ISSN 1010-0121
~ JPr.f))n
1}@(ri t
201
~~~!Jj4~
..
~~~!f/J4~
Measurements of eolian processes on
sandy surfaces in Iceland
Hjalti Sigurj6nssonJ
Fanney Gislad6ttirOO)
and
Olafur ArnaldsJ
J
Agricultural Research InstItute
oJ SolfConservation
Service
~~~~~".
. .
.'" '. -- ,""
'-"'.,'»'~~~~~~~
Publlsher/Otgefanci:
Rannsoknastofnun landbunaoarins
Keldnaholti, 112-Reykjavik
Agricultural Research Institute
Keldnaholt,IS-112 Reykjavfk, Iceland
Managing edltor/Umsj6n meO CltgOfu:
Tryggvi Gunnarsson
~,,~~i:~~,~~?~~~,m~,x"v'
""'-"""","'0.«"-"'-"-"«".,",x""""""«",««"",«-,»"",,,
FJOLRITRALA NR. 201
3
Content
.OVERVIEW
4
1 .INTRODUCTION
5
1.1/ce/andicsandydeserls
1.2Aeo/iantransporl
1.3 Characteristics of sandy surfaces. . . . . . . . . . . . . . . . . . . . . . . . . .
2 .MASSFLUX
8
2.1/ntroduction
2.2 Theory
2.2.1 BSNEtraps
2.2.2 Sur1acetraps
2.2.3 SENSITinstrument
.2.3Resu/ts
2.3.1 BSNEtraps
2.3.2 Sur1acetraps
2.4 Discussion... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 THRESHOLDVELOCITY
3.1/ntroduction
3.2 Theory
8
8
8
9
10
10
10
11
11
13
'
'
3.2.1 .Effectofatmosphericinstability
3.3Resu/ts
13
13
14
16
.
3.4 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 AERODYNAMICROUGHNESS
4.1/ntroduction
4.2 Theory
4.3Resu/ts
4.4 Discussion...
5
5
6
.........................................
5 CONCLUSIONS
17
19
19
19
20
21
23
REFERENCES.
.................................................
24
ApPENDIX
A
25
A.1 .Themassfluxdensityfunction
A.1.1 Thecaseofprojectilemotion
ApPENDIXB
25
26
27
B.1 Numericalsolutionof the VolterraEquation. . . . . . . . . . . . . . . . . . .
27
4
EOLIANPROCESSESON SANDY SURFACESIN ICELAND
Overview
Sandy deserts are common geomorphologic surfaces in Iceland. They are
mostly madeof basalticvolcanic glass,in
contrast with the quartz-dominateddeserts of the world. The Icelandic deserts
cover over 20,000 km2 and are made of
several sandy landforms (Arnalds et at.
1997). The sandy surfaces are unstable
and intense aeolian processescause a
widespread redistribution of airborne
sediments.Someof thesesurfacesare expanding,and advancingsand-frontscause
lossesof rich and fully vegetatedareas,
replacing them with sandy deserts.It is
therefore important to improve understandingof aeolianprocessesin Iceland.
Modelling of wind erosion calls for the
determinationof key aeolian parameters.
Resultsof erosionmodelling haveseveral
practical implications such as predicting
how the sandyareasmay evolve.
This paper summarisesthe results of
wind erosionresearchon sandydesertsin
Iceland.Most of the datawas collectedin
the summersof 1996, 1997and 1998.Researchrelated to this paper will be presentedby Gislad6ttir (2000) and Arnalds
et at. (2000). Threshold values of wind
friction velocity (u.) was determinedfor
several sandy surfacetypes and aerodynamic roughnessof severalsurfacetypes
was obtained.Methodsfor calculatingthe
flux of blowing material and material
creepingover surfaceare also described
in this publication.
The paper is divided into five main
sections. The first part introduces the
variousconceptsrelatedto the study.The
next three chaptersare devoted to individual partsof the study: Chapter2 to the
calculation of transport of material,
Chapter3 to the calculation of threshold
velocity under field conditions, and
Chapter4 to calculatingaerodynamicsurfaceroughness.Chapter5 summarisesthe
main findings of the study.
5
FJOLRIT RAtA NR. 201
J' INTRODUCTION
~ ~
t. t Icelandicsandy
.. deserts
interior
cover
active
volcanic
areas.Thisglaciers
resultsin
periodic
floods
of melt
Iceland is an Island m the Nort~Atlantic ocean,locatedbetweenapproXlmately 63.5° and ~6.5°N, and 13° and
24°W. It has extensIv~sandydesertsthat
are seldom reported m surveys of. lar~e
san~y areas of the world. ~~ clImatIc
enVIronmentand the composItIonof the
sand makes these desertsunusual,esp:ciall~ when the vastnessof theseareasIS
consIdered.
water from sub-glacialthermal areasthat
contributelarge quantitiesof silt and sand
to aeolian sources at the margins and
along floodplains.Catastrophicfloods associatedwith volcanic eruptionsare also
importantcontributorsto the sandsources
(Arnalds et al. 1997). In addition to the
sandy areasthat are primarily of glacial
and glacio-fluvial origin, there are ~idespread volcanic ash deposits assocIated
The
20,000
sandy
km2,
deserts
extending
are
fro~
more
than
coast!ine
sand-fieldsto remotedesertsm the hIghlands with a broad range of generalsurface characteristics.Their climate ranges
from rather arid «400 rom) to very ~~mid regimes (>2000
~
with the active volcanic
Sandy sedimentary
zone in Iceland.
rock also contributes
to the sourcesof aeolianmaterials.All of
thesesandy depositsare subjectedto intense aeolian activity. The sand has
spreadover large areas away from the
annual precIp~- original sand sources, and this results in
tation). The parentmaterIalof the sandIS large desertareaswhich are mainly charmainly basaltic volcanic glass together acterisedby aeolianprocesses.
with porous tephra and basaltic crystalline materials.The black sandysurfaces 1.2 Aeoliantransport
characteriseover 20% of Icel~dic surAeolian processeshave beenreviewed
faces. They were mapped dUrIng a Na- in many publications, such as by Bagntional Erosion S.urve~(Amalds e~ al. old (1943), Chepil and Woodruff (1963),
1997), and descrIbedm more detaIl by and Pye and Tsoar (1990). Aeolian sand
Amalds et al. (1998).
has three main modes of transportation.
Iceland is windy and the sandy areas Saltation is the most efficient mode, a
are subjectedto intenseaeolianprocesses bouncing motion of the sand grains.
that have devastatedlarge areasthat for- Forces act on sand grains close to the
merly were coveredwith fertile soils and ground becauseof high wind velocity
vegetation.The aeolianactivity influences gradient.The grainsare launchedat mean
the natureof all Icelandicsoils dueto aeo- anglesbetween30° and 50° (e.g., Anderliansedimentation
(e.g.Amalds1999).
son1989,Cookeet al. 1993).Soonafter
The origin of the aeolianmaterialswas the grain is lifted from the ground, liftreviewed by Arnalds et al. (2000). Much forces ceaseto act and the tr~jectory of
of the sand is made of volcanic glass of the grain is determinedby gravIty and the
alacial origin. Glaciers cover now about drag of wind. In most casesgrainsrise to
10,000 km2. The sediment load of the a few centimetresheight. By th~t time
glacial rivers is high and large quantit~es they have acquired most of the~r moof sedimentsare depositedon floodplams mentumand they descendand strIke the
and at the glacial margins. Someof the ground under an angle of 10-12°. There
6
EOLIAN PROCESSESON SANDY SURFACESIN ICELAND
they bounce off again and may cause
other grainsto becomeair-bornaswell.
Another mode of transport is suspension. A simple distinction betweensaltation and suspensioncan be madeby the
ratio of the friction velocity (u.), to the
terminal fall velocity of the grain (uJ, as
suspensionoccurs if u';ut<l. Thus, only
smaller grains take part in suspension,
and they follow the turbulent motions of
the air. Cohesive forces between small
grains are strong and it is generally acceptedthat saltationbombardmentis necessaryto break the inter-particle bounds
andmakegrainsentersuspension.
