Typical wind spectra taken at Poker Flat, Alaska, using the vertically oriented antenna show velocities of 10's of cm to meters per second and spectral widths winds of 0.5 to 1 m/s. The potential errors in such measurements can be broken down into three categories: (1) those due to instrumental parameters and data processing, (2) those due to specular returns from non-horizontal surfaces, and (3) those due to other physical effects. Error analysis in vertical velocity measurement is further discussed

Riddle, A. C.

English

NASA Technical Reports Server

227 
3.4B ACcDaACY OF VERTICAL VELOCITY DETERMINATION 
A. C. Riddle 
CIRES/NOAA Aeronomy Laboratory 
Boulder, CO 80303 
Typical wind spectra  taken a t  Poker F la t ,  Alaska, using the v e r t i c a l l y  
or iented antenna show ve loc i t i e s  of 10's of cm t o  meters per second and spec t r a l  
widths winds of 0.5 t o  1 m / s .  
broken down i n t o  three categories:  (1) those due t o  instrumental  parameters and 
data  processing, (2) those due t o  specular r e tu rns  from non-horizontal surfaces,  
and (3) those due to  other  physical effects .  
10 t o  20 cm scl. 
mination errors.  
the average of the two adjacent points i n  order t o  avoid dc o f f s e t  problems. 
For small v e l o c i t i e s  and narrow spec t r a l  widths, t h i s  could cause systematic 
e r r o r s  of n, 1 c m / s .  However, s ince the e r r o r s  are symmetric with respect to 
zero ve loc i ty  they w i l l  not cause noticeable e r ro r s  i n  v e l o c i t i e s  averaged over 
s ign i f i can t  t i m e s  (2 112 h r ) .  
instrumental  parameters o r  data processing. 
The po ten t i a l  e r r o r s  i n  such measurements can be 
A t  Poker F l a t  the typical  v e r t i c a l  veloci ty  spectrum has data points w e r y  
This spacing i s  small enough t o  prevent ve loc i ty  deter- 
The cen t r a l  point  i n  the spectrum (0 veloci ty)  i s  replaced by 
Hence w e  expect no s ign i f i can t  e r r o r s  due t o  
On the other hand, fo r  f i n i t e  width antenna beams, specular re turns  from 
nonhorizontal surfaces can occur. W e  have no real estimate of the e r r o r s  
caused by t h i s  e f f ec t .  However, w e  do expect it t o  be a random e f fec t  with zero 
mean and hence again w e  expect no e r r o r s  i n  long-term averages of v e r t i c a l  velo- 
c i ty .  
v e l o c i t i e s  derived from turbulent echoes and v e r t i c a l  v e l o c i t i e s  a t  higher 
a l t i t u d e s  from meteor echoes show the same general trend. Since the meteor 
echoes cannot be so affected w e  assert that ,  on the average, specular re turns  i n  
the mesosphere from t i l t e d  surfaces cause no systematic e r ro r .  
These expectations are borne out i n  the mesosphere where v e r t i c a l  
There a r e  a number of po ten t i a l  e f f e c t s  i n  the th i rd  category. F i r s t  we 
consider the p o s s i b i l i t y  t h a t  the bean i s  not v e r t i c a l .  
hor izontal  veloci ty  of % 50 m e t e r s  per second t o  cause an e r ro r  of l e s s  than 10 
cm/s it i s  e s s e n t i a l  t h a t  the beam i s  no more than 0.1" off  ve r t i ca l .  A t  
Poker F l a t  the typ ica l  monthly mean v e r t i c a l  ve loc i ty  i n  the troposphere i s  l e s s  
than 1 cm/s and hence the beam i s  considerably less than 0.1" o f f  v e r t i c a l .  
I n  the mesosphere several  physical e f f e c t s  could cause an error  i n  the 
For a typical  
v e r t i c a l  veloci ty  measurements t h a t  should increase with height. 
sidered beam bending by the magnetic f i e l d ,  beam bending by nonvertical  iono- 
spheric gradients ,  phase s h i f t s  ( interpreted a s  v e l o c i t i e s )  introduced by 
changing electron density and e l e c t r i c  f i e l d s  i n  the ionosphere (REID, 1983). 
