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First Time At Niche Modeling?
This is a blog on the power of numeracy. My first book — Niche Modeling — is now in print.The first six chapters are tutorial topics in R programming and theoretical topics in niche modeling: functions, data, spatial, topology, environmental data collections, and examples. The last six chapters are about using niche modeling to detect errors: bias, autocorrelation, non-linearity, long term persistence, circularity and fraud - useful information for any biological modeler.
May 26, 2008
Models of Greenhouse Effect
F — Solar flux in
Su — Surface flux up
Eu — Atmospheric flux up
Ed — Atmospheric flux down
They can be represented as equations of linear algebra:
1.1 F = Su - F + Ed - Eu — overall energy balance equation
1.2 0 = F - Eu — energy balance at top of atmosphere
The following are different three constraints:
2.1 0 = Ed - Eu — the steel greenhouse, top of atmosphere constraint.
2.2 0 = Su - Ed — the Kirchhoff’s law, IR radiative equilibrium between surface and atmosphere
2.3 0 = Su - F — the third option, for completeness.
By substituting each of 2.1, 2.2 and 2.3 into 1.1 and 1.2 we get three different solutions for surface temperature with three decreasing levels of greenhouse effects.
3.1 Su=2F
3.2 Su=3F/2
3.3 Su=F
The three models of greenhouse effect are shown in the figure below, ordered by increasing surface temperature. Below the diagrams are representation of the modeled and equilibrium lapse rates, the increase in air temperature with altitude for each of the models.
Here are a few points of interest that argue that the middle semi-transparent model is the correct model:
- In the left-hand model the model lapse rate increases faster than the equilibrium lapse rate — a quasi-stable atmospheric condition called an inversion. In the right-hand model the lapse rate increases more slowly than the equilibrium value — an atmospheric situation where large volumes of air rise through the profile. In each of these situations the equilibrium is eventually reestablished to the middle model, where the lapse rate is ‘just right’.
- Note that the models on the left and right side also have a discontinuity between the surface and the lower atmosphere. The center does not. Only the center model minimizes energy and maximizes entropy. Temperature discontinuities are not consistent with maximizing entropy.
- The three options could also represent zonal difference, from high to tropical latitudes.
Note that this simple model represents only the overall conservation of energy constraints on the system, and a number of other constraint and processes are in play (more discussed in the category Miskolczi above left). However, the central Kirchhoff law model is the only plausible solution with radiative balance throughout the whole atmosphere. However, this model suggests that all of the processes that contribute to the greenhouse effect are already contributing their maximum warming effect, as they cannot increase beyond the limits set by energy conservation. Miskolczi concludes that global warming must therefore be due to other mechanisms and not greenhouse gases.
May 24, 2008
Radiative Equilibrium (Miskolczi Part 4)
I have tried to simplify the equations down to their essentials, to highlight the assumptions behind the different approaches using M’s overall balance balance equation (7). I look at three solutions to finding greenhouse effect on surface temperatures based on radiative equilibrium in the atmosphere: Willis Essenba



