Tangled in Words. Atmospheric Dynamics, Stefan Boltzmann Calculations and Energy Balance (by Diego Fdez-Sevilla, PhD.)


Tangled in Words. Atmospheric Dynamics, Stefan Boltzmann Calculations and Energy Balance (by Diego Fdez-Sevilla, PhD.)

(Updates on the 11th and 13 March 2016. Updated with video talk 17 March2016)

Researchgate DOI: 10.13140/RG.2.2.28443.57120

Recently I have been aware of the existence of a discussion about the validity of “applying Stefan Boltzmann calculations to explain that the whole radiative forcing greenhouse conjecture fails to explain reality”.

In a system at equilibrium the radiation is in equilibrium with the molecules, at the same temperature. Conversely, Temperature is a characteristic of an equilibrium system. Therefore, in a system at equilibrium the populations of energy levels are described by the black-body radiation law and Boltzmann statistics. Accordingly, a system at equilibrium may be described by a temperature. HOWEVER, without equilibrium, there is no defined temperature.

So I want to share what I said in a discussion about it and incorporate my thoughts into my research so any follower can have access to it.

The following is the literal transcription from a LinkedIn discussion.

Transcription

Basically I see a basic principle being applied which under my point of view crumbles any following dissertation. “Thermal energy is being transferred by diffusion”. Heat is thermal energy. It can be transferred from one place to another by conduction, convection and radiation. Conduction and convection involve particles, radiation involves electromagnetic waves. Heat can only be transferred between “existent” molecules. Without them, like in out-space, there is not temperature or heat transference. Our atmosphere contains heat because it contains molecular compounds absorbing and transferring heat. The case of GHGs is that they are among the most thermal conductive molecular compounds found in the atmosphere. It is like cooking dry food. You need a substance to transfer the heat to cook aliments. Oil is good but water gets the heat inside the food cause its heat properties. There is no diffusion of heat in a vacuum of thermal flask. Thus it is important to identify the type and concentration of atmospheric gases.

When it is applied on this matter the idea of that “The surface is cooled by GHG’s in the atmosphere. It is the atmosphere itself that is warmed as infrared light, reflected from earths surface, travels back toward space. This reflected light is absorbed by GHG’s and the air is warmed. This is the heat trapping property of GHG’s”

I would say that such point is similar to what happens by the role played by sweat in cooling the body by allowing water to evaporate off the skin. The problem from GHGs is that their presence above the earth’s surface reduce the difference in temperature between them and the surface. In that way the reduction in the difference reduces the capacity of the atmosphere to diffuse the heat received at the surface. That creates positive feedback loop which moves towards increasing the amount of heat being contained in both parts of the column.

“You cannot add back radiation to solar radiation and use the total in Stefan Boltzmann calculations to explain the mean surface temperature. The 324W/m^2 of back radiation is overstated because the wrong emissivity value of the atmosphere has been used in calculating that back radiation from measurements. On Venus, using emissivity of 0.19 for carbon dioxide, the atmosphere would have to be over 350 degrees hotter than the surface for its radiation to support the surface temperature. Even if you use the 324 figure (as is implied in the energy diagrams which show 168+324-102 = 390W/m^2 into the surface) that 390 figure (being a mean of variable flux) gives you a mean temperature close to zero C, not 15C.” So it’s all totally wrong and the whole radiative forcing greenhouse conjecture fails to explain reality.

I have to say the following:

“May be” the Stefan Boltzmann calculations can not be applied to explain the mean surface temperature of a body which is not homogeneous in composition in any of its parts, solid-liquid and gaseous, none-uniform on its surface albedo, thermodynamically active on its core and atmosphere, irregularly shaped, not flat neither a perfect sphere, in constant motion and with 50% of its surface solar radiated meanwhile the other 50% is not. All those contrasts in the horizontal and the vertical assessments are relevant. Maybe the stratification of heat could be explain by S-B for a uniform body like the Sun, and yet At 20,000-25,000 km away from the solar surface the corona has an average temperature of 1,000,000 to 2,000,000 million degrees Celsius. But the density is very low, about 1 billion times less dense than water.

