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Eddy-correlation measurements above a maize crop using a simple cruciform hot-wire anemometer
Agricultural Meteorology, 20(1979) 397--410 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
397
EDDY-CORRELATION MEASUREMENTS ABOVE A MAIZE CROP USING A SIMPLE CRUCIFORM HOT-WIRE ANEMOMETER
F. A. BOTTEMANNE
Department of Physics and Meteorology, Agricultural University, Wageningen (The Netherlands) (Received February 4, 1978; accepted August 9, 1978)
ABSTRACT Bottemanne, F. A., 1979. Eddy-correlation measurements above a maize crop using a simple cruciform hot-wire anemometer. Agric. Meteorol., 20: 397--410. For measurements of the vertical transport of heat and momentum in the turbulent and slightly unstable boundary layer above a maize crop eddy-correlation techniques were applied. In addition to a vertical Gill-propellor anemometer and a Gill-propellor bivane, a cruciform hot-wire probe, mounted on a small windvane, were used. With this hot-wire system the heat and m o m e n t u m fluxes could be measured in a relatively simple way. The possibilities and limitations of this system were checked.
INTRODUCTION I n a g r i c u l t u r a l p r a c t i c e t h e r e is a n e e d f o r s i m p l e r o u t i n e m e a s u r e m e n t s o f the heat transfer and evapotranspiration of a crop canopy. To check more r o u t i n e m e t h o d s , s u c h as a e r o d y n a m i c a l m e a s u r e m e n t s w i t h c u p a n e m o m e t e r s or eddy-correlation measurements with a Gill-propellor anemometer, a simple cruciform hot-wire system has been developed. After an old idea of Swinbank (1951) a so-called X-probe was mounted on a light windvane following the h o r i z o n t a l w i n d v e c t o r Vh, s e e F i g . 1 . I n t h i s w a y a r e l a t i v e l y s i m p l e a n d c h e a p i n s t r u m e n t h a s b e e n c o n s t r u c t e d w h i c h c o u l d b e u s e d as a s u b - s t a n d a r d w i t h i n certain limitations. This instrument has been tested during the summer of 1976 above a maize crop. From correlation of wind velocity and temperature f l u c t u a t i o n s w e c a n r e a d f o r t h e v e r t i c a l f l u x e s in c o n v e n t i o n a l n o t a t i o n : Heat transfer Momentum
transfer
H = pcpw'T' T = - - p U'W'
T h e s h e a r s t r e s s r is also d e f i n e d as r = pu2., a n d so t h e f r i c t i o n v e l o c i t y r v _1 u . = ( - - u w )2. W i t h h o t - w i r e a n e m o m e t e r s a n d a c o l d - w i r e t h e r m o m e t e r fluctuations u', w' and T' have been measured.
(1) the
39.~
Fig.1. Photograph of the cruciform hot-wire probe mounted on a light wind vane together with a fast-response cold-wire thermometer. T h e r e l a t i o n b e t w e e n t h e dissipation r a t e ~ o f a h o t wire w i t h a resistance R at t e m p e r a t u r e T w a n d the e f f e c t i v e cooling v e l o c i t y u is given b y King's law. Using R -- R 0 {1 + a ( T w - - To)} this law can be w r i t t e n in t h e f o r m : .... - ~ - - -
R --R0
: A' + B'u ~
(2)
w i t h a wire resistance R 0 at t h e a m b i e n t t e m p e r a t u r e To. O p e r a t i n g at a c o n s t a n t d i s s i p a t i o n rate ¢ it f o l l o w s t h a t : _1
= A + Bu ~
(3)
R --R0 Because, f o r e x a m p l e , o f t h e c a l i b r a t i o n drift, a h o t wire is n o t a v e r y suitable i n s t r u m e n t f o r m e a n v e l o c i t y m e a s u r e m e n t s , especially in t h e a t m o s p h e r e . If t h e v e l o c i t y is f l u c t u a t i n g a f l u c t u a t i o n o f the wire voltage can be w r i t t e n as: I
e = S • u
I
(4) 1
w i t h S ~ u-~. This r e l a t i o n is a l m o s t l i n e ~ f o r n o t t o o large f l u c t u a t i o n s , i m p l y i n g a nottoo-large relative t u r b u l e n t i n t e n s i t y . F r o m this "small-signal m e t h o d " , a h o t wire is suitable f o r m e a s u r e m e n t o f f l u c t u a t i o n s in a simple w a y , in: p a r t i c u l a r in r e l a t i o n to h i g h - f r e q u e n c y a t m o s p h e r i c f l u c t u a t i o n s . Using an X - p r o b e we can s e p a r a t e t h e h o r i z o n t a l and vertical w i n d - v e l o c i t y f l u c t u a t i o n s . D i r e c t i n g this p r o b e on the m e a n v e l o c i t y (see Fig.2) we can see t h a t h o t w i r e I is sensitive to (u' - - w ' ) a n d wire 2 to (u' + w ' ) . M o u n t e d on a w i n d v a n e the X - p r o b e is d i r e c t e d on t h e h o r i z o n t a l w i n d v e c t o r Vh. B o t h wires w e r e c o n n e c t e d to a W h e a t s t o n e bridge in such a w a y t h a t the e l e v a t i o n (or inclination} o f t h e t o t a l w i n d v e c t o r V was m e a s u r e d . T h e c o m p l e t e bridge
399 was c o n s t r u c t e d on t o p o f t h e vane. T h e s u p p l y and signal wires were conn e c t e d to silver sliprings.
22ram
w1
................ 30mm
" "NlO!um ¢
Q
Fig.2. The X-probe to separate the horizontal and vertical wind fluctuations.
THE CROSS-WIRE ANEMOMETER
T h e X - p r o b e has b e e n c o n s t r u c t e d f r o m 10 p m - d i a m e t e r p l a t i n u m wire. B o t h wires have an e f f e c t i v e length o f a b o u t 11 m m , v e r y a c c u r a t e l y m a k i n g angles o f 45 ° w i t h t h e p r o b e axis, a n d a " c o l d r e s i s t a n c e " o f a b o u t 14.9 at 20°C. In Fig.3 t h e c o n s t a n t voltage bridge is shown. F o r wire 1 w i t h a x
[
V1 •
I x
I
R1
'VVX~
V2
R2
•
'k/k/V'
1
IE Fig.& Both wires of the X-probe are connected to a constant voltage Wheatstone bridge. resistance R ~ and a c o n s t a n t bridge a r m resistance x we can write: RI
V, -
E
x+R
(4)
1
F o r a wire w i t h a resistance R0 at air t e m p e r a t u r e T O it follows: R0 Vo - - x+R
o
E
(5)
We can d e d u c e f o r vl = V1 - - V0, t h a t : 1 N vl - R , - - R 0
+M
(6)
with N = (x + R0) 2 and M = x + R0. So v L is measured in regard to a bridge
xE
xE
arm with R I = R o. For a constant dissipation rate @it follows from eqs. 3 and 6: 1
± -
Pl
plul
2
+ql
(7a)
400 a n d a n a l o g o u s l y to wire 2: --= P2
(7b)
P2U2 + q2
w i t h t h e c o o l i n g velocities f o r b o t h wires ul = ~ + u' - - w' a n d u2 -- u + u' + w'. I t a p p e a r s t h a t ¢ is c o n s t a n t in a s y m m e t r i c bridge. P l o t t i n g 1/Vl and 1/v 2 as • -t a f u n c t i o n o f u~, it f o l l o w s t h a t .for i < fi < 8 m s-1 r e l a t i o n 7 is a l m o s t valid. We h a d t a k e n x = 22.1 ~2 a n d E = 3.00 V. T o s e p a r a t e u ' a n d w ' it is i m p o r t a n t t h a t e f f e c t i v e cooling v e l o c i t y can be t a k e n o n l y as t h a t v e l o c i t y c o m p o n e n t p e r p e n d i c u l a r to t h e wire. I f in a d d i t i o n t o t h e c o m p o n e n t ql, parallel t o the p r o b e axis, b o t h t h e o t h e r c o m p o n e n t q2 p e r p e n d i c u l a r t o the wire a n d t h e t a n g e n t i a l c o m p o n e n t q3 exist, t h e n t h e e f f e c t i v e v e l o c i t y Ve f o l l o w s f r o m : Ve 2 = q l 2 + k 1 2 q 2 2
+ k22q32
(8)
Using a wire w i t h a r a t i o l e n g t h - d i a m e t e r ~ 1000, the " y a w " f a c t o r k 2 ~ 0 ( B r a d s h a w , 1971). T h e " p i t c h " f a c t o r kl can be t a k e n as e q u a l t o 1. It a p p e a r s t h a t f o r p r a c t i c a l s i t u a t i o n s in a n e a r - n e u t r a l a t m o s p h e r e t h e d i s c r e p a n c i e s b e t w e e n Ve a n d q I are smaller t h a n 1%. F r o m Fig,2 a n d in a b s e n c e o f q2 the e f f e c t i v e velocities f o r wires 1 a n d 2 can be w r i t t e n as: Vie = ul c o s 45 a n d V2e
=
122 COS 45
w i t h Ul = ~ + U' - - w' a n d u2 = ~ + u' + w ' . D e f i n i n g p 1 a n d p 2 cos 45 are already taken into account. T h e f l u c t u a t i o n s u] = u p - - w # a n d u2? = u f + W f lead t o f l u c t u a t i o n s V'l and
v~: F PI = - - p I 2 p l
1 ~ Z • UA
2u ,
P2 =
--p22p2
(9)
U'~~ " -U- 2
2u
or: u t _
vl = - - C ~ •
w p
2fi ........ t
t
U
(10)
! +W
v2 = - - C 2 •
2a 2
_L
2
i
With Ct = rl p l u ~ and C2 ~- P2 p2u-C M o s t wires are not altogether identical, but can be m a t c h e d so that C I and C 2 are equal within a calibration accuracy ..t of about 1%. For identical wires w e can define C = CI = C2 = uo2pu z, With ro = vl = u2 and p = 171 = P2.
