<p>First off, I am rather certain that by <em><a href="https://en.wikipedia.org/wiki/Diatom" rel="nofollow noreferrer">diatom</a> bloom</em> you refer to <a href="https://en.wikipedia.org/wiki/Algal_bloom" rel="nofollow noreferrer">algal bloom</a> which is a seasonal change of sea color, at least here on Earth, the only system we have observed yet. Your question is indeed rather hypothetical, but from a astronomy/ physics points indeed an interesting one.</p>
<p>Next, let me summarize the assumptions I am reading out of your question:</p>
<ol>
<li><p>You assume an exoplanet that is mainly covered by water. Such a <a href="https://en.wikipedia.org/wiki/Waterworld" rel="nofollow noreferrer">waterworld</a> is not only existing in movies, but also a common toy system in climate science (of Earth).</p>
</li>
<li><p>The exoplanet is not only habitable, but also has some kind of algae living in its ocean. A strong assumption indeed, but for our calculation, it gives us numbers for how the color and thus the emissivity of the planet changes.</p>
</li>
<li><p>Indirectly, you also assume our hypothetical waterworld has an atmosphere. Why? An waterworld exoplanet would otherwise have already quickly evaoprated evaporated into space. In terms of greenhouse calculation later on, we will assume that the atmosphere consists only of water vapor. This means that our hypothetical exo-algae on waterworld would not necessary be <a href="https://en.wikipedia.org/wiki/Aerobic_organism" rel="nofollow noreferrer">aerobic</a>. After all, we are after the physics here.</p>
</li>
</ol>
<p><strong>Could algae bloom affect the albedo of an exoplanet?</strong> Definitivley yes, but the question is, how much. And if we could observe that from Earth would be a whole different question.</p>
<h3>What do the assumptions mean in numbers?</h3>
<p>The <a href="https://en.wikipedia.org/wiki/Albedo" rel="nofollow noreferrer">albedo</a> of open ocean water (on Earth) is <span class="math-container">$\alpha_O = 0.06$</span>. Concerning the algal albedo <span class="math-container">$\alpha_A$</span>, I found e.g.</p>
<ul>
<li>a <a href="https://www.researchgate.net/profile/Ian-Jenkinson/publication/333311293_181019-ICHA-Poster/links/5ce668b4a6fdccc9ddc740bd/181019-ICHA-Poster.pdf" rel="nofollow noreferrer">poster &quot;Algal blooms: how are they harming models used for climate management?&quot; by Ian Jenkinson</a></li>
<li>an article <a href="https://www.tandfonline.com/doi/full/10.1080/09670262.2017.1362593" rel="nofollow noreferrer">John Raven: <em>The possible roles of algae in restricting the increase in atmospheric CO2 and global temperature</em></a></li>
<li>another article by <a href="https://pubmed.ncbi.nlm.nih.gov/20168905/" rel="nofollow noreferrer">H Gordon, M Jacobs: <em>Albedo of the ocean-atmosphere system: influence of sea foam</em></a>.</li>
</ul>
<p>In short: Algae do not only change the color of the ocean (which color depends on the involved species), but also may produce foam (with <span class="math-container">$\alpha_A \approx 1$</span>). The latter seems to have the largger effect since <span class="math-container">$\alpha_A \gg \alpha_O$</span>. One of the above mentioned papers suggests a 10% coverage of the ocean with foam, an assumption which sounds appealing to me.</p>
<h3>Some calculations</h3>
<p>For a planet with radius <span class="math-container">$r$</span> in thermal equilibrium, the incident radiation equals the black body radiation:</p>
<p><span class="math-container">$$ \pi r^2 E (1- \alpha) = 4 \pi r^2 \sigma T_{\rm eqi}^4 \Longleftrightarrow 
T_{\rm eqi} =\sqrt[4]{\frac{E (1-\alpha)}{4 \sigma}}$$</span></p>
<p>In this formula, <span class="math-container">$E$</span> is the solar constant (<span class="math-container">$E_{\rm Earth} = 1368 {\rm W}/{\rm m^2}$</span>), <span class="math-container">$\alpha$</span> is the (overall averaged) albedo (<span class="math-container">$\alpha_{\rm Earth} = 0.3$</span>) and <span class="math-container">$\sigma = 5.67 \cdot 10^{-8} {\rm W\cdot m^{-2}K^{-4}}$</span> the Stefan-Boltzmann constant. For Earth this leads to <span class="math-container">$T_{\rm Earth,eqi} = -18^\circ {\rm C}$</span> which shows that we have to include the Greenhouse effect, i.e. that the atmosphere absorbs part of the outgoing radiation. We do that by introducing a  factor <span class="math-container">$\beta$</span>:</p>
<p><span class="math-container">$$T =\sqrt[4]{\frac{E (1-\alpha)}{4 \sigma \beta}}$$</span></p>
<p>On Earth, all Greenhouse gases (<span class="math-container">${\rm H_2O, CO_2, CH_4}$</span>) contribute to an average <span class="math-container">$\beta \approx 0.62$</span> which leads to a more realistic global average temperature of <span class="math-container">$T = 15^\circ {\rm C}$</span> for Earth.</p>
<p>For a water world (without algae) we may use <span class="math-container">$\alpha = 0.1$</span> which leads to <span class="math-container">$T_{\rm WW} = 32^\circ {\rm C}$</span> which compares to a snowball planet with <span class="math-container">$\alpha = 0.8$</span> and <span class="math-container">$T_{\rm SB} = -63^\circ {\rm C}$</span>.</p>