“Nothing gets hotter than a blackbody for a certain amount of radiation. Back radiation does not even penetrate warmer ocean surfaces – see my 2012 paper on radiation. In any event, the variable radiation that the Earth’s surface receives will not raise its temperature within even 8 degrees of the temperature that uniform flux with the same mean would attain for a flat Earth without day or night. So the IPCC’s 390W/m^2 (incorrectly including back radiation) would not achieve above 7°C as a mean surface temperature anyway.”

I guess we all have a theory. You share yours and I share mine in my blog.

My only point may be too easy to be consider relevant but, temperature is not only a measure of Energy, it is a measurement of the state for the density of a particular type of matter. Without matter there is no temperature. So, wherever yo measure temperature there is matter. Which type of matter exists at each point where we measure temperature is the main relevant point in environmental assessments. And then, which conditions allow for such matter to be there, in such concentration and physical state, latitude and altitude. If temperature at Earth’s surface is increasingly spread over higher latitudes and altitudes, as they are, it is because there is molecular matter holding it. If water vapour carries heat at the surface might be because at higher levels GHG,s are doing their job retaining heat radiated from above and bellow from escaping to out space. That creates a positive feedback through the whole atmospheric column and in latitude.

If only variations in external radiation under a low Solar activity period does not explain the current raise in temperatures we have to look at which type of matter is holding and transferring heat radiated from within the Earth’s system. That means atmospheric composition and thermal conductivity, therefore, molecular compounds and GHG’s. The Earth is not an homogeneous inert blackbody under still conditions and the constant transformations between forms of Energy are not contemplated in S-B in an open system. How much energy radiated over the Earth is getting transformed in biochemical, latent, kinetic, …? And how much that relation has changed over time due to anthropogenic influence?

“Temperature is not related to density of molecules, only to mean molecular kinetic energy. You use the word “heat” incorrectly, but if you mean thermal (kinetic) energy then nitrogen and oxygen molecules hold about 98% of the thermal (kinetic) energy in the atmosphere and IR-active (so-called “greenhouse”) molecules act like holes in a blanket as they radiate energy out of the atmosphere. My study showed that more moist regions have lower daily maximum an minimum temperatures than drier regions at similar latitude and altitude. My hypothesis explains why and I’m afraid I only have time to respond to genuine questions about the entropy and thermodynamic issues therein.”

“I only have time to respond to genuine questions”.

Point taken. We both will be benefited from, either us or somebody else finding the right approach to foresee relevant issues to come and unify efforts to cope with them. My profile might not be genuine enough for some to take my research seriously and it is not my job, neither my intention to convince anybody about anything. Only sharing understanding will make sense to me. That is why I publicly offer my research for public and multidisciplinary review through my blog. Good luck with your research, we all need to find some sense in this matter. Though I don´t see it in your theory doesn’t mean anything, and it might be due to my limitations, or the other way around. So far I find lots of sense in what I see and how I see it. If “T is not related to density of molecules” So you don´t consider variations in volume affecting your calculations? The behaviour of the Polar Jet Stream says otherwise, that is my theory.

End of transcription. ——————–

Now, is my interpretation a good answer?

Well, here is where we can get tangled in words.

Under my point of view it is good, and functional, because it explains the connections describing coexisting dynamics for our entire ecosystem, solid, liquid and gaseous. At tropospheric and stratospheric level, in the non-Biotic and the Biotic systems. I consciously make an effort to make comprehensible my interpretations in order to engage with a multidisciplinary and multilevel audience. Such approach could interfere with the judgement applied over the value of the information shared. And yet, I believe that those with a clear understanding on the topics discussed would be able to see through as well as new incomers could find easier connections between fields.

