Articles | Volume 11, issue 1
https://doi.org/10.5194/esd-11-1-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esd-11-1-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
07 Jan 2020
Research article |
| 07 Jan 2020
| 07 Jan 2020
Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time
M. Levent Kavvas
CORRESPONDING AUTHOR
Hydrologic Research Laboratory, Department of Civil and Environmental Engineering, University of California, Davis, CA 95616, USA
Tongbi Tu
J. Amorocho Hydraulics Laboratory (JAHL), Department of Civil and
Environmental Engineering, University of California, Davis, CA 95616, USA
now at: Department of Environmental Science, Policy, and Management,
University of California, Berkeley, CA 94720, USA
Ali Ercan
J. Amorocho Hydraulics Laboratory (JAHL), Department of Civil and
Environmental Engineering, University of California, Davis, CA 95616, USA
James Polsinelli
Hydrologic Research Laboratory, Department of Civil and Environmental Engineering, University of California, Davis, CA 95616, USA
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A new method is proposed to solve the stochastic unsteady open-channel flow system in only one single simulation, as opposed to the many simulations usually done in the popular Monte Carlo approach. The derivation of this new method gave a deterministic and linear Fokker–Planck equation whose solution provided a powerful and effective approach for quantifying the ensemble behavior and variability of such a stochastic system, regardless of the number of parameters causing its uncertainty.
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A dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First a continuity equation for groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. An equation of water flux is also developed. The governing equation of transient groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained.
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A simple method is presented to model movement of water through soil in general conditions. Specifically, this method was designed to provide a rectangular profile approximation (e.g. the water moves through the soil like a piston) where the water content in the soil volumes is less than saturation. This method reverts to the classical saturated rectangular profile technique under heavy rainfall.
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Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2017-665, https://doi.org/10.5194/hess-2017-665, 2018
Preprint withdrawn
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Tongbi Tu, Ali Ercan, and M. Levent Kavvas
Earth Syst. Dynam., 8, 931–949, https://doi.org/10.5194/esd-8-931-2017, https://doi.org/10.5194/esd-8-931-2017, 2017
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Groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior, and the underlying distribution exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics. The estimated Hurst exponent is highly dependent on the length and the specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist.
M. Levent Kavvas, Tongbi Tu, Ali Ercan, and James Polsinelli
Earth Syst. Dynam., 8, 921–929, https://doi.org/10.5194/esd-8-921-2017, https://doi.org/10.5194/esd-8-921-2017, 2017
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A dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First a continuity equation for groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. An equation of water flux is also developed. The governing equation of transient groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained.
M. Levent Kavvas, Ali Ercan, and James Polsinelli
Hydrol. Earth Syst. Sci., 21, 1547–1557, https://doi.org/10.5194/hess-21-1547-2017, https://doi.org/10.5194/hess-21-1547-2017, 2017
Short summary
Short summary
In this study dimensionally consistent governing equations of continuity and motion for transient soil water flow and water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. By the introduction of the Brooks–Corey constitutive relationships, an explicit form of the equations is obtained. The developed governing equations, in their fractional time but integer space forms, show behavior consistent with the previous experimental observations.
Ali Ercan and M. Levent Kavvas
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2016-364, https://doi.org/10.5194/hess-2016-364, 2016
Manuscript not accepted for further review
Short summary
Short summary
A finite difference numerical approach is proposed to solve the time-space fractional governing equations of one-dimensional unsteady/non-uniform open channel flow process. Numerical simulations showed that flow discharge and water depth can exhibit heavier tails in downstream locations as space and time fractional derivative powers decrease from 1. The fractional governing equations under consideration are generalizations of the well-known Saint Venant equations.
James Polsinelli and M. Levent Kavvas
Hydrol. Earth Syst. Sci., 20, 2669–2678, https://doi.org/10.5194/hess-20-2669-2016, https://doi.org/10.5194/hess-20-2669-2016, 2016
Short summary
Short summary
This article summarizes the theory and demonstrates the technique of a new scaling method known as the Lie scaling. In the course of applying the method to two example problems, classical notions of dynamical and kinematic scaling are incorporated. The two example problems are a 2-D unconfined groundwater problem in a heterogeneous soil and a 1-D contaminant transport problem. The article concludes with comments on the relative strengths and weaknesses of Lie scaling and classical scaling.