The third transport mode is surface
creep. This term relatesto severalnearsurface processes,where actual surface
creepis one process,but they aredifficult
to distinguish and are most often referred
to as creep (Cooke et at. 1993). Surface
creepis the rolling of grains, inducedby
saltation impacts,and the rolling induced
by gravity into craterscreatedby removal
of grainscausedby saltationimpacts.The
grains that are moved by surface cre~p
can be much larger than those in moved
by saltation.
rivers, and also in the vicinity of active
volcanoes.Sand-fieldsare also common
along the shore, especially at the southcoast where the sedimentloads of large
glacial rivers and catastrophic glaciofluvial floods aredeposited.
1.:; Characteristicsof sandy surfaces
Sandy surfaces in Iceland have been
divided into three groups: sand (sandfields), sandy gravel, and sandylava surfaces(Arnalds et at. 1997,seealsoGislad6ttir 2000, and Arnalds et at. 2000).The
surfaceof the sand-fieldsis mostly coveredwith grains smallerthan 2 mm in diameter (Figure 1.1). When the cover of ,stones and pebbles exceeds5-15% the
surfaceis classifiedas sandygravel.Such
areas are divided into three sub-categories, depending on the proportion of
sandcover on the surface(Figure 1.2).
The sand-fields are common in the
highlands close to glacial margins and
F.JOLRITRALA NR. 201
7
The sandy gravel surface is the most
common of the three sandy landforms.
This geomorphic surface dominatesthe
highlandsin areaswhereerosionhasbeen
active for a long time. Someof theseareas were previously vegetated.The old
soil surfaceandvegetationcoverhasbeen
removed,exposingglacial till surfaceunderneath.Later, sandhas moved over the
till surfacesand sand is accumulatedunder the gravel surface as the gravel is
continuously lifted up by frost-heaving
(seeArnalds e~ai. 1997).
Sandy lavas (Figure 1.3) are found
close to active sandy areas. Sand is
moved over the Holocene lava surfaces
and gradually covering them. If the lava
surfacesare rough, they act as a sink for
the sand, since airborne sedimentssettle
in the depressions.However,the lava surfaces will eventually fill up with sand,
.
and the sandthen continuesits advance- FJg~r~
t
men
over
.t
I.
.
. ..
Map 1 illustrates
the dIstrIbutIon
and
as
)
sandy
cO,
.
lava.
.
TheO!le
c.\
oQthe
t~~fil.1ed;up:~lthsand.;;;;:;\;,:
:;;'
'::;
ughtlsmo~\qr)';
;:;;
:;1:..c;",i,r~;~;,
:;,;;;;;,;,):;1
types of sandy deserts in Iceland.
{,
'~
';~
;~
;
~ ';
",'
,i
):j
1i'
"'e
c""'
~
;:
8
2
MASS FLUX
2..1 Introduction
Flux by saltationandsuspensionat different heights was measuredin the filed
by a column of BSNE dust traps (Fryrear
1986). The BSNE (Big SpringsNumber
Eight) traps are designedfor collecting
eroding material in the field with minimum interference with the wind-flow.
They canbe describedasa diffiIsers;after
wind entersits openingit slows down and
sand settles in a pan at its bottom. Air
passesout of the trap througha fine mesh
at the top (Figure 2.1).
Sand flux was also measuredby the
SENSIT instrument.A piezoelectriccrystal within it detectsmoving materialsand
I I..=~~:~.
c
1111.1.
transmitsan electricpulse when grains
impinge upon it (Gillette and Stockton
1986, Stocktonand Gillette 1990). Scaling is requiredto convert its responseto
a~tualmassflux. To scalethe instrument
dIrect flux measurementmust be madeat
the sametime and sameheight.
An attemptwas madeto measuremass
transportby surfacecreep.In order to do
so, surface traps were designed (Gislad6ttir 2000).The surfacetrap is a box, 14
by 26 cm, dug into the ground, with the
upper edges set level with the surface.
The longer side is aligned perpendicular
to the main wind direction. All material
creepingtowardsthe trap will fall into it,
but also some of the material travelling
by saltation.To interpret these measurements, the flux by saltation must be
known, and the proportion entering the
surface trap must be determined.Then,
that amount can be subtractedfrom the
total in the trap to obtain the masstransportedby surfacecreep.
2..2. Theory
2.2.1 BSNE traps
;.
1
,
,
...
[
'!
!
.:
,
I
",:
"'!
Flux at each trap height is calculated
by dividing the trappedmassby the area
of the trap opening and the time over
which the sandis collected.Samplingefficiency was assumed90% accordingto
Fryrear (1986). An empirical equation
proposedby Fryrearet al. (1991):
F(z)=Fo(l+zlojP
(2.1.1)
was fitted to measured flux values. Fo, 0"
andfJ areparametersto be determined,F 0
Figu,re2.1. The BSN,Etrap. T9P; individu~,
i~ the flux where z=O, 0" has the dimen-
compollents,
pan,supportw,ithtail and,dlf,
l~jser:'Be!ow;,1:.hetrap
Sionof length (m) andfJ is dimensionless.
E~uation(2.1.1) can be integratedto obtarn Q, the masstransportper unit width,
'c
FJ6LRITRALA
9
NR. 201
Q
-
-~
jectory
P+ 1
1
(2.1.2)
L L 2 Surface traps
.
A
S
d b ~.
mentlone
eiore,
.
mterpretatIon
tIme
near
the
upper
f
boundary
than near the lower. Let P(z,h)L1z
be the
proportion .of the to~l flux within the
layer that IS on the mterval (z, z+L1z),
h2'z2'O.That is,
Jp(z,h)dz= 1
0
saltating
grains.
b 1.
P(z,h)
0
surface trap measurementsrequires that
the flux by saltation is known. The proportion of the total amount of saltating
materialenteringthe surfacetrap must be
determinedand subtractedfrom the total
in the trap for retrieving flux by surface
creep.
To calculatethe proportion of saltating
materialthat entersthe surfacetrap, mass
flux as a function of saltationlengthmust
be found. Mass flux as a function of saltation height, can be derivedfrom the behaviour of saltating grains, and the observedflux profile. As a first approximation, it will be assumedthat saltation
length is proportional to saltationheight.
In the caseof projectile motion of particlesthat is true if the particlesare ejected
at a constantangle, no matter how great
the initial velocity is.
In order to derive the flux as a function of saltation height, considera layer
of grains in saltation, where all grains
reach the same height h. This may be
called a saltation layer with thicknessh.
Horizontalmasstransportwithin the layer
increasesas the upper boundary is approached,becausevertical velo~ity component decreases
and the grams dwell
.
longer
of
.
.
If
grains
travel
a ong para 0 lC trajectorIes, the fl ux density is
1
=
/,
2h"\,'
"
1 -
z
(2.1.4)
I h
The real flux density function is more
complicated,but this expressionis convenientand will be usedas a rough estimate for the flux density. The massflux
densityfunction is discussedin more detail in AppendixA.
Given the flux density function for a
layer of arbitrary thickness,the observed
flux profile can be constructedby a combinationof an infinite numberof layersof
different thickness,extending from zero
to infinite. Massflux is different from one
layerto another.Let k(h) be the massflux
within a layer of thicknessh. Then, k(h)
integratedover a finite interval,yields the
flux of grains reaching the top of their
trajectorieson that interval. The contribution of one layer of thicknessh to the
total flux on the interval (z, z+L1z)where
z<h is k(h)P(z,h)dz. The total flux on
that interval is the sum of such contributions from all layers having a thickness
greaterthanz, i.e.
00
fk(h)P(z,h)dzdh
h==
That flux can also be calculated as
F \Z/LlZ,
t:.).4- were
h
F t:'
\z/ j. IS th e 0 b serve d fl ux a t
.
z, so 1t canbe conc1uded that
F(z) = jk(h)P(z,h)dh
h==
(2.1.5)
Th. .
.
IS IS a Volterra mtegral equationof
(2.1.3) the first kind (Hochstadt1989).In general
it can only be solvednumerically,see
P(z,h) is the flux density as a function AppendixB.
of z, for grains saltating to the height h.
Oncek(z), the amountof grainsjumpP(z,h) must be determinedfrom the tra- ing to height z, has beenfound, it is pos-
10
EOLIAN PROCESSESON SANDY SURFACES IN ICELAND
sible to calculatewhat proportion of the 2.3 Results
saltating material will enter the trap, 2.31 BSNE traps
given the width of the trap, assuming
. m
. the fiIeId 0f t he SENSIT
. proportlona
. 1 WI.th sa1- . Cal I.bratIon
. 1ength IS
sa1tatlon
.
