16-018 Matsuzawa Snow Transport.pptx

A Technique for Estimating
Snow Transport Rate from the
Mass Flux at a Given Height
MasaruMATSUZAWAandSatoshiOMIYA
CivilEngineeringResearchIns>tuteforColdRegion,
PublicWorksResearchIns>tute,Japan
1
Introduc)on
Snow transport rate (Q)： the
mass of blowing snow particles
that pass through a unit width per
unit time
(g m-1 sec-1)
When planning and
designing blowingsnow control facilities, it
is necessary to know
the cumulative annual
snow transport. Tabler (1994)
Introduc)on
Thesnowtransportrate(Q)isgenerallyes>mated
byusingempiricalequa>ons.
𝑙𝑜𝑔𝑄=1.22+0.0859​𝑉↓10 •  Buddetal.(1966)
𝑄=0.00428​𝑉↓10↑3.8 •  Tabler(2003)
𝑄=0.0029​𝑉↓1↑4.16 •  Takeuchi(1980)
𝑄=0.03(​𝑉↓1 −1.3)3
•  Kobayashi(1972)
•  Matsuzawaetal.(2010)
𝑄=0.05​𝑉↓1.2 4
Vx:windspeedattheheightofx(m)
Accurate determination of actual snow transport
rate by using wind speed is difficult.
Massfluxandthesnowpar)clecounter(SPC)
Massflux(q):massofthesnowpar>clesthat
passthroughaunitareaperunit>me(gm-2sec-1)
SPC can measure
An
Transmitter:
mass flux continuously.Super Luminescent Diode
Slit
Snow Particles
25 mm
Receiver:
Photo Diode
Slit
0.5 mm
2 mm
The SPC optically
measures the number
and size of airborne
snow particles that pass
between transmitter and
receiver. To clarify the relationship between the
mass flux at a given height and the snow
transport rate of blowing snow
Fieldobserva)onoverview
Themassfluxofsnowwasmeasuredattheheightsof0.02,0.05,0.07and0.1m
usingabox-shapednet-typeblowingsnowtrap,andattheheightsof0.1,0.3,0.5,
1.0and2.0musingacylindricalnet-typeblowingsnowtrap.
Box-shaped net-type
blowing-snow trap
Cylindrical net-type
blowing-snow trap
5
Meteorologicaldatafor
thedaysofmeasurement
Date
Air
Windspeedatthe
temperature heightof1m(m/
(°C)
s)
-4.9~-6.5
9.2~12.9
Feb.21,
2012
Feb.3,2013 -6.3~-7.8
Jan.31,
-4.9~-5.9
2014
Mar.6,2014 -4.8~-5.9
Precipita)on
(mm/h)
0.0
9.7~10.5
6.1~12.5
0.0
0.0~1.2
5.6~7.7
0.0~0.6
6
Calcula)onmethodtodeterminesnow
transportratefrommassfluxofsnow
7
Results
Therela>onalequa>onQ=kq(kisapropor>onalconstant)was
obtainedfortheheightof0.5mandtheheightof1.0m
Q=3.0q0.5
q0.5:Massfluxat0.5mheight
Q=5.4q1
8
q1:Massfluxat1.0mheight
Discussion
Es#ma#onmodelofsnowtransportrate
Modes of transport
Wind
Qtotal ≅ Qsal + Qsus
Suspension
Qsus
SaltationQ
Creep
sal
Takeuchi (1990)
