Bed-Sediment Transport Conditions Along the Sagavanirktok River in Northern Alaska, USA

water

Article Bed-Sediment Transport Conditions along the Sagavanirktok River in Northern Alaska, USA

Horacio Toniolo

Water and Environmental Research Center, University of Alaska Fairbanks, Fairbanks, AK 99775, USA; [email protected]; Tel.: +1-907-474-7977 Received: 13 December 2019; Accepted: 8 March 2020; Published: 11 March 2020

Abstract: This manuscript presents a study in predicting bed-sediment transport rates along the Sagavanirktok River in Alaska. Extensive field activities took place to accomplish this goal: four hydro-meteorological stations were installed in a 150 km reach along the river in summer 2015. During the same year, pits were excavated near the stations, and in subsequent summers, the pits were surveyed multiple times in conjunction with taking discharge measurements. Water slope was measured and bed sediment was characterized. Site-specific relationships between water levels and cross-section water depths were developed. Volume change between consecutive surveys was calculated, and main flood events between surveys were identified. Finally, the first bed-sediment transport equations valid for the Sagavanirktok River were developed. Considering the intrinsic error in sediment transport predictions, the agreement between predicted and measured sediment transport values is good. These equations could be used by resource managers when predicting the expected time for an excavated material site in the Sagavanirktok River to refill.

Keywords: bed-sediment transport; gravel-bed rivers; arctic environments

1. Introduction In general, Alaska—the northernmost state in the U.S.—is characterized by extreme cold weather, vast uninhabited areas, and sparse hydro-meteorological data. The lack of data is especially pronounced in aspects related to sediment transport processes in rivers. Efforts to develop new data sets and to improve our knowledge of arctic rivers are usually carried out in response to natural disasters. A multiyear hydro-sedimentological study of an area along an approximately 150 km reach on the Sagavanirktok River was performed in response to an unprecedented flood event that occurred during spring 2015, when the river overtopped and severely damaged the Dalton Highway near Deadhorse, an oil-support town located in northern Alaska [1]. The Dalton Highway, which provides the only terrestrial access to Deadhorse, parallels the Sagavanirktok River along the study area (Figure1). Immediately after the flood, the Alaska Department of Transportation and Public Facilities (ADOT&PF) began work on a project to raise the highway. The road improvement work required a substantial amount of material, which in this remote location of Alaska was acquired by extracting sediment from the river. Questions about the sediment replenishment rates were raised by resource managers, but data on Sagavanirktok River bed-sediment transport rates were nonexistent. The hydro-sedimentological study discussed here was conducted to fill the information gap. This manuscript presents field activities and analysis performed to develop the first set of bed-sediment transport equations for the Sagavanirktok River.

Water 2020, 12, 774; doi:10.3390/w12030774 www.mdpi.com/journal/water Water 2020, 12, x FOR PEER REVIEW 2 of 12

2. Geographic Location The Sagavanirktok River flows north, from the Brooks Range to the Beaufort Sea. The river is parallel to the Dalton Highway for approximately 160 km [1]. The Sagavanirktok River basin has three distinct areas, characterized by increasing slopes: the coastal plain, foothills, and mountain region [2]. The total watershed area is roughly 13,500 km2, with two sub-basins in the mountain region: the Upper Sagavanirktok, 6500 km2, and the Ivishak, 5200 km2 [1]. Figure 1 shows the Water 2020, 12, 774 2 of 12 watershed boundaries as well as the Dalton Highway.

