcus, 2010]. Motivated by this prospect, this investiga-tion demonstrated the feasibility of mapping the bathymetryof clear-flowing gravel bed rivers from satellite image data.Using field measurements and WV2 imagery from twostreams in the northern Rocky Mountains, we showed thatinformation on flow depth can be retrieved from multispec-tral data across a range of channel sizes from approximately20–60 m in width and 0.2–1.25 m in mean depth. A simple

band ratio-based algorithm, calibrated using either spectraextracted from the image or measured directly in thefield, provided reliable depth estimates. The results of thisstudy thus imply that satellite-based mapping of riverbathymetry could become a viable tool for river researchand management.

4.1. Constraints on Spectrally-Based BathymetricMapping

[51] Although the potential for remote sensing methods tocontribute to the riverine sciences is justifiable cause forexcitement [Marcus and Fonstad, 2010], we advocate acautious approach that acknowledges the constraints as wellas the capabilities associated with this new technology. Theretrieval of water depth from passive optical image data, forexample, is subject to some important caveats. The mostsignificant constraint on the spectrally-based approach is thelimited range of stream conditions under which bathymetrycan be mapped reliably. For rivers having greater depths (onthe order of several meters) and/or more turbid water due tohigher amounts of suspended sediment and/or organic mat-ter, accurate depth estimates are less likely, and much of thechannel might exceed the maximum detectable depth [e.g.,Legleiter et al., 2011b, 2011a]. Overhanging vegetation,shadows, mixed pixels along channel margins, dark sub-strates (resulting in low LB(l) values), sun glint from thewater surface, and hazy atmospheric conditions can alsocompromise, if not preclude, effective depth retrieval[Legleiter et al., 2009].[52] In addition to these environmental factors, the extent

to which an image data set can satisfy the informationrequirements of a particular investigation also depends onthe sensor itself. For example, the imaging system must havesufficient spatial resolution to detect the channel features ofinterest. Similarly, instruments with greater spectral resolu-tion might enable more accurate bathymetric mapping byproviding radiance measurements in a larger number ofnarrower wavelength bands, some of which could be highlyresponsive to changes in depth. Radiometric resolutionrefers to a sensor’s ability to detect subtle differences inradiance, such as those associated with small variations inwater depth, and thus exerts a primary control on both theprecision of depth estimates and the maximum detectabledepth. Forward image modeling, which involves simulatingan image “from the streambed up” given information on themorphology and optical characteristics of the channel andthe technical specifications of the sensor, provides a meansof determining a priori the accuracy, precision, and dynamicrange of image-derived depth estimates. This approachallows tradeoffs among spatial, spectral, and radiometricresolution to be evaluated in the context of a specific river ofinterest [Legleiter and Roberts, 2009].[53] In this study, rather than resort to modeling, we made

direct measurements of water column attenuation in a pair ofgravel bed rivers and used these data to quantify the limita-tions of spectrally-based depth retrieval. Vertical profiles ofdownwelling spectral irradiance were used to calculatevalues of the diffuse attenuation coefficient Kd(l) that werein turn used to determine the smallest detectable change indepth and maximum detectable depth via the theoreticalframework established by Philpot [1989]; this analysis wasperformed for hypothetical imaging systems with specified


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levels of radiometric resolution. Our results indicated that forthese clear-flowing streams, a typical instrument with aDLN(l)/LB(l) ratio of 0.01 would yield depth estimates witha precision on the order of 0.01–0.04 m and a maximumdetectable depth ranging from 5 m in the green portion of thevisible spectrum to 1.3 m in the NIR. More sensitiveinstrumentation would yield more precise estimates andincrease the dynamic range of depth retrieval, but, con-versely, less sophisticated sensors would provide estimatessubject to greater uncertainty over a more restricted range ofdepths. These theoretical calculations were consistent withour analysis of actual satellite image data and correspondingfield-based depth measurements. Typical errors of 0.238 and0.094 m for the larger and smaller of our study streams,respectively, corresponded to 20% and 42% of the meanflow depths for the two reaches examined in detail. Depthestimates calibrated using field measurements representativeof the overall distribution of depths within each reach wereless reliable in deeper water, so the maximum detectabledepth was not as well-constrained by our data, but poolsover 2.5 m deep were captured by satellite-based bathy-metric maps. A combination of in situ observations of watercolumn optical properties, theoretical calculations, andcareful accuracy assessment will be most effective in defin-ing the constraints associated with remote sensing of riverbathymetry.

