Project

Dynamic-Atmosphere Energy-Transport Climate Model

Goal: To study the application of a mathematical model to the climate structure of the atmosphere surrounding the solar system terrestrial planets Venus, Earth, Mars and also of Titan, the moon of Saturn.

Date: 1 January 2019

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Philip Mulholland
added a research item
We present here the results of an eXcel spreadsheet designed to calculate the pressure profile for the Venus atmosphere at 1 metre increments from the surface to the lower stratosphere, a modelled vertical height of 100 kilometres. Two equations of state are used here, the pressure, volume, temperature (PVT) version of Boyle’s law, and the application of Newton’s gravity law of spherical shells, used to calculate the reduction in strength of the gravity field as the height above the surface of Venus increases. Using a set of four linked predictive lapse rate equations based on published data as the fundamental temperature control of the atmospheric pressure profile, the profile is calibrated to a surface datum global average temperature for Venus of 699 Kelvin.
Philip Mulholland
added an update
From this analysis we conclude that the high surface temperatures observed at the surface of Venus are a direct consequence of, and maintained by, a process of topside thermal radiant capture by the air followed by mass motion energy delivery to the surface.
 
Philip Mulholland
added 2 research items
Excel workbook containing the source algorithms, tables, figures and references for the formulation of a predictive temperature constrained pressure profile for the atmosphere of Venus.
The application of a lapse rate controlled pressure profile for the atmosphere of Venus as a calibration check for the DAET climate model.
Philip Mulholland
added 3 research items
Abstract: In this paper we present the results of a modelling analysis of the climate of Titan [2], in which we apply the techniques presented by Kiehl and Trenberth (1997) [3], and that were used by them to study the climate of the Earth. Our purpose here is to follow the fundamental concept that a terrestrial body that supports the surface presence of a volatile liquid, is cooled by the meteorological processes of Thermals, Evaporation, and Radiative loss. We have applied this precept to Titan and suggest that a system energy drain will be created within its troposphere. Because it has episodes of liquid precipitation of methane, evaporation of this liquid volatile, both from the surface of the moon and also by virga processes will cool the tropics of Titan. The supply of the energy for this latent heat of evaporation of liquid methane will create both surface and atmospheric cooling within the meteorological processes of Titan. : To study this, we created a pressure profile curve for the atmosphere of Titan based on an application of Boyle’s law and Newton’s gravity law of spherical shells. The temperature lapse rate used in our analysis is based on data [6] that constrains three predictive equations, one each for the troposphere, tropopause and lower stratosphere respectively. With this atmospheric pressure profile model, we are then able to explore the results of the previous application of our Dynamic Atmosphere Energy-Transport (DAET) climate model to Titan [2]. : Finally, a sensitivity test was made of our DAET climate model by creating a zero-albedo version of Titan which we have called Clarity. With this model we are able to establish the dynamic limits of extreme albedo induced climate change for the moon Titan. : In studying the science of atmospheres that are gravitationally bound to the surface of an orbiting, rotating, solar illuminated, terrestrial body, we must first establish the key mechanisms of atmospheric dynamics and apply these to Titan. The questions addressed are how the processes of high-frequency radiant energy capture, mechanical energy storage of specific heat and low-frequency radiant energy loss occur, and where they take place within the mobile fluid atmosphere that surrounds Titan. Our analysis using the traditional tools of climate science fully confirms that there is a greenhouse effect in the climate of Titan, and that it is located in the troposphere of that moon. Our formulation of a pressure temperature profile for Titan built on data and first principles, has established that the vast bulk of the methane within its atmosphere occurs in solid particulate form. : Our climate model of Titan, that we have now calibrated against the results of the traditional climate science approach, shows that the lack of application of the tools of meteorology, namely the study of CAPE (convectively available potential energy) has resulted in a focus on only half of the story. Our modelling analysis has demonstrated both the existence and the effect of two complementary and opposing processes within an atmosphere that dynamically stabilise and ensure its long-term existence within tightly controlled thermal limits. : These two processes are, the diabatic thermal radiant process of an equipartition flux cascade that manifests in the thermal radiant clarity of the low-pressure stratosphere, and the adiabatic thermal mass motion process of solar radiant forced convection. It is the adiabatic process of mass motion energy flux transport that manifests in and defines the troposphere. This is because it requires an environment where mass motion pressure forcing is the dominant energy flux process. The adiabatic process acts as a unidirectional energy gate, either removing energy from or delivering energy back to the site of thermal radiant disequilibrium within the troposphere. : The results of our analysis demonstrate that the Greenhouse Effect in the thermally opaque, frozen methane particulate containing atmosphere of Titan is a tropospheric mass motion pressure induced adiabatic thermal effect, and not a diabatic atmospheric thermal radiant effect.
Tables and Workflow Methodology for "Clarity". Used in the Sensitivity Test of the DAET Climate Model of Titan.
Tables and Workflow Methodology used in the Re-analysis of the Climate of Titan.
Philip Mulholland
added an update
The purpose for creating a model pressure and temperature profile using Boyle’s law for the atmosphere of Venus is to provide a calibration check of the previously presented Dynamic Atmosphere Energy Transport (DAET) climate model of the planet Venus (Mulholland and Wilde, 2020).
Our spreadsheet analysis of the pressure profile of the Venusian atmosphere is based on the following Baseline Parameters.
1. The surface pressure measured in Pascal.
2. The surface temperature measured in Kelvin.
3. The Molecular Weight of the Venus atmosphere measured in g/mole.
4. The surface gravity of Venus measured in m/s2..
5. The planetary mass of Venus in kg.
6. The mean radius of Venus in m.
7. A corrected atmospheric Lapse Rate for the troposphere of Venus measured in K/m.
8. The observed height of the Venusian Tropopause in Km.
9. Using the two physical relationships of Boyle’s gas law, and Newton’s spherical shell gravity law a pressure profile is created for the atmosphere, assuming a constant temperature lapse rate of 8.244 * 10-3 K/m.
Using this model pressure profile the atmospheric pressure of the DAET modelled thermal emission surface at the top of the atmosphere is calculated and compared with published observations of the Venusian atmospheric cloud veil.
References:
Jenkins, J.M., Steffes, P.G., Hinson, D.P., Twicken, J.D. and Tyler, G.L., 1994. Radio occultation studies of the Venus atmosphere with the Magellan spacecraft: 2. Results from the October 1991 experiments. Icarus, 110(1), pp.79-94
Mulholland, P. and Wilde, S.P.R., 2020. Inverse Climate Modelling Study of the Planet Venus. International Journal of Atmospheric and Oceanic Sciences, 4(1), pp.20-35.
Young, A.T. 1973. Are the clouds of venus sulfuric acid? Icarus 18(4), pp. 564-582.
 
