Variable contribution of wood to the hydraulic resistance of headwater tropical streams

Authors

  • Daniel Cadol,

    Corresponding author
    1. Department of Geosciences, Colorado State University, Fort Collins, Colorado, USA
    2. Now at Department of Earth and Environmental Sciences, New Mexico Institute of Mining and Technology, Socorro, New Mexico, USA
    • Corresponding author: D. Cadol, Department of Geosciences, Colorado State University, Fort Collins, CO 80523-1482, USA. (dcadol@nmt.edu)

    Search for more papers by this author
  • Ellen Wohl

    1. Department of Geosciences, Colorado State University, Fort Collins, Colorado, USA
    Search for more papers by this author

Abstract

[1] We investigated the relative contribution of wood to total flow resistance in a tropical setting by measuring wood load and hydraulic resistance in six forested headwater sites at a range of subformative discharges. We evaluated the effectiveness of wood in increasing resistance by comparing measured velocity with predicted velocity from nondimensional hydraulic geometry equations that include slope, unit discharge, and either bed grain size (D84) or bed elevation variation (σt). The predictive equation that uses D84 as the characteristic roughness length successfully predicts velocity in the steep, coarse-bed study reaches, but greatly overpredicts velocity in the low-energy, sand-bed study reaches. The degree of overprediction correlates with a dimensionless wood load metric (α*), which incorporates projected area of wood per unit volume of flow in the reach (α) and average wood diameter (dave). We use this correlation to suggest a wood load adjustment factor for the D84-based predictive equation. The equation that uses σt as the roughness length successfully predicted velocity in the sand-bed reaches, where large wood pieces incorporated into the bed and oriented perpendicular to flow cause most bed elevation variation. In our study sites, frequent and flashy floods appear to reorganize the wood in high-energy reaches, leaving wood that is concentrated in low-velocity zones along the channel margins and streamlined to flow, thus reducing wood resistance compared to similar streams in snowmelt-dominated or spring-fed hydrologic settings. However, in our low-energy, sand-bed study reaches, wood contributes strongly to flow resistance by increasing channel bed and margin complexity.

1. Introduction

[2] The energy available for sediment transport in streams is controlled by the balance between the kinetic energy imparted to water flowing downstream and the dissipation of this energy by internal and external flow resistance, i.e., turbulence and friction [Knighton, 1998]. Quantifying flow resistance requires knowledge of slope, velocity, and discharge or flow depth, the latter three of which are difficult to measure during high flows when most sediment transport is expected to occur. Therefore, researchers have attempted to separate flow resistance into constituent components that are related to more easily measurable stream characteristics [e.g., Einstein and Barbarossa, 1952; Leopold et al., 1964; Millar, 1999]. Grain size [Parker and Peterson, 1980], bed topography [Griffiths, 1989], hydraulic jumps at steps [Leopold et al., 1960; Comiti et al., 2009], and wood load [Buffington and Montgomery, 1999] have all been proposed as predictors of some component of flow resistance.

[3] The components of flow resistance (grain, form, spill, and wood) are commonly treated as linearly additive [Einstein and Barbarossa, 1952; Millar, 1999; Comiti et al., 2009], although flume experiments reveal significant interactions between grain, form, and wood resistance that call this assumption into question [Wilcox and Wohl, 2006]. Increasing discharge will, in most cases, reduce the flow resistance contribution of individual roughness elements, as the elements affect a smaller proportion of the total flow. In this way, high flows are doubly important in transporting sediment and shaping channel morphology: higher energy results from increased discharge and a greater proportion of the energy is available for sediment transport [Yager et al., 2007; Nitsche et al., 2011; Rickenmann, 2012].

[4] The contribution of wood to both the frictional and turbulent components of flow resistance is well documented [Buffington and Montgomery, 1999; Manga and Kirchner, 2000; Curran and Wohl, 2003; Faustini and Jones, 2003], although the hydraulic effects of wood are extremely complicated and not readily modeled numerically. The effects of an individual wood piece depend on the blockage caused by the wood and the respective distances between the wood and the water surface and the wood and the streambed. For wood near the water surface, resistance increases as the Froude number increases, whereas for wood near the streambed, pieces with a diameter much greater than grain or bedform roughness exert a greater influence [Hygelund and Manga, 2003; Mutz, 2003]. The effects also vary through time in channels with readily deformable boundaries. Drag force decreases with time in sand-bed channels, for example, as flow erodes channel boundaries around wood obstructions [Wallerstein et al., 2001]. The effects of wood accumulations or jams depend on the arrangement, density, and mobility of the wood [Daniels and Rhoads, 2004, 2007; Manners et al., 2007].

[5] Direct measurement of wood resistance may be deceptive because interactions between different sources of flow resistance are not necessarily additive [Wilcox and Wohl, 2006]. Consequently, an alternate method for estimating the influence of wood may be preferable. In this study, we compare measured total resistance with resistance predicted by nondimensional hydraulic geometry relationships in order to estimate wood influence. Numerous researchers have successfully employed such equations to relate flow velocity to discharge using slope, gravitational acceleration, and either grain size or bed-elevation standard deviation to transform flow variables into dimensionless equivalents [Rickenmann, 1991, 1994; Aberle and Smart, 2003; Comiti et al., 2007; Ferguson, 2007; Zimmermann, 2010; Rickenmann and Recking, 2011].

[6] The purpose of this research was to evaluate the influence of wood on flow resistance in six 50 m long Costa Rican stream reaches for which we have detailed surveys of the large wood and direct measurements of flow resistance and velocity across a range of subformative discharges. To do this, we estimated velocity using dimensionless relationships with unit discharge, a characteristic roughness length, and slope, and then tested for correlations between wood load and the error of the predictions. Relatively few studies have examined the contribution of wood to hydraulic resistance in natural channels, and we are not aware of any study that examines the influence of wood in a tropical hydrologic setting. The total wood load in these Costa Rican study streams is similar to many temperate streams [Cadol et al., 2009], but it is generally more transient, which may reduce its geomorphic impact [Cadol and Wohl, 2010].

