Articles | Volume 30, issue 3
https://doi.org/10.5194/npg-30-311-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-30-311-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Review article: Scaling, dynamical regimes, and stratification. How long does weather last? How big is a cloud?
Physics, McGill University, 3600 University st., Montreal, Que. H3A
2T8, Canada
Related authors
Nicolás Acuña Reyes, Elwin van't Wout, Shaun Lovejoy, and Fabrice Lambert
Clim. Past, 20, 1579–1594, https://doi.org/10.5194/cp-20-1579-2024, https://doi.org/10.5194/cp-20-1579-2024, 2024
Short summary
Short summary
This study employs Haar fluctuations to analyse global atmospheric variability over the Last Glacial Cycle, revealing a latitudinal dependency in the transition from macroweather to climate regimes. Findings indicate faster synchronisation between poles and lower latitudes, supporting the pivotal role of poles as climate change drivers.
Shaun Lovejoy
Nonlin. Processes Geophys., 29, 93–121, https://doi.org/10.5194/npg-29-93-2022, https://doi.org/10.5194/npg-29-93-2022, 2022
Short summary
Short summary
The difference between the energy that the Earth receives from the Sun and the energy it emits as black-body radiation is stored in a scaling hierarchy of structures in the ocean, soil and hydrosphere. The simplest scaling storage model leads to the fractional energy balance equation (FEBE). We examine the statistical properties of FEBE when it is driven by random fluctuations. In this paper, we explore the statistical properties of this mathematically simple yet neglected equation.
Roman Procyk, Shaun Lovejoy, and Raphael Hébert
Earth Syst. Dynam., 13, 81–107, https://doi.org/10.5194/esd-13-81-2022, https://doi.org/10.5194/esd-13-81-2022, 2022
Short summary
Short summary
This paper presents a new class of energy balance model that accounts for the long memory within the Earth's energy storage. The model is calibrated on instrumental temperature records and the historical energy budget of the Earth using an error model predicted by the model itself. Our equilibrium climate sensitivity and future temperature projection estimates are consistent with those estimated by complex climate models.
Shaun Lovejoy
Earth Syst. Dynam., 12, 469–487, https://doi.org/10.5194/esd-12-469-2021, https://doi.org/10.5194/esd-12-469-2021, 2021
Short summary
Short summary
Monthly scale, seasonal-scale, and decadal-scale modeling of the atmosphere is possible using the principle of energy balance. Yet the scope of classical approaches is limited because they do not adequately deal with energy storage in the Earth system. We show that the introduction of a vertical coordinate implies that the storage has a huge memory. This memory can be used for macroweather (long-range) forecasts and climate projections.
Shaun Lovejoy
Earth Syst. Dynam., 12, 489–511, https://doi.org/10.5194/esd-12-489-2021, https://doi.org/10.5194/esd-12-489-2021, 2021
Short summary
Short summary
Radiant energy is exchanged between the Earth's surface and outer space. Some of the local imbalances are stored in the subsurface, and some are transported horizontally. In Part 1 I showed how – in a horizontally homogeneous Earth – these classical approaches imply long-memory storage useful for seasonal forecasting and multidecadal projections. In this Part 2, I show how to apply these results to the heterogeneous real Earth.
Shaun Lovejoy and Fabrice Lambert
Clim. Past, 15, 1999–2017, https://doi.org/10.5194/cp-15-1999-2019, https://doi.org/10.5194/cp-15-1999-2019, 2019
Short summary
Short summary
We analyze the statistical properties of the eight past glacial–interglacial cycles as well as subsections of a generic glacial cycle using the high-resolution dust flux dataset from the Antarctic EPICA Dome C ice core. We show that the high southern latitude climate during glacial maxima, interglacial, and glacial inception is generally more stable but more drought-prone than during mid-glacial conditions.
Shaun Lovejoy and Fabrice Lambert
Clim. Past Discuss., https://doi.org/10.5194/cp-2018-110, https://doi.org/10.5194/cp-2018-110, 2018
Manuscript not accepted for further review
Short summary
Short summary
The Holocene has been strikingly long and stable when compared to earlier interglacials, and some have argued that the Holocene's exceptional stability permitted the development of agriculture and the spread of civilization. We characterize the past 800 000 years using a high resolution dust record from an Antarctic ice core. We find that although the Holocene is particularly stable when compared to other interglacials, it is not an outlier and other factors may have kickstarted civilization.