Philip Mulholland
added a research item
Abstract: In this paper we quantify and attribute by inspection the constituent elements of the power intensity radiant flux transmission for the atmosphere of the Earth, as recorded in the following two published sources; Oklahoma Climatological Survey and Kiehl and Trenberth. The purpose of our analysis is to establish the common elements of the approach used in the formulation of these works, and to conduct an assessment of the two approaches by establishing a common format for their comparison. By applying the standard analysis of a geometric infinite series feed-back loop to an equipartition (half up and half down) diabatic distribution used for the atmospheric radiant flux to all elements of the climate model; our analysis establishes the relative roles of radiant and mass-motion carried energy fluxes that are implicitly used by the authors in their respective analyses. Having established the key controls on energy flux within each model, we then conduct for the canonical model a series of “what-if” scenarios to establish the limits of temperature rise that can be achieved for specific variations in the controls used to calculate the global average temperature. Our analysis establishes that, for the current insolation and Bond albedo, the maximum temperature that can be achieved for a thermally radiant opaque atmosphere is a rise to 29°C. This global average temperature is achieved by a total blocking of the surface-to-space atmospheric window. In order to raise the global average atmospheric temperature to the expected value of 36°C for a putative Cretaceous hothouse world, it is therefore necessary to reduce the planetary Bond albedo. The lack of continental icecaps, and the presence of flooded continental shelves with epeiric seas in a global eustatic high stand sea level, is invoked as an explanation to support the modelling concept of a reduced global Bond albedo during the Cretaceous Period. The geological evidence for this supposition is mentioned with reference to published sources.
Philip Mulholland
added an update
Reference:
Stephen Paul Rathbone Wilde, Philip Mulholland. An Analysis of the Earth’s Energy Budget. International Journal of Atmospheric and Oceanic Sciences. Vol. 4, No. 2, 2020, pp. 54-64. doi: 10.11648/j.ijaos.20200402.12
 
