Itydrologists have studied base-flow recessions for one hundred years or more. By the early nineteen hundreds much of the basic mathematical development was completed, and some methods of hydrograph analysis were known. Recent mathematical work, although repetitive to some extent of the earlier efforts, has the advantage that it assesses more closely the effects of the simplifying assumptions used to obtain solutions. Most workers have preferred to follow graphical or statistical rather than mathematical approaches. The reasons appear to lie mainly in problems caused by the assumptions and in difficulties in interpreting the real stream hydrograph. Also, base flow can come from numerous sources besides ground water. Other complications arise from the question of whether the basin response is linear or nonlinear, because the response is a function of various geologic and hydrologic factors in addition to those considered in the mathematical derivations. (Key words: Base flow; drainage basin characteristics) SYMBOLS B, constant discharge; H, saturated thickness; K, constant; Kr -exp (-•), recession constant; L, length from stream bank to valley wall; P, hydraulic conductivity; Q, discharge at time t; Q0, initial discharge at time t -0; Q•, Q•., initial discharge for two components at time t -0; T, t -]-1/•, transformed time; V, storage volume at time t; a, Q0• b --constant; b, n/(1 -n), constant exponent; exp, exponential; f, t • •'• --transformed time; m, constant exponent; n, constant exponent; t, time; a, •-•'PH/4L•'• --recession constant; a•, a•, recession constants for two components; /•, 0.434• --recession constant; •, specific yield or coefficient of storage for confined flow; •, recession constant; •, (9PH)/(2L•'•)# --recessioa constant. x Published with the approval of the Director of the New Hampshire Agricultural Experiment Station as Scientific Contribution No. 417. water flow, low flow, percolation flow, underrun, seepage flow, and sustained flow. This paper emphasizes primarily the nature and significance of base-flow recessions, as determined from stream hydrographs. Base flow is defined, for the purposes of this review, as the portion of flow that comes from groundwater storage or other delayed sources. The stream hydrograph is composed of base flow 973 9'74 rR•NC•S R. HALL during periods of no recharge with superim-hydrologists seem to have interpreted it [Mailposed components that are commonly referred let, 1902]. to as interflow and direct runoff at, all otherNowhere in Dausse's commonly cited paper stages of flow except when the stream is dry. of 1842 is the law explicitly s•ated and, al-The components of the hydrograph have been though he realized the importance of evaporaof great interest for more than a hundred years, tion, Dausse did not seem to appreciate the and hydrologists have been working to analyze significance of transpiration. Actually, he was base flow, sometimes in close communication concerned with the effects of deforestation on but at other times seemingly without knowl-summer ...
Flow and head variations in stationary linear stream‐aquifer systems are obtained through application of the convolution equation. Four highly idealized cases involving finite and semi‐infinite aquifers, with and without semipervious stream banks, are considered. Equations for the instantaneous unit impulse response function, the unit step response function, and the derivative of the unit step response function are given for each case. Head fluctuations in the aquifer due to an arbitrarily varying flood pulse are obtained for the cases involving a finite aquifer with and without a semipervious stream bank. Flow in and out of the aquifer at the stream bank is determined for the same cases and demonstrates the value of the convolution equation in evaluating the base flow. Head variations, and to a lesser extent flow variations, are apparently relatively insensitive to variations in aquifer diffusivity.
With the increasing interest in the relationships between dissolved constituents and discharge in streams a reasonable basis is needed for the selection of possible models that might aid in analyzing the data. A series of simple mixing models based on mass balance calculations is presented along with derivations and solutions for certain assumptions about the mixing volumes and the storage volume-discharge relationship. If concentration and discharge data show a hysteresis or loop relationship with time, then the commonly assumed direct relationship between total volume of water in the stream channel and stream discharge is probably not valid. The relationship of the constants in the derived equations to physical or chemical factors is masked at the present time by the nature of the initial assumptions and the method of derivation.
Six mixing models and a number of equations derived from them have been proposed for some possible dissolved solids‐discharge relationships in streams. The equations can be put in a form suitable for statistical analysis by digital computer. In actual application, however, a major problem arises in determining which equation or model is most applicable because the data tend to fit two or more equations equally well. A particular difficulty is encountered in deciding whether a constant component of dissolved solids is present. This decision is most critical when only total dissolved solids or electrical conductivity is used for concentration. An examination of other chemical data, if available, along with knowledge of the stream help decide which model is most suitable. Other problems may arise from factors such as nonrandom trends and variations in the storage volume‐discharge relationship. Under these circumstances, an extension of the equations beyond the range of actual data or inferences about physical or chemical significance of the equations or constant terms should be made with caution.
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