arXiv subjects

Timothy J. Garrett

Publications and source records attributed to Timothy J. Garrett.

15 recordsLinked to original sources

arXiv2025

Global sonde datasets do not support a mesoscale transition in the turbulent energy cascade

Conceptual and theoretical models describing the dynamics of the atmosphere often assume a hierarchy of dynamic regimes, each operating over some limited range of spatial scales. The largest scales are presumed to be governed by quasi-two-dimensional geostrophic turbulence, mesoscale dynamics by gravity waves, and the smallest scales by 3D isotropic turbulence. In theory, this hierarchy should be observable as clear scale breaks in turbulent kinetic energy spectra as one physical mechanism transitions to the next. Here, we show that this view is not supported by global dropsonde and radiosonde datasets of horizontal winds. Instead, the structure function for horizontal wind calculated for vertical separations between 200 m and 8 km has a Hurst exponent of $H_v \approx 0.6$, which is inconsistent with either gravity waves ($H_v = 1$) or 3D turbulence ($H_v = 1/3$). For horizontal separations between 200 km and 1800 km, the Hurst exponent is $H_h \approx 0.4$, which is inconsistent with quasi-geostrophic dynamics ($H_h = 1$). We argue that sonde observations are most consistent with a lesser known "Lovejoy-Schertzer" model for stratified turbulence where, at all scales, the dynamics of the atmosphere obey a single anisotropic turbulent cascade with $H_v=3/5$ and $H_h =1/3$. While separation scales smaller than 200 m are not explored here due to measurement limitations, the analysis nonetheless supports a single cohesive theoretical framework for describing atmospheric dynamics, one that might substitute for the more traditional hierarchy of mechanisms that depends on spatial scale.

physics.ao-ph↗

arXiv2021

Economists' erroneous estimates of damages from climate change

Economists have predicted that damages from global warming will be as low as 2.1% of global economic production for a 3$^\circ$C rise in global average surface temperature, and 7.9% for a 6$^\circ$C rise. Such relatively trivial estimates of economic damages -- when these economists otherwise assume that human economic productivity will be an order of magnitude higher than today -- contrast strongly with predictions made by scientists of significantly reduced human habitability from climate change. Nonetheless, the coupled economic and climate models used to make such predictions have been influential in the international climate change debate and policy prescriptions. Here we review the empirical work done by economists and show that it severely underestimates damages from climate change by committing several methodological errors, including neglecting tipping points, and assuming that economic sectors not exposed to the weather are insulated from climate change. Most fundamentally, the influential Integrated Assessment Model DICE is shown to be incapable of generating an economic collapse, regardless of the level of damages. Given these flaws, economists' empirical estimates of economic damages from global warming should be rejected as unscientific, and models that have been calibrated to them, such as DICE, should not be used to evaluate economic risks from climate change, or in the development of policy to attenuate damages.

econ.GN↗

arXiv2020

Numerical simulations and Arctic observations of surface wind effects on Multi-Angle Snowflake Camera measurements

Ground-based measurements of frozen precipitation are heavily influenced by interactions of surface winds with gauge-shield geometry. The Multi-Angle Snowflake Camera (MASC), which photographs hydrometeors in free-fall from three different angles while simultaneously measuring their fall speed, has been used in the field at multiple mid-latitude and polar locations both with and without wind shielding. Here we show results of computational fluid dynamics (CFD) simulations of the airflow and corresponding particle trajectories around the unshielded MASC and compare these results to Arctic field observations with and without a Belfort double Alter shield. Simulations in the absence of a wind shield show a separation of flow at the upstream side of the instrument, with an upward velocity component just above the aperture, which decreases the mean particle fall speed by 55%(74%) for a wind speed of 5 m/s(10 m/s). MASC-measured fall speeds compare well with Ka-band Atmospheric Radiation Measurement (ARM) Zenith Radar (KAZR) mean Doppler velocities only when winds are light (<5 m/s) and the MASC is shielded. MASC-measured fall speeds that do not match KAZR measured velocities tend to fall below a threshold value that increases approximately linearly with wind speed but is generally <0.5 m/s. For those events with wind speeds <1.5 m/s, hydrometeors fall with an orientation angle mode of 12 degrees from the horizontal plane, and large, low-density aggregates are as much as five times more likely to be observed. We conclude that accurate MASC observations of the microphysical, orientation, and fall speed characteristics of snow particles require shielding by a double wind fence and restriction of analysis to events where winds are light (<5 m/s). Hydrometeors do not generally fall in still air, so adjustments to these properties' distributions within natural turbulence remain to be determined.