[7] We hypothesized that because tropical streams typically have greater magnitudes of peak discharge per unit drainage area, which may increase wood mobility, wood will contribute less to total hydraulic resistance in this setting than in similarly sized temperate streams. During three years of study at this site, we observed relatively constant wood loads within each channel segment through time, although individual wood pieces had a relatively short residence time [Cadol and Wohl, 2010]. Recruitment of new wood from the riparian zone and fluvial import closely balanced with fluvial export. Reduced wood residence time at least partly reflects the prevalence of frequent, high magnitude, short duration floods, which have high transport capacities. This flow regime may impact channel organization, grain size distribution, wood distribution, and therefore, flow resistance. We thus hypothesized that in steep stream segments, frequent floods maintain a relatively coarse bed and concentrate wood into low-energy sites near the channel margins or transport wood downstream. This would lead to a high grain roughness contribution to total resistance and a reduced wood contribution. We also hypothesized that in lower gradient segments frequent floods deform the sandy bed and facilitate partial burial of wood or downstream transport of wood out of the reach. These effects may increase or decrease total roughness, for example, through bedform initiation or burial, but would both tend to decrease wood roughness.

2. Study Site

[8] Field measurements come from the streams draining La Selva Biological Station, a 16 km2 rain forest preserve in northeastern Costa Rica (Figure 1). La Selva is located at the transition from the Central Volcanic Cordillera to the Caribbean coastal plain at elevations ranging from 40 to 150 m. We selected six representative study reaches from 10 reaches for which wood load was monitored for 3 years [Cadol and Wohl, 2010]. These 10 reaches were a subset of 30 reaches for which wood load was initially measured [Cadol et al., 2009]. Reaches were selected to cover the full range of bed material size and gradient observed at La Selva. All reaches were at least 50 m in length, ranging from 50.1 to 57.4 m.

Figure 1.

Site map showing location of six study reaches within La Selva Biological Station.

[9] Of the six study sites where flow resistance was measured, three are located on Quebrada Esquina, which forms the eastern boundary of La Selva, two are on El Surá, which drains 4.8 km2 of La Selva and Braulio Carillo National Park to the south, and one is on the Taconazo, a tributary of El Surá (Figure 1). The two lowest elevation sites (Taconazo 01 and Sura 03, Figure 1) are on the floodplain of the Río Puerto Viejo and backflooding is observed at these sites when the larger river floods. These two sites have sandy beds, whereas the three Esquina sites (Esquina 17, 20, and 21) are gravel-cobble bedded, and the higher Surá site (Sura 05) is boulder dominated (Table 1).

Table 1. Channel, Flow Resistance, Bed Surface Material, and Wood Data for All Runsa
SiteDate (day/month/year)w (m)h (m)w:h ratioA (m2)Sv (m/s)Q (m3/s)fσt (m)D50 (mm)D84 (mm)Rh/D84Vw (m3)β* (–)aw (m2)α (m−1)α* (–)
  1. a

    Italic indicates sand-bed, low-energy, high-submergence reaches. Additional reach data in Cadol et al. [2009].

Taco 019 Jul. 20072.30.15150.350.00320.1200.0422.630.1122267.10.750.0433.140.1810.029
Taco 014 Mar. 20092.50.12200.320.00210.1140.0361.500.1122259.20.680.0423.300.2050.031
Taco 0120 Jun. 20091.80.09200.160.00350.0860.0143.230.1122241.60.550.0683.050.3720.054
Taco 0113 Nov. 20081.80.10190.180.00250.0740.0133.360.1122243.20.600.0682.890.3270.050
Sura 036 Jul. 20077.90.48173.750.00230.3791.4200.590.12911425.114.530.07131.100.1530.039
Sura 0316 Jul. 20077.60.41183.150.00240.2390.7521.370.12911373.314.000.08229.400.1720.045
Sura 0321 Nov. 20087.30.38192.800.00230.2620.7340.990.12911347.614.800.09732.030.2110.051
Sura 0313 Nov. 20086.90.43163.000.00230.2400.7221.320.12911384.514.410.08831.520.1940.046
Sura 033 Mar. 20097.80.27293.120.00310.2250.7021.300.12911372.416.270.09634.720.2050.051
Sura 0318 Jun. 20086.90.46153.160.00320.2180.6892.430.12911406.414.980.08733.660.1970.047
Sura 056 Jul. 20077.80.35222.740.00980.2350.6434.920.1133656300.5132.680.0207.450.0540.012
Sura 0519 Nov. 20096.80.33212.200.01190.1970.4337.860.1133656300.4721.390.0135.070.0460.010
Sura 0518 Nov. 20087.00.29242.040.01240.2010.4107.010.1133656300.4282.210.0227.210.0710.014
Sura 0516 Jul. 0077.00.29242.050.01070.1710.3518.460.1133656300.4311.600.0165.120.0500.010
Sura 053 Mar. 20097.20.28262.020.01130.1700.3458.530.1133656300.4142.030.0205.920.0580.011
Sura 0521 Nov. 20086.60.24271.620.01260.1680.2728.490.1133656300.3601.570.0195.650.0700.014
Sura 0515 Nov. 20086.80.25281.680.01270.1420.23812.160.1133656300.3641.520.0185.190.0620.012
Sura 0519 Jun. 20097.20.19371.400.01170.1210.16912.070.1133656300.2920.900.0133.230.0460.008
Esq 177 Mar. 20094.90.18270.900.03090.4260.3832.420.1801803500.4830.240.0051.180.0250.004
Esq 178 Jul. 20074.50.21210.940.03170.3550.3334.170.1801803500.5500.140.0030.640.0130.002
Esq 1719 Jun. 20084.50.14310.630.03250.1890.12010.140.1801803500.3810.310.0090.920.0280.007
Esq 1719 Nov. 20083.80.16240.600.03130.1740.10412.870.1801803500.4180.320.0100.960.0310.006
Esq 207 Mar. 20095.90.48122.830.00490.2710.7682.490.216501103.7601.380.0092.660.0180.004
Esq 208 Jul. 20076.40.33192.140.00790.2160.4634.410.216501102.7401.160.0101.980.0170.003
Esq 2021 Jun. 20095.40.14390.750.00940.2340.1741.860.216501101.1971.050.0271.600.0410.010
Esq 2019 Nov. 20085.10.19260.970.01110.1620.1576.360.216501101.6191.350.0262.520.0490.012
Esq 217 Mar. 20096.30.18361.130.00820.6290.7110.290.079902200.7681.430.0223.780.0580.011
Esq 2121 Jun. 20096.30.09700.560.00730.3650.2030.380.079902200.3930.550.0171.820.0570.008
Esq 2119 Nov. 20085.90.11540.640.00780.2660.1710.950.079902200.4780.630.0171.690.0460.007
Esq 2124 Jun. 20084.80.10460.500.00740.3070.1540.640.079902200.4550.790.0282.600.0900.016

