• Weather radar (radio detection and ranging) is another very useful remote sensing tool used in meteorological forecasting.
• Microwave radar was developed in early World
War II to aid in spotting distant ships and airplanes. It was noticed early on that during adverse weather conditions widespread interference often appeared on the radar screen and obscured the military objects of interest.
• A large body of theoretical and experimental work in the 1940s showed that this “weather clutter” arose from the scattering of radar waves by precipitation.

• These early findings have been refined and elaborated to the point that most of the measurable properties of radar signals
- amplitude, phase, polarization, and frequency - can be interpreted in terms of the sizes, shapes, motions or thermodynamic phase of the precipitation particles.
• Because of their ability to observe and measure precipitation quickly, accurately, and from great distances, radars have become essential in weather observation and forecasting.

• Heavier precipitation reflects more microwave energy back to a radar than lighter rain. However, more distant rain also gives a weaker return signal. A rangecorrected and equipment-calibrated measure of reflectivity from rain is given by:
• log( Z ) = log(received power) + 2 log(range)
+ constant
• where Z is the radar reflectivity factor .
Because Z has such a wide range of values, the reflectivity is usually expressed as decibels dB of Z .

• dB Z = 10 log( Z )
• Larger and more numerous drops reflect more radar energy:
• Z = ΣD 6 / V
• where D is drop diameter, V is volume of air holding the drops, and the sum is over all raindrops within that volume.

• But the number and diameter of drops also determines the rainfall rate.
• When the above three equations are combined and empirically tuned to the observations, the result is a formula for converting radar echo intensity in dB Z to rainfall rate R :
• R = c
R
10 0.0625dB
Z
• where c
R
= 0.036 mm h -1 .
[Eqn 1]
• Six discrete levels of radar echo intensity are often used, corresponding to descriptive rainfall categories.

Figure 8-12: Rainfall intensity chart (Stull 2000)

• Owing to their particular shapes, snowflakes produce echoes of different intensity than raindrops of the same size.
• The snowfall rate S is therefore often inferred from the radar reflectivity factor from:
• S = c
S
10 0.05dBZ
• where c
S
= 0.018 cm h -1 .
• This relationship assumes that 1 cm of melted snow equates 1 mm of water, i.e. that the falling snow has a density of 100 kg m -3 .

• Question: What is the rainfall rate R for an echo of 43 dB Z ?
• Answer: Use Eqn 1:
• R = c
R
10 0.0625dB
Z = 0.036 mm/h(10 0.0625*43 )
= 17.5 mm/h

• Question: What is the reflectivity Z for an echo of 43 dB Z ?
• Answer: Use dB Z = 10 log( Z )
• Then log( Z) = dB Z/ 10 = 43/10 = 4.3
• Thus Z = 10 4.3
= 19952.6

• There are several major types of radar displays:
• Plan Position Indicator (PPI): This is a map displaying radar reflectivity or echoes on polar coordinates in plan view.
• With elevation angle fixed, the antenna scans 360 o in azimuth with the beam sweeping across a conical surface in space.
• The data are then used to give the horizontal echo structure.

• Range Height Indicator (RHI): This is similar to a PPI, where the antenna scans in elevation with azimuth fixed, and emphasizes the vertical structure of a precipitating system.

• Constant-Altitude Plan Position Indicator
(CAPPI): It is a composite radar display constructed by assembling radar data from many PPIs at successive elevation angles to obtain the pattern of the data at a specified constant altitude.
• CAPPIs are the common radar images displayed by Environment Canada (at 1.5 km above the surface from the radar site).

• A Doppler radar is a weather radar that detects and interprets the Doppler effect in terms of radial velocity of a target.
• The signal received by a radar from a moving target differs in frequency from the transmitted frequency by an amount that is proportional to the radial component of the velocity relative to the radar.

• A useful introduction to Doppler radar can be found on NOAA's website .
• Canada is in the process of converting all of its weather radars to Doppler radars.
• The full Canadian network of weather radars, including the one at Baldy Hughes,
B.C. (~40 km southwest of Prince George) can be found on Environment Canada's website .

• You are provided with two sequences of Doppler radar imagery covering parts of North America:
• A sequence of Doppler radar images of a severe thunderstorm outbreak that occurred in the midwestern U.S. (near St. Louis, Missouri) in
May of 2003.
• Another sequence of Doppler radar images of the winter storm that affected the Prince George area on 26-27 February 2006.

• 1) Examine carefully the sequence of CAPPI images (base reflectivity) for the midwestern
U.S. assuming ambient air temperatures are well above 0 o C and answer the following questions:
• A) What is the precipitation rate for the maximum echoes observed on these radar images (65 dB Z )?
• B) What type of precipitation does this intensity typically represent?
• C) What is the radar reflectivity factor ( Z ) for this echo?

• D) What is the precipitation rate for an average echo observed on these radar images (30 dB Z )?
• E) Observe the evolution of the severe thunderstorm just to the south of St. Louis.
Track the location of its maximum echoes over time on a map of the area. From this trajectory, linearly extrapolate the direction in which the storm is expected to move if it does not dissipate. Highlight the areas where a severe thunderstorm warning should be issued.

• 2) Now examine the other sequence of CAPPI images based on the Baldy Hughes Doppler weather radar
(centre point on the images) recorded between 1850
UTC and 2220 UTC on 27 February 2006 assuming ambient air temperatures are below freezing and answer the following questions:
• A) Tabulate and plot the approximate precipitation rate for Prince George over time during the storm. When does the snow finally end falling in Prince George?
• B) Integrate in time the snowfall rate over Prince George to obtain the total snow accumulation during this period.
• C) Are the observations from Prince George Airport consistent with the radar observations? Recall that there is an 8-hour difference between Pacific Standard Time
(PST) and Universal Time Coordinates (UTC).

• D) Focus on a persistent and coherent radar echo over several images. Based on the time elapsed between images and the distance between concentric circles on the maps, determine the approximate speed of the system.
Please indicate the approximate area on which your calculations are based.
• E) What do the radar echoes between Burns
Lake and Fort St. James (140 km northwest of
Baldy Hughes) represent? Do you observe similar echoes elsewhere?
• F) What other errors of interpretation may arise from the remote sensing of precipitation by landbased weather radar? You may consult
Environment Canada's website for hints.

• G) What is the horizontal resolution of the
CAPPI images from the Baldy Hughes weather radar?
• H) A typical value of the radar reflectivity factor for this snowstorm is Z = 30 dB Z . Convert this quantity into a snowfall rate and express it in units of mm h -1 snow water equivalent (swe) using the assumption that the snow has a density of 100 kg m -3 .
• I) Compare the precipitation rate for the average echo of Z = 30 dB Z deduced for rain (U.S. midwestern case) and for snow (Prince George case).

• J) Discuss some of the possible reasons that would explain differences in the average precipitation rates observed in the two case studies.
• K) Bonus Question: Imagine a situation in which solid precipitation is falling from clouds situated several kilometres above the surface. The air temperature in the clouds is about -15 o C whereas the near-surface air temperature is 5 o C.
As the snow falls into a layer of above freezing air near the surface, it will melt. What will be the impact of this phase change on the radar reflectivity if it set to detect snowfall only?

• Environment Canada
• United States National Weather Service
• McGill Weather Radar