physics.ao-ph↗

arXiv2020

On the Maxey-Riley equation of motion and its extension to high Reynolds numbers

The inertial response of a particle to turbulent flows is a problem of relevance to a wide range of environmental and engineering problems. The equation most often used to describe the force balance is the Maxey-Riley equation, which includes in addition to buoyancy and steady drag forces, an unsteady Basset drag force related to past particle acceleration. Here we provide a historical review of how the Maxey-Riley equation was developed and how it is only suited for studies where the Reynolds number is less than unity. Revisiting the innovative mathematical methods employed by Basset (1888), we introduce an alternative formulation for the unsteady drag for application to a broader range of particle motions. While the Basset unsteady drag is negligible at higher Reynolds numbers, the revised unsteady drag is not.

physics.flu-dyn↗

arXiv2020

Past production constrains current energy demands: persistent scaling in global energy consumption and implications for climate change mitigation

Climate change has become intertwined with the global economy. Here, we describe the importance of inertia to continued growth in energy consumption. Drawing from thermodynamic arguments, and using 38 years of available statistics between 1980 to 2017, we find a persistent time-independent scaling between the historical time integral $W$ of world inflation-adjusted economic production $Y$, or $W\left(t\right) = \int_0^t Y\left(t'\right)dt'$, and current rates of world primary energy consumption $\mathcal E$, such that $λ= \mathcal{E}/W = 5.9\pm0.1$ Gigawatts per trillion 2010 US dollars. This empirical result implies that population expansion is a symptom rather than a cause of the current exponential rise in $\mathcal E$ and carbon dioxide emissions $C$, and that it is past innovation of economic production efficiency $Y/\mathcal{E}$ that has been the primary driver of growth, at predicted rates that agree well with data. Options for stabilizing $C$ are then limited to rapid decarbonization of $\mathcal E$ through sustained implementation of over one Gigawatt of renewable or nuclear power capacity per day. Alternatively, assuming continued reliance on fossil fuels, civilization could shift to a steady-state economy that devotes economic production exclusively to maintenance rather than expansion. If this were instituted immediately, continual energy consumption would still be required, so atmospheric carbon dioxide concentrations would not balance natural sinks until concentrations exceeded 500 ppmv, and double pre-industrial levels if the steady-state was attained by 2030.

econ.GN↗

arXiv2019

Analytical Estimation of the Width of Hadley Cells in the Solar System

The angular width of Earth's Hadley cell has been related to the square root of the product of the tropospheric thickness and the buoyancy frequency, and to the inverse of the square root of the angular velocity and the planetary radius. Here, this formulation is examined for other planetary bodies in the solar system. Generally good consistency is found between predictions and observations for terrestrial planets provided the pressure scale height rather than the tropopause height is assumed to determine the thickness of the tropospheric circulation. For gas giants, the relevant thickness is deeper than the scale height, possibly due to the internal heat produced by Kelvin-Helmholtz contraction. On Earth, latent heat release within deep convection may play a similar role in deepening and widening the Hadley Cell.

astro-ph.EP↗

arXiv2019

Analytical solutions for precipitation size distributions at steady-state

Analytical solutions are derived for the steady-state size distributions of precipitating rain and snow particles assuming growth via collection of suspended cloud particles. Application of the Liouville equation to the transfer of precipitating mass through size bins in a cascade yields a characteristic gamma distribution with a "Marshall-Palmer" exponential tail with respect to particle diameter. For rain, the principle parameters controlling size distribution shape are cloud droplet liquid water path and cloud updraft speed. Stronger updrafts lead to greater concentrations of large precipitating drops and a peak in the size distribution. The solutions provide a means for relating size distributions measured in the air or on the ground to cloud bulk microphysical and dynamic properties.