401
W i t h v ' ' = V'l -- v'2 it f o l l o w s : C
v'
C2
v'22
v', 2 -
,
=~-W U
pt2 =
C2 ~
(-u'w')
(11)
W'2
A n d correlating with temperature fluctuations
T'; this leads
with
A 2 = v'l 2 - - v~ 2 t o :
w'T' --U ' W'
:-du
A 2
=
•
W t2
v'T'
U 2
.
(12)
,2
------C~p
For relative turbulent intensity larger than 0.1, higher order terms should be taken into account (Hinze, 1959). Second order terms in eq. 11 lead only to: v'
C
C
"
u'w'"
F r o m h e r e w e c a n see t h a t a d i s c r e p a n c y o f t h e small signal a p p r o x i m a t i o n o n l y leads t o an a p p a r e n t l y m e a s u r e d m e a n v e r t i c a l v e l o c i t y : -7 u --7= u, 2 w =~-" v 2~
(14)
This will lead t o a p r i n c i p a l l y p o s i t i v e ~ . F o r t h e 1 9 7 6 m e a s u r e m e n t s w i t h ~ --~ 3 - - 4 m s -~ this a p p a r e n t ~ c o u l d be c a l c u l a t e d as a p p r o x i m a t e l y 5 c m s-l. D u r i n g t h a t s e a s o n w e m e a s u r e d w . . ~ 6 c m s -1. Neglecting third- and higher-order terms means that we don't consider correlation terms as w , u , 2 , w , 8 , w ' u ' w ' , u ' w ' T ' etc, thus neglecting vertical diffusion of turbulent energy and shear stress and the horizontal diffusion of vertical heat transfer. Calibration of the X-probe may be carried out using eq. 11a. Adjusting the probe in a windtunnel with an elevation angle e with regard to the wind velocity V, the voltage v = VI -- V2 is read as v ~ C tg e. In Table I characteristic values for C are given as a function of ~ and 6. The values for 6 = 0 are calculated from vi2piu ~ ~ v22p2u~. First we see C is slightly dependent on the mean wind velocity. For every run period we adapted C concerning the
402 TABLEI C h a r a c t e r i s t i c c a l i b r a t i o n values (C in volts) of t h e h o t - c r o s s wire a n e m o m e t e r h-
e = 0
~ = 5°
c = I0°
0.113 0.120 0.121 0.122 0.121 0.121 0.120 0.119
0.116 0.122 0.126 0.126 0.124 0.125 0.122 0.121
116 124 127 127 126 125 124 122
(ms -1) 1 2 3 4 5 6 7 8
relevant mean wind velocity. Secondly we see clearly an e-dependency, This systematical deviation cannot be explained by discrepancies of the small-signal approximation, neglection of higher order terms, asymmetry, non-constant dissipation rate, or a yaw factor, but is caused by the aerodynamical disturbance by probe and prongs (Strohl, 1971), Field measurements showed a standard deviation of the elevation angle o f about 10 °, so we carried out our calibration also at 10 °. In this way C c o u t d b e measured with an accuracy of approximately 1%. TEMPERATURE
DEPENDENCY
A change of the mean air temperature To leads to changes m R o and B. We can calculate a T O dependency of C of a b o u t --1 fi 2% K -1. From direct calibration we f o u n d a dependency of --1% K -1. Relating C to the mean temperature To during every run, long term variations of R0 have no influence on the correlation terms. However, concerning the dissipation rate ¢, faster fluctuations of To also cause fluctuations of the wire resistance R. For identical wires eq. 10 can now be written as:
, CI (u'--w') 2 +,yT, } , C{ (u' +w')+~/T, I u2 = -~ 2 1)1 =
with ~/
_
xE
(15)
R + x aR°-C; a is the tem~rat~are coefficient of platinum, tn eq. 12
this only leads to
403 T h u s f o r a positive h e a t f l u x t h e t e m p e r a t u r e f l u c t u a t i o n s cause an o v e r r a t i n g
w'T'
in m e a s u r i n g u , . D u r i n g t h e season 1 9 7 6 7 - - ~
/2,
~ 2%.