Even under extreme conditions only the latter mechanism could introduce 
measurable e f f ec t s .  The s imi l a r i t y  of Poker F la t  mesospheric v e r t i c a l  monthly 
averages over 25 km range (70 t o  95 km) iddicate  t h a t  none of these po ten t i a l  
e r ro r  sources are s ignif icant .  
We have con- 
REFERENCE 
Reid, G.  C. (1983), The influence of e l e c t r i c  f i e l d s  on radar measurements of 
winds i n  the upper mesosphere, Radio Science. 18, 1028-1034. 
https://ntrs.nasa.gov/search.jsp?R=19840019044 2020-03-22T09:44:33+00:00Z
228 
3.5A IMPLICATION ON DATA INTERPRETATION BY SHORT- AND LONG-PERIOD OSCILLATIONS 
0. Jioyrvik 
Aeronomy Labor a t  or y 
Department of Electrical Engineering 
University of I l l i n o i s  
Urbana, I L  61801 
OBSERVATION OF HORIZONTAL VELOCITY VARIATIONS 
Measurements of horizontal  ve loc i t i e s  i n  the upper atmosphere have been 
attempted using a multitude of techniques with associated assumptions about the 
wind f i e l d .  One example i s  the Doppler beam swinging radar where line-of-sight 
wind measurements are made with the antenna positioned i n  th ree  d i f f e ren t  direc- 
t i ons  and then the three-dimensional wind f i e l d  i s  calculated under the assump- 
t i o n  t h a t  the wind f i e l d  i s  constant Over t i m e  and space spanning these measure- 
ments. This assumption i s  reasonable when t i d a l  o s c i l l a t i o n s  and the mean wind 
are considered. 
t h a t  are in t eg ra l  f r ac t ions  of a so l a r  day (24-12-8 hours). 
the sca l e  of the temporal and s p a t i a l  va r i a t ions  a r e  wen  larger .  
concluded t h a t  there  are no problems i n  measuring the mean wind and t i d e s  using 
the  Doppler beam swinging (DBS) technique, or any other technique based on the 
assumption of s ta t ionary wind f i e lds .  
Tides have wavelengths of thousands of kilometers and periods 
For the mean wind 
Thus it i s  
The problem arises when short-period horizontal  o s c i l l a t i o n s  are measured. 
COUNTRYMAN and BOWRILL (1979) using the Jicamarca radar i n  a DBS experiment have 
shown t h a t  the horizontal  wavelength of short-period gravity waves are of the 
order of 20 km. 
layer observed by MOREELS and HERSE (1977) showing horizontal  wavelengths as 
short  as 20 km. 
beam d i r ec t ions  of about 5" or more w i l l  span a substant ia l  f r ac t ion  of the 
horizontal  wavelength i n  the mesosphere and thus the assumption of s imilar  wind 
f i e l d s  i s  violated.  So it appears t h a t  short-period horizontal  veloci ty  osci l -  
l a t i o n s  can not be easi ly  measured by the use of the DBS technique. 
appears t o  be generally accepted i n  the MST radar community. 
This agrees w e l l  with observations of gravity waves i n  the OH 
It i s  thus c l e a r  t h a t  a DBS radar with angular separation i n  
This 
Similar considerations a r e  v a l i d  fo r  the spaced antenna d r i f t s  technique 
Howwer, there  have been claims i n  the l i t e r a t u r e  t h a t  t h i s  technique (SAD). 
should be able  to  measure short-period horizontal  o sc i l l a t ions ,  so it  i s  
reasonable to  discuss  t h i s  technique i n  more d e t a i l .  The SAD technique i s  based 
upon the recognition of an interference pat tern d r i f t i n g  across  a set of spaced 
receiving antennas (ROYRVIK 1983a). 
Under idea l  conditions, i t  i s  clear t h a t  the veloci ty  of the interference 
Bowwer, i t  pat tern over the ground can be measured with reasonable accuracy. 
remains t o  be shown t h a t  t h i s  veloci ty  i s  r e l a t ed  t o  the bulk horizontal  motion 
of the ionosphere a t  the a l t i t u d e  probed. It i s  reasonable t o  expect t o  f ind 
short-period gravi ty  waves i n  the mesosphere tha t  have approximately the same 
amplitude i n  the horizontal  and v e r t i c a l  wind component, and horizontal  wave- 
length as short  as 20 km. The e f f ec t  of such short-period waves upon the SAD 
experiment's a b i l i t y  t o  measure wind has not previously been taken i n t o  account. 
