Geology Reports⌕ Search

Geology topics

G. P. Williams

Publications and source records attributed to G. P. Williams.

13 recordsLinked to original sources

Paleohydrological methods and some examples from Swedish fluvial environments I. Cobble and boulder deposits

This article establishes approximate empirical relations for determining the minimum unit stream power, bed shear stress and mean flow velocity capable of moving cobbles and boulders on streambeds. The derived equations then are used to estimate the minimum paleoflows that could have transported the boulders of two ancient fluvial deposits in Sweden. The flow estimates are compared with those made by more conventional hydraulic methods. Bankfull flows also are estimated for one of the two deposits, using various hydraulic equations.

Sweden↗

Paleohydrological methods and some examples from Swedish fluvial environments. II - River meanders

Empirical relations are developed between river-meander features and water-discharge characteristics for 19 reaches along Swedish rivers. In these relations, either average channel width or average radius of curvature of meander arcs can be used to estimate average annual peak discharge and average daily discharge. By accepting certain assumptions, the relations can be applied to other meandering Swedish rivers, present or ancient. The Öster-Dalälven River near Mora is used as an example.

Geografiska Annaler, Series A↗

Comparison of structural and least-squares lines for estimating geologic relations

Two different goals in fitting straight lines to data are to estimate a "true" linear relation (physical law) and to predict values of the dependent variable with the smallest possible error. Regarding the first goal, a Monte Carlo study indicated that the structural-analysis (SA) method of fitting straight lines to data is superior to the ordinary least-squares (OLS) method for estimating "true" straight-line relations. Number of data points, slope and intercept of the true relation, and variances of the errors associated with the independent (X) and dependent (Y) variables influence the degree of agreement. For example, differences between the two line-fitting methods decrease as error in X becomes small relative to error in Y. Regarding the second goal-predicting the dependent variable-OLS is better than SA. Again, the difference diminishes as X takes on less error relative to Y. With respect to estimation of slope and intercept and prediction of Y, agreement between Monte Carlo results and large-sample theory was very good for sample sizes of 100, and fair to good for sample sizes of 20. The procedures and error measures are illustrated with two geologic examples. ?? 1990 International Association for Mathematical Geology.

Mathematical Geology↗

Sediment concentration versus water discharge during single hydrologic events in rivers

Relations between sediment concentration ( C ) and water discharge ( Q ) for a hydrologic event, such as a flood, are studied qualitatively by analyzing "smoothed" temporal graphs (discharge and concentration vs. time) in terms of mode, spread, and skewness. Comparing C Q ratios at a given discharge on the rising and falling limbs of the discharge hydrograph provides a consistent, reliable method for categorizing C-Q relations. Five common classes of such relations are single-valued (straight or curved), clockwise loop, counterclockwise loop, single-valued plus a loop, and figure eight. Temporal-graph mode and skewness influence the type of relation, whereas temporal-graph spread affects the details of the particular C-Q relation (its graphical breadth, shape, orientation, and plotted location). Field examples of the various types of relations are given, including varieties that heretofore have received little attention, such as the figure eight. Explanations for each type of C-Q relation are discussed.

Journal of Hydrology↗

Sediment yield and spurious correlation-toward a better portrayal of the annual suspendend-sediment load of rivers

Bivariate relations between annual sediment yield (tons per year per unit drainage area) and drainage-basin area are spurious because drainage-basin area is common to both axes. Two alternative methods for portraying the annual suspended-sediment load of a river are suggested. One method consists of plotting suspended-sediment load (tons per year) against distance downstream. Such plots indicate that annual suspended-sediment load does not necessarily have a linear relationship with distance. The second method consists of plotting annual suspended-sediment load against drainage-basin area. Both methods more accurately portray fundamental relations between annual sediment load and drainage-basin characteristics than does the yield-area relation because spurious correlation is avoided. Plots were made of annual suspended-sediment load versus time for several stations along each of eight rivers for the 10–15 years of available data. The plots are in-phase with respect to relative magnitude of annual sediment loads.