INFLUENCE OF THE VANE RESPONSE L e t us first a s s u m e the v a n e is f o l l o w i n g the h o r i z o n t a l f l u c t u a t i o n s i n s t a n t a n e o u s l y . T h e h o r i z o n t a l w i n d v e l o c i t y can be w r i t t e n as: Vh ~ u
(
1 +-
,
~
+ v'2 2~ 2
)
and:
(17)
O(~2 w i t h o , 2 = ~2 ~ v,Z/Etz, a n d ~ t h e f l u c t u a t i n g a z i m u t h angle. F o r eq. 12 we can simply deduce:
w'T'
Yh
u'T'
(18) --lttW t
=_ g h2 A2 C2
T h u s using Vh instead o f g eqs. 12 and 18 are identical, w h e r e C is r e l a t e d t o Vh. H o w e v e r , a w i n d v a n e has a lag in r e s p o n s e , especially w i t h high f r e q u e n c y f l u c t u a t i o n s . This m e a n s a w i n d c o m p o n e n t p e r p e n d i c u l a r to t h e X - p l a n e of the p r o b e d o e s e x i s t causing a n " e x t r a " c o n t r i b u t i o n o n t h e e f f e c t i v e cooling v e l o c i t y . B u t this c o n t r i b u t i o n leads o n b o t h wires to the s a m e e f f e c t a n d t h e r e f o r e we can h a r d l y e x p e c t a n y i n f l u e n c e o n t h e d i f f e r e n t i a l m e t h o d used here. A w i n d v a n e can be d e s c r i b e d as a s e c o n d o r d e r s y s t e m and t h e d a m p i n g f o l l o w s f r o m eq. 19 (see, e.g., Larsen a n d Busch, 1974): 1 d2fi + 2 ~ d / 3 Oje2 d t 2 ~/+/3 = ~
(19)
H e r e (~ is t h e w i n d d i r e c t i o n and/3 is t h e vane d e f l e c t i o n , w i t h r e s p e c t to the m e a n w i n d d i r e c t i o n . 09e is t h e r e s o n a n c e angular f r e q u e n c y o f t h e v a n e and is t h e d a m p i n g ratio. I m p o r t a n t is the so-called " n a t u r a l wave l e n g t h " k 0 = 2~'U/~e, a n d this is a b o u t equal to the d a m p i n g w a v e l e n g t h , k0/21r can be c o n s i d e r e d as a d i s t a n t c o n s t a n t o f the i n s t r u m e n t . This vane h a s a n a t u r a l w a v e l e n g t h o f a b o u t 3 m a n d a d a m p i n g r a t i o ~ = 0 . 4 - - 0 . 6 . This m e a n s f o r = 3 m s-1 a r e s o n a n c e f r e q u e n c y n e ~ 1 H z , a n d w i t h a m e a s u r i n g h e i g h t z --~ 3 m a n o n - d i m e n s i o n a l f r e q u e n c y fe ~ 1. It a p p e a r s t h a t f o r f > 3 this vane can h a r d l y f o l l o w f l u c t u a t i o n s o f t h e h o r i z o n t a l wind v e l o c i t y . F o r
404
lower frequencies however, a vane deflection must also be taken into account. Decomposing the instantaneous horizontal wind velocity Vh into a longitudinal c o m p o n e n t V1 and a tangential c o m p o n e n t Vt perpendicular to the X-plane of the probe it follows: VI = Vh cos 7--~ Vh 1 - - - ~
(20)
Vt = Vh sin7 ~ V h " 7 with 7 = (~
~, assumed to be small, and:
V, -~ Vh 1
~-
(21)
Vt ~ Vh o ~ = 0
with 072 = 72. And using V 1 instead of ~ this leads again to equations identical to
w'T'
(12):
V1 ,~, ".I
= ~-V
-u'w'
(22)
V'2
=-6-
When C is also related to V 1. Thus it is a good approxinmtion to state that the damping of the windvane does n o t cause errors in the correlation terms w'T' and --u~w~if we use only the mean wind velocity that is sensed by the vane itself. In this case it is very important t h a t we can negtect errors in correlation measurements caused by a " c u t o f f ' frequency also in the region of ~ e r frequencies. This is confirmed by the results of Larsen and Btmch (1976), where only an influence of the vane response can be established in the correlation spectra for the lateral velocity in which we are not interested here. TILT E R R O R
If the probe system i s t i l t e d with an angle 6 to the mean wind with regard to the " t r u e vertical" a m a x i m u m tilt error must be considered. We can define the true vertical as that ~ c t i o n for which holds ~ = 0 during a certain period. For positive and no ~ o large 8-values we can derive:
w'T'~ = w'T'o (1 - u'~T'~ "6) 2 --u
' w' ~
=
- - U 'W ' o
(
l + aU
(23) - - Ow 2
u, 2
"8)
For unstable conditions the heat~lux is overrated for positive 8-values because
405 o f a negative u'T'-term. A l s o - - u ' w ' is o v e r r a t e d f o r positive 5-values. During the e x p e r i m e n t s in 1 9 7 6 an overall m e a n vertical wind v e l o c i t y has b e e n systematically f o u n d o f ~ = +1 c m s-1. This m e a n s f o r u = 3 m s-1 a m a x i m u m tilt e r r o r o f - - 1 % in --u'w' and w'T '. M e a s u r e m e n t s have n o t been c o r r e c t e d f o r these errors. CUT-OFF FREQUENCY AND FILTERING T h e X - p r o b e is m o u n t e d in f r o n t o f the vane o n 14 cm distance f r o m the pivot. F r o m t h e previous sections it a p p e a r e d t h a t in a first a p p r o x i m a t i o n n o loss of the calculated c o r r e l a t i o n t e r m s caused b y a lag o f t h e vane response can be e x p e c t e d . B o t h the wind sensor and t h e t e m p e r a t u r e sensor have b e e n c o n s t r u c t e d f r o m fast-response 10 p m d i a m e t e r p l a t i n u m wires, with a c u t - o f f f r e q u e n c y o f a b o u t 50 Hz at ~ = 3 m s-1. T h e t h e r m o m e t e r , h o w e v e r , is m o u n t e d 4 c m b e l o w the X - p r o b e and is d i r e c t e d o n the m e a n wind. T h e m a x i m u m distance b e t w e e n t h e r m o m e t e r and the X - p r o b e caused b y t h e vane m o v e m e n t was a b o u t 15 cm. This m e a n s a c u t - o f f f r e q u e n c y o f a b o u t 3 ~ 4 Hz at ~ ~ 3 m s-1. T h e wind and t e m p e r a t u r e signals were t r e n d - c o r r e c t e d b y m e a n s of a highpass filter w i t h T = 53 s. This caused a c u t - o f f f r e q u e n c y o f a p p r o x i m a t e l y 0 . 0 0 3 Hz. T h e r u n p e r i o d o f 30 min caused a c u t - o f f frequency, o f 0 . 0 0 0 5 Hz. T h e m e a s u r e m e n t s were carried o u t a b o v e a maize field with a f e t c h o f a b o u t 300 m. This resulted in a characteristic f r e q u e n c y o f a b o u t 0.01 Hz. T h e signals were filtered b y a t h i r d - o r d e r 10 Hz low-pass filter and a n a l y z e d " o n l i n e " b y a D e c k PDP 8 c o m p u t e r . In a d d i t i o n to this on-line analysis d u r i n g some days w' and T ' d a t a were s t o r e d o n m a g n e t i c tape. T h e s e r e c o r d e d d a t a were spectral analyzed. Using this X - p r o b e n o i n d e p e n d e n t m e a s u r e m e n t s o f t h e w ' and u' c o m p o n e n t s were possible so spectral analysis of w' and u' d a t a had n o sense. THERMOMETER
A t first t h e c o r r e l a t i o n m e a s u r e m e n t s were carried o u t b y m e a n s of a 0.2 m m d i a m e t e r m a n g a n i n - - c o n s t a n t a n t h e r m a l couple. H o w e v e r , t o avoid r a d i a t i o n errors and low r e s p o n s e discrepancies, an X - p r o b e has b e e n used as a cold-wire t h e r m o m e t e r . T h e p l a t i n u m resistance was c o n n e c t e d in a c o n s t a n t voltage W h e a t s t o n e bridge. T h e bridge gave a linear r e s p o n s e t o t e m p e r a t u r e , a b o u t 50 p V K -1. T h e t h e r m o m e t e r has an o v e r h e a t i n g t e m p e r a t u r e ~ 0.01 K at ~ ~ 1 m s-1. RESULTS AND CONCLUSIONS F r o m s e v e n t e e n d a y s o f m e a s u r e m e n t s in A u g u s t 1 9 7 6 above a 10 h a maize c r o p , seven days are chosen. Considering a t m o s p h e r i c stability, wind v e l o c i t y ,
406 etc., 80 runs with a run period of 30 min were selected for comparison of the correlation data. The measuring heights of the eddy-correlation instruments were chosen at about 2.50 m above the zeroplane displacement, locating within the adapted boundary layer with a m a x i m u m fetch of ~ 3 0 0 m. During most of the runs the atmospheric situations were near neutral, 0 > z / L > --0.05. From 36 runs results from simultaneous profile measurements were available. This experimental project is described in more detail by Reitsma (1978) and Van Oosterum (1977). From five days, seventeen runs were selected for spectral analysis. This analysis is described by Van Oosterum (1977). As mentioned earlier the hot-wire anemometer is not very suitable for accurate measurement of the mean wind velocity sensed by the X-probe. Therefore we used the mean total wind velocity V from the propellor bivane corrected for an overrating of about 2% in relation to Yh. In Fig.4 p , is plotted against u , from profile measurements. The profile r
0.6
aug
_
_
14-15-19-20~
~0.6
aug 14-15-16-18-19-20 3~~.