[10] Mean annual precipitation from 1963 to 2008 was 4365 mm, with the driest month on average being March with 168 mm, and the wettest months being July and December with 533 and 458 mm, respectively [Organization for Tropical Studies, 2010]. Hurricanes seldom reach the area, but intense rains are generated from November to January by the establishment of a cold front and polar trough that penetrates the air mass over the Caribbean Sea to as low as 10°N [Janzen, 1983]. Flow in the streams of La Selva is highly variable temporally, with flood hydrographs at a gaged stream in La Selva exhibiting flashy behavior [Cadol and Wohl, 2010] (Figure 2).

Figure 2.

Discharge data from site Sura 05 on El Surá, La Selva Biological Station, Costa Rica (drainage area = 3.4 km2) and East Saint Louis Creek, Frasier Experimental Forest, Colorado (drainage area = 8.7 km2).

3. Methods

3.1. Channel Morphology and Flow Measurement

[11] Bed surface grain characteristics were quantified for each reach at the beginning of the study. We measured the intermediate diameter of 100 clasts sampled in a random walk, and calculated median diameter (D50) and the 84th percentile of the grain size distribution (D84). For sand-bed reaches, 100 point samples were categorized qualitatively (very coarse sand, coarse sand, etc.) and each class was assigned a corresponding diameter value for size distribution analysis. We surveyed the thalweg of each study reach at the beginning of the study using a total station and prism, with points taken at 1–3 m intervals to capture breaks in slope. We calculated the standard deviation of the detrended thalweg elevation (σt) as a measure of bed form roughness.

[12] We collected flow resistance data using field surveys and salt slug discharge and velocity measurements. Flow resistance was measured at as broad a range of stages as possible during our field campaigns and each study reach was measured from 4 to 8 times. At the time of each resistance measurement, we surveyed water surface width (w) in five locations and calculated average water surface slope (S) using these same 10 water surface elevation points. Conductivity probes set to a logging frequency of 1 Hz were used to track the passage of a slug of salt water introduced to the stream ∼50 m upstream of the top of the reach. One probe was placed at the top of the reach and one at the bottom. We calculated the harmonic mean travel time of the salt tracer to each probe [Calkins and Dunne, 1970; Waldon, 2004], and divided the difference in mean times by the reach length to find reach average flow velocity (v). Discharge (Q) was calculated using the known mass of salt added to the stream and the integral of salt concentration as a function of time derived from the conductivity probe data. Reach-average cross-sectional area (A) was calculated from continuity as Qv−1, and reach-average depth (h) was calculated as Qv−1w−1. The Darcy-Weisbach friction factor (f) was calculated as a measure of flow resistance:

display math(1)

where g is acceleration due to gravity (9.8 m/s2) and h, S, and v are as described above. Manning's n was calculated, but not used in further analysis because of documented shortcomings of the Manning equation in shallow flows such as those encountered in this study [Ferguson, 2010]. We calculated unit discharge (q) as Qw−1, the discharge per unit top width of channel. We calculated relative submergence (Rh/D84) after calculating Rh as AP−1, where P is wetted perimeter. We assumed a rectangular cross section in the estimate of P, so that P = w + 2h. Detailed cross-section surveys indicate that this estimate of P may underestimate the actual value by as much as 6% in the boulder-bed reaches, but by less than 1% in the sand-bed reaches.

3.2. Submerged Wood Estimation

[13] We surveyed wood within the bankfull limits of each stream prior to each flow resistance measurement using a total station, with points taken at the two endpoints of each wood piece. We measured the midpoint diameter (d) of each piece with a tape. Wood was included in the survey if a piece was in or above the bankfull channel, which was identified visually by bank slope changes and vegetation distribution. Wood that is not in contact with the water during any given flow measurement will not, however, alter flow dynamics. Therefore, the wood survey data were postprocessed in ArcGIS in conjunction with the water surface survey for each flow resistance measurement to find the submerged volume of wood at the time of measurement. A set of wood piece lines were created by linking surveyed piece endpoints and then these were cut by a three-dimensional surface connecting the water surface bank points. All pieces or piece segments that were above the water surface were discarded. This yielded a set of submerged piece lengths (Lws) that were used with the associated d values to find the submerged volume of each piece (Vwi) assuming a cylindrical form, using the equation Vwi = Lws π (d/2)2. The total submerged volume of all pieces within each reach for each resistance measurement (Vw) is the sum of the Vwi values for that run.

