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Self-organization of river channels as a critical filter on climate signals

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Science  06 May 2016:
Vol. 352, Issue 6286, pp. 694-697
DOI: 10.1126/science.aad3348

Filtering out the effect of large floods

Large floods should seemingly influence the depth and width of rivers. Phillips and Jerolmack, however, suggest that the self-organization of bedrock river channels blunts the impact of extreme rainfall events. River channel geometries from a wide range of course-grained rivers across the United States show that larger floods have very limited additional impact on channel geometry. River channel sculpting does increase as flood size increases, but the effect is most pronounced for moderate floods. This relationship may explain the long-term stability of rivers across shifts in climate.

Science, this issue p. 694

Abstract

Spatial and temporal variations in rainfall are hypothesized to influence landscape evolution through erosion and sediment transport by rivers. However, determining the relation between rainfall and river dynamics requires a greater understanding of the feedbacks between flooding and a river’s capacity to transport sediment. We analyzed channel geometry and stream-flow records from 186 coarse-grained rivers across the United States. We found that channels adjust their shape so that floods slightly exceed the critical shear velocity needed to transport bed sediment, independently of climatic, tectonic, and bedrock controls. The distribution of fluid shear velocity associated with floods is universal, indicating that self-organization of near-critical channels filters the climate signal evident in discharge. This effect blunts the impact of extreme rainfall events on landscape evolution.

Understanding the control of climate on the geometry and erosion rate of rivers is essential for reconstructing the geologic history of landscapes and for predicting the response of rivers to human-accelerated climate change. A natural assumption is to link river erosion to climate through precipitation (13), yet demonstrating a clear relation is unexpectedly challenging (47). One reason is that bedrock river incision occurs primarily by abrasion due to the collision of particles with the stream bed (8) and “plucking” of loose blocks (2), and therefore it depends on sediment supply as well as precipitation. Another reason is that bedrock channel geometry both influences and adjusts to incision rate (4, 911). The effects of climatic variability (1113) and bedrock channel geometry (9, 10) on river incision rates have been explored primarily with numerical models, but empirical observations remain limited.

In contrast to the case of bedrock systems, our understanding of the geometry of alluvial rivers (channels whose bed and banks are composed of mobile sediment) is built upon two empirically vetted theoretical principles. The first is “geomorphic work,” in which the wide range of flows generated by climate—defined here as the magnitude, frequency, and phase of precipitation—is represented by a characteristic flood (14). This “bankfull” flood is the event whose frequency and magnitude combine to move the most sediment in the long-time limit, and it dictates channel size (Fig. 1). The second principle applies to gravel-bed rivers (median bed particle diameter, D ≥ 10 mm), where sediment moves predominantly as bed load. Gravel-bed rivers adjust their geometry so that the width-averaged fluid shear velocity (U*, meters per second) slightly exceeds the critical value (U*c) at bankfull conditions. This is called the near-threshold channel, for which data and theory indicate that U*/U*c ≈ 1.1 (Fig. 1) (15, 16). Some studies, however, suggest that this treatment ignores details of climatic variability that may exert a substantial influence on landscape evolution (1, 17, 18). Observations reveal that the statistical distributions of discharge in many rivers possess a power-law tail (12, 13, 19), whose exponent changes with climatic setting (17). These observations have been interpreted to mean that channel shape may be controlled by climate and, for rivers with sufficiently heavy-tailed (log-log slope < –2) discharge distributions, that the rate of sediment transport could be dominated by extreme events due to climatic variability (17), which prevents rivers from achieving an equilibrium geometry over geologic timescales (1, 3). Understanding the role of rivers in landscape evolution requires reconciling the proposed importance of climatic variability on channel form and dynamics with the apparent equilibrium behavior implied by near-universal hydraulic geometry scaling relations (15, 20, 21).

Fig. 1 Definition sketches.

(A) Channel cross section illustrating adjustment to near-threshold bed-load transport; red regions are above the threshold of motion. The top panel shows flow exceeding bankfull conditions that induces transport on the banks, resulting in erosion and widening of the channel, which returns the system to near-threshold conditions (bottom). U*bf was computed from channel surveys of S and hbf. (B) Definition sketch of a flood, with relevant parameters shown. The gray shaded area (from the starting time ts to the finishing time tf) represents the part of a flood that is included in the integral for potential transport, which is calculated as Embedded Image for U* ≥ U*c (26).