James Polsinelli and M. Levent Kavvas
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2016-75, https://doi.org/10.5194/hess-2016-75, 2016
Revised manuscript has not been submitted
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A simple method is presented to model movement of water through soil in general conditions. Specifically, this method was designed to provide a rectangular profile approximation (e.g. the water moves through the soil like a piston) where the water content in the soil volumes is less than saturation. This method reverts to the classical saturated rectangular profile technique under heavy rainfall.
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Mikhail Y. Verbitsky and Michel Crucifix
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With the development of computer capacities, simpler models like energy balance models have not disappeared, and a stronger emphasis has been given to the concept of a hierarchy of models. The global temperature is calculated by the radiation budget through the incoming energy from the Sun and the outgoing energy from the Earth. The argument that the temperature can be calculated by a simple radiation budget is revisited, and it is found that the effective heat capacity matters.
Benjamin Sanderson
Earth Syst. Dynam., 11, 721–735, https://doi.org/10.5194/esd-11-721-2020, https://doi.org/10.5194/esd-11-721-2020, 2020
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Here, we assess the degree to which the idealized responses to transient forcing increase and step change forcing increase relate to warming under future scenarios. We find a possible explanation for the poor performance of transient metrics (relative to equilibrium response) as a metric of high-emission future warming in terms of their sensitivity to non-equilibrated initial conditions, and propose alternative metrics which better describe warming under high mitigation scenarios.
Benjamin Sanderson
Earth Syst. Dynam., 11, 563–577, https://doi.org/10.5194/esd-11-563-2020, https://doi.org/10.5194/esd-11-563-2020, 2020
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Levels of future temperature change are often used interchangeably with carbon budget allowances in climate policy, a relatively robust relationship on the timescale of this century. However, recent advances in understanding underline that continued warming after net-zero emissions have been achieved cannot be ruled out by observations of warming to date. We consider here how such behavior could be constrained and how policy can be framed in the context of these uncertainties.
Jonathan F. Donges, Jobst Heitzig, Wolfram Barfuss, Marc Wiedermann, Johannes A. Kassel, Tim Kittel, Jakob J. Kolb, Till Kolster, Finn Müller-Hansen, Ilona M. Otto, Kilian B. Zimmerer, and Wolfgang Lucht
Earth Syst. Dynam., 11, 395–413, https://doi.org/10.5194/esd-11-395-2020, https://doi.org/10.5194/esd-11-395-2020, 2020
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We present an open-source software framework for developing so-called
world–Earth modelsthat link physical, chemical and biological processes with social, economic and cultural processes to study the Earth system's future trajectories in the Anthropocene. Due to its modular structure, the software allows interdisciplinary studies of global change and sustainable development that combine stylized model components from Earth system science, climatology, economics, ecology and sociology.
Mikhail Y. Verbitsky and Michel Crucifix
Earth Syst. Dynam., 11, 281–289, https://doi.org/10.5194/esd-11-281-2020, https://doi.org/10.5194/esd-11-281-2020, 2020
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Using the central theorem of dimensional analysis, the π theorem, we show that the relationship between the amplitude and duration of glacial cycles is governed by a property of scale invariance that does not depend on the physical nature of the underlying positive and negative feedbacks incorporated by the system. It thus turns out to be one of the most fundamental properties of the Pleistocene climate.
Miguel D. Mahecha, Fabian Gans, Gunnar Brandt, Rune Christiansen, Sarah E. Cornell, Normann Fomferra, Guido Kraemer, Jonas Peters, Paul Bodesheim, Gustau Camps-Valls, Jonathan F. Donges, Wouter Dorigo, Lina M. Estupinan-Suarez, Victor H. Gutierrez-Velez, Martin Gutwin, Martin Jung, Maria C. Londoño, Diego G. Miralles, Phillip Papastefanou, and Markus Reichstein
Earth Syst. Dynam., 11, 201–234, https://doi.org/10.5194/esd-11-201-2020, https://doi.org/10.5194/esd-11-201-2020, 2020
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The ever-growing availability of data streams on different subsystems of the Earth brings unprecedented scientific opportunities. However, researching a data-rich world brings novel challenges. We present the concept of
Earth system data cubesto study the complex dynamics of multiple climate and ecosystem variables across space and time. Using a series of example studies, we highlight the potential of effectively considering the full multivariate nature of processes in the Earth system.
