<p>Yes, there are horizontal radiation fluxes. <a href="https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JD094iD13p16277" rel="nofollow noreferrer">These can change the heating rate by 10-40 K hr<span class="math-container">$^{-1}$</span>.</a> <a href="https://journals.ametsoc.org/jas/article/62/8/2939/26087/The-Impact-of-Model-Resolution-on-Differences" rel="nofollow noreferrer">They also change depending on the extent of the atmosphere you may be considering</a>. One can also imagine that they are a bit stronger during the sunrise and sunset, when the sun is not directly overhead and the beam has a larger horizontal path length.</p>
<p>There is work, such as the <a href="https://www.sciencedirect.com/science/article/abs/pii/S0022407315002964" rel="nofollow noreferrer">Neighboring Column Approximation</a> which tries to get around that. There's another paper, but I can't find it right now that also tries to resolve this issue.</p>

CC BY-SA 4.0
2020-07-14T15:05:41.073Z
2020-07-14T15:05:41.073Z
BarocliniCplusplus
<p>I've noticed that in many <a href="https://doi.org/10.1029/2018JD030092" rel="nofollow noreferrer">papers</a> it's common to assume the (daily or longer averaged)  vertically integrated radiative heating can be expressed <span class="math-container">$F_z(\text{TOA})-F_z(\text{SURF})$</span>, where <span class="math-container">$F_z$</span> is the vertical component of radiative flux, and <span class="math-container">$\text{TOA}$</span> and <span class="math-container">$\text{SURF}$</span> denote the top of atmosphere and surface respectively, with &quot;top of atmosphere&quot; usually either taken as <span class="math-container">$z\to \infty$</span>, or as the tropopause height, depending on the context.</p>
<p>I assume this basically reflects the fact that if we express radiative heating <span class="math-container">$Q$</span> as a flux divergence <span class="math-container">$Q=\nabla \cdot (F_x,F_y,F_z)$</span>, vertical integration gives
<span class="math-container">\begin{align}
\int_\text{SURF}^\text{TOA} Q \,dz &amp;= \int_\text{SURF}^\text{TOA} \nabla_H \cdot (F_x, F_y) \,dz + \int_\text{SURF}^\text{TOA} \frac{\partial F_z}{\partial z} \,dz \\ 
&amp;= \int_\text{SURF}^\text{TOA} \nabla_H \cdot (F_x, F_y) \,dz + F_z(\text{TOA})-F_z(\text{SURF}).
\end{align}</span></p>
<p>It seems natural to assume the <span class="math-container">$\int_\text{SURF}^\text{TOA} \nabla_H \cdot (F_x, F_y) \,dz$</span> term, which is the net horizontal flux divergence out of the column, will be small compared to the <span class="math-container">$F_z(\text{TOA})-F_z(\text{SURF})$</span> term, but does anyone know <em>just how much smaller</em>? What are some reasonable scale estimates for these terms? Are there situations in atmospheric science where net horizontal radiative flux divergence can't be neglected?</p>
<p>For example, I'm imagining a column with a single spherical cloud in it, and the sun directly overhead, but no clouds in any other nearby columns. In such a situation, wouldn't there be a horizontal radiative flux divergence, i.e. a net horizontal radiative flux out of the column? Would this effect still have a negligible impact on net column heating, or does nothing like this occur in real atmospheres?</p>

<atmospheric-radiation><energy-balance><radiation-balance>
Can Horizontal Radiation Fluxes Contribute to Net Column Heating?
Ewan
# Can Horizontal Radiation Fluxes Contribute to Net Column Heating?

(Asked by: username_0 on 2020-07-14)

I've noticed that in many [papers](https://doi.org/10.1029/2018JD030092) it's common to assume the (daily or longer averaged) vertically integrated radiative heating can be expressed $F\_z(\text{TOA})-F\_z(\text{SURF})$, where $F\_z$ is the vertical component of radiative flux, and $\text{TOA}$ and $\text{SURF}$ denote the top of atmosphere and surface respectively, with "top of atmosphere" usually either taken as $z\to \infty$, or as the tropopause height, depending on the context.

I assume this basically reflects the fact that if we express radiative heating $Q$ as a flux divergence $Q=\nabla \cdot (F\_x,F\_y,F\_z)$, vertical integration gives
\begin{align}
\int\_\text{SURF}^\text{TOA} Q \,dz &= \int\_\text{SURF}^\text{TOA} \nabla\_H \cdot (F\_x, F\_y) \,dz + \int\_\text{SURF}^\text{TOA} \frac{\partial F\_z}{\partial z} \,dz \\
&= \int\_\text{SURF}^\text{TOA} \nabla\_H \cdot (F\_x, F\_y) \,dz + F\_z(\text{TOA})-F\_z(\text{SURF}).
\end{align}

It seems natural to assume the $\int\_\text{SURF}^\text{TOA} \nabla\_H \cdot (F\_x, F\_y) \,dz$ term, which is the net horizontal flux divergence out of the column, will be small compared to the $F\_z(\text{TOA})-F\_z(\text{SURF})$ term, but does anyone know *just how much smaller*? What are some reasonable scale estimates for these terms? Are there situations in atmospheric science where net horizontal radiative flux divergence can't be neglected?

For example, I'm imagining a column with a single spherical cloud in it, and the sun directly overhead, but no clouds in any other nearby columns. In such a situation, wouldn't there be a horizontal radiative flux divergence, i.e. a net horizontal radiative flux out of the column? Would this effect still have a negligible impact on net column heating, or does nothing like this occur in real atmospheres?

**Tags:** atmospheric-radiation, energy-balance, radiation-balance


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## 1 answers

### Answer by username_1 on 2020-07-14. Score: 1 | Accepted answer

Yes, there are horizontal radiation fluxes. [These can change the heating rate by 10-40 K hr$^{-1}$.](https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/JD094iD13p16277) [They also change depending on the extent of the atmosphere you may be considering](https://journals.ametsoc.org/jas/article/62/8/2939/26087/The-Impact-of-Model-Resolution-on-Differences). One can also imagine that they are a bit stronger during the sunrise and sunset, when the sun is not directly overhead and the beam has a larger horizontal path length.

There is work, such as the [Neighboring Column Approximation](https://www.sciencedirect.com/science/article/abs/pii/S0022407315002964) which tries to get around that. There's another paper, but I can't find it right now that also tries to resolve this issue.


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