Philip Mulholland
added an update
The attached files relate to the publication of An Analysis of the Earth’s Energy Budget.
Figure 7 The Atmospheric Reservoir Energy Recycling Process does not form part of the paper and is included for interest to show how the original concept diagram can be adapted to a globe with a lit day and unlit night hemisphere.
The day and night time terrestrial radiation values used in Figure 7 derive from the Earth PVT model and sum to the required 470 W/m2 balance figure for a single lit hemisphere.
The purpose of the Figure 7 diagram is to demonstrate how, using published climate science metrics, it is possible to build an energy balance model for the Earth in which the critical feature is this; that the model is only ever instantaneously illuminated over one full day lit hemisphere.
In presenting this diagram there are a number of key points:
  1. That the power of the Sun is only divided by two and not by four, therefore the surface emission processes in the model must be multiplied by two.
  2. That the atmospheric reservoir stores a flux that is double the quantity of the intercepted flux (This doubling in the reservoir is the limit of the infinite series of sums of halves of halves for a lossy process).
  3. That the process of energy transfer to the unlit hemisphere involves mass motion and thermal inertia, processes which are clearly not instantaneous and therefore must involve energy storage and temporal thermal lags.
  4. That the partition of energy between the day and night hemisphere in the model assumes for simplicity that all convective processes are daylight phenomena and that all night time processes are driven by energy stored either in the mobile fluid atmosphere or in the heated ground surface.
  5. The values for the radiation to space derive from the application of our Dynamic Atmosphere Energy Transport (DAET) model and demonstrate a known feature of the planetary atmosphere, namely that the troposphere expands under day time solar radiant heating and contracts under night-time thermal radiant cooling.
 
Philip Mulholland
added an update
Stephen Paul Rathbone Wilde, Philip Mulholland, Return to Earth: A New Mathematical Model of the Earth’s Climate, International Journal of Atmospheric and Oceanic Sciences. Vol. 4, No. 2, 2020, pp. 36-53. doi: 10.11648/j.ijaos.20200402.11
 
Philip Mulholland
added a research item
In this paper we use the inverse modelling technique, first applied to the atmosphere of the planet Venus, to demonstrate that the process of convective atmospheric mass motion can be invoked to explain the greenhouse effect of the Earth's climate. We propose that the atmospheric cell is the fundamental element of climate, and have developed an alternative climate model based on this process of atmospheric circulation for a hypothetical tidally locked world. The concept of climate derives from studies by the Greek philosopher Aristotle, who identified the three main climatic zones known to the ancient world; the equatorial torrid zone, the polar frigid zone and in between the favoured temperate zone of the Mediterranean world. Aristotle's three climatic zones can be directly linked to the three main atmospheric circulation cells that we now recognise within the Earth's atmosphere. These three cells are the Hadley cell, the Polar cell and the Ferrel cell. Based on the clear association between the traditional Greek concept of climate and the modern meteorological concept of atmospheric circulation cells, we propose that climate be defined as the presence and action of a particular circulation cell type within a given planetary latitudinal zone. We discuss how with knowledge of three simple meteorological parameters of tropopause elevation, tropopause temperature and lapse rate for each atmospheric cell, combined with the measurement of the area of that cell, the average global surface temperature can be calculated. By means of a mathematical model, the Dynamic-Atmosphere Energy-Transport (DAET) climate model we apply an individual climate analysis to each of the three atmospheric cells, and next generate a parallel composite model of the Earth's planetary climate using these data. We apply the concepts and techniques of the adiabatic version of the DAET climate model, and show how this model can be compared with the published NASA image of the Earth's outgoing long-wave radiation recorded by the CERES (Clouds and the Earth's Radiant Energy System) Instrument onboard the NASA Aqua Satellite. Our analysis of the CERES image suggests that the Tibetan plateau forms a permanent geological thermal radiant leak point in the Earth's atmosphere. We also compare the observed temperature found at the maximum elevation of the Antarctic ice cap with the freezing point of super-cooled water, and suggest that there is therefore a temperature controlled and latent heat related upper limit to the vertical development of a continental icecap.
Philip Mulholland
added an update
Philip Mulholland, Stephen Paul Rathbone Wilde, Inverse Climate Modelling Study of the Planet Venus, International Journal of Atmospheric and Oceanic Sciences. Vol. 4, No. 1, 2020, pp. 20-35. doi: 10.11648/j.ijaos.20200401.13
 
