Figure captions
Figure 1: Conceptual regimes of lateral flow in the soil, defined by the
depth below which rainfall or percolation intensity exceeds vertical
hydraulic conductivity. Conditions are expected to change over time
between and during storms, and to exhibit spatial variability.
Figure 2:
(a)Topography for example run.
‘Smoothish’ surface: 320 x 320 m (128 x 128 cells) area. 2m contours.
5% gradient
Divide at top: rolling lateral margins.
(b) Total storm discharge for example run on surface of (a). Total storm
discharge (mm x cells) from a 120 mm storm at 30 mm/hour
Figure 3.
(a)Total storm discharge as a function of drainage area for 3 lateral
transects (x = 20, 64, 118) across the area.
120 mm storm at 30mm/hr. Discharge increases less than linearly, so that
runoff is declining downslope (r~
A-.4).
(b) Total storm runoff as a function of drainage area for 3 lateral
transects across the area. 30 mm storm at 60mm/hr., with 4x higher
infiltration rates. Note the divergence of individual transect trends.
Figure 4: Modelled evolution over time of spatially averaged surface
detention, runoff, near-surface and total soil storage during and after
2 hour storms of uniform intensity.
30 mm storm at 15 mm.hr-1
120 mm storm at 60 mm.hr-1
Figure 5: Total storm slope base runoff and total storage for uniform
storms of different total rainfall.
Note log scales for rainfall & runoff. Arithmetic scale for storage.
Regressions apply to upper and lower portions of the curves separately.
Storms of 2-hour total duration (varying intensity)
Storms at 60 mm/hr (varying duration)
For small storms, almost all rain infiltrates, so that storage
=rainfall, and total runoff is small, generated by low infiltration
patches close to the base of the slope. This behaves as a power law of
storm rainfall (with exponent 2-5) .
For large storms, ultimate storage depends on duration, scaled to steady
long-term infiltration rate. Total runoff is controlled by the limiting
storage, which depends on total storm (and runoff) duration.
Figure 6. The effect of slope length on the dependence of storm runoff
and storm total storage on storm rainfall
(a) & (b): For storms of 2-hour duration
(c) & (d): for storms at 60 mm/hr
In each case, curves show the relationship for slopes of length 8, 16,
32 and 128 cells (20-320 m). For low rainfalls, storage lies close to
the 1:1 line, at which all rainfall infiltrates.
Figure 7. Comparison between Total storm (a) Storage and (b) Runoff
estimated from full model simulation in 128x128 cell grid, and
regression model of equations (4) to (6) with the following parameter
values: a = 10 mm.hr-1; b = 10 mm; c = 2 mm;
L0 =2.5 m; m=4
In graph legends, x = length in number of 2.5m cells
Input values for slope length, L = 20-320 m,
Storm rainfall R = 8 – 480 mm, Storm Duration, T = 8 min
– 8 hr.
(c) Full model storage vs. SCS model for CN = 80 & 90
Figure 8: View of the study plot at the Sierra de Enguera experimental
station. Bare plots of width x length 1x1, 1x2, 1x4, 2x8, 4x16 m. Runoff
collectors in the foreground. Inset location map of SE Spain.
Figure 9: Sierra de Enguera runoff plots: Regression estimate compared
with measured runoff data.
Data for 220 events with measured runoff, 2005-2014.
Maximum event = 230 mm rainfall with 115 mm runoff.
Estimated storage, S = Θ/[1+(Θ
/R)2]0.5
Estimated runoff, r = R-S
Where R = storm rainfall, S = storm storage, Θ =storage threshold.
Lines bracket 90% of the data points around the 1:1 line
(b) Storage threshold, Θ as a function of plot length, L.
Θ =26.5 L0.57
(c) Event storage, S as a function of R & Θ. Data points are binned
values, each the average for 10 events in rank order.
Figure 10: Response of runoff coefficient to storm size, storm intensity
and slope length, following equation (5). Note non-zero responses to
small storms. Parameter values as for Sierra de Enguera site. Dotted
curves are for SCS curve number method for comparison.
Figure 11: Extrapolated response of runoff coefficient to slope length
for a range of storm rainfalls (R )following equation (5), with
parameter values as for Sierra de Enguera site. Shorter slopes imply
higher drainage densities.