physics.ao-ph↗

arXiv2018

Thermodynamic constraints on the size distributions of tropical clouds

Tropical convective clouds evolve over a wide range of temporal and spatial scales, and this makes them difficult to simulate numerically. Here, we propose that their statistical properties can be derived within a simplified time-independent co-ordinate system of cloud number $n$, saturated static energy $h^\star$, and cloud perimeter $λ$. Under the constraint that circulations around cloud edge compete for buoyant energy and air, we show that the product of cloud number and cloud perimeter $nλ$ is invariant with $λ$ and that cloud number follows a negative exponential with respect to cloud-edge deviations of $h^\star$ from the mean. Overall, the summed perimeter of all clouds scales as the square root of the atmospheric static stability, which suggests that the complexity of cloud field structures can be viewed statistically as an emergent property of atmospheric bulk thermodynamics. Analytically derived conclusions are compared with a detailed tropical cloud field simulation and found generally to agree to within $<$13%. For the sake of developing hypotheses about cloud temporal evolution that are testable in high resolution simulations, the shapes of tropical cloud perimeter distributions are predicted to be invariant as climate warms, although with a modest increase in total cloud amount.

physics.ao-ph↗

arXiv2016

Long-run evolution of the global economy - Part 2: Hindcasts of innovation and growth

Long-range climate forecasts use integrated assessment models to link the global economy to greenhouse gas emissions. This paper evaluates an alternative economic framework outlined in part 1 of this study (Garrett, 2014) that approaches the global economy using purely physical principles rather than explicitly resolved societal dynamics. If this model is initialized with economic data from the 1950s, it yields hindcasts for how fast global economic production and energy consumption grew between 2000 and 2010 with skill scores > 90 % relative to a model of persistence in trends. The model appears to attain high skill partly because there was a strong impulse of discovery of fossil fuel energy reserves in the mid-twentieth century that helped civilization to grow rapidly as a deterministic physical response. Forecasting the coming century may prove more of a challenge because the effect of the energy impulse appears to have nearly run its course. Nonetheless, an understanding of the external forces that drive civilization may help development of constrained futures for the coupled evolution of civilization and climate during the Anthropocene.

q-fin.GN↗

arXiv2013

Thermodynamics of long-run economic innovation and growth

This article derives prognostic expressions for the evolution of globally aggregated economic wealth, productivity, inflation, technological change, innovation and growth. The approach is to treat civilization as an open, non-equilibrium thermodynamic system that dissipates energy and diffuses matter in order to sustain existing circulations and to further its material growth. Appealing to a prior result that established a fixed relationship between a very general representation of global economic wealth and rates of global primary energy consumption, physically derived expressions for economic quantities follow. The analysis suggests that wealth can be expressed in terms of the length density of civilization's networks and the availability of energy resources. Rates of return on wealth are accelerated by energy reserve discovery, improvements to human and infrastructure longevity, and a more common culture, or a lowering of the amount of energy required to diffuse raw materials into civilization's bulk. According to a logistic equation, rates of return are slowed by past growth, and if rates of return approach zero, such "slowing down" makes civilization fragile with respect to externally imposed network decay. If past technological change has been especially rapid, then civilization is particularly vulnerable to newly unfavorable conditions that might force a switch into a mode of accelerating collapse.

q-fin.GN↗

arXiv2012

Can we predict long-run economic growth?

For those concerned with the long-term value of their accounts, it can be a challenge to plan in the present for inflation-adjusted economic growth over coming decades. Here, I argue that there exists an economic constant that carries through time, and that this can help us to anticipate the more distant future: global economic wealth has a fixed link to civilization's overall rate of energy consumption from all sources; the ratio of these two quantities has not changed over the past 40 years that statistics are available. Power production and wealth rise equally quickly because civilization, like any other system in the universe, must consume and dissipate its energy reserves in order to sustain its current size. One perspective might be that financial wealth must ultimately collapse as we deplete our energy reserves. However, we can also expect that highly aggregated quantities like global wealth have inertia, and that growth rates must persist. Exceptionally rapid innovation in the two decades following 1950 allowed for unprecedented acceleration of inflation-adjusted rates of return. But today, real innovation rates are more stagnant. This means that, over the coming decade or so, global GDP and wealth should rise fairly steadily at an inflation-adjusted rate of about 2.2% per year.