Philip Mulholland
added a research item
The terrestrial planet Venus is classified by astronomers as an inferior planet because it is located closer to the Sun than the Earth. Venus orbits the Sun at a mean distance of 108.21 Million Km and receives an average annual solar irradiance of 2601.3 W/m 2 , which is 1.911 times that of the Earth. A set of linked forward and inverse climate modelling studies were undertaken to determine whether a process of atmospheric energy retention and recycling could be established by a mechanism of energy partition between the solid illuminated surface and an overlying fully transparent, non-greenhouse gas atmosphere. Further, that this atmospheric process could then be used to account for the observed discrepancy between the average annual solar insolation flux and the surface tropospheric average annual temperature for Venus. Using a geometric climate model with a globular shape that preserves the key fundamental property of an illuminated globe, namely the presence on its surface of the dual environments of both a lit and an unlit hemisphere; we established that the internal energy flux within our climate model is constrained by a process of energy partition at the surface interface between the illuminated ground and the overlying air. The dual environment model we have designed permits the exploration and verification of the fundamental role that the atmospheric processes of thermal conduction and convection have in establishing and maintaining surface thermal enhancement within the troposphere of this terrestrial planet. We believe that the duality of energy partition ratio between the lit and unlit hemispheres applied to the model, fully accounts for the extreme atmospheric "greenhouse effect" of the planet Venus. We show that it is the meteorological process of air mass movement and energy recycling through the mechanism of convection and atmospheric advection, associated with the latitudinal hemisphere encompassing Hadley Cell that accounts for the planet's observed enhanced atmospheric surface warming. Using our model, we explore the form, nature and geological timing of the climatic transition that turned Venus from a paleo water world into a high-temperature, high-pressure carbon dioxide world.
Philip Mulholland
added an update
Text Figures for Return to Earth: A New Predictive Model of The Earth's Climate P Mulholland & SPR Wilde Published WUWT 27Jun19
 
Philip Mulholland
added a research item
Titan, the giant moon of the planet Saturn, is recognized to have meteorological processes involving liquid methane that are analogous to the water generated atmospheric dynamics of planet Earth. We propose here that the climatic features of Titan by contrast are more akin to those of the planet Venus, and that this structural similarity is a direct result of the slow daily rotation rate of these two terrestrial bodies. We present here a simple mathematical climate model based on meteorological principles, and intended to be a replacement for the standard radiation balance equation used in current studies of planetary climate. The Dynamic-Atmosphere Energy-Transport climate model (DAET) is designed to be applied to terrestrial bodies that have sufficient mass and surface gravity to be able to retain a dense atmosphere under a given solar radiation loading. All solar orbiting bodies have both an illuminated hemisphere of net energy collection and a dark hemisphere of net energy loss. The DAET model acknowledges the existence of these dual day and nighttime radiation environments and uses a fully transparent non-condensing atmosphere as the primary mechanism of energy storage and transport in a metrological process that links the two hemispheres. The DAET model has the following distinct advantages as a founding model of climate: It can be applied to all terrestrial planets, including those that are tidally locked. It is an atmospheric mass motion and energy circulation process, and so is fully representative of a Hadley cell; the observed fundamental meteorological process of a terrestrial planet's climate. The diabatic form of the DAET model fully replicates the traditional vacuum planet equation, and as it applies to a totally transparent atmosphere it therefore demonstrates that thermal radiant opacity, due to the presence of polyatomic molecular gases, is not a fundamental requirement for atmospheric energy retention. For the adiabatic form of the DAET model, where the turbulent asymmetric daytime process of forced radiant convection applies, the intercepted solar energy is preferentially retained by the ascending air. The adiabatic DAET climate model shows that the atmospheric greenhouse effect of surface thermal enhancement is a mass motion process, and that it is completely independent of an atmosphere's thermal radiant opacity.
Philip Mulholland
added an update
Philip Mulholland, Stephen Paul Rathbone Wilde, An Iterative Mathematical Climate Model of the Atmosphere of Titan, Journal of Water Resources and Ocean Science. Vol. 9, No. 1, 2020, pp. 15-28. doi: 10.11648/j.wros.20200901.13
 
Philip Mulholland
added an update
Individual links to online comments and criticisms of the essays has been added for each pre-print.
The online comments are hosted here:
1. Calibrating the CERES Image of the Earth's Radiant Emission to Space.
2. An Analysis of the Earth’s Energy Budget.
3. Modelling the Climate of Noonworld: A New Look at Venus.
4. Return to Earth: A New Predictive Model of the Earth’s Climate.
5. Using an Iterative Adiabatic Model to study the Climate of Titan.
 