0.5
0.4
0.4 0.3 0.2
0,2 0
0.8 0.7
0.2
0.4
0.6 0.8 prof. U. (m/s)
~.12~;o.o/'i
0.1 0 0 o'.1 o:2 o13 o',4 0'.5 o'.6 o.7 u~ (m/s)
Fig.4. Friction velocity data from hot-wire measurements compared with results from profile measurements. Fig. 5. The relation of the standard deviation of the vertical wind and the friction velocity. data axe calculated using a ratio zeroplane displacement/crop height d/h = 0.55. The profile data are related to Vh instead of ~ which explains an overrating of 6--8% in u , . We found a total ovexspeeding of the cup anemometers o f about 12% in comparison with ~ (Reitsma, 1978). This overspeeding is in agreement with, e.g., Businger et al. (1971). Fig.5 shows the relation of the standard deviation of the vertical wind and the friction velocity from the cross-wire anemometer data. The ratio ow/u, is believed to be a universal constant only depending on the stability (Lumley and Panofsky, 1964). We found a ratio of aw/u, = 1.23. Estimation of this value for neutral situation gives Ow/U, ~ 1.19 (see Fig.6). These values
407 2.0 ~1~ 1.8
aug 14-15-16-18-19-20-26
1.6 1.4 1.2 1.0
0
0.2
0.1
Fig.6.The ratio Ow/U, as a function of stability.
-z/L
are in excellent agreement with Lumley and Panofsky (1964) and with Shaw's et al. (1974) results also above a maize crop. Fig.7 shows the comparison of the heat flux measured with the hot-wire system H and the Gill system H G. On this day the hot-wire signals were correlated with those of the fast-response resistance thermometer, and the vertical Gill propellor with a 0.2 mm diameter thermo-couple. It is much easier to apply a thermo-couple instead of a fast-response resistance thermometer, and the response characteristics of this 0.2 m thermo-couple and a Gill propellor are very similar (Van Oosterum, 1977). The ratio H / H G = 1.26, but this should be corrected for an radiation error of the thermo-couple of some percents. Thus the heat fluxes measured by means of a vertical Gill propellor, 2.5 m above the zeroplane of maize, should be corrected with an empirical factor of about 1.3. This is in good agreement with the Tsimlyansk-experiment 101
150 &-E v t
aug
100
26~
c
50/ 00
,g.
~ 1.26±0.03
10 0
aug 26
lO-2 ........................... 10-2 10-1 100 101 n(z-d)/Q Fig.7. Heat flux data from the hot-wire measurements compared with measurements from a vertical Gill-propellor system.
,50
100
~so
HG (W/m2)
Fig.8. Measured power spectrum of vertical velocity compared with the Kansasexperiment.
408 (Tsvang et al., 1970), with a correction factor of 1.33 for unstable situations and a measuring height of 4 m above steppe grass. In Figs. 8 and 9 the power spectra of vertical velocity and of temperature are plotted for a day when we used the fast.response thermometer compared with results from the Kansas-experiment for neutral conditions (Kaimal et al., 1972). These spectra are normalized by means of the variance aw 2 and aT 2 and represent the average spectra from three runs with a total duration of 90 min. From the graphs we can see that the sensors do n o t present a lag response up to 6 Hz. Analyzing the recorded data, a 10 Hz low-pass filter has been used to avoid aliasing errors (Van Oosterum, 1977). The influence of these filters is already noticeable at about 6 Hz. This upper limit of 6 Hz is n o t a result of the characteristics of the sensors, but of the applied filters and analyzing technique. Fig.8 gives no reason to suppose any influence of the vane m o v e m e n t on the measurements of vertical velocity. The agreement with the Kansas-curves is very striking. Fig. 10 shows the corresponding Co-spectrum. At first the underrating in 101
101 oQ
~
• •
100
10°
aug 26 10-1
10-1
10-2 0-2
10 - 2
10-1
10° n(z-d)/L]
101
10-2
.........................
10-1
]
100 n(z-d)/Q
Fig.9. Measured power spectrum of temperature compared with the Kansas-experiment. Fig.10. Measured Co-spectrum of vertical velocity and temperature compared with the Kansas-experiment.
comparison with the Kansas-curve for the left part of the spectrum must be mentioned. This may be a result of normalization. However, discrepancies with the Kansas curve are not exceptional. (e.g., Kaimat et al., 1972; Jacobs et al., 1977; Panofsky and Mares, 1968.) More striking is the scattering of our data for frequencies between f = 2 and 6, We believe this scatter is due to the horizontal m o v e m e n t o f the anomemeter above the fixed thermometer. This effect will diminish after decreasing the distance of the X-probe from the vane pivot. However, the scattering is symmetric around the Kansas-curve
101
409 o n average, so we can c o n c l u d e t h a t this scattering will n o t i n f l u e n c e the m e a s u r e m e n t o f the h e a t flux It appears t h a t this r a t h e r simple and c h e a p h o t - w i r e s y s t e m can be applied f o r a c c u r a t e e d d y - c o r r e l a t i o n m e a s u r e m e n t s o f the vertical fluxes of h e a t and m o m e n t u m . In c o m b i n a t i o n with a m e a n w i n d v e l o c i t y a n e m o m e t e r and a small on-line m i n i - c o m p u t e r a very flexible e q u i p m e n t is available f o r field experiments.
pcpw'T'.
ACKNOWLEDGEMENTS I wish to t h a n k Mr. A. E. J a n s e n a n d Mr. W. Hillen f o r c o n s t r u c t i n g the w i n d v a n e a n d the X-probes. W i t h o u t their great t e c h n i c a l skill this kind o f m e a s u r e m e n t w o u l d n o t be possible. I wish to t h a n k Ir. J. Birnie a n d Mr. P. J a n s e n f o r t h e i r help w i t h e l e c t r o n i c s a n d Ir. J. L e n g k e e k f o r his help with the on-line c o m p u t e r facilities and spectral analysis. I a m grateful to M o n i c a van O o s t e r u m , w h o dealt w i t h this e x p e r i m e n t as a m e t e o r o l o g i c a l s t u d e n t , f o r her c o n s i d e r a b l e assistance.
REFERENCES Bradshaw, P., 1971. An Introduction to Turbulence and its Measurements. Pergamon Press. Businger, J. A., Wijngaard, J. C., Izumi, Y. and Bradley, E. F., 1971. Flux-profile relationship in the atmospheric surface layer. J. Atmos. Sci., 28: 181--189. Hinze, J. O., 1959. Turbulence. McGraw-Hill, New York. Jacobs, A. F. G., Nieuwvelt, C., Wartena, L. andde Vries, D. A., 1977. Eddy-correlation measurements of fluxes of heat and momentum over grassland in The Netherlands. Arch. Meteorol. Geophys. Bioklimatol., Set. A, 26: 51--71. Kaimal, J. C., Wijngaard, J. C., Izumi, Y. and Cot~, O. R., 1972. Spectral characteristics of surface-layer-turbulence. Q.J.R. Meteorol. Soc., 98: 563--589. Larsen, S. E. and Busch, N. E., 1974. Hot-wire measurements in the atmosphere. Part I. Disa-Information, no. 16:15--36. Larsen, S. E. and Busch, N. E., 1976. Hot-wire measurements in the atmosphere. Part II. Disa-Information, no. 20: 5--21. Lumley, J. L. and Panofsky, H. A., 1964. The structure of the atmospheric turbulence. John Wiley, New York. Panofsky, H. A. and Mares, E., 1968. Recent measurements of cospectra for heat flux and stress. Q.J.R. Meteorol. Soc., 94: 581--585. Reitsma, T., 1978. Windprofile Measurements above a Maizecrop. Thesis, Wageningen (The Netherlands). Shaw, R. H., Silversides, R. H. and Thurtell, G. W., 1974. Some observations of turbulence and turbulent transport within and above plant canopies. Boundary-Layer Meteorol., 5: 429--449. Strohl, A., 1971. Contribution aux Technique de Mesures par Anemometrie ~ fil chaud. Th~se, Universit~ Claude Bernard, Lyon no d'ordre 31. Swinbank, W. C., 1951. The measurement of vertical transfer of heat and water vapor by eddies in the lower atmosphere. J. Meteorol., 8: pp. 135--145. Tsvang, L. R., Koprov, B. M., Zubkovskii, S. L., Dyer, A. J., Hicks, B., Miyake, M., Stewart, R. W. and McDonald, J. W., 1970. A comparison of turbulence measurements
410 by different instruments: Tsimlyansk field experiment 1970. Boundary-Layer Meteorol, 3: 499--521. Van Oosterum, M. A. M., 1977. Eddy-correlatie metingen boven mais. Afstudeerverslag, Wageningen.