Consider the simplified s i t u a t i o n  given i n  Figure 1 where only two 
sca t t e r ing  i r r e g u l a r i t i e s  are present i n  the  antenna beam a t  equal but opposite 
angular distances away from the zenith. 
from each i r r egu la r i ty .  
s ca t t e r ing  from each of the two i r r e g u l a r i t i e s  may be wri t ten 
The same amount of power i s  scat tered 
The e l e c t r i c  f i e l d s  on the ground r e su l t i ng  from 
229 
Figure 1. Radar s i t u a t i o n  wi th  two s c a t t e r i n g  i r r e g u l a r i t i e s  moving 
under the  influence of a short-wavelength gravi ty  wave. 
2n x sin6 2a z cos6 + 
A I  E l  = Eoexp il(Wo + w l ) t  - h 
2 a  x sin6 2 a  z cos0 + X I  E 2  = Eoexp i[(w, + w2)t + 
In these equations E O  i s  the  amplitude of the sca t te red  wave, w o  the  angular 
frequency of the transmitted radar  wave, w 1  and w2 the  Doppler s h i f t s  i n  
frequency, and X = i s  t h e  f r e e  space wavelength. gene rally,^^ and w2 are 
independent, and wew@an express them as a function of a mean frequency s h l f t  W m  
and a d i f f e r e n t i a l  frequency s h i f t  Wd so t ha t  
w1 = am - Wd and W2 = a,,, + ad 
Since the antenna beam width is generally small we may add the  e l e c t r i c  f i e l d s  
without accounting fo r  po la r i za t ion  e f f ec t s .  
ground then becomes 
The t o t a l  e l e c t r i c  f i e l d  on the  
1 2n cos0 
h E = E l  + E 2 =  E o  exp i [ ( W O  + w,,-)t + 
230 
The exponential pa r t  of t h i s  function represents a wave propagating v e r t i c a l l y  
i n  the negative z d i r ec t ion  with a frequency ( w e  + wm). The amplitude of t h i s  
wave i s  modulated i n  the horizontal  plane i n  the form of a propagating wave 
given by 
27r x s ine  
A(x,t) = 2EOcos( wdt) 
where the frequency of the wave i s  given by wd = ( ~ 2  - ~ 1 ) / 2 .  
s h i f t  frequencies w 1  and w 2  r e su l t i ng  from the act ion of an in t e rna l  gravity 
wave can be expressed a s  a function of the two line-of-sight v e l o c i t i e s  
The two Doppler 
and 
For radars with half  beam width 0 less than 15" it i s  a good approximation t o  
s e t  cos8 = 1 thus simplifying the expressions fo r  w 1  and w2. 
asymptotic r e l a t ionsh ips  fo r  i n t e rna l  gravi ty  waves we can express w 1  and w 2  
a s  a function of amplitude, frequency and wavelength of the gravi ty  wave giving 
Using the 
and 
Here it  has been assumed t h a t  the v e r t i c a l  and horizontal  veloci ty  components 
a r e  90" out of phase. 
but leads t o  s implif icat ions of the r e s u l t  and w i l l  not  a f f ec t  the basic  con- 
clusions. Q i s  the frequency of the in t e rna l  gravity wave, and V ,  and V, are 
the v e r t i c a l  and horizontal  components of the wind f i e l d ,  respectively.  
t he  phase difference between the o s c i l l a t i o n s  i n  the two scat ter ing volumes 
which can be approximated by 
This may not be very r e a l i s t i c  under a l l  circumstances, 
ed i s  
~ R Z  s ine  
'd - L 
where L i s  the horizontal  wavelength of the gravi ty  wave. 
equations give the expression 
Combining these 
wd = w' ( v , ~ s i n ( ~  t - 8,) - s i n n  t l  
-V,sin[cos(Q t - ed) + cosQ t l  } 
and 
w, = c W O   sin(^ t - 8d) + sinQ t ]  + Vxsine[cosQ t - cos(Q t - ed)] 1 
It i s  c l e a r  from the expression for  wd tha t  the horizontal  veloci ty  of the 
ground pat tern w i l l  be a q u i t e  complicated function of several  physical para- 
meters unless 8d I: 0. However, consider a not unreasonable s i t ua t ion  of an 
antenna half beam width of 5", two sca t t e r ing  i r r e g u l a r i t i e s  a t  85 km as  shown 
i n  Figure 1, a horizontal  wavelength of 30 km and a wave period of 10 minutes. 