Christine Ramadhin and Chuixiang Yi
Earth Syst. Dynam., 11, 13–16, https://doi.org/10.5194/esd-11-13-2020, https://doi.org/10.5194/esd-11-13-2020, 2020
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Here we explore ancient climate transitions from warm periods to ice ages and from ice ages to warm periods of the last 400 000 years. The changeovers from warm to ice age conditions are slower than those from ice age to warm conditions. We propose the presence of strong negative sea–ice feedbacks may be responsible for slowing the transition from warm to full ice age conditions. By improving understanding of past abrupt changes, we may have improved knowledge of future system behavior.
Krishna-Pillai Sukumara-Pillai Krishnamohan, Govindasamy Bala, Long Cao, Lei Duan, and Ken Caldeira
Earth Syst. Dynam., 10, 885–900, https://doi.org/10.5194/esd-10-885-2019, https://doi.org/10.5194/esd-10-885-2019, 2019
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We find that sulfate aerosols are more effective in cooling the climate system when they reside higher in the stratosphere. We explain this sensitivity in terms of radiative forcing at the top of the atmosphere. Sulfate aerosols heat the stratospheric layers, causing an increase in stratospheric water vapor content and a reduction in high clouds. These changes are larger when aerosols are prescribed near the tropopause, offsetting part of the aerosol-induced negative radiative forcing/cooling.
Davide Faranda, Yuzuru Sato, Gabriele Messori, Nicholas R. Moloney, and Pascal Yiou
Earth Syst. Dynam., 10, 555–567, https://doi.org/10.5194/esd-10-555-2019, https://doi.org/10.5194/esd-10-555-2019, 2019
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We show how the complex dynamics of the jet stream at midlatitude can be described by a simple mathematical model. We match the properties of the model to those obtained by the jet data derived from observations.
Stefanie Talento, Lea Schneider, Johannes Werner, and Jürg Luterbacher
Earth Syst. Dynam., 10, 347–364, https://doi.org/10.5194/esd-10-347-2019, https://doi.org/10.5194/esd-10-347-2019, 2019
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Quantifying hydroclimate variability beyond the instrumental period is essential for putting fluctuations into long-term perspective and providing a validation for climate models. We evaluate, in a virtual setup, the potential for generating millennium-long summer precipitation reconstructions over south-eastern Asia.
We find that performing a real-world reconstruction with the current available proxy network is indeed feasible, as virtual-world reconstructions are skilful in most areas.
Lennert B. Stap, Peter Köhler, and Gerrit Lohmann
Earth Syst. Dynam., 10, 333–345, https://doi.org/10.5194/esd-10-333-2019, https://doi.org/10.5194/esd-10-333-2019, 2019
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Processes causing the same global-average radiative forcing might lead to different global temperature changes. We expand the theoretical framework by which we calculate paleoclimate sensitivity with an efficacy factor. Applying the revised approach to radiative forcing caused by CO2 and land ice albedo perturbations, inferred from data of the past 800 000 years, gives a new paleo-based estimate of climate sensitivity.
Luis Gimeno-Sotelo, Raquel Nieto, Marta Vázquez, and Luis Gimeno
Earth Syst. Dynam., 10, 121–133, https://doi.org/10.5194/esd-10-121-2019, https://doi.org/10.5194/esd-10-121-2019, 2019
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Ice melting at the scale of inter-annual fluctuations against the trend is favoured by an increase in moisture transport in summer, autumn, and winter and a decrease in spring. On a daily basis extreme humidity transport increases the formation of ice in winter and decreases it in spring, summer, and autumn; in these three seasons it thus contributes to Arctic sea ice melting. These patterns differ sharply from that linked to decline, especially in summer when the opposite trend applies.