397
EDDY-CORRELATION MEASUREMENTS ABOVE A MAIZE CROP USING A SIMPLE CRUCIFORM HOT-WIRE ANEMOMETER
F. A. BOTTEMANNE
Department of Physics and Meteorology, Agricultural University, Wageningen (The Netherlands) (Received February 4, 1978; accepted August 9, 1978)
ABSTRACT Bottemanne, F. A., 1979. Eddy-correlation measurements above a maize crop using a simple cruciform hot-wire anemometer. Agric. Meteorol., 20: 397--410. For measurements of the vertical transport of heat and momentum in the turbulent and slightly unstable boundary layer above a maize crop eddy-correlation techniques were applied. In addition to a vertical Gill-propellor anemometer and a Gill-propellor bivane, a cruciform hot-wire probe, mounted on a small windvane, were used. With this hot-wire system the heat and m o m e n t u m fluxes could be measured in a relatively simple way. The possibilities and limitations of this system were checked.
INTRODUCTION I n a g r i c u l t u r a l p r a c t i c e t h e r e is a n e e d f o r s i m p l e r o u t i n e m e a s u r e m e n t s o f the heat transfer and evapotranspiration of a crop canopy. To check more r o u t i n e m e t h o d s , s u c h as a e r o d y n a m i c a l m e a s u r e m e n t s w i t h c u p a n e m o m e t e r s or eddy-correlation measurements with a Gill-propellor anemometer, a simple cruciform hot-wire system has been developed. After an old idea of Swinbank (1951) a so-called X-probe was mounted on a light windvane following the h o r i z o n t a l w i n d v e c t o r Vh, s e e F i g . 1 . I n t h i s w a y a r e l a t i v e l y s i m p l e a n d c h e a p i n s t r u m e n t h a s b e e n c o n s t r u c t e d w h i c h c o u l d b e u s e d as a s u b - s t a n d a r d w i t h i n certain limitations. This instrument has been tested during the summer of 1976 above a maize crop. From correlation of wind velocity and temperature f l u c t u a t i o n s w e c a n r e a d f o r t h e v e r t i c a l f l u x e s in c o n v e n t i o n a l n o t a t i o n : Heat transfer Momentum
transfer
H = pcpw'T' T = - - p U'W'
T h e s h e a r s t r e s s r is also d e f i n e d as r = pu2., a n d so t h e f r i c t i o n v e l o c i t y r v _1 u . = ( - - u w )2. W i t h h o t - w i r e a n e m o m e t e r s a n d a c o l d - w i r e t h e r m o m e t e r fluctuations u', w' and T' have been measured.
(1) the
39.~
Fig.1. Photograph of the cruciform hot-wire probe mounted on a light wind vane together with a fast-response cold-wire thermometer. T h e r e l a t i o n b e t w e e n t h e dissipation r a t e ~ o f a h o t wire w i t h a resistance R at t e m p e r a t u r e T w a n d the e f f e c t i v e cooling v e l o c i t y u is given b y King's law. Using R -- R 0 {1 + a ( T w - - To)} this law can be w r i t t e n in t h e f o r m : .... - ~ - - -
R --R0
: A' + B'u ~
(2)
w i t h a wire resistance R 0 at t h e a m b i e n t t e m p e r a t u r e To. O p e r a t i n g at a c o n s t a n t d i s s i p a t i o n rate ¢ it f o l l o w s t h a t : _1
= A + Bu ~
(3)
R --R0 Because, f o r e x a m p l e , o f t h e c a l i b r a t i o n drift, a h o t wire is n o t a v e r y suitable i n s t r u m e n t f o r m e a n v e l o c i t y m e a s u r e m e n t s , especially in t h e a t m o s p h e r e . If t h e v e l o c i t y is f l u c t u a t i n g a f l u c t u a t i o n o f the wire voltage can be w r i t t e n as: I
e = S • u
I
(4) 1
w i t h S ~ u-~. This r e l a t i o n is a l m o s t l i n e ~ f o r n o t t o o large f l u c t u a t i o n s , i m p l y i n g a nottoo-large relative t u r b u l e n t i n t e n s i t y . F r o m this "small-signal m e t h o d " , a h o t wire is suitable f o r m e a s u r e m e n t o f f l u c t u a t i o n s in a simple w a y , in: p a r t i c u l a r in r e l a t i o n to h i g h - f r e q u e n c y a t m o s p h e r i c f l u c t u a t i o n s . Using an X - p r o b e we can s e p a r a t e t h e h o r i z o n t a l and vertical w i n d - v e l o c i t y f l u c t u a t i o n s . D i r e c t i n g this p r o b e on the m e a n v e l o c i t y (see Fig.2) we can see t h a t h o t w i r e I is sensitive to (u' - - w ' ) a n d wire 2 to (u' + w ' ) . M o u n t e d on a w i n d v a n e the X - p r o b e is d i r e c t e d on t h e h o r i z o n t a l w i n d v e c t o r Vh. B o t h wires w e r e c o n n e c t e d to a W h e a t s t o n e bridge in such a w a y t h a t the e l e v a t i o n (or inclination} o f t h e t o t a l w i n d v e c t o r V was m e a s u r e d . T h e c o m p l e t e bridge
399 was c o n s t r u c t e d on t o p o f t h e vane. T h e s u p p l y and signal wires were conn e c t e d to silver sliprings.
22ram
w1
................ 30mm
" "NlO!um ¢
Q
Fig.2. The X-probe to separate the horizontal and vertical wind fluctuations.
THE CROSS-WIRE ANEMOMETER
T h e X - p r o b e has b e e n c o n s t r u c t e d f r o m 10 p m - d i a m e t e r p l a t i n u m wire. B o t h wires have an e f f e c t i v e length o f a b o u t 11 m m , v e r y a c c u r a t e l y m a k i n g angles o f 45 ° w i t h t h e p r o b e axis, a n d a " c o l d r e s i s t a n c e " o f a b o u t 14.9 at 20°C. In Fig.3 t h e c o n s t a n t voltage bridge is shown. F o r wire 1 w i t h a x
[
V1 •
I x
I
R1
'VVX~
V2
R2
•
'k/k/V'
1
IE Fig.& Both wires of the X-probe are connected to a constant voltage Wheatstone bridge. resistance R ~ and a c o n s t a n t bridge a r m resistance x we can write: RI
V, -
E
x+R
(4)
1
F o r a wire w i t h a resistance R0 at air t e m p e r a t u r e T O it follows: R0 Vo - - x+R
o
E
(5)
We can d e d u c e f o r vl = V1 - - V0, t h a t : 1 N vl - R , - - R 0
+M
(6)
with N = (x + R0) 2 and M = x + R0. So v L is measured in regard to a bridge
xE
xE
arm with R I = R o. For a constant dissipation rate @it follows from eqs. 3 and 6: 1
± -
Pl
plul
2
+ql
(7a)
400 a n d a n a l o g o u s l y to wire 2: --= P2
(7b)
P2U2 + q2
w i t h t h e c o o l i n g velocities f o r b o t h wires ul = ~ + u' - - w' a n d u2 -- u + u' + w'. I t a p p e a r s t h a t ¢ is c o n s t a n t in a s y m m e t r i c bridge. P l o t t i n g 1/Vl and 1/v 2 as • -t a f u n c t i o n o f u~, it f o l l o w s t h a t .for i < fi < 8 m s-1 r e l a t i o n 7 is a l m o s t valid. We h a d t a k e n x = 22.1 ~2 a n d E = 3.00 V. T o s e p a r a t e u ' a n d w ' it is i m p o r t a n t t h a t e f f e c t i v e cooling v e l o c i t y can be t a k e n o n l y as t h a t v e l o c i t y c o m p o n e n t p e r p e n d i c u l a r to t h e wire. I f in a d d i t i o n t o t h e c o m p o n e n t ql, parallel t o the p r o b e axis, b o t h t h e o t h e r c o m p o n e n t q2 p e r p e n d i c u l a r t o the wire a n d t h e t a n g e n t i a l c o m p o n e n t q3 exist, t h e n t h e e f f e c t i v e v e l o c i t y Ve f o l l o w s f r o m : Ve 2 = q l 2 + k 1 2 q 2 2
+ k22q32
(8)
Using a wire w i t h a r a t i o l e n g t h - d i a m e t e r ~ 1000, the " y a w " f a c t o r k 2 ~ 0 ( B r a d s h a w , 1971). T h e " p i t c h " f a c t o r kl can be t a k e n as e q u a l t o 1. It a p p e a r s t h a t f o r p r a c t i c a l s i t u a t i o n s in a n e a r - n e u t r a l a t m o s p h e r e t h e d i s c r e p a n c i e s b e t w e e n Ve a n d q I are smaller t h a n 1%. F r o m Fig,2 a n d in a b s e n c e o f q2 the e f f e c t i v e velocities f o r wires 1 a n d 2 can be w r i t t e n as: Vie = ul c o s 45 a n d V2e
=
122 COS 45
w i t h Ul = ~ + U' - - w' a n d u2 = ~ + u' + w ' . D e f i n i n g p 1 a n d p 2 cos 45 are already taken into account. T h e f l u c t u a t i o n s u] = u p - - w # a n d u2? = u f + W f lead t o f l u c t u a t i o n s V'l and
v~: F PI = - - p I 2 p l
1 ~ Z • UA
2u ,
P2 =
--p22p2
(9)
U'~~ " -U- 2
2u
or: u t _
vl = - - C ~ •
w p
2fi ........ t
t
U
(10)
! +W
v2 = - - C 2 •
2a 2
_L
2
i
With Ct = rl p l u ~ and C2 ~- P2 p2u-C M o s t wires are not altogether identical, but can be m a t c h e d so that C I and C 2 are equal within a calibration accuracy ..t of about 1%. For identical wires w e can define C = CI = C2 = uo2pu z, With ro = vl = u2 and p = 171 = P2.