[14] There are errors associated with assuming a cylindrical shape for irregularly shaped wood pieces. For example, if the wood tapers such that a truncated cone is a better representation, then the midpoint diameter will underestimate volume. This is typically a small error, on the order of 4% if the large end diameter is twice the small end diameter. In the extreme case of a cone, the calculated cylinder volume will be 75% of the cone volume. Except for a few branching pieces, we did not observe any markedly tapering pieces in the field. The branching of pieces, however, is a greater obstacle to accurate volume estimation, as are decayed pieces of wood that are elongate or arched in cross section, as though a hollow log was shattered into long strips. For branching pieces, which were typically sinuous, length was measured along the curve of the wood and only the largest limb was considered. Diameter, however, was measured in the area before the branching occurred, leading to partially canceling errors. For sheet-like pieces, the average of the thickness and width was used as the diameter. This leads to zero error for pieces that are 0.27 times wider than they are thick, increasing through about 20% overestimation for pieces that are 4 times wider than they are thick, a typical ratio for such pieces. Both branching and sheet-like pieces were rare, together accounting for less than 5% of the pieces surveyed.

[15] Previous investigators have suggested that the projected area of the wood, that is the area normal to the flow direction, is a more relevant metric than volume [e.g., Nepf, 1999], so we also calculated the projected area of each piece of submerged wood (awi) and summed the values within each reach for each run (aw). The angle in space between the central axis of the wood piece and the flow direction (ϕw) is a major control on awi and was calculated using the formula ϕw = cos−1(cos(θh) cos(θv)), where θh is the angle in the horizontal plane between the piece centerline and the nearest thalweg survey segment and θv is the vertical angle of the piece from horizontal. The projected area of each submerged wood piece was calculated as

display math(2)

again assuming a cylindrical form with flat ends, where the first term on the right represents the area projected by the sides of the log and the second term represents the area projected by the flat ends of the log. For logs extending above the water surface, this equation overestimates the projected area by one half times the second term. Such logs were identified and their awi values were adjusted accordingly. Reach-summed values of aw and Vw were then normalized by dividing by the estimated volume of flow in the reach (Vf) to give the projected vegetation density (α = aw/Vf) in units of m−1 [Nepf, 1999] and the dimensionless wood concentration (β* = Vw/Vf). To obtain a dimensionless wood load value that incorporates orientation information (α*), α for each run was multiplied by the average wood diameter, weighted by piece length (dave) for that run. If all logs were to be oriented perpendicular to flow and were to have equal diameters, then α* would be proportional to β*, with β*/α* = π/4.

3.3. Correlations and Regressions

[16] Multiple regression analyses were performed using the variables w, h, w/h, Rh, Q, q, aw, Vw, α, α*, β*, D50, D84, Rh/D84, and σt to predict f. Best subsets of predictor variables were identified using the Akaike Information Criterion (AIC) as the selection criterion [Akaike, 1973]. Unlike R2 values, the AIC penalizes overparameterization. We tested models using from 1 to 6 predictor variables. Regressions, correlations, and AIC values were calculated using the R statistical software package [R Development Core Team, 2011].

3.4. Hydraulic Geometry Analysis

[17] We used nondimensional and dimensional hydraulic geometry equations as predictors of what might be expected in a wood-free situation and compared the results to the field data in order to determine the influence of wood. Dimensional equations that estimate v while taking into account S, q, g, and roughness may use a representative grain size (e.g., D84, D90) as the characteristic roughness length, as in the equation proposed by Rickenmann [1991, 1994],

display math(3)

or they may use the standard deviation of the bed elevation, as in the equation proposed by Aberle and Smart [2003],

display math(4)

[18] Both equations are dimensionally correct, and may be simplified and nondimensonalized using dimensionless versions of v and q. Thus, for each resistance measurement, we calculated

display math(5a)
display math(5b)

after Comiti et al. [2007], and

display math(6a)
display math(6b)

after Rickenmann and Recking [2011]. In equations (5) and (6), D84 may be replaced by any characteristic roughness length [Nitsche et al., 2012]. In this paper we will identify the use of σt as the roughness length with the notation v**(σt) and q**(σt). These nondimensionalizations normalize across bed roughness, and in the case of equations (6a) and (6b) slope as well, but do not explicitly account for wood load. Nonetheless, wood has the potential to directly affect σt where logs are incorporated into the streambed, where jams trap sediment wedges, and where flow around logs induces scour.

[19] Ferguson [2007] recognized that combining equations (3) and (5a), (5b) gives a hydraulic geometry equation for shallow flows that is similar in form to hydraulic geometry equations developed from the Manning-Strickler conceptualization of resistance in deep flows. He neatly synthesized these preexisting lines of research into the nondimensional hydraulic geometry equation

display math(7)

where a and m are empirical constants that may obtain differing values between relatively shallow and deep flows, with the value of Rh/D84 differentiating shallow and deep flows. For deep flows, which fit the Manning-Strickler conceptualization, m = 0.4 and a = aMS ≈ 5–8, depending on the data used to fit the equation. For shallow flows, which fit the roughness layer conceptualization, m = 0.6 and a = aRL ≈ 1–4, depending on assumptions made about the obstacles and roughness height [Ferguson, 2007]. Equation (7) can be thought of as discharge based, in that it relates a measure of resistance to discharge. It has depth- or submergence-based equivalents of the form (8/f)1/2 = aMS(Rh/D84)1/6 for deep, Manning-Strickler type flows, and (8/f)1/2 = aRL(Rh/D84) for shallow, roughness-layer resistance flows [Ferguson, 2007]. Ferguson [2007] combined these two into a variable power equation (VPE),

display math(8)

which can be used across the range of relative depths. In our analysis, we use aMS = 6.5 for deep flows and aRL = 2.5 for shallow flows, following Rickenmann and Recking [2011].

[20] The dimensionless parameters v** and q** allow for further simplification, as equation (7) can now be rewritten as

display math(9)

[Rickenmann and Recking, 2011; Nitsche et al., 2012]. The previously cited values of a are applicable if using D84 as the roughness length in calculating v** and q**, and if σt is used as the roughness length, then equation (4) is equivalent to the shallow water case of equation (9) (m = 0.6) where a = 0.9. Rickenmann and Recking [2011] plotted v** against q** for a large data set and reported the data to be fit well by the equation

display math(10)

which is a logarithmic matching combination of the two power functions for deep and shallow flow reported by Ferguson [2007]. Equation (10) is an explicit, discharge-based equivalent to the submergence-based equation (8) with aMS = 6.5 and aRL = 2.5 [Rickenmann and Recking, 2011].