.dth f th mstrumentsrequIresthat the BSNE traps
t t . h . ht L t b b th
a Ion elg . e
e e WI
0 e.
.
tr
d
ap
t b
an
th
e
.
e Jump
1
gth
en
f
.
grams.
0
are
emptied
repeatedly
after
a
relatively
..
According to Owen (1980) mean jump
lengthis twelve-fold thejump height.Assumethat is valid for all grains.Then all
grains not jumping higher than onetwelfth of the trap width will fall into it.
short penod durmg a sandstorm. °n.e
san~ storm event was ~ecordedfor ca.lI~r;:g
the :ENSI~ ms~~ents WIth
tra~s. t was one unng a storm
at LandeYJasand~
2~th July 1997.How-
..
ever,
the
samplmg
m
the
BSNE
traps
t>b the proportIon
. 0f sand-fl ux m
. d. tIon
. a
t entenng
f
. .the trap.
.
gIvesa good mIca
. bl ! Th th
IS II.
en, e amoun 0 gramsJumpmg
.
.
.
t h .ght
d
t .
th tr
. storm event of moderatemtenslty. Wmd
0 el
z an en enng e ap IS
.
.
b/12
T
bt
.
th
t t 1
t
f
speed
was
estimated
as approXImately
11
k /.'\
{Z/
z.
0 0
am
e
0 a
amoun
0
-I
th .
T bl 2 1 .
.
th o
t b
. t
t d ~
11
m s
at
e time.
a
e
.
gIves
the cograms,
IS mus
e m egra
e
lor
a
..
.
1 gth fr
t . fi .ty
efficlents m equation(2.1.1) and the total
.
Jump en s om zero 0 m ml , so
fl b
t.
ux y equaIon..(2 12).
When
b
h/12
~
k(z)
Q,rup
= fk(z)dz +12 f -;-dz
Th
en
Q
(2.1.6)
"'"
h/12
0
. th
trap IS
...
'J:J'
:fable2.1.()QefficlentscharactenSl!1gthe.~::
.
.
e mass per unIt WI dth
:Width ~r110urand t11eflux bysa/tati ...;:~l:'
""~I
:n~e:ingthe s~rfacetrap.
L.L..:;SENSIT Instrument
:li~:",'(iJp'c'
..
Accordmg
response
of
proportional
'
to GIllette
the
SENSIT
et at. (1997)
.
to mass flux,
mstrument
the
.
IS
but different
R
:,:c:':c-:::'"
'::::'c'..
j':'~II;",::
ill.ii':'c,ilcJ:,.
'c:,
'c
a particular
site
must
be
calibrated
using particlesthat are involved in a dust
storm at that site.
..
..
The calIbration equation IS
F
=kS
QJ
-j,
'!o"'i:"::(~):":'c
c,,{k:g,mc:hr
:r~:'!:ic:c::j,'Cc,:::ci,jjjJ
-1
),,{kgm
,:J:jJJ'!~
'iJi~:FI
:~:::h;r~
':,c
,:c :£'I.~;'
":C:"C:"l11:ilit,
iI!Oj~~::J
,O;60:'::-7;9:6, 2695:' ,k,,:" ill05~!~1i'
'Iifb
,:'
c,':
;;:
'ii"",::
i.\i~ :0.38i1"~.64i1 396:5:.\'1;li264"Ji
particles produce different constants of
proportionality. That is, measurements i1,j~L
:0:;4:8' -8;,03:
:'
from
cc
::~
,i4i1cc
,
.1..J3:
:,
'13.78:
',}Iii.!!
3154',.\,':
c207,;~1
,
,,"
c:'1846
,:.:,:
:.163:"i'::: il~ji1
c,
",cc
:)5;:,
iO.26,:::
1i"-'5;24c
,
-,
4648'
279:k1lli1:
CCv"
c:,16iil''1,..18:'C.:.t16.98
:iI:cil1:'::'.,",J",cc.:
3329
246:":;);::
::::'J!1iI1
,:11;;2;53, -31,3911",197QJ,:.:;' 164 Ilil1..;,
(2.1.7)
F (massper unit areaper unit time) is
the actual massflux, k is the calibration
constantand S is the SENSIT response
per unit time. The calibration constantk
can be determinedby plotting F againstS
and finding the slope of line drawn
throughthe points obtained.
Cil;iI!:,'jj!!f;1
The flux values vary from about 164
kg m-1hr-1 to about 280 kg m-1 hr-1. If
flux by surface creep is assumedto be
one third of the flux by saltation (Bagnold 1943),the total flux reachesup to 370
kg m-1hr-1.
FJOLRITRALA NR. 201
:"
11
'...c
{2.1.6),cQlrap
'tc
~!f(~g~c.}cc~(m)
,609;','c,?c';C
c'
:13,01 ,:
-I
0:068cc::-;2.6,
c
Cc
26.0cc;,0:q2cl:c.16.85
,c",cc;",;cc;;c;,c,ccc",;cc
'0,032 c',-19"
,:;,
c : ,,;8.47,.;c
c
cllr~l"
0;33;,'
cccc,c,ccc,;c"""'""
44J ,,;';c:;,';'0 32";c';:c;"',;21'81
2.32 Surfacetraps
Three measUrements
of sanddrift with
surface traps south of Langjokull were
investigated,all on a sandy gravel area
south of 1>6risjokullglacier. Table 2.2
gives the coefficients characterisingthe
vertical flux profile and the relevant
quantitiesfor calculatingthe flux by Sufface creep.The resulting flux (Qc) is also
indicated.The time over which the sand
was collected is not known, as the traps
':,:,:c'1'.56
c
'
lOJ~,";I::
were left during a considerabletime, and
sand-drift occurred only during a small
portion of that period.
Figure 2.2 shows the mass flux as a
function of saltation height. The curves
arescaledso that the total areaundereach
of them is equalto one.
The last column of Table 2.2 indicates
that the ratio of creepingmaterial to saltating material is between 1:3 and 1:6.
The results conform with rather wide
range of ratios reportedby otherssuch
as 1:3 by Bagnold
(1943) and 1:8 by
Bor6wka(1980).
".1" OIscusslon
.
.
I!:.
It is interesting to
see that in all three
cases, very close to
one-third of the sal-
,[
tating material enters
the ~urfacetr~ps.AssumIng that In gen-
I;c
,
0
,','
~:
0
",
0,05
0,1
0,15
0,25
z(m)
0,3
0.35
0,4
0,45
.
;'i1;I:f.,;"
-fsaltatlon herghLThen1ass,flux;,"
FIgure
2.2.cMasstluxasafunctJono
.. ; c;
...
-~ c
;
c, :';'
,:;c
c"c;
eral about one third
~i~l~:t::~::~u~::~~
trap, t h e tota1fl ux
by
ls:scaledby di.Vldmg
k(z),by;Q,-,fF:(z)1.;;csothe'area
underthe;cu~es, saltation and creep
;':;'::':;'
,:equalscl.c,TreemeasurtementscoI.Ja
"
'c::;;;::():,',
c
POTisjokulr(!flacler."see map i
',:;,:;;c.c.J,c-':;'=I,::I""
csaJ
'c.,c",c..,cc
, ldy
graYel;surface'south:::,8~:,
'C:Cc., , c..c"c.';"c,c""
::,:,c.;:;lc.canb
e
c
:,',:::"""
roughly
as-
sesse,
d on1y by surface traps. This is
12
EOLIAN PROCESSESON SANDY SURFACESIN ICELAND
considerablyeasier and less costly than
the BSNE or SENSIT instrumentation.If
the flux of materialinto the surfacetrap is
Qlrap=Qc+Q/3where Qc is the flux by
creep and Qs flux by saltation, and
Qc=Q/3, (cf. Bagnold 1943)then the total flux, Qlolal=Qs+Qc=2Qlrap.
That is, the
total flux is approximatelytwice the flux
enteringthe trap.
b .
d.
An 0 VIOUSlsadvantageof the surface
trap is that its samplingefficiency is dependenton wind direction.That could be
avoided by using a circular opening.