401
W i t h v ' ' = V'l -- v'2 it f o l l o w s : C
v'
C2
v'22
v', 2 -
,
=~-W U
pt2 =
C2 ~
(-u'w')
(11)
W'2
A n d correlating with temperature fluctuations
T'; this leads
with
A 2 = v'l 2 - - v~ 2 t o :
w'T' --U ' W'
:-du
A 2
=
•
W t2
v'T'
U 2
.
(12)
,2
------C~p
For relative turbulent intensity larger than 0.1, higher order terms should be taken into account (Hinze, 1959). Second order terms in eq. 11 lead only to: v'
C
C
"
u'w'"
F r o m h e r e w e c a n see t h a t a d i s c r e p a n c y o f t h e small signal a p p r o x i m a t i o n o n l y leads t o an a p p a r e n t l y m e a s u r e d m e a n v e r t i c a l v e l o c i t y : -7 u --7= u, 2 w =~-" v 2~
(14)
This will lead t o a p r i n c i p a l l y p o s i t i v e ~ . F o r t h e 1 9 7 6 m e a s u r e m e n t s w i t h ~ --~ 3 - - 4 m s -~ this a p p a r e n t ~ c o u l d be c a l c u l a t e d as a p p r o x i m a t e l y 5 c m s-l. D u r i n g t h a t s e a s o n w e m e a s u r e d w . . ~ 6 c m s -1. Neglecting third- and higher-order terms means that we don't consider correlation terms as w , u , 2 , w , 8 , w ' u ' w ' , u ' w ' T ' etc, thus neglecting vertical diffusion of turbulent energy and shear stress and the horizontal diffusion of vertical heat transfer. Calibration of the X-probe may be carried out using eq. 11a. Adjusting the probe in a windtunnel with an elevation angle e with regard to the wind velocity V, the voltage v = VI -- V2 is read as v ~ C tg e. In Table I characteristic values for C are given as a function of ~ and 6. The values for 6 = 0 are calculated from vi2piu ~ ~ v22p2u~. First we see C is slightly dependent on the mean wind velocity. For every run period we adapted C concerning the
402 TABLEI C h a r a c t e r i s t i c c a l i b r a t i o n values (C in volts) of t h e h o t - c r o s s wire a n e m o m e t e r h-
e = 0
~ = 5°
c = I0°
0.113 0.120 0.121 0.122 0.121 0.121 0.120 0.119
0.116 0.122 0.126 0.126 0.124 0.125 0.122 0.121
116 124 127 127 126 125 124 122
(ms -1) 1 2 3 4 5 6 7 8
relevant mean wind velocity. Secondly we see clearly an e-dependency, This systematical deviation cannot be explained by discrepancies of the small-signal approximation, neglection of higher order terms, asymmetry, non-constant dissipation rate, or a yaw factor, but is caused by the aerodynamical disturbance by probe and prongs (Strohl, 1971), Field measurements showed a standard deviation of the elevation angle o f about 10 °, so we carried out our calibration also at 10 °. In this way C c o u t d b e measured with an accuracy of approximately 1%. TEMPERATURE
DEPENDENCY
A change of the mean air temperature To leads to changes m R o and B. We can calculate a T O dependency of C of a b o u t --1 fi 2% K -1. From direct calibration we f o u n d a dependency of --1% K -1. Relating C to the mean temperature To during every run, long term variations of R0 have no influence on the correlation terms. However, concerning the dissipation rate ¢, faster fluctuations of To also cause fluctuations of the wire resistance R. For identical wires eq. 10 can now be written as:
, CI (u'--w') 2 +,yT, } , C{ (u' +w')+~/T, I u2 = -~ 2 1)1 =
with ~/
_
xE
(15)
R + x aR°-C; a is the tem~rat~are coefficient of platinum, tn eq. 12
this only leads to
403 T h u s f o r a positive h e a t f l u x t h e t e m p e r a t u r e f l u c t u a t i o n s cause an o v e r r a t i n g
w'T'
in m e a s u r i n g u , . D u r i n g t h e season 1 9 7 6 7 - - ~
/2,
~ 2%.
