Splash-saltation of sand due to
wind-driven rain
Wim Cornelis, Greet Oltenfreiter,
Donald Gabriels & Roger Hartmann
WEPP-WEPS workshop, Ghent-Wageningen, 2003
Outline of presentation
• Introduction: some theory
• Materials and methods
• Results
• Conclusions
Introduction – some theory
Rainless conditions
Saltation
Introduction – some theory
Rainless conditions
Saltation
Q  Cu
c,
*
e.g.
u
c
*
 u*tc

Owen (1964)
Lettau & Lettau (1977)
Introduction – some theory
Windfree conditions
detachment
Splash
Introduction – some theory
Windfree conditions
Splash
D  K d E  E t 
e.g.
or Qr
Sharma & Gupta (1989)
Introduction – some theory
Wind-driven rain conditions
Rainsplash-saltation
Introduction – some theory
Wind-driven rain conditions
Rainsplash-saltation
Introduction – some theory
Total sediment transport rate
Q '  Qr
for u*  0
Q'  Qwr  Qw
for u*  0
Introduction – some theory
Objectives:
• Determine sediment mass flux qx and qz (kg m-2 s-1)
and express them as function of x and z resp.
under wind-driven rain (and rainless wind) conditions
• Determine sediment transport rate Qwr (kg m-1 s-1)
and relate them to rain and wind erosivity (KE or M and u*)
Materials and methods
1.
qx ~ F( x )
qz ~ F( z )
Vertical deposition flux in kg m-2 s-1
Horizontal mass flux in kg m-2 s-1
ICE wind-tunnel experiments
(dune sand, under different u* and KE or M)
Kinetic energy KEz or Momentum Mz
splash cups
Shear velocity u*
5 vane probes
(a)
trough
y (m)
0.8
wind
Mass flux qx
23 troughs
0.4
z
(b)
0.8
7 x = 0 8
y (m) tray with test material
6
9
10
wind-tunnel wall
11
12
x (m)
wind
Mass flux qz
4 W&C bottles
0.4
z
6
7 x = 0
8
9
10
Wilson and Cooke catcher
11
12
x (m)
Materials and methods
Shear velocity
Shear velocity u*
wind-velocity profiles
5 vane probes
Materials and methods
Shear velocity
101
height z (m)
100
10-1
u*
z
u 
ln

z0
10-2
10-3
Eq. [7]
u*= 0.50 m s-1
u* = 0.39 m s-1
u* = 0.27 m s-1
10-4
10-5
0
2
4
6
8
10
wind velocity u (m s-1)
12
14
Materials and methods
Shear velocity
u*  0.050  0.037 u ref
0.6
Observed data
Eq. [9]; R² = 0.999
u* (m s-1)
0.5
0.4
0.3
0.2
6
8
10
-1
uref (m s )
12
Materials and methods
Kinetic energy or Momentum
1
KE  m v 2
2
M  mv
v from nomograph of
Laws (1941)
S (rainsplash from cup)
Materials and methods
Kinetic energy or Momentum
-1
-2
-2
0.4
momentum Mz (kg m s )
Observed data
Eq. [10] or [11]; R² = 0.857
-1
kinetic energy KEz (J m s )
1.5
0.3
1.0
0.2
0.5
0.1
0.0
0.0
0
2
4
6
8
rainsplash from splash cups S (g m-2 s-1)
KE z  0.010  0.141 S
M z  0.003  0.042 S
Materials and methods
Sensit “KE of rain field sensor”
Saltiphone
Did not work properly under given circumstances
Materials and methods
2.
Q  F( E, u* )
Mass transport rate in kg m-1 s-1
xmax
Qx 
q
x
Calibration
dx
0
Contribution of
E (KEz or Mz)
u*
z max
Qz 

0
qz dz
Validation
-1
measured rainfall intensity I (mm h )
Materials and methods
150
p = 75 kPa
p = 100 kPa
p = 150 kPa
Eq. [8]; R² = 0.995
100
50
0
0.2
0.3
0.4
0.5
-1
shear velocity u* (m s )
I  119  387 u*2.43
0.6
Results – wind-driven rain
Vertical deposition flux qx (g m-2 s-1)
1
0
0
0
1
1
2
u
;
K
E
s
=
0
.
2
7
m
s
=
0
.
2
5
0
J
m
z
*
1
1
2
u
;
K
E
s
=
0
.
3
9
m
s
=
0
.
4
5
5
J
m
z
*
1
0
0
qx(gm -2 s -1)
1
1
2
u
;
K
E
s
=
0
.
5
0
m
s
=
0
.
5
9
1
J
m
z
*
1
0
1
0
.
1
0
.
0
1
0
.
0
0
1
0
1

2
3
4
x
(
m
)
5
Results – wind-driven rain
Vertical deposition flux qx (g m-2 s-1)
1
0
0
0
1
1
2
u
;
K
E
s
=
0
.
2
7
m
s
=
0
.
2
5
0
J
m
z
*
1
1
2
u
;
K
E
s
=
0
.
3
9
m
s
=
0
.
4
5
5
J
m
z
*
1
0
0
qx(gm -2 s -1)
1
1
2
u
;
K
E
s
=
0
.
5
0
m
s
=
0
.
5
9
1
J
m
z
*
E
q
.
(
8
.
9
)
1
0
1
0
.
1
0
.
0
1
0
.
0
0
1
0
1