Climatic effects on river dynamics are typically characterized by discharge (Q, cubic meters per second), which is strongly related to precipitation (22), and erosion is often modeled using stream power (the product of discharge and slope, S). Bed-load motion, however, is driven by applied fluid momentum represented by the shear velocity, U*= Embedded Image, where g is gravity and h (in meters) is the width-averaged flow depth (Fig. 1B). For within-channel flows, shear velocity scales only weakly with discharge (U* ~ h1/2~ Q1/6) (15), and the relation is even weaker when flows exceed bankfull conditions and increases in Q contribute primarily to overbank flooding (20). We propose a set of parameters to examine the relations among hydrology, channel geometry, and bed-load transport for both bedrock and alluvial rivers, using a common framework: (i) the bankfull shear velocity, U*bf (Fig. 1A); (ii) the distribution of floods, f(U* ≥ U*c), characterized by the frequency-magnitude distribution of flows exceeding critical conditions (Fig. 2D); and (iii) the potential transport volume per unit width of bed load during a flood, T (Fig. 1B) (23). For bedrock-influenced rivers, the actual transport rate depends on the degree of alluvial cover and will be less than T, but T should nevertheless characterize the relative magnitude of different floods. We hypothesize that alluvial and bedrock-influenced gravel-bedded streams are near-threshold channels, and we predict that U*bf/U*c ≈ 1.1 (15, 16) and that peak sediment transport (T) occurs as a result of intermediate floods, not the largest floods (14).

Fig. 2 The Mameyes River case study.

(A) Lidar map of the Mameyes River catchment (red outline). The blue diamond shows the location of the USGS stream gage, and the red and green circles indicate the locations of the alluvial and the steep bedrock-alluvial tributary tracer studies, respectively. Flow is from south to north along the blue trace of the river. (B) Representative hydrograph from 2003 of discharge (blue) and shear velocity (red), measured every 15 min and normalized by the threshold of motion. The inset shows a single storm event. (C) Magnitude-frequency distribution of discharge (blue line, shown next to a slope of –2 for comparison) and of shear velocity (red line, shown next to an exponential function for comparison), indicating heavy-tail and thin-tail behavior, respectively (CDF, cumulative distribution function). A log-log slope shallower than –2 indicates infinite variance, meaning that a characteristic discharge cannot be obtained. (D) Magnitude-frequency distribution (semi-log scale) of U* (blue line), which is well described by an exponential function for flows in excess of U*c. The red diamond and blue circle represent bankfull shear velocity (U*bf) and the average flood 〈f(U* ≥ U*c)〉, respectively. The inset shows a PDF of ln(T).

We undertook a study of the Mameyes River in the Luquillo Critical Zone Observatory in northeastern Puerto Rico (Fig. 2A), which is subject to frequent large flash floods (23) due to orographic storms and hurricanes (24). We used tracer cobbles placed in a steep mixed bedrock-alluvial tributary (S = 1.2 × 10−1, D = 120 mm) and a lower-gradient alluvial reach (S = 7.8 × 10−3, D = 110 mm) to estimate U*c for each site and to demonstrate that bed-load transport is proportional to T (25, 26). Discharge records for the alluvial reach (Fig. 2A) show heavy-tailed (nonconvergent) scaling (Fig. 2C) (27). The data for the mixed bedrock-alluvial tributary are of insufficient duration for similar statistical analysis. Recorded peak discharges during flash floods can be up to 20 times the discharge associated with critical conditions (Qc = 22 m3 s−1) (Fig. 2B). Although the threshold of motion is often exceeded more than 20 times per year (28, 29), the associated shear velocity values for recorded floods are restricted to the range U*c ≤ U*2U*c (Fig. 2B). Even the largest floods are near-threshold.

