1. 7. Radar Meteorology References Battan (1973) Atlas (1989)
Radar theory
Atlas (1989)
Early history of radar in meteorology.
Doviak and Zrnic (1984)
Recent developments and doppler techniques.

2. 7.1 Introduction
* Clouds appear mainly on the convective and mesoscale,
most difficult to obtain atmospheric data
* Clouds and mesoscale phenomena are too small to be
resolved by conventional surface and upper-air networks,
and too large to be observed locally
* Radar is most effective instrument for obtaining
observations in cloud systems.
* Radar can observe the precipitation with mesoscale
coverage (~200km) and convective-scale resolution (~1km)
* Radar can also receive signals from cloud particles
* Has been installed on land, ships, aircraft and spacecraft

3. Three main components 7.2 General principles of radar Transmitter
Generates a short pulse of electromagnetic energy.
Antenna
Focuses energy into a narrow beam
Generally 1 degree beamwidth.
Receiver
Detect the back-scattered signal from target if large enough.

6. Primary Function
Detect the range and direction of back-scattered signal.
Range: timing circuit
PRF - Pulse repetition frequency.
Velocity of propagation: c = speed of light.
Depends on density and water content of air.
Always within 0.03% of c.
Direction: Antenna azimuth and elevation at the instant the signal is received.

7. Typical Parameters Peak Power, Pt: Radio frequency, : Wavelength, :
10 to 1000 kW.
Radio frequency, :
3 to 30 GHz.
Wavelength, :
1 to 10 cm.
PRF, fr :
200 to 2000 Hz
Pulse duration, :
0.1 to 5 s.
Antenna area,
Antenna gain,
Beamwidth,

8. 7.3 Radar equation 1. General Radar 2. Weather Radar
Distributed Targets
Many scattering elements simultaneously illuminated by a transmitted pulse.
Raindrops, snowflakes, and cloud droplets.
Resolution volume: Volume containing those particles that are simultaneously illuminated.
Function of beamwidth and pulse length.
Targets move relative to each other.
Power returned fluctuates in time.
The instantaneous power depends on the arrangement of scatters and their motion.
Not simply related to the backscatter cross-section.

9. Rayleigh Scattering Law
Applies to particles that are small compared to the wavelength () of the radar.
Raindrops and snowflakes are good Rayleigh scatters to good approximation at ’s of cm.
Common ’s for weather radars.
K is a function of temperature (T), wavelength (), and sphere composition
|K|2  0.93 for water.
|K|2  0.21 for ice.
Ice sphere has a radar cross section about 2/9 or 6.5 dB less than a water sphere.

10. Reflectivity
The main power received is determined by radar parameters, range, and two factors that depend upon the scatterers.
|K|2 and  D6.
Reflectivity
Number of drops
Size (diameter) of drops.
This is really what we are interested in from the radar equation.
For raindrops: N(D) is the drop-size distribution.
For snowflakes: N(D) is the distribution of melted diameters.
If this convention is not included, a density adjustment would need to appear in |K|2.

11. Average gain < axial gain.
Gain adjustment
Beamwidth: angular separation between points where the transmitted intensity has fallen off to half its maximum value, or 3 dB below the maximum.
Typically 1 degree.
Assume a Gaussian beam pattern.
Assumption: the antenna gain is uniform within its 3 dB limits.
Average gain < axial gain.

12. 7.4 Z-R relations for rain and snow
Relating reflectivity to precipitation: to estimate
the precipitation rate;
the precipitation content of the air; and
the fall speed of the precipitation at the surface.

13. Bright band Snow and frozen precipitation will usually have a smaller
value of reflectivity (dBZ) because it is made of ice.
When frozen precipitation falls to a level where the
temperature is above freezing it begins to melt.
The water surface on the outside will cause an increase in
dBZ, which produces a bright band on the radar image at
the height near the freezing level.
The bright band does not extend to the surface because
once the snowflake completely melts it falls faster. The drop
concentration decreases as altitude decreases, resulting in
less dBZ.

14. Radar Display Systems:
Plan Position Indicator (PPI): maps the received signals
on polar coordinates in plan view.
Range Height Indicator (RHI): shows the vertical structure
of echoes which is generated when the antenna scans in
elevation with azimuth fixed.
Microprocessors are used to convert the signals to
reflectivity Z or rainfall rate.

15. 7.5 Doppler Velocity Measurements
Klystron transmitters: pulse-modulating a
free-running stable oscillator, the frequency
of the transmitted signal is constant,
each pulse bears the same phase relation.
Because the target is moving, the frequency
(amplitude and phase) of reflected waves
will change with time.
Two successive pulses will result in a
frequency difference.

16. The radial velocity is related to this frequency shift:
The backscattered radiation comes from the
population of precipitation particles in the radar
resolution volume
The scatters are all moving at somewhat
different velocities

17. Homework (6-7) 1. The precipitation water content (L) is given as
Meteorology 342
Homework (6-7)
1. The precipitation water content (L) is given as
For the Marshall-Palmer distribution (10.1), show that
2. If a droplet population consists of droplets of a single size and fall speed (D=2 mm, u=5m/s),
and the droplet density is 25 drops per cubic meter. Calculate the rainfall rate in mm/hr.
3. Use the Marshall-Palmer distribution (10.1), show that
u (=5m/s) is the mean fall velocity of raindrops. Use this formula to find Z (in ) and dBZ for
a rainfall rate of 1 inch per hour.
4. Problem 11.1
5. Problem 11.2