An extreme value analysis of the flow of Burbage Brook

An extreme value analysis of the flow of Burbage Brook is carried out by modelling peaks over a high threshold. The aims are to illustrate recently developed statistical techniques and to report on interesting features of the flow of the brook over a 58-year period. Peak flows are found to show marked seasonal variation and a downward trend. Then-year return level is estimated for various values ofn, and the reliability of the estimates is assessed.     

Experimental study of the effect of roughness and Reynolds number on fluid flow in rough‐walled single fractures: a check of local cubic law

Local cubic law (LCL) is one of the most commonly applied physical laws for flow in single fractures (SF) and fractured media. The foundation of LCL is Darcian flow. This experimental study examines if LCL is valid for flow in a single rough fracture and how the fracture roughness and Reynolds number (Re) affect flow. Similar to the Moody diagram for flow in pipes, a diagram for flow in a single rough fracture has been generated to relate the friction coefficient with Re and the roughness. Under the experimental condition of this study, flow appears to be substantially different from Darcian flow. The flow law of q ∝ eⁿJ^m appears to be valid for describing the flow scheme where q, e, and J are the unit width flux, the average aperture, and the hydraulic gradient. The value of the power index m is found to be around 0·83 ～ 0·98, less than what has been used in Darcian flow (m = 1). The power index n is around 11·2 and 13·0, much greater than the n value used in the LCL (n = 3), and it increases with the average velocity. The Moody type of diagram shows that the friction factor for flow in SFs is influenced by Re and the roughness. It decreases with Re when Re is small, and becomes less sensitive to Re when Re is large enough. It also increases with the roughness. Copyright © 2010 John Wiley & Sons, Ltd.     

Impacts of sediment load on Manning coefficient in supercritical shallow flow on steep slopes

The Manning equation is one of the most widely used formulae for calculating the velocity of shallow overland flow in hydrological and erosion models. Precise estimation of the Manning's friction coefficient (n) is critical to determining overland flow and soil erosion processes. Few studies have been conducted to quantify the effects of sediment load on Manning's n on steep slopes. This study was conducted to investigate the potential effects of sediment load on Manning's n in a flume with a fixed bed, under wide ranges of hydraulics and sediment loads. Slope gradient varied from 8·7 to 34·2%, unit flow rate from 0·66 to 5·26 × 10^?3 m² s^?1, and sediment load from 0 to 6·95 kg m^?1 s^?1. The Reynolds number ranged from 350 to 5899. Results showed that Manning's n varied in both sediment‐free and sediment‐laden flows ranging from 0·012 to 0·055. The apparent Manning's coefficients of sediment‐laden flow were much greater than those of sediment‐free flow. The mean Manning coefficient of sediment‐laden flow was 51·27% greater than the mean value of sediment‐free flow. For sediment‐laden flow, Manning's n could be estimated with a power function of unit flow discharge and sediment content. Further studies are needed to quantify the potential effects of sediment load on the Manning's n on erodible beds and in fields. Copyright © 2010 John Wiley & Sons, Ltd.     

Static deformation of a multilayered half-space by a very long strike-slip fault

Summary The formulas for the elastic residual field of a very long strike-slip fault in a multilayered elastic half-space are given. It is assumed that the medium is made up ofn parallel, isotropic and homogeneous layers lying over an isotropic, homogeneous half-space and being in welded contact. The formulas which allow the calculation of the displacement and stress fields due to an arbitrary very long strike-slip fault are derived. The explicit expressions of coefficients which appear in these formulas are listed for the casesn=1 andn=2.     