Also, it would be betterif saltatingmaterial could by avoided, which would be
possibleby using a very narrow opening
on the surfacetrap, in the samemanner
Bagnoldusedin wind tunnel experiments
(Bagnold 1943). However, this can be
difficult under field conditionswith alternating wet and dry conditionswith subsequent blocking of narrow openings.Two
traps with linear openings aligned perpendicularto one anothermight provide
results less dependentof wind direction,
since the two traps measuredtwo independent componentsof the flux vector,
say Qx and Qy. The total flux could be
obtainedby adding the two components
vectorally,that is,
- 2 2 0.5
Qlolal-(Qx+Qy)
The main finding presented in this
chapter is a method for interpreting
measurementswith surface traps. These
findings are valuable for further data collection for calibrating flux calculationsin
relation to sand drift models and allows
for less costly and convenientmeansfor
estimating flux for large areas.In addition, ratio of creepingto saltatingmaterials found by other authors were confirmed, to the extent the accuracyof the
surfacetrapsallows.
FJOLRITRALA NR.201
13
.;
THRESHOLD
VELOCITY
.~.1 Introduction
The determination of threshold velocity is of key importance in characterising
aeolian processes. The only such determination for Icelandic sandy environments was done in wind tunnel experiments conducted in co-operation with the
USDA-ARS in Big Springs in Texas (Arnalds 1990). Icelandic aeolian processes
involve basaltic volcanic glass materials,
when transport is occurring, the nature of
the wind-profile over the surface is different from that when no sand is blowing,
as was noted by Bagnold (1943). The reason for this is that momentum is transferred from the wind to the blowing sand
grains. The transition from one regime to
the other can be identified by a change in
the ratio between wind velocities taken at
two different heights above ground.
which are rather uncommon constituents
in the world's
aeolian environments
(Edgett and Lancaster 1993).
The method used for determining the
threshold velocity is based on monitoring
sand movement by the SENSIT instrument with simultaneous measurements of
wind velocity, relative humidity, temperature and wind direction. The methods
are described in greater details in Chapter
Two anemometers were used to record
wind velocity, one at 2 m height and one
either at 0,3 or 0,4 m height (Figure 3.1).
Three SENSIT instruments were used and
mounted at different
heights
above
ground. Ten or thirty minutes wind speed
averages were measured except when
eroding material was detected by the
SENSIT instrument, then one minute averages were recorded by the datalogger.
3.2.
Another method of determining thresh-
3.2 Theory
old velocity is also explored by analysing
the wind data. It is based on the fact that
It is well established that wind velocity
above a rough surface can be described
by the equation
u(z)=u.ln(zlzo)/k
(3.1)
where Zo is a roughness length, k is von
Karman's constant and u. is friction velocity. The friction velocity, U', depends
only on the shear stress exerted on the
surface by the friction of wind. When
sand begins to blow, equation (3.1) ceases
to hold. A new one, similar in form becomes valid,
u(z)=u.ln(zlhYk+vh
(3.2)
An extra term Vh has been added and a
.
.,.'
it,
new roughness length, h is introduced,
~lgu~c3.~, EquJpment.forme~llrtn~thre~h.
see Owen (1964). According to Owen
( 1964) h
b .
d
.
oJdveloclty,anemometers,the
S~=SENSIT:iffit"
tr:a"" s:: S
c:::
can e mterprete as the thlckf th
1 .
c :strumentandiii
c
'c
C c colrifu;6fB
!
1~'"
p.c
ee"
::~s6 Figure4-..1c.c
c
:c:c
ness 0
e sa tauon 1ayer and Vh can be
interpreted as the mean wind velocity at
14
EOLIAN PROCESSESON SANDY SURFACESIN ICELAND
the top of the layer. The new roughness Zoto yield the correspondingcoefficients
factor (h) will increaseas the wind gets for wind below threshold velocity. So,
stronger,and is thereforenot a constant, when Uj is plotted againstU2,one should
unlike zoo
expect to see a straight line extending
Let wind velocity at two different from the origin of the Uj-U2 coordinate
heights Zj and Z2 be Uj and U2 respec- systemto the threshold values, then the
tively. According to equation (3.2), Uj= slopeof the line would decreaseabruptly,
u.ln(zjlhYk+vh and u2=u.ln(z~hYk+vh. and might decreasemore as wind gets
By eliminating the friction velocity from stronger(seeFigure3.2).
these two equationsand solving for Uj,
The point wherethe slopechangesrepone finds that
resents the threshold velocity. This
uj=au2+b
(3.3) methodof measuringthresholdvelocities
h
canprove to be a valuableadditionto the
were
.
SENSIT methodsused m the field, thus
a = ~~
(3.4) involving lower cost equipmentwhich is
In(z2/ h)
possibleto leave for extensiveperiodsof
and
time in the field. The authorsof this paper
b =v (I-a)
(3.5) are not awaret~a~this method has been
h
used for determInIngthresholdvalues in
This is valid when wind is above the field.
threshold velocity, but as a special case
we can put Vhto zero and substituteh by
32.1 Effect of atmospheric instability
.0
In many cases,the
best line through
points below thresh-
.
old velocitydoesnot
.
seemto crossthe origin of the co-ordinate
T
system. The most
-.
'1
. .
likely explanation is
that the logarithmic
.
equatIon was not
valid at the time the
measurements took
place. The logarithmic e
I.
.
~
,
,
I
0
.
2
.
7
.
..0
q uation
"
..("",, I... 'j
II
Figure 3.2. ObservedUrU] curve on a sandy sunace,lt consistS6f
two Ji.i.1esofdifferent sJ,opes. .TJlechangein
theslonP
~
,..- markstbe
,
c'
I ~bresho.1d
.
1bl
J
IC.
co d
. owmg sandlsue.C
:I'CCCCCCC
strument, squarescarecmmwm averageSW.ften
ctectedccccccccccccccc
cc,'
c/
0"
Cc
c////
/c
0
/
c!..r~
1
C
is
valid
only when air is in
neutral equilibrium.
When air is either
stable or unstable I.
t
must be account ed
tIor byastallty b.l.
function,
FJCLRITRALA NR. 201
~
az
where
=
15
~
~
kz"
(3
</1mis the stability
and Hicks
(1970)
6)
.
function.
proposed
Dyer
the following
.
Equation
perature
(3.7)
are unstable,
on sand,
gradient.
number
temperature
equation
(3.9)
profile
(3.9)
assumed
-0.5
ifJ.,=(1-16Rz)
conditions
shines
zero,
gradient
reduced
is
defined
causing
Ri
is the
equation.
was
integrated
temperature
up to
0,001
m.
was
assumed
gradient
tions
Richardson
personal
in
similar
Lubbock,
to
Texas
communication).
Figure
The
3.3
and
The
observa-
(John
Stout,
result
shown
on
neutral
the
line
stability
values
of u. and the corresponding
for comparison.
where g is gravity and T is absolute tem-
veloc~ty at 0,4 and 2
~ thus fo~d..
perature
resultmg
IS shown
/ az
in
(Stull
1988).
equation
(3.6)
By
one
( u. ) 4 )
2
+ 64 T"&"
for
obtains
)
( ( g aT
au
gaT
&" = 8T"&"
solving
+"k.;
3.4
and
for
neutral
Uj-U2 curv~
for
comparison
equilibrium
According.
°'25
perature
(3.9)
the
of
to
Figure
gradIent
wind
The
m FIgure
Uj-U2
curve
air.
3.4,
high
tem-
has the ef!fect of sh.ift~g
the Uj-U2 curve when wmd
more than 1 m S-I. When
slower
bends
&~
--'
is
for
Equation(3.9)was integratedfor few
(3.8)
au
=
Zo
steep tem-
(~ )
K~
T az
be
aT / az =5,47e-j,86z
as
Ri =
to
as is when
2
au
to
2 m height.The roughnessfactor was
2
sun
the
is
the logarithmic
form for </1m,
when
When
/ az
aT
,
:
2
velocIty IS
winds get
the curve
and ulti-
mately
crosses
the
origin.
That
ex-
plains the frequently
t
observed
Uj-U2
allows
..
,
IF
'"
!lgure
for more
ac-
non
curate
.
friction
velocity
i!i'"
~
values.
Adjacent
~:
dots
~~
~"
of
determinathreshold
on
different
curves on Figure
3.4
representthe same
.""
0
0,'
,
"
2
2,'
I
..,
.!;
Wind,,'oc..,fmo.')