INFLUENCE OF THE VANE RESPONSE L e t us first a s s u m e the v a n e is f o l l o w i n g the h o r i z o n t a l f l u c t u a t i o n s i n s t a n t a n e o u s l y . T h e h o r i z o n t a l w i n d v e l o c i t y can be w r i t t e n as: Vh ~ u
(
1 +-
,
~
+ v'2 2~ 2
)
and:
(17)
O(~2 w i t h o , 2 = ~2 ~ v,Z/Etz, a n d ~ t h e f l u c t u a t i n g a z i m u t h angle. F o r eq. 12 we can simply deduce:
w'T'
Yh
u'T'
(18) --lttW t
=_ g h2 A2 C2
T h u s using Vh instead o f g eqs. 12 and 18 are identical, w h e r e C is r e l a t e d t o Vh. H o w e v e r , a w i n d v a n e has a lag in r e s p o n s e , especially w i t h high f r e q u e n c y f l u c t u a t i o n s . This m e a n s a w i n d c o m p o n e n t p e r p e n d i c u l a r to t h e X - p l a n e of the p r o b e d o e s e x i s t causing a n " e x t r a " c o n t r i b u t i o n o n t h e e f f e c t i v e cooling v e l o c i t y . B u t this c o n t r i b u t i o n leads o n b o t h wires to the s a m e e f f e c t a n d t h e r e f o r e we can h a r d l y e x p e c t a n y i n f l u e n c e o n t h e d i f f e r e n t i a l m e t h o d used here. A w i n d v a n e can be d e s c r i b e d as a s e c o n d o r d e r s y s t e m and t h e d a m p i n g f o l l o w s f r o m eq. 19 (see, e.g., Larsen a n d Busch, 1974): 1 d2fi + 2 ~ d / 3 Oje2 d t 2 ~/+/3 = ~
(19)
H e r e (~ is t h e w i n d d i r e c t i o n and/3 is t h e vane d e f l e c t i o n , w i t h r e s p e c t to the m e a n w i n d d i r e c t i o n . 09e is t h e r e s o n a n c e angular f r e q u e n c y o f t h e v a n e and is t h e d a m p i n g ratio. I m p o r t a n t is the so-called " n a t u r a l wave l e n g t h " k 0 = 2~'U/~e, a n d this is a b o u t equal to the d a m p i n g w a v e l e n g t h , k0/21r can be c o n s i d e r e d as a d i s t a n t c o n s t a n t o f the i n s t r u m e n t . This vane h a s a n a t u r a l w a v e l e n g t h o f a b o u t 3 m a n d a d a m p i n g r a t i o ~ = 0 . 4 - - 0 . 6 . This m e a n s f o r = 3 m s-1 a r e s o n a n c e f r e q u e n c y n e ~ 1 H z , a n d w i t h a m e a s u r i n g h e i g h t z --~ 3 m a n o n - d i m e n s i o n a l f r e q u e n c y fe ~ 1. It a p p e a r s t h a t f o r f > 3 this vane can h a r d l y f o l l o w f l u c t u a t i o n s o f t h e h o r i z o n t a l wind v e l o c i t y . F o r
404
lower frequencies however, a vane deflection must also be taken into account. Decomposing the instantaneous horizontal wind velocity Vh into a longitudinal c o m p o n e n t V1 and a tangential c o m p o n e n t Vt perpendicular to the X-plane of the probe it follows: VI = Vh cos 7--~ Vh 1 - - - ~
(20)
Vt = Vh sin7 ~ V h " 7 with 7 = (~
~, assumed to be small, and:
V, -~ Vh 1
~-
(21)
Vt ~ Vh o ~ = 0
with 072 = 72. And using V 1 instead of ~ this leads again to equations identical to
w'T'
(12):
V1 ,~, ".I
= ~-V
-u'w'
(22)
V'2
=-6-
When C is also related to V 1. Thus it is a good approxinmtion to state that the damping of the windvane does n o t cause errors in the correlation terms w'T' and --u~w~if we use only the mean wind velocity that is sensed by the vane itself. In this case it is very important t h a t we can negtect errors in correlation measurements caused by a " c u t o f f ' frequency also in the region of ~ e r frequencies. This is confirmed by the results of Larsen and Btmch (1976), where only an influence of the vane response can be established in the correlation spectra for the lateral velocity in which we are not interested here. TILT E R R O R
If the probe system i s t i l t e d with an angle 6 to the mean wind with regard to the " t r u e vertical" a m a x i m u m tilt error must be considered. We can define the true vertical as that ~ c t i o n for which holds ~ = 0 during a certain period. For positive and no ~ o large 8-values we can derive:
w'T'~ = w'T'o (1 - u'~T'~ "6) 2 --u
' w' ~
=
- - U 'W ' o
(
l + aU
(23) - - Ow 2
u, 2
"8)
For unstable conditions the heat~lux is overrated for positive 8-values because
405 o f a negative u'T'-term. A l s o - - u ' w ' is o v e r r a t e d f o r positive 5-values. During the e x p e r i m e n t s in 1 9 7 6 an overall m e a n vertical wind v e l o c i t y has b e e n systematically f o u n d o f ~ = +1 c m s-1. This m e a n s f o r u = 3 m s-1 a m a x i m u m tilt e r r o r o f - - 1 % in --u'w' and w'T '. M e a s u r e m e n t s have n o t been c o r r e c t e d f o r these errors. CUT-OFF FREQUENCY AND FILTERING T h e X - p r o b e is m o u n t e d in f r o n t o f the vane o n 14 cm distance f r o m the pivot. F r o m t h e previous sections it a p p e a r e d t h a t in a first a p p r o x i m a t i o n n o loss of the calculated c o r r e l a t i o n t e r m s caused b y a lag o f t h e vane response can be e x p e c t e d . B o t h the wind sensor and t h e t e m p e r a t u r e sensor have b e e n c o n s t r u c t e d f r o m fast-response 10 p m d i a m e t e r p l a t i n u m wires, with a c u t - o f f f r e q u e n c y o f a b o u t 50 Hz at ~ = 3 m s-1. T h e t h e r m o m e t e r , h o w e v e r , is m o u n t e d 4 c m b e l o w the X - p r o b e and is d i r e c t e d o n the m e a n wind. T h e m a x i m u m distance b e t w e e n t h e r m o m e t e r and the X - p r o b e caused b y t h e vane m o v e m e n t was a b o u t 15 cm. This m e a n s a c u t - o f f f r e q u e n c y o f a b o u t 3 ~ 4 Hz at ~ ~ 3 m s-1. T h e wind and t e m p e r a t u r e signals were t r e n d - c o r r e c t e d b y m e a n s of a highpass filter w i t h T = 53 s. This caused a c u t - o f f f r e q u e n c y o f a p p r o x i m a t e l y 0 . 0 0 3 Hz. T h e r u n p e r i o d o f 30 min caused a c u t - o f f frequency, o f 0 . 0 0 0 5 Hz. T h e m e a s u r e m e n t s were carried o u t a b o v e a maize field with a f e t c h o f a b o u t 300 m. This resulted in a characteristic f r e q u e n c y o f a b o u t 0.01 Hz. T h e signals were filtered b y a t h i r d - o r d e r 10 Hz low-pass filter and a n a l y z e d " o n l i n e " b y a D e c k PDP 8 c o m p u t e r . In a d d i t i o n to this on-line analysis d u r i n g some days w' and T ' d a t a were s t o r e d o n m a g n e t i c tape. T h e s e r e c o r d e d d a t a were spectral analyzed. Using this X - p r o b e n o i n d e p e n d e n t m e a s u r e m e n t s o f t h e w ' and u' c o m p o n e n t s were possible so spectral analysis of w' and u' d a t a had n o sense. THERMOMETER
A t first t h e c o r r e l a t i o n m e a s u r e m e n t s were carried o u t b y m e a n s of a 0.2 m m d i a m e t e r m a n g a n i n - - c o n s t a n t a n t h e r m a l couple. H o w e v e r , t o avoid r a d i a t i o n errors and low r e s p o n s e discrepancies, an X - p r o b e has b e e n used as a cold-wire t h e r m o m e t e r . T h e p l a t i n u m resistance was c o n n e c t e d in a c o n s t a n t voltage W h e a t s t o n e bridge. T h e bridge gave a linear r e s p o n s e t o t e m p e r a t u r e , a b o u t 50 p V K -1. T h e t h e r m o m e t e r has an o v e r h e a t i n g t e m p e r a t u r e ~ 0.01 K at ~ ~ 1 m s-1. RESULTS AND CONCLUSIONS F r o m s e v e n t e e n d a y s o f m e a s u r e m e n t s in A u g u s t 1 9 7 6 above a 10 h a maize c r o p , seven days are chosen. Considering a t m o s p h e r i c stability, wind v e l o c i t y ,
406 etc., 80 runs with a run period of 30 min were selected for comparison of the correlation data. The measuring heights of the eddy-correlation instruments were chosen at about 2.50 m above the zeroplane displacement, locating within the adapted boundary layer with a m a x i m u m fetch of ~ 3 0 0 m. During most of the runs the atmospheric situations were near neutral, 0 > z / L > --0.05. From 36 runs results from simultaneous profile measurements were available. This experimental project is described in more detail by Reitsma (1978) and Van Oosterum (1977). From five days, seventeen runs were selected for spectral analysis. This analysis is described by Van Oosterum (1977). As mentioned earlier the hot-wire anemometer is not very suitable for accurate measurement of the mean wind velocity sensed by the X-probe. Therefore we used the mean total wind velocity V from the propellor bivane corrected for an overrating of about 2% in relation to Yh. In Fig.4 p , is plotted against u , from profile measurements. The profile r
0.6
aug
_
_
14-15-19-20~
~0.6
aug 14-15-16-18-19-20 3~~.
