le
nt
AS
ut
ef
ge
O-
or
at
in
Laboratory Field
Treatment f m T sitel site2
tsa/ma
relation between | before and |1.12 1.27 1.44 | 1stdate 1.34 1.22
total surface area | afterrain |1.02 1.14 1.37 | 2nddate 1.23 1.13
and map area
RRC
Index according | before and [2.3 43 85 Istdate 7.7 53
to Currence and after rain 11:4 3.2 7.5 2nd date 7.0 4.0
Lovely (1970)
Table 2: Indices from microrelief describing DEMs
the field. An increase in the microrelief roughness
doubled the value for RRC. The microrelief differences
are well characterized by this index. For the field ex-
periments the decrease of RRC due to rainfall was minor
than but still comparable to that of the laboratory
treatments. Thus both indices seem to be capable to
characterize microrelief and changes due to rainfall in
the field as well as in the laboratory.
Semivariograms were calculated in order to identify
possible spatial patterns. Figs. 3a and 3b show semi-
variograms for the rough and fine surfaces, each before
and after rainfall. In the beginning all curves show a
sharp rise with the lag, until a sill is reached at greater
lag values. The range within which a spatial dependence
of the investigated parameter is visible, is marked by
arrows in the figures. For the rough surface, the range
corresponds to a lag h of 25, while the range is about
12 to 14 in the medium treatment, not shown here.
These lag values are equivalent to 50 mm and 25 mm,
respectively (1 h = 2 mm). This corresponds to the open-
ings of the sieves that were used to fill in the soil
material and depicts the maximum diameters of the
largest aggregates or clods in each microrelief type.
After rainfall range tended to increase slightly, which
might be due to a relative flattening of the bigger
clods. Thus, with the help of semivariograms, it is
possible to confirm the importance of big clods as
surface shaping elements. For the fine treatment there
is no clearly identifiable sill, just a lowered gradient in
the range of 7 to 10. In this case there is no reliable
identification of the largest clods (10 mm diameter)
since this is just four times the height value spacing
and within this comparably high-frequent range no
characteristic sill is possible. The sills in the semivario-
grams are significantly different. Rainfall led to a relative
reduction of the sill by about 2096 for the rough, 5096
for the medium, and 2596 for the fine treatment, respect-
ively. The absence of nugget variance in all semivario-
grams indicates that the grid distance is small enough
to fully characterize the variation in surface microrelief.
Higher resolution in microrelief variation would not
yield any further information. Results of the semivario-
grams from the field experiment DEMs were similar to
those of the medium treatment above. Here nugget
variance was missing, too.
Semivariance
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0 5 10. 15..20 4.25. 30. 35 40 45
a) Lagh
6 ut
Semivariance
fine 9300809999900
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ee
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b) Lagh
Fig. 3: Semivariograms for (a) rough and (b) fine surfaces
before and after rainfall (lag h = 2 mm).
Energy dissipation
The kinetic energy of raindrops impinging on the soil
surface leads to surface sealing, which is the actual
trigger mechanism for runoff formation. As discussed
earlier, the TSA/MA ratio affects the total input of rainfall
energy. The effective normal component of impact force
with respect to impact angle is also relevant to splash
detachment and thus to sealing. Table 3 shows the
calculated effective energy (the normal component of
impact force with respect to the TSA) in percent of the
kinetic energy as simulated in the laboratory experi-
ments.
Laboratory Field
Treatment f m r site 1 site 2
E.eff (%)
before and 84 65 56 1st date 62 71
after rain 95 80 67 2nd date 71 82
Table 3: effective rainfall energy E.eff (/m* tsa) in per-
cent of the kinetic rainfall energy (J/m* ma)
The effective rainfall energy for the rough treatments
is only about one half of its kinetic energy. This share
is significantly larger for the medium and fine areas.
Even after the rain there is considerable energy reduct-
ion in the rough and medium areas. To verify the
theory that the microrelief induced effective rain energy
substantially influences silting and surface runoff, we
must compare the runoff measured in the laboratory
with the effective rain energy. Figures 4a and 4b show
runoff curves. In fig. 4a the cumulated runoff is plotted
against cumulated kinetic energy as it is usual in
literature.