":
of
and
~:
~
-
shift
curves,
3 .. 'fhl
"
oJ."
. h
e ogant
".
-
I
.,.
-
mlcveoc.ltvprofife;(strallZhtllne
u. values under dif..1
.
"""
~:
ferent
conditions
"",'.
,
!)"!
(stable
i,,~::: bl e).
) and vel.ocitti'.!:
and
unsta-
They m
. dIcate
.
profile
~a:lc:ulated
(accord.l~g
t? !observat.ro~s
1?at a rough correcmQmmUllIcatlo.n)",curved:une.l).
Is'.0,25"l11s!
an~surfacetemperaturei:non can be done by
y:':lowerwhenairisunStable:"ic.:ii
Projecting
the Point
"
" """
,,' :':
""
",,- ",,'
i""
J
:20°C.Ve!Qcity:at21nis!corisicletabl
"
i
""
:"
,,"
representing
thresh-
16
EOLIAN PROCESSESON SANDY SURFACESIN ICELAND
'",w""
,-
,""~,W.o;"
ill"
~Wo'.ili'
.ili,ili"'~
ill"
",,",..
~~ Results
,
7
I
'
When measured
under field condi-
~i
tions, threshold val-
!
ues vary between
measurementintervals. The lowest
valuesare shown in
Table 3.1. Temperature gradient has
been accounted for
when necessary(in
s
) .
i
~3
2
most cases), by
1
projecting the point
of threshold values
11
~j
:~
00
1
2
3
.
::J
S
8
7
I
0(2m),
(ms"')
"
,'Ccc"..
"a onto the curve for
,:Ji~ht~s~
.
-
'ccc_c
cc,
cc,c"
"
c
'c.
.:cc
:,~ben.atr
JSu~stablethe:tWo!;:urv~sare,~ost1yp~aUel
whe~~md'v~J";
'iOCltv1StJreater1han
'c.
c;
C,Ccc
c c,CCt".:CCccC,C""C"'C
"cc'C
",,0' ,,'-s
'.litiS":'
c
c
c'
c
""c
neutral
ng stability
so aer.oFor
dydol.
.
namlC roughness
must be known as
explainedin chapter
3.1.1,but it is not in
old values, almost parallel with the horiall cases.
zontal axis of the co-ordinatesystemonto
Pointson a Uj-U2graphfor one minute
the line for neutral stability. The line for wind speed averages,taken when the
neutralstability is determinedonly by the SENSIT instrumentrecordsmoving parsurfaceroughnessas indicated by equa- ticles, are often very scattered.For obtion (3.4), where h has beenreplacedby taining accuratethresholdvelocity it can
zoo
be helpful investigating the change in
'):'V;--:-7;":::;,::
I '-' h ' -. M ,c".
fi d
c",.c."-.
kll
cC
15
-"'
;,gr03ve,
"",are,a
most1 esamem, yyatnsorre,cannear:YVrlsjo U"'C c
;;c,';."');;:""'"
,~9~tIOn.
:
"IJafideyjasandur
..!
...
'Sand
Q7
,
Sandy gravel,;4
:;:",
Near
Sandy
,
gravel
5
Myvatnsorrefi
,
..
Sand
0.7
Sand
0.7
Myvatnsora:fi
:Myvatnsora:fi
10.6
c::'cc;'.!!if;:::;;
;"
);5c
S
"
;
2:8,,!
1I.T
. c." k u 11
""ear" '"
YOrlSjO
d C14
an y ava",
,10.4
' 7 5'
; ",:"
c c-,
:
,!SandygraveI5;i:,!
"0.9
,:
8;3
!:'"
:Ne"arpOrISjokull
porlsjokull
""i,,,::!:;;::}:};;
";;:"1'c-l;,,)"::;cc~~~,j
zo(mm):::U(lm)(m"sc,,),' u.;(m;s:!,,;,,; 'f!u.{m:~;,~~:~
Surfacetype
",,;:
!
"'","i"'c
c
cc
"
,,4..8c
,
c,
7.4
'
10,2
,::,,'c
0..42c":
,"
,;::,j)::!,!
o.d~;'l;i::!::
!!"'c::!!:;::
0.64
0.02.:::.:.!:!]':
"0.58
0..02':~rJ
. ,,"
cO.76
0.24
0.37
cO.53
C""}.,,
0.02";:?k,:}
"kk::
0.0.1 ,,;:,::,;,!
'!.!!L
O.OtL;i1.;:!:;
k "k'C""
0.02~'i~,:
FJ6LRITRALA
slope
of
NR. 201
U/-U2
averages
(10
17
curves,
using
the
or 30 minutes)
longer
and conse-
..,
quentl y less scattered Pomts.
In
..,".'
some
;:JJ"
sal.1durand"Myyatl.1s<?rrefi"are
"c"r"
-
"takenfro~"
""
"
cases (see for example Figure 3.2) the
thresholdcouldjust aswell be determined "tatl~g~ams:Th.e"
porlaksbofnsamplelsfF~w
.
~suifacetrap,smce..n°" samplefroma"BSNE
only from the changem slope.
~.1
.;. "
D
.
Iscusslon
.
AeolIan
.
in por)akshotn can "be estimated"s)ih,not.\;;;
JeSS
.c""S'.c/"
.
p ort
trans
.
IS commonl
thantboseofLandeyjasal1dur;ol'cabout.Oi~R.!i
c"
c
..
y mItI-I
ated at wmd speeds between 5 m s
f1 .
b th d .f ~
-I
/mm.,,;
cic
c ,,/,,'RR
and
.
'
c ,,"
cicic
R
c
",.",Rci$j,
"ci,,!jj!ill'
RR!ci1iii1jil.fR!I'
',;'/ ci.'ccCcci.
..CC ci,;;
"..c~jRinri~!r
c","c"
C c " LandeV1a" /porJaksMvv~m"r,
,,_:JJ,
...
~'l"J,'Ri:r
csandur
/
hofn,"
o~,:!t':
cic
"
cl
Rc
:!ciR;;~i}
11 m s , re ectmg 0 .. I lerences
li':c,R
. . m ",Pr<?peqle$
surfaceroughnessand clImatic
condItions
"c';
.
;
when sand-drift began. Lowest numbers ;d::mean
(mm)
c
are recorded
fi
ld
b
Ie
s,
for the nearly level sandy
th
h
ut
eyare
.
h
fi
Ig
er
'Skewness"
e
more
f
'il;
ciC.,
c
l';;;l~i',
C
;cD,isp,ersion;
th
or
c
0..30; ;,;,;cO.3.7;
o..l~.:ilf~&:
;,
'c;;;';1".I'
;;0.3;} " ,;,;/,;0..45 ;/0..4~i;!ij!t'i1i
;
;
~.O.7,;;,,;c;;Rc
0.00
O;o0!iRi
;
l;!,;;;;;;,;";;!;:cc:,,,;;;/;c;c;;;;..;,:;
";KurtosIS"
:!'i
c;';:vl)[c;;;cCi;C09
;tl0/'
,
~:~
~~;;ur::e~s,
:a:~~o~~~; ~~~
served during wet conditions in very
strong winds (Gislad6ttir 2000), with
considerablyhigher thresholdvaluesthan
canbe expectedfor dry conditions.
Textural properties for these sites are
shown in Table 3.2. The MYvatn sand is
somewhatfiner than the other surfaces,
with threshold velocity as low as 0.24
m S-l, (lessthan 5 m
S-I at 2 m height).
The Landeyjasandur
and
I>orlakshofn
sand
also
measuredfriction velocity threshold of
0.24-0.43m S-I for tephraand allophanic
soil materialsand sanddominatedby volcanic glass.His results showeda threshold value of 0.4 m S-I for coarse,light
densitytephra with median grain size of
0.93 mm, considerably larger than the
threshold values (8.3
-1
and 6.0 m s
at 2 m
considered
)
low
corres p ond
with
t .
ame
tunne
nalds
numbers
d
.
I . mT
m
1990).
a
exas
well
ob-
. d
wm
(
Arnalds
Ar-
'"
/
4TH
5 BI-SOIL
..!:~
(1960
6 GR
10
;C1
(1982) 7 BI-SURFACE
;1,
8 BI-SIEVEDfine
0
.
m
Iceland. The
. threshold velocIty values
'"
FromAmalds (1990): ti,
.