Philip Mulholland
added an update
The following pre-print essays and associated method files have been added to this project.
1. Calibrating the CERES Image of the Earth's Radiant Emission to Space.
1a. CERES Image Calibration Tables 12Apr19
2. An Analysis of the Earth's Energy Budget.
2a. Analysis of Earth Energy Budget Diagrams 21May19
3. Modelling the Climate of Noonworld: A New Look at Venus.
3a. Noonworld Tables 31May19
4. Return to Earth: A New Predictive Model of the Earth’s Climate.
4a. Earth Adiabatic Parallel Model 20Jun19
4b. Earth Adiabatic PVT Model 20Jun19
5. Using an Iterative Adiabatic Model to study the Climate of Titan.
5a. Titan Climate Models 08Jul19
 
Philip Mulholland
added 7 research items
Tables and Work flow Methodology used in the analysis of the Climate of Titan. (Loaded as Excel 97 because all previous versions of this file would not download)
Tables and Work flow methodology used in creating the Noonworld model.
In this essay we introduce the concept of Noonworld, a hypothetical solar illuminated tidally locked planet. We develop a climate model based on the meteorological principles of a lit daytime hemisphere of energy surplus that is coupled to a dark nighttime hemisphere of energy deficit. In the model the fundamental mechanism of power intensity flux distribution across the surface of Noonworld is mediated by the process of atmospheric mass motion. The capture, distribution and loss to space of solar radiant energy is studied for a hypothetical fully transparent atmosphere. In this first instance the model assumes that all processes of flux transformation are equipartition in type and occur at the solid surface of the planet. Our initial model is diabatic in concept and fully replicates the low temperature atmosphere of the standard Vacuum Planet equation. We next adjust the model to account for the process of sunlit forced convection by partitioning energy capture in favour of the air. Our model now retains additional flux within the atmospheric reservoir, and thereby causes the global atmospheric temperature to rise. We call this process of flux capture and distribution by atmospheric mass motion the adiabatic model.
Philip Mulholland
added 2 research items
Abstract. A mathematical model has been created based on meteorological principles, and intended to be applied as a correlative to the standard radiation balance equation used in current climate studies. The Dynamic-Atmosphere Energy-Transport climate model (DAET) is designed to account for the dual environmental nature of all terrestrial globes and moons, with sufficient mass and surface gravity to hold an atmosphere under a given solar radiation loading. The model consists of two distinct environments, a solar lit hemisphere dominated by surface radiative heating with an energy surplus, and a dark night-time hemisphere of energy deficit dominated by surface cooling, caused by direct through the atmosphere thermal radiative energy loss to space. Energy exchange between the two hemispheres of energy surplus and energy deficit is mediated by a series of linked atmospheric mass movement processes. On the lit surface of energy surplus adiabatic convection and atmospheric overturning occurs. The lifted energy rich air then undergoes horizontal mass transport in the upper atmosphere. This process, characterized by air movement and energy transport towards the region of surface energy deficit, is representative of a thermal Hadley cell. The energy rich advected air subsequently descends onto the surface of the dark hemisphere which is under the influence of surface diabatic atmospheric cooling, and thermal radiant energy loss to space. This process is representative of the surface induced radiative cooling of a night time thermal environment. Near-surface advection of surface cooled dense air back to the energy rich sunlit environment, then completes the cyclical process of air mass transport and energy delivery.
Philip Mulholland
added 2 research items
Example test of a full hemisphere adiabatic model with a fixed dark side partition ratio of 50% : 50%
This Excel Workbook contains the design features and data used to create and control the Dynamic-Atmosphere Energy-Transport Climate Model for the Earth's three atmospheric cells.
Philip Mulholland
added a research item
Précis We describe the use of a climate model based on the adiabatic meteorological process of daytime lit hemisphere solar radiant forced convection, coupled to the nighttime dark hemisphere process of surface diabatic radiant cooling to space. The model is design to study the relationships between the interlinked parameters of Top of Atmosphere (TOA) Solar Irradiance, Planetary Bond albedo, atmospheric pressure, adiabatic lapse rate and average temperature for atmospheric circulation cells. The Excel spread sheet model is built with a cascaded series of interlocking calculations that tend towards a geometric limit sum with increasing precision. The structure of the model uses the specific metrics of irradiance and Bond albedo to establish the average temperature for a given atmospheric cell. Using the process of inverse modelling the controlling values of the flux partition ratio (a surface pressure proxy) can be established for a given cell temperature and associated tropopause height. We are in essence using the adiabatic climate model to study a Pressure Volume Temperature relationship for planetary atmospheres.
Philip Mulholland
added a project goal
To study the application of a mathematical model to the climate structure of the atmosphere surrounding the solar system terrestrial planets Venus, Earth, Mars and also of Titan, the moon of Saturn.