CC BY-SA 4.0
2021-03-24T19:43:15.957Z
Absolutely correct.
sflitman
CC BY-SA 4.0
2021-04-08T19:35:04.833Z
@sflitman I finally managed to do some calculations. If it helps you, I would continue.
B--rian
CC BY-SA 4.0
2021-04-11T03:45:34.147Z
That is fantastic, thanks!   Therefore a bloom could be detected at interstellar distances, if our hypothetical telescope had sufficient optical resolution.
sflitman
CC BY-SA 4.0
2021-04-13T08:17:33.883Z
@sflitman I guess you have to compare the *mean* planetary temperatures for $\alpha_{\rm WW}=0.1$ with those for $\alpha_{\rm bloom} = 0.9\cdot0.1+0.1\cdot 1$, that's much less $\Delta T$ you have to resolve than $(T_{\rm WW}-T_{\rm SB})$ what I calculated. If I have time later, I might add another paragraph to my post.
B--rian
CC BY-SA 4.0
2021-03-23T17:04:49.783Z
2021-04-08T19:33:11.660Z
2021-04-08T19:33:11.660Z
B--rian
<p>And perhaps display a seasonal variation if the exoplanet has an axial tilt, providing proof of an Earth-like world supporting at least oceans with microbial life?</p>

CC BY-SA 3.0
2018-04-12T09:11:42.240Z
Could you elaborate your question a bit more: What are diatom blooms? And be aware that we're barely able to measure albedos for giant planets. We're still far away from albedo variations, especially for small, rocky planets.
AtmosphericPrisonEscape
CC BY-SA 3.0
2018-04-12T17:24:53.343Z
Well, yes, they'll affect the albedo unless the non-diatomic surface has the same reflectivity.  There's the question of how much.
Carl Witthoft
CC BY-SA 3.0
2018-04-12T22:12:34.833Z
Detecting any albedo change would be a challenge-- we just don't have the capability to pick out the reflected light of an earth-sized planet from the light of its star.
antlersoft
<exoplanet><albedo><climate>
Could diatom blooms affect albedo of an exoplanet?
sflitman
# Could diatom blooms affect albedo of an exoplanet?

(Asked by: username_0 on 2018-04-12)

And perhaps display a seasonal variation if the exoplanet has an axial tilt, providing proof of an Earth-like world supporting at least oceans with microbial life?

**Tags:** exoplanet, albedo, climate
> **Comments:**
> **username_1**: Could you elaborate your question a bit more: What are diatom blooms? And be aware that we're barely able to measure albedos for giant planets. We're still far away from albedo variations, especially for small, rocky planets.  
> **username_2**: Well, yes, they'll affect the albedo unless the non-diatomic surface has the same reflectivity.  There's the question of how much.  
> **username_3**: Detecting any albedo change would be a challenge-- we just don't have the capability to pick out the reflected light of an earth-sized planet from the light of its star.  

---

## 1 answers

### Answer by username_4 on 2021-03-23. Score: 3 | Accepted answer

First off, I am rather certain that by *[diatom](https://en.wikipedia.org/wiki/Diatom) bloom* you refer to [algal bloom](https://en.wikipedia.org/wiki/Algal_bloom) which is a seasonal change of sea color, at least here on Earth, the only system we have observed yet. Your question is indeed rather hypothetical, but from a astronomy/ physics points indeed an interesting one.