. d
d
smce
wm -spee s
this high or higher
.
are quIte common
,j:'
-}
3 Myvatnsorrefi
heig
. ht,) w hIC
. h can
be
i:~"
I Landeyjasandllr
2 p"rlakshofn
have
,i!
9 BI-SIEVED coarse ::',j
.01
10
'c
;R
/
d (mm)
c;
"c;:
;
c;
:
;,,;"
:;,"R:
,i"
compar~a:i
cwithicurves forc thresho.ld:ifriction;yelocities
cas a,.function.!.iofgrain
i
;
i;;
"
i'
i
diam~ter.ilversenalld
White takeinto;account;variationsiin
Re'"jwld;"
cohesiv;e;forces. NLlmbers:obtained;for;1celandicmaterials in windi
ld
l i.c;"..;
;
I C;';
(i;
:t~ne ;ieXpe!1ment.A;ma s ,;1990); a soiil.l1cluded. After;;;Pyec& Ts<>ari:
(
;1
"'
9
"
90)
"
;,
cC'"'
"r;
C
;"C
" ""
i;:",:,,;:
.;
',,;l
"
i:j;;
C
C"""
i",il.;
18
EOLIANPROCESSES
ONSANDYSURFACES
IN ICELAND
0.84 rnm which is often usedin wind erosion models as grains too large to move
(Skidmoreet al. 1994).
Thresholdvelocity values obtained in
this study and thosemeasuredby Arnalds
(1990) are plotted on Figure 3.5, for
comparison with theoretical curves for
thresholdvelocity as a function of grain
diameter.Most data are located close to
the theoretical curves, but somewhat
higher,becauseof wider grain-sizedistribution in the natural sand comparedto
uniform distribution.
.:~
,..~
1:1
FJOLRITRALA NR. 201
19
-1 AERODYNAMIC
ROUGHNESS
&.1 Introduction
Aerodynamic roughnessis an important factor for modellingwind erosion,reflecting the roughnessof the surfaceand
the resultingwind profile.
Surfaceroughnessis determinedfrom
the vertical wind velocity profile. Anemometersare used to record wind speed
at different heightsabovethe surfaceand
the resultsusedto obtainthe wind profile
(Figure 4.1). The measurements
usedhere
were carried out on two different occasions.Becausethe configurationof measurement instrumentswas slightly different, resultswill be representedseparately.
A one minute averagewind speedwas recorded for approximately20 minutes at
three or four different heights over each
surface.
During the first set of measurementof
aerodynamic roughness, wind profiles
were recorded on six different surfaces.
Anemometer~were placedat 2 m, 0.3 m
and 0.1 m heights.
During the second set of measurements,wind profiles wererecordedon six
different surfaces. Anemometers were
placedat 2.15 m, 1.04m, 0.53 m and 0.05
m on two of the first locations.In the four
last locations, three anemometerswere
used,placed at 2.15 m, 1.04 m, and 0.05
m.
4.2 Theory
In theory, the aerodynamicroughness
of a surface,Zo, appearingin the logarithmic wind profile equation
(
u. (
UZ)=T1n;
Z
)
(4.1)
"j
"
is easily determinedby fitting a line to
points on a In(z)-u graph. Supposethe
linethusobtainedhastheform
U(Z)=aln(z) +b
:
(4.2)
where a and b are constants.Then the
aerodynamicroughnesslength is
Zo
= e-%
(4.3)
However, air must be in neutral stability for equation(4.1) to be valid as noted
in Chapter3.
1
IgU!c..
easurlngequlpmel~t
oraero
Y-!
I namlc roughness.TllCbox containsa data1og"1 If onl~ two anemo~et~rs are prese~t,
: gerchargedwith asuncel1placedon its top. ..':] as often is when erOSionis measured m
:'
:
:
.~~
;
the field, surfaceroughnesscan be cal-
-f" I
20
EOLIAN PROCESSESON SANDY SURFACESIN ICELAND
c
c
:cc
c
':;;!cc"Ccic...
ccCcc
ciic,.ccC
ccc,c
Cc!ciC
c
c
cCc,...
iccicic
.
iiCCli'
c
cC
.
c,:cc,c,:,:c
,,:Cccj,;!j!J
iCc
ic,CcCCiiCiC9
i!
i;i':"'~!;!;
i,::i;;!",
.'i
ici$tltfaCe!rypei
!"c,i!,:,'!;Cc,:ZOA
,,2:!Sandycgravel
cc'Cc'
(mm)
,ii;':~;]?":':ii!
,'ccCCc,c,'
iiLl1
ccccciiccc
c'ii
ci,;i;~;j
C
l1Z0A{mm)Cii
ci'C,ii!i
iccc~""'c',:i'c'.'c
i"'
2'
"'
cCCCCicc!ciCCc'CCCC
!'ic
Cii!!
i!:;!"'!C' !';!'t
i;iSttffacerype,:cc
C:i C c;;,
ci2Sandygravel~
!ic!i!"C
ZOA\riirii)C!j
'c,c!!icc
c
i
ci,l1Zo1Jc(m"ll4!;]
O,93"ii!!!",:!"
i'!;iciC!cc
ccCC
;;;c:ci;;cct
C
j! !'i!;,l1ZhA(mm)c
2.40;iicc,:!i!c!i':!':
zOIJ\mm)c
i!,:?'CciCc,:
ccCCccCc
CC '
Cicci'C!iCiiiiccCCiii?"
C
cO'.06
(c1
;cc?!;An
J dOO
!,
C!ii,i
,:anuiatic.l ('4;4)
5CCi!
'm.!.c
l c'!~'iz".
O4cccman!"."
c 5 mflerg
c'"
,C ht \n..mesv4,..
I'" C'i':"'CCC!
CCeq
';""at.i'~n
cc!!Cj,!",j)
Ciii!;':":;";';!!!
c.
"'!c
c':!}!-'!.
cCC!,
cO.19,:!I'1;
:::
ciCciiiic,:CC;,;'Cici1C!cCC
;ei:ghtciniiJiheS'il!a'ilat~c~!
i cc,;c!!
Ci"!"
ccr""f.'
CCi!Ci!i
;iCC;C;
cc ;",c!:
,i,i,j':;iCCZO1J,:(mm) c,,;Ci;!!C!C;l1Z01J(riim~',,:,:~1
cO,13cc!iici!i!,",
236ii!Cii,,:,,!!,".!Cc'i
0.2c':':
cO:24i,i
ic5iiSandyCgravel'
cc CC,:ccCC!1-40ciCC"iC!cCC
Oi08,iCiicC!iiii
155
ici,:ciii!iii?
culatedby plotting Uj againstU2,finding 4.~ Results
the slope of the line a and solving for Zo
Roughness was calculated by two
from equation(3.4). Then,
methods,accordingto equations(4.3) and
I
(4.4) above. When applying equation
( ZU ) ~
Zo = -:-
(4.4)
(4.4) the lowest and highest anemometers
were used.
I
.
.
ThiS.was shown to .be sufficiently ac-
~uratem most cases,if one anemometer
IS placed close t? ground (5-10 c.m)and
other at approximately 2 m height. If
anemometersare placedat 2 m and 0.4 ~
heights,Zois very sensitivefor errors m
a andz.
Table 4.1 contains roughness factors of
areas visited in the first field trip and the
correspondingerror limits, calculatedby
equation (4.3), (ZOA)and by equation
(4.4), (ZOB).
Table 4.2 containsroughness
factorson areasvisited in the secondfield
trip, calculated by equation (4.3), (ZOA)
andthenby equation(4.4), (ZOB)'
RALA NR.201
FJOLRIT
21
-
'~ '-"""'""""-""~"".""i£'"""'""""""'",""""""""""",,,,,
~t
QO1
,
ness of five out of
""""""""_."""
six surfaces classi-
,
!~
fied as sandy gravel
fall within the interval reported by
.'r:i
"11
lW
(if
::.;:
Wieringa
"5J
f,; ~
;::
'I!;
'::
I
length obtained for
a lava surface (zo=
2 73
) .
.th.
QOO1
.
~::
,;;
~
IS WI
In
the surfaces classl-
~
'6
~eda~sandygravel
;:~'
,{I N
.
, . . . ,.
In thIS study
~~:::::sbl~:ea=~
".".'.'.""."":..'1'.'j..1.")";;.