The frequency-magnitude scaling of U* converges to an exponential function for above-critical values (Fig. 2D), and we computed 〈f(U* ≥ U*c)〉/U*c = 0.38 m s−1/0.35 m s−1 = 1.1 (23), where the angle brackets denote the ensemble average value. The estimate for the channel-forming flood [〈f(U* ≥ U*c)〉= 0.38 m s−1] is close to the bankfull shear velocity (U*bf = 0.40 m s−1) determined independently from morphologic surveys (24) of the channel (Fig. 1A); both are in agreement with near-threshold channel theory (15). As U* approaches the maximum value, the tail decays faster than exponentially, indicating undersampling of the largest events (27, 28). The probability density function (PDF) of T (Fig. 2D) possesses a peak, indicating the existence of a characteristic and moderate flood that transports the most sediment. Having shown that the hydrologic record of the mixed alluvial-bedrock Mameyes River displays near-critical behavior, we used measurements of channel geometry, slope, and grain size (fig. S1, A to E) (23) collected across bedrock and alluvial areas to test the generality of this result for the length of the river. Our calculations reveal that the ratio U*bf/U*c has no trend with downstream distance (〈U*bf/U*c〉= 1.3), despite substantial downstream decreases in channel slope and bedrock influence (fig. S1G), and indicates near-threshold transport throughout. Thus, an extreme distribution of discharge is not sufficient evidence to demonstrate control by infrequent, large flood events. The river's ability to adjust its width, depth, and grain size to near-critical conditions appears to decouple the distribution of U* from the distribution of discharge imposed by climate. This critical filter confirms model predictions (30, 31) that threshold sediment-transporting systems can shred external environmental signals.

We examined a wide range of gravel-bedded alluvial and bedrock-influenced streams located near U.S. Geological Survey (USGS) gages (23) across the United States (Fig. 3) to test the generality of the critical filter. The distributions of discharge [f(Q ≥ Qc)] vary widely among the rivers examined (Fig. 4A), as expected from previous research that indicates that this is predominantly an effect of spatial variation in climate (fig. S4) (12, 17, 23). In contrast, we can describe f(U* ≥ U*c) with a global exponential function (Fig. 4B) (23). The average value for all streams is in agreement with near-threshold channel theory (15). Our data show that this characteristic flood magnitude is about equal to the morphologic U*bf (Fig. 4C) (23), verifying the adjustment of both bedrock-influenced and alluvial rivers to the same near-critical conditions. The agreement is best for field sites where U*c has been locally determined from observations (23), suggesting that much of the scatter in Fig. 4C is due to the notorious problem of estimation errors in determining the threshold of motion (26). We found a peak in T for all rivers that corresponds to moderate floods (Fig. 4C, inset), providing additional evidence that extreme events do not dominate channel form (fig. S7).

Fig. 3 Gaging stations used in this study.

(A) Map of the continental United States and Puerto Rico (inset) with the locations of alluvial and bedrock-influenced stream gages used in this study (26), indicating where U*c was measured or estimated. The easternmost gaging station in the map of Puerto Rico is the Mameyes River. (B) Halfmoon Creek (S = 0.0084, D = 50 mm), an alluvial-gravel river in the Colorado Rocky Mountains. (C) Bear Creek (S = 0.021, D = 152 mm), a bedrock-influenced river in Maryland. (D) Umpqua River (S = 0.00067, D = 51 mm), which drains a tectonically active region in the Oregon coastal and Cascade mountains. (E) Alluvial portion of the Mameyes River (S = 0.013, D = 152 mm). [Photo credits: D. N. Bradley (B), S. M. Baker and USGS (C), J. E. O'Connor (D)]

Fig. 4 Demonstration of the critical filter for all rivers examined.

(A) Discharge magnitude-frequency distributions for all rivers (n = 185) show high variability; normalization by the mean excess discharge does not collapse the data (fig. S4) (26). Critical discharge is shown by the vertical dashed black line. Three rivers that are representative of heavy-tailed, intermediate-tailed, and thin-tailed distributions are shown in green, orange, and purple, respectively; all other rivers are shown in gray. The slope of –12 represents the steepest observed slope in the discharge data. (B) Magnitude-frequency distribution for U*/〈f(U* ≥ U*c)〉 for all stream gages, with same colors as (A); normalization by the mean reasonably collapses the data onto a single curve. The mean is indicated by the bold blue line. The inset shows the data on a semi-log plot, with light blue indicating ±1 SD. The dashed red line is an exponential fit to the mean for values of U* greater than U*c (dashed vertical black line). The tail decays faster than exponentially, indicating undersampling of the largest events (27, 28). (C) Relation between 〈f(U* ≥ U*c)〉 and U*bf, determined from independent surveys. The relation is strongest for rivers in which U*c was measured. The inset shows the averaged distribution of T from all rivers, with light blue indicating the first and third quartiles (each river was standardized by using its mean μ and SD σ) (fig. S6). The peak indicates that moderate floods, and not extreme events, have sculpted the channels (fig. S7) (26).