Is it representative of the current state of knowledge?

My approach follows the implementation of physical laws into the environment at micro and macro scales which anybody can find through different resources and references.

Should anybody believe on it just because I say so? Definitely NO.

You should look for your own understanding over it and contrast and even add new light into any incoherence you might find.

Offering my own references could be seen as introducing bias to defend my arguments. Furthermore, it could deviate the focus of attention away from the conceptual framework under discussion. So you should look for the information available and create your own criteria if you don´t have one yet.

However, I can point to some references which I believe can serve to help you decide if my understanding in the subject is biased under your own assessment:

Academic, general principles. Space Research Institute of the Russian Academy of Sciences (link)

  • Black-body radiation. (Link)
  • Foundations of radiative transfer theory (Link)

Scientific Media. The Earth Observatory. NASA.

  • Climate and Earth’s Energy Budget (Link)

HyperPhysics.edu. Web dedicated to explain physics (main menu link). Feel free to explore all the links they offer.

You can also start with:

  • Heat and Thermodynamics (Link)
  • What is Temperature? (Link)

University of Washington. Notes for lectures.

  • How do we calculate the Earth’s effective temperature? Limitations of Applying the Stefan-Boltzmann calculation. Link

Roe, Gerard (2009). Feedbacks, Timescales, and Seeing Red. Annu. Rev. Earth Planet. Sci.  37:93–115 (Link)

More discussion on this topic can be found in other blogs such as:

(updated 17March2016) Ultimately, I would encourage anybody interested in this subject to see the full talk by Michael Mishchenko covering the disciplines of electromagnetic scattering, radiative transfer, and remote sensing entitled “How much first-principle physics do we need in remote-sensing and atmospheric-radiation research”. Here you can have a broad discussion on the subject and you can move into the min 29 where he addresses directly the applicability of equations defining the effect of radiative transfer into the Earth system.

Why is this issue relevant to understand?

Since the original publication of my theory on energetic interactions and dynamics in the atmosphere back in 2014, I have discussed the relevance of understanding the synergistic interaction between contrasts existent in our environment. Those contrasts are driving the dynamics of change in our weather patterns, atmospheric dynamics and climatic regimens. Our environment is characterised by being non-uniform in composition, state, physical and energetic properties and distribution of matter. But also, by the differences in the type and strength of forces and interactions present. Our environment is a complex mixture of different “systems”, each one with singular states of internal dynamics moving towards finding equilibrium within and with their surroundings.

Through my career as Environmental Biologist and Aerobiologist I have studied the impact that asymmetries existent through space and time for atmospheric variables exert over the composition and behaviour of the atmospheric medium influencing life cycles. Scenarios such as the Urban Heat Island Effect or the coastline/inland contrasts only highlight the strong connection existent between biotic and non-biotic components.

I have also looked into the aerodynamic behaviour resultant from combining air masses with different properties (T, Humidity, velocity) and airborne particles with different aerodynamics properties (settling speeds). The broad sets of masses of air being formed in the atmosphere as a result of multiple sources and forces interacting (micro and macro, physical and physico-chemical) induce the development of boundary layers. Through observing streamlines and particle positioning over trapping surfaces I studied the behaviour resultant from the existence of boundary layers at micro and macro scales, identifying a strong influence between the aerodynamic behaviour of each component interacting in the atmosphere.

Those studies and the posterior research included in this blog only confirms the relevant role that boundaries play in understanding the dynamics of our atmosphere and the entire environment.

By applying my experience in observing the stream lines defined by water vapour through our atmosphere I have been studying the boundaries defining margins for systems with their own entropy state in the micro and macro world. The interactions between systems with different states of entropy generate an instability which creates a dynamic flow of energy inside different eco-“systems”, but also it serves to fuel the continuum momentum of the global atmospheric dynamics protecting natural cycles from stalling. Therefore, the Stefan Boltzmann calculations applied to describe feedbacks in an idealised system in thermodynamic equilibrium can not be applied to define the state of a global system for which its primary driving force is the mere existence of instability.

