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Article Grain Size Distribution of Bedload Transport in a Glaciated Catchment (Baranowski , King George Island, Western )

Joanna Sziło 1,* and Robert Józef Bialik 2 1 Institute of Geophysics, Polish Academy of Sciences, 01-452 Warsaw, Poland 2 Institute of Biochemistry and Biophysics, Polish Academy of Sciences, 02-106 Warsaw, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-504-595-266

 Received: 20 February 2018; Accepted: 20 March 2018; Published: 23 March 2018 

Abstract: The relationships among grain size distribution (GSD), water discharge, and GSD parameters are investigated to identify regularities in the evolution of two gravel-bed proglacial troughs: Fosa Creek and Siodło Creek. In addition, the potential application of certain parameters obtained from the GSD analysis for the assessment of the formation stage of both creeks is comprehensively discussed. To achieve these goals, River Bedload Traps (RBTs) were used to collect the bedload, and a sieving method for dry material was applied to obtain the GSDs. Statistical comparisons between both streams showed significant differences in flow velocity; however, the lack of significant differences in bedload transport clearly indicated that meteorological conditions are among the most important factors in the erosive process for this catchment. In particular, the instability of flow conditions during high water discharge resulted in an increase in the proportion of medium and coarse gravels. The poorly sorted fine and very fine gravels observed in Siodło Creek suggest that this trough is more susceptible to erosion and less stabilized than Fosa Creek. The results suggest that GSD analyses can be used to define the stage of development of riverbeds relative to that of other riverbeds in polar regions.

Keywords: GSD; proglacial channels; bedload transport; field measurements; fluvial erosion

1. Introduction One of the most important challenges in studies of bedload transport is investigating the differences between mobile and bottom particle sizes and taking these relations into account in new transport models [1–4]. This problem is mostly based on the lack of complex datasets for flow velocity, transport, and grain size distribution (GSD) of the bedload and bottom particles [2]. The lack of sufficient field observations and datasets collected during high flows when active transport is observed [5,6] is not the only problem associated with model development and geomorphological process assessments in Arctic or Antarctic catchments. The limited application of current models to natural gravel-bed rivers [7], and methods of predicting the sediment flux to the global ocean from small rivers [8] represent other problems that remain to be resolved. Bedload transport is one of the main factors associated with changes in the morphology of troughs [9–14], and the difficulty describing the relationships among water flow conditions, GSD, and deposition processes was identified decades ago (e.g., [15–18]). Although a substantial amount of progress has been made in this field because of research conducted in laboratory channels (e.g., [19–21])and field studies (e.g., [22–26]) and with the use of bedload transport models (e.g., [1,2,27–30]), the relationships among the factors associated with bedload transport are poorly understood in natural gravel-bed channels in general and in those located in polar regions in particular [31].

Water 2018, 10, 360; doi:10.3390/w10040360 www.mdpi.com/journal/water Water 2018, 10, 360 2 of 15

GhoshalWater 2018, et 10, al. x FOR [32 PEER] claimed REVIEW that the bedload has a large influence on the GSD and determines2 of 15 the concentration of each size fraction of noncohesive particles under changing hydrological conditions. GSD analyses30]), the relationships have frequently amongbeen the factors used associated as indicators with bedload of the threshold transport are for poorly the initiation understood of in particle motion,natural and sheargravel- stressbed channels dictates in general the specific and in role those of located particles in polar in this regions process in particular [10,33–37 [31].]. Johnson [38] Ghoshal et al. [32] claimed that the bedload has a large influence on the GSD and determines the suggested that the geomorphology of the bed as well as the sediment transport rate should be concentration of each size fraction of noncohesive particles under changing hydrological conditions. considered because of their relationship with grain size and shape. Moreover, the distribution of GSD analyses have frequently been used as indicators of the threshold for the initiation of particle particlesmotion, also and depends shear stress on the dictates mechanism the specific of fluvial role of transportparticles in and this canprocess be used[10,33 to–37] define. Johnson the [38] influence of flowsuggested conditions that on the the geomorphology geomorphology of the of bed the as channel, well as theas stated sediment by transport Kociuba rate and should Janicki be [ 31] or Lisle [23considered]. Although because the coarserof their fractionrelationship is entrained with grain with size greaterand shape. discharge Moreover, [39 ], the because distribution of protrusion of and hidingparticles effects, also depends particles on larger the mechanism than the mean of fluvial grain transport size are and easier can tobe moveused to than define smaller the influence ones [40 –42]. The above-mentionedof flow conditions on situation the geomorphology may be understood of the channel by using, as stated the by GSD Kociuba for the and analysis Janicki [31] of selectiveor bedloadLisle transport [23]. Although in natural the gravel-bedcoarser fraction channels is entrained [43] or with by performing greater discharge a direct [39], analysis because of of certain protrusion and hiding effects, particles larger than the mean grain size are easier to move than smaller parameters, such as the mean grain size, sorting, or skewness, which can be used to predict the ones [40–42]. The above-mentioned situation may be understood by using the GSD for the analysis directionof selective of sediment bedload transport transport [in27 natural,44]. These gravel parameters-bed channels allow [43] or us by to performing obtain information a direct analysis about the predominantof certain size parameters, of the transported such as the mean particles, grain theirsize, sorting dispersal, or skewness, during this which process, can be andused their to pre symmetrydict or preferentialthe direction dispersal of sediment to one transport side of[27,44]. theaverage. These parameters Ashworth allow et us al. to [ 45obtain] concluded information that about sediment sortingthe can predominant occur during size entrainment, of the transported transport, particles, or deposition. their dispersal In during this research, this process, sediment and their sorting is calculatedsymmetry based or on preferential the sediment dispersal caught to one in trapsside of during the average. bedload Ashworth transport. et al. [45] concluded that Thesediment objective sorting of thiscan studyoccur during is to answer entrainment, the following transport questions:, or deposition. (1) HowIn this is research, GSD modified sediment during sorting is calculated based on the sediment caught in traps during bedload transport. the times of peak discharge in a polar catchment? (2) What is the relationship between the GSD The objective of this study is to answer the following questions: (1) How is GSD modified during and GSDthe times parameters of peak discharge and the in amount a polar catchment? of transported (2) What material is the relationship in gravel-bed between rivers? the GSD (3) and Does the modificationGSD parameters of GSDs and during the efficientamount of bedload transported transport material events in gravel allow-bed for rivers? the identification (3) Does the of the developmentmodification stage of of GSDs river during troughs efficient during bedload changing transport meteorological events allow conditions? for the identification of the Todevelopment answer these stage questions, of river troughs insightful during measurements changing meteorological have been conditions? performed in Fosa and Siodło creeks, twoTo proglacialanswer these gravel-bed questions, insightful channels measurements located on the have forefield been performed of the Baranowskiin Fosa and Siodło Glacier on King Georgecreeks, two Island proglacial in Western gravel Antarctica-bed channels (Figure located1). on This the forefield study is of a the continuation Baranowski andGlacier development on King of George Island in Western Antarctica (Figure 1). This study is a continuation and development of the the results presented by Sziło and Bialik [46], who identified the relationship between bedload transport results presented by Sziło and Bialik [46], who identified the relationship between bedload transport and rapidand rapid outflow outflow and and high high water water discharge discharge in in thethe form of of eight eight-loop-loop hysteresis hysteresis for these for these creeks. creeks.