Shaun Lovejoy and Costas Varotsos
Earth Syst. Dynam., 7, 133–150, https://doi.org/10.5194/esd-7-133-2016, https://doi.org/10.5194/esd-7-133-2016, 2016
Short summary
Short summary
We compare the statistical properties of solar, volcanic and combined forcings over the range from 1 to 1000 years to see over which scale ranges they additively combine, a prediction of linear response. The main findings are (a) that the variability in the Zebiac–Cane model and GCMs are too weak at centennial and longer scales; (b) for longer than ≈ 50 years, the forcings combine subadditively; and (c) at shorter scales, strong (intermittency, e.g. volcanic) forcings are nonlinear.
F. Landais, F. Schmidt, and S. Lovejoy
Nonlin. Processes Geophys., 22, 713–722, https://doi.org/10.5194/npg-22-713-2015, https://doi.org/10.5194/npg-22-713-2015, 2015
Short summary
Short summary
In the present study, we investigate the scaling properties of the topography of Mars. Planetary topographic fields are well known to exhibit (mono)fractal behavior. Indeed, fractal formalism is efficient in reproducing the variability observed in topography. Our results suggest a multifractal behavior from the planetary scale down to 10 km. From 10 km to 300 m, the topography seems to be simple monofractal.
S. Lovejoy, L. del Rio Amador, and R. Hébert
Earth Syst. Dynam., 6, 637–658, https://doi.org/10.5194/esd-6-637-2015, https://doi.org/10.5194/esd-6-637-2015, 2015
Short summary
Short summary
Numerical climate models forecast the weather well beyond the deterministic limit. In this “macroweather” regime, they are random number generators. Stochastic models can have more realistic noises and can be forced to converge to the real-world climate. Existing stochastic models do not exploit the very long atmospheric and oceanic memories. With skill up to decades, our new ScaLIng Macroweather Model (SLIMM) exploits this to make forecasts more accurate than GCMs.
C. A. Varotsos, S. Lovejoy, N. V. Sarlis, C. G. Tzanis, and M. N. Efstathiou
Atmos. Chem. Phys., 15, 7301–7306, https://doi.org/10.5194/acp-15-7301-2015, https://doi.org/10.5194/acp-15-7301-2015, 2015
Short summary
Short summary
Varotsos et al. (Theor. Appl. Climatol., 114, 725–727, 2013) found that the solar ultraviolet (UV) wavelengths exhibit 1/f-type power-law correlations. In this study, we show that the residues of the spectral solar incident flux with respect to the Planck law over a wider range of wavelengths (i.e. UV-visible) have a scaling regime too.
J. Pinel and S. Lovejoy
Atmos. Chem. Phys., 14, 3195–3210, https://doi.org/10.5194/acp-14-3195-2014, https://doi.org/10.5194/acp-14-3195-2014, 2014
G. A. Schmidt, J. D. Annan, P. J. Bartlein, B. I. Cook, E. Guilyardi, J. C. Hargreaves, S. P. Harrison, M. Kageyama, A. N. LeGrande, B. Konecky, S. Lovejoy, M. E. Mann, V. Masson-Delmotte, C. Risi, D. Thompson, A. Timmermann, L.-B. Tremblay, and P. Yiou
Clim. Past, 10, 221–250, https://doi.org/10.5194/cp-10-221-2014, https://doi.org/10.5194/cp-10-221-2014, 2014
S. Lovejoy, D. Schertzer, and D. Varon
Earth Syst. Dynam., 4, 439–454, https://doi.org/10.5194/esd-4-439-2013, https://doi.org/10.5194/esd-4-439-2013, 2013
A. Gires, I. Tchiguirinskaia, D. Schertzer, and S. Lovejoy
Nonlin. Processes Geophys., 20, 343–356, https://doi.org/10.5194/npg-20-343-2013, https://doi.org/10.5194/npg-20-343-2013, 2013
Nicolás Acuña Reyes, Elwin van't Wout, Shaun Lovejoy, and Fabrice Lambert
Clim. Past, 20, 1579–1594, https://doi.org/10.5194/cp-20-1579-2024, https://doi.org/10.5194/cp-20-1579-2024, 2024
Short summary
Short summary
This study employs Haar fluctuations to analyse global atmospheric variability over the Last Glacial Cycle, revealing a latitudinal dependency in the transition from macroweather to climate regimes. Findings indicate faster synchronisation between poles and lower latitudes, supporting the pivotal role of poles as climate change drivers.