: :::::::
Q
QaDI
: :::::::
has
others, and above
QOO1
QO1 :;i
the range given by
r~
Wieringa(1993).A
,(IT}lheafo.ra~l:2-r~ara~Lm:J
Zo
~j'
ffi
t¥
:':
,:::::
mm
thatinterval.One~f
!~:
J::
(1993).
Also, the roughness
::::,:::::::':
:', :,
:,::,,:
:::
::::
,:::::,,'
::,::::,:::;::
': :;:: :::
,:",::::,:,:,;:,,::
_ghness,:de_ temlined::bv:tWo;different:m~:4:"
J:'1igure:4,2;Aero~vnamicrou:
:::,"
,:,,:'
: ,.-,
gravel surface (me-
1
h.
.
ur,wlchlsqulte
.
common
In Iceland)
.
was found to have
roughness 0f about
;':::..;:,:;:::,:.";"::;::
1 cm. These relatively high numbers
should be taken
. These results are also presented on cautiously, since their determinationreFIgure4.2.
lies on a small set of measurementsand
the terrain could be inhomogeneous.A
11.11
Discussion
sandy lava surface was found to have
'::
11
-:
d
~quaygo(!' ;::
'coco::::
:"
Roughnessof eroding areasin Iceland
according to our observationsspansthe
rangefrom 0.2-10 mrn.
Wieringa (1993) reported roughness
lengthsof various homogeneoussurfaces.
They were selectedfrom various sources,
where observations satisfied a certain
quality criteria. The roughnessof loose
sand reportedthere is approximately0.2
mm, dependenton wind speed,and the
roughnessof anotherbare surfacewas 14 mm. The roughnessof sandreportedin
this study is a factor of two or three
greater than those of Wieringa. Rough-
"",
:::::,
:
""':
: :::: : ,i;';:;
roughnessof 5.40 mrn, which also is
above the range given by Wieringa.
However, lava surfacescan appearconsiderablyrougherthan othertypes of bare
surfaces.Consideringthat the roughness
of rough rafted sea-iceis 7:t4 mrn (Wieringa, 1993), lava roughness of 5 mm
seemsreasonable.
The numbers reported here indicate
that the roughnessof Icelandicsandysurfacescanbe characterised
numerically for
modelling of the development of the
sandy surfaces. However, researchers
must select measurementsites carefully~
22
EOLIAN PROCESSESON SANDY SURFACESIN ICELAND
considering the homogeneity and take
into accountthe stability of air.
Since the difference in results produced by the two different methodspresentedin Chapter4.2 is minor it seems
that fairly good results can producedby
only two anemometersplaced close to
groundand in approximately2 m height.
However Wieringa (1993) doubtsthe reliability of roughnesslengthsobtainedby
only two anemometers.
FJOLRIT
RALA NR.201
23
!; CONCLUSIONS
In this paper we have presentedpre- studying threshold values was explored.
liminary results of field-measurementof When threshold velocity is reached,the
parametersimportant to physically-based wind profile changes.This changecan be
sanddrift model.
identified by only two anemometers10BSNE (Big Springs Number Eight) cated at two different heights above the
traps proved very practical for measuring ground. The instrumentation for this
massflux by saltation.Measurementsare methodis thereforemuch less costly than
simple to perform and to interpret. Our the SENSIT equipmentand can allow for
results indicate that in moderate sand- extensive data gathering for relatively
storms in Iceland, mass flux with salta- low cost. This method can therefore be
tion amountsto between200 and 300 kg valuable to obtain threshold values unm-l hr-1.
der natural conditions for relatively low
A theory for transformingmassflux as cost.
a function of height aboveground,to flux
Roughnesslengths reported here are
as a function of saltationheight was de- between0.2 mm for a smooth lava rock
rived, in order to interpret measurements to 10 mm for a rough gravel surface.
with surfacetraps, providing a relatively Most of these values correspond with
inexpensive method for determining sand
flux. The results show that the material
entering surfacetraps reflects about half
of the total flux, saltation and surface
creep.The proportionof the saltatingmaterial entering the surface trap seemsto
be rather stable, about one third of the
saltating material enters it according to
this study.
Aeolian transport is commonly initiated at wind speedsbetween5 and 11 m
S-I. The SENSIT instrumentationgives a
good indication of thresholdvaluesunder
field conditions. Another method for
characteristic results and surface roughness values selected by Wieringa (1993),
and are likely to be correct.However resuIts for a sandy surfacewas two times
greater than Wieringa reported (1993),
and a gravel surfacehas a factor that is
two times greaterthan expectedfor most
bare surfaces according to Wieringa
1993.
According to our results roughness
length can be carried out by only two
anemometers,where one is placed close
to ground (5-10 cm) and the other at approximately 2 m height.
,
;;;.~
~,
j
.";
;;1\E,:1:~[~
24
EOLIAN PROCESSESON SANDY SURFACESIN ICELAND
REFERENCES
Arn;alds, O. 1998. Sandur - Sandfok. Gr~3um
Island VI: 69-82.
Arnalds,O. 1990.Characterizationand erosion of
Andisols in Iceland. Ph.D. Dissertation,
Texas A&M University, College Station,
Texas.
Arnalds,O. 1999. Soils and soil erosion in Iceland. In: H. Armansson (Ed.), Geochemistry
of the Earth's Surface, pp. 135-138. Balkema,Rotterdam.
Arnalds, 0., F.O. Gisladottir & H. Sigurjonsson
2000. Sandy deserts of Iceland. Journal of
Arid Environments.Submitted.
Arnalds, 0., E.F. porarinsdottir, S. Metusalemsson, A. Jonsson, E. Gretarsson& A. Arnorsson 1997. Soil Erosion in Iceland. Soil
Conservation Service and Agricultural Research Institute, Reykjavik. English translation published in 2000.
Bagnold, R.A. 1943. The Physicsof Blown Sand
and Desert Dunes. William Morrow, New
York.
Chepil, W.S. 1951. Propertiesof soil which influence wind erosion: IV. Stateof dry aggregate structure.Soil Science72: 387-401.
Chepil, W.S. & N.P. Siddoway 1963. The physics of wind erosion and its control. Advances
in Agronomy 15: 211-302.
Cooke, R., A. Warren & A. Goudie 1993. Desert
Geomorphology.UCL Press,London.
Dyer, A.J. & B.B. Hicks 1970. Flux-gradient relationships in the constant flux layer. Quarterly Journal of the Royal Meteorological Society96: 715-721.
Edgett, K.S. & N. Lancaster1993.Volcaniclastic
aeolian dunes:terrestrial examplesand application to martian sands.Journalof Arid Environments25: 271-297.
Fryrear, D.W. 1986.A field dust sampler.Journal
of Soil and Water Conservation41: 117-120.
F
0 W J E St t L J H
& ED
ryrear, . ., ..
ou, ..
agen
..
Vories 199]. Wind erosion: field measurement and analysis.Transactionsof the ASAE
34: 155-]60.
Gilette, D.A. & P.H. Stockton 1986. Mass, momentum and kinetic energy fluxes of saltating
particles. In: W.G. Nickling (Ed.), Aeolian
Geomorphology, pp. 35-36. Allen and Unwin, Boston, MA.
Gillette, D.A., D.W. Fryrear, X.J. Bing, P.
Stockton, D. Ono, P.J. Helm, T.E. Gill & T.
Ley 1997. Large scale variability of wind
erosion mass flux rates at Owens Lake. 1.
Vertical profiles of horizontal massfluxes of
wind eroded particles with diameter greater
than 50 J.lm.J. Geophysical Research 102,
022: 2597~-25987.
Gisladottir, F.O. 2000. Umhverfisbreytingar og
vindrof sunnan Langjokuls (Environmental
chan~~ and eol~an processes.south.of the
Lang)okull Glacier). M.S. thesIs, UnIversity
of Iceland, Reykjavik. English Summary.
Hochstadt,H. 1989 Integral Equations.John Wiley & Sons,New York.
Horikawa, K. & K.W. Shen 1960. Sand movement by wind action. US Army, Corps of Engineers, Beach Erosion Board, Tech. Memo.
119.
Iversen, J.D. & B.R. White 1982. Saltation
threshold on Earth, Mars and Venus. Sedimentology29: 111-119.
Owen, P.R. 1964. Saltation of uniform grains in
air. J. Fluid Mechanics20: 225-242.