FigureFigure 1. Sagavanirktok1. Sagavanirktok watershed watershed area area and and hydrological hydrological stations stations along along the the river. river. 2. Geographic Location 3. Methodology and Analysis The Sagavanirktok River flows north, from the Brooks Range to the Beaufort Sea. The river is Given the location (far from population centers) and the characteristics of the study reach parallel to the Dalton Highway for approximately 160 km [1]. The Sagavanirktok River basin has three (limited river access), commonly used methodologies in bed-sediment transport research, such as distinct areas, characterized by increasing slopes: the coastal plain, foothills, and mountain region [2]. Helley-Smith type samplers and tracers, could not be applied in this study. Seven pits dug in the river The total watershed area is roughly 13,500 km2, with two sub-basins in the mountain region: the Upper bed (Figure 2) were used as study sites in this effort to quantify bed-sediment transport rates in the Sagavanirktok, 6500 km2, and the Ivishak, 5200 km2 [1]. Figure1 shows the watershed boundaries as Sagavanirktok River. Hydrological data (nearly continuous water levels and discrete discharge well as the Dalton Highway. measurements) were collected in the vicinity of the pits. The pits were excavated in fall 2015 at four 3. Methodologylocations in the and Sagavanirktok Analysis River channel and active floodplain (near the Dalton Highway at MP [milepost] 405 [DSS1], downstream of the Ivishak River confluence [DSS2], at Happy Valley [DSS3], Given the location (far from population centers) and the characteristics of the study reach (limited and near MP318 [DSS4]). Sediment extracted from the pits was spread over the adjacent river bed. river access), commonly used methodologies in bed-sediment transport research, such as Helley-Smith No significant changes in local topography were made. The pits were 2–3 m in depth and 8–18 m in type samplers and tracers, could not be applied in this study. Seven pits dug in the river bed (Figure2) the direction perpendicular to the flow. ADOT&PF excavated two pits at DSS2, DSS3, and DSS4, and were used as study sites in this effort to quantify bed-sediment transport rates in the Sagavanirktok excavated only one pit at the west channel near DSS1 [3]. The pits are referred to as wet and dry River. Hydrological data (nearly continuous water levels and discrete discharge measurements) were because of where they were excavated. Wet pits were excavated in water near the edge of the active collected in the vicinity of the pits. The pits were excavated in fall 2015 at four locations in the channel; dry pits were excavated at gravel bars farther away from the main channel [4]. In a literature Sagavanirktok River channel and active floodplain (near the Dalton Highway at MP [milepost] 405 search, no reports of similar studies on rivers in arctic regions were found. [DSS1], downstream of the Ivishak River confluence [DSS2], at Happy Valley [DSS3], and near MP318 [DSS4]). Sediment extracted from the pits was spread over the adjacent river bed. No significant changes in local topography were made. The pits were 2–3 m in depth and 8–18 m in the direction perpendicular to the flow. ADOT&PF excavated two pits at DSS2, DSS3, and DSS4, and excavated only one pit at the west channel near DSS1 [3]. The pits are referred to as wet and dry because of where they were excavated. Wet pits were excavated in water near the edge of the active channel; dry pits were excavated at gravel bars farther away from the main channel [4]. In a literature search, no reports of similar studies on rivers in arctic regions were found. Water 2020, 12, 774 3 of 12 Water 2020, 12, x FOR PEER REVIEW 3 of 12

FigureFigure 2.2. Field excavation of a wet wet pit pit ( (leftleft)) and and a a dry dry pit pit ( (rightright).).

FollowingFollowing excavation of of the the pits, pits, the the sites sites were were surveyed surveyed using using a real a-time real-time kinematic kinematic (RTK) GPS, (RTK) GPS,and the and bathymetry the bathymetry was recorded was recorded using usingan acoustic an acoustic Doppler Doppler current current profiler proﬁler (ADCP) (ADCP) or an echo or an echosounder. sounder. The The equipment equipment used used achieves achieves horizontal horizontal and and vertical vertical accuracies accuracies of 0.7 of0.7 m m and and 0.01 0.01 m, m, respectively.respectively. BeginningBeginning inin JuneJune 2016, the pits were resurveyed at at approximately approximately 1 1-month-month intervals intervals throughoutthroughout the the summer summer (3 (3 surveys surveys per per season) season) to to monitor monitor volume volume changes. changes. Table Table1 presents1 presents the the date date of eachof each bathymetric bathymetric survey survey of the of pits.the pits. On numerousOn numerous occasions, occasions, bathymetric bathymetric surveys surveys in the in wet the pitwet could pit notcould be conductednot be conducted because because neither neither a motorboat a motorboat nor kayak nor kayak could becould launched be launched safely safely with the with survey the equipmentsurvey equipment during highduring water high events water [events3]. Topo-bathymetric [3]. Topo-bathymetric maps were maps generated were generated after each after survey, each andsurvey, the volumeand the ofvolume each pit of waseach calculated. pit was calcul Waterated. slopes Water were slopes measured were measured over a 2–5 over km a reach 2–5 km using reach the using the GPS equipment (each pit was located near the middle of this distance) on both margins of GPS equipment (each pit was located near the middle of this distance) on both margins of the river. the river. Table 1. Date of bathymetric surveys at pits. Table 1. Date of bathymetric surveys at pits. Site Name 2015 2016 2017 2018 Site Name 2015 2016 2017 2018 June 27–28, Sagavanirktok River July 8, August 5, July 5, August 9, September 14 JunAuguste 27 1,–28, SagavanirktokMP405 (DSS1) River JulSeptembery 8, Aug 6ust 5, JulSeptembery 5, Aug 10ust 9, September 14 SeptemberAugust 11, MP405 (DSS1) September 6 JulySep 4,tember August 7, 10 Sagavanirktok River JuneSep 30–Julytember 1, 1 July 9, August 6, September 10, September 13 downstream Ivishak August 2, September 7 (dry July 4, August 7, Sagavanirktok River September 13 June 30–July 1, July 9, August 6, (dry pit only), October 23 River (DSS2) September 10, August 31 pit only) September 13 (dry downstream Ivishak August 2, September 7 (dry pit only) Sagavanirktok River at September 13 July 2, Aug 3, July 7, August 4, Augustpit only), 11, September October 7, 23 River (DSS2) September 18 August 31 (dry pit only) Happy Valley (DSS3) September 3 September 5 October(dry 24 (dry pit pitonly) only) Sagavanirktok River July 3, August 4, Sagavanirktok River September 16 July 6, September 4 AugustAugust 12 11, near MP318 (DSS4) JulAugy 2, 30Aug 3, July 7, August 4, at Happy Valley September 18 September 7, October September 3 September 5 (DSS3) 24 (dry pit only) To track the water level changes, vented pressure transducers were installed in the river bed at Sagavanirktok River July 3, August 4, July 6, the hydrological stations,Sep neartember the pits. 16 These sensors were set to record data every 15Aug min.ust Collected 12 near MP318 (DSS4) Aug 30 September 4 data were transmitted via a complex telemetry system from each of the sites (DSS1 to DSS4 in Figure1) in near-real-timeTo track the andwater reported level changes, online [ 4vented]. pressure transducers were installed in the river bed at the hydrologicalDischarge measurements stations, near were the pits. carried These out sensors near the were stations set whento record the pitsdata were every dug 15 and,min. onCollected average, everydata were month transmitted during summers via a complex 2016–2018. telemetry These system measurements from each were of the coincident sites (DSS1 with to DSS4 the pit in surveys.Figure An1) in ADCP near-real and-time a GPS and were reported mounted online on [4] a kayak. or motorboat. The measurements paired with the respectiveDischarge water measurements levels were used were to carried develop out rating near curvesthe stations for each when station the pits [3]. were Average dug geometric and, on dimensionsaverage, every (width month and during depth) summers of river cross-sections2016–2018. These were measurements extracted from were the coinc ADCP-generatedident with the datapit ﬁles.surveys. The An geometric ADCP and data a were GPS usedwere tomounted generate on empirical a kayak or relationships motorboat. atThe each measurements site (DSS1–DSS4) paired to estimatewith the average respective water water depth levels on the were main used river to channel.develop Detailsrating curves on these for relationships each station are [3] provided. Average in thegeometric following dimensions paragraphs. (width and depth) of river cross-sections were extracted from the ADCP- generated data files. The geometric data were used to generate empirical relationships at each site

