How well can the subsurface storage–discharge relation be interpreted and predicted using the geometric factors in headwater areas?

Headwater storage–discharge (S–Q) remains one of the least understood processes, and there is renewed interest in the S–Q relation. How well can the S–Q relation be interpreted mechanistically using geometric factors? In this paper, the hillslope storage Boussinesq and hillslope storage kinematic wave equation were adopted to guide the theoretical derivations. Analytical solutions were derived based on the hsKW equation for nine idealized hillslope aquifers, which were subdivided into two groups, i.e. hillslope aquifers with exponential hillslope width function (C1) and hillslope aquifers with Gaussian hillslope width function (C2). We found that analytical expressions of the S–Q relation can be derived for C1 hillslope aquifers. For more compound hillslope aquifers, i.e. C2, no explicit S–Q relation can be obtained. The whole subsurface recession after a rainstorm is simulated by applying the initial saturation condition. We found that the simulated S–Q processes can be characterized by a two‐phase recession, i.e. quick and slow recession. The time (t_b) at the dividing point of the quick and slow recessions depends on the geometric factors, such as the plan and profile curvature. In the quick recession for C1, many of the S–Q curves can be described as linear or quasi‐linear functions, which indicate that linear reservoir models can be applied approximately for recession simulations. However, during the slow recession phase of C1 and during the whole recession of C2, the S–Q relations are highly non‐linear. Finally, we compared the hillslope storage kinematic wave and hillslope storage Boussinesq models for simulating subsurface water recession after a rainstorm event in a real‐world headwater catchment (G5) in China. Through comparison of the recession slope curves, we found that the simulated results of the models employing the Gaussian hillslope width function match the observed hydrograph. The results indicated that appropriate organization of the hillslope geometric factors enhances our ability to make S–Q predictions. Copyright © 2016 John Wiley & Sons, Ltd.     

A rational sediment transport scaling relation based on dimensionless stream power

The concept of stream channel grade – according to which a stream channel reach will adjust its gradient, S, in order to transport the imposed sediment load having magnitude Q_b and characteristic grain size D_b, with the available discharge Q (Mackin, 1948 , Geological Society of America Bulletin 59 : 463–512; Lane, 1955 , American Society of Civil Engineers, Proceedings 81 : 1–17) is one of the most influential ideas in fluvial geomorphology. Herein, we derive a scaling relation that describes how externally imposed changes in either Q_b or Q can be accommodated by changes in the channel configuration, described by the energy gradient, mean flow depth, characteristic grain size and a parameter describing the effect of bed surface structures on grain entrainment. One version of this scaling relation is based on the dimensionless bed material transport parameter (W*) presented by Parker and Klingeman ( 1982 , Water Resources Research 18 : 1409–1423). An equivalent version is based on a new dimensionless transport parameter (E*) using dimensionless unit stream power. This version is nearly identical to the relation based on W*, except that it is independent of flow resistance. Both versions of the scaling relation are directly comparable to Lane's original relation. In order to generate this stream power‐based scaling relation, we derived an empirical transport function relation relating E* to dimensionless stream power using data from a wide range of stable, bed load‐dominated channels: the form of that transport function is based on the understanding that, while grain entrainment is related to the forces acting on the bed (described by dimensionless shear stress), sediment transport rate is related to the transfer of momentum from the fluid to the bed material (described by dimensionless stream power). Copyright © 2010 John Wiley & Sons, Ltd.     

Sensitivity of soil parameters in unsaturated zone modelling and the relation between effective,laboratory and in situ estimates

