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Radar Rainfall, Beam Heights and Motion Geometry

Inspect entered radar Z–R relationships, effective-Earth beam heights and two-frame constant motion, with measurement and model limits visible.

Use this result well

Inputs that matter
Reflectivity (dBZ), Z–R coefficient a, Z–R exponent b, Sources and assumptions, and 15 more
Output to expect
Rain rate from an entered Z–R relationship, Radar beam centre and edge heights, Two-frame constant-motion projection
  • Check the units and required inputs before comparing results.
  • Keep the assumptions with a copied result so you can reproduce the calculation later.
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Reference & details

How it works

Rain rate from an entered Z–R relationship

Convert dBZ to linear reflectivity and then an estimated liquid-rain rate using your documented coefficients. The illustrative 200/1.6 relationship is one empirical model, not a universal precipitation or hail classifier.

Z = 10^(dBZ/10), in mm⁶/m³; Z = a R^b, R = exp((ln Z − ln a)/b), in mm/h.

Radar beam centre and edge heights

Calculate idealized radar-ray heights above mean sea level from slant range, antenna height, elevation and beam width. Use a specified effective-Earth radius; beam edges are geometric rays, not hard detection boundaries.

h = √(r² + (k Re + h0)² + 2r(k Re + h0) sin θ) − k Re. Evaluate θ and θ ± beam width/2.

Two-frame constant-motion projection

Derive a motion vector from the same tracked feature in two timestamped frames. Project its closest approach and entry into a target circle under unchanged speed and direction. This is a geometric exercise, not a storm warning or a chasing plan.

Velocity = (position2 − position1)/(time2 − time1). Solve |position2 − target + velocity × t| = radius for future t ≥ 0.

Updated: September 2026

Example Scenarios

Inspect the example and its input basis, then substitute your own documented measurements or matched cases.

Reflectivity (dBZ): 40Z–R coefficient a: 200Z–R exponent b: 1.6

→ 11.530715391 mm/h modeled liquid-rain rate

Inspect the example and its input basis, then substitute your own documented measurements or matched cases.

Slant range (km): 100Beam elevation (degrees): 0.5Full beam width (degrees): 1Antenna altitude MSL (m): 100Effective-Earth model: standardCustom k (used only in entered-k mode): 1

→ 1,561.125576 m MSL beam centre

Inspect the example and its input basis, then substitute your own documented measurements or matched cases.

First frame UTC: 2026-09-01T00:00:00ZSecond frame UTC: 2026-09-01T00:10:00ZFirst position east (km): 0First position north (km): 0Second position east (km): 10Second position north (km): 0Target east (km): 30Target north (km): 0Target-circle radius (km): 5

→ 15 min to modeled target-circle entry

Common Mistakes to Avoid

Mixing observation and model inputs

Use the exact units, timestamp, level and measurement or model basis stated by the selected mode. A similar quantity from another instrument or product is not automatically interchangeable.

Treating an illustrative case as a measurement

Replace the example with your own sourced inputs. Retain missing values and method limits, and keep raw source data alongside a saved calculation.

FAQ

Convert dBZ to linear reflectivity and then an estimated liquid-rain rate using your documented coefficients. The illustrative 200/1.6 relationship is one empirical model, not a universal precipitation or hail classifier. Calculate idealized radar-ray heights above mean sea level from slant range, antenna height, elevation and beam width. Use a specified effective-Earth radius; beam edges are geometric rays, not hard detection boundaries. Derive a motion vector from the same tracked feature in two timestamped frames. Project its closest approach and entry into a target circle under unchanged speed and direction. This is a geometric exercise, not a storm warning or a chasing plan.

Retain the station or profile identity, observation or issue/valid time, measurement units, quality flags, source and stated method. Missing values, trace precipitation and known zeros have different meanings.

Save weather case keeps an explicit local record. Copy MD includes current inputs and notes; Download CSV includes the current result breakdown. Keep portable copies separately and retain raw source data.

About Radar Rainfall, Beam Heights and Motion Geometry

Convert dBZ to linear reflectivity and then an estimated liquid-rain rate using your documented coefficients. The illustrative 200/1.6 relationship is one empirical model, not a universal precipitation or hail classifier. Calculate idealized radar-ray heights above mean sea level from slant range, antenna height, elevation and beam width. Use a specified effective-Earth radius; beam edges are geometric rays, not hard detection boundaries. Derive a motion vector from the same tracked feature in two timestamped frames. Project its closest approach and entry into a target circle under unchanged speed and direction. This is a geometric exercise, not a storm warning or a chasing plan.