SME
Meteorology · Problem type
Rain rate from radar reflectivity
Use this for “Steady rain falls at 10 mm/h. What reflectivity does the radar see, in dBZ? What rain rate gives 50 dBZ?”
Chart
R(39.01) = 10
This is an example. Type your own values to start a new problem.
Z (mm⁶/m³)
=
200
×
R
1.6
ZdB (dBZ)
=
10
log₁₀(
Z
)
Formulas
Z
=
200
×
R
1.6
7,962.1434
=
200 ×
10
1.6
ZdB
=
10
×
log₁₀(
Z
)
39.0103 = 10 × log₁₀(7,962.1434)
Assumptions
•
Marshall–Palmer, Z = 200R1.6 with R in mm/h and Z in mm⁶/m³, fits steady rain.
•
dBZ = 10 log₁₀ Z squeezes Z’s huge range into numbers from about −10 to 75.
•
Hail and wet snow return far more than their rain, so above about 55 dBZ the rate is too high.
Step-by-step
WE KNOW
R = 10 mm/h
FIND
reflectivity (Z), reflectivity level (ZdB)
Step 1 · Find reflectivity (Z)
Use Z = 200 × R1.6
More rain means more and bigger drops, and each drop returns as its diameter to the sixth power.
Z
=
200 ×
10
1.6
Z
=
200
×
39.81
Z
=
7,962.143
mm⁶/
m
3
Step 2 · Find reflectivity level (ZdB)
Use ZdB = 10 × log₁₀(Z)
Decibels count powers of ten, 10 dBZ for each.
ZdB = 10 × log₁₀(7,962.143)
ZdB = 10 × 3.901
ZdB = 39.0103 dBZ
Check
Put the numbers back in. Both sides should match.
7,962.143
=
200 ×
10
1.6
✓
39.0103 = 10 × log₁₀(7,962.143) ✓
Topic check
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