One of those relevant boundary layers found in our macro atmosphere is the Polar Jet Stream. A current of air moving West to East created by the thermal contrast generated between Arctic Polar Cold and dry air masses and Mid Latitude warm and wet air masses. The difference in the characteristics for the composition and thermodynamic behaviour of each mass of air had the tendency of generating such strong barrier that the mixture between both was a slow process due to the rigid configuration of the Polar Jet Stream blocking masses of air from crossing over. Such configuration kept atmospheric conditions within stable margins through gradual transitions over yearly cycles of seasonality generating different climatic regimes and the zonification of different terrestrial ecosystems.

In my research I have discussed how such configuration has shown to have changed in the recent years with plenty of implications for the atmospheric dynamics and seasonal behaviour at the NH. (e.g. Theoretical proposal, Observational assessment and Seasonal developments).

In a system at equilibrium the radiation is in equilibrium with the molecules, at the same temperature and it may be described by temperature. HOWEVER,  without equilibrium, there is no defined temperature.

Not only the atmosphere is composed by gaseous compounds of different nature, molecular composition and thermodynamic behaviour but also by solid particles called aerosols.

If the medium includes inhomogeneities in the form of small particles, then radiation, while passing through this medium, will be scattered in all directions. For example, particles of dust or drops of water in the atmosphere scatter electromagnetic waves passing through such a medium, as well as the thermal radiation formed in other spatial parts of a medium. If the supposition of a local thermodynamic equilibrium is inapplicable for the studied system, then the emission of radiation by a substance becomes a function of energetic states in the system, and the problem of radiative transfer in such media is, at the least, complicated.

Dimensionality and Time

The expression of local thermodynamic equilibrium (LTE), particularly in astrophysics and atmospheric science, is simply a way of expressing that local behaviour (say at a certain altitude in the atmosphere) is reasonably well described as being in equilibrium and characterized by a temperature. And yet, on larger scales, as we know for the atmospheric structure, this cannot be the case, since the temperature, the molecular structure and composition, as well as the physical and energetic states and interactions of all the substances coexisting are far from uniform and distant from the behaviour expected from an ideal gas at constant pressure.

But moreover, we have to keep in mind the fact that the effect triggered by a concentration of molecules in the atmosphere, such as of those conforming a water clouds or from GHGs, is asymmetric over its surroundings. Consider a beam of radiation with intensity propagating in the absorbing, emitting and scattering medium in a given direction. The energy of radiation will decrease owing to its absorption by substance and owing to the deviation of a part of the radiation from the initial trajectory as a result of scattering in all directions. But, at the same time, the energy will increase because of thermal radiation emission by the substance volume. The absorption, scattering and emission of radiation by a substance have effect on the energy of a radiation beam that propagates in it. In this case the total balance of change of the initial intensity can be, certainly, both positive and negative. Besides, a strong inhomogeneity of the energy balance, both over the substance volume and over the observation direction, is possible.

The same as when we address the effects at the atmosphere from the molecular composition in the absorbing, emitting and scattering gaseous medium, we have to include same considerations by the composition and structure of the solid phase at surface level.

The problem we face to define the behaviour of a dynamic, heterogeneous and multidimensional system is that few things keep constant through time and location, if any. The idealization required to apply a constant relationship demands to consider the behaviour of the atmosphere following idealized conditions impossible to be found outdoors.

And those variations are getting wider and wilder through latitudes and longitudes creating hot and cold waves:

Eumetsat Natural Colour Diego FdezSevilla

Cold bursts of Polar Air moving towards Europe on Winter 2016

1st week monthly intervals Temp Anomaly Wester Europe 2015 by Diego Fdez-Sevilla

Heat waves through Europe over Summer 2015

As well as in altitude, generating what it is being to be called Sudden Stratospheric Warming processes.

