(As part of Rabett Run's Gerlich and Tscheuschner project, Eli has started drafting parts of a response, which we will gift wrap in Bozo paper and send to some unsuspecting journal, but certainly arXiv. We have spent a lot of time being serious, but for the introduction/conclusion all may enjoy a snark break. The Editorial Board expresses its thanks for your patience =:> . Some of this comes from previous posts, some from Georg Hoffmann on Prima Klima and some from somewhere. Suggestions for changes and additions are welcome.
UPDATE: Some changes to reflect Arthur's comments 3/25 11 PM EDT
Gerlich and Tscheuschner  have published a polemic in the International Journal of Modern Physics B, full of error, irrelevancy, and accusation. Long known from its arXiv versions and well refuted, it is difficult to understand how their work could appear in a respected journal, however, recent history has shown that such papers are occasionally published where editors and referees are not familiar with the underlying science, or themselves are outliers with respect to the field in which the paper lies. This is often the case where expertise in one area is generalized to arrogance about another. A refutation is needed lest anyone be mislead.
This comment will clearly demonstrate major errors in simple physics that Gerlich and Tscheuschner's make, invalidating their entire paper. Supplementary material deals with Gerlich and Tscheuschner's errors in detail. The first twenty or so pages of Ref. 1 are devoted to showing that the greenhouse effect has nothing in common with how a glass greenhouse works, a commonplace taught in and useful for every introductory atmospheric science course. A simple paragraph would have sufficed. Concisely, greenhouses work by restricting the outward flow of thermal energy by convection, the greenhouse effect limits the flow of thermal energy to space by radiation.
A careful, although painful, reading of the rest of the paper shows that there are only two physically based criticisms of the greenhouse effect in Ref. 1, embedded into a mass of opinion and commonplace knowledge badly stated
Gerlich and Tscheuschner assert that Clausius' statement of the second law of thermodynamics forbids transfer of heat from a colder atmosphere to a warmer surface. Their entire 90 page argument rests on this claim. As made clear below, the second law requires consideration of all heat flows in a process, so one must simultaneously include the larger transfer of thermal energy from the surface to the atmosphere. Ref. 1 does not do this and thus errs. When done properly, there is no contradiction
The fundamental equations of radiative transfer have the Second Law of Thermodynamics built into them, via Kirchoff's Law, which can be derived directly from the Second Law. When solved numerically the solutions perforce obey the 2nd law. This applies equally well to simple models, and to the most elaborate line-by-line calculations. All show that the presence of greenhouse gases in the atmosphere results in a warmer surface than in their absence.
Next, following Arthur Smith's criticism  of an earlier version of Ref. 1, we consider a non-uniform distribution of temperature on the surface of a planet. It is shown that when doing this, Gerlich and Tscheuschner obtain an absurd result by using a ridiculous assumption, that each part of the planet's surface immediately cools or heats to reach an equilibrium with the locally impinging solar radiation thereby neglecting the thermal inertia of the oceans, atmosphere and ground. Were this to be the case, all parts of the Earth would cool to well below 200 K (-73 C) at night. It is shown that a uniform surface temperature model provides a lower, but useful, bound on the greenhouse effect, the commonly quoted ~33 K.
These two points alone invalidate Gerlich and Tscheuschner's entire paper, and show that the radiative greenhouse effect does significantly increases the surface temperature of the Earth. Beyond this readers with basic understanding of physics and climate cannot help but be amused by the rich bounty of irrelevancies, silly errors, lack of understanding and significant omissions that Gerlich and Tscheuschner provide. Coupled with the authors' embarrassing false pride, the manuscript would pass from hand to hand labelled as a revenge of social scientists for Alan Sokol's joke, were it not for the demonstrated capacity of this paper to mislead the naive and those hungering to be mislead. It is only this that makes a reply necessary.
Section 2 below disposes of Ref. 1's arguments about the second law of thermodynamics, principally laid out in their Section 3.9. As a part of that, in Section 3, simple models are introduced and then used to demonstrate Gerlich and Tscheuschner's aphysical picture of heat flow on a rotating planet (Section 3.7).