Simulation of soil moisture content requires effective soil hydraulic parameters that are valid at the modelling scale. This study investigates how these parameters can be estimated by inverse modelling using soil moisture measurements at 25 locations at three different depths (at the surface, at 30 and 60 cm depth) on an 80 by 20 m hillslope. The study presents two global sensitivity analyses to investigate the sensitivity in simulated soil moisture content of the different hydraulic parameters used in a one‐dimensional unsaturated zone model based on Richards' equation. For estimation of the effective parameters the shuffled complex evolution algorithm is applied. These estimated parameters are compared to their measured laboratory and in situ equivalents. Soil hydraulic functions were estimated in the laboratory on 100 cm³ undisturbed soil cores collected at 115 locations situated in two horizons in three profile pits along the hillslope. Furthermore, in situ field saturated hydraulic conductivity was estimated at 120 locations using single‐ring pressure infiltrometer measurements. The sensitivity analysis of 13 soil physical parameters (saturated hydraulic conductivity (K_s), saturated moisture content (θ_s), residual moisture content (θ_r), inverse of the air‐entry value (α), van Genuchten shape parameter (n), Averjanov shape parameter (N) for both horizons, and depth (d) from surface to B horizon) in a two‐layer single column model showed that the parameter N is the least sensitive parameter. K_s of both horizons, θ_s of the A horizon and d were found to be the most sensitive parameters. Distributions over all locations of the effective parameters and the distributions of the estimated soil physical parameters from the undisturbed soil samples and the single‐ring pressure infiltrometer estimates were found significantly different at a 5% level for all parameters except for α of the A horizon and K_s and θ_s of the B horizon. Different reasons are discussed to explain these large differences. Copyright © 2004 John Wiley & Sons, Ltd.     

Saturated area dynamics and streamflow generation from coupled surface–subsurface simulations and field observations

A distributed physically-based model describing coupled surface–subsurface flows is applied to an instrumented catchment to investigate the links between runoff generation processes and the dynamics of saturated areas. The spatial characterization of the system is obtained through geophysical measurements and in situ observations. The model is able to reproduce the dynamics of the system through the calibration of only few parameters with a clear physical interpretation, providing a solid basis for our numerical investigations. Such investigations demonstrate the important control exerted by surface topography on the time evolution of saturated area patterns, mainly mediated by topographic curvature, that dictates both the dominant streamflow generation process at the local scale and the connection-disconnection dynamics of saturated areas. The relation between hillslope water storage and streamflow, Q = f(V), is shown to be highly hysteretical and dependent on the mean saturation of the catchment: higher degrees of saturation tend to yield one-to-one relationships between streamflow and water storage. On the contrary, streamflow-water storage relations are importantly affected by the specific configuration of saturated areas connected to the outlet when the system is far from complete saturation. This observation contradicts common assumptions of a one-to-one relationship Q = f(V) often used to justify widely observed power-law Q vs. dQ/dt recession curves. Furthermore, even when Q = f(V) becomes unique at high degrees of saturation, no power-law form emerged in our runs, speculatively because of the small size of the catchment formed by a single incision and the corresponding hillslope.     

Channel flow competence and sediment transport in upland streams in southeast Australia

Bedload transport data from planebed and step‐pool reach types are used to determine grain size transport thresholds for selected upland streams in southeast Australia. Morphological differences between the reach types allow the effects of frictional losses from bedforms, microtopography and bed packing to be incorporated into the dimensionless critical shear stress value. Local sediment transport data are also included in a regime model and applied to mountain streams, to investigate whether empirical data improve the delineation of reach types on the basis of dimensionless discharge per unit width (q*) and dimensionless bedload transport (q_b*). Instrumented planebed and step‐pool sites are not competent to transport surface median grains (D_50s) at bankfull discharge (Q_bf). Application of a locally parametrized entrainment equation to the full range of reach types in the study area indicates that the majority of cascades, cascade‐pools, step‐pools and planebeds are also not competent at Q_bf and require a 10 year recurrence interval flood to mobilize their D_50s. Consequently, the hydraulic parameters of the regime diagram, which assume equilibrium conditions at bankfull, are ill suited to these streams and provide a poor basis of channel delineation. Modifying the diagram to better reflect the dominant transported bedload size (equivalent to the D₁₆ of surface sediment) made only slight improvements to reach delineation and had greatest effect on the morphologies with smaller surface grain sizes such as forced pool‐riffles and planebeds. Likewise, the Corey shape factor was incorporated into the regime diagram as an objective method for adjusting a base dimensionless critical shear stress (τ*_c50b) to account for lithologically controlled grain shape on bed packing and entrainment. However, it too provided only minor adjustments to reach type delineation. Copyright © 2007 John Wiley & Sons, Ltd.     