Polar vortex 4th Jan 2016 ECMWF NOAA Diego Fdez-Sevilla

The conformation of our macro-climate is the result of the complex synergistic interaction of many micro-climates. The coalescence of those micro-climates creates regional climates and their interaction conform the global climate as we have been used to know it.

Climate-zones

But things are changing not only over our heads, but also around our feet:

Water vapor_Temp and NDVI Anomalies North 60 N

Tangled in Words.

I am sure Einstein had more things in his mind than what he was able to put into written expressions or even words. Every knows how frustrating is to have a perception over something and not being able to find the right words to make it understandable for others. This is a simple situation we all can relate to either in science or just by moving into a country were you don´t speak the language.

Sometimes it seems very easy to forget how much our limitations in developing ideas come from the limitations in the methodologies, either throughout the application of languages/formulas or the materials/technology available. Discovering is about making up names for things which we are able to identify within the limitations of our methods. Because you can name it does not mean you understand it, and because you can not find how to name it does not mean you do not understand it. e.g. Gravity existed before the apples start falling from the trees. But names restrict the full meaning of anything.

I consider myself a methodologist whom doesn´t know everything, but I like to use everything I know. So every piece of constructive feedback is welcome.

I have chosen one methodology to look at the dynamics driving our environment among many. I don´t try to match formulas to numbers for a reason. I believe that it is more  reliable to observe events and find scientific reasoning behind them.

The applicability of those thoughts

This is a difficult topic to approach with words and I only know how many different ways of written it down I have tried and reshape.

Since cooking is all about thermodynamics I have applied analogies from it in previous publications in order to make intuitive for a multidisciplinary audience the arguments which play a role in atmospheric dynamics and climatic developments. (climate and environmental feedbacks, atmospheric thermal conductivity and Arctic/Antarctic bipolarity)

I thought this time about using a Solar cooker to make a point about thermal radiation and temperature, but I was worry about diminishing the value of my arguments on it.

Ultimately I considered that I should use some more “academic-ish” approach and yet keeping it somehow intuitive for a multidisciplinary approach.

I have kept many thoughts in the bag though. One is the mechanic effect of GHGs enhancing convective mixing due to increased thermal energy and thermal conductivity in the atmosphere (heat displacements/waves reaching higher in latitude and Sudden Stratospheric Warming in Winter). GHGs don´t heat up the Earth surface, but they avoid the surface from cooling as it would happen with lower concentration of them. (see also addendum at the bottom).

Similarly, the cooling effect of sweat in a sauna is reduced because there is a saturated atmosphere with steam/water vapour in the enclosed atmosphere. Outdoors, the difference in thermal energy between your skin and the air surrounding it is such that the energy applied to evaporate sweat is taken from the skin and get introduced into the lower energetic non-saturated atmosphere. Furthermore, as the wind blows, in addition to heat from our bodies being directly carried away by the air (aka convective heat transfer), water evaporates more quickly.

In the atmosphere, the accumulation of warm and wet masses of air usually is contained in the volume occupied at Mid Latitudes. The polar Jets Streams are the limit. Enhancing the capacity of the atmosphere to trap thermal energy through GHGs enhance the power for this volume to expand into higher latitudes into the poles and in altitude giving stratospheric warming bursts (SSA). The asymmetries between the poles could be explain by the asymmetries in surface composition and emissions rates for both Hemispheres.

Stratospheric Warming 5 March2016 Diego Fdez-Sevillatime_pres_TEMP_ANOM_JFM_NH_2016

Cold Burst of Polar Air moving south over Europe. Eumetsat. Diego Fdez-Sevilla

Another Cold Burst of Polar Air moving south over Europe the 9th March 2016. Eumetsat. Diego Fdez-Sevilla

Lava lamp

Looking at the bursts of polar cold air seen in Europe and North America, my assessment for this Winter 2016 is that we have seen one after another displacements of cold air from the Arctic due convective forcing from warmer masses of air getting into high latitudes and altitudes.

