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Double-mass curves, with a section fitting curves to cyclic data

The double.-mass curve is used to check the consistency of many kinds of hydrologic data by comparing data for a single station with that of a pattern composed of the data from several other stations in the area The double-mass curve can be used to adjust inconsistent precipitation data. The graph of the cumulative data of one variable versus the cumulative data of a related variable is a straight line so long as the relation between the variables is a fixed ratio. Breaks in the double-mass curve of such variables are caused by changes in the relation between the variables. These changes may be due to changes in the method of data collection or to physical changes that affect the relation. Applications of the double-mass curve to precipitation, streamflow, and sediment data, and to precipitation-runoff relations are described. A statistical test for significance of an apparent break in the slope of the double-mass curve is described by an example. Poor correlation between the variables can prevent detection of inconsistencies in a record, but an increase in the length of record tends to offset the effect of poor correlation. The residual-mass curve, which is a modification of the double-mass curve, magnifies imperceptible breaks in the double-mass curve for detailed study. Of the several methods of fitting a smooth curve to cyclic or periodic data, the moving-arc method and the double-integration method deserve greater use in hydrology. Both methods are described in this manual. The moving-arc method has general applicability, and the double integration method is useful in fitting a curve to cycles of sinusoidal form.

Water Supply Paper↗

Graphical correlation of gaging-station records

A gaging-station record is a sample of the rate of flow of a stream at a given site. This sample can be used to estimate the magnitude and distribution of future flows if the record is long enough to be representative of the long-term flow of the stream. The reliability of a short-term record for estimating future flow characteristics can be improved through correlation with a long-term record. Correlation can be either numerical or graphical, but graphical correlation of gaging-station records has several advantages. The graphical correlation method is described in a step-by-step procedure with an illustrative problem of simple correlation, illustrative problems of three examples of multiple correlation--removing seasonal effect--and two examples of correlation of one record with two other records. Except in the problem on removal of seasonal effect, the same group of stations is used in the illustrative problems. The purpose of the problems is to illustrate the method--not to show the improvement that can result from multiple correlation as compared with simple correlation. Hydrologic factors determine whether a usable relation exists between gaging-station records. Statistics is only a tool for evaluating and using an existing relation, and the investigator must be guided by a knowledge of hydrology.

Water Supply Paper↗

Flow-duration curves

The flow-duration curve is a cumulative frequency curve that shows the percent of time specified discharges were equaled or exceeded during a given period. It combines in one curve the flow characteristics of a stream throughout the range of discharge, without regard to the sequence of occurrence. If the period upon which the curve is based represents the long-term flow of a stream, the curve may be used to predict the distribution of future flows for water- power, water-supply, and pollution studies. This report shows that differences in geology affect the low-flow ends of flow-duration curves of streams in adjacent basins. Thus, duration curves are useful in appraising the geologic characteristics of drainage basins. A method for adjusting flow-duration curves of short periods to represent long-term conditions is presented. The adjustment is made by correlating the records of a short-term station with those of a long-term station.

Water Supply Paper↗

Flood-frequency analyses, Manual of Hydrology: Part 3

This report describes the method used by the U.S. Geological Survey to determine the magnitude and frequency of momentary peak discharges at any place on a stream, whether a gaging-station record is available or not. The method is applicable to a region of any size, as a river basin or a State, so long as the region is hydrologically homogeneous. The analysis provides two curves. The first expresses the flood discharge-time relation, showing variation of peak discharge, expressed as a ratio to the mean annual flood, with recurrence interval. The second relates the mean annual flood to the size of drainage area alone, or to the size area and other significant basin characteristics. A frequency curve may be defined for any place in the region by use of these two curves. The procedure is: (a) measure the drainage area and other appropriate basin characteristics from maps; (b) from the second curve, select the mean annual flood corresponding to the proper drainage area factors; (c) from the first curve, select ratios of peak discharge to mean annual flood for selected recurrence intervals, as 2, 10, 25, and 50 years; and (d) multiply these ratios by the mean annual flood and plot the resulting discharges of known frequency to define the frequency curve. Two reports not previously given general circulation are included as sections of this report. These are 'Plotting Positions in Frequency Analysis' by W. B. Langbein, and 'Characteristics of Frequency Curves Based on a Theoretical 1,000-Year Record' by M. A. Benson.

Water Supply Paper↗

Storage and flood routing

The basic equations used in flood routing are developed from the law of continuity. In each method the assumptions are discussed to enable the user to select an appropriate technique. In the stage-storage method the storage is related to the mean gage height in the reach under consideration. In the discharge-storage method the storage is determined, from weighted values of inflow and outflow discharge. In the reservoir-storage method the storage is considered as a function of outflow discharge alone. A detailed example is given for each method to illustrate that particular technique.