Spatial patterns of sediment delivery to valley floors: sensitivity to sediment transport capacity and hillslope hydrology relations

There is considerable interest in large‐scale spatial patterns of sediment transport in catchments, and this topic is often approached using terrain‐based modelling. In such models topography influences the discharge of overland flow and its sediment transport capacity. The sediment transport capacity of overland flow is commonly expressed as a power function of slope and discharge (i.e. q_s=k₁q^βS^γ). The relationship between discharge and contributing area can also be expressed as a power function. Several reviews reveal a limited range of values for the two exponents β and γ. In this paper we examine the sensitivity of catchment‐scale patterns of sediment delivery to valley floors to a range of sediment transport capacity and hillslope hydrology parameterizations, using two catchments on the southern tablelands of New South Wales. The results indicate that, over the limited range of β and γ identified within the literature, sediment deliveries to valley floors across the two catchments are similar for all but one of five sediment transport capacity relationships. The patterns are dominated by the trend in slope through each catchment. The sensitivity to hillslope hydrology of predicted sediment delivery patterns is strong in the catchment with systematic variation in unit hillslope area, and weak in the catchment for which there are no systematic trends in unit hillslope area. We believe there is less experimental evidence to restrict choice of hillslope hydrology parameters than there is for sediment transport capacity. Copyright © 2001 John Wiley & Sons, Ltd.     

Hydraulic characteristics of a small Coastal Plain stream of the southeastern United States: effects of hydrology and season

Various physical and biological properties affect solute transport patterns in streams. We measured hydraulic characteristics of Payne Creek, a low‐gradient upper Coastal Plain stream, using tracer experiments and parameter estimation with OTIS‐P (one‐dimensional transport with inflow and storage with parameter optimization). The primary objective of this study was to estimate the effects of varying discharge, season, and litter accumulation on hydraulic parameters. Channel area A ranged from 0·081 to 0·371 m² and transient storage area A_s ranged from 0·027 to 0·111 m². Dispersion D ranged from 1·5 to 11·1 m² min⁻¹ and exchange coefficient α ranged from 0·009 to 0·038 min⁻¹. Channel area and dispersion were positively correlated to discharge Q, whereas storage area and exchange coefficient were not. Relative storage size A_s/A ranged from 0·17 to 0·59, and was higher during fall than other seasons under a similar Q. The fraction of median travel time due to transient storage ranged from 8·8 to 34·5% and was significantly correlated with Q through a negative power function. Both metrics indicated that transient storage was a significant component affecting solute transport in Payne Creek, especially during the fall. Comparison between the measured channel area A_c and A suggested that surface storage was dominant in Payne Creek. During fall, accumulation of leaf litter resulted in larger A and A_s and lower velocity and D than during other seasons with similar discharge. Seasonal changes in discharge and organic matter accumulation, and dynamic channel morphology affected the magnitude of transient storage and overall hydraulic characteristics of Payne Creek. Copyright © 2005 John Wiley & Sons, Ltd.     

Two-Dimensional Probabilistic Infiltration Analysis in a Hillslope Using First-Order Moment Approach

A first-order moment analysis method is introduced to evaluate the pore-water pressure variability within a hillslope due to spatial variability in saturated hydraulic conductivity (K_s) during rainfall. The influences of the variance of the natural logarithm of K_s(ln K_s), spatial structure anisotropy of ln K_s, and normalized vertical infiltration flux (q) on the evaluations of the pore-water pressure uncertainty are investigated. Results indicate different responses of pressure head variability in the unsaturated region and the saturated region. In the unsaturated region, a larger variance of ln K_s, a higher spatial structure anisotropy, and a smaller q lead to a larger variability in pressure head, while in the saturated region, the variability in pressure head increases with the increase of variance of ln K_s, the decrease of spatial structure anisotropy, or the increase of q. These variables have great impacts on the range of fluctuation of the phreatic surface within the hillslope. The influences of these three variables on the variance of pressure head within the saturated region are greater than those within the unsaturated region, and the variance of ln K_s has the greatest impact. These results yield useful insight into the effects of heterogeneity on pressure head and uncertainty associated with predicted flow field.     