Next, let me summarize the assumptions I am reading out of your question:

1. You assume an exoplanet that is mainly covered by water. Such a [waterworld](https://en.wikipedia.org/wiki/Waterworld) is not only existing in movies, but also a common toy system in climate science (of Earth).
2. The exoplanet is not only habitable, but also has some kind of algae living in its ocean. A strong assumption indeed, but for our calculation, it gives us numbers for how the color and thus the emissivity of the planet changes.
3. Indirectly, you also assume our hypothetical waterworld has an atmosphere. Why? An waterworld exoplanet would otherwise have already quickly evaoprated evaporated into space. In terms of greenhouse calculation later on, we will assume that the atmosphere consists only of water vapor. This means that our hypothetical exo-algae on waterworld would not necessary be [aerobic](https://en.wikipedia.org/wiki/Aerobic_organism). After all, we are after the physics here.

**Could algae bloom affect the albedo of an exoplanet?** Definitivley yes, but the question is, how much. And if we could observe that from Earth would be a whole different question.

### What do the assumptions mean in numbers?

The [albedo](https://en.wikipedia.org/wiki/Albedo) of open ocean water (on Earth) is $\alpha\_O = 0.06$. Concerning the algal albedo $\alpha\_A$, I found e.g.

* a [poster "Algal blooms: how are they harming models used for climate management?" by Ian Jenkinson](https://www.researchgate.net/profile/Ian-Jenkinson/publication/333311293_181019-ICHA-Poster/links/5ce668b4a6fdccc9ddc740bd/181019-ICHA-Poster.pdf)
* an article [John Raven: *The possible roles of algae in restricting the increase in atmospheric CO2 and global temperature*](https://www.tandfonline.com/doi/full/10.1080/09670262.2017.1362593)
* another article by [H Gordon, M Jacobs: *Albedo of the ocean-atmosphere system: influence of sea foam*](https://pubmed.ncbi.nlm.nih.gov/20168905/).

In short: Algae do not only change the color of the ocean (which color depends on the involved species), but also may produce foam (with $\alpha\_A \approx 1$). The latter seems to have the largger effect since $\alpha\_A \gg \alpha\_O$. One of the above mentioned papers suggests a 10% coverage of the ocean with foam, an assumption which sounds appealing to me.

### Some calculations

For a planet with radius $r$ in thermal equilibrium, the incident radiation equals the black body radiation:

$$ \pi r^2 E (1- \alpha) = 4 \pi r^2 \sigma T\_{\rm eqi}^4 \Longleftrightarrow
T\_{\rm eqi} =\sqrt[4]{\frac{E (1-\alpha)}{4 \sigma}}$$

In this formula, $E$ is the solar constant ($E\_{\rm Earth} = 1368 {\rm W}/{\rm m^2}$), $\alpha$ is the (overall averaged) albedo ($\alpha\_{\rm Earth} = 0.3$) and $\sigma = 5.67 \cdot 10^{-8} {\rm W\cdot m^{-2}K^{-4}}$ the Stefan-Boltzmann constant. For Earth this leads to $T\_{\rm Earth,eqi} = -18^\circ {\rm C}$ which shows that we have to include the Greenhouse effect, i.e. that the atmosphere absorbs part of the outgoing radiation. We do that by introducing a factor $\beta$:

$$T =\sqrt[4]{\frac{E (1-\alpha)}{4 \sigma \beta}}$$

On Earth, all Greenhouse gases (${\rm H\_2O, CO\_2, CH\_4}$) contribute to an average $\beta \approx 0.62$ which leads to a more realistic global average temperature of $T = 15^\circ {\rm C}$ for Earth.

For a water world (without algae) we may use $\alpha = 0.1$ which leads to $T\_{\rm WW} = 32^\circ {\rm C}$ which compares to a snowball planet with $\alpha = 0.8$ and $T\_{\rm SB} = -63^\circ {\rm C}$.

> **Comments:**
> **username_0**: Absolutely correct.  
> **username_4**: @sflitman I finally managed to do some calculations. If it helps you, I would continue.  
> **username_0**: That is fantastic, thanks!   Therefore a bloom could be detected at interstellar distances, if our hypothetical telescope had sufficient optical resolution.  
> **username_4**: @sflitman I guess you have to compare the *mean* planetary temperatures for $\alpha_{\rm WW}=0.1$ with those for $\alpha_{\rm bloom} = 0.9\cdot0.1+0.1\cdot 1$, that's much less $\Delta T$ you have to resolve than $(T_{\rm WW}-T_{\rm SB})$ what I calculated. If I have time later, I might add another paragraph to my post.  

---