The rivers that we examined act as a filter, converting the wide range of climatically driven discharge distributions into a universal distribution of excess shear velocity. Flows greatly exceeding critical conditions cannot occur for long without leading to bank erosion, channel widening, and the restoration of flow conditions to near-critical (Fig. 1). This filtering is a logical consequence of the self-organization of rivers to a near-threshold channel geometry. We extend this reasoning beyond alluvial gravel-bedded rivers to bedrock-influenced rivers. The apparent generality of the critical filter calls into question the proposed links between extreme precipitation events, climate variability, and long-term river incision (1, 3, 17). Although large floods occur, they do not appear to control channel geometry for the rivers that we studied. An important caveat, however, is that we lack data for the steepest-slope rivers, where stream gages are rare, and for rapidly uplifting landscapes, where steep-walled gorges may violate our reported relations. The time scale of channel adjustment to external forcing is an important parameter, because this represents the time necessary to decouple f(U* ≥ U*c) from discharge. Our results suggest that channel geometry has adjusted to the current hydrologic regime in almost all the rivers that we examined, even though some of these are influenced by bedrock. How, and for how long, this adjustment plays out is not well understood. Other studies have shown that alluvial (29) and bedrock (32) channels may respond to hydrologic perturbations on decadal time scales. Laboratory experiments (33, 34) have demonstrated that coarse-grained bedrock channels may ultimately evolve their geometry and slope toward near-threshold transport conditions under an imposed sediment load. Although adjustments in the slope of natural rivers may take centuries to millions of years (9, 35), our analysis indicates that channel geometry adjusts rapidly to accommodate bed-load transport under an imposed slope and grain size. Another possibility is that rivers with more resistant banks may sort sediment rapidly under an imposed channel geometry, so that the grain sizes remaining on the channel bottom are near-threshold for the bankfull flood. Both mechanisms of adjustment may be present within a single catchment (32). We suggest that landscape evolution models could implement a channel closure scheme by assuming U*bf/U*c = 1.1. In addition, a fixed-magnitude flood event with an intermittency factor (36) may be adequate for modeling the influence of climate on erosion over long time scales. Our results lend support to empirical studies that found that modest transport events perform the bulk of incision in bedrock-influenced rivers (37, 38).

The critical filter that we have described here eliminates a substantial portion of the spectrum of environmental forcing, helping to explain how landscape patterns such as rivers remain stable in the face of highly stochastic driving. Channel adjustment decouples the sediment transport rate within a river from climatic influence. The delivery and removal of coarse sediment may determine the speed limit for river incision and landscape evolution (8), because bed-load transport remains near-threshold regardless of climate in bedrock-influenced and alluvial rivers.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/352/6286/694/suppl/DC1

Materials and Methods

Figs. S1 to S7

Table S1

References (3991)

REFERENCES AND NOTES

  1. Materials and methods are available as supplementary materials on Science Online.
Acknowledgments: Research was supported by the NSF Luquillo Critical Zone Observatory (LCZO) (grant EAR-1331841 to D.J.J.), the NSF INSPIRE program (Integrated NSF Support Promoting Interdisciplinary Research and Education; grant EAR-1344280 to D.J.J.), and an NSF Postdoctoral Fellowship (grant EAR-1349776 to C.B.P.). We thank M. Brandon for encouraging this study; J. Willenbring, P. Wilcock, C. Paola, J. Kirchner, D. Furbish, and three anonymous reviewers for comments that improved this manuscript; and J. Buffington, W. Dietrich, G. Grant, J. O'Connor, A. Pike, J. Scheingross, M. Singer, L. Sklar, and J. Warrick for assistance in acquiring additional stream data. The authors declare that they have no competing financial interests. The data in this study are available from multiple sources: Field site data are compiled in table S1; all unprocessed stream gage data are freely available from the USGS National Water Information System; and lidar data are available from the LCZO. The Mameyes stream morphology and derived hydrograph data are available at https://figshare.com/authors/Colin_Phillips/644773.
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