A new version of the USLE‐MM for predicting bare plot soil loss at the Sparacia (South Italy) experimental site

Improving empirical prediction of plot soil erosion at the event temporal scale has both scientific and practical importance. In this investigation, 492 runoff and soil loss data from plots of different lengths, λ (11 ≤ λ ≤ 44 m), and steepness, s (14.9 ≤ s ≤ 26.0%), established at the Sparacia experimental station, in Sicily, South Italy, were used to derive a new version of Universal Soil Loss Equation (USLE)‐MM model, by only assuming a value of one for the topographic length, L, and steepness, S, factors for λ = 22 m and s = 9%, respectively. An erosivity index equal to (Q_REI₃₀)^b1, Q_R and EI₃₀ being the runoff coefficient and the event rainfall erosivity index, respectively, with b₁ > 1 was found to be an appropriate choice for the Sparacia area. The specifically developed functions for L and S did not differ appreciably from other, more widely accepted relationships (maximum differences by a factor of 1.22 for L and 1.09 for S). The new version of the USLE‐MM performed particularly well for highly erosive events, because predicted soil loss differed by not more than a factor of 1.19 from the measured soil loss for measured values of more than 100 Mg ha^?1. The choice of the relationships to predict topographic effects on plot soil loss should not represent a point of particular concern in the application of the USLE‐MM in other environments. However, tests of the empirical approach should be carried out in other experimental areas in an attempt to develop analytical tools, usable at the event temporal scale, reasonably simple and of wide validity. Copyright © 2015 John Wiley & Sons, Ltd.     

Persistence of road runoff generation in a logged catchment in Peninsular Malaysia

Measurements of saturated hydraulic conductivity (K_s) and diagnostic model simulations show that all types of logging road/trail in the 14·4 ha Bukit Tarek Experimental Catchment 3 (BTEC3) generate substantial Horton overland flow (HOF) during most storms, regardless of design and level of trafficking. Near‐surface K_s(0–0·05 m) on the main logging road, skid trails and newly constructed logging terraces was less than 1, 2 and 34 mm h^?1, respectively. Near‐surface K_s on an abandoned skid trail in an adjacent basin was higher (62 mm h^?1), owing to the development of a thin organic‐rich layer on the running surface over the past 40 years. Saturated hydraulic conductivity measured at 0·25 m below the surface of all roads was not different (all <6 mm h^?1) and corresponded to the K_s of the adjacent hillslope subsoil, as most roads were excavated into the regolith more than 0·5–1 m. After 40 years, only limited recovery in near‐surface K_s occurred on the abandoned skid trail. This road generated HOF after the storage capacity of the upper near‐surface layer was exceeded during events larger than about 20 mm. Thus, excavation into low‐K_s substrate had a greater influence on the persistence of surface runoff production than did surface compaction by machinery during construction and subsequent use during logging operations. Overland flow on BTEC3 roads was also augmented by the interception of shallow subsurface flow traveling along the soil–saprolite/bedrock interface and return flow emerging from the cutbank through shallow biogenic pipes. The most feasible strategy for reducing long‐term road‐related impacts in BTEC3 is limiting the depth of excavation and designing a more efficient road network, including minimizing the length and connectivity of roads and skid trails. Copyright © 2007 John Wiley & Sons, Ltd.     