Figure 1. Location of the study site: (a) King George Island; (b) Baranowski Glacier catchment; (c) Figureforefield 1. Location of the glacier of the and study measurement site:( sites.a) King Reference George system: Island; WGS 1984, (b) Baranowski UTM zone 21S, Glacier geoid EGM96. catchment; (c ) forefield of the glacier and measurement sites. Reference system: WGS 1984, UTM zone 21S, geoid EGM96. Water 2018, 10, 360 3 of 15

2. Materials and Methods The field campaign was conducted at two sites established in Fosa and Siodło creeks from 9 January to 11 February 2016 (Figure1). Data on the bedload transport associated with water flow conditions measurements were collected at 24 h intervals over 35 days in both creeks. However, the measurements in Fosa Creek were extended to 2 March, and during those additional 14 days, bedload transport was not observed.

2.1. Study Site The Antarctic Peninsula region, where the study site is located, is prone to climatic fluctuations [47–52]. The total catchment area of the creeks is 6.8 km2 of which 69.1% (4.7 km2) is covered by the glacier (including Windy Glacier). The area of the forefield is 2.1 km2 and is expanding yearly (status for 2017). The frontal part of the glacier is divided into two tongues: Northern and Southern. The Northern tongue is currently terminating on a narrow strip of land close to the shallow lagoon, and the Southern tongue presents several creeks flowing through the forefield. All measurements were initiated in two gravel-bed troughs of the Fosa and Siodło proglacial creeks, which were selected because of their continuous and dynamic water flows during the entire summer season. Fosa Creek receives water mainly from Ginger Lake and the Baranowski Glacier, whereas Siodło Creek is a subglacial outflow from the Baranowski Glacier. Both creeks are fed by meltwater from the glacier in the season (which may represent the primary source of water) and intensive rainfalls. The measurement site in Fosa Creek was established in a location where ablation water cut the trough into cover between 1988 and 1995, whereas in Siodło Creek, this trough was cut between 2001 and 2005. The total lengths (L) of Fosa and Siodło creeks are 1.40 km and 0.42 km, respectively; the longitudinal water surface slopes (S) are 0.07 mm−1 and 0.08 mm−1 for Fosa Creek and Siodło Creek, respectively (Table1). Furthermore, Reynolds and Froude numbers are also presented for both creeks (Figure2a,b).

Table 1. Basic hydraulic parameters of Fosa and Siodło creeks.

Total Average Average Longitudinal Maximum Maximum Parameter Length (L) Bankfull Bankfull Water Surface Discharge (Qmax) Velocity (Vmax) [km] Width (w) [m] Depth (d) [m] Slope (S) [mm−1] [m3 s−1] 1 [ms−1] 2 Fosa Creek 1.40 2.82 0.14 0.07 0.75 0.91 Siodło Creek 0.42 2.15 0.09 0.08 0.26 1.25 1 2 Note: Qmax: maximum water discharge measured at one day during field campaign; Vmax: maximum water velocity measured at one point during field campaign.

Figure 2. Cont. WaterWater 20182018, ,1010, ,x 360 FOR PEER REVIEW 44 of of 15 15

FigureFigure 2. 2. TemporalTemporal changes changes in in ( (aa)) Reynolds Reynolds number number and and ( (bb)) Froude Froude number number for for both both creeks. creeks.

TheThe period period of of the the fi fieldeld campaign campaign was was characterized characterized by by higher higher air air temperatures temperatures relative relative to to other other summersummer months months over over the the last last decade decade [49 [49,5,050,5,353]. ].The The mean mean monthly monthly air air temperature temperature was was +1.0 +1.0 °C ◦inC Januaryin January and and +1.1 +1.1 °C ◦inC inFebruary February for for the the period period from from 2007 2007 to to 2016 2016 [5 [544].]. However, However, the the mean mean air air temperaturetemperature during during the the field field campaign campaign was was +1.8 +1.8 °C ,◦ C,with with a maximum a maximum of +5.9 of +5.9 °C on◦C 29 on January. 29 January. On theOn same the same day, day, the thehighest highest precipitation precipitation of of8.8 8.8 mm mm was was recorded. recorded. During During the the 35 35 days days of of continuous continuous measurements,measurements, 16 16 days days were were without without precipitation precipitation and and 12 12 days days had had precipitation precipitation >1.0 >1.0 mm. mm. The The total total precipitationprecipitation over the the whole whole period period was was 47.7 47.7 mm. mm. Meteorological Meteorological conditions conditions that contributed that contributed to greater to greaterwater discharge water discharge were observed were observed 2 days after2 days intense after intense rainfall rainfall (Figure 3(Figure)[46]. 3) [46].

FigureFigure 3 3.. MeanMean daily daily air air temper temperature,ature, precipitation precipitation,, and and discharge discharge during during the the field field campaign campaign in in 2016 2016 fromfrom Bellingshausen Bellingshausen Station. Station.