Es#ma#onmodelofsnowtransportrate,
Discussion(cont’)
1)Qinthesuspensionlayer:Qsus
q( z ) = N ( z ) ⋅ V ( z )
･･･(1)
Qsus ( z ) = ∫ q( z )dz = ∫ N ( z ) ⋅ V ( z )dz
･･･(2)
P ⎛
P ⎞⎛ z ⎞
⎟⎟ ⎜⎜ ⎟⎟
N(z) =
+ ⎜⎜ Nt −
wf ⎝
w f ⎠ ⎝ z1 ⎠
u* ⎛ z ⎞
V ( z ) = ln⎜⎜ ⎟⎟
k ⎝ z0 ⎠
−
wb
ku *
･･･(3)
Matsuzawa and Takeuchi (2002)
･･･(4)
where, N(z):blowingsnowdensity,V(z):windvelocity,
P:precipita>onintensity,Nt:blowingsnowdensityatreferenceheightz1,
wf:fallingspeedofsnowfallpar>cles,
wb:fallingspeedofsuspendedpar>cles
k:Karmancoefficient(0.4),u*:fric>onvelocity,z0:surfaceroughness 10
Discussion(cont’)
1)Qinthesuspensionlayer:Qsus
⎛a
⎞ b
Pu*
a b
(ln z − ln z0 ) + b ⋅ z ln z − ⎜⎜ b ln z0 ⎟⎟ ⋅ z
q( z ) =
kw
z1
⎝ z1
⎠
wb
b=−
ku*
where,a = ⎛⎜ N − P ⎞⎟ u*
⎜ t w ⎟k
f ⎠
⎝
Qsus
･･･(5)
b +1
⎡ Pu* z ⎛ z
⎞
a z
⎜⎜ ln − 1⎟⎟ +
=⎢
b
kw
z
b
+
1
z
f ⎝
0
1
⎠
⎣
z2
⎛ z
1 ⎞⎤
⎜⎜ ln −
⎟⎟⎥
⎝ z0 b + 1⎠⎦ z1
･･･(6)
2)Qinthesalta#onlayer:Qsal
Qsal = 0.03(V1 − 1.3)
3
･･･(7)
Kobayashi (1972)
Q = Qsal + Qsus
･･･(8)
11
Discussion(cont’)
Calcula#on
Qsus
b +1
⎡ Pu* z ⎛ z
⎞
a z
⎜⎜ ln − 1⎟⎟ +
=⎢
b
kw
z
b
+
1
z
f ⎝
0
1
⎠
⎣
Where,
⎛
P ⎞ u*
⎜
⎟⎟
a = ⎜ Nt −
wf ⎠ k
⎝
z2
⎛ z
1 ⎞⎤
⎜⎜ ln −
⎟⎟⎥
⎝ z0 b + 1⎠⎦ z1
wb
b=−
ku*
Qsal = 0.03(V1 − 1.3)3
･･･(6)
･･･(7)
The following values are assigned to equation (6).
z0=1.5x10-4(m),wf=1.2(m/s),wb=0.25(m/s)
z1=0.15(m),z2=5.0(m)
u*=0.036V10(m/s)
Nt=0.021exp(0.401V10)(g/m3)　Cases for calculation of Q Precipita>on:0,1,2(mm/h)
Windvelocity(V10):5.7–16.7(m/s)
12
Fromobserveddata:
Q=3.0q0.5
Q(gm-1s-1)
Massfluxofsnowattheheightof
0.5m(q0.5)vs.snowtransportrateQ
200
180
160
140
120
100
80
60
40
20
0
The calculated values
are roughly the same
as the observed values.
P=0
P=1
P=2
Q=3.0q
0
20
40
60
80
q0.5(gm-2s-1)
P is precipitation (mm/h).
13
Summary
•  Thefollowingrela>onalequa>onsbetweenthesnowtransport
rateQandthemassfluxqatagivenheightwereobtainedfrom
fieldobserva>ons.
Q=3.0q0.5
Q=5.4q1
Where,
q0.5:massfluxofblowingsnowattheheightof0.5m
q1:massfluxofblowingsnowattheheightof1m
•  Addi>onally,amodelfores>ma>ngthesnowtransportrate
fromthemassfluxwasderived.
•  Thecalculatedvaluesarefoundtoberoughlythesameasthe
observedvalues.
•  Itisconsideredthattheempiricalequa>onsobtainedfromthis
studycanbeusedtoes>matethesnowtransportrate.
14
Thankyouforyourajen>on!
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