Assessing the effect of vegetation‐related bank strength on channel morphology and stability in gravel‐bed streams using numerical models

Bank strength due to vegetation dominates the geometry of small stream channels, but has virtually no effect on the geometry of larger ones. The dependence of bank strength on channel scale affects the form of downstream hydraulic geometry relations and the meandering‐braiding threshold. It is also associated with a lateral migration threshold discharge, below which channels do not migrate appreciably across their floodplains. A rational regime model is used to explore these scale effects: it parameterizes vegetation‐related bank strength using a dimensionless effective cohesion, C_r*. The scale effects are explored primarily using an alluvial state space defined by the dimensionless formative discharge, Q*, and channel slope, S, which is analogous to the Q–S diagrams originally used to explore meandering‐braiding thresholds. The analyses show that the effect of vegetation on both downstream hydraulic geometry and the meandering‐braiding threshold is strongest for the smallest streams in a watershed, but that the effect disappears for Q* > 10⁶. The analysis of the migration threshold suggests that the critical discharge ranges from about 5 m³/s to 50 m³/s, depending on the characteristic rooting depth for the vegetation. The analysis also suggests that, where fires frequently affect riparian forests, channels may alternate between laterally stable gravel plane‐bed channels and laterally active riffle‐pool channels. These channels likely do not exhibit the classic dynamic equilibrium associated with alluvial streams, but instead exhibit a cyclical morphologic evolution, oscillating between laterally stable and laterally unstable end‐members with a frequency determined by the forest fire recurrence interval. Copyright © 2008 John Wiley & Sons, Ltd.     

OUTBURST FLOODS FROM GLACIER-DAMMED LAKES: THE EFFECT OF MODE OF LAKE DRAINAGE ON FLOOD MAGNITUDE

Published accounts of outburst floods from glacier-dammed lakes show that a significant number of such floods are associated not with drainage through a tunnel incised into the basal ice—the process generally assumed—but rather with ice-marginal drainage, mechanical failure of part of the ice dam, or both. Non-tunnel floods are strongly correlated with formation of an ice dam by a glacier advancing from a tributary drainage into either a main river valley or a pre-existing body of water (lake or fiord). For a given lake volume, non-tunnel floods tend to have significantly higher peak discharges than tunnel-drainage floods. Statistical analysis of data for floods associated with subglacial tunnels yields the following empirical relation between lake volume V and peak discharge Q_p : Q_p = 46V^0.66 (r² = 0.70), when Q_p is expressed in metres per second and V in millions of cubic metres. This updates the so-called Clague–Mathews relation. For non-tunnel floods, the analogous relation is Q_p = 1100V^0.44 (r² = 0.58). The latter relation is close to one found by Costa (1988) for failure of constructed earthen dams. This closeness is probably not coincidental but rather reflects similarities in modes of dam failure and lake drainage. We develop a simple physical model of the breach-widening process for non-tunnel floods, assuming that (1) the rate of breach widening is controlled by melting of the ice, (2) outflow from the lake is regulated by the hydraulic condition of critical flow where water enters the breach, and (3) the effect of lake temperature may be dealt with as done by Clarke (1982). Calculations based on the model simulate quite well outbursts from Lake George, Alaska. Dimensional analysis leads to two approximations of the form Q_p ∝ V^qf(h_i, θ₀), where q = 0.5 to 0.6, h_i is initial lake depth, θ₀ is lake temperature, and the form of f (h_i, θ₀) depends on the relative importance of viscous dissipation and the lake's thermal energy in determining the rate of breach opening. These expressions, along with the regression relations, should prove useful for assessing the probable magnitude of breach-type outburst floods.     