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(DSS1–DSS4) to estimate average water depth on the main river channel. Details on these Water 2020, 12, 774 4 of 12 relationships are provided in the following paragraphs. Figure 3 shows a schematic of an entire river cross-section with a main channel. In the figure, it is possibleFigure to3 seeshows that a at schematic low or medium of an entire flows, river all cross-section discharge measurements with a main channel. will be Indone the inside figure, the it is mainpossible channel. to see At that higher at low wate or mediumr levels flows, (lines all C discharge and D in measurements the figure), the will channel be done width inside increases the main significantly.channel. At higherThus, the water average levels water (lines Cdepth and Dover in the the figure), cross-section the channel decreases. width However, increases significantly.it is water depthThus, in the the average main channel, water depth which over is needed the cross-section for calculating decreases. basic However,sediment ittransport is water para depthmeters in the, that main ischannel, of interest which. is needed for calculating basic sediment transport parameters, that is of interest.

FigureFigure 3. 3. Schematic representation representation of aof river a river cross-section cross-section showing showing a main channel. a main Line channel. A corresponds Line A correspondsto low water to level; low linewater B indicateslevel; line a B near indicates bankfull a near condition bankfull at the condition main channel; at the main lines Cchannel; and D represent lines C andwater D represent levels during water flood levels events. during Vertical flood arrows events. denote Vertical water arrows depth denote at the water main channeldepth at (fromthe main [3]). channel (from [3]). Basic summary data collected by the ADCP during a given discharge measurement (i.e., channel widthBasic and summary average depth)data collected and the by corresponding the ADCP during gauge a given height discharge for each summermeasurement measurement (i.e., channel were widthplotted and to average estimate depth) the average and the water corresponding depth at bankfull gauge conditionheight for ineach the summer main channel. measurement were plottedThe to calculationestimate the of average bed shear water stress, depthτ0, at is givenbankfull by condition the following in the equation: main channel. The calculation of bed shear stress, , is given by the following equation: τ0 = γHS (1) = (1) wherewhere γγ isis the the specific specific gravity gravity of of water, water, HH isis the the average average water water depth, depth, and and SS isis the the water water slope slope.. W Waterater depthsdepths in in the the main main channel channel were determined byby addingadding the the extra extra layer layer of of water water (above (above bankfull) bankfull to) theto thedepth depth corresponding corresponding to bankfullto bankfull conditions conditions in thein the main main channel. channel. ShieldsShields [5] [5 ]pioneer pioneereded research, research, involvinginvolving dimensionaldimensional analysis analysis and and laboratory laboratory experiments, experiments, on on the thethreshold threshold of motion of motion of non-cohesive of non-cohesive bed-sediment bed-sediment particles. particles. He defined He a defined dimensionless a dimensionles parameter,s parameter,the Shields the number, Shieldsτ *,number, as *, as τ0 τ∗ = (2) ρRgD ∗ = (2) where ρ is the density of water, R is the submerged specific gravity of natural sediments (R = 1.65 for wherequartz), ρ isg theis gravity, density and of water,D is the R is sediment the submerged diameter. specific gravity of natural sediments (R = 1.65 for quartz),Shields g is gravity, determined and D that is the a minimum sediment value diameter. is needed to initiate the motion of particles. This value is knownShields as determined the critical that Shields a minimum number, valueτc*, is which needed ranges to initiate from the 0.03 motion to 0.06 of forparticles. gravel-bed This value rivers, isas known reported as the in thecritical published Shields literature number, [6c].*, Thiswhich variation ranges from in τc* 0.03 imposes to 0.06 an for additional gravel-bed complication rivers, as reportedwhen developing in the published a bed-sediment literature [6] transport. This variation equation. in c A* imposes common an value additional used complication in several sediment when developingtransport equationsa bed-sediment is 0.047 transport [6]. Wilcock equation. et al. A [ 7common] suggested value a valueused in of several 0.03 for sediment rivers with transport coarse equationssediments, is similar0.047 [6] to. theWilcock Sagavanirktok et al. [7] suggested River. a value of 0.03 for rivers with coarse sediments, similarCommon, to the Sagavanirktok single-size,bed-sediment River. transport equations take the following general form, Common, single-size, bed-sediment transport equations take the following general form, 1.5 q∗ = α(τ∗ τ∗) (3) ∗ ∗ c∗ . = ( −− ) (3) wherewhere q∗∗isis the the dimensionless dimensionless sediment sediment transport transport rate rate per per unit unit widt width,h, which which is is defined defined as as