Shaun Lovejoy
Nonlin. Processes Geophys., 29, 93–121, https://doi.org/10.5194/npg-29-93-2022, https://doi.org/10.5194/npg-29-93-2022, 2022
Short summary
Short summary
The difference between the energy that the Earth receives from the Sun and the energy it emits as black-body radiation is stored in a scaling hierarchy of structures in the ocean, soil and hydrosphere. The simplest scaling storage model leads to the fractional energy balance equation (FEBE). We examine the statistical properties of FEBE when it is driven by random fluctuations. In this paper, we explore the statistical properties of this mathematically simple yet neglected equation.
Roman Procyk, Shaun Lovejoy, and Raphael Hébert
Earth Syst. Dynam., 13, 81–107, https://doi.org/10.5194/esd-13-81-2022, https://doi.org/10.5194/esd-13-81-2022, 2022
Short summary
Short summary
This paper presents a new class of energy balance model that accounts for the long memory within the Earth's energy storage. The model is calibrated on instrumental temperature records and the historical energy budget of the Earth using an error model predicted by the model itself. Our equilibrium climate sensitivity and future temperature projection estimates are consistent with those estimated by complex climate models.
Shaun Lovejoy
Earth Syst. Dynam., 12, 469–487, https://doi.org/10.5194/esd-12-469-2021, https://doi.org/10.5194/esd-12-469-2021, 2021
Short summary
Short summary
Monthly scale, seasonal-scale, and decadal-scale modeling of the atmosphere is possible using the principle of energy balance. Yet the scope of classical approaches is limited because they do not adequately deal with energy storage in the Earth system. We show that the introduction of a vertical coordinate implies that the storage has a huge memory. This memory can be used for macroweather (long-range) forecasts and climate projections.
Shaun Lovejoy
Earth Syst. Dynam., 12, 489–511, https://doi.org/10.5194/esd-12-489-2021, https://doi.org/10.5194/esd-12-489-2021, 2021
Short summary
Short summary
Radiant energy is exchanged between the Earth's surface and outer space. Some of the local imbalances are stored in the subsurface, and some are transported horizontally. In Part 1 I showed how – in a horizontally homogeneous Earth – these classical approaches imply long-memory storage useful for seasonal forecasting and multidecadal projections. In this Part 2, I show how to apply these results to the heterogeneous real Earth.
Shaun Lovejoy and Fabrice Lambert
Clim. Past, 15, 1999–2017, https://doi.org/10.5194/cp-15-1999-2019, https://doi.org/10.5194/cp-15-1999-2019, 2019
Short summary
Short summary
We analyze the statistical properties of the eight past glacial–interglacial cycles as well as subsections of a generic glacial cycle using the high-resolution dust flux dataset from the Antarctic EPICA Dome C ice core. We show that the high southern latitude climate during glacial maxima, interglacial, and glacial inception is generally more stable but more drought-prone than during mid-glacial conditions.
Shaun Lovejoy and Fabrice Lambert
Clim. Past Discuss., https://doi.org/10.5194/cp-2018-110, https://doi.org/10.5194/cp-2018-110, 2018
Manuscript not accepted for further review
Short summary
Short summary
The Holocene has been strikingly long and stable when compared to earlier interglacials, and some have argued that the Holocene's exceptional stability permitted the development of agriculture and the spread of civilization. We characterize the past 800 000 years using a high resolution dust record from an Antarctic ice core. We find that although the Holocene is particularly stable when compared to other interglacials, it is not an outlier and other factors may have kickstarted civilization.
Shaun Lovejoy and Costas Varotsos
Earth Syst. Dynam., 7, 133–150, https://doi.org/10.5194/esd-7-133-2016, https://doi.org/10.5194/esd-7-133-2016, 2016
Short summary
Short summary
We compare the statistical properties of solar, volcanic and combined forcings over the range from 1 to 1000 years to see over which scale ranges they additively combine, a prediction of linear response. The main findings are (a) that the variability in the Zebiac–Cane model and GCMs are too weak at centennial and longer scales; (b) for longer than ≈ 50 years, the forcings combine subadditively; and (c) at shorter scales, strong (intermittency, e.g. volcanic) forcings are nonlinear.