2
3
4
5
x
(
m
)
q   e   Δx   e  Δx
R2 > 0.99
Results – wind-driven rain
Horizontal flux qz (g m-2 s-1)
1
1
2
u
;
K
E
s
=
0
.
2
7
m
s
=
0
.
2
5
0
J
m
z
*
qz(gm -2 s -1)
1
0
0
0
1
0
0
1
1
2
u
;
K
E
s
=
0
.
3
9
m
s
=
0
.
4
5
5
J
m
z
*
1
1
2
u
;
K
E
s
=
0
.
5
0
m
s
=
0
.
5
9
1
J
m
z
*
1
0
1
0
.
1
0
.
0
1
0
.
0
0
.
1
0
.
2
z
(
m
)
0
.
3
Results – wind-driven rain
Horizontal flux qz (g m-2 s-1)
1
1
2
u
;
K
E
s
=
0
.
2
7
m
s
=
0
.
2
5
0
J
m
z
*
qz(gm -2 s -1)
1
0
0
0
1
0
0
1
1
2
u
;
K
E
s
=
0
.
3
9
m
s
=
0
.
4
5
5
J
m
z
*
1
1
2
u
;
K
E
s
=
0
.
5
0
m
s
=
0
.
5
9
1
J
m
z
*
E
q
.
(
8
.
1
2
)
1
0
1
0
.
1
0
.
0
1
0
.
0
0
.
1
0
.
2
0
.
3
z
(
m
)
q  ae
b z
R2 > 0.98
Results – wind-driven rain
Transport rate Q (g m-1 s-1)
xmax
Qx 
q
x
Calibration
dx
0
Contribution of
E (KEz or Mz)
u*
z max
Qz 

0
qz dz
Validation
Results – wind-driven rain
Transport rate Q (g m-1 s-1)
3
Q
d
a
t
a
x
E
q
.
(
9
.
1
1
)
;
R
²
=
0
.
9
5
6
Q (gm -1 s -1)
2
1
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
4
(
K
E
K
E
)
u
(
)
z
z
t
*
Q  4.5 10 3 KEz  KEzt u*0.4
Results – wind-driven rain
Transport rate Q (g m-1 s-1)
3
Q
d
a
t
a
x
Q
d
a
t
a
z
E
q
.
(
9
.
1
1
)
;
R
²
=
0
.
9
5
6
Q (gm -1 s -1)
2
1
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
0
.
4
(
K
E
K
E
)
u
(
)
z
z
t
*
Q  4.5 10 3 KEz  KEzt u*0.4
Results – wind-driven rain
Transport rate Q (g m-1 s-1)
Q  K d Ez  E zt  u*0.4
R2 = 0.96
Q  K d E z  E zt 
R2 = 0.93
Q  K d E z  E zt 
R2 = 0.92
1.2
Results – wind-driven rain
u* and KEz or Mz
Results – rainless wind (control)
Vertical deposition flux qx (g m-2 s-1)
1000
u* = 0.33 m s-1
(d)
u* = 0.36 m s-1
u* = 0.39 m s-1
u* = 0.50 m s-1
10
Eq. [13]
-2
-1
qx (g m s )
100
1
0.1
0.01
0.001
0
1
2
3
4
x (m)
q   e   Δx   e  Δx
5
Results – rainless wind (control)
Horizontal flux qz (g m-2 s-1)
u* = 0.33 m s-1
(d)
-2
-1
qx (g m s )
1000
u* = 0.36 m s-1
u* = 0.39 m s-1
100
u* = 0.50 m s-1
Eq. [5]
10
1
0.1
0.01
0.0
0.1
0.2
x (m)
q  ae
b z
0.3
Results – rainless wind (control)
140
Eq. [8]
Qx data
-1
-1
sediment transport rate Q (g m s )
Transport rate Q (g m-1 s-1)
120
100
80
60
40
20
0
0
1
2
3
4
5
3
(u* - u*t) (-)
Q  18.6 10 3 u*  u*t 
3
6
Results – rainless wind (control)
140
Qz data
-1
-1
sediment transport rate Q (g m s )
Transport rate Q (g m-1 s-1)
Eq. [8]
Qx data
120
100
80
60
40
20
0
0
1
2
3
4
5
3
(u* - u*t) (-)
Q  18.6 10 3 u*  u*t 
3
6
Results – wind-driven rain vs. rainless wind
wind-driven rain
-1
-1
-1
rainless wind
2
-1
-1
-1
-1
2
-1
Q (g m s )
u* (m s )
KEz (J m s )
Q (g m s )
u* (m s )
KEz (J m s )
0.44
0.27
0.185
0.16
0.33
0
2.08
0.5
0.653
168.32
0.5
0
Conclusions
• Vertical deposition flux of sand was described with double
exponential equation, q = f(x).
• Horizontal flux of sand was described with single
exponential equation, q = f(z).
• Same expressions (and same equipment) can be used for
wind-driven rain and rainless wind conditions.
But model coefficients are different.
Conclusions
• Sediment transport rate Q relates well to normal component
of KE or M (R2 = 0.93).
• Observed variation is better explained if u* is considered as
well (R2 = 0.96).
• Qwr > Qw at low shear velocities
Qw >> Qwr at high shear velocities