[21] In our analysis, we used equation (10) with characteristic roughness length D84 as one possible indicator of wood-free resistance. As an alternative indicator, we used equation (9) with roughness length σt and empirical constants consistent with equation (4) [Aberle and Smart, 2003]. We compared predictions of v** to measured values and tested for correlations between prediction error and wood load metrics to explore possible correction factors that improved predictions. We also explored correction factors that incorporated slope or stream power, as surrogates for the ability of the flow to mobilize and reorganize wood, because wood that is concentrated near the margins of a channel may contribute less resistance than an equal load spread evenly throughout the channel.

4. Results

4.1. Correlations and Regressions

[22] Calculated values of f varied from 0.17 to 12 and tended to decrease at a site with increasing discharge (Figure 3). Both Vw and aw varied through time as a result of wood inputs and outputs in addition to stage-driven variation (Table 1). β* and α* tended to decrease as stage and discharge increased, but not monotonically because of the import and export of wood through time and the irregular vertical distribution of wood.

Figure 3.

Variation of friction factor (f) with discharge (Q).

[23] Wood metrics alone were poor predictors of f, both within sites and among sites. The correlation coefficient (ρ) between f and β* for all measurements at all sites combined was −0.49, and for f and α* was −0.44. Bed material was a better predictor of f, with a ρ of 0.74 between f and D84 for all measurements at all sites, and ρ of 0.75 between f and D50. Two sites had sand-dominated bed material. The median grain size at the other four sites ranged from 50 to 365 mm (Table 1). No other single variable was well correlated with f.

[24] The best subset multiple regression model limited to four predictors selected D50, q, σt, and Rh/D84 as the predictor variables (Table 2). All four parameters in this model were significant at the p = 0.02 level, and the multiple R2 value was 0.78. The model indicates that f correlates positively with D50, Rh/D84, and σt, and negatively with q. The best three-parameter model included D50, q, and σt, with a multiple R2 value of 0.73, and the best two-parameter model included D50 and q, with a multiple R2 value of 0.62 (Table 2). The R2 value of a regression using D50 alone, the best single predictor, was 0.56. The wood-related variables were never selected as a best subset model until six parameters were forced into the model; however, the second best five-parameter model included projected wood area (D50, q, σt, Rh/D84, and aw). Similarly, the four-parameter model that included D50, q, σt, and aw was nearly as good (multiple R2 = 0.765) as the best four-parameter model. The maximum parameter p value in this model was 0.055, for aw, and the model indicates that f correlates positively with D50, σt, and aw, and negatively with q, as we expected.

Table 2. Regression Models: Parameters and Statistics
PredictorsaR2 (mult.)bAICcHighest p ValuedModel p Value
  1. a

    Predictors are listed in order of increasing p value (decreasing value of |t|). Smaller p values indicate greater statistical significance for that predictor. A plus sign indicates a positive individual parameter estimate, and a minus sign indicates a negative estimate.

  2. b

    Multiple R2 value.

  3. c

    Lower AIC values indicate better models, but there is no meaning to the absolute value.

  4. d

    Highest p value for an individual predictor. All models had model p values much smaller than 0.001.

D50+     0.56146.9<0.001<0.001
D50+q    0.62144.50.048<0.001
D50+qσt+   0.73136.90.010<0.001
D50+qσt+Rh/D84+  0.78132.40.020<0.001
D50+qσt+aw+  0.77134.40.055<0.001
D84+qσt+Rh/D84+w/h 0.80131.10.078<0.001
D50+qσt+Rh/D84+aw 0.80131.50.136<0.001
D50+qw/hawVw+Rh/D840.82130.40.118<0.001

4.2. Hydraulic Geometry

[25] Estimating velocity by first calculating v** using equation (10) with D84 as the roughness measure and then converting back to v yielded good agreement with measured velocity in the two steep boulder-bedded reaches, Esq 17 and Sura 05 (Figure 4a). Equation (10) underestimated velocity in reach Esq 21, a plane-bed, gravel-dominated reach (Figure 4a). It overestimated velocity in reach Esq 20, a reach that included a large 1 m deep 15 m long pool in its upstream end, as well as in reaches Taco 01 and Sura 03, two sand-bed reaches with much higher wood load values (β* and α*) than the other sites. Of the two boulder-bed reaches, Esq 17 was 4–5 m wide and had a regular, channel-spanning step-pool sequence, while Sura 05 was 7–8 m wide and had a more irregular step and pool distribution with few bedforms that spanned the channel, but equation (10) appeared to perform equally well in both. For comparison, we calculated v* using equation (7) and then converted back to v and found nearly identical results (not shown in Figure 4), which is unsurprising considering that equation (10) is a continuous combination of the deep and shallow cases of equation (7) [Rickenmann and Recking, 2011]. Estimating velocity using equation (9) with roughness length σt yielded good estimates at the two sand-bed reaches, Taco 01 and Sura 03, as well as at the boulder bed reach with a better developed step-pool sequence, Esq 17, and the large pool reach, Esq 20 (Figure 4b). Equation (9) overestimated velocity at the irregular boulder-bedded reach, Sura 05, and underestimated velocity at the plane-bed reach, Esq 21. We have low confidence in the representativeness of our measurement of σt in Sura 05, potentially leading to the observed overestimation in this reach (see section 5.1).

Figure 4.

Relationship between observed velocity and velocity predicted using (a) equation (10) with D84 as roughness length and (b) equation (9) using σt as roughness length. Dashed lines indicate perfect fit.