q ∗ = s q∗ 1 (4)(4) ((RgD3))2

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Water 2020, 12, x FOR PEER REVIEW 5 of 12 where α (Equation (3)) is a constant coefficient, which is different for various published equations; wherefor instance, (Equation 8 Meyer-Peter (3)) is a constant and Muller coefficient [8], 5.7, Fernandez which is different Luque andfor various Van Beek published [9], 3.97 equations Wong and; fParkeror instance [10],, and8 Meyer where-Peterqs (Equation and Muller (4)) [8] is the, 5.7 bed Fernandez load transport Luque rate and per Van unit Beek width. [9], 3.97 Wong and ParkerFurthermore, [10], and where thetotal qs (Equation bed load (4 transport)) is the bed rate, loadQs, transport can be calculated rate per asunit width. Furthermore, the total bed load transport rate, Qs, can be calculated as Qs = qsB (5) = (5) where B is the channel width. where B is the channel width. To estimate bed-sediment transport at each site (DSS1–DSS4) between bathymetric surveys from To estimate bed-sediment transport at each site (DSS1–DSS4) between bathymetric surveys from the river’s hydraulic conditions, the hydrographs between surveys were analyzed. After identifying the river’s hydraulic conditions, the hydrographs between surveys were analyzed. After identifying the major event(s) between surveys (Figure4), the hydrographs were simplified, retaining the key the major event(s) between surveys (Figure 4), the hydrographs were simplified, retaining the key inflection points, and the relative time between these points was recorded (see Figure5 as an example). inflection points, and the relative time between these points was recorded (see Figure 5 as an The average water depths for each of the points were then calculated using the empirical relationships example). The average water depths for each of the points were then calculated using the empirical previously described. relationships previously described. To investigate if any of the commonly used, and simplistic, bed-sediment transport equations To investigate if any of the commonly used, and simplistic, bed-sediment transport equations predicted the sediment transport estimated from successive pit surveys in the field, Laurio [11], applied predicted the sediment transport estimated from successive pit surveys in the field, Laurio [11], several single-size bed-sediment transport equations to the Sagavanirktok River. The equations used applied several single-size bed-sediment transport equations to the Sagavanirktok River. The in Laurio’s work were Meyer-Peter and Muller [8], Wong and Parker [10], Ashida and Michiue [12], equations used in Laurio’s work were Meyer-Peter and Muller [8], Wong and Parker [10], Ashida Fernandez Luque and Van Beek [9], Engelund and Fredsoe [13], Lajeunesse et al. [14], Wilson [15], Parker and Michiue [12], Fernandez Luque and Van Beek [9], Engelund and Fredsoe [13], Lajeunesse et al. fit to Einstein [16], as well as ACRONYM [17], software which is capable of estimating bed-sediment [14], Wilson [15], Parker fit to Einstein [16], as well as ACRONYM [17], software which is capable of transport for a given grain-size distribution and is freely available. Laurio [11], concluded that none of estimating bed-sediment transport for a given grain-size distribution and is freely available. Laurio the sediment transport equations applied successfully reproduced the sediment transport estimated [11], concluded that none of the sediment transport equations applied successfully reproduced the from successive pit surveys in the field. sediment transport estimated from successive pit surveys in the field. Consequently, the development of an equation capable of reproducing the data collected in the field Consequently, the development of an equation capable of reproducing the data collected in the for the Sagavanirktok River was needed. A simple structure similar to that of Equation (3) was thought field for the Sagavanirktok River was needed. A simple structure similar to that of Equation (3) was to accomplish this task. Two main challenges were encountered during the development of such an thought to accomplish this task. Two main challenges were encountered during the development of equation: finding the correct τc∗ value and∗ defining the α value in Equation (3). The methodologies such an equation: finding the correct value and defining the value in Equation (3). The used to define the τc∗ and α values are∗ discussed in the following paragraphs. methodologies used to define the and values are discussed in the following paragraphs.

