Articles | Volume 8, issue 4
https://doi.org/10.5194/esd-8-921-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Special issue:
https://doi.org/10.5194/esd-8-921-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
16 Oct 2017
Research article |
| 16 Oct 2017
Fractional governing equations of transient groundwater flow in confined 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
Hydrologic Research Laboratory, Department of Civil and Environmental Engineering, University of California, Davis, CA 95616, USA
Ali Ercan
Hydrologic Research Laboratory, 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
Related authors
M. Levent Kavvas, Tongbi Tu, Ali Ercan, and James Polsinelli
Earth Syst. Dynam., 11, 1–12, https://doi.org/10.5194/esd-11-1-2020, https://doi.org/10.5194/esd-11-1-2020, 2020
Short summary
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.
Alain Dib and M. Levent Kavvas
Hydrol. Earth Syst. Sci., 22, 1993–2005, https://doi.org/10.5194/hess-22-1993-2018, https://doi.org/10.5194/hess-22-1993-2018, 2018
Short summary
Short summary
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.
Alain Dib and M. Levent Kavvas
Hydrol. Earth Syst. Sci., 22, 2007–2021, https://doi.org/10.5194/hess-22-2007-2018, https://doi.org/10.5194/hess-22-2007-2018, 2018
Short summary
Short summary
A newly proposed method is applied to solve a stochastic unsteady open-channel flow system (with an uncertain roughness coefficient) in only one simulation. After comparing its results to those of the Monte Carlo simulations, the new method was found to adequately predict the temporal and spatial evolution of the probability density of the flow variables of the system. This revealed the effectiveness, strength, and time efficiency of this new method as compared to other popular approaches.
Mathieu Mure-Ravaud, Alain Dib, M. Levent Kavvas, and Elena Yegorova
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2017-665, https://doi.org/10.5194/hess-2017-665, 2018
Preprint withdrawn
Short summary
Short summary
This article introduces a new storm transposition method designed for the transposition (i.e. spatial shifting) of Tropical Cyclones (TCs). This method is based on the shifting of the initial vortex of the TC at the simulation start date. The objective of this method is to find the amount of shift which maximizes the precipitation depth over a given target area. The transposition method was applied to four hurricanes that had spawned torrential precipitation in the United States.
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
Short summary
Short summary
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, 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
Short summary
Short summary
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.
Tongtiegang Zhao, Haoling Chen, Quanxi Shao, Tongbi Tu, Yu Tian, and Xiaohong Chen
Hydrol. Earth Syst. Sci., 25, 5717–5732, https://doi.org/10.5194/hess-25-5717-2021, https://doi.org/10.5194/hess-25-5717-2021, 2021
Short summary
Short summary
This paper develops a novel approach to attributing correlation skill of dynamical GCM forecasts to statistical El Niño–Southern Oscillation (ENSO) teleconnection using the coefficient of determination. Three cases of attribution are effectively facilitated, which are significantly positive anomaly correlation attributable to positive ENSO teleconnection, attributable to negative ENSO teleconnection and not attributable to ENSO teleconnection.
M. Levent Kavvas, Tongbi Tu, Ali Ercan, and James Polsinelli
Earth Syst. Dynam., 11, 1–12, https://doi.org/10.5194/esd-11-1-2020, https://doi.org/10.5194/esd-11-1-2020, 2020
Short summary
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.
Alain Dib and M. Levent Kavvas
Hydrol. Earth Syst. Sci., 22, 1993–2005, https://doi.org/10.5194/hess-22-1993-2018, https://doi.org/10.5194/hess-22-1993-2018, 2018
Short summary
Short summary
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.
Alain Dib and M. Levent Kavvas
Hydrol. Earth Syst. Sci., 22, 2007–2021, https://doi.org/10.5194/hess-22-2007-2018, https://doi.org/10.5194/hess-22-2007-2018, 2018
Short summary
Short summary
A newly proposed method is applied to solve a stochastic unsteady open-channel flow system (with an uncertain roughness coefficient) in only one simulation. After comparing its results to those of the Monte Carlo simulations, the new method was found to adequately predict the temporal and spatial evolution of the probability density of the flow variables of the system. This revealed the effectiveness, strength, and time efficiency of this new method as compared to other popular approaches.