[26] Comparing observed resistance to predicted resistance using equation (8) showed good agreement in the two reaches with highest D84 (Figure 5a, Table 1). The two reaches with lowest D84 and high submergence had greater resistance than predicted. Similar trends were found for the relationship between observed v** and the v** predictions of equation (10) (Figure 5c). Observed values in the relatively shallow roughness-length regime were reasonably close to the prediction envelope defined by the range of a values suggested by Ferguson [2007]. In the deeper Manning-Strickler flow regime, however, observations fell well below prediction. The value of a would need to be ∼1 in order to match the data, well below the suggested range of 5–8. In contrast, the bed-form roughness approach, predicting v**(σt) from q**(σt) using equation (9) parameterized according to the results of Aberle and Smart [2003], did not have systematic errors with changing q**(σt) and typically yielded good fits to the data (Figure 5b).

Figure 5.

(a) Variation of (8/f)0.5 with relative submergence (Rh/D84). The lines represent three approaches to describing friction explored by Ferguson [2007]: Manning-Strickler, (8/f)1/2 = aMS(Rh/D84)1/6; roughness-layer resistance, (8/f)1/2 = aRL(Rh/D84); and a variable power equation (VPE) that combines the two, equation (8). We use aMS = 6.5 and aRL = 2.5, following Rickenmann and Recking [2011]. (b) q**(σt) versus observed v**(σt) and predicted v**(σt) using equation (9) with m = 0.6, a = 0.9, and σt for the roughness length [Aberle and Smart, 2003]. (c) q**(D84) versus observed v**(D84) and predicted v**(D84) using equation (10) [Rickenmann and Recking, 2011]. Envelopes are shown for the range of aMS values from 5 to 8 and aRL values from 1 to 4. (d) q**(D84) versus observed v**(D84) (colored by site); q**(D84) versus predicted v**(D84) using a normalized wood load (α*)-based adjustment, equation (11) (black); and q**(D84) versus predicted v**(D84) using an α* and slope-based adjustment, equation (12) (pink).

[27] The percent error of the v**(D84) prediction from equation (10), calculated as [v**(equation (10)) − v**(equation (6a))]/v**(equation (6a)), and the value of α* were well correlated (ρ = 0.90), with the data clustering into a high wood load group and a low wood load group (Figure 6a). The percent error of the v* prediction from equation (7) and the value of α* were likewise well correlated (ρ = 0.89). However, the percent error of the v**(σt) prediction from equation (9) was poorly correlated with any wood metric (Figure 6b). We used the regression of the v** prediction error against α* to create an adjustment factor (a2) for equation (10) of the form

display math(11)

where b is the slope of the v** prediction error regression with intercept set to 0 (Figure 6a). This adjustment factor approach is similar in principle to that employed by Nitsche et al. [2012] to account for boulder concentration. Our data yield a value of 45.9 for b. If β*, which is easier to measure, is used as the wood metric instead of α*, our data yield a b value of 26.8 and result in similar a2 values. Multiplying the result of equation (10) for each run by the a2 calculated from α* for that run yields a wood-corrected prediction of v** (Figure 5d). The correction factor is 1 for no wood, and decreases as wood load increases. The run with the highest value of α*, 0.0524 for Taco 01 in summer of 2009, yielded a correction factor of 0.29, reducing the v** estimate to about one third of its initial prediction. The correction factor improved predictions at high-wood sites and had little effect at low-wood sites, but it reduced accuracy at reach Sura 05, where wood loads are intermediate but slope and stream power are relatively high and over 64% of the wood is concentrated near the channel margins (see Cadol et al. [2009] for stream power and lateral wood distribution data).

Figure 6.

(a) Correlation of normalized wood density (α*) with the error of v** predicted using equation (10), calculated as [v**(equation (10)) − v**(equation (6a))]/v**(equation (6a)). D84 is used as the roughness length in calculating q** and v**. The regression line was assigned an intercept of 0. (b) Correlation of normalized vegetation density (α*) with the error of v**(σt) predicted using equation (9) with m = 0.6, a = 0.9, and σt for the roughness length in calculating q** and v**. The regression line excludes data from Sura 05 due to low confidence in the representativeness of σt measured at that site.

[28] If the influence of wood on flow resistance is marginalized in steep streams, we can modify equation (11) to account for this by dividing α* by slope or stream power. We obtained good results calculating the adjustment factor with the equation

display math(12)

with 70% of the predictions falling within 25% of the measured value, but there were no improved fits using stream power to adjust α*. In any case, such a complex adjustment factor should probably not be developed with our small data set due to the risk of spurious or site-specific correlations.

5. Discussion

5.1. Wood Contribution to Resistance

[29] Resistance was adequately assessed by equations (7) and (10) in the reaches with coarse beds and low relative submergence, but not in the sand-bed reaches where D84 was much smaller than the dominant roughness elements, whether wood or bedforms. The six study reaches cluster into similar groups using several factors, making interpretation difficult. The low-submergence reaches had water surface slopes > 0.005, D84 > 100 mm, wood loads (α) < 0.1 m2/m3, and relative roughness values indicative of shallow flow. The high-submergence reaches had gentler slopes, sandy bed material, greater wood loads (α > 0.15 m2/m3) and were classified as deep flow. σt did not differ systematically between the two groups. Because equation (10) includes S and D84 in its implementation, it is reasonable to assume that variation in these parameters should not contribute excessively to its failure, unless these values have moved beyond the calibration range. Rickenmann and Recking's [2011] calibration data set had dense data up to q** = 104, and sparse data that maintained the same trend to nearly q** = 108. The highest q** value in our data set is 3.8 × 104, well within this range.