F. Landais, F. Schmidt, and S. Lovejoy
Nonlin. Processes Geophys., 22, 713–722, https://doi.org/10.5194/npg-22-713-2015, https://doi.org/10.5194/npg-22-713-2015, 2015
Short summary
Short summary
In the present study, we investigate the scaling properties of the topography of Mars. Planetary topographic fields are well known to exhibit (mono)fractal behavior. Indeed, fractal formalism is efficient in reproducing the variability observed in topography. Our results suggest a multifractal behavior from the planetary scale down to 10 km. From 10 km to 300 m, the topography seems to be simple monofractal.
S. Lovejoy, L. del Rio Amador, and R. Hébert
Earth Syst. Dynam., 6, 637–658, https://doi.org/10.5194/esd-6-637-2015, https://doi.org/10.5194/esd-6-637-2015, 2015
Short summary
Short summary
Numerical climate models forecast the weather well beyond the deterministic limit. In this “macroweather” regime, they are random number generators. Stochastic models can have more realistic noises and can be forced to converge to the real-world climate. Existing stochastic models do not exploit the very long atmospheric and oceanic memories. With skill up to decades, our new ScaLIng Macroweather Model (SLIMM) exploits this to make forecasts more accurate than GCMs.
C. A. Varotsos, S. Lovejoy, N. V. Sarlis, C. G. Tzanis, and M. N. Efstathiou
Atmos. Chem. Phys., 15, 7301–7306, https://doi.org/10.5194/acp-15-7301-2015, https://doi.org/10.5194/acp-15-7301-2015, 2015
Short summary
Short summary
Varotsos et al. (Theor. Appl. Climatol., 114, 725–727, 2013) found that the solar ultraviolet (UV) wavelengths exhibit 1/f-type power-law correlations. In this study, we show that the residues of the spectral solar incident flux with respect to the Planck law over a wider range of wavelengths (i.e. UV-visible) have a scaling regime too.
J. Pinel and S. Lovejoy
Atmos. Chem. Phys., 14, 3195–3210, https://doi.org/10.5194/acp-14-3195-2014, https://doi.org/10.5194/acp-14-3195-2014, 2014
G. A. Schmidt, J. D. Annan, P. J. Bartlein, B. I. Cook, E. Guilyardi, J. C. Hargreaves, S. P. Harrison, M. Kageyama, A. N. LeGrande, B. Konecky, S. Lovejoy, M. E. Mann, V. Masson-Delmotte, C. Risi, D. Thompson, A. Timmermann, L.-B. Tremblay, and P. Yiou
Clim. Past, 10, 221–250, https://doi.org/10.5194/cp-10-221-2014, https://doi.org/10.5194/cp-10-221-2014, 2014
S. Lovejoy, D. Schertzer, and D. Varon
Earth Syst. Dynam., 4, 439–454, https://doi.org/10.5194/esd-4-439-2013, https://doi.org/10.5194/esd-4-439-2013, 2013
A. Gires, I. Tchiguirinskaia, D. Schertzer, and S. Lovejoy
Nonlin. Processes Geophys., 20, 343–356, https://doi.org/10.5194/npg-20-343-2013, https://doi.org/10.5194/npg-20-343-2013, 2013
Related subject area
Subject: Scaling, multifractals, turbulence, complex systems, self-organized criticality | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere | Techniques: Theory
A global analysis of the fractal properties of clouds revealing anisotropy of turbulence across scales
Stieltjes functions and spectral analysis in the physics of sea ice
Brief communication: Climate science as a social process – history, climatic determinism, Mertonian norms and post-normality
Characteristics of intrinsic non-stationarity and its effect on eddy-covariance measurements of CO2 fluxes
How many modes are needed to predict climate bifurcations? Lessons from an experiment
Non-linear hydrologic organization
The impact of entrained air on ocean waves
Approximate multifractal correlation and products of universal multifractal fields, with application to rainfall data
Karlie N. Rees, Timothy J. Garrett, Thomas D. DeWitt, Corey Bois, Steven K. Krueger, and Jérôme C. Riedi
EGUsphere, https://doi.org/10.5194/egusphere-2024-552, https://doi.org/10.5194/egusphere-2024-552, 2024
Short summary
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The shapes of clouds viewed from space reflect both vertical and horizontal motions in the atmosphere. The turbulence that shapes clouds is similarly described and related theoretically to the measured complexity of cloud perimeters from various satellites and a numerical model. We find agreement between theory and observations, and, remarkably, that the theory applies globally using only basic planetary physical parameters from the smallest scales of turbulence to the planetary scale.
