A parameter‐efficient hydrologic infiltration model

Abstract

By adopting two extreme assumptions concerning the behavior of unsaturated soil hydraulic conductivity K near saturation, we derived a two-branched model for pending time and infiltration rate decay for arbitrary rainfall rates. One assumption was that K varies slowly near saturation and leads to an expression for pending time and infiltration decay. For initially ponded conditions, pending time is zero, and with rainfall rate r -• •o, the familiar Green and Ampt (191 l) expression results. The other, rather opposite assumption was that K varies rapidly, e.g., exponentially, near saturation. This model also holds for both rainfall and ponded surface conditions, and for ponded conditions the expression is identical to that of Parlange (1971). Each model uses only two parameters, saturated soil conductivity K8 and a parameter that is roughly related to sorptivity and responds nearly linearly to variations in initial saturation. Both parameters are physically related to measurable soil properties. Methods are presented to estimate parameters of either model from infiltrometer tests. The two models are compared with a precise numerical solution of the unsaturated soil water diffusion equations for three soils that represent a range of soil behaviors near saturation. Our results show that either assumption would be an excellent model for most hydrologic purposes, and the relative goodness of fit of each model is generally consistent with the appropriate behavior of K(0 -• 08). K -D(OO/Oz) = r(t)This equation may be integrated and combined with an expression of conservation of mass [Parlange and Smith, 1976] to yield fot f•' O(O) dO (5) r dt = , (0-Or) r-K(O-'-----'•where subscript 1 refers to conditions at the surface and i refers to initial conditions. Pending time occurs when 0• = Os (saturated water content), and therefore the left integral limit is t = t•o.Paper number 8W0017.

Avaliação do efeito da urbanização na produção de sedimentos da bacia do rio Jacarecica/AL mediante uso de modelo hidrossedimentológico distribuído

“…O modelo utiliza também uma variável da saturação relativa inicial do solo S i (m 3 /m 3 ), cujo valor é dado por θ t /ϕ, em que θ i é o índice de umidade inicial do solo. O cálculo da taxa de infiltração ƒ(c) (m/s) é feito pela seguinte equação (Smith & Parlange, 1978):…”

“…O parâmetro α representa o tipo de solo; quando α se aproxima de 0 para areia, a equação 1 aproxima-se à equação de Green-Ampt; e quando α se aproxima de 1 para um solo franco bem uniforme, a equação 1 representa a equação de infiltração de Smith-Parlange (Smith & Parlange, 1978). Sugere-se que a maioria dos tipos de solo é mais bem representada por um valor de á igual a 0,85.…”

A simple accurate method to predict time of ponding under variable intensity rainfall

“…Many mathematical expressions are available for f cap (t) [e.g., Green and Ampt, 1911;Kostiakov, 1932;Horton, 1940;Philip, 1957a;Smith and Parlange, 1978;Parlange et al, 1999], most of which can be readily adapted to represent f cap (F cap ). Alternatively, simple expressions can be fitted to measured f cap data.…”

“…Analytical and empirical mathematical expressions have been proposed to provide a quantitative description of f cap (t) and f (t) [e.g., Green and Ampt, 1911;Kostiakov, 1932;Horton, 1940;Philip, 1957a;Smith and Parlange, 1978;Parlange et al, 1999]. From these results expressions have been derived to estimate the time when ponding occurs, t p [e.g., Chow et al, 1988;Kutilek and Nielsen, 1994;Parlange et al, 1999;Smith et al, 2002;Brutsaert, 2005].…”

La modélisation hydrologique et la gestion de l'eau

“…The first type of mode! views the watershed as an ensemble of inter-connected réservoirs and mimics water routing with various types of discharge expressions and conceptual models (e.g., the infiltration models of GREEN and AMPT (1911), HOLTAN (1961) or SMITH and PARLANGE (1978); the unit hydrographs of SHERMAN (1932) and DOOGE (1973) and the geomorphological unit hydrograph of RODRIGUEZ-ITURBE and VALDES (1979); the ground water discharge mode) of BEVEN and KIRBY (1979);etc.). It is noteworthy that the pioneering Stanford Watershed Model of CRAWFORD and LINSLEY (1966) led to the development of many currently used hydroiogical models including HBV (BERGSTRÔM and FORSMAN, 1973), SLURP (KITE, 1978), TOPMODEL (BEVEN and KIRBY, 1979) and CEQUEAU (MORIN étal., 1981), to name a few.…”