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<br />
<br />than 0,01. The failure may be attributed to the
<br />accuracy of computation specified in interpolating
<br />the physical properties of soil for 9 less than om (see
<br />Table 2). There seems no apparent difficulty in
<br />testing the upper limit of 90 value.
<br />
<br />Effect of ponding depth (h)
<br />
<br />Various immediate ponding situations with the
<br />ponding depth, h, equal to 0,4, 16, and 64 cm were
<br />tested on the same finite-difference model, as shown
<br />in Figure 10, with the (y size this time being kept at
<br />0.5 cm and 90 = 0.2. lt can ,eadily be seen from
<br />Figure 10 that computational oscillation is amplified
<br />and prolonged as the ponding depth increases.
<br />Especially, at h = 64 cm, the computation by using a
<br />J:i.z size of 0.5 em has come near the margin of
<br />breakdown, as demonstrated by big fluctuations a, b.
<br />and c, in Figure 10. This result clearly indicates that a
<br />smaller !:.Z size should be used with such a big
<br />ponding depth,
<br />
<br />Combined effect of rainfall intensity (r)
<br />and space-step size (!:.z)
<br />
<br />To test the effect of the rainfall intensity, " on
<br />the accuracy of the prescnt numerical model requires
<br />the proper selection of!:.z sizes for the different r
<br />values under study, though a very small!:.z always
<br />makes all the computations possible, As shown in
<br />Figure 11, til. = 0,1,0.25,0.5, and 2.5 cm are used in
<br />the analysis of problems involving r = 50, 25, 10, and
<br />
<br /> 102
<br /> ~
<br /> 6
<br /> 5
<br />" 4
<br />.c
<br />..... 3
<br />E
<br />u
<br />, 2
<br />~
<br />. 109
<br />~
<br />.
<br />"
<br />"
<br />0 6
<br />.~ 5
<br />~
<br />.
<br />" 4
<br />~
<br />~
<br />,~ 3
<br />~
<br />"
<br />~
<br /> Z
<br />
<br />0,
<br />
<br />"
<br />
<br />o 0
<br />
<br />o
<br />
<br />.....
<br />o '6i:~
<br />" '..... .....
<br />C;-- ~ll_O .......
<br />..... .....
<br />o "'.....
<br />"''''_0 ~
<br />----
<br />
<br />5 cmlhr, respectively. Computed infiltration rates for
<br />different r values are marked in different symbols and
<br />compared with a best-tit infiltration decay curve
<br />(broken line) which is replotted from Figure 8 for a
<br />hypothetical immediate punding case. Unlike the
<br />results shown in Figure 6, the computed inmtration
<br />rate in Figure II for each r suddenly rises at the time
<br />of ponding. TI'cre are two possibilities which may
<br />cause this rapid rise in the computed f value at the
<br />time of ponding: One is a discontinuity in the upper
<br />boundary condition imposed at the time of ponding
<br />and the other, a discontinuity in the 9-llnelation at
<br />saturation beyond which 8 cannot increase whereas '"
<br />can (I.e" the diffusivily becomes undefined), In
<br />Figure 6 the h value that changes gradually from zero
<br />was obtained from Eq, J 8, while in Figure J I the h
<br />value was fixed at 4 cm immediately after ponding,
<br />As mentioned previously, an imposition of the h
<br />value, if different from zero, after ponding could
<br />become a source of computational oscillation at the
<br />time of ponding. Nevertheless, if computativnal
<br />oscillation damps out before ponding starts, such as
<br />the cases for all ,'s except r = 5 cm/hr in Figure 11,
<br />the discontinuity in the upper boundary condition
<br />can only cause a big single rise in the computed f at
<br />the time of ponding. On the other hand, if computa-
<br />tional oscillation has not damped out yet before
<br />ponding starts, such as the case of r = 5 cmlhr, the
<br />computational oscillation continues for a while even
<br />after ponding. It is not surprising to see from Figure
<br />II that all the computed infiltration decay curves for
<br />the various r values become asymptotic at large t to
<br />
<br />-0- 90 = 0.1
<br />~eo=o.z
<br />__ 6 = 0,3
<br />o
<br />-0- 60 = 0,4
<br />
<br />
<br />~~J(". e
<br />"'* 0
<br />.n:xll'll'1I11'~
<br />C~---~i.::::-
<br />--..::.0: -.:::-
<br />- -- - - --Q'="-
<br />
<br />_ _ _ _ _ ..L~= '::'3 ::::/hr __
<br />
<br />1
<br />10-3
<br />
<br />Z 3 4 56789
<br />t
<br />
<br />2 3 4 5 6 789
<br />10
<br />
<br />2 3 4 5 6789 -2
<br />10
<br />
<br />2 3456789
<br />10-1
<br />
<br />Time - t - hour
<br />
<br />Figure 9. Examples of the effect of initial moisture content (90) on computed infiltration rate (f) under a hypo.
<br />thetical immediate ponding situation,
<br />
<br />27
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