2.2.2.2. Bedload Bedload Transport Transport Measurements Measurements ToTo collect collect the the transported transported material, material, River River Bedload Bedload Traps Traps (RBT) (RBT) [ [5555,56,56]] were were anchored anchored at at the the bottomsbottoms of of the the troughs troughs in in two two cross cross sections sections (Figure (Figure 4).4 ).In InFosa Fosa Creek, Creek, a set a setof two of two RBT RBT modules modules at a distanceat a distance of 300 of m 300 from m fromthe forehead the forehead of the of glacier the glacier was installed, was installed, and in and Siodło in SiodłoCreek, Creek, a set of a three set of RBTthree modules RBT modules at a distance at a distance of 15 m offrom 15 mthe from front the of frontthe glacier of the was glacier installed. was installed. One additional One additional module wasmodule established was established in Siodło Creek in Siodło because Creek less because rinsing less of the rinsing bottom of of the the bottom trough of occurred the trough in this occurred creek comparedin this creek with compared in Fosa Creek with inand Fosa a finer Creek bedload and a was finer visible bedload at the was beginning visible at of the the beginning measurements. of the Themeasurements. assumption The was assumption that the bedloa was thatd can the move bedload more can easily move inmore a trough easily in in a an trough early in stage an early of developmentstage of development (Siodło Creek) (Siodło than Creek) in a thanlater instage a later of development stage of development [46]. The locations [46]. The of locations the modules of the in the profiles were chosen based on the most intense currents. modules in the profiles were chosen based on the most intense currents.

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FigureFigure 4 4.. RiverRiver Bedload Bedload Traps Traps ( (RBT)RBT) in in ( (aa)) Fosa Fosa Creek Creek and and ( (bb)) Siodło Siodło Creek Creek (modified (modified from from Sziło Sziło and and BialikBialik [46] [46]);); ( (cc)) schematic schematic diagram diagram for for the the bedload bedload transport transport technique technique (Kociuba [ 56]).]).

2.3. Sieve Method and GSD Analysis 2.3. Sieve Method and GSD Analysis To obtain the GSD, each of the collected samples of the bedload was transported, drained, To obtain the GSD, each of the collected samples of the bedload was transported, drained, sieved, and weighed in the laboratory of the Henryk Arctowski Polish Antarctic Station. sieved, and weighed in the laboratory of the Henryk Arctowski Polish Antarctic Station. Furthermore, a comparison of the dry and wet sample weights was performed to determine the most Furthermore, a comparison of the dry and wet sample weights was performed to determine the reliable method of preparing the data for further analysis. Each sample that had a greater than 1% most reliable method of preparing the data for further analysis. Each sample that had a greater proportion of grain size <2 mm was truncated to exclude sediment that was predominantly than 1% proportion of grain size <2 mm was truncated to exclude sediment that was predominantly suspended and because of limitations of the mesh diameter of the net. The upper limit to remove the suspended and because of limitations of the mesh diameter of the net. The upper limit to remove samples because of the selective rejection of particles by the sample was set up at 32 mm [23]. the samples because of the selective rejection of particles by the sample was set up at 32 mm [23]. Furthermore, for the GSD analysis, average weight values lower than 3% (chosen arbitrarily) for all Furthermore, for the GSD analysis, average weight values lower than 3% (chosen arbitrarily) for all collected data were rejected as not statistically important. To obtain information on the sedimentary collected data were rejected as not statistically important. To obtain information on the sedimentary environment, such as the sediment provenance, transport, and deposition conditions (e.g., [15,18,24]), environment, such as the sediment provenance, transport, and deposition conditions (e.g., [15,18,24]), the GSD parameters were evaluated. The Folk and Ward [15] method was employed to obtain the the GSD parameters were evaluated. The Folk and Ward [15] method was employed to obtain the GSD GSD parameters of mean grain size (Mz), standard variation (σϕ), sorting (σ), skewness (Skl), and parameters of mean grain size (Mz), standard variation (σφ), sorting (σ), skewness (Skl), and kurtosis kurtosis (KG), which according to Blot and Pye [57] describe (a) the average size of grains (Mz); (b) (KG), which according to Blot and Pye [57] describe (a) the average size of grains (Mz); (b) the spread of the spread of the sizes around the average (σ); (c) the preferential spread to one side of the average the sizes around the average (σ); (c) the preferential spread to one side of the average (Skl); and (d) the (Skl); and (d) the degree of concentration of the grains relative to the average (KG). As suggested by degree of concentration of the grains relative to the average (KG). As suggested by Blot and Pye [57], Blot and Pye [57], the Folk and Ward [15] method provides the most robust basis for routine comparisons the Folk and Ward [15] method provides the most robust basis for routine comparisons of compositionally of compositionally variable sediments in the cases when the skewness or kurtosis of grain sizes are variable sediments in the cases when the skewness or kurtosis of grain sizes are calculated. It should calculated. It should be noted that besides the presentation of grain diameters in metric units, be noted that besides the presentation of grain diameters in metric units, according to standard according to standard procedure [15,57], data will be also shown and analyzed in phi (φ) units, which procedure [15,57], data will be also shown and analyzed in phi (ϕ) units, which is the negative log to is the negative log to base 2 of the diameter in mm. base 2 of the diameter in mm.

2.4.2.4. Bedload Bedload Transport Transport Rate

The bedload transport rate (qb) was calculated from the weighted arithmetic mean formula [46] The bedload transport rate (qb) was calculated from the weighted arithmetic mean formula [46] givengiven in in Equation Equation (1): (1): 퐺Gs q = 푠 ·W (1) 푞푏b = S t∙ 푊푡t (1) 푆푤w푡 where Gs represents the bedload material (kg), Sw represents the width of the module inlet (m), Wt where Gs represents the bedload material (kg), Sw represents the width of the module inlet (m), Wt t representsrepresents the the width width of of the the trough trough (m (m),), and and t representsrepresents the the measurement measurement time time (day (day).). In addition, In addition, the the water velocity was measured with an Electromagnetic Open Channel Flow Meter (manufactured by water velocity was measured with an Electromagnetic Open Channel Flow Meter (manufactured by Valeport,Valeport, model 801). For details, details, see Sziło Sziło and Bialik Bialik [46]. [46]. The The average average water water velocity velocity was was measured measured at least two times [46] at each measurement section for 30 seconds [58]. If the standard deviation of at least two times [46] at each measurement section for 30 seconds [58]. If the standard deviation of the measurement values was higher than 10%, the measurements were repeated until an acceptable the measurement values was higher than 10%, the measurements were repeated until an acceptable standard deviation was obtained. Based on the values of creek bathymetry and water velocities for standard deviation was obtained. Based on the values of creek bathymetry and water velocities for eaceachh section, section, the the water water discharge discharge was was calculated calculated following following the the standard standard procedure procedure [58]. [58]. The The accuracy accuracy ± ofof equipment equipment employed employed for for measurements measurements was ±0.5%0.5% of of reading reading values values plus plus 5 5 mm/s. mm/s.