Kenneth M. Golden, N. Benjamin Murphy, Daniel Hallman, and Elena Cherkaev
Nonlin. Processes Geophys., 30, 527–552, https://doi.org/10.5194/npg-30-527-2023, https://doi.org/10.5194/npg-30-527-2023, 2023
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Our paper tours powerful methods of finding the effective behavior of complex systems, which can be applied well beyond the initial setting of sea ice. Applications include transport properties of porous and polycrystalline media, such as rocks and glacial ice, and advection diffusion processes that arise throughout geophysics. Connections to random matrix theory establish unexpected parallels of these geophysical problems with semiconductor physics and Anderson localization phenomena.
Hans von Storch
Nonlin. Processes Geophys., 30, 31–36, https://doi.org/10.5194/npg-30-31-2023, https://doi.org/10.5194/npg-30-31-2023, 2023
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Climate science is, as all sciences, a social process and as such conditioned by the zeitgeist of the time. It has an old history and has attained different political significances. Today, it is the challenge of anthropogenic climate change – and societies want answers about how to deal with it. In earlier times, it was mostly the ideology of climate determinism which led people to construct superiority and eventually colonialism.
Lei Liu, Yu Shi, and Fei Hu
Nonlin. Processes Geophys., 29, 123–131, https://doi.org/10.5194/npg-29-123-2022, https://doi.org/10.5194/npg-29-123-2022, 2022
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We find a new kind of non-stationarity. This new kind of non-stationarity is caused by the intrinsic randomness. Results show that the new kind of non-stationarity is widespread in small-scale variations of CO2 turbulent fluxes. This finding reminds us that we need to handle the short-term averaged turbulent fluxes carefully, and we also need to re-screen the existing non-stationarity diagnosis methods because they could make a wrong diagnosis due to this new kind of non-stationarity.
Bérengère Dubrulle, François Daviaud, Davide Faranda, Louis Marié, and Brice Saint-Michel
Nonlin. Processes Geophys., 29, 17–35, https://doi.org/10.5194/npg-29-17-2022, https://doi.org/10.5194/npg-29-17-2022, 2022
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Present climate models discuss climate change but show no sign of bifurcation in the future. Is this because there is none or because they are in essence too simplified to be able to capture them? To get elements of an answer, we ran a laboratory experiment and discovered that the answer is not so simple.
Allen Hunt, Boris Faybishenko, and Behzad Ghanbarian
Nonlin. Processes Geophys., 28, 599–614, https://doi.org/10.5194/npg-28-599-2021, https://doi.org/10.5194/npg-28-599-2021, 2021
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The same power law we previously used to quantify growth of tree roots in time describes equally the assemblage of river networks in time. Even the basic length scale of both networks is the same. The one difference is that the basic time scale is ca. 10 times shorter for drainage networks than for tree roots, since the relevant flow rate is 10 times faster. This result overturns the understanding of drainage networks and forms a basis to organize thoughts about surface and subsurface hydrology.
Juan M. Restrepo, Alex Ayet, and Luigi Cavaleri
Nonlin. Processes Geophys., 28, 285–293, https://doi.org/10.5194/npg-28-285-2021, https://doi.org/10.5194/npg-28-285-2021, 2021
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A homogenization of Navier–Stokes to wave scales allows us to determine that air bubbles suspended near the ocean surface modify the momentum equation, specifically enhancing the vorticity in the flow. A model was derived that relates the rain rate to the production of air bubbles near the ocean surface. At wave scales, the air bubbles enhance the wave dissipation for small gravity or capillary waves.
Auguste Gires, Ioulia Tchiguirinskaia, and Daniel Schertzer
Nonlin. Processes Geophys., 27, 133–145, https://doi.org/10.5194/npg-27-133-2020, https://doi.org/10.5194/npg-27-133-2020, 2020
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This paper aims to analyse and simulate correlations between two fields in a scale-invariant framework. It starts by theoretically assessing and numerically confirming the behaviour of renormalized multiplicative power law combinations of two fields with known scale-invariant properties. Then a new indicator of correlation is suggested and tested on rainfall data to study the correlation between the common rain rate and drop size distribution features.
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Short summary
How big is a cloud?and
How long does the weather last?require scaling to answer. We review the advances in scaling that have occurred over the last 4 decades: (a) intermittency (multifractality) and (b) stratified and rotating scaling notions (generalized scale invariance). Although scaling theory and the data are now voluminous, atmospheric phenomena are too often viewed through an outdated scalebound lens, and turbulence remains confined to isotropic theories of little relevance.
How big is a cloud?and
How long does the weather last?require scaling to answer. We review the...