Figure 4. Water level elevations during the study period at station MP405 (DSS1). Figure 4. Water level elevations during the study period at station MP405 (DSS1).

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FigureFigure 5. CCompleteomplete hydrograph hydrograph from from sensors sensors (black, (black, continuous continuous line) line) and and simplified simpliﬁed hydrograph hydrograph consideredconsidered (red, (red, dashed dashed line). line).

AsAs mentioned, mentioned, o onene of of the the key key components components in inthe the process process was was selection selection of the of thec* value.τc* value. To accomplishTo accomplish this this task, task, the the maximum maximum sediment sediment size size that that could could be be moved moved during during the the largest largest annual annual summersummer hydrological hydrological event event (i.e., (i.e., annual annual maximum maximum water water level level elevation) elevation) was was estimated estimated in in the the SagavanirktokSagavanirktok River for the years years 2016, 2016, 2017, 2017, and and 2018. 2018. The The analysis analysis was was not not conducted conducted for for the the sprin springg breakupbreakup period period because because anchor anchor ice ice and and froze frozenn streambed streambed often often prohibit prohibit the the movement movement of of sediment sediment duringduring much much of of breakup. breakup. TheThe average average water water depth depth in in the the main main channel, channel, corresponding corresponding to to the the annual annual maximum maximum water water levellevel elevation elevation,, was was estimated estimated from from the the empirical empirical relationships relationships derived derived from from all all summer summer disch dischargearge measurementsmeasurements available available at at each each site. site. The The information information collected collected in in the the field field was was used used to to calculate calculate an an averageaverage slope slope (the (the slopes slopes on on both both margins margins were were averaged). averaged). A Aset set of ofdifferent different c*τ valuesc* values was was used used in combinationin combination with with the the maximum maximum shear shear stress stress value value,, calculated calculated from from Equation Equation (1 (1),), to to estimate estimate the the maximummaximum sediment sediment diameter diameter that could be moved by the the river river using using Equation Equation ( (2).2). These These values values were were thenthen compared compared with with grain grain-size-size distributions distributions collected in the field. field. AfterAfter the the correct correct τc*c *value value was was selected, selected, a aco computermputer program program was was written written to tofind find the the α valueα value in Equationin Equation (3), (3), the the second second challenge challenge in in developing developing the the bed bed-sediment-sediment transport transport equation equationss for for the the SagavanirktokSagavanirktok River River..

4.4. Results Results FigureFigure 66 shows the plot of channel width and average water depth as a function of gauge height aboveabove mean mean sea sea level level (AMSL) (AMSL) for for the the station station at at MP405 MP405 (DSS1). (DSS1). An An inspection inspection of of the the data data in in the the figure figure indicatesindicates that that water water depths depths increased increased with with increasing increasing gauge gauge height height to about to about 25.42 25.42 m AMSL, m AMSL, while while the channelthe channel width width remained remained relatively relatively const constant.ant. At Atgauge gauge heights heights above above 25.42 25.42 m m AMLS, AMLS, the the average average waterwater depth depth decreased decreased,, and and the the channel channel width width increased increased significantly. significantly. Consequently, Consequently, the the channel channel is is consideredconsidered at at bankfull bankfull with with a a gauge gauge height height of of 25.42 25.42 m m AMSL AMSL (the (the red red oval oval in in the the figure figure indicates indicates the the water depth that is considered bankfull depth at the main channel). The water depths corresponding to bankfull conditions for other stations were determined similarly.

Water 2020, 12, 774 7 of 12 water depth that is considered bankfull depth at the main channel). The water depths corresponding to bankfull conditions for other stations were determined similarly. Water 2020, 12, x FOR PEER REVIEW 7 of 12

Figure 6. CompleteComplete c channelhannel width width and and average average water water depth depth as as functions functions of of gauge gauge height height fo forr the SagavanirktokSagavanirktok River River west west channel channel near near MP405 (DSS1). Bankfull Bankfull water water depth depth at at the the main main channel channel is is clearlyclearly defined deﬁned in the plot (red oval).