Mathieu Mure-Ravaud, Alain Dib, M. Levent Kavvas, and Elena Yegorova
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2017-665, https://doi.org/10.5194/hess-2017-665, 2018
Preprint withdrawn
Short summary
Short summary
This article introduces a new storm transposition method designed for the transposition (i.e. spatial shifting) of Tropical Cyclones (TCs). This method is based on the shifting of the initial vortex of the TC at the simulation start date. The objective of this method is to find the amount of shift which maximizes the precipitation depth over a given target area. The transposition method was applied to four hurricanes that had spawned torrential precipitation in the United States.
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
Short summary
Short summary
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, 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
Short summary
Short summary
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.
Related subject area
Dynamics of the Earth system: models
Regime-oriented causal model evaluation of Atlantic–Pacific teleconnections in CMIP6
Seasonal forecasting skill for the High Mountain Asia region in the Goddard Earth Observing System
Assessing sensitivities of climate model weighting to multiple methods, variables, and domains in the south-central United States
Global and northern-high-latitude net ecosystem production in the 21st century from CMIP6 experiments
Potential for bias in effective climate sensitivity from state-dependent energetic imbalance
Regional dynamical and statistical downscaling temperature, humidity and wind speed for the Beijing region under stratospheric aerosol injection geoengineering
Process-based estimate of global-mean sea-level changes in the Common Era
Present and future European heat wave magnitudes: climatologies, trends, and their associated uncertainties in GCM-RCM model chains
Improving the prediction of the Madden–Julian Oscillation of the ECMWF model by post-processing
The future of the El Niño-Southern Oscillation: Using large ensembles to illuminate time-varying responses and inter-model differences
Estimating the lateral transfer of organic carbon through the European river network using a land surface model
Effect of the Atlantic Meridional Overturning Circulation on atmospheric pCO2 variations
A methodology for the spatiotemporal identification of compound hazards: wind and precipitation extremes in Great Britain (1979–2019)
MESMER-M: an Earth system model emulator for spatially resolved monthly temperature
Evaluation of convection-permitting extreme precipitation simulations for the south of France
Agricultural management effects on mean and extreme temperature trends
Weakened impact of the Atlantic Niño on the future equatorial Atlantic and Guinea Coast rainfall
The fractional energy balance equation for climate projections through 2100
Climate change in the High Mountain Asia in CMIP6
The sensitivity of the El Niño–Southern Oscillation to volcanic aerosol spatial distribution in the MPI Grand Ensemble
Coupled regional Earth system modeling in the Baltic Sea region
Climate change projections of terrestrial primary productivity over the Hindu Kush Himalayan forests
Bookkeeping estimates of the net land-use change flux – a sensitivity study with the CMIP6 land-use dataset
Climate-controlled root zone parameters show potential to improve water flux simulations by land surface models
Space–time dependence of compound hot–dry events in the United States: assessment using a multi-site multi-variable weather generator
First assessment of the earth heat inventory within CMIP5 historical simulations
The thermal response of small and shallow lakes to climate change: new insights from 3D hindcast modelling
Labrador Sea subsurface density as a precursor of multidecadal variability in the North Atlantic: a multi-model study
How modelling paradigms affect simulated future land use change
Identifying meteorological drivers of extreme impacts: an application to simulated crop yields
Simulating compound weather extremes responsible for critical crop failure with stochastic weather generators
Characterisation of Atlantic meridional overturning hysteresis using Langevin dynamics
Evaluating the dependence structure of compound precipitation and wind speed extremes
Future sea level contribution from Antarctica inferred from CMIP5 model forcing and its dependence on precipitation ansatz
The extremely warm summer of 2018 in Sweden – set in a historical context
Effect of changing ocean circulation on deep ocean temperature in the last millennium
How large does a large ensemble need to be?
Reconstructing coupled time series in climate systems using three kinds of machine-learning methods
An investigation of weighting schemes suitable for incorporating large ensembles into multi-model ensembles
What could we learn about climate sensitivity from variability in the surface temperature record?