2.5. Statistical Analysis An analysis of variance (ANOVA) test was performed to determine whether or not the two investigated creeks had statistically significant differences in terms of bedload transport and

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2.5. Statistical Analysis An analysis of variance (ANOVA) test was performed to determine whether or not the two investigatedWater 2018, 10, creeksx FOR PEER had REVIEW statistically significant differences in terms of bedload transport6 of 15 and hydrologicalhydrologicalWater 2018 conditions., 10, x conditions.FOR PEER The REVIEW Anderson–Darling The Anderson –Darling test test was was used used to checkto check for for normality, normality, and and Bartlett’s Bartlett’s6 of 15 test was usedtest to was check used for to the check homogeneity for the homogeneity of variance of variance to meet to the meet assumptions the assumptions of the ANOVA.of the ANOVA. To provide To a betterprovidehydrological description a better conditions. of thedescription changes The ofAnderson that the occurred changes–Darling that in the testoccurred channels was used in ofthe to both channelscheck creeks, for ofnormality, both sediment creeks, and samples sedimentBartlett’s from the individualsamplestest was trapsfromused theto were check individual analyzed for the traps homogeneity independently were analy ofz edvariance even independently when to meet collected the even assumptions when from collected the of same the from ANOVA. creek. the same To creek.provide a better description of the changes that occurred in the channels of both creeks, sediment 3. Resultssamples from the individual traps were analyzed independently even when collected from the same 3.creek. Results 3.1. Statistical Analysis: Water Discharge, Flow Velocity, and Bedload Transport 3.1.3. Results Statistical Analysis: Water Discharge, Flow Velocity, and Bedload Transport Figure5 shows the bedload transport, water discharge, and flow velocity data for Fosa and Siodło creeks.3.1. Unfortunately, StatisticalFigure 5 Analysis shows the assumptions the: Water bedload Discharge transport, of normality, Flow V waterelocity and discharge, and homogeneity Bedload, and Transport flow of variance velocity data were for not Fosa observed and for all presentedSiodło creeks. data. Unfortunately, When a variable the assumptions does not of fit normality the assumptions and homogeneity required of for variance the ANOVA were not test, observedFigure for 5 all shows presented the bedload data. Whentransport, a variable water discharge does not , fitand the flow assumptions velocity data required for Fosa for and the the data are usually transformed (log or square root) [59]. The square root transformation was used for ANOVASiodło creeks. test, Unfortunately, the data are the usually assumptions transformed of normality (log or and square homogeneity root) [59] of. variance The square were rootnot water dischargetransformationobserved forand all flow was presented velocity, used for data. and water When the discharge double a variable square and does flow root not velocity, transformation fit the assumptions and the was double required used square for for bedload root the transport;transformationANOVA the transformed test, the was data used variables are for usually bedload met the transformed above transport assumptions. ; (ltheog or transformed square A comparison root) variables [59]. of The met the square theresults above root of all transformedassumptions.transformation data indicated A comparison was used only for of one the water ofresultsthe discharge variablesof all transformed and (flow flow velocity) velocity,data indicated between and theonly double theone creeksof the square variables presented root statistically(flowtransformationsignificant velocity) between was differences used the creeks for (p -value bedload presented < 0.05). transport statistically; the significant transformed differences variables (p-value met < the0.05). above assumptions. A comparison of the results of all transformed data indicated only one of the variables (flow velocity) between the creeks presented statistically significant differences (p-value < 0.05).

Figure 5. Bedload transport (a), water discharge (b), and flow velocity (c) data for Fosa Creek (1) and Figure 5. Bedload transport (a), water discharge (b), and flow velocity (c) data for Fosa Creek (1) and Siodło Creek (2). Siodło Creek (2). Figure 5. Bedload transport (a), water discharge (b), and flow velocity (c) data for Fosa Creek (1) and 3.2. SievingSiodło CProcedurereek (2). Comparison (Wet and Dry) 3.2. Sieving Procedure Comparison (Wet and Dry) 3.2. SievingAlthough Procedure standard Comparison procedures (Wet forand wet Dry sieving) are acceptable for determining the GSD (e.g., Although[31]), the standard form of sieving procedures (wet or for dry) wet may sieving influence are acceptable the particle for distribution determining [60,61 the]. To GSD investigate (e.g., [31 ]), the formhow of sievingAlthoughthe drying (wet standardprocess or dry) can procedures mayinfluence influence the for GSD, wet the sieving the particle weights are distribution acceptable of randomly for [60 chosen determining,61]. Towet investigate and the dry GSD bedload how(e.g.,s the drying processnot[31] lower), the can formthan influence 10of kgsieving were the (wetcompared GSD, or thedry) (Figure weights may influence 6). ofThe randomly results the particle of chosenthe analysis distribution wet revealed and dry[60,61 that bedloads]. To the investigate difference not lower how the drying process can influence the GSD, the weights of randomly chosen wet and dry bedloads than 10between kg were the compared weights (Figure ranged 6 from). The 15 results% to 28% of (Figurethe analysis 6). Hence, revealed in this that research, the difference only the between dried bedloadnot lower was than considered 10 kg were in compared further analyses. (Figure 6). The results of the analysis revealed that the difference the weightsbetween ranged the weights from 15% ranged to 28% from (Figure 15% to6 ). 28% Hence, (Figure in this 6). Hence, research, in this only research, the dried only bedload the dried was consideredbedload in further was considered analyses. in further analyses.

Figure 6. Weight fractions of the wet and dry samples.

Figure 6 . Weight fractions of the wet and dry samples. Figure 6. Weight fractions of the wet and dry samples.