A simple two‐parameter model for scaling hillslope surface runoff

The objective of this research was to develop and parameterise a physically justified yet low‐parameter model to quantify observed changes in surface runoff ratios with hillslope length. The approach starts with the assumption that a unit of rainfall‐excess runoff generated at a point is a fraction β of precipitation P (m) which travels some variable distance down a slope before reinfiltrating, depending on the local rainfall, climate, soils, etc. If this random distance travelled Y is represented by a distribution, then a survival function will describe the probability of this unit of runoff travelling further than some distance x (m). The total amount of per unit width runoff Q (m²) flowing across the lower boundary of a slope of length λ (m) may be considered the sum of all the proportions of the units of rainfall excess runoff integrated from the lower boundary x = 0 to the upper boundary x = λ of the slope. Using these assumptions we derive a model Q(λ) = βPμλ/(μ + λ), (μ > 0, 0 ≤ β ≤ 1, λ ≥ 0) that describes the change in surface runoff with slope length, where μ (m) is the mean of the random variable Y. Dividing both sides of this equation by Pλ yields a simple two‐parameter equation for the dimensionless hillslope runoff ratio Q_h(λ) = βμ/(μ + λ). The model was parameterised with new rainfall and runoff data collected from three replicates of bounded 2 m wide plots of four different lengths (0.5, 1.0, 2.0 and 4.0 m) for 2 years from a forested SE Australian site, and with 32 slope length–runoff data sets from 12 other published studies undertaken between 1934 and 2010. Using the parameterised model resulted in a Nash and Sutcliffe statistic between observed and predicted runoff ratio (for all data sets combined) of 0.93, compared with –2.1 when the runoff ratio was fixed at the value measured from the shortest plot. Copyright © 2014 John Wiley & Sons, Ltd.     

Attenuation of High Frequency P and S Waves in the Gujarat Region,India

The local earthquake waveforms recorded on broadband seismograph network of Institute of Seismological Research in Gujarat, India have been analyzed to understand the attenuation of high frequency (2–25 Hz) P and S waves in the region. The frequency dependent relationships for quality factors for P (Q _P) and S (Q _S) waves have been obtained using the spectral ratio method for three regions namely, Kachchh, Saurashtra and Mainland Gujarat. The earthquakes recorded at nine stations of Kachchh, five stations of Saurashtra and one station in mainland Gujarat have been used for this analysis. The estimated relations for average Q _P and Q _S are: Q _P = (105 ± 2) f ^{0.82 ± 0.01}, Q _S = (74 ± 2) f ^{1.06 ± 0.01} for Kachchh region; Q _P = (148 ± 2) f ^{0.92 ± 0.01}, Q _S = (149 ± 14) f ^{1.43 ± 0.05} for Saurashtra region and Q _P = (163 ± 7) f ^{0.77 ± 0.03}, Q _S = (118 ± 34) f ^{0.65 ± 0.14} for mainland Gujarat region. The low Q (<200) and high exponent of f (>0.5) as obtained from present analysis indicate the predominant seismic activities in the region. The lowest Q values obtained for the Kachchh region implies that the area is relatively more attenuative and heterogeneous than other two regions. A comparison between Q _S estimated in this study and coda Q (Qc) previously reported by others for Kachchh region shows that Q _C > Q _S for the frequency range of interest showing the enrichment of coda waves and the importance of scattering attenuation to the attenuation of S waves in the Kachchh region infested with faults and fractures. The Q _S/Q _P ratio is found to be less than 1 for Kachchh and Mainland Gujarat regions and close to unity for Saurashtra region. This reflects the difference in the geological composition of rocks in the regions. The frequency dependent relations developed in this study could be used for the estimation of earthquake source parameters as well as for simulating the strong earthquake ground motions in the region.     

Prediction of concentrated flow width in ephemeral gully channels

Empirical prediction equations of the form W = aQ^b have been reported for rills and rivers, but not for ephemeral gullies. In this study six experimental data sets are used to establish a relationship between channel width (W, m) and flow discharge (Q, m³ s^?1) for ephemeral gullies formed on cropland. The resulting regression equation (W = 2·51 Q^0·412; R² = 0·72; n = 67) predicts observed channel width reasonably well. Owing to logistic limitations related to the respective experimental set ups, only relatively small runoff discharges (i.e. Q < 0·02 m³s^?1) were covered. Using field data, where measured ephemeral gully channel width was attributed to a calculated peak runoff discharge on sealed cropland, the application field of the regression equation was extended towards larger discharges (i.e. 5 × 10^?4m³s^?1 < Q < 0·1 m³s^?1). Comparing W–Q relationships for concentrated flow channels revealed that the discharge exponent (b) varies from 0·3 for rills over 0·4 for gullies to 0·5 for rivers. This shift in b may be the result of: (i) differences in flow shear stress distribution over the wetted perimeter between rills, gullies and rivers, (ii) a decrease in probability of a channel formed in soil material with uniform erosion resistance from rills over gullies to rivers and (iii) a decrease in average surface slope from rills over gullies to rivers. The proposed W–Q equation for ephemeral gullies is valid for (sealed) cropland with no significant change in erosion resistance with depth. Two examples illustrate limitations of the W–Q approach. In a first example, vertical erosion is hindered by a frozen subsoil. The second example relates to a typical summer situation where the soil moisture profile of an agricultural field makes the top 0·02 m five times more erodible than the underlying soil material. For both cases observed W values are larger than those predicted by the established channel width equation for concentrated flow on cropland. For the frozen soils the equation W = 3·17 Q^0·368 (R² = 0·78; n = 617) was established, but for the summer soils no equation could be established. Copyright © 2002 John Wiley & Sons, Ltd.     