Maximum annualannual summer summer water water level level elevations elevations at each at station each station were used were to calculate used to maximum calculate maximumsediment sizesediment that could size that be cou movedld be along moved the along main the channel. main channel. In the In calculations, the calculations, water water slope slope was wasconsidered considered constant constant at each at each station station (S (=S 0.0012= 0.0012 at at DSS1; DSS1;S S= = 0.0022 at DSS2; DSS2; SS == 0.00320.0032 at atDSS3; DSS3; S =S 0.0032= 0.0032 at DSS4) at DSS4).. Some Some could could maintain maintain that that the theselection selection of a of constant a constant slope slope poses poses a limitation a limitation to the to analysis;the analysis; however, however, it is it argued is argued that that the the approach approach used used here here is is reasonable, reasonable, given given the the field ﬁeld logistical logistical constraints.constraints. In In addition, addition, similar similar approaches approaches have have been been reported reported in in the the literature literature [6 [6,, 77].]. The critical Shields number, number,τ c*,c*, was was set set to 0.03. to 0.03. The The slope slope at DSS1 at DSS1 is close is toclose 0.00135, to 0.00135 reported, reported in an early in geological an early geologicalstudy conducted study conducted near Prudhoe near Bay Prudhoe [18]. Tables Bay [18].2 and Table3 provides 2 and the 3 maximumprovide the sediment maximum diameter sediment at diameterstations DSS3 at stations and DSS4 DSS3 along and DSS4 the Sagavanirktok along the Sagavanirktok River. These River. maximum These maximum diameters werediameters compared were comparedwith surface with sediment surface randomlysediment extractedrandomly fromextracted the pits from during the pits the during 2018/19 the winter. 2018/19 The winter maximum. The maximumsediment diameterssediment (i.e.,diametersb axis ( ofi.e., pebbles) b axis of from pebbles) the pits from were the 0.12pits mwere and 0.12 0.15 m m and for 0.15 DSS3 m and for DSS4,DSS3 andrespectively. DSS4, respectively. The agreement The between agreement maximum between sampled maximum sediment sampled and maximum sediment calculated and maximum sediment calculatedwas remarkable. sediment Grain was size remarkable distributions. Grain upstream size distributions of the pits at upstream DSS3 and of DSS4 the pits are at shown DSS3 in and Figure DSS47. are shown in Figure 7. Table 2. Maximum particle size moved after breakup—Sagavanirktok River at Happy Valley (DSS3). Table 2. Maximum particle size moved after breakup—Sagavanirktok River at Happy Valley (DSS3). Maximum Water Average Water Sediment 2 Date MaximumLevel Elevation Water DepthAverage in the Water Main DepthSlope τ0 (N/m ) τ *crit SedimentDiameter  crit Date Level(m Elevation AMSL) inChannel the Main (m) Channel Slope * Diameter(m) (N/m2) 6/21/2016(m 289.53AMSL) 1.42(m) 0.0032 44.577 0.03 0.092(m) 7/25/2017 289.56 1.45 0.0032 45.518 0.03 0.094 6/21/20168/18/2018 289.5 289.883 1.771.42 0.00320.0032 55.564 44.577 0.030.03 0.09 0.1142 7/25/2017 289.56 1.45 0.0032 45.518 0.03 0.094 8/18/2018 289.88 1.77 0.0032 55.564 0.03 0.114

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Table 3. Maximum particle size moved after breakup—Sagavanirktok River near MP318 (DSS4). Table 3. Maximum particle size moved after breakup—Sagavanirktok River near MP318 (DSS4). Maximum Average Water Sediment MaximumWater Level Water DepthAverage in Water the Sediment Date Slope 2  *crit Diameter Date LevelElevation Elevation DepthMain inChannel the Main Slope τ0 (N/m(N/m 2)) τ *crit Diameter (m AMSL) Channel (m) (m)(m) (m AMSL) (m) 6/22/20166/22/2016 370.24 370.24 1.93 1.93 0.0032 60.58760.587 0.03 0.125 0.125 7/25/2017 370.2 1.89 0.0032 59.331 0.03 0.122 7/25/20179/1/2018 370.2 370.5 1.89 2.19 0.0032 68.74859.331 0.03 0.122 0.142 9/1/2018 370.5 2.19 0.0032 68.748 0.03 0.142

Table4 shows the volume change between consecutive surveys. From the water level data, major Table 4 shows the volume change between consecutive surveys. From the water level data, major hydrographs were identiﬁed between the surveys. Water depths in the channel were estimated based hydrographs were identified between the surveys. Water depths in the channel were estimated based on the empirical relationships developed for each station (see Figure6 for instance). on the empirical relationships developed for each station (see Figure 6 for instance).

Figure 7. Grain size distributions from samples collected upstream of pits at DSS3 and DSS4. Figure 7. Grain size distributions from samples collected upstream of pits at DSS3 and DSS4.

TableTable 4. Pit volume change between consecutive surveys.