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3.3.3.3. GSD GSD Parameters Parameters and and Variation Variation of of Characteristic Characteristic DiametersDiameters (D) of the Bedload Bedload Transport Transport Rate Rate 3.3. GSD Parameters and Variation of Characteristic Diameters (D) of the Bedload Transport Rate FiguresFigures7 and 7 and8 show 8 show the the relationship relationship between between σ and MzMz forfor all all data, data, for for both both creeks creeks separately, separately, Figures 7 and 8 show the relationship between σ and Mz for all data, for both creeks separately, andand for for the the individual individual traps. traps. The The analysis analysis of of the theσ andσ andMz Mzin in the the profiles profiles established established in in the the Fosa Fosa and and the and for the individual traps. The analysis of the σ and Mz in the profiles established in the Fosa and Siodłothe Siodło troughs troughs suggested suggested that linear thatcorrelations linear correlatio occurredns occurred with those with indicators, those indicators, and the correlation and the the Siodło troughs suggested that linear correlations occurred with those indicators, and the correlation coefficients2 (R2) were 0.82–0.92 (Figure 7). Moreover, an increase in Mz presents a coefficientscorrelation (R coefficients) were 0.82–0.92 (R2) were (Figure 0.827–).0.92 Moreover, (Figure 7). an Moreover, increase in anMz increasepresents in aMz corresponding presents a corresponding increase in grain variability. The mean diameter of sediment from Fosa Creek for all increasecorresponding in grain increase variability. in grain The meanvariability. diameter The mean of sediment diameter from of sediment Fosa Creek from for Fosa all measurementCreek for all measurement days varied from 2.9 mm to 6.2 mm and was higher than that in Siodło Creek, which daysmeasurement varied from days 2.9 mmvaried to from 6.2 mm 2.9 andmm wasto 6.2 higher mm and than was that higher in Siodło than Creek, that in whichSiodło variedCreek, fromwhich 1.5 varied from 1.5 mm to 3.6 mm. Furthermore, larger ranges of Mz values were observed for the mmvaried to 3.6 from mm. 1.5 Furthermore, mm to 3.6 mm. larger Furthermore, ranges of Mz largervalues ranges were of observed Mz values for were the individual observed for traps the in individual traps in Siodło Creek than for those in Fosa Creek, and a maximum of 10.4 mm was Siodłoindividual Creek trapsthan for in Siodłothose in Creek Fosa than Creek, for and those a maximum in Fosa Creek, of 10.4 and mm a maximumwas observed of 10.4 on 6 mm February was observed on 6 February (Figure 8a,b). The strongest correlation for the material collected in the trap (Figureobserved8a,b). on The 6 February strongest (Figure correlation 8a,b). The for thestrongest material correlation collected for in the the material trap occurred collected in in the the Siodło trap occurred in the2 Siodło middle (M) at R2 = 0.96 (Figure 8b), for which 77% of the data ranged from 2.3 middleoccurred (M) in at the R =Siodło 0.96 (Figuremiddle8 (M)b), forat R which2 = 0.96 77% (Figure of the 8b), data for rangedwhich 77% from of 2.3 the to data 3.9 mm,ranged whereas from 2.3 for to 3.9 mm, whereas for the Siodło left (L), 80% of the data were in the interval from 4.1 to 8.9 mm. theto Siodło 3.9 mm, left whereas (L), 80% for of the the Siodło data were left (L), in the80% interval of the data from were 4.1 toin 8.9the mm.interval from 4.1 to 8.9 mm.

Figure 7. Relation between sorting (σ) and mean grain size (Mz) in Fosa and Siodło creeks in all Figure 7. Relation between sorting (σ) and mean grain size (Mz) in Fosa and Siodło creeks in all Figureprofiles. 7. Relation between sorting (σ) and mean grain size (Mz) in Fosa and Siodło creeks in all profiles. profiles.

Figure 8. Relation between sorting (σ) and mean grain size (Mz) in Fosa (a) and Siodło (b) creeks in FigureFigure 8. 8Relation. Relation between between sorting sorting (σ(σ)) andand meanmean graingrain size ( Mz)) in in Fosa Fosa ( (aa)) and and Siodło Siodło (b (b) )creeks creeks in in individual traps. individualindividual traps. traps.

The temporal changes in bedload transport and σ for the studied creeks are presented in Figure TheThe temporal temporal changes changes in in bedload bedload transport transport and andσ σfor for the the studied studied creeks creeks areare presentedpresented inin FigureFigure9 . 9. The σ in individual traps varied from 1 mm to 1.5 mm in 93% of the samples, which means that the The9. σThein σ individual in individual traps traps varied varied from from 1 mm1 mm to to 1.5 1.5 mm mm in in 93% 93% ofof thethe samples,samples, which which means means that that the the collected sediments in both cross sections were poorly sorted (Figure 9a,b). Furthermore, after the collectedcollected sediments sediments in in both both cross cross sections sections werewere poorlypoorly sortedsorted (Figure 99a,b).a,b). Furthermore, after after the the peak bedload transport, which appeared from 29 to 30 January, an inversion of σ occurred from lower peakpeak bedload bedload transport, transport, which which appeared appeared from from 2929 toto 3030 January, an inversion of of σσ occurredoccurred from from lower lower values in the Fosa right (R) section compared with in the Fosa left (L) section, where higher values valuesvalues in in the the Fosa Fosa right right (R) (R) section section compared compared withwith inin thethe Fosa left (L) section, section, where where higher higher values values were observed (Figure 9a). A similar situation occurred in the Siodło trough: after both of the bedload werewere observed observed (Figure (Figure9a). 9a). A A similar similar situation situation occurred occurred in in the the SiodłoSiodło trough:trough: after both both of of the the bedload bedload transport peaks (on 1 and 5 February), inversions of σ in the left trap from highest to lowest and then transporttransport peaks peaks (on (on 1 and1 and 5 February),5 February), inversions inversions of ofσ σin in the the left left trap trap from from highest highest to to lowest lowest and and then then to to highest values again were noticed (Figure 9b). Furthermore, the results suggest that better σ highestto highes valuest values again again were noticed were noticed (Figure (Figure9b). Furthermore, 9b). Furthermore, the results the suggest results suggest that better thatσ betteroccurred σ occurred in both troughs after each peak in bedload transport (Figure 9a,b). inoccurred both troughs in both after troughs each peakafter ineach bedload peak in transport bedload (Figuretransport9a,b). (Figure 9a,b).

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FigureFigure 9. Bedload 9. Bedload transport transport and and sorting sorting inin individualindividual traps traps in in the the Fosa Fosa (a) (anda) and Siodło Siodło (b) creeks. (b) creeks.

