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<br />
<br />decay curve is drawn on log-log scale. ]n this typical
<br />problem, the initial moisture content, () 0' of Vernal
<br />sandy clay loam is specified arbitrarily at 0.30 and
<br />the given rainfall intensity, r, is 5 cm/hT. For
<br />simplicity, the soil surface is assumed horizontal so
<br />that Eq, 18 is applied to the computation of the
<br />ponding depth, h, As expected, computational oscilla-
<br />tion is significantly large at the beginning of the
<br />computation, but quickly damps out after t = 0.147
<br />hours, The computed infiltration rate (m~rked by
<br />dots) is compatible with the "theoretical" curve
<br />(marked by a broken line) that consists of the 5
<br />cm/hr line from Eq, 3 before ponding and, of course,
<br />an unknown decay curve after ponding. A theoretical
<br />decay curve after ponding cannot be exactly plotted,
<br />The broken curve after ponding plotted in Figure 6 is
<br />merely a line connecting those computed points
<br />which do not seemingly fluctuate or, in the more
<br />strict sense, a best.fit line of the computed points.
<br />
<br />3
<br />10
<br />
<br />2
<br />10
<br />
<br />
<br />"
<br />~
<br />N
<br />E
<br />"
<br />
<br />10
<br />
<br />"
<br />
<br />:::
<br />:E
<br />.
<br />,g
<br />:;;
<br />.
<br />"
<br />~
<br />'0
<br />E
<br />~
<br />
<br />to-I
<br />
<br />lO~2
<br />o
<br />
<br />0, I
<br />
<br />0,2
<br />
<br />0,3
<br />
<br />0.'
<br />
<br />SOU moi.ture content - 9
<br />
<br />Figure 5, Functional relationship between soU mois-
<br />ture diffusivity (D) and soU moisture con.
<br />tent (0) for Vernal sandy clay loam,
<br />
<br />The oscillation also manifests itself on the
<br />saturation front depth (Lr) versus time curve and the
<br />ponding depth versus time relationship, as shown in
<br />Figure 7. For illustration of the significance of
<br />oscillation at early stage, they arc also plotted on
<br />log-log scale, It is conceivable that oscillation in the
<br />computer results appears in the computation of all
<br />the f(t), Le(t), and h(t) values because of their
<br />interrelated roles through Eqs, 16, 17, and 18.
<br />
<br />The validity of the present, numerical model
<br />and the accompanying computational oscillation due
<br />to the adopted numerical scheme were further in-
<br />vestigated by solving a hypothetical problem which
<br />was so formulated that the performance charac-
<br />teristics and the related or interrelated roles of
<br />variables in the model could manifest themselves in
<br />the solution. For example, the magnitude of the
<br />infiltration rate after ponding depends largely on the
<br />ponding depth and this dependence varies with
<br />infiltration time (Philip, 1958). However, the ponding
<br />depth that changes with time cannot be determined
<br />unless surface flow conditions are known_ Only for
<br />water on the horizontal soil surface, can the ponding
<br />depth be computed by using Eq, 18, Therefore, for
<br />convenience, the ponding depth was hypothetically
<br />assumed constant immediately after ponding. The
<br />
<br />t..I,50hr
<br />1,,1.IOhr
<br />,.
<br />
<br />'I
<br />.'
<br />..
<br />]3
<br />~,
<br />
<br />
<br />Given, r.. 5 cm/hr
<br />I} ..0.1
<br />,
<br />
<br />r..:~..:~~~14Thr
<br />
<br />, . -""'---
<br />_L~~.~C~~ __________-.:~~:
<br />
<br />0.5
<br />
<br />, .
<br />10-1
<br />
<br />3456789
<br />
<br />2 3 45 &789
<br />"
<br />
<br />10.1.
<br />
<br />TlJne. t _ bOllr
<br />
<br />Figure 6, Typical computer solutions for rain infUtra-
<br />tion.
<br />
<br />23
<br />
<br />y.cm
<br />
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