Wim Cornelis, Greet Oltenfreiter,Donald Gabriels & Roger Hartmann
WEPP-WEPS workshop, Ghent-Wageningen, 2003
Splash-saltation of sand due towind-driven rain
Outline of presentation
• Introduction: some theory
• Materials and methods
• Results
• Conclusions
Introduction – some theory
Rainless conditions Saltation
c*t
c*
c* uuuCQ
,
e.g. Owen (1964)Lettau & Lettau (1977)
Rainless conditions Saltation
Introduction – some theory
Windfree conditions Splash
detachment
Introduction – some theory
td EEKD
Windfree conditions Splash
e.g. Sharma & Gupta (1989)
or Qr
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
wwr
r
QQQ
'
'
0for
0for
*
*
u
u
Introduction – some theory
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*)
1. )(F~ xqx )(F~ zqz
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)
wind-tunnel wall
w ind
z
y (m )
x (m )6 7 8 9 10 11 12
trough
0.4
0.8
x = 0
tray w ith test m ateria l
(a)
wind
z
y (m )
x (m )6 7 8 9 10 11 12
0.4
0.8
x = 0
W ilson and Cooke catcher
(b)
Kinetic energy KEz or Momentum Mz
splash cups
Shear velocity u*
5 vane probes
Mass flux qx
23 troughs
Mass flux qz
4 W&C bottles
Materials and methods
Shear velocity u*
wind-velocity profiles5 vane probes
Materials and methods
Shear velocity
Eq. [7]
wind velocity u (m s-1)
0 2 4 6 8 10 12 14
hei
gh
t z
(m)
10-5
10-4
10-3
10-2
10-1
100
101
u* = 0.27 m s-1
u* = 0.39 m s-1u*= 0.50 m s-1
Materials and methods
Shear velocity
0
* lnz
zuu
uref (m s-1)
6 8 10 12
u* (
m s
-1)
0.2
0.3
0.4
0.5
0.6Observed dataEq. [9]; R² = 0.999
Materials and methods
Shear velocityrefuu 037.0050.0*
Materials and methods
Kinetic energy or Momentum
2
2
1vmKE
vmM
v from nomograph of Laws (1941)
S (rainsplash from cup)
Materials and methods
Kinetic energy or Momentum
SKE z 141.0010.0 SM z 04200030 ..
rainsplash from splash cups S (g m-2 s-1)
0 2 4 6 8
kin
etic
en
erg
y K
Ez
(J m
-2 s
-1)
0.0
0.5
1.0
1.5
mo
men
tum
Mz
(kg
m-1
s-2
)
0.0
0.1
0.2
0.3
0.4Observed dataEq. [10] or [11]; R² = 0.857
Materials and methods
SaltiphoneSensit “KE of rain field sensor”
Did not work properly under given circumstances
2.
),(F *uEQ Mass transport rate in kg m-1 s-1
xqQ
x
xx max
0
dCalibration
Contribution ofE (KEz or Mz)u*
ValidationzqQ
z
zz max
0
d
Materials and methods
Materials and methods
shear velocity u* (m s-1)
0.2 0.3 0.4 0.5 0.6
mea
sure
d r
ain
fall
inte
nsi
ty I
(mm
h-1
)
0
50
100
150p = 75 kPap = 100 kPap = 150 kPaEq. [8]; R² = 0.995
43.2387119 *uI
Results – wind-driven rain
Vertical deposition flux qx (g m-2 s-1)
x (m)
0 1 2 3 4 5
qx
(g m
-2 s
-1)
0.001
0.01
0.1
1
10
100
1000u
* = 0.27 m s-1; KEz
= 0.250 J m-2 s-1
u* = 0.39 m s-1; KEz
= 0.455 J m-2 s-1