Geomorphology↗

The Manti, Utah, landslide

PART A: The Manti landslide is in Manti Canyon on the west side of the Wasatch Plateau in central Utah. In early June 1974, coincident with the melting of a snowpack, a rock slump/debris flow occurred on the south rim of Manti Canyon. Part of the slumped material mixed with meltwater and mobilized into a series of debris flows that traveled down the slope a distance of as much as 1.2 km. Most of the flows were deposited either at the base of the steep rocks of the canyon rim or at the site of an old, silted reservoir. A small part of the debris flow deposit stopped on the head of the very large, relatively inactive Manti landslide. The upper part of the landslide began moving as cracks propagated downslope. A little more than a year later, August 1975, movement extended the full length of the old landslide, and about 19 million m 3 of debris about 3 km long and as much as 800 m wide threatened to block the canyon. The upper part of the landslide apparently had moved small amounts between 1939 and 1974. This part of the landslide, identifiable on pre-1974 aerial photographs, consisted of well-defined linears on the landslide flanks and two large internal toe bulges about 2 km downslope from the head. The abrupt reactivation in 1974 proceeded quickly after the debris flows had provided a surcharge in the head and crown area. Movement propagated downslope at 4-5 m/h for the first few days following reactivation. During 1974, the reactivation probably encompassed all the parts of the landslide that had moved small amounts between 1939 and 1974. Movement nearly or completely stopped during the winter of 1974-75, but began again in the spring of 1975. The landslide enlarged from the flanks of the internal toe bulges to Manti Creek at a rate of 2-3 m/h. Movement stopped again during the winter of 1975-76 and began again in the spring of 1976. Thereafter, the displacements have been small compared to earlier. The displacement rates for the landslide were variable depending on where and when they were measured. At the waterline crossing, about 500 m downslope from the head, the maximum rate was about 1 mid, and the peak rate occurred within the first 30 days following reactivation. Almost a year later, during the spring of 1975, the rates there were 0.1-0.3 mid. By the time movement had propagated 2.5 km downslope to Manti Creek, more than 40 m of displacement had occurred at the waterline. Cracks were first noted at Manti Creek on June 21,1975, but movement was initially very slow there. The maximum rate of sliding of about 3.1 mid occurred during the period September 1-19,1975, and the movement decreased and stopped during the winter of 1975-76. At the time the lower part of the landslide was moving rapidly, the rate farther upslope was small. The result was that the landslide changed from being in compression, which was caused by loading from above, to being in extension, which was caused by the lower part moving faster than the upper part. One of the results of the extension was that the landslide pulled apart on a steeper segment of the slope and exposed the failure surface. Since the fall of 1975, the landslide has been separated into two independent parts. There has been no movement in the lower part, whereas movements in the upper part have continued at a rate of a few meters per year. Although the landslide is 6.5 km from the nearest permanent dwelling, it cost nearly $2 million in actual damages and in preparation for a major disaster that did not occur. The waterline for the city of Manti was replaced and a well was drilled to provide an emergency water supply. PART B: The Manti landslide abuts, at its toe, another large landslide called the North slide. In 1975, public officials were concerned that continued movement of the Manti landslide would trigger reactivation of the North slide. In response to this threat, four borings were placed in the North slide to obtain samples for testing and information

Utah↗

River meanders and channel size

This study uses an enlarged data set to (1) compare measured meander geometry to that predicted by the Langbein and Leopold (1966) theory, (2) examine the frequency distribution of the ratio radius of curvature/channel width, and (3) derive 40 empirical equations (31 of which are original) involving meander and channel size features. The data set, part of which comes from publications by other authors, consists of 194 sites from a large variety of physiographic environments in various countries. The Langbein-Leopold sine-generated-curve theory for predicting radius of curvature agrees very well with the field data (78 sites). The ratio radius of curvature/channel width has a modal value in the range of 2 to 3, in accordance with earlier work; about one third of the 79 values is less than 2.0. The 40 empirical relations, most of which include only two variables, involve channel cross-section dimensions (bankfull area, width, and mean depth) and meander features (wavelength, bend length, radius of curvature, and belt width). These relations have very high correlation coefficients, most being in the range of 0.95-0.99. Although channel width traditionally has served as a scale indicator, bankfull cross-sectional area and mean depth also can be used for this purpose.

Journal of Hydrology↗

Improper use of regression equations in earth sciences

A regression equation used to estimate a variable is appropriately used only to estimate the dependent variable of that equation; the equation is inappropriately used when solved for an independent variable. Examples given here of this misuse of regression equations are based on actual cases in sedimentologic, geomorphologic, and paleohydrologic literature. The error involved can amount to several hundred percent.

Geology↗