At the $CO_2$ 15um wavelength, there is almost no outgoing radiation. OK, it sounds logical, because $CO_2$ absorbs that range of radiation.

But since $CO_2$ is a good absorber, according to Kirchhoff's law it should be a good emitter at the same wavelengths.

The radiation equation in its simplest form says:

$$I_\nu = I_\nu(0) e^{-\tau\nu} + I_\nu^B [1-e^{-\tau_\nu}]$$

I understand that when the optical thickness is large, the outgoing radiation is dominated by the $I_\nu^B$, the Boltzmann value for black-body radiation.

When the atmosphere is optically thick, we would have this situation and, therefore, according to that picture, there should be outgoing radiation also at those wavelengths. Even taking into account the lower temperature of the atmosphere can, in my opinion, not explain, why outgoing radiation is almost zero.

But why is this the case?

However, in the same lecture we learned that clouds do have a positive feedback, which means (in my opinion), that by increasing temperature we have an increased amount of net radiation to earth. How is this to be understood? Does it mean that higher temperature gives rise to less clouds and therefore more net radiation?

Somehow, this appears not very intuitive, because on the one hand clouds are "good for cooling", on the other hand they have positive feedback, which is "worse for cooling". Is there a way to understand this "tradeoff" on a pure qualitative level?

I know, that clouds are quite complex and not well understood, but maybe there is a convincing explanation for that "discrepancy".

[1] https://journals.ametsoc.org/view/journals/clim/31/2/jcli-d-17-0208.1.xml

Based on the image below temperatures $T_s$ and $T_a$ are derived by a fairly simple calculation:

$$T_s = T_e \left(\frac{2}{2-\epsilon}\right)^{1/4} \tag{1}$$

$$T_a = T_e \left(\frac{1}{2}\right)^{1/4} \tag{2}$$

where $T_s$ denotes the ideal earth temperature without atmosphere.

Although quite logical I feel a slight kind of inconsistency in it: We calculate the temperature of the atmosphere to be lower than that from earth by a fixed factor 0,84. But nothing is said about the height of this atmospheric layer. How can this be, because the temperature in an atmosphere's layer is (at least to some degree) given by an adiabatic temperature gradient and, therefore, there is no additional freedom in temperature in a given height when temperature on ground is given.

My conclusion would be, that under equilibrium conditions the part of the atmosphere which contributes most to outgoing radiation ("the single layer") corresponds to a height, where temperature matches equation (2). OK. But on the other hand, the portion of atmosphere, which radiates directly into open space must be within a layer of optical thickness of about $\tau \approx 1$ measured from TOA down, because layers below should be opaque from the outside view. So there is also no freedom in the height of the emitting layer, because it is solely given by optical thickness and the more greenhouse gases there are, the higher this "last emitting" layer must be.

Additionally, to make my confusion complete, when viewed from earth's surface, radiation received by surface must be from a layer within about optical thickness $\tau \approx 1$ measured from surface level up. But this height must be significantly lower as compared to the height of the layer which radiates into space - otherwise atmosphere would be transparent for IR. So how can we speak of a "single layer" and why does it give correct numbers?

So I don't get along with this description at all, although I would like it for its simplicity, not least because it gives a result consistent with data. Where is my misconception? I've been pondering this for a good month now and nobody can tell me what I'm doing wrong. Up to now, the field of meteorology appears a bit alchemistic for me.

我正试图估计云层向下的长波强迫。我有入射短波辐射的直接和扩散成分的原位测量，我也有大气顶部入射短波通量(来自重新分析)。在我的场景中，云层覆盖率为100%，但其厚度未知，尽管我有温度/压力/湿度的无线电探空仪剖面。我的理论是，漫射:直接辐射的比率越高，云层就越厚。此外，与入射辐射相比，全局(直接+扩散)短波辐射越少，它就越厚。如果我知道入射的短波通量，以及流出的短波通量，我就可以把剩余的能量分成吸收的和反射的——我能在一些假设下估计出有多少能量变成了长波并发射下来吗?我特别想的是我可以用温度曲线吗?< / p >

Clearly this assumption would neglect the upward longwave power from the ground that is re-emmitted downwards from the cloud deck.