In another hand, I believe that the positive phase of the ENSO has overstimulated Pacific circulation into one big cell. As I have discussed in previous posts, I believe that such scenario is due to the conditions in atmospheric circulation promoted by a trans-Arctic connection between Atlantic and Pacific basins.  Throughout the end of 2015 the Pacific circulation changed from a two cell configuration into a one big one. I suggest that this one cell is the result from the two previous cells coalescing as consequence of the positive ENSO phase. I believe that with the return into neutral conditions the circulation at the Pacific will regain a pattern with two cell of atm rivers as those seen in 2013-14 (for more see my previous publications following this link).

Water vapour circulation globally 7th Sept 2015 DiegoFdezSevillaMulti IR Global Dec 2015 Diego Fdez-Sevilla

One of the observations that I find relevant to support the idea of that the two cell configuration will comeback is the fact that the blocking patterns over California and the Atlantic have always been around since before and through the positive ENSO.

Blocking patterns 21 Jan 2016 By Diego Fdez-Sevilla

Addendum

(Updated 17 March 2016. The conversation at LinkedIn keeps going on, so here are the last comments I made as part of this thread).

What GHGs effect is triggering in the climate is an increase in entropy in the whole column. That is the problem with GHGs. And that takes the system out of thermodynamic equilibrium. And that makes Boltzman statistics inappropriate.

A system in thermodynamics equilibrium means that the Energy coming in (let say Ei) equals the Energy going out (Eo) of the system. In simplistic terms we can say that a system can be composed by Potential Energy (P) in its mass, and kinetic (K) energy with the vibration of the molecules from this mass. Since GHGs are among those substances with mass entering the system, that in itself breaks thermodynamic equilibrium. So Stefan-Blotzman equations do not apply here. In order to have thermodynamic equilibrium we would need a compensation going out of the system either in the form of Potential energy (mass) or kinetic energy (thermal energy). In both cases, such situation is not contemplated by Stefan-Blotzman equations. And then, apart from mere quantities of GHGs and aerosols with atomic mass entering the system, we have to consider molecular constitution and thermal qualities absorbing, emitting and scattering radiation. And zonification in space, biochemical reactions, …

Since what it is entering the system is an increase in atomic mass (we are in a period of low radiation in the solar cycle) but this increase in mass is not compensated by mass leaving the system, the second law of thermodynamics applies towards equilibrium increasing thermal energy in the system. Which would leave the system only once it reaches the outer layers of the atmosphere. And that process would be more difficult since there are more molecules absorbing and scattering radiation. And that under a state of non equilibrium due to the constant variation of the mass entering the system due to GHGs and aerosols. I would extend my assessments here but I don´t want to occupy somebody else’s thread. If anybody is interested you can always visit my blog diegofdezsevilla.wordpress.com Always open to “constructive” feedback.

Agenda

The debate on climatic developments and anthropogenic responsibility is a very delicate one since it compromises the economic stability of many sectors. But it also touches the deepest inner feelings of human perception on ourselves and our fellow habitants. That touches social differences as much as cultural differences.

My agenda is oriented towards enhancing discussion over topics in a scientific and functional manner for a multidisciplinary audience. Firstly because I believe that is the way to move forward in science and that is why I follow my own agenda. Also because I reject the idea of that a researcher can not produce unless is part of an institution. And hopefully, because my Intellectual Portfolio will allow me to show my capabilities and stand out from the crowd in order to find economic and institutional support to keep working on my research skills to bring new outcomes.

—xxx—

PerspectiveSince October 2013 I have been studying the behaviour of the Polar Jet Stream and the weather events associated as well as the implications derived into atmospheric dynamics and environmental synergies.