Iago Algarra, Jorge Eiras-Barca, Gonzalo Miguez-Macho, Raquel Nieto, and Luis Gimeno
Earth Syst. Dynam., 10, 107–119, https://doi.org/10.5194/esd-10-107-2019, https://doi.org/10.5194/esd-10-107-2019, 2019
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We analyse moisture transport triggered by the Great Plains low-level jet (GPLLJ), a maximum in wind speed fields located within the first kilometre of the US Great Plain's troposphere, through the innovative Eulerian Weather Research and Forecasting Model tracer tool. Much moisture associated with this low-level jet has been found in northern regions located in a vast extension of the continent, highlighting the key role played by the GPLLJ in North America's advective transport of moisture.
Gerrit Lohmann
Earth Syst. Dynam., 9, 1279–1281, https://doi.org/10.5194/esd-9-1279-2018, https://doi.org/10.5194/esd-9-1279-2018, 2018
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Long-term sea surface temperature trends and variability are underestimated in models compared to paleoclimate data. The idea is presented that the trends and variability are related, which is elaborated in a conceptual model framework. The temperature spectrum can be used to estimate the timescale-dependent climate sensitivity.
Mark M. Dekker, Anna S. von der Heydt, and Henk A. Dijkstra
Earth Syst. Dynam., 9, 1243–1260, https://doi.org/10.5194/esd-9-1243-2018, https://doi.org/10.5194/esd-9-1243-2018, 2018
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We introduce a framework of cascading tipping, i.e. a sequence of abrupt transitions occurring because a transition in one system affects the background conditions of another system. Using bifurcation theory, various types of these events are considered and early warning indicators are suggested. An illustration of such an event is found in a conceptual model, coupling the North Atlantic Ocean with the equatorial Pacific. This demonstrates the possibility of events such as this in nature.
Uwe Mikolajewicz, Florian Ziemen, Guido Cioni, Martin Claussen, Klaus Fraedrich, Marvin Heidkamp, Cathy Hohenegger, Diego Jimenez de la Cuesta, Marie-Luise Kapsch, Alexander Lemburg, Thorsten Mauritsen, Katharina Meraner, Niklas Röber, Hauke Schmidt, Katharina D. Six, Irene Stemmler, Talia Tamarin-Brodsky, Alexander Winkler, Xiuhua Zhu, and Bjorn Stevens
Earth Syst. Dynam., 9, 1191–1215, https://doi.org/10.5194/esd-9-1191-2018, https://doi.org/10.5194/esd-9-1191-2018, 2018
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Model experiments show that changing the sense of Earth's rotation has relatively little impact on the globally and zonally averaged energy budgets but leads to large shifts in continental climates and patterns of precipitation. The retrograde world is greener as the desert area shrinks. Deep water formation shifts from the North Atlantic to the North Pacific with subsequent changes in ocean overturning. Over large areas of the Indian Ocean, cyanobacteria dominate over bulk phytoplankton.
Axel Kleidon and Maik Renner
Earth Syst. Dynam., 9, 1127–1140, https://doi.org/10.5194/esd-9-1127-2018, https://doi.org/10.5194/esd-9-1127-2018, 2018
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Turbulent fluxes represent an efficient way to transport heat and moisture from the surface into the atmosphere. Due to their inherently highly complex nature, they are commonly described by semiempirical relationships. What we show here is that these fluxes can also be predicted by viewing them as the outcome of a heat engine that operates between the warm surface and the cooler atmosphere and that works at its limit.
Marc Schleiss
Earth Syst. Dynam., 9, 955–968, https://doi.org/10.5194/esd-9-955-2018, https://doi.org/10.5194/esd-9-955-2018, 2018
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The present study aims at explaining how intermittency (i.e., the alternation of dry and rainy periods) affects the rate at which precipitation extremes increase with temperature. Using high-resolution rainfall data from 99 stations in the United States, we show that at scales beyond a few hours, intermittency causes rainfall extremes to deviate substantially from Clausius–Clapeyron. A new model is proposed to better represent and predict these changes across scales.
