<p>Yes you appear to understand the situation correctly, assuming I do.</p>
<p>The sixth power is part of the radar:particle interaction, this is a form of <a href="https://en.wikipedia.org/wiki/Rayleigh_scattering" rel="nofollow noreferrer">Rayleigh Scattering</a> which scales with the sixth power of the particle diameter being hit by the rain radar.</p>
<p>Yes on the detection scale of rain radar creatures like birds, butterflies, clouds of fish, etc... are enormous and will show up exceedingly well.</p>

CC BY-SA 4.0
2024-07-25T11:00:39.897Z
2024-07-25T11:00:39.897Z
Ash
<p>I was watching <a href="https://en.wikipedia.org/wiki/Typhoon_Gaemi" rel="nofollow noreferrer">Typhoon Gaemi</a>'s strange path and shape using the Taiwan Central Weather Bureau radar data, and noticed that the intensity scale is in <a href="https://en.wikipedia.org/wiki/DBZ_(meteorology)" rel="nofollow noreferrer">dBZ</a> units. It's a decibel unit so every increase of 10 (say 30 to 40) is a <em>factor of ten</em> increase.</p>
<p>Based on the linked Wikipedia article, I think that a concentration of one 1 mm diameter droplet per cubic meter corresponds to dBZ value of 0.</p>
<p>The signal is expected to be <em>linear</em> with droplet density - if we <em>double the density</em> from one droplet per cubic meter to two, we should expect a factor of 2 increase in the signal, or about 3 dB.</p>
<p><strong>However</strong>, from what I understand so far, if each of those droplets instead <em>doubled in size</em> to 2 mm diameter, the signal would increase by a factor of <span class="math-container">$2^6$</span> or 18 dB.</p>
<p><strong>Question(s):</strong></p>
<ol>
<li>Have I got all of that right? Am I understanding correctly so far?</li>
<li>Where does the exponent of 6 come from?</li>
<li>Is this why groups of migrating birds and even butterflies show up so well in weather radar?</li>
</ol>
<p><a href="https://i.sstatic.net/Jp4PSpd2.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Jp4PSpd2.png" alt="weather radar map of typhoon Gaemi from Taiwan Central Weather Bureau https://www.cwa.gov.tw/V8/E/W/OBS_Radar.html" /></a></p>
<p>Source: <a href="https://www.cwa.gov.tw/V8/E/W/OBS_Radar.html" rel="nofollow noreferrer">https://www.cwa.gov.tw/V8/E/W/OBS_Radar.html</a></p>

CC BY-SA 4.0
2024-07-25T10:51:32.327Z
Quick comment regarding 2.: If I remember correctly for radar observations you assume $\lambda \gg D$, $\lambda$ being wavelength and $D$ being diameter, and hence we are in the Rayleigh limit as far as scattering is concerned. The (Rayleigh) scattering cross section scales with $D^6$. I believe that is why there is a power of 6 in the radar reflectivity.
Joscha Fregin
<data-analysis><radar><weatherdata>
How to understand the dBZ scale for weather radar and the reference (1 mm^6 per m^3)? Where does the 6 come from?
uhoh
# How to understand the dBZ scale for weather radar and the reference (1 mm^6 per m^3)? Where does the 6 come from?

(Asked by: username_0 on 2024-07-25)

I was watching [Typhoon Gaemi](https://en.wikipedia.org/wiki/Typhoon_Gaemi)'s strange path and shape using the Taiwan Central Weather Bureau radar data, and noticed that the intensity scale is in [dBZ](https://en.wikipedia.org/wiki/DBZ_(meteorology)) units. It's a decibel unit so every increase of 10 (say 30 to 40) is a *factor of ten* increase.

Based on the linked Wikipedia article, I think that a concentration of one 1 mm diameter droplet per cubic meter corresponds to dBZ value of 0.

The signal is expected to be *linear* with droplet density - if we *double the density* from one droplet per cubic meter to two, we should expect a factor of 2 increase in the signal, or about 3 dB.

**However**, from what I understand so far, if each of those droplets instead *doubled in size* to 2 mm diameter, the signal would increase by a factor of $2^6$ or 18 dB.

**Question(s):**

1. Have I got all of that right? Am I understanding correctly so far?
2. Where does the exponent of 6 come from?
3. Is this why groups of migrating birds and even butterflies show up so well in weather radar?

[![weather radar map of typhoon Gaemi from Taiwan Central Weather Bureau https://www.cwa.gov.tw/V8/E/W/OBS_Radar.html](https://i.sstatic.net/Jp4PSpd2.png)](https://i.sstatic.net/Jp4PSpd2.png)

Source: <https://www.cwa.gov.tw/V8/E/W/OBS_Radar.html>

**Tags:** data-analysis, radar, weatherdata

> **Comments:**
> **username_1**: Quick comment regarding 2.: If I remember correctly for radar observations you assume $\lambda \gg D$, $\lambda$ being wavelength and $D$ being diameter, and hence we are in the Rayleigh limit as far as scattering is concerned. The (Rayleigh) scattering cross section scales with $D^6$. I believe that is why there is a power of 6 in the radar reflectivity.  

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## 1 answers

### Answer by username_2 on 2024-07-25. Score: 1

Yes you appear to understand the situation correctly, assuming I do.

The sixth power is part of the radar:particle interaction, this is a form of [Rayleigh Scattering](https://en.wikipedia.org/wiki/Rayleigh_scattering) which scales with the sixth power of the particle diameter being hit by the rain radar.

Yes on the detection scale of rain radar creatures like birds, butterflies, clouds of fish, etc... are enormous and will show up exceedingly well.


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