The relation between bedload transport and σ was inversely proportional before and directly The relationFigure 9 between. Bedload transport bedload and transport sorting in individual and σ was traps inversely in the Fosa proportional (a) and Siodło ( beforeb) creeks. and directly proportional after the peaks in bedload transport (Figure 10a,b). All bedload transport data from proportional after the peaks in bedload transport (Figure 10a,b). All bedload transport data from Siodło Siodło Creek were negatively skewed, which means that a large proportion of coarse sediment Creek wereThe negatively relation between skewed, bedload which transport means and that σ awas large inversely proportion proportional of coarse before sediment and directly occurred proportionaloccurred (Figure after 10c), the peaksand this in findingbedload is transport also confirmed (Figure based 10a,b). on All the bedload percentage transport of gravels data in from the (Figure 10c), and this finding is also confirmed based on the percentage of gravels in the collected Siodłocollected Creek material were (Figure negatively 11a,b). skewed, An increase which in mean waters that discharge a large and proportion a consequential of coarse increase sediment in materialoccurredbedload (Figure trans(Figure 11porta,b). 10c), resulted Anand increasethisin symmetrical finding in is water also Skl confirmedand discharge leptokurtic based and KG on a consequential(Figurethe percentage 10c,d). Before of increase gravels 31 January inin bedloadthe transportcollectedand after resulted material 4 February, in symmetrical (Figure when 11a,b). theSkl An maximumand increase leptokurtic discharge in waterKG dischargewas(Figure observed, 10 andc,d). a strongly consequential Before negative 31 January increase Skl andwas in after 4 February,bedloadobserved when trans in Siodłoport the maximum resulted(Figure 10c).in dischargesymmetrical Under low was Skldischarge observed, and leptokurtic conditions, strongly KG leptokurtic negative(Figure 10 SklKGc,d). wasw Beforeas observed. observed 31 January in Siodło (Figureand 10 The afterc). Underbedload 4 February, low transport discharge when rate the and conditions, maximum grain size leptokurtic dischargevariation analyses wasKG observed,was indicate observed. strongly that an inverse negative correlation Skl was Theobservedoccurred bedload forin Siodło both transport creeks. (Figure In rate 10c). Fosa and Under Creek, grain lowthe size graindischarge variation size variations conditions, analyses decrease leptokurtic indicate when thatKG the w anbedloadas inverseobserved. transport correlation occurredrate increases,The for bothbedload creeks.whereas transport In in FosaSiodło rate Creek, and Creek, grain the the size graingrain variation size variations variations analyses are indicate decrease directly that whenproportional an inverse the bedload tocorrelation increases transport in bedload transport rate. Furthermore, in Fosa Creek, the D-value correlations increase from 0.15 for rate increases,occurred for whereas both creeks. in Siodło In Fosa Creek, Creek, the the graingrain size size variations variations decrease are directly when proportionalthe bedload transport to increases D50 to 0.26 for D95, which is inconsistent with the data from Siodło Creek, where the correlation for in bedloadrate increases, transport whereas rate. in Furthermore, Siodło Creek, in the Fosa grain Creek, size variations the D-value are directly correlations proportional increase to increases from 0.15 for inD50 bedload of 0.29 decreasestransport rate.to 0.11 Furthermore, for D95 (Figure in Fosa 11a, b).Creek, the D-value correlations increase from 0.15 for D50 to 0.26 for D95, which is inconsistent with the data from Siodło Creek, where the correlation for D50 to 0.26 for D95, which is inconsistent with the data from Siodło Creek, where the correlation for D of 0.29 decreases to 0.11 for D (Figure 11a,b). 50 D50 of 0.29 decreases to 0.11 for D9595 (Figure 11a,b).

Figure 10. Cont. Water 2018, 10, x FOR PEER REVIEW 9 of 15 Water 2018, 10, 360 9 of 15 Water 2018, 10, x FOR PEER REVIEW 9 of 15

Figure 10. Grain size parameters (by Folk and Ward, 1957) for Fosa and Siodło Creeks: bedload Figure 10. Grain size parameters (by Folk and Ward, 1957) for Fosa and Siodło Creeks: bedload Figuretransport 10. Grain rate size and parameterssorting for Fosa (by (a Folk) and Siodło and Ward, (b); skewness 1957) for (c); Fosaand kurtosis and Siodło (d). Creeks: bedload transport raterate andand sortingsorting forfor FosaFosa ((aa)) andand SiodłoSiodło ((bb);); skewnessskewness ((cc);); andand kurtosiskurtosis ((dd).).

Figure 11. Correlation between bedload transport rate and characteristic diameters Db for Fosa (a) and Siodło (b) creeks, where b stands for the percentage of the weight of the sample finer than this value.

Figure 11.11. Correlation between bedload transport rate and characteristic diameters Db for Fosa (aa) and 3.4. SelectiveCorrelation Transport between and Bedload bedload Transport transport versu rates Water and Discharge characteristic and diametersWater Velocity Db for Fosa ( ) and Siodło (b)) creeks,creeks, wherewhere bb standsstands forfor thethe percentagepercentage ofof thethe weightweight of the sample sample finer finer than than this this value value.. Fine (4–8 mm) and very fine (2–4 mm) gravel accounted for 40 to 99% of the total sample weight 3.4. Selectivein the troughs Transport for andeachand Bedload Bedloadday of the TransportTransport measurement versusversu campaign.s WaterWater DischargeDischarge Nevertheless, and and Water Water a higher Velocity Velocity proportion of these gravels (2–8 mm) was observed in Siodło Creek, with the value reaching at least 63%. This increase Finewas (4–8(4especially–8 mm) clear and verybefore finefine the (2–4peaks(2–4 mm) of water gravel discharge accounted on 19 forand 40 29 toJanuary, 99% of when the total the fine sample and very weight in the fine troughs gravel for constituted each day almost of the measurement the entirety of the campaign. Siodło Creek Nevertheless, samples. Furthermore, a higher proportion because of of the these gravelsincrease (2–8(2–8 mm) in wat waser discharge, observed the in proportion Siodło Creek, of medium with the (8– value6 mm) reachingreachingand coarse atat (16 leastleast–22 63%.mm)63%. gravel This increasealso was especiallyincreased clearin both before creeks, the particularly peaks of water on 29 dischargeto 31 January on 19and and 4 to 29 5 January,February when(Figure the 12a,b), finefine when and very the highest water discharge occurred. In addition to the previously mentioned periods when the low finefine gravelgravel constituted almost the entirety of the SiodłoSiodło Creek samples.samples. Furthermore, because of the increasewater in watdischargeer discharge, was observed, the proportion certain coarse of medium sediment (8 samples–6 mm) were and identified.coarse (16 Nonetheless,–22 mm) gravel these also increasesamples in water had discharge, insignificant the weight proportion fractions of medium and were (8–6 disrupted mm) and by the coarse presence (16–22 of mm) a few gravel coarse also increased in both creeks, particularly on 29 to 31 January and 4 to 5 February (Figure 12a,b), when increasedpebbles. in both A similar creeks, situation particularly was observ on 29ed towhen 31 January the water and discharge 4 to 5 Februarypeaked. At (Figure that time, 12 a,b),several when the highestboulders water were discharge caught in occurred.the Siodło trough, In addition which to contributed the previously more thanmentio mentioned 50%ned of the periods sample when in certain the low water cases, dischargedischarge although waswas the observed,observed, water discharge certaincertain was coarsecoarse two sedimentsedimenttimes lower samplessamples than that werewere in Fosa identified.identified. Creek. Nonetheless, these samples had had insignificant insignificant weight weight fractions fractions and and were were disrupted disrupted by the by presence the presence of a few of coarse a few pebbles. coarse Apebbles. similar A situation similar situation was observed was observ whened the when water the discharge water discharge peaked. Atpeaked. that time, At that several time, boulders several boulders were caught in the Siodło trough, which contributed more than 50% of the sample in certain were caught in the Siodło trough, which contributed more than 50% of the sample in certain cases, althoughcases, although the water the dischargewater discharge was two was times two lowertimes thanlower that than in that Fosa in Creek. Fosa Creek.