Ragnhild Bieltvedt Skeie, Terje Berntsen, Magne Aldrin, Marit Holden, and Gunnar Myhre
Earth Syst. Dynam., 9, 879–894, https://doi.org/10.5194/esd-9-879-2018, https://doi.org/10.5194/esd-9-879-2018, 2018
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A key question in climate science is how the global mean surface temperature responds to changes in greenhouse gases. This dependency is quantified by the climate sensitivity, which is determined by the complex feedbacks in the climate system. In this study observations of past climate change are used to estimate this sensitivity. Our estimate is consistent with values for the equilibrium climate sensitivity estimated by complex climate models but sensitive to the use of uncertain input data.
Dieter Gerten, Martin Schönfeld, and Bernhard Schauberger
Earth Syst. Dynam., 9, 849–863, https://doi.org/10.5194/esd-9-849-2018, https://doi.org/10.5194/esd-9-849-2018, 2018
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Cultural processes are underrepresented in Earth system models, although they decisively shape humanity’s planetary imprint. We set forth ideas on how Earth system analysis can be enriched by formalising aspects of religion (understood broadly as a collective belief in things held sacred). We sketch possible modelling avenues (extensions of existing Earth system models and new co-evolutionary models) and suggest research primers to explicate and quantify mental aspects of the Anthropocene.
Stefan Lange
Earth Syst. Dynam., 9, 627–645, https://doi.org/10.5194/esd-9-627-2018, https://doi.org/10.5194/esd-9-627-2018, 2018
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The bias correction of surface downwelling longwave and shortwave radiation using parametric quantile mapping methods is shown to be more effective (i) at the daily than at the monthly timescale, (ii) if the spatial resolution gap between the reference data and the data to be corrected is bridged in a more suitable manner than by bilinear interpolation, and (iii) if physical upper limits are taken into account during the adjustment of either radiation component.
Camilla Mathison, Chetan Deva, Pete Falloon, and Andrew J. Challinor
Earth Syst. Dynam., 9, 563–592, https://doi.org/10.5194/esd-9-563-2018, https://doi.org/10.5194/esd-9-563-2018, 2018
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Sowing and harvest dates are a significant source of uncertainty within crop models. South Asia is one region with a large uncertainty. We aim to provide more accurate sowing and harvest dates than currently available and that are relevant for climate impact assessments. This method reproduces the present day sowing and harvest dates for most parts of India and when applied to two future periods provides a useful way of modelling potential growing season adaptations to changes in future climate.
Dario A. Zappalà, Marcelo Barreiro, and Cristina Masoller
Earth Syst. Dynam., 9, 383–391, https://doi.org/10.5194/esd-9-383-2018, https://doi.org/10.5194/esd-9-383-2018, 2018
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The dynamics of our climate involves multiple timescales, and while a lot of work has been devoted to quantifying variations in time-averaged variables or variations in their seasonal cycles, variations in daily variability that occur over several decades still remain poorly understood. Here we analyse daily surface air temperature and demonstrate that inter-decadal changes can be precisely identified and quantified with the Hilbert analysis tool.
Nadine Mengis, David P. Keller, and Andreas Oschlies
Earth Syst. Dynam., 9, 15–31, https://doi.org/10.5194/esd-9-15-2018, https://doi.org/10.5194/esd-9-15-2018, 2018
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The Systematic Correlation Matrix Evaluation (SCoMaE) method applies statistical information to systematically select, transparent, nonredundant indicators for a comprehensive assessment of the Earth system state. We show that due to changing climate forcing, such as anthropogenic climate change, the ad hoc assessment indicators might need to be reevaluated. Within an iterative process, this method would allow us to select scientifically consistent and societally relevant assessment indicators.
Liga Bethere, Juris Sennikovs, and Uldis Bethers
Earth Syst. Dynam., 8, 951–962, https://doi.org/10.5194/esd-8-951-2017, https://doi.org/10.5194/esd-8-951-2017, 2017
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We define three new climate indices based on monthly mean temperature and total precipitation values that describe the main features of the climate in the Baltic states. Higher values in each index correspond to (1) less distinct seasonality and (2) warmer and (3) wetter climate. It was calculated that in the future all three indices will increase. Such indices summarize and illustrate the spatial features of the Baltic climate, and they can be used in further analysis of climate change impact.