4.2. Alternative Approaches to Remote Measurementof River Morphology

[54] This study focused on retrieving water depth frompassive optical image data using a single, relatively simpleband ratio algorithm, but several alternative strategies forremote sensing of river morphology are available as well.For example, the same type of forward image modelingdescribed in Section 4.1 forms the basis of more advancedspectrum-matching methods now favored by the coastalresearch community for mapping depth, bottom composi-tion, and concentrations of various optically significantconstituents of the water column [e.g., Lee et al., 1999;Mobley et al., 2005]. In theory, these techniques could beadapted for application to riverine environments, but thisprospect has yet to be explored. Implementing such anapproach would require additional data on the spectralcharacteristics of different fluvial substrates and water types,as well as significant modeling effort. In this study, we madesome initial progress toward this goal by making fieldmeasurements of reflectance and apparent and inherentoptical properties of the water column for a pair of clear-flowing gravel bed rivers. If a suitable database can bedeveloped, this physics-based approach could allow forgreater generality and thus eliminate the need to coordinateremotely sensed data collection with field measurements toestablish relationships between image-derived quantities andobserved flow depths. Continued reliance upon this type ofempirical calibration, which involves regressing in situ depthmeasurements against image pixel values, would undermineone of the principal advantages of remote sensing.[55] A complementary technology for characterizing river

morphology is light detection and ranging, or LiDAR.Although LiDAR has become a preferred method of mea-suring topography [Slatton et al., 2007], typical LiDARsystems cannot measure submerged bed elevations because

water strongly absorbs the NIR laser pulses emitted by theseinstruments. To obtain a complete, hybrid representationof the fluvial environment, LiDAR topography fromexposed bars and floodplains can be combined withchannel bathymetry derived from passive optical imagedata, although such data fusion involves various technicalchallenges [Legleiter, 2012a]. Newly developed, water-penetrating green LiDAR systems provide a more directsolution for measuring both subaerial and submerged sur-faces [e.g., McKean et al., 2008]. Originally developed forcoastal applications, these bathymetric LiDARs provide arelatively large laser spot size and low point density andtend to over-estimate bed elevations in riverine settings[Kinzel et al., 2007]. In addition, laser returns from thewater surface, water column, and streambed can be diffi-cult to distinguish in shallow channels [Kinzel et al., 2012].Thus, although green LiDAR has outstanding potential formeasuring riverine topography, these systems remainexperimental and have yet to achieve operational status as aviable monitoring tool.[56] Passive optical remote sensing, in contrast, has

become routine, with image data acquired on a regular basisand made freely available to the public. For example, aerialphotography acquired through the National AgricultureImagery Program is accessible online and has been shown toprovide reasonably accurate bathymetric information forclear-flowing gravel bed rivers. The low radiometric reso-lution of these basic image data resulted in saturation of theradiance signal, however, and the full depth of pools couldnot be detected [Legleiter, 2012c]. For focused scientificinvestigations or any application for which precise estimatesacross a broad range of depths are necessary, acquiring task-specific data with more advanced multi or hyperspectralsensors might be more appropriate. This type of airbornedata collection requires careful planning and can be com-plicated by a number of different factors. In our experience,logistical coordination of pilots, planes, and instrumentationcan prove difficult, particularly if image acquisition is to besynchronized with field-based measurements for purposes ofcalibration and validation. Weather, mechanical problems,and other unforeseen circumstances can derail even the mostwell-thought out missions. In sensitive areas, such as theNational Parks where we conducted this investigation, flightpermits must be secured and restrictions on flying heightabove terrain can compromise spatial resolution and sensorsignal-to-noise. For larger study areas or channels that do notfollow a straight course, multiple flight lines might beneeded, resulting in multiple images that must be geo-referenced and mosaicked and might not be consistent withone another in terms of atmospheric conditions and viewingand illumination geometry. For these reasons, airborne datamight not be optimal for remote sensing of rivers.