On the normal mode instability of harmonic waves on a sphere

Abstract

The normal mode instability of harmonic waves in an ideal incompressible fluid on a rotating sphere is analytically studied. By the harmonic wave is meant a Legendrepolynomial flow αP_n(μ) (n ≥ 1) and steady Rossby-Haurwitz wave of set F ₁ ⊕ H_n where H_n is the subspace of homogeneous spherical polynomials of the degree n(n ≥ 2), and F ₁ is the one-dimensional subspace generated by the Legendre-polynomial P₁(μ). A necessary condition for the normal mode instability of the harmonic wave is obtained. By this condition, Fjörtoft's (1953) average spectral number of the amplitude of each unstable mode must be equal to . It is noted that flow αP_n (μ) is Liapunov (and hence, exponentially and algebraically) stable to all the disturbances whose zonal wavenumber m satisfies condition |m| ≥ n. The bounds of the growth rate of unstable normal modes are estimated as well. It is also shown that the amplitude of each unstable, decaying or non-stationary mode is orthogonal to the harmonic wave.

The new instability condition can be useful in the search of unstable perturbations to a harmonic wave and on trials of numerical stability study algorithms. For a Legendre-polynomial flow, it complements Kuo's (1949) condition in the sense that while the latter is related to the basic flow structure; the former characterizes the structure of a growing perturbation.     

Deterministic signals in precipitation in Arkansas,Louisiana, and Mississippi

Evidence for a signal near 19 years is found in 51 out of 65 rain gauge records in the tri-state region of Arkansas, Louisiana, and Mississippi, While another term with period 10 to 11 years is found in 39 instances. These are identified as the 18.6-year luni-solarM _n and solar cycleS _c signals in climate variability. In terms of both amplitude and phase the luni-solar wave trains are highly nonstationary; in particular, the waves commonly change phase by 180°. Examples of theM _n andS _c terms in corn yield for Arkansas and Missouri are presented, and the implications for economic science briefly discussed.     

Linking the recruitment and survivorship of a freshwater stream-specialist fish species to flow metrics in Mediterranean climate temporary streams

Novel modelling was utilised in the present study to reveal significant relationships between the abundance of the Australian freshwater stream-specialist fish Galaxias olidus and metrics defining flow regimes across a region dominated by temporary streams. It was revealed that increases in total abundance were linked to metrics (both 1- and 3-year periods) that indicate greater water availability and the persistence of water in pools across the year, namely the average duration of zero-flow days over the low-flow season (negatively) and total duration of bankfull flows across the year (positively). The analysis identified 3-year metrics as being more important to the abundance of 0+ fish rather than annual ones. Taken together, these findings describing the flow requirements of a stream specialist will help to guide implementation of environmental flows, but will also highlight the need for continued exploration of flow–ecology relationships.     

Simulating hydrological response for the R‐5 catchment: comparison of two models and the impact of the roads

In this paper the performance of two hydrological‐response models is evaluated and compared based upon simulations for a single rainfall–runoff event. The two models are QPBRRM, a relatively simple model of Horton overland flow, and InHM, a comprehensive physics‐based model of each of the known streamflow generation mechanisms. The rainfall–runoff event focused upon in this study is from the small rangeland catchment in Oklahoma known as R‐5. When calibrated, both QPBRRM and InHM are shown to effectively simulate the R‐5 event. The calibration procedures used in this study for QPBRRM and InHM were quite different. The calibration of QPBRRM was a curve fitting exercise, whereas the calibration of InHM was based upon an internally valid estimate of the continuous head field. In this study QPBRRM did not perform well outside of the calibrated range. The impact of the roads cutting across the R‐5 catchment is simulated with InHM and discussed for the first time in the study reported here. The relative merits of QPBRRM and InHM are each discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Regionalization of floods in New Brunswick (Canada)

This study uses the method of peaks over threshold (P.O.T.) to estimate the flood flow quantiles for a number of hydrometric stations in the province of New Brunswick, Canada. The peak values exceeding the base level (threshold), or `exceedances', are fitted by a generalized Pareto distribution. It is known that under the assumption of Poisson process arrival for flood exceedances, the P.O.T. model leads to a generalized extreme value distribution (GEV) for yearly maximum discharge values. The P.O.T. model can then be applied to calculate the quantiles X <sub>T</sub> corresponding to different return periods T, in years. A regionalization of floods in New Brunswick, which consists of dividing the province into `homogeneous regions', is performed using the method of the `region of influence'. The 100-year flood is subsequently estimated using a regionally estimated value of the shape parameter of the generalized Pareto distribution and a regression of the 100-year flood on the drainage area. The jackknife sampling method is then used to contrast the regional results with the values estimated at site. The variability of these results is presented in box-plot form. Received: June 1, 1997     

Regionalization of floods in New Brunswick (Canada)

This study uses the method of peaks over threshold (P.O.T.) to estimate the flood flow quantiles for a number of hydrometric stations in the province of New Brunswick, Canada. The peak values exceeding the base level (threshold), or `exceedances', are fitted by a generalized Pareto distribution. It is known that under the assumption of Poisson process arrival for flood exceedances, the P.O.T. model leads to a generalized extreme value distribution (GEV) for yearly maximum discharge values. The P.O.T. model can then be applied to calculate the quantiles X <sub>T</sub> corresponding to different return periods T, in years. A regionalization of floods in New Brunswick, which consists of dividing the province into `homogeneous regions', is performed using the method of the `region of influence'. The 100-year flood is subsequently estimated using a regionally estimated value of the shape parameter of the generalized Pareto distribution and a regression of the 100-year flood on the drainage area. The jackknife sampling method is then used to contrast the regional results with the values estimated at site. The variability of these results is presented in box-plot form. Received: June 1, 1997     

Grid size effects analysis and hydrological similarity of surface runoff in flatland basins

The effects of grid-size modification on the derived topographic attributes are analysed and a procedure for scaling model parameters and similarity assessment between flow variables is proposed. Hydrological simulations are performed with a physically-based and spatially-distributed quasi-2D mathematical model. The scaled model parameters are the effective roughness coefficient associated with overland flow (n_ov) and the transverse slope in the cell (TSC). To scale the selected parameters, the criterion of equilibrium storage conservation between the different grid sizes is applied. Three basins of the central-east region of Argentina are modelled. The spatial variability of basin geomorphology is quantified using the entropy concept. The simulation results show that when grid size is increased, to obtain similar hydrological responses it is necessary to increase the n_ov or to reduce the TSC. In terms of similarity, the best results are achieved when TSC is scaled, particularly when water depths are considered.     

Luni-solar 18.6-year signal in tree-rings from Argentina and Chile

Spectrum analysis of 32 tree-ring chronologies from Argentina and Chile yields evidence for two peaks with periods 19.2±1.6 years (30 out of 32 records) and 10.5±0.4 years in 22 instances. Tests by thet-statistic show that the long-period peak is significant at a confidence level of 99%. This signal is identified as the luni-solar 18.6-year M _n term reported earlier byCurrie (1983) in two treering chronologies from the same region, and later in tree-rings from North America, Tasmania, New Zealand, and South Africa (Currie, 1991a-c). Amplitude and phase of the M _n signal are nonstationary with respect to both time and geography. In particular, abrupt 180° phase changes in wave polarity are often observed.     

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.     

Measuring the flow resistance of submerged grass

Through laboratory experiments conducted in a grass‐lined flume, the hydraulic resistance of grass is measured and quantified. For the grass examined, it is found that Manning's n value is greater than those recommended in well‐established texts such as Chow (1959. Open Channel Flow. McGraw‐Hill: Singapore), relatively lower than those predicted by n‐UR methods, but corresponds well with the value found from calibration studies of two‐ and three‐dimensional numerical models. The assumption of a uniform Manning's n value with flow depth, which is often made in numerical modelling, may be invalid depending on the relative submergence of the vegetation. Drag coefficients are evaluated for a method applicable to three‐dimensional numerical models. Further detailed experimental investigation and application of these approaches within a numerical modelling framework is now recommended. Copyright © 2002 John Wiley & Sons, Ltd.     

A method of estimating the stress exponent in the flow law for rocks using fold shape

On the basis of experiment and theory, we expect rocks to deform in a linear fashion when diffusive processes control deformation, and nonlinearly in most other situations. The geometric characteristics of buckle folds in layered materials are dependent on rheological parameters, and in particular depend strongly on the stress exponent,n _L , of the stiff layers involved. Thus, information about the deformation rocks have undergone and their rheological state during deformation can be obtained by studying fold shapes and strain distributions. This is important because there is uncertainty in extrapolating laboratory-derived flow laws to the very slow natural strain rates and large strains found in nature.We have studied the development of buckle folds in linear and nonlinear materials using finite-element modeling, and interpolated the numerical results to construct plots relating several geometric parameters to variations in power-law exponent,n _L , and viscosity ratio,m, of layer to matrix. Such plots allow for a comparison of the results of numerical models with data for many natural and experimentally-produced folds, and there is consistency among the data for folds produced in physical models, using both linear and nonlinear materials and the numerical simulations. data for folds from the Appalachian Mountains, the Alps and elsewhere, however, suggest high values ofn _L in the flow laws for a number of rock types. The unexpectedly high estimates ofn _L suggest that other factors, such as strain softening or anisotropy, may influence fold shape, and thus complicate the estimation of the rheological properties of rocks.     

A quantitative evaluation of Playfair's law and its use in testing long‐term stream erosion models

Playfair's law (J. Playfair, illustrations of the Huttonian Theory of the Earth, 1802) requires any two tributaries in a river network to lower at the same rate near their junction. Although this law holds exactly at the junction, it is unclear how well it holds in the vicinity of the junction. This issue has practical importance because Playfair's law has been used to estimate parameters for detachment‐limited models of erosion. If the incision rate of a stream is modelled as βA^mSⁿ, where β is an erodibility parameter, A is the area drained by the stream, and S is the local gradient of the channel, then the ratio of the parameters m/n can be estimated from junctions by assuming that Playfair's law holds over the distance used to determine S for each tributary. In this paper, Playfair's law and associated m/n estimates are evaluated for simulated basins with constant and temporally varying uplift rates (or baselevel lowering rates). The results demonstrate that estimates of m/n may be biased for basins with upward‐concave stream profiles because the local slope must be approximated with an average upstream slope. In addition, when uplift rate varies temporally, knickpoints are shown to travel through the basins with constant vertical velocity. Because incision rates vary within the basin, Playfair's law only holds exactly at the junctions. These effects are more important when slopes are measured over longer distances. Finally, measurement techniques are presented which address these potential biases. Copyright © 2001 John Wiley & Sons, Ltd.     

Sensitivity analysis of hydraulic conductivity and Manning's n parameters lead to new method to scale effective hydraulic conductivity across model resolutions

Hydrological modelling is an important tool for research, policy, and management, but uncertainty remains about parameters transferability from field observations made at small scale to models at the catchment scale and larger. This uncertainty compels the need to develop parameter relationships that are translatable across scale. In this study, we compare the changes to modelled processes as resolution is coarsened from 100‐m to 1‐km in a topographically complex, 255‐km² Colorado River headwater catchment. We conducted a sensitivity analysis for hydraulic conductivity (K) and Manning's n parameters across four orders of magnitude. Results showed that K acts as a moderator between surface and subsurface contributions to streamflow, whereas n moderates the duration of high intensity, infiltration‐excess flow. The parametric sensitivity analysis informed development of a new method to scale effective hydraulic conductivity across modelling resolutions in order to compensate for the loss of topographic gradients as resolution is coarsened. A similar mathematical relationship between n and lateral resolution changes was not found, possibly because n is also sensitive to time discretization. This research provides an approach to translate hydraulic conductivity parameters from a calibrated coarse model to higher resolutions where the number of simulations are limited by computational demand.     

Steady flows at the top of the core from geomagnetic field models: The steady motions theorem

Abstract

It is demonstrated that the steady tangential velocity v_s at the closed surface δK of a perfect fluid conductor bounded by a rigid, impenetrable exterior can be uniquely determined from knowledge of the normal component of the time varying magnetic flux density B _n, on δK. In the context of a simple earth model consisting of an electrically insulating mantle surrounding a perfectly conducting core, the assumption of steady flow provides enough extra information to eliminate the toroidal ambiguity in B _nv and to allow derivation of a unique, global flow at the top of the core from a model of the geomagnetic field.     

Large values of hydraulic roughness in subglacial conduits during conduit enlargement: implications for modeling conduit evolution

Hydraulic roughness accounts for energy dissipated as heat and should exert an important control on rates of subglacial conduit enlargement by melting. Few studies, however, have quantified how subglacial conduit roughness evolves over time or how that evolution affects models of conduit enlargement. To address this knowledge gap, we calculated values for two roughness parameters, the Darcy–Weisbach friction factor (f) and the Manning roughness coefficient (n), using dye tracing data from a mapped subglacial conduit at Rieperbreen, Svalbard. Values of f and n calculated from dye traces were compared with values of f and n calculated from commonly used relationships between surface roughness heights and conduit hydraulic diameters. Roughness values calculated from dye tracing ranged from 75–0.97 for f and from 0.68–0.09 s m^‐1/3 for n. Equations that calculate roughness parameters from surface roughness heights underpredicted values of f by as much as a factor of 326 and values of n by a factor of 17 relative to values obtained from the dye tracing study. We argue these large underpredictions occur because relative roughness in subglacial conduits during the early stages of conduit enlargement exceeds the 5% range of relative roughness that can be used to directly relate values of f and n to flow depth and surface roughness heights. Simple conduit hydrological models presented here show how parameterization of roughness impacts models of conduit discharge and enlargement rate. We used relationships between conduit relative roughness and values of f and n calculated from our dye tracing study to parameterize a model of conduit enlargement. Assuming a fixed hydraulic gradient of 0.01 and ignoring creep closure, it took conduits 9.25 days to enlarge from a diameter of 0.44 m to 3 m, which was 6–7‐fold longer than using common roughness parameterizations. Copyright © 2013 John Wiley & Sons, Ltd.     

Rheological information from geological structures

The contrast in rheological properties between layers of different composition or texture, and between stiff inclusions and their matrix, gives rise to perturbations in flow that result in structures. Theory and modeling allow us to understand the conditions necessary for such structures to form and, conversely, we can use the form of the structures to infer possible rheological conditions for the rocks during natural deformation. We review here several structures and their use as indicators of rheological behavior, based on theory, numerical and experimental models, and observations on naturl structures.Theory predicts that a dominant wavelength/thickness (L _d /h) exists for both folding and boudinage that depends on the ratio of viscosities of layer to matrix, the homogeneous shortening undergone by the layer, and the exponent,n, in a flow law of power-law type. The measurement of averageL/h, and of the shortening within the layers allows an estimate of the power-law exponent of the stiff layer to be made. Also, numerical modeling shows that fold hinges become sharper asn increases and the limbs become relatively longer and straighter. The dynamic growth of pinch and swell instabilities only overcomes the kinematic decay in nonlinear flow, thus the existence of pinch and swell is by itself evidence of nonlinear behavior.Strain rate and strain, increase more rapidly away from the neutral surface for a layer of power-law rheology (withn>1) than for a layer of Newtonian rheology. Thus, strain gradient across a fold hinge, at fixed amplitude or limb dip, increases with increasingn.Porphyroclasts in mylonites develop characteristic rims of recrystallized grains that are drawn out into trails of or ° shape by the perturbed flow of the, material around the clast. Experimental evidence suggests that shapes occur if flow is linear, whereas nonlinear flow may give rise to the shape.The inference of rheological behavior from structures is complementary to the determination of rheological properties of rocks in the laboratory. What data there is suggest that constitutive relations for rocks undergoing ductile deformation in which many structures develop are highly nonlinear. There is general qualitative agreement between flow laws inferred on the basis of experimental results and those inferred from observation of structural characteristics.