Lumped Thermal Impedance Modeling of Anthropogenic Global Warming of the Troposphere

Geert Willems, Wim Fyen, Philippe Roussel, Jan Van Houdt

Anthropogenic global warming has reached a level so high that it is now possible to an-
alyze its dynamics and spatial variation. Spatially varying Surface Air Temperature (SAT)
anomalies [1] can be well described by exponential functions with increase rates that range
from 2.1 to 3.7% per year, depending on the region. The Northern Hemisphere has warmed
significantly more than the Southern Hemisphere and is also warming more rapidly. In this
work, small-signal, lumped thermal impedance (LTI) modeling of the Earth thermal system
is introduced as an efficient method to model the temporal and spatial variation of SAT
across the globe at continental scale since the industrial revolution. SAT is, in first-order,
determined by the warming of the troposphere as a consequence of energy sources dissipating heat in it. Due to its small thermal capacity, it has a high sensitivity to these sources.
The thermal sensitivity of the troposphere is estimated to be 5.4±0.9K per W/m2 of dissi-
pated energy. This value is derived from the troposphere’s thermal response to the 11-year
solar cycle. The spatially varied increase of 2.1 to 3.7% per year of SAT-anomaly cannot
be simply explained by global uniform warming by uniformly distributed greenhouse gases
(GHGs), dominated by CO2, of which the concentration increases at a rate of only 1.9%
per year. Within the framework of a small-signal LTI-model for the troposphere volumes
above the Northern and Southern Hemisphere’s oceans and land masses, respectively, three effective small-signal anthropogenic troposphere heat sources are identified and quantified consistent with the observed region-dependent exponential increase in SAT. These are: (i) IRTA: Infrared Radiation Absorption in the Troposphere determined by GHG-emission and quantified from the Southern Hemisphere ocean SAT-evolution; (ii) AHR: Anthropogenic Heat Release which directly heats the troposphere, independently derived from global primary energy consumption data; (iii) SITA: Solar Irradiation Absorption in the Troposphere increasing rapidly (>3% per year) attributed to increasing levels of short-lived Anthropogenic Chemicals Emission (ACE). This heat source is quantified by fitting the impedance model equations to the continental SAT-evolutions since 1990. It amounts to an increase of close to +0.2% in solar irradiation absorption over the Northern Hemisphere’s land. The global average increase in SITA coincides with the increase in OH-anomaly since 1990, consistent with the hypothesized chemical origin of SITA-warming [2]. The presented LTI-model quantifies the accelerating and spatially varying global warming as a result of exponentially increasing anthropogenic heat sources (IRTA, AHR, SITA) that cause a region-dependent exponentially increasing SAT since the industrial revolution. The results are derived within a small-signal, lumped linear thermal impedance framework and are bounded by the LTI-model structure, its linearization, and the estimations of the effective impedance parameters derived from SAT and Total Solar Irradiation measurements.