VolumeVolume Change Change (m (m3) 3) Period Period DSS1DSS1 DSS2 DSS2 DSS3 DSS3DSS4 DSS4 2015/20162015/2016 140140 136 136 and and 126 126 64 and 64 21 and 35 21 and 10 35 and 10 2016/20172016/2017 62 62 9 9 2017/20182017/2018 5858 84 84 52 5215 15 20182018 5858 46 46

A computer program was developed to identify the best alpha value that that matched matched the sediment sediment deposited in each pit. The representative diameter, D50, of grain-size distribution at each site was 0.03 deposited in each pit. The representative diameter, D50, of grain-size distribution at each site was 0.03 m, m,0.03 0.03 m, m, 0.06 0.06 m, m, 0.075 0.075 m m for for DSS1, DSS1, DSS2, DSS2, DSS3, DSS3, and and DSS4, DSS4, respectively. respectively. TheThe pitpit width perpendicular toto flow ﬂow direction direction was was 16.5 16.5 m m (DSS1), (DSS1), 12.5 12.5 m (DSS2 m (DSS2 wet), wet), 17 m 17 (DSS2 m (DSS2 dry), dry),9.5 m 9.5 (DSS3 m (DSS3 wet), 9 wet), m (DSS3 9 m dry),(DSS3 8.5 dry), m (DSS4 8.5 m wet), (DSS4 and wet), 8.5 andm (DSS4 8.5 m dry). (DSS4 A dry).porosity A porosity of 0.4 was of 0.4used was in the used calculations. in the calculations. Table 5 showsTable5 theshows range the and range average and average alpha alpha values values for each for station, each station, as well as well as the as average the average error error in the in sedimentthe sediment deposit deposit volume volume (last (last column column in in Table Table 5).5). Thus, Thus, one one can can conclude conclude that the the developed developed equations adequately reproduce the bed-sedimentbed-sediment transport conditions along the study sites.

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Table 5. Alpha values and associated error for each station.

Alpha Station Average Error (%) Range Average DSS1 0.04 to 0.06 0.045 5 DSS2 0.01 to 0.02 0.015 37 DSS3 0.02 to 0.07 0.037 31 DSS4 0.006 to 0.02 0.012 25

5. Discussion Table4 shows that there was appreciable sedimentation only in a few surveys, while Figure4, which represents an example of the stations, shows that sedimentation did not occur even with similar water levels. These facts manifest the importance of bed armoring in sediment transport processes in gravel-bed rivers. Bed armoring is defined as a coarse surface layer on the river bed, which protects the finer sediments located in the substrate from being entrained in the current [19–21]. Two types of armoring layers are recognized in the literature: static armoring and dynamic armoring. Static armoring develops as a result of a long period of flows over a sediment mixture constituted by coarse and fine sediments (for instance, gravel and sand). The shear stresses generated by the flows are smaller than that needed to move the largest particle but are large enough to entrain the fines. Over time, the fine sediment is winnowed from the bed surface [19]. Sediment transport in a developed static armored layer can be zero or negligible [22]. Consequently, when the sediment transport of a gravel bed is estimated from the grain-size distribution of the bed surface without considering the surface structure, the results often over-predict the transport rates [23]. In addition, it is important to re-emphasize that previously reported alpha values [8–10] were obtained considering uniform grain-size distributions. Consequently, armoring was not present in the derivations of those alpha coefficients. One could argue that the small alpha values obtained for the Sagavanirktok River (Table5) intrinsically account for bed armoring, which was reported in an area near Prudhoe Bay [18]. The armor layer can break during the rising limb of high flow events, which creates a sudden increase in the sediment transport rate and will re-develop during the falling limb of these events [19]. Dynamic armoring is formed when the shear stresses are big enough to move all the particles present in the river bed. The dynamic armoring is insensitive to additional changes in the flow conditions [22]. The prediction of armoring breakup is still a challenging task because our current knowledge on the subject is somewhat limited [24]. Available literature on armoring also indicates that lift is as important as shear stress when estimating a particle’s threshold condition. Key factors in dynamic lift include the ramping duration and the ramping rate, as well as the total increase in discharge [25]. It is speculated here that spring breakup characteristics (fast vs. slow) play a fundamental role in maintaining or destroying the armored layer. In this work, fast spring breakup is defined as a process characterized by a quick increase in water depth, where the bottom ice is lifted by the mechanical action of flowing water. Under these circumstances, the ice will lift the bottom sediment attached to it and the armored layer will be destroyed. A slow spring breakup is characterized by a gradual increase in water depth. The bottom ice decays gradually in place. Consequently, the armored layer is not destroyed. This is the reason why summer events with similar water elevations produce or do not produce sediment transport. Additionally, if summer events are not strong enough to destroy the armored layer, no sedimentation inside the pits should be expected. See for instance, the main event during summer 2017 (shown in Figure4). The work reported here consisted of developing a set of simple equations capable of estimating bed-sediment transport rates along the Sagavanirktok River. However, an issue related to the research approach was raised during the review process. This issue is addressed below in the context of replies to rhetorical comments. Water 2020, 12, 774 10 of 12 Water 2020, 12, x FOR PEER REVIEW 10 of 12 Because of the rough approximations (constant slope, use of one particle size, ignoring mixed Because of the rough approximations (constant slope, use of one particle size, ignoring mixed bed material etc.) used to build the model, at least a sensitivity analysis of the parameters (critical bed material etc.) used to build the model, at least a sensitivity analysis of the parameters (critical Shields number and exponent) would have been justified. Even though the exponent in Equation (3) is Shields number and exponent) would have been justified. Even though the exponent in Equation (3) fixed (1.5) in equations with similar structure, and the commonly reported value for τc* in gravel-bed is fixed (1.5) in equations with similar structure, and the commonly reported value for τc* in gravel- rivers is 0.03, a sensitivity analysis of these two parameters was performed. Figure8 shows the alpha bed rivers is 0.03, a sensitivity analysis of these two parameters was performed. Figure 8 shows the values required to match a measured sediment deposit at DSS2. The results indicate that the alpha alpha values required to match a measured sediment deposit at DSS2. The results indicate that the values are small, even when the τc* is doubled and the exponent is increased. alpha values are small, even when the τc* is doubled and the exponent is increased.