4.3. Potential Advantages of Mapping RiverBathymetry From Space

[57] Satellite imagery could prove to be a viable alternativewith several distinct advantages. A number of commercialsatellites, such as QuickBird, GeoEye, and WorldView, nowprovide the kind of spatial resolution required to map small-to medium-sized gravel bed rivers, with pixel sizes of 2 m orless for multispectral images and 0.5 m for panchromaticimages. These sensors also feature off-nadir pointing


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capabilities that provide greater flexibility for tasked datacollection during an acquisition window specified by theuser. Because the platform is already in orbit, logistical pro-blems associated with remotely sensed data collection areless likely and obtaining flight permits is not an issue; plan-ning can instead focus on field activities. Satellite imagestypically encompass a larger area than could be acquiredalong an aerial flight line, so longer river segments or evenentire watersheds can be captured in a single scene withuniform radiometry, rather than a mosaic of multiple flightstrips. For cases where the entire image is not relevant,commercial providers often market data on a per km2 basis tomatch the user’s area of interest, so satellite imagery might bemore cost-effective as well. Because these data productsoften are geo-referenced and atmospherically corrected, sat-ellite images can be used as delivered, without the need forextensive pre-processing that could require specialized soft-ware and expertise. In addition, obtaining repeat coverage tocharacterize channel change is more feasible because orbitingsatellites can be tasked on an as-needed basis in response to ageomorphically significant event, whereas acquiring post-flood aerial data would involve a second round of complexlogistical arrangements. For application-oriented users moreconcerned with information derived via remote sensing andless interested in the details of flight planning and imageprocessing, satellite data might provide a simpler, moreconsistent solution.

5. Conclusion

[58] Efforts to characterize and understand the morphol-ogy and dynamics of alluvial river channels are often com-promised by the difficulty of measuring their form andbehavior via conventional, ground-based field methods. Thisstudy explored the potential to map river bathymetry frompassive optical images acquired from spaceborne satelliteplatforms that provide high resolution data, such as the 2 m-pixel WorldView2 images evaluated here. Our results indi-cate that water depths in clear-flowing, mid- to large-sizedgravel bed rivers with depths <3 m and widths <60 m can beestimated reliably from multispectral data. Direct measure-ments of water column optical properties were used toquantify some of the key constraints associated with suchspectrally-based depth retrieval. For typical levels of sensorradiometric resolution, the smallest detectable change indepth was calculated to be on the order of 0.01–0.04 m andthe maximum detectable depth to vary with wavelength from>5 m for green bands to <2 m in the NIR. A simple, bandratio-based algorithm for selecting appropriate combinationsof wavelengths and calibrating relationships between fieldmeasurements of depth and image-derived quantities wasshown to be effective when applied to spectra extracted froman image or recorded directly in the field, although a dif-ferent pair of bands was selected for each of the streamsexamined. Adding a quadratic term to these relationshipsprovided only a marginal improvement in bathymetricaccuracy in a deeper river. Similarly, neither panchromaticnor pan-sharpened multispectral images with greater spatialresolution yielded more accurate depth estimates, even in asmaller stream for which the pixel size was 10% of the meanchannel width. These results implied that spectral informa-tion content was crucial to reliable depth retrieval. The

principal conclusion of this investigation is that, underappropriate circumstances that include clear water condi-tions and shallow to moderate depths, river bathymetry canbe mapped from space, provided that field measurements ofdepth are available for calibration. By exploiting this capa-bility, while also acknowledging the limitations associatedwith remote sensing, scientists might gain novel insight onthe dynamics of certain types of fluvial systems.

[59] Acknowledgments. This investigation was supported by a grantfrom the Office of Naval Research Littoral Geosciences and Optics Program(grant N000141010873). The National Park Service granted permission toconduct research in Yellowstone and Grand Teton National Parks. The Uni-versity of Wyoming-National Park Service Research Center and the Yel-lowstone Ecological Research Center provided logistical support. The ac-9 instrument was borrowed from the Naval Research Laboratory and theUnited States Geological Survey loaned suspended sediment samplingequipment and processed water samples. Gregory Miecznik of DigitalGlobecoordinated acquisition of the WorldView-2 images used in this study. C.L.Rawlins and Floyd Legleiter assisted with field work. The editor, associateeditor, and three anonymous reviewers provided useful comments on anearlier version of this paper.

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mapping gravel bed river bathymetry from space

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