THE PROBLEM OF LONG-TERM STORAGE IN RESERVOIRS

Abstract

The geometry of a meandering stream depends strongly on the relative stream size (Q ^2/5 / g ^1/5)/D, on the valley slope, Sv, and on the charge, Q _s/Q, where Q and Q _s are the fluid and sediment discharges respectively, g is acceleration due to gravity and D is the mean sediment size. The geometry depends less strongly on the relative settling size of sediment, D/(v ^2/3 / g ^1/3), where v is the kinematic viscosity. For constant values of Q, S _v and D, the effect of increase of charge reduces the meander length, M _L, and the mean channel surface width, B, whereas meander width, M _B, bend radius, R _M, and mean channel depth, H, increase, For a constant value of (Q ^2/5 / g^1/5)/D the values of M _L, M _B, R _M and B increase with the increase of valley slope but the value of H tends to decrease.     

Rill hydraulics on a semiarid hillslope,southern Arizona

Seventy field experiments were conducted in seven rills located on a semiarid rangeland hillslope underlain by gravelly soils at Walnut Gulch, Arizona. The rills, which are characterized by wide, shallow cross-sections and gravel-covered beds, have mean at-a-station hydraulic geometry exponents of b = 0·33, f = 0·34 and m = 0·33. Although the differences between these values and typical values of b = 0·30, f = 0·40 and m = 0·30 for cropland rills are not statistically significant, they are thought to be real, as cropland rills often have more rectangular cross-sections and steeper sides than the rangeland rills under study. For rills formed in silty loamy soils, Govers developed an empirical relation between mean flow velocity and discharge. Emphasizing the generality of this relation, he suggested that it may be used as a simple means of routing runoff through rills. He also noted that this relation appeared to be unaffected by either slope or soil materials. The present data represent rills underlain by coarser and somewhat more varied gravel-rich soils. These data do not conform to Govers' relation, and a multiple regression analysis reveals that slope and soil materials, either directly or indirectly through bed roughness, exert almost as much influence on flow velocity as does discharge. Three alternative methods are developed for predicting flow velocity in the rills under study. All three methods give good results with the largest root mean square deviation being 3·115 cm s⁻¹.     

Estimation of Q p and Q s of Kinnaur Himalaya

The attenuation characteristics of the Kinnaur area of the North West Himalayas were studied using local earthquakes that occurred during 2008–2009. Most of the analyzed events are from the vicinity of the Panjal Thrust (PT) and South Tibetan Detachment Thrust, which are well-defined tectonic discontinuities in the Himalayas. The frequency-dependent attenuation of P and S waves was estimated using the extended coda normalization method. Data from 64 local earthquakes recorded at 10 broadband stations were used. The coda normalization of the spectral amplitudes of P and S waves was done at central frequencies of 1.5, 3, 6, 9, and 12 Hz. Q _p increases from about 58 at 1.5 Hz to 706 at 12 Hz, and Q _s increases from 105 at 1.5 Hz to 1,207 at 12 Hz. The results show that the quality factors for both P and S waves (Q _p and Q _s) increase as a function of frequency according to the relation Q?=?Q _o f ⁿ , where Q _o is the corresponding Q value at 1 Hz frequency and “n” is the frequency relation parameter. We obtained Q _p?=?(47?±?2)f ^(1.04±0.04) and Q _s?=?(86?±?4)f ^(0.96±0.03) by fitting power law dependency model for the estimated values of the entire study region. The Q ₀ and n values show that the region is seismically very active and the crust is highly heterogeneous. There was no systematic variation of values of Q _p and Q _s at different frequencies from one tectonic unit to another. As a consequence, average values of these parameters were obtained for each frequency for the entire region, and these were used for interpretation and for comparison with worldwide data. Q _p values lie within the range of values observed for some tectonically active regions of the world, whereas Q _s values were the lowest among the values compared for different parts of the world. Q _s/Q _p values were >1 for the entire range of frequencies studied. All these factors indicate that the crust is highly heterogeneous in the study region. The high Q _s/Q _p values also indicate that the region is partially saturated with fluids.     