u* = 0.50 m s-1; KEz
= 0.591 J m-2 s-1
x (m)
0 1 2 3 4 5
qx
(g m
-2 s
-1)
0.001
0.01
0.1
1
10
100
1000u
* = 0.27 m s-1; KEz
= 0.250 J m-2 s-1
u* = 0.39 m s-1; KEz
= 0.455 J m-2 s-1
u* = 0.50 m s-1; KEz
= 0.591 J m-2 s-1
Eq. (8.9)
Vertical deposition flux qx (g m-2 s-1)
xxq ΔΔ ee
Results – wind-driven rain
R2 > 0.99
z (m)
0.0 0.1 0.2 0.3
qz
(g m
-2 s
-1)
0.01
0.1
1
10
100
1000u
* = 0.27 m s-1; KEz
= 0.250 J m-2 s-1
u* = 0.39 m s-1; KEz
= 0.455 J m-2 s-1
u* = 0.50 m s-1; KEz
= 0.591 J m-2 s-1
Horizontal flux qz (g m-2 s-1)
Results – wind-driven rain
Horizontal flux qz (g m-2 s-1)
z (m)
0.0 0.1 0.2 0.3
qz
(g m
-2 s
-1)
0.01
0.1
1
10
100
1000u
* = 0.27 m s-1; KEz
= 0.250 J m-2 s-1
u* = 0.39 m s-1; KEz
= 0.455 J m-2 s-1
u* = 0.50 m s-1; KEz
= 0.591 J m-2 s-1
Eq. (8.12)
zbaq e
Results – wind-driven rain
R2 > 0.98
xqQ
x
xx max
0
dCalibration
Contribution ofE (KEz or Mz)u*
ValidationzqQ
z
zz max
0
d
Transport rate Q (g m-1 s-1)
Results – wind-driven rain
(KEz - KEzt) u*0.4 (-)
0.1 0.2 0.3 0.4 0.5
Q (
g m
-1 s
-1)
0
1
2
3Qx data
Eq. (9.11); R² = 0.956
4.0*
3105.4 uKEKEQ ztz
Transport rate Q (g m-1 s-1)
Results – wind-driven rain
4.0*
3105.4 uKEKEQ ztz
Transport rate Q (g m-1 s-1)
(KEz - KEzt) u*0.4 (-)
0.1 0.2 0.3 0.4 0.5
Q (
g m
-1 s
-1)
0
1
2
3Qx data
Qz data
Eq. (9.11); R² = 0.956
Results – wind-driven rain
Transport rate Q (g m-1 s-1)
2.1ztzd EEKQ
R2 = 0.96 4.0*uEEKQ ztzd
ztzd EEKQ
R2 = 0.93
R2 = 0.92
Results – wind-driven rain
u* and KEz or Mz
Results – wind-driven rain
Results – rainless wind (control)
(d)
x (m)
0 1 2 3 4 5
qx
(g m
-2 s
-1)
0.001
0.01
0.1
1
10
100
1000u
* = 0.33 m s-1
u* = 0.36 m s-1
u* = 0.39 m s-1
u* = 0.50 m s-1
Eq. [13]
Vertical deposition flux qx (g m-2 s-1)
xxq ΔΔ ee
Horizontal flux qz (g m-2 s-1)
Results – rainless wind (control)
(d)
x (m)
0.0 0.1 0.2 0.3
qx
(g m
-2 s
-1)
0.01
0.1
1
10
100
1000u
* = 0.33 m s-1
u* = 0.36 m s-1
u* = 0.39 m s-1
u* = 0.50 m s-1
Eq. [5]
zbaq e
Transport rate Q (g m-1 s-1)
Results – rainless wind (control)
3**
3106.18 tuuQ
(u* - u*t)3 (-)
0 1 2 3 4 5 6
sed
imen
t tr
ansp
ort
rat
e Q
(g
m-1
s-1
)
0
20
40
60
80
100
120
140Eq. [8]Qx data
Transport rate Q (g m-1 s-1)
Results – rainless wind (control)
3**
3106.18 tuuQ
(u* - u*t)3 (-)
0 1 2 3 4 5 6
sed
imen
t tr
ansp
ort
rat
e Q
(g
m-1
s-1
)
0
20
40
60
80
100
120
140Qz data
Eq. [8]Qx data
Results – wind-driven rain vs. rainless wind
wind-driven rain rainless wind
Q (g m-1 s-1) u* (m s-1) KEz (J m2 s-1) Q (g m-1 s-1) u*
(m s-1) KEz (J m2 s-1)
0.44 0.27 0.185 0.16 0.33 0
2.08 0.5 0.653 168.32 0.5 0
• 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 velocitiesQw >> Qwr at high shear velocities
Conclusions