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Figure 12. Percentage of bedload vs water discharge for Fosa (a) and Siodło (b) creeks. Figure 12. Percentage of bedload vs water discharge for Fosa (a) and Siodło (b) creeks. Figure 12. Percentage of bedload vs water discharge for Fosa (a) and Siodło (b) creeks. Because of the high proportions of fine and very fine gravel in each sample, those grain sizes haveBecause been chosen ofof thethe high forhigh our proportions proportions examination of of fine fine of and theand very correlation very fine fine gravel gravel between in each in each bedload sample, sample, those transport those grain grain an sizesd water havesizes beenhavedischarge chosen been or chosen forwater our velocity for examination our (Figures examination of the 13 correlationand of 14). the The correlation between correlation bedload between between transport bedload water anddischarge transport water dischargeand an dbedload water or waterdischargetransport velocity wasor water (Figuresequal velocity to 13 0.65 and (Figures in 14 the). The Fosa 13 correlation and and 14). 0.55 The betweenin correlationthe Siodło, water between and discharge these water correlations and discharge bedload were transport and strongerbedload was equaltransportthan those to 0.65 was between in equal the Fosa bedload to and0.65 0.55 intransport the in theFosa Siodło,and and water 0.55 and velocity,in these the correlationsSiodło, which and were werethese 0.53 stronger correlations in Fosa than and thosewere0.28 in betweenstronger Siodło; bedloadthanthis is those likely transport between due to and thebedloadwater changes transport velocity, of the whichandcreek water beds were velocity, and 0.53 shapes, in Fosa which due and were to 0.28 the 0.53 in existence Siodło; in Fosa this andof scouring is 0.28 likely in Siodło dueeffects to; thethis[56] changes is and likely because ofdue the to creekonly the changes beds grains and withof shapes, the diameter creek due beds to lower the and existence thanshapes, 22 of due mm scouring to w theere effectsexistencetaken [56 into ]of and scouringaccount because foreffects only the grains[56]anal ysis. and with becauseThus, diameter the only increase lower grains than in with water 22 mm diameter discharge were taken lower was into than observable account 22 mm for with thewere analysis.the taken simultaneous into Thus, account the increase for the inin wateranalbedloadysis. discharge transportThus, wasthe, increaseand observable the in intensity with water the discharge or simultaneous correlation was observableincrease in the relations in bedload with the between transport, simultaneous water and velocity the increase intensity and in orbedload correlation transport transport in the ,was relationsand lower. the intensitybetween water or correlation velocity and in the bedload relations transport between was lower.water velocity and bedload transport was lower.

FigureFigure 13.13. RelationshipRelationship betweenbetween waterwater dischargedischarge andand quantityquantity ofof finefine andand veryvery finefine gravelgravel in Fosa (a)) Figure 13. Relationship between water discharge and quantity of fine and very fine gravel in Fosa (a) andand SiodłoSiodło ((bb)) creeks.creeks. and Siodło (b) creeks.

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FigureFigure 14.14. RelationshipRelationship between between water water velocity velocity and and quantity quantity of fineof fine and and very very fine fine gravel gravel in Fosa in Fosa (a) and (a) Siodłoand Siodło (b) creeks. (b) creeks.

