Base‐Flow Recessions—A Review

Abstract

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 ...

Longitudinal hydraulic analysis of river‐aquifer exchanges

“…[43] Various methods have been used to represent streamflow recession over longer times including solution of the Boussinesq equation, development of empirical equations, and superimposition of hydrographs of groundwater discharge produced either by distinct processes (e.g., release of bank storage, shallow hillslope drainage, and deeper aquifer discharge) or by recharge events (impulses) over time [Rorabaugh, 1964;Hall, 1968;Yates and Snyder, 1975;Brutsaert and Nieber, 1997;Tallaksen, 1995]. For the Methow River example, streamflow recession can be represented for about 2 months by a power function of time (Q(t) = 122 t À0.9 ) compared with weeks for relationship based on a simple linear time exponent (Figure 5).…”

“…For the analysis of river-aquifer exchanges, the Boussinesq equation is typically applied to calculate groundwater discharge for a valley cross section (i.e., is oriented perpendicular to the river channel) assuming horizontal flow where the river channel fully penetrates the aquifer and thus intercepts all groundwater flow [Cooper and Rorabaugh, 1963;Hornberger et al, 1970;Hall and Moench, 1972;Brutsaert and Nieber, 1997;Ostfeld et al, 1999;Troch et al, 2003]. Under these assumptions, solutions to the Boussinesq equation provide a theoretical basis for either linear or nonlinear exponential streamflow recession generated by a draining aquifer, which are characteristic of many rivers [Hall, 1968;Tallaksen, 1995].…”

Comparative analysis between analytical approximations and numerical solutions describing recession flow in unconfined hillslope aquifers

“…Results presented herein suggest that the issue of linearity and non-linearity, stressed by different authors (Hall, 1968;Burtsaert and Lopez, 1998;Wittenberg, 1999;Dewandel et al, 2003 likely because the effect of gravity might be overestimated with this particular expression. The analytical solution for aquifers with concave floor, having an exponential form, produces up to a certain extent similar outflows as MODFLOW.…”

The hydrological response of baseflow in fractured mountain areas

“…Despite the heterogeneity which exists in the composition of baseflow (Hewlet, 1961;Tallaksen, 1995), it can be defined as the portion of surface flow originating from subterranean storage (Hall, 1968), where most of the input comes from saturated soil, and in most cases, from shallow, generally unconfined, aquifers (Wittenberg and Sivapalan, 1999). Their "hidden" nature and the problems in obtaining data for water storage in the subsoil present an added difficulty to their study when compared with surface techniques, where it is possible to obtain information either through direct methods (gauging sites, weather stations, etc.)…”