Tongbi Tu, Ali Ercan, and M. Levent Kavvas
Earth Syst. Dynam., 8, 931–949, https://doi.org/10.5194/esd-8-931-2017, https://doi.org/10.5194/esd-8-931-2017, 2017
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Groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior, and the underlying distribution exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics. The estimated Hurst exponent is highly dependent on the length and the specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist.
Axel Kleidon and Maik Renner
Earth Syst. Dynam., 8, 849–864, https://doi.org/10.5194/esd-8-849-2017, https://doi.org/10.5194/esd-8-849-2017, 2017
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We provide an explanation why land temperatures respond more strongly to global warming than ocean temperatures, a robust finding in observations and models that has so far not been understood well. We explain it by the different ways by which ocean and land surfaces buffer the strong variation in solar radiation and demonstrate this with a simple, physically based model. Our explanation also illustrates why nighttime temperatures warm more strongly, another robust finding of global warming.
Milan Flach, Fabian Gans, Alexander Brenning, Joachim Denzler, Markus Reichstein, Erik Rodner, Sebastian Bathiany, Paul Bodesheim, Yanira Guanche, Sebastian Sippel, and Miguel D. Mahecha
Earth Syst. Dynam., 8, 677–696, https://doi.org/10.5194/esd-8-677-2017, https://doi.org/10.5194/esd-8-677-2017, 2017
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Anomalies and extremes are often detected using univariate peak-over-threshold approaches in the geoscience community. The Earth system is highly multivariate. We compare eight multivariate anomaly detection algorithms and combinations of data preprocessing. We identify three anomaly detection algorithms that outperform univariate extreme event detection approaches. The workflows have the potential to reveal novelties in data. Remarks on their application to real Earth observations are provided.
James Hansen, Makiko Sato, Pushker Kharecha, Karina von Schuckmann, David J. Beerling, Junji Cao, Shaun Marcott, Valerie Masson-Delmotte, Michael J. Prather, Eelco J. Rohling, Jeremy Shakun, Pete Smith, Andrew Lacis, Gary Russell, and Reto Ruedy
Earth Syst. Dynam., 8, 577–616, https://doi.org/10.5194/esd-8-577-2017, https://doi.org/10.5194/esd-8-577-2017, 2017
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Global temperature now exceeds +1.25 °C relative to 1880–1920, similar to warmth of the Eemian period. Keeping warming less than 1.5 °C or CO2 below 350 ppm now requires extraction of CO2 from the air. If rapid phaseout of fossil fuel emissions begins soon, most extraction can be via improved agricultural and forestry practices. In contrast, continued high emissions places a burden on young people of massive technological CO2 extraction with large risks, high costs and uncertain feasibility.
Marianne T. Lund, Borgar Aamaas, Terje Berntsen, Lisa Bock, Ulrike Burkhardt, Jan S. Fuglestvedt, and Keith P. Shine
Earth Syst. Dynam., 8, 547–563, https://doi.org/10.5194/esd-8-547-2017, https://doi.org/10.5194/esd-8-547-2017, 2017
Francine J. Schevenhoven and Frank M. Selten
Earth Syst. Dynam., 8, 429–438, https://doi.org/10.5194/esd-8-429-2017, https://doi.org/10.5194/esd-8-429-2017, 2017
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Weather and climate models have improved steadily over time, but the models remain imperfect. Given these imperfect models, predictions might be improved by combining the models into a so-called “supermodel”. In this paper we show a new method to construct such a supermodel. The results indicate that the supermodel has superior forecast quality compared to the individual models.
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Short summary
After deriving a fractional continuity equation, a previously-developed equation for water flux in porous media was combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. As demonstrated in the numerical application, the orders of the fractional space and time derivatives modulate the speed of groundwater table evolution, slowing the process with the decrease in the powers of the fractional derivatives from 1.
After deriving a fractional continuity equation, a previously-developed equation for water flux...
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