Much of the rest of Ref. 1 is simply argumentative and irrelevant. A humorous example is the denigration of a simple net energy flow schematic for the earth because such diagrams (pp 322)
(1) cannot represent radiation intensities, the most natural interpretation of the arrows depicted in Fig. 23, as already explained in Secs. 2.1.2 and 2.1.5;It is legitimately hard to decide which of these four points is the most ridiculous. (1) and (2) might charitably be called querulous, demanding a full vector representation of all the heat/energy flows of a schematic representation. Gerlich and Tscheuschner might be pleased to know that the angular dependence of the heat flows is captured in radiative transfer and global circulation models (GCMs are commonly known today as global climate models, but originally were called global circulation models, and are built on fluid dynamics). GCMs solve the non-linear Navier-Stokes equation for fluid flow. Fig. 1 is not meant to be a GCM, but an illustration of the vertical thermal energy flow from the sun, the surface and in the atmosphere. Importantly, each of the energy flows has been linked back to experimentally measured global averages.
(2) cannot represent sourceless fluxes, i.e., a divergence free vector fields in three dimensions, since a vanishing three-dimensional divergence still allows that a portion of the field goes sidewards;
(3) do not fit in the framework of Feynman diagrams, which represent mathematical expressions clearly defined in quantum field theory.159
(4) do not fit in the standard language of system theory or system engineering.
(3) and (4) are risible. Why should representations of a total thermal energy flow require a Feynman diagram? Worse, how would such a Feynman diagram be constructed. (4) is the engineering equivalent. Finally the authors might reconsider their standard representations of heat engine (Fig 31 and 32 in  and Fig. 3 below) which uses the same sort of arrows.
Less amusing are Gerlich and Tscheuschner's libelous attacks on others. Perhaps the most notable of these, is upon Stephan Bakan and Ehrhart Raschke for using Fig. 2.
Figure 13 is an obscene picture, since it is physically misleading. The obscenity will not remain in the eye of the beholder, if the latter takes a look at the obscure scaling factors already applied by Bakan and Raschke in an undocumented way in their paper on the so-called natural greenhouse effect.102 This is scientific misconduct as is the missing citation. Bakan and Raschke borrowed this figure from Ref. 103 where the scaling factors, which are of utmost importance for the whole discussion, are left unspecified. This is scientific misconduct as wellAccording to Gerlich and Tscheuschner, Bakan and Raschke's scientific misconduct was to scale the incoming solar and outgoing terrestrial radiation to the same size. Referring to Fig. 1, the outgoing terrestrial radiation at the top of the atmosphere is 239 W/m2 on average which is balanced by the amount of solar energy absorbed in the atmosphere and by the surface. With much hemming and hawing Ref. 1. arrives at about the same numbers. In other words, Bakan and Raschke took note of the observed energy balance to construct their figure. Gerlich and Tscheuschner are not only misleading, they are wrong on this point, and insulting to Bakan and Raschke.
We close the introduction by discussing a simple illustrative example that the two authors, trained physicists, Gerlich and Tscheuschner completely misunderstand. They discuss experiments carried out by a physics obsessed housewife
In Sec. 3.3.5, it was indicated how simple it is to falsify the atmospheric greenhouse hypotheses, namely by observing a water pot on the stove: Without water filled in, the bottom of the pot will soon become glowing red. However, with water filled in, the bottom of the pot will be substantially colder.This, of course, neglects the latent heat carried away from the pot and thus the heating element by evaporation of the water in the pot. Since it is well known that people who are physics obsessed are often forgetful, we postulate that the housewife forgets that she has put the pot on the range, and all the water boils away. At that point, when all the water has evaporated, measurements show that the heating element rises to a higher temperature than it was before the tea pot was placed on it.
In particular, such an experiment can be performed on a glass-ceramic stove. The role of the Sun is played by the electrical heating coils or by infrared halogen lamps that are used as heating elements. Glass-ceramic has a very low heat conduction coefficient, but lets infrared radiation pass very well. The dihydrogen monoxide in the pot, which not only plays the role of the “greenhouse gas” but also realizes a very dense phase of such a magic substance, absorbs the infrared extremely well. Nevertheless, there is no additional “backwarming” effect of the bottom of the pot. In the opposite, the ground becomes colder.