Then ed f R and wa reduces t o  
231 
Thus i t  i s  seen t h a t  fo r  t h i s ,  and other  similar choices where Bdz IT 
hor izontal  motion of the pat tern over the ground i s  caused by the horizontal  
va r i a t ions  i n  the v e r t i c a l  veloci ty  only. 
0 << ed < IT, wd w i l l  be dominated by v e r t i c a l  veloci ty  differences because of 
the addi t ional  f ac to r  s i n e  i n  the contribution from the horizontal  velocity.  
The preceding calculat ions show t h a t  small s p a t i a l  va r i a t ions  i n  the 
v e r t i c a l  veloci ty  within the antenna beam can d ras t i ca l ly  a f f e c t  the horizontal  
veloci ty  measured. 
of 10" such v e r t i c a l  veloci ty  va r i a t ions  could be caused by short-period gravi ty  
waves. For an antenna beamwidth of the order of 1" large-scale turbulent motion 
i s  more l i ke ly  t o  cause erroneous horizontal  wind measurements. A s  i s  shown i n  
another paper (ROYRVIK, 1983b) there  a re  indicat ions of large-scale (200-400 m) 
Kelvin-Helmholtz billows with a c i r cu la r  motion i n  the mesosphere. These occur 
in t e rmi t t en t ly  and may cause l a rge  disturbances i n  the calculated horizontal  
ve loc i t i e s  when a narrow beam antenna is used. 
the 
However, even fo r  other values where 
It was shown tha t  i f  the antenna beamwidth i s  of the order 
Thus it  appears t h a t  both the SAD and the  DBS techniques require 
integrat ion over several  periods of the short-period o s c i l l a t i o n s  t o  obtain a 
horizontal  veloci ty  measurement. Estimates show t h a t  integrat ion wer 
approximately one hour gives reasonably accurate horizontal  veloci ty  estimates. 
Two other l e s s  known techniques may be be t t e r  sui ted t o  measure short- 
period horizontal  veloci ty  osc i l l a t ions .  
technique and the cross-beam d r i f t  (CBD) technique. 
based upon the horizontal  d r i f t  of s p a t i a l l y  l imited sca t t e r ing  volumes. In the 
IFR mode the horizontal  motion of the i r r e g u l a r i t i e s  could be traced as a change 
i n  r e l a t i v e  phase between the  s ignals  received i n  a set of spa t i a l ly  separated 
receivers.  I n  the CBD mode the horizontal  d r i f t  would manifest i t s e l f  as a 
lagged maximum i n  the cross correlat ion of s ignal  amplitudes received i n  a s e t  
of antennas i n  looking d i f f e r e n t  directions.  
These are the interferometer (IFR) 
Both these techniques a r e  
The use of these techniques w i l l  depend on a proper s p a t i a l  and temporal 
d i s t r ibu t ion  of the sca t t e r ing  i r r e g u l a r i t i e s  i n  the upper atmosphere, and as 
f a r  as i s  known it has not been show t h a t  these d i s t r ibu t ions  exist. 
ACKNOWLEEMENT 
The work described was supported by the National Science Foundation under 
Grant ATM 80-19563. 
REFERENCES 
Countryman, I. D. and S. A. Bowhill (1979), Wind and wave observations i n  the 
mesosphere using coherent-scatter radar,  Aeron. Rep. No. 89, Aeron. Lab., 
Dep. Elec. Eng. , Univ. Ill., Urbana-Champaign. 
Moreels, G. and M. Herse (1977), Photographic evidence of waves around the 85 km 
l eve l ,  Planet. Space Sci.. 25, 265. 
Royrvik, 0. (1983a), Spaced antenna d r i f t s  a t  Jicamarca, Mesospheric 
measurements, Radio Sci., 461-476. 
Royrvik. 0. (1983131, VBF radio s ignals  s ca t t e r ed  from the equator ia l  mesosphere, 
Radio Sci. , 1325-1335. 


Accuracy of vertical velocity determination

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