[30] If systematic failure of equation (10) is discounted, then the unaccounted-for influence of wood may explain the overprediction of velocity in the sand-bed reaches. The relative success of equation (10) in the gravel- to boulder-bed reaches, in spite of the measured presence of wood, can be explained by the effect of the frequent floods that occur in the tropical climate and the relative steepness of these reaches. Floods appear to effectively reorganize the wood, conveying many pieces downstream to lower gradient reaches and only leaving those pieces that are in a streamlined orientation or in low-energy zones along the channel margin. In other words, we infer that wood in the steep reaches contributes very little effective hydraulic resistance, so that neglect of wood in equation (10) does not result in underprediction of measured resistance.

[31] The best performance of equation (10) was in the steepest, coarsest reaches. It overpredicted resistance in Esq 21, a plane-bed reach with a nearly uniform gravel bed. It is possible that this morphology is underrepresented in the training data set and has significantly less resistance than a step-pool or pool-riffle channel with similar D84 and S. Equation (10) underpredicted resistance in reach Esq 20, most likely because of the large pool in that reach, which created backwater conditions that are inconsistent with the theoretical development of equations (7) and (10). Esq 20 is also the only site for which markedly different velocity estimates are found for different salt slug data analysis methods. When v** was recalculated using the travel time of the salt peak, rather than the harmonic mean travel time of the salt slug, the performance of equation (10) at Esq 20 improved. There was apparently a central jet through the pool, and using the salt peaks alone discounted the important proportion of the salt that took slower paths through the pool. We followed the recommendation of Waldon [2004] and Zimmermann [2010] in using the harmonic mean travel time to calculate velocity, but other data sets that measure velocity with salt tracers may not have employed this practice, potentially leading to unreliable estimations in reaches with similar hydraulics.

[32] In contrast to equation (10), equation (9) using σt performed relatively well in the sand-bed reaches as well as several of the coarse-bed reaches, and only performed worse than equation (10) in Sura 05. The underprediction of resistance in Sura 05, a steep, boulder-bed reach, is easily accounted for by the inference that the ∼2 m spacing of thalweg elevation points that we collected does not capture bed elevation variation in adequate detail for this analysis [Yochum et al., 2012]. The coarse bed (D84 = 630 mm) creates numerous peaks and crevices that alter flow but that were not surveyed, although the step-pool/cascade morphology is well captured in the survey, with at least five distinct pools present in the reach with an average crest-to-crest step height of 0.2 m.

[33] The underprediction of velocity in the plane-bed morphology reach, Esq 21, is more difficult to explain. The two predictions, using either D84 or σt as roughness length, are in agreement at this site, and the field data here would match both predictions equally well if velocity measurements were reduced by 30%. But although there is much less attenuation of the salt slug in this reach compared to the others, there is no indication that the data are unreliable. Interestingly, this site plots closer to the values predicted by the Manning-Strickler approach of Ferguson [2007] rather than the roughness-layer resistance approach (Figure 3b) in spite of the relatively low value of relative submergence (Rh/D84 = 0.39–0.77). A possible explanation could be that shear stresses are particularly low in this low-gradient, small-flow-depth, flat-bedded reach compared to other study reaches.

[34] The positive correlation between wood load and v** estimation error from equation (10) (Figure 6a) suggests that wood is an effective source of resistance in some reaches. And the success of equations (4) and (9), using σt as roughness length, in the sand-bed reaches suggests that the effectiveness of wood in contributing to flow resistance is driven by its ability to increase channel complexity as it is incorporated into the substrate. Field observations confirm that positive deviations in the longitudinal profiles of these reaches are typically at submerged log steps, and negative deviations are typically at locations where the channel is partially blocked by wood and concentrated flow has scoured the bed, similar to previous observations in sand-bed streams with wood [Wallerstein and Thorne, 2004]. This finding is also consistent with results from steeper streams in Colorado, USA, where wood in contact with the bed influences flow resistance and where thalweg elevation deviation, as influenced by wood, is a better predictor of resistance than grain size alone [Yochum et al., 2012]. Thus, the effectiveness of wood in creating roughness is inversely related to the capacity of the stream to mobilize wood. Because bed grain size is likely to be an indicator of transport capacity, we would expect coarser bedded channels to have less sensitivity to wood load for a given climate or flow regime.

[35] These two inferences, that flood-streamlined wood contributes little to resistance and that persistent wood primarily influences flow resistance by altering channel shape, suggest that wood orientation is as important to quantify as wood abundance. These interpretations also agree with previous modeling work on the importance of wood orientation [Cherry and Beschta, 1989; Gippel, 1995; Braudrick and Grant, 2000; Wallerstein et al., 2001; Hygelund and Manga, 2003]. Nonetheless, the correlation between β*, which neglects wood orientation, and the magnitude of error in the v** prediction using equation (10), ρ(β*, Err_v**) = 0.87, is slightly better than between α and the v** error, ρ(α, Err_v**) = 0.84, and only slightly worse than between α* and the v** error, ρ(α*, Err_v**) = 0.90.

[36] In streams where D84σt, using D84 as the characteristic roughness scale gives results that are no worse than those found using σt. Site Sura5 would probably fit in this category as well if we had taken more frequent thalweg elevation points, though as it is D84 noticeably outperforms σt (Figures 5b and 5c). This conclusion is in agreement with the findings of the field study of Nitsche et al. [2012], but in disagreement with the flume data analyzed by Aberle and Smart [2003]. But phrased another way, it appears that σt (measured at an appropriate scale) is equally good at predicting flow resistance as D84 in coarse-bedded situations and is significantly better than D84 in fine-bedded situations. From the point of view of applying wood load corrections to equation (10), the difficulty is in determining whether high σt values that dominate over D84 are caused by wood (as in the case of Sura 03 and Taco 01) or not (as may be the case for Esq 20). Stream power or slope, as a surrogate for wood-mobility, may address this question, as suggested by the improved performance of equation (12) relative to equation (11).