Consistency between hydrological models and field observations: linking processes at the hillslope scale to hydrological responses at the watershed scale

The purpose of this paper is to identify simple connections between observations of hydrological processes at the hillslope scale and observations of the response of watersheds following rainfall, with a view to building a parsimonious model of catchment processes. The focus is on the well‐studied Panola Mountain Research Watershed (PMRW), Georgia, USA. Recession analysis of discharge Q shows that while the relationship between dQ/dt and Q is approximately consistent with a linear reservoir for the hillslope, there is a deviation from linearity that becomes progressively larger with increasing spatial scale. To account for these scale differences conceptual models of streamflow recession are defined at both the hillslope scale and the watershed scale, and an assessment made as to whether models at the hillslope scale can be aggregated to be consistent with models at the watershed scale. Results from this study show that a model with parallel linear reservoirs provides the most plausible explanation (of those tested) for both the linear hillslope response to rainfall and non‐linear recession behaviour observed at the watershed outlet. In this model each linear reservoir is associated with a landscape type. The parallel reservoir model is consistent with both geochemical analyses of hydrological flow paths and water balance estimates of bedrock recharge. Overall, this study demonstrates that standard approaches of using recession analysis to identify the functional form of storage–discharge relationships identify model structures that are inconsistent with field evidence, and that recession analysis at multiple spatial scales can provide useful insights into catchment behaviour. Copyright © 2008 John Wiley & Sons, Ltd.     

Sediment flux-driven channel geometry adjustment of bedrock and mixed gravel–bedrock rivers

Sediment supply (Q_s) is often overlooked in modelling studies of landscape evolution, despite sediment playing a key role in the physical processes that drive erosion and sedimentation in river channels. Here, we show the direct impact of the supply of coarse-grained, hard sediment on the geometry of bedrock channels from the Rangitikei River, New Zealand. Channels receiving a coarse bedload sediment supply are systematically (up to an order of magnitude) wider than channels with no bedload sediment input for a given discharge. We also present physical model experiments of a bedrock river channel with a fixed water discharge (1.5 l min⁻¹) under different Q_s (between 0 and 20 g l⁻¹) that allow the quantification of the role of sediment in setting the width and slope of channels and the distribution of shear stress within channels. The addition of bedload sediment increases the width, slope and width-to-depth ratio of the channels, and increasing sediment loads promote emerging complexity in channel morphology and shear stress distributions. Channels with low Q_s are characterized by simple in-channel morphologies with a uniform distribution of shear stress within the channel while channels with high Q_s are characterized by dynamic channels with multiple active threads and a non-uniform distribution of shear stress. We compare bedrock channel geometries from the Rangitikei and the experiments to alluvial channels and demonstrate that the behaviour is similar, with a transition from single-thread and uniform channels to multiple threads occurring when bedload sediment is present. In the experimental bedrock channels, this threshold Q_s is when the input sediment supply exceeds the transport capacity of the channel. Caution is required when using the channel geometry to reconstruct past environmental conditions or to invert for tectonic uplift rates, because multiple configurations of channel geometry can exist for a given discharge, solely due to input Q_s. © 2020 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd