Pierre Y. Julien

Sediment Transport Capacity of Overland Flow

ABSTRACT OVERLAND flow runoff can be either laminar or turbulent depending on the Reynolds number. The rate of soil erosion may be limited by the sediment transport capacity which depends on the type of flow. Sediment transport equations based on velocity were found to give different results than those based on shear stress. Most of the sediment transport equations developed for turbulent streams should not be applied to soil erosion by overland flow. A general relationship supported by dimensional analysis was derived. The recommended sediment transport capacity relationship can be written as a power function of slope and discharge and the range of exponents was defined from empirical relationships.

Runoff sensitivity to temporal and spatial rainfall variability at runoff plane and small basin scales

Surface runoff sensitivity to spatial and temporal variability of rainfall is examined using physically based numerical runoff models. Rainfall duration tr and temporal sampling interval δt are varied systematically, and normalized by the time to equilibrium te. The relative sensitivity Rs is defined as the total volume of outflow variability over 50 Monte Carlo simulations normalized by the rainfall volume and the coefficient of variation of rainfall. Relative sensitivity to temporal rainfall variability increases with both tr and δt. An asymptotic Rs value proportional to (δt/te1/2) is approached as tr ≫ te. Two-dimensional surface runoff simulations with spatially variable rainfall, without temporal variability, on two watersheds indicate that Rs decreases as tr/te increases. Normalized Rs versus tr/te curves are identical for two watersheds and a one-dimensional overland flow plane. These findings indicate that spatial variability is dominant when tr te, particularly for larger values of δt/te.

Mechanics of jet scour downstream of a headcut

Scour immediately downstream of a headcut is analyzed by considering the effect of jet diffusion on sediment detachment. The analytical development results in equations for: 1. the equilibrium scour depth; 2. the rate of scour hole development. These equations are applicable for a variety of jet configurations and any bed material including cohesive soils. The equations are tested in laboratory simulated headcuts on bed materials consisting of two noncohesive uniform sands and one cohesive natural soil. The agreement between measured and predicted rates of scour depth increase shows that scour does not increase as a semi-logarithmic function of time. The rate of scour depth increase is very rapid for depths less than 95% of the equilibrium scour depth. Graphical solutions for the rate of scour depth increase are in agreement with the experimental measurements.

Runoff model sensitivity to radar rainfall resolution

Rainfall rates estimated from polarimetric weather radar measurements of a convective rainstorm are used as input to a two-dimensional physically based rainfall-runoff model. The correlation length of the input rainfall field LS is 2.3 km. Runoff simulations are performed on two semi-arid watersheds covering 32 km2 and 121 km2 at basin data grid sizes LM of 125 m and 200 m, respectively. The characteristic basin length scale LW is taken as the square root of the watershed area. Rainfall data at resolutions LR of 1, 2, 3, 4, 6 and 8 km serve as model input to determine the effect of precipitation data spatial resolution on computed outflow hydrographs. Two dimensionless length parameters are identified which describe the similarity of the effect of rainfall data aggregation on both basins. The first parameter, LRLS, describes ‘storm smearing’, and the second parameter, LRLW, describes ‘watershed smearing’. Results from simulations without infiltration show storm smearing occurring as LR → LS. Watershed smearing causes more significant deviations from simulations using the finest-resolution data when LRLW exceeds 0.4. Results with infiltration reveal that excess rainfall volumes decrease with increasing LRLW. Additionally, excess rainfall volumes do not converge as LRLW is decreased to the practical lower limit provided by contemporary weather radars, which is of the order of 1 km.

Direct measurements of secondary currents in a meandering sand-bed river

Natural channels often adopt a meandering course. Water flow in meander bends is three-dimensional, consisting of primary velocities which are tangential to the bend, and secondary velocities, which are in the radial plane. The pattern of secondary flow strongly affects the distribution of primary velocities. This in turn affects the distribution of erosion and deposition in the bend and the way in which the channel shifts and changes shape. Measurements of primary and secondary flows in a meandering gravel-bed river1,2 show that, in addition to the widely recognized main secondary circulation driving surface water outwards and bed water inwards, there can be a small cell of reverse rotation at the outer bank. Further data have been collected in a sand-bedded river at low, intermediate and high discharges. The results confirm the existence of the main and outer bank cells but also indicate that in some bends the main cell does not extend to the inner bank. In fact, secondary flow at the inner bank of wide, shallow bends is directed radially outwards over the whole flow depth at all in-channel flows. This indicates that some models of bend flow and channel development may be significantly in error.

Similarity in Catchment Response: 1. Stationary Rainstorms

The variability in Hortonian surface runoff discharge and volume produced by stationary rainstorms on watersheds with spatially distributed soil saturated hydraulic conductivity is examined using a two-dimensional runoff model and a Monte Carlo methodology. Results indicate that rainfall duration tr, rainfall intensity i, representative time to equilibrium tre, mean saturated hydraulic conductivityKm, and coefficient of variation Cυ play major roles in the variability of surface runoff. Similarity in surface runoff generated on heterogeneous soils is governed by the following dimensionless parameters: T* = tr/tre, K* = Km/i, and Cυ. The variability in both discharge and runoff volume for randomly distributed systems increases with K* and Cυ, compared to the runoff generated from uniformly distributed systems. Runoff variability decreases whenT* increases unless the mean value of hydraulic conductivity approaches the rainfall intensity (K* → 1). In highly pervious watersheds the steady state discharge depends on the spatial distribution of hydraulic conductivity. Lumped values of saturated hydraulic conductivity are found to typically underestimate the peak discharge and runoff volume.

Turbulent velocity profiles in sediment-laden flows

A theoretical analysis shows that velocity profiles in sediment-laden flows are similar to those in clear water. The modified log-wake law, which is developed for clear water by Guo, is also valid in sediment-laden flows. The analysis of the effects of sediment suspension on turbulent kinetic energy and turbulent diffusion shows that: (1) sediment suspension increases mean flow energy loss; (2) sediment suspension weakens turbulent diffusion in the vertical direction and then increases velocity gradient; and (3) sediment suspension affects velocity profile in two ways: average concentration and density gradient. The comparison with narrow-channel laboratory data confirms the theoretical analysis and shows that: (1) the modified log-wake law agrees well with experimental data for sediment-laden flows; (2) both average concentration and density gradient reduce the von Karman constant; and (3) for a given width-depth ratio, sediment concentration slightly increases the wake strength while density gradient has little effect on it. In addition, the modified log-wake law can reproduce experimental data where the maximum velocity occurs below the water surface.

Similarity in Catchment Response: 2. Moving Rainstorms

The influence of storm motion on runoff is explored, with a focus on dimensionless hydrologic similarity parameters. One- and two-dimensional physically based runoff models are subjected to moving rainstorms. A dimensionless storm speed parameterUte/Lp, where U is the storm speed, te is the runoff plane kinematic time to equilibrium, and Lp is the length of the runoff plane, is identified as a similarity condition. Storm motion effects on the peak discharge are greatest when the storm is traversing a one-dimensional runoff plane in the downslope direction at a dimensionless speed of Ute/Lp = 0.5. This conclusion holds for all values of the dimensionless storm sizes Ls/Lp where Ls is the length of the storm in the direction of motion. Simulations with a two-dimensional rainfall-runoff model confirm the applicability of this similarity parameter on natural watershed topography. Results indicate that the detailed simulation of storm motion is necessary when the storm is moving near the velocity of maximum effect, which is considerably slower than typical storm velocities.

Runoff hydrograph simulation based on time variable isochrone technique

Abstract A new method based on an extension to time–area (TA) concept is proposed for rainfall–runoff transformation in watersheds. The method uses time variable isochrones, such that the runoff hydrograph responds well to temporal changes in excess rainfall intensity. The method employs a kinematic-based travel time scheme, which improves existing isochrone extraction techniques. A raster-based approach deals with spatial domain discretization and supports rainfall–runoff simulations in a modular distributed model. The model uses digital elevation model (DEM) data, ground slope, flow direction, and flow accumulation maps to characterize the watershed terrain. The time series of travel time (or isochrones) maps constitute the basis for incremental and total runoff hydrograph computations. The model was calibrated and validated on a small catchment. The methods and modeling algorithms extend the original TA routing method to a distributed terrain-driven, hydraulic-based, and GIS-compatible technique where isochrones vary as the storm intensity and infiltration rate develop.

Time to equilibrium for spatially variable watersheds

Abstract An algorithm for calculating the time to equilibrium of complex watersheds is developed for spatially varied watershed characteristics and excess rainfall intensity. The wave travel time through the flow path originating from the hydraulically most remote point in the basin essentially determines the equilibrium time of the system. The wave travel time is computed for two distinct phases: overland flow and channel flow. The hydraulically most remote point is stationary for all spatially uniform rainstorms but may vary for spatially distributed storms. The time to equilibrium varies inversely with rainfall intensity raised to the power 0.4. Using a raster-based approach, algorithms were developed to determine the distance-drainage area relationship and to perform the numerical integration of the time to equilibrium. Although approximate, the algorithm provides maps showing the isochromes of surface runoff and travel time to the outlet, along with time-area histograms for uniform or spatially distributed rainstorms. Isochrones determine the response time required for water, dilute suspensions and pollutants to reach the watershed outlet under complete equilibrium. The effects of infiltration in delaying the time to equilibrium are significant only when δ / K is large.