Radar equation for Engineers

Drop size
distribution from
WXT weather
transmitter?
Heikki Pohjola,
Application specialist
Thanks to Elena
Weather Transmitter
acoustic rain sensor
Ultrasonic wind sensor
CPU board
PTU module
screw terminal
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The Equations.
Output of radar systems is expressed in Z or dBZ.
Z is reflectivity factor, Z = NiDi6
Ni number of particles with diameter Di
per unit volume of the atmosphere.
Z varies from 0.0000001 to 10000000 so we use
instead logarithmic dBZ
In Hydrology, this rainfall intensity is then estimated from
Z = aRb where a and b are empirical parameters
e.g. Z = 200R1.6
where R = rainfall rate in mm/h
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WXT_Z
Raincap sensor of WXT works as a disdrometer, and
measures N and D in time unit.
Thus, we can calculate reflectivity on ground
Zg = NiDi6
and avoid all fuzzy Z/R conversions
2006-07-22 10:31 - 11:31
800
600
N 400
200
0
1.00
1.25
1.60
2.00
2.50
Drop diameter [mm]
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3.20
4.00
5.00
DSD field test measurements in Vantaa, July 2006
Drop size distribution varies in time and place
two sets during the same day, same site
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2006-07-22 10:31 - 11:31
150
800
600
100
N
N 400
50
200
0
0
1.00
1.25
1.60
2.00
2.50
Drop diameter [mm]
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3.20
4.00
5.00
1.00
1.25
1.60
2.00
2.50
Drop diameter [mm]
3.20
4.00
5.00
The Danger
•Changes in time
in one place are similar to
changes in place on one
moment
•Thus, using one
observation
for interpreting the
entire image is no good
(Not the same day, just a scematic image)
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Application
Set one or more WXTs to
blocked sectors of radar
Combine dBZ values
for each image (every
2, 5, 6, 10 or 15 minutes)
Metman3 and IRIS have tools for this
using Barnes method for radar+gauge
combination
(see IRIS hydromet option)
(Barnes, S.L., 1964: A technique for maximising details in
numerical weather map analysis. Jour_. AppI_Meteor.,
_3,396-409)
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A very bad case of beam blocking in
mountaineus environment
Other applications
•Gapfilling between radars
•Ground reference for vertical profile of reflectivity
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Data
•Drop size distribution data from WXT, disdrometer (RD-69) and POSS
from Järvenpää
•WXT: 21.8. ->
•RD-69: All Testbed campaings
•POSS: All Testbed campaings
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Is WXT´s DSD data accurate enough?
•Comparison between disdrometer, WXT and POSS data. (In WXT
specs accumation accuracy 5 %.)
In future:
•If results are promising:
• Weather radar applications like WXT-beam blockage correction, -cap
filling, -adjustment, ...
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Back up slides
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FYI: Radar equation
P rr 2
LC|K|2
=Z
Where
Pr is the power in watts – this is what radar technically measure
L is attenuation and other losses
C is radar constant (set in calibration)
|K|2 is the dielectric factor (roughly, ice or water)
r is distance from radar
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The Opportunity
Global distribution of DSD is badly known (as disdrometers are expensive and
thus rare)
Climatological research, especially global precipitation projects such as GPM
could benefit of a bunch of reasonably priced identical disdrometers at each
ground validation site.
The Global Precipitation Measurement (GPM) Program
Objectives:
• obtain increased understanding of clouds and rainfall processes
• make frequent rainfall measurements on a global basis.
Continuation of the partnership of Tropical Rainfall Measuring Mission (TRMM).
Partners: NASA, ESA, Japanese Aviation Exploration Agency
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Attenuation
When there is precipitation between the radar and the target, some
microwave power is lost.
This is called attenuation, and it is a problem in C-band and X-band.
Dual polarization has solutions.
On single polarization radars, the attenuation correction is in form of
where C and E are empirical parameters, which depend on drop size
distribution. Research of this could be interesting (in one of the Tekes
projects ?) as in Kumpula we have the independent measure of real
attenuation (from dual pol).
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Attenuation is a problem in C-band; dual polarization shows
maginitude and promises a fix correction scheme
Corrected
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Not corrected
Validation with gauges (1h accumulation)
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Note on dBZ-based dBZ attenuation correction
This is notorious, as any errors cumulate and the correction
can explode with range. However, in single pol radar it is
the best we can get. Sigmet colution against exploding
correction has been set of two thresholds as below.
I do admit dual pol solutions are better. But, we have even
single pol radars in the product family.
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