0.5
0.4
0.4 0.3 0.2
0,2 0
0.8 0.7
0.2
0.4
0.6 0.8 prof. U. (m/s)
~.12~;o.o/'i
0.1 0 0 o'.1 o:2 o13 o',4 0'.5 o'.6 o.7 u~ (m/s)
Fig.4. Friction velocity data from hot-wire measurements compared with results from profile measurements. Fig. 5. The relation of the standard deviation of the vertical wind and the friction velocity. data axe calculated using a ratio zeroplane displacement/crop height d/h = 0.55. The profile data are related to Vh instead of ~ which explains an overrating of 6--8% in u , . We found a total ovexspeeding of the cup anemometers o f about 12% in comparison with ~ (Reitsma, 1978). This overspeeding is in agreement with, e.g., Businger et al. (1971). Fig.5 shows the relation of the standard deviation of the vertical wind and the friction velocity from the cross-wire anemometer data. The ratio ow/u, is believed to be a universal constant only depending on the stability (Lumley and Panofsky, 1964). We found a ratio of aw/u, = 1.23. Estimation of this value for neutral situation gives Ow/U, ~ 1.19 (see Fig.6). These values
407 2.0 ~1~ 1.8
aug 14-15-16-18-19-20-26
1.6 1.4 1.2 1.0
0
0.2
0.1
Fig.6.The ratio Ow/U, as a function of stability.
-z/L
are in excellent agreement with Lumley and Panofsky (1964) and with Shaw's et al. (1974) results also above a maize crop. Fig.7 shows the comparison of the heat flux measured with the hot-wire system H and the Gill system H G. On this day the hot-wire signals were correlated with those of the fast-response resistance thermometer, and the vertical Gill propellor with a 0.2 mm diameter thermo-couple. It is much easier to apply a thermo-couple instead of a fast-response resistance thermometer, and the response characteristics of this 0.2 m thermo-couple and a Gill propellor are very similar (Van Oosterum, 1977). The ratio H / H G = 1.26, but this should be corrected for an radiation error of the thermo-couple of some percents. Thus the heat fluxes measured by means of a vertical Gill propellor, 2.5 m above the zeroplane of maize, should be corrected with an empirical factor of about 1.3. This is in good agreement with the Tsimlyansk-experiment 101
150 &-E v t
aug
100
26~
c
50/ 00
,g.
~ 1.26±0.03
10 0
aug 26
lO-2 ........................... 10-2 10-1 100 101 n(z-d)/Q Fig.7. Heat flux data from the hot-wire measurements compared with measurements from a vertical Gill-propellor system.
,50
100
~so
HG (W/m2)
Fig.8. Measured power spectrum of vertical velocity compared with the Kansasexperiment.
408 (Tsvang et al., 1970), with a correction factor of 1.33 for unstable situations and a measuring height of 4 m above steppe grass. In Figs. 8 and 9 the power spectra of vertical velocity and of temperature are plotted for a day when we used the fast.response thermometer compared with results from the Kansas-experiment for neutral conditions (Kaimal et al., 1972). These spectra are normalized by means of the variance aw 2 and aT 2 and represent the average spectra from three runs with a total duration of 90 min. From the graphs we can see that the sensors do n o t present a lag response up to 6 Hz. Analyzing the recorded data, a 10 Hz low-pass filter has been used to avoid aliasing errors (Van Oosterum, 1977). The influence of these filters is already noticeable at about 6 Hz. This upper limit of 6 Hz is n o t a result of the characteristics of the sensors, but of the applied filters and analyzing technique. Fig.8 gives no reason to suppose any influence of the vane m o v e m e n t on the measurements of vertical velocity. The agreement with the Kansas-curves is very striking. Fig. 10 shows the corresponding Co-spectrum. At first the underrating in 101
101 oQ
~
• •
100
10°
aug 26 10-1
10-1
10-2 0-2
10 - 2
10-1
10° n(z-d)/L]
101
10-2
.........................
10-1
]
100 n(z-d)/Q
Fig.9. Measured power spectrum of temperature compared with the Kansas-experiment. Fig.10. Measured Co-spectrum of vertical velocity and temperature compared with the Kansas-experiment.
comparison with the Kansas-curve for the left part of the spectrum must be mentioned. This may be a result of normalization. However, discrepancies with the Kansas curve are not exceptional. (e.g., Kaimat et al., 1972; Jacobs et al., 1977; Panofsky and Mares, 1968.) More striking is the scattering of our data for frequencies between f = 2 and 6, We believe this scatter is due to the horizontal m o v e m e n t o f the anomemeter above the fixed thermometer. This effect will diminish after decreasing the distance of the X-probe from the vane pivot. However, the scattering is symmetric around the Kansas-curve
101
409 o n average, so we can c o n c l u d e t h a t this scattering will n o t i n f l u e n c e the m e a s u r e m e n t o f the h e a t flux It appears t h a t this r a t h e r simple and c h e a p h o t - w i r e s y s t e m can be applied f o r a c c u r a t e e d d y - c o r r e l a t i o n m e a s u r e m e n t s o f the vertical fluxes of h e a t and m o m e n t u m . In c o m b i n a t i o n with a m e a n w i n d v e l o c i t y a n e m o m e t e r and a small on-line m i n i - c o m p u t e r a very flexible e q u i p m e n t is available f o r field experiments.
pcpw'T'.
ACKNOWLEDGEMENTS I wish to t h a n k Mr. A. E. J a n s e n a n d Mr. W. Hillen f o r c o n s t r u c t i n g the w i n d v a n e a n d the X-probes. W i t h o u t their great t e c h n i c a l skill this kind o f m e a s u r e m e n t w o u l d n o t be possible. I wish to t h a n k Ir. J. Birnie a n d Mr. P. J a n s e n f o r t h e i r help w i t h e l e c t r o n i c s a n d Ir. J. L e n g k e e k f o r his help with the on-line c o m p u t e r facilities and spectral analysis. I a m grateful to M o n i c a van O o s t e r u m , w h o dealt w i t h this e x p e r i m e n t as a m e t e o r o l o g i c a l s t u d e n t , f o r her c o n s i d e r a b l e assistance.
REFERENCES Bradshaw, P., 1971. An Introduction to Turbulence and its Measurements. Pergamon Press. Businger, J. A., Wijngaard, J. C., Izumi, Y. and Bradley, E. F., 1971. Flux-profile relationship in the atmospheric surface layer. J. Atmos. Sci., 28: 181--189. Hinze, J. O., 1959. Turbulence. McGraw-Hill, New York. Jacobs, A. F. G., Nieuwvelt, C., Wartena, L. andde Vries, D. A., 1977. Eddy-correlation measurements of fluxes of heat and momentum over grassland in The Netherlands. Arch. Meteorol. Geophys. Bioklimatol., Set. A, 26: 51--71. Kaimal, J. C., Wijngaard, J. C., Izumi, Y. and Cot~, O. R., 1972. Spectral characteristics of surface-layer-turbulence. Q.J.R. Meteorol. Soc., 98: 563--589. Larsen, S. E. and Busch, N. E., 1974. Hot-wire measurements in the atmosphere. Part I. Disa-Information, no. 16:15--36. Larsen, S. E. and Busch, N. E., 1976. Hot-wire measurements in the atmosphere. Part II. Disa-Information, no. 20: 5--21. Lumley, J. L. and Panofsky, H. A., 1964. The structure of the atmospheric turbulence. John Wiley, New York. Panofsky, H. A. and Mares, E., 1968. Recent measurements of cospectra for heat flux and stress. Q.J.R. Meteorol. Soc., 94: 581--585. Reitsma, T., 1978. Windprofile Measurements above a Maizecrop. Thesis, Wageningen (The Netherlands). Shaw, R. H., Silversides, R. H. and Thurtell, G. W., 1974. Some observations of turbulence and turbulent transport within and above plant canopies. Boundary-Layer Meteorol., 5: 429--449. Strohl, A., 1971. Contribution aux Technique de Mesures par Anemometrie ~ fil chaud. Th~se, Universit~ Claude Bernard, Lyon no d'ordre 31. Swinbank, W. C., 1951. The measurement of vertical transfer of heat and water vapor by eddies in the lower atmosphere. J. Meteorol., 8: pp. 135--145. Tsvang, L. R., Koprov, B. M., Zubkovskii, S. L., Dyer, A. J., Hicks, B., Miyake, M., Stewart, R. W. and McDonald, J. W., 1970. A comparison of turbulence measurements
410 by different instruments: Tsimlyansk field experiment 1970. Boundary-Layer Meteorol, 3: 499--521. Van Oosterum, M. A. M., 1977. Eddy-correlatie metingen boven mais. Afstudeerverslag, Wageningen.