[37] Another issue regarding wood mobility is that our sand-bed sites may collect more wood than is typical in tropical streams of similar gradient because of the influence of backflooding from the Rio Puerto Viejo. When the larger river floods, the rise in stage can produce nearly zero-velocity flow conditions at sites Taco 01 and Sura 03, although this did not affect any of our resistance measurements. Backflooding temporarily prevents downstream wood transport and floats some loose pieces that are then redeposited in random orientations. This does not necessarily stop all transport through the reach, because local high flows do not always correlate with regional floods, but we do expect this backflooding to contribute to greater wood retention.

5.2. Variation in Wood Influence With Gradient and Climate

[38] This research highlights the variability of the influence of wood on flow resistance. The influence of wood depends on gradient, flow regime, and any other factors that may alter the ability of the stream to mobilize wood. Wood is more easily transported through river networks to low-gradient reaches than rocks of equivalent size so that in reaches without boulders or bedrock, which are typically low gradient, wood pieces may be the largest roughness elements present [Wohl and Cadol, 2011]. In unaltered tropical watersheds with forested headwaters, we expect a constant input of wood to the downstream, low-gradient reaches, creating roughness, dissipating energy, and contributing to aggradation and possibly increased gradients in alluvial reaches. Removal of snags or clearing of forests would remove this source of resistance, possibly leading to channel erosion, as observed on the Cann River, Australia [Brooks et al., 2003].

[39] Large floods have the potential to reorganize wood and reduce resistance, especially in steep reaches. In environments with fewer flows capable of mobilizing wood, we expect fallen trees to persist in the stream in unstreamlined positions, even at relatively high gradients. Wood load then primarily depends on the decay rate; as wood decays into smaller pieces, the likelihood of transport increases [e.g., McHenry et al., 1998]. In this situation, the expected resistance from wood would be higher than in a flow regime with greater transport capacity for wood, because wood has not been reorganized by the flow. Comparing our high-energy streams against the equally steep streams studied by Yochum et al. [2012] in Colorado supports this interpretation. In Colorado, where less intense snowmelt floods are the primary source of high flows (Figure 2), wood commonly rests on the streambed and is oriented perpendicular to flow or at a high angle to flow, creating substantial variation in bed elevation. In these streams, thalweg elevation deviation is a better predictor of resistance than grain diameter [David et al., 2010; Yochum et al., 2012]. We may extend this reasoning to even more stable flow regimes by considering the spring-fed Cultus River, Oregon, studied by Manga and Kirchner [2000]. Here, annual peak flows are not observed to exceed twice the mean flow, and wood introduced from the banks remains perpendicular to flow with very low probability of mobilization. Wood spacing is the dominant control on shear stress partitioning between the wood and the bed material, with wood contributing nearly half of the flow resistance at the time of the study [Manga and Kirchner, 2000].

[40] In Costa Rica, where the flow regime is flashier and floods are of higher magnitude, wood is reorganized by flow and grain size alone is a good predictor of resistance in steep, coarse-grained streams. This is in spite of the high productivity of the tropical forest and the greater wood input to the Costa Rican streams relative to streams studied in Colorado and Oregon [Lienkaemper and Swanson, 1987; Wohl and Goode, 2008; Cadol and Wohl, 2010]. Even though total wood load may be similar, the wood in high-energy Costa Rican streams is reorganized to minimize flow resistance and is concentrated near the banks [Cadol et al., 2009]. A possible result is that tropical headwaters are steeper than temperate headwaters, because they have fewer logjams that can create forced alluvial reaches [Montgomery et al., 1996]. This may also lead to tropical headwaters being less morphologically sensitive to forest removal than snowmelt- or spring-dominated headwaters because tropical instream wood is relatively ineffective at creating hydraulic resistance. In the downstream, low-gradient alluvial reaches, however, greater wood flux and temporary wood storage may lead to channel gradients in equilibrium with greater resistance, thus creating greater sensitivity to upstream forest removal.

6. Conclusions

[41] A total of 30 flow resistance measurements at six sites across a range of subformative discharges at our tropical study area indicate that the nondimensional hydraulic geometry equation of Ferguson [2007] and Rickenback and Recking [2011], equation (10), which does not consider any possible effects of wood, performs well in steep, high-energy reaches with boulder to gravel beds, in spite of the significant wood delivery documented at the sites [Cadol and Wohl, 2010]. The reorganization of wood during the frequent tropical floods may account for the apparently negligible contribution of wood resistance to total resistance.

[42] In low gradient, sand-bed reaches, however, equation (10) underpredicts resistance in a way that is roughly proportional to dimensionless metrics of wood load (Figure 6a), suggesting that wood may be an important component of total resistance. Additionally, the hydraulic geometry equation of Aberle and Smart [2003] converted to a dimensionless form, equation (9), which considers the standard deviation of the longitudinal thalweg elevation profile, performs well in the low-energy reaches. This suggests that the major mechanism by which wood increases resistance in these sand-bed streams is by creating steps and chutes as wood is incorporated into the bed.

[43] The relative unimportance of wood in our high-gradient tropical study sites contrasts with the documented importance of wood in contributing to roughness in steep snowmelt-dominated [Yochum et al., 2012] and spring-fed [Manga and Kirchner, 2000] hydrologic regimes. We infer that flows in the snowmelt streams are not able to reorganize the wood as effectively as the tropical streams, leaving wood pieces to be incorporated into the channel bed in whatever orientation they fell. Thus, both gradient and flow regime must be considered when evaluating the relative contribution of wood resistance.

Acknowledgments

[44] We would like to thank our field assistants who helped collect the flow resistance data: Beth Cadol, who assisted with all of the field campaigns, Sarah Schmeer, Patrick Kelly, Holly Hagena, Liz Gilliam, and Zan Ruben. Critical logistical support was provided by the staff of La Selva Biological Station under the auspices of the Organization for Tropical Studies. The manuscript benefited greatly from the insightful and constructive comments of three anonymous reviewers. Comments from Sara Rathburn and Dan Cenderelli also helped improve an earlier version of this work. This research was funded by National Science Foundation grant EAR-0808255, with supplemental funding from the Geological Society of America student research grant program.