我在想(在最简单的模型中)，地球每单位时间发射$N$光子，一些比例$p$击中温室气体粒子，并将以$0.5$的概率重新发射回地球。因此，温室气体粒子越多，$p$就越大，地球的温度也就越高。< / p >

For an improved model, I'm thinking the atmosphere acts more like a continuous media with the photons bouncing around between particles and heating them. In this case, is there a simple analogy or maybe a 1 dimensional differential equation model (like heat flow through a medium)? Does heat diffusing through a material behave in a similar way as radiation propagating through the atmosphere?

I am interested in simple and easy to understand and roughly accurate models for understanding greenhouse gases.

Such "run-away" heating scenarios do seem to violate the Stephan-Boltzman Law, and the general laws of thermodynamics, even after allowing for the "back-radiation", that effectively provides the "insulation" that slows the escape of the long-wave (i.e., infrared) radiation. While "greenhouse" gas insulation is the colder body (in daytime), it cannot do a net transfer heat to the plant's surface, which is the hotter body. At night time, however, the greenhouse gas may be the hotter body -- for a while -- and thus transfer some heat back to surface, before morning sun rise. This is how I see it. Is that wrong?

可能我没有抓住这些研究的重点。它的想法可能更多的是令人惊讶聚集发生尽管 RCE，因为RCE应该代表一个平衡的平衡状态。这是否意味着聚合会破坏RCE，而RCE实际上是“不稳定的”?平衡?< / p >

我注意到在许多论文通常假设(每日或更长的平均)垂直集成辐射加热可以表示$F_z(\text{TOA})-F_z(\text{SURF})$，其中$F_z$是辐射通量的垂直分量，和$\text{TOA}$和$\text{SURF}$分别表示大气顶部和表面，其中"top of atmosphere"通常作为$z\to \infty$，或者作为对流层顶高度，这取决于上下文。< / p >

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?

$$Rad\_len[mmday^{-1}] = \frac{SolRad[MJm^{-2}day{-1}]}{2.45}$$

即使在将$langleysday^{-1}$转换为$MJm^{-2}day{-1}$(可以使用因子0.041868)之后，我也看不到这两个方程之间的任何相似之处。第一个方程应用于Jensen和Haise, 1963(2)给出的辐射蒸散发估算方法。

(1) Allen, R. G.， Pereira, L. S.， Raes, D.， &史密斯(1998)。作物蒸散量-作物需水量计算指南-粮农组织灌溉和排水文件56。粮农，罗马，300(9)，D05109。< / p >

(2) Jensen, M. E., & Haise, H. R. (1963). Estimating evapotranspiration from solar radiation. Proceedings of the American Society of Civil Engineers, Journal of the Irrigation and Drainage Division, 89, 15-41

I have included a photo showing how the electromagnetic wave types are partitioned in the radiation balance. It is from NASA's CERES page. As you can see, more infrared is leaving Earth than enters as solar radiation and yet this is still a picture of equilibrium where the net radiation is zero.

假设我们将在未来50年排放一定量的温室气体(例如，总共1000亿吨二氧化碳当量)。如果我在早期(例如0-10年)实施一定的温室气体减排努力，减少相同数量的温室气体(例如封存200亿吨二氧化碳当量)，而在后期(40-50年)会发生什么?我想早点减排会更好，因为全球变暖是一连串的正反馈?还有其他一些类似的问题，比如在前10年削减相同数量的温室气体(但此后不再削减)，还是将削减的目标分散到整个50年。有哪些主要的考虑?通常来说，尽早削减温室气体排放更好吗?< / p >

(问题从物理学转移到地球科学)

地球大江南体育网页版气是否达到了一个平衡，在这个平衡中输入的辐射能量大致等于输出的辐射能量，还是输出的辐射能量显著低于输入的辐射能量，因为能量被用来加热物质?换句话说，如果大气的成分与现在完全相同，那么大气是会继续变暖，还是会保持现在的温度?如果查克·诺里斯瞬间从大气中去除所有人为和奶牛制造的温室气体，大气温度会在几年后恢复“正常”吗?还是会因为大气、海洋和陆地的高热容量而出现明显的滞后?

解释为什么太阳辐射在大气“长波”计算中被忽略，而地球辐射在大气“短波”计算中被忽略。

我意识到被认为是短波辐射的波长是那些小于或等于4$\mu m$的波长。我知道我们说随着波长的增加，来自地球的辐射会增加，而太阳辐射也会增加。< / p >

As a result of this, Why are the sun's long-wave radiation and the Earth's short-wave radiation neglected?

Any explanation would be much appreciated!