Water Supply Paper↗

An application of thermometry to the study of ground water

Except for studies of temperature data related to ground-water developments that induce infiltration from streams, little attention has been given to the possibility of using temperature fluctuations as a tool for studying the elements of the hydrologic cycle involving ground water. The temperature of the water discharged from large installations that induce river infiltration through alluvial deposits depends primarily on the following factors: (a) the porosity of the aquifer, (b) the specific heat of the rocks or mineral grains making it up, (c) the temperature of the ground water in storage, (d) the temperature of the river water, and (e) the amount of mixing that occurs as a result of pumping. In six installations of this type, where the annual rivertemperature fluctuations ranged from 44° to 52°F, the average range in groundwater temperature was 22 °F. The cycles of ground-water temperature lagged behind the river-temperature cycles by 1 to 5 1 / 2 months. Under the conditions that existed, the lag of the minima of the cycles was much greater than that of the maxima, largely because of variations in pumpage and of the effect of viscosity differences on the rate of flow. An experimental study was made at Worthington in southwestern Minnesota to determine whether temperature fluctuations could be used to study rates and directions of ground-water movement or to evaluate recharge conditions. Three shallow glacial-outwash aquifers were studied by measuring temperatures at approximately monthly intervals in three municipal-supply wells whose average yields were about 60 to 150 gpm (gallons per minute). Temperatures were read with an accuracy of 0.01° to 0.02°C, and the data were analyzed graphically and correlated in detail with lake levels, lake temperatures, precipitation, and groundwater levels. Thermographs for 2 wells, 1 completed in a semiconfined aquifer about 200 feet from Okabena Lake and the other in a water-table aquifer about 850 feet from the lake, indicate that pumping induces water to move from the lake into the aquifers. A larger percentage of cold lake water was mixed with ground water from January to March 1958 than from January to March 1959. On the assumption that the cold or warm lake water was a distinct mass, the average time required for water to move from the lake to the well 200 feet away, under the prevailing hydraulic gradient, was 2 to 4 months; and to the well 850 feet away, 5 to 7 months. The thermograph for a well 1,800 feet from the lake, completed in an artesian aquifer that is confined by relatively impervious glacial till, indicates that the till acts as an insulating medium. However, despite the apparently low permeability of the till, the thermograph suggests that the lowering of artesian pressure, which results from pumping, induces warmer water to move downward through the till. The infiltration of relatively warm spring and summer rainfall can be detected on the thermographs of all the wells. The precise measurement of fluctuations in ground-water temperature, based on monthly readings in shallow glacial-outwash aquifers (up to about 70 feet deep), is useful in the study of ground-water movement and recharge. In addition to the study of natural phenomena in the hydrologic cycle, thermometry may be used as a tool in making detailed studies of (1) the effects of inducing the infiltration of surface water, (2) artificial recharge, (3) the effects of injecting petroleum products or radioactive or other wastes into the ground, and (4) ground-water movement in mines.

Water Supply Paper↗

A field method for measurement of infiltration

The determination of infiltration--the downward entry of water into a soil (or sediment)--is receiving increasing attention in hydrologic studies because of the need for more quantitative data on all phases of the hydrologic cycle. A measure of infiltration, the infiltration rate, is usually determined in the field by flooding basins or furrows, sprinkling, or measuring water entry from cylinders (infiltrometer rings). Rates determined by ponding in large areas are considered most reliable, but the high cost usually dictates that infiltrometer rings, preferably 2 feet in diameter or larger, be used. The hydrology of subsurface materials is critical in the study of infiltration. The zone controlling the rate of infiltration is usually the least permeable zone. Many other factors affect infiltration rate--the sediment (soil) structure, the condition of the sediment surface, the distribution of soil moisture or soil- moisture tension, the chemical and physical nature of the sediments, the head of applied water, the depth to ground water, the chemical quality and the turbidity of the applied water, the temperature of the water and the sediments, the percentage of entrapped air in the sediments, the atmospheric pressure, the length of time of application of water, the biological activity in the sediments, and the type of equipment or method used. It is concluded that specific values of the infiltration rate for a particular type of sediment are probably nonexistent and that measured rates are primarily for comparative use. A standard field-test method for determining infiltration rates by means of single- or double-ring infiltrometers is described and the construction, installation, and operation of the infiltrometers are discussed in detail.

Water Supply Paper↗