Many of the atmospheric configurations and weather and climate events we see these days are very similar with the progression followed since 2013. Please take a look at posts addressing those events from previous publications in this blog or look at the categories in the top menu. Also at research-gate. Feedback is always welcomed either in this blog or at my email (d.fdezsevilla(at)gmail.com). All my work is part of my Intellectual Portfolio, registered under Creative Commons Attribution-NonCommercial 4.0 International License,  WordPress.com license and it is being implemented at my profile in researchgate. I will fight for its recognition in case of misuse.

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About Diego Fdez-Sevilla, PhD.

Citing This Site "Title", published online "Month"+"Year", retrieved on "Month""Day", "Year" from http://www.diegofdezsevilla.wordpress.com. By Diego Fdez-Sevilla, PhD. More guidance on citing this web as a source can be found at NASA webpage: http://solarsystem.nasa.gov/bibliography/citations#! DOIs can be generated on demand by request at email: d.fdezsevilla(at)gmail.com for those publications missing at the ResearchGate profile vinculated with this project. **Author´s profile: Born in 1974. Bachelor in General Biology, Masters degree "Licenciado" in Environmental Sciences (2001, Spain). PhD in Aerobiology (2007, UK). Lived, acquired training and worked in Spain, UK, Germany and Poland. I have shared the outcome from my work previous to 2013 as scientific speaker in events held in those countries as well as in Switzerland and Finland. After 12 years performing research and working in institutions linked with environmental research and management, in 2013 I found myself in a period of transition searching for a new position or funding to support my own line of research. In the current competitive scenario, in order to demonstrate my capacities instead of just moving my cv waiting for my next opportunity to arrive, I decided to invest my energy and time in opening my own line of research sharing it in this blog. In March 2017 the budget reserved for this project has ended and its weekly basis time frame discontinued until new forms of economic and/or institutional support are incorporated into the project. The value of the data and the original nature of the research presented in this platform and at LinkedIn has proved to be worthy of consideration by the scientific community as well as for publication in scientific journals. However, without a position as member of an institution, it becomes very challenging to be published. I hope that this handicap do not overshadow the value of my achievements and that the Intellectual Property Rights generated with the license of attribution attached are respected and considered by the scientist involved in similar lines of research. **Any comment and feedback aimed to be constructive is welcome as well as any approach exploring professional opportunities to be part of.** In this blog I publish pieces of research focused on addressing relevant environmental questions. Furthermore, I try to break the barrier that academic publications very often offer isolating scientific findings from the general public. In that way I address those topics which I am familiar with, thanks to my training in environmental research, making them available throughout my posts. (see "Framework and Timeline" for a complete index). At this moment, 2017, I am living in Spain with no affiliation attachments. Free to relocate geographically worldwide. If you feel that I could be a contribution to your institution, team and projects don´t hesitate in contact me at d.fdezsevilla (at) gmail.com or consult my profile at LinkedIn, ResearchGate and Academia.edu. Also, I'd appreciate information about any opportunity that you might know and believe it could match with my aptitudes. The conclusions and ideas expressed in each post as part of my own creativity are part of my Intellectual Portfolio and are protected by Intellectual Property Laws. Licensed under Creative Commons Attribution-NonCommercial conditions. In citing my work from this website, be sure to include the date of access. (c)Diego Fdez-Sevilla, PhD, 2017. Filling in or Finding Out the gaps around. Publication accessed 20YY-MM-DD at https://diegofdezsevilla.wordpress.com/
This entry was posted in Aerobiology, Aerosols, Air, Biological productivity, Cultural Cognition, Energy Balance, Environmental Resilience, Extreme climatic events, Filling in, Finding out, Influence of Continentality, Inland Water Bodies and Water Cycle, Opinion, Polar vortex and Jet Stream, Solar activity, Water vapour and tagged , , , , , , , , . Bookmark the permalink.

53 Responses to Tangled in Words. Atmospheric Dynamics, Stefan Boltzmann Calculations and Energy Balance (by Diego Fdez-Sevilla, PhD.)

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