4. Discussion 4. Discussion TheThe weightsweights ofof the the wetwet and and dry dry samples samples differdiffer significantly—by significantly—by as as muchmuch as as 28% 28% andand byby anan average of 21.5%. These results are inconsistent with those of Kociuba and Janicki [31], who reported average of 21.5%. These results are inconsistent with those of Kociuba and Janicki [31], who reported that the average water amount in a natural gravel-bed channel was 6%. In this situation, the error in that the average water amount in a natural gravel-bed channel was 6%. In this situation, the error in −1 thethe calculationcalculation cancan reachreach maximummaximum valuesvalues ofof 20.1–21.320.1–21.3 kgkg dd−1 for thethe meanmean transporttransport raterate [[31]31] andand 33.3–67.8 kg d−1 for the mean daily bedload flux [62] based on exemplary data from the Scott River 33.3–67.8 kg d−1 for the mean daily bedload flux [62] based on exemplary data from the Scott River (Svalbard). (Svalbard). The flow velocity analysis for both creeks suggests that a statistically significant difference (p- The flow velocity analysis for both creeks suggests that a statistically significant difference (p-value value < 0.05) occurred in the hydraulic conditions. A stronger correlation with bedload transport was < 0.05) occurred in the hydraulic conditions. A stronger correlation with bedload transport was revealed revealed for water discharge than for water velocity, which was estimated based on the measured for water discharge than for water velocity, which was estimated based on the measured values of values of the water velocity. This result explained the previously reported findings of Sziło and Bialik the water velocity. This result explained the previously reported findings of Sziło and Bialik [46], who [46], who suggested that a similar relationship occurred between water discharge and bedload suggested that a similar relationship occurred between water discharge and bedload transport for Fosa transport for Fosa and Siodło creeks. Moreover, the lack of significant differences in bedload and Siodło creeks. Moreover, the lack of significant differences in bedload transport clearly indicated transport clearly indicated that this catchment process was strongly associated with meteorological that this catchment process was strongly associated with meteorological conditions, as presented conditions, as presented in Figure 2. Certain differences noted by the authors in their previous work in Figure2. Certain differences noted by the authors in their previous work were likely caused by were likely caused by differences in the geomorphological features of the analyzed troughs, which differences in the geomorphological features of the analyzed troughs, which could be explained based could be explained based on the GSD analysis. on the GSD analysis. The detailed GSD analysis has shown that σ is inversely proportional to Mz, which is consistent The detailed GSD analysis has shown that σ is inversely proportional to Mz, which is consistent with the results of studies in the Scott River performed by Kociuba and Janicki [31]. Kociuba and with the results of studies in the Scott River performed by Kociuba and Janicki [31]. Kociuba and Janicki suggested that the bed material was poorly sorted, which is similar to the results from the Janicki suggested that the bed material was poorly sorted, which is similar to the results from the Fosa and Siodło creeks (Figure 8a,b). Moreover, grains in the investigated troughs were finer (3 mm) Fosa and Siodło creeks (Figure8a,b). Moreover, grains in the investigated troughs were finer (3 mm) than those in the Scott River (10 mm) [31]), which is likely because both creeks in this study are in the than those in the Scott River (10 mm) [31]), which is likely because both creeks in this study are in earlier stages of formation and more sensitive to morphological changes (especially Siodło Creek, as the earlier stages of formation and more sensitive to morphological changes (especially Siodło Creek, suggested by Sziło and Bialik [46]) in relation to the Scott River. These troughs were cut down into as suggested by Sziło and Bialik [46]) in relation to the Scott River. These troughs were cut down moraine cover later (in recent decades, Figure 1) than was the trough of the Scott River [63]. Poorly into moraine cover later (in recent decades, Figure1) than was the trough of the Scott River [ 63]. sorted bedload (Figure 9a,b) suggests high energetic differentiation of the particles and rapid changes Poorly sorted bedload (Figure9a,b) suggests high energetic differentiation of the particles and rapid in the geomorphology of both troughs. Significant bedload transport rates based on the definition of changes in the geomorphology of both troughs. Significant bedload transport rates based on the Batalla et al. [36] of 1 gm−1s−1 were observed on 30 January and 1 February in the troughs. definition of Batalla et al. [36] of 1 gm−1s−1 were observed on 30 January and 1 February in the −1 −1 Nevertheless, the bedload transport peak was defined as qb > 0.1 gm s . As− a1 consequence,−1 the sizes troughs. Nevertheless, the bedload transport peak was defined as qb > 0.1 gm s . As a consequence, of movable grains are more variable and present a larger proportion of finer grains compared with the sizes of movable grains are more variable and present a larger proportion of finer grains compared that in the bed channels, where they could have already been rinsed. This finding could be related to with that in the bed channels, where they could have already been rinsed. This finding could be the higher transport of the bedload and faster changes in the morphology of the troughs. Other GSD related to the higher transport of the bedload and faster changes in the morphology of the troughs. parameters, e.g., negative Skl, are typical for natural gravel-bed channels [23,31,64,65]. The Other GSD parameters, e.g., negative Skl, are typical for natural gravel-bed channels [23,31,64,65]. investigation of the correlation between grain size variations and bedload transport rate revealed that both troughs were characterized by an inverse correlation. In Fosa Creek, this correlation increased proportionally to the D values and was strongest for D95, which is more sensitive to water flow as

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The investigation of the correlation between grain size variations and bedload transport rate revealed that both troughs were characterized by an inverse correlation. In Fosa Creek, this correlation increased proportionally to the D values and was strongest for D95, which is more sensitive to water flow as concluded by Batalla et al. [36]. This result is similar to findings for the Salty River [36] and the Scott River [31]. Nevertheless, for Siodło Creek, a higher value was observed for D50 than for D95. For both creeks, finer bedload is transported before the peak of water discharge than that transported during and after this phenomenon, which is consistent with findings of the previous studies (e.g., [23]). Generally, two phases of selective transport can be distinguished in both creeks (Figure 11). In the first phase, very fine gravel was predominantly entrained; this was followed by the second phase, where gravel dominated. Similar observations of two-phase selective transport have been reported in previous studies of other natural gravel-bed channels [31,36,66,67]. Furthermore, the higher proportions of fine and very fine gravel in Siodło Creek compared with those in Fosa Creek over the entire field campaign confirm the previous hypothesis posed by Sziło and Bialik [46], who assumed that the Siodło trough may be in an earlier stage of formation than the Fosa trough and thus exhibit a more obvious erosive process. In addition, fine material collected from the Siodło, which constituted at least 63% in each sample, can also provide evidence that the channel is not yet armored and paved like the Fosa trough, and bottom erosion may occur faster [33]. Moreover, the presence of boulders (>64 mm) during the peaks of water discharge not exceeding even one-fourth bankfull, mostly in the Siodło trough [46], may suggest that the greater part of the sediment was entrained rather than laterally eroded, as has been observed in other gravel-bed channels during near-bankfull discharge [23,31].

5. Conclusions According to the aims of this study, the analysis confirmed that the variability and modification of GSDs are strongly related to the daily variability of bedload transport dynamics, which was suggested for the first time for polar catchments by Kociuba and Janicki [31]. During the measurement period, i.e., the ablation period, the weather conditions played a significant role in the processes observed in the bed channels of streams, especially when low water discharge occurred. In addition, the increased proportion of medium and coarse gravel was strictly proportional to the increases in water discharge. The simultaneous measurements performed in two creeks that are located in the same catchment but present partial differences in the sources of the material (i.e., Fosa Creek was also fed with lake material) indicated the processes occurring in both troughs. The bedload material from Siodło Creek consisted mostly of fine and very fine gravels, suggesting an early stage of formation and an efficient erosive process, which is confirmed by the general conditions of both streams. Fosa Creek has been free of ice cover for more than 30 years and is at a more stable development stage in which water discharge is the predominant control mechanism for the channel geometry. However, the GSD analysis showed that bedload transport can also significantly influence this process.

Acknowledgments: This publication has been partially financed by funds from the Leading National Research Centre (KNOW) received by the Centre for Polar Studies for the period 2014–2018. Author Contributions: J.S. and R.J.B. designed the study and conducted the field campaign and laboratory analysis. J.S. conducted the majority of the data analysis and wrote the majority of the paper. J.S. and R.J.B. both contributed to the final version of the manuscript. Conflicts of Interest: The authors declare no conflicts of interest.

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