q-fin.GN↗

arXiv2012

Modes of Growth in Dynamic Systems

Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct modes that depend on the availability of material and energetic resources. These modes include a law of diminishing returns, logistic behavior and, if resources are expanding very rapidly, super-exponential growth. For a case where a system has a resolved sink as well as a source, growth and decay can be characterized in terms of a slightly modified form of the predator-prey equations commonly employed in ecology, where the perturbation formulation of these equations is equivalent to a damped simple harmonic oscillator. Thus, the framework presented here suggests a common theoretical under-pinning for emergent behaviors in the physical and life sciences. Specific examples are described for phenomena as seemingly dissimilar as the development of rain and the evolution of fish stocks.

physics.ao-ph↗

arXiv2012

No way out? The double-bind in seeking global prosperity alongside mitigated climate change

In a prior study, I introduced a simple economic growth model designed to be consistent with general thermodynamic laws. Unlike traditional economic models, civilization is viewed only as a well-mixed global whole with no distinction made between individual nations, economic sectors, labor, or capital investments. At the model core is an observationally supported hypothesis that the global economy's current rate of primary energy consumption is tied through a constant to a very general representation of its historically accumulated wealth. Here, this growth model is coupled to a linear formulation for the evolution of globally well-mixed atmospheric CO2 concentrations. While very simple, the coupled model provides faithful multi-decadal hindcasts of trajectories in gross world product (GWP) and CO2. Extending the model to the future, the model suggests that the well-known IPCC SRES scenarios substantially underestimate how much CO2 levels will rise for a given level of future economic prosperity. For one, global CO2 emission rates cannot be decoupled from wealth through efficiency gains. For another, like a long-term natural disaster, future greenhouse warming can be expected to act as an inflationary drag on the real growth of global wealth. For atmospheric CO2 concentrations to remain below a "dangerous" level of 450 ppmv, model forecasts suggest that there will have to be some combination of an unrealistically rapid rate of energy decarbonization and nearly immediate reductions in global civilization wealth. Effectively, it appears that civilization may be in a double-bind. If civilization does not collapse quickly this century, then CO2 levels will likely end up exceeding 1000 ppmv; but, if CO2 levels rise by this much, then the risk is that civilization will gradually tend towards collapse.

physics.ao-ph↗

arXiv2011

How persistent is civilization growth?

In a recent study (Garrett, 2011), I described theoretical arguments and empirical evidence showing how civilization evolution might be considered from a purely physical basis. One implication is that civilization exhibits the property of persistence in its growth. Here, this argument is elaborated further, and specific near-term forecasts are provided for key economic variables and anthropogenic CO2 emission rates at global scales. Absent some external shock, civilization wealth, energy consumption and carbon dioxide emissions will continue to grow exponentially at an average rate of about 2.3% per year.

physics.soc-ph↗

arXiv2009

Are there basic physical constraints on future anthropogenic emissions of carbon dioxide?

Global Climate Models (GCMs) provide forecasts of future climate warming using a wide variety of highly sophisticated anthropogenic CO2 emissions models as input, each based on the evolution of four emissions "drivers": population p, standard of living g, energy productivity (or efficiency) f and energy carbonization c. The range of scenarios considered is extremely broad, however, and this is a primary source of forecast uncertainty. Here, it is shown both theoretically and observationally how the evolution of the human system can be considered from a surprisingly simple thermodynamic perspective in which it is unnecessary to explicitly model two of the emissions drivers: population and standard of living. Specifically, the human system grows through a self-perpetuating feedback loop in which the consumption rate of primary energy resources stays tied to the historical accumulation of global economic production - or p times g - through a time-independent factor of 9.7 +/- 0.3 milliwatts per inflation-adjusted 1990 US dollar. This important constraint, and the fact that f and c have historically varied rather slowly, points towards substantially narrowed visions of future emissions scenarios for implementation in GCMs.

physics.ao-ph↗