FigureFigure 8. 8. ExampleExample of of sensitivity sensitivity analysis analysis performed performed at at DSS2. DSS2.

66.. Conclusions Conclusions InformationInformation gathered gathered from from extensive extensive fieldwork fieldwork on on the the Sagavanirktok River, River, which which included installationinstallation of of several hydrological stations, multiple discharge measurements, bedbed-sediment-sediment characterization,characterization, water water slope slope measurements, measurements, and and multi multi-year-year topo topo-bathymetric-bathymetric surveys, surveys, was was used used to to establishestablish relationships relationships between between water water level levelss AMSL AMSL and and water water depths depths in in the the river river channel channel at at each each studystudy site. site. AA value value of of τcc** == 0.030.03 for for the the Sagavanirktok Sagavanirktok River River was was defined defined after after computing computing the the shear shear stress stress conditionsconditions and and comparing comparing maximum maximum sediment sediment diameters diameters that that could could be be moved moved under under those those hydraulic hydraulic coconditions,nditions, with with maximum maximum diameters diameters found found inside inside the the pits. The The agreement agreement between between calculated calculated and and fieldfield diameters diameters is is remarkable. remarkable. AA computer computer program program was was developed developed to to find find the the best best a alphalpha value value (Equation (Equation ( (3))3)) that that reproduces reproduces thethe bed bed-sediment-sediment conditions conditions for for all all the the study study sites sites (DSS1 (DSS1–DSS4).–DSS4). Consequently, Consequently, a a basic basic bed bed-sediment-sediment transporttransport equation equation for for each each site site was was defined. defined. The The calculated calculated average average errors errors between between measured measured and and calculatedcalculated sediment sediment volumes volumes are are relatively relatively small, small, which which indicates indicates the the strength strength of of the the developed developed eqequations.uations. When When comparing comparing the the alpha alpha values values with with reported reported values values in in similar similar types types of of equations (Equation(Equation ( (3))3)) obtained obtained considering considering uniform uniform sediments, sediments, it it is is found found that that the the alpha alpha values values for for the the SagavanirktokSagavanirktok River River are are smaller smaller than than the the published published values. values. It It is is argued argued here here that that the the newly newly reported reported valuesvalues account account for for bed armoring conditions in the channel. Because Because the the degree degree of of armoring varies varies widelywidely from streamstream to to stream stream [7 ],[7], caution caution is recommendedis recommended when when applying applying the equations the equations to other to rivers.other rivers.Resource managers could use these equations as a rough and first-order estimation of expected time to refillResource of material manag sitesers excavated could use in these the Sagavanirktok equations as River.a rough In and a broader first-order application, estimation the methodology of expected time to refill of material sites excavated in the Sagavanirktok River. In a broader application, the methodology developed in this study could be applied to other rivers located in extreme cold environments, which, in general, are characterized by limited accessibility.

Water 2020, 12, 774 11 of 12 developed in this study could be applied to other rivers located in extreme cold environments, which, in general, are characterized by limited accessibility.

Funding: This work is part of the Sagavanirktok hydro-sedimentological study, which is funded by the Alaska Department of Transportation and Public Facilities, under grant #ADN2572616 to the University of Alaska Fairbanks. Acknowledgments: The author expressly acknowledges the following UAF project team personnel, given in alphabetical order: Joel Bailey, Allen Bondurant, Joel Homan, John Keech, Isaac Ladines, Eric LaMesjerant, Jenah Laurio, Ravi Paturi, Kathy Petersen, Emily Youcha, and Dragos Vas. All of them participated in data collection and/or data processing efforts. Without their efforts, this manuscript would not be possible. Conflicts of Interest: The author declares no conflict of interest.

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