Owen, P.R. 1980. The physics of sand movement. Lecture notes,workshop on physics of
flow in deserts. International Centre for
Theoretical Physics,Trieste.
Pye, K. & H. Tsoar 1990.Aeolian Sandand Sand
Dunes.Unwin Hyman, London.
Skidmore, E.L., L. Hagen, D.V. Armbrust, A.A.
Durar, D.W. Fryrear, K.N. Potter, L.E. Wagner & T.M. Zobeck 1994.Methods for investigating basic processesand condition affecting wind erosion. In: R. Lal (Ed.), Soil
Erosion Researc~Metho.ds.2nd edn. Soil and
Water ConservationSocltety,Ankeny, Iowa.
Stockton, P. & D.A. Gillette 1990. Field measu:ements of .the sheltering effect of vegetatlon on erodIble surfaces.Land Degradation
and Rehabilitation 2: 77-85.
Stull, R.B. 1988. An Introduction to Boundary
Layer Meteorology. Kluwer Academic Publishers, Dordrecht.
Wieringa, J. 1993. Representativeroyghnessparameters for homogeneous terrain. Boundary
Layer Meteorology 63: 323-364.
25
ApPENDIX A
In the following text the mass flux
which is independentof the vertical ve-
density function mentionedin Chapter locity componentVz. Therefore,Fz(z)is
2.1.2 will be discussedmore thoroughly.
In section A.l it will be derived generally, in terms of the velocity components
of the grains and dislodgementrate per
unit area,and in A.l.l the form of function for the caseof projectile motion of
grainsis deduced.
constant(with respectto height z) and can
be interpretedas the dislodgementrate of
materialper unit area,that is the massof
particlesthat leavea squareon the ground
of areadA=dxdy in a time interval of dt.
Define D as the dislodgementrate per
unit area,
1:..1 The mass flux densityfunction
D = -.!!!!!.-
(AS)
dAdt
Considerflux of grainsthat are ejected
The concentrationof material at height
fr~m ground and all rea~h the. same z can be obtained by dividing the dis?eIght h. The flux at a gI~en heIgh~z lodgement rate by the vertical velocity
IS
madeupwards
up of fluxorof downwards.
partIcles movIng
either
Let componentat that height'
ii(z,h) = (ux(z,h),u:(z,h)) denote the velocity of upgoing particles and
v(z,h) = (vx(z,h),v: (z,h)) denote the velocity of downgoing particles in a saltation layer of thicknessh.
First investigate the flux of upgoing
particles. The horizontal flux of material
is the concentrationof material(massper
C = !?-(A6)
u:(z,h)
Thenby combiningequations(AI) and
(A6) it can be concludedthat the flux at
height z is proportionalwith ratio of the
horizontalvelocity componentto the vertical, and the constantof proportionality
is the dislodgementrate,i.e.
unit
volume) timesthe horizontalvelocity
component
,
(At )
Fx (z, h) = C(z'.rh)u (z, h)
Fx(z,h) = D ux'(z h)
u:(z,h)
where C is the concentration,
dm
C =dV
(A7)
. holds for downThe same reasomng
going particles, D has the same magnitude as for upgoing particles since the
(A2) number of particles leaving and arriving
d dV dxd dz I th
h
an .
=
y . n ...e same sense' t e
ground is equal but has reverse sign. So,
. can be concluded that the total hon-.
1t
t I fl
t h . ht .
flux of up-gOIng partIcles IS conth
. 1 I .
zon a ux a eig z IS
.
.
centration tImes e vertica ve OCIty
component,
(z,h) = ~u_(z,h )
(A3)
u:(z,h) v:(z,h)
vertIcal
Fx(z,h)=D
-
F_
dV
-
..
By wntmg dxdy=dA, .andhence dV=
dAdz; and u==dz/dtequatIon(A2) can be
reWrIttenas
dm
F:(z,h)="d:4""d(
(A4)
(
u
x
(z
,
h)
-
v
x,
(z
h)
}
(A8)
The mass flux density function P(z,h)
has exactly the same form as equation
(AS) but has a different constantof proportionality, which mustbe determinedso
that the integral over F(z) to the maxi-
mumjump heighth equalsunity.Thatis,
26
EOLIAN PROCESSESON SANDY SURFACESIN ICELAND
cFx(z,
h)=P(z,h)
(A9) velocity component as a function of
fl d . fu .
h
heightwill be
. th
IS e mass ux ensity nction w en c
is selectedso that
u:(z,h) = .J2gh(1-z/ h)
(AI2)
By combiningequations(All)
h
c fFx(z,h)dz= 1
(AIO) (AI2) oneobtains
and
:-0
whereh is the maximumheight of grains.
Fx(z,h)=
K
(AI3)
.Ji-=ill
whereall constantshavebeentakento-
1,.1.1 The case of projectilemotion
In the case of projectile motion getherin one, K. Then, a new constantc
ux=vx=constantwith respect to height, mustbe found so that
and Uz= -Vz, since the vertical components
are equal in size, but in opposite direc-
tions.Equation(A8) simplifiesto
Fx(z,h) = D
(
2
)
UX
"
cf~dz=l
0
(AI I)
~
(AI4)
It turns out that c must be equal to 1/2h
for equation (AI4) to be satisfied, so the
u:(z,h)
massflux density function for projectile
Whena particle is ejected to height h motion of grainsis
in gravity, it can be found by equatingthe
1
sum of kinetic energy and potential enP(z,h) =.JI-=-;-7h
(A15)
ergy to the total energy,that the vertical
2h 1- z / h
FJOLRITRALA NR.201
27
ApPENDIX B
In Chapter2.1.2 it was deducedthat an
observedflux profile F(z), can be converted to flux as a function of saltation
height,k(z). k(z) is the solution of an integral equation, Volterra equation of the
first kind, see equation (2.1.5). Also, it
was pointed out, that the equationcan in
generalonly be solvednumerically.In the
next section,
d . b adfinite. difference solution
metho will
e escnbed.
E 1 Nume:ical solution of the Volterra
Equation
By dividing z into small intervals,
equation (2.1.5) can be approximated by a
sum of an infmite number of terms,
( )~l~~P (~i,~V+t)
~
F ~i
j
( C.
I
~C
x k -N (; + l.2) -'V,
N
.
~
(BI)
= 0,1,2...co
Here z=ci/N, h=cO+%)/Nand dh=c/N.
Equation(B 1) describesan infinite set of
equations,one for each i. Infinite sets of
equationscannot be solved, so the number of terms usedmust be restrictedto a
finite value. That is equivalent to integrating to a finite height, insteadof inte.
. to m
. fimity.
gratmg
Th
b d f th . t
I
t
e upper oun 0 e m egra mus
be seIect ed so that the 0bserved fl ux
above it can be considerednegligible.
Then k(h) must also be very small above
that height and contribute very little to
F(z) below that height. If N in equation
(Bl) is a finite number,then c is the up-
per limit of the integral, so F(z) can be
approximatedas
c
F(z) ~ fk(h)P(z,h)dh
(B2)
h=z
if c is sufficiently large.This integral can
be approximatedby a fmite number of
terms.Equation(B 1) reducesto
~-i )~L ~-i,-V+t)
C
N-l
N
j-;
(
C
)
C
N N
(B3)
-I
V + .12)) .5:- 'V,.-- O,I,2,...N
N
N
Equation (B3) corresponds to N equations, one for each i. They contain N uDknowns, which are the values of k(z) at
the points z=C(i+Y2)/N.
xk
.E.I:
Thesetof equations
canbewrittenas
- =F
(B4)
Pk
"" anNxN matrixWiththeentries
whereP is
Pi.j =P(ti,tV+t)).
It is apparentthat P
is an uppertriangularmatrix. k and Fare
N xl vectors. The solution vector k can
be obtainedby multiplying equation(B4)
by the inverse of P, symbolisedby p-l,
thus,
-Ik- =P F
(B5)
.
The entries of k are as noted before the
'.
1
values
f4 '=0 of
I k(z)
N-l at the pomts z=c(l+Y2)/N
or i "...
.
In calculationsin Chapter2.3.2, c was
taken as I m, but less than 1 percentof
the t~tal flux is above one meter. N in
equatIon(B3) was takenas 1000.
j)
:'i::-'
~