Using a nested single-model large ensemble to assess the internal variability of the North Atlantic Oscillation and its climatic implications for central Europe
Climate change in a conceptual atmosphere–phytoplankton model
Variability of surface climate in simulations of past and future
Statistical estimation of global surface temperature response to forcing under the assumption of temporal scaling
Emulating Earth system model temperatures with MESMER: from global mean temperature trajectories to grid-point-level realizations on land
A global semi-empirical glacial isostatic adjustment (GIA) model based on Gravity Recovery and Climate Experiment (GRACE) data
Improvement in the decadal prediction skill of the North Atlantic extratropical winter circulation through increased model resolution
Societal breakdown as an emergent property of large-scale behavioural models of land use change
Improving weather and climate predictions by training of supermodels
Evaluating climate emulation: fundamental impulse testing of simple climate models
Soufiane Karmouche, Evgenia Galytska, Jakob Runge, Gerald A. Meehl, Adam S. Phillips, Katja Weigel, and Veronika Eyring
Earth Syst. Dynam., 14, 309–344, https://doi.org/10.5194/esd-14-309-2023, https://doi.org/10.5194/esd-14-309-2023, 2023
Short summary
Short summary
This study uses a causal discovery method to evaluate the ability of climate models to represent the interactions between the Atlantic multidecadal variability (AMV) and the Pacific decadal variability (PDV). The approach and findings in this study present a powerful methodology that can be applied to a number of environment-related topics, offering tremendous insights to improve the understanding of the complex Earth system and the state of the art of climate modeling.
Elias C. Massoud, Lauren Andrews, Rolf Reichle, Andrea Molod, Jongmin Park, Sophie Ruehr, and Manuela Girotto
Earth Syst. Dynam., 14, 147–171, https://doi.org/10.5194/esd-14-147-2023, https://doi.org/10.5194/esd-14-147-2023, 2023
Short summary
Short summary
In this study, we benchmark the forecast skill of the NASA’s Goddard Earth Observing System subseasonal-to-seasonal (GEOS-S2S version 2) hydrometeorological forecasts in the High Mountain Asia (HMA) region. Hydrometeorological forecast skill is dependent on the forecast lead time, the memory of the variable within the physical system, and the validation dataset used. Overall, these results benchmark the GEOS-S2S system’s ability to forecast HMA hydrometeorology on the seasonal timescale.
Adrienne M. Wootten, Elias C. Massoud, Duane E. Waliser, and Huikyo Lee
Earth Syst. Dynam., 14, 121–145, https://doi.org/10.5194/esd-14-121-2023, https://doi.org/10.5194/esd-14-121-2023, 2023
Short summary
Short summary
Climate projections and multi-model ensemble weighting are increasingly used for climate assessments. This study examines the sensitivity of projections to multi-model ensemble weighting strategies in the south-central United States. Model weighting and ensemble means are sensitive to the domain and variable used. There are numerous findings regarding the improvement in skill with model weighting and the sensitivity associated with various strategies.
Han Qiu, Dalei Hao, Yelu Zeng, Xuesong Zhang, and Min Chen
Earth Syst. Dynam., 14, 1–16, https://doi.org/10.5194/esd-14-1-2023, https://doi.org/10.5194/esd-14-1-2023, 2023
Short summary
Short summary
The carbon cycling in terrestrial ecosystems is complex. In our analyses, we found that both the global and the northern-high-latitude (NHL) ecosystems will continue to have positive net ecosystem production (NEP) in the next few decades under four global change scenarios but with large uncertainties. NHL ecosystems will experience faster climate warming but steadily contribute a small fraction of the global NEP. However, the relative uncertainty of NHL NEP is much larger than the global values.
Benjamin M. Sanderson and Maria Rugenstein
Earth Syst. Dynam., 13, 1715–1736, https://doi.org/10.5194/esd-13-1715-2022, https://doi.org/10.5194/esd-13-1715-2022, 2022
Short summary
Short summary
Equilibrium climate sensitivity (ECS) is a measure of how much