: A system is described which: (a) replaces existing sets of diverse terrain indices with a group of statistics for point-characteristics; (b) calculates all of these statistics in a single computer run from a single data set; and (c) utilizes available altitude matrix data The procedures are applicable to Altitude matrix data at any grid mesh From altitudes in each 3 x 3 submatrix, a quadratic surface is fitted and solved for its first and second horizontal and vertical derivatives at the central point This yields the slope gradient, slope aspect, profile convexity, and plan convexity at every point in the original matrix, except for the peripheral rows and columns These 'point' descriptors are presented as: (1) line-printer shaded maps; (2) histograms; (3) scatter plots of each pair; (4) matrix of pair-wise correlations, plus circular regressions on aspect, and several multiple regressions, and (5) summary (moment-based) statistics In general, the five basic descriptors have little relation to each other, except that gradient is usually a quadratic function of altitude A comparison is made with other approaches, such as spectral analysis and fractal modelling The long-distance persistence properties of terrain mean that considerable extra variance at long wavelengths is usually incorporated when the study area is extended Hence the auto correlation function varies with the length of series or size of area Variance of derivatives are also affected, but means, skews, and kurtoses are not

Statistical Characterization of Altitude Matrices by Computer. Report 6. An Integrated System of Terrain Analysis and Slope Mapping.

This comprehensive handbook on the hydraulic design of labyrinth spillways—from theory to current practice—presents a state-of-the-art method for the effective design of labyrinth weirs. The book provides a fundamental understanding of the theory of labyrinth weirs and continues with detailed sections on significant factors that affect the discharge characteristics of labyrinth weirs, such as crest shape, weir height, and sidewall angle. The most common design curves are discussed, and from these a recommendation is developed for only one design curve to be used in future designs. But because site conditions often vary so much from ideal conditions described in this book, a section on site-specific modeling criteria is included for making accurate predictions of prototype performance. In its review of past studies, the book closely examines many long-held concepts, especially concerning the idea of interference, nappe oscillation, and the definition of which head to use in design computations, and revises them in an effort to advance current thinking based on the latest research.

Hydraulic Design of Labyrinth Weirs

Low-head labyrinth weir control structures installed on mild sloping channels or where the channel downstream of the weir is constricting and/or heavily vegetated can experience submergence. Weir submergence occurs when the tailwater surpasses the weir crest elevation, causing an increase in the upstream driving head for a given discharge, relative to a free-discharge condition. The most familiar relationship for predicting submerged weir head-discharge relationships is likely that of James R. Villemonte, which he published in 1947 for sharp-crested linear weirs. For lack of a better alternative, Villemonte’s relation has also been applied to predicting submerged labyrinth weir performance. A new dimensionless submerged head relationship developed in this study is presented for submerged labyrinth weirs. A similar relationship is also presented for linear sharp-crested weirs. The accuracy of the submerged linear weir relationship was equivalent to Villemonte’s and is simpler to solve when working in terms...

Head-Discharge Relationships for Submerged Labyrinth Weirs

A method is presented for the hydraulic design and analysis of labyrinth weirs based upon the experimental results of physical modeling. Discharge coefficient data for labyrinth weirs with quarter-round and half-round crest shapes are presented for sidewall angles ranging from 6 to 35°. Cycle efficiency is also introduced as a design aid, which compares the hydraulic performance of different cycle geometries. Geometric parameters that affect flow performance are discussed. The predictive accuracy of the design method is evaluated through comparisons to previously published labyrinth weir head-discharge data. The companion paper examines nappe behaviors that affect flow performance and presents hydraulic design considerations specific to nappe characteristics.

Hydraulic Design and Analysis of Labyrinth Weirs. I: Discharge Relationships

Determination of capacity of labyrinth side weir by CFD

The capacity of a labyrinth spillway is a function of the total head, the effective crest length, and the crest coefficient. The crest coefficient depends on the total head, weir height, thickness, crest shape, apex configuration, and the angle of the side legs. Data and a procedure are presented for designing labyrinth weirs for angles between 6° and 35°, and for a range of heads. The design procedure allows the angle of the side legs and the number of cycles to be varied until the desired layout and capacity are achieved. The solution is presented in a spreadsheet format that automatically calculates the dimensions for the labyrinth. Even though the design procedure is quite accurate, it is recommended that the capacity and performance be verified with a model study. The model can evaluate factors not included in the design procedure, like aeration effects at low heads, unusual flow conditions in the approach channel, and flow conditions in the discharge channel.

Design of Labyrinth Spillways

Physically based modelling of sheet erosion (detachment and deposition processes) in complex hillslopes

The geometry of hillslopes (plan and profile) affects soil erosion under rainfall-runoff processes. This issue comprises of several factors, which must be identified and assessed if efficient control measures are to be designed. The main aim of the current research was to investigate the impact of surface Roughness Coefficients (RCs) and Complex Hillslopes (CHs) on runoff variables viz. time of generation, time of concentration, and peak discharge value. A total of 81 experiments were conducted with a rainfall intensity of 7 L min−1 on three types of soils with different RCs (i.e., low = 0.015, medium = 0.016, and high = 0.018) and CHs (i.e., profile curvature and plan shape). An inclination of 20% was used for three replications. The results indicate a significant difference (p-value ≤ 0.001) in the above-mentioned runoff variables under different RCs and CHs. Our investigation of the combined effects of RCs and CHs on the runoff variables shows that the plan and profile impacts are consistent with a variation in RC. This can implicate that at low RC, the effect of the plan shape (i.e., convergent) on runoff variables increases but at high RC, the impact of the profile curvature overcomes the plan shapes and the profile curvature’s changes become the criteria for changing the behavior of the runoff variables. The lowest mean values of runoff generation and time of concentration were obtained in the convex-convergent and the convex-divergent at 1.15 min and 2.68 min, respectively, for the soil with an RC of 0.015. The highest mean of peak discharge was obtained in the concave-divergent CH in the soil with an RC of 0.018. We conclude that these results can be useful in order to design planned soil erosion control measures where the soil roughness and slope morphology play a key role in activating runoff generation.

Effects of Roughness Coefficients and Complex Hillslope Morphology on Runoff Variables under Laboratory Conditions

\n Scouring in the downstream of all weirs, including Piano Key Weirs (PKWs), can have major safety implications. Since the research on downstream scouring of PKWs is very limited, and the weir geometry is also known to have an impact on downstream scouring, this study investigated scouring in the downstream of PKWs with rectangular and trapezoidal geometries and two different heights. The scour hole measurements showed that in both rectangular and trapezoidal models, scour hole parameters increased both with the increase in discharge rate and the increase in weir height. Under similar discharge conditions, the scour depth downstream from the rectangular model was greater than that downstream from the trapezoidal model. The dimensionless maximum scour depth, the distance of maximum scour depth from the weir toe, and the scour hole length for the trapezoidal PKW were, on average, 6, 13, and 11% lower than the corresponding ones for the rectangular PKW, respectively. However, these differences decreased with the increase in falling height. For both weir geometries, the maximum scour depth was aligned with the outlet keys. In addition, the maximum scour depth under the outlet keys was 13% greater than the one under the inlet keys.

Nosratollah Amanian

Papers

Design of Labyrinth Spillways

Physically based modelling of sheet erosion (detachment and deposition processes) in complex hillslopes

Effects of Roughness Coefficients and Complex Hillslope Morphology on Runoff Variables under Laboratory Conditions

Effects of weir geometry on scour development in the downstream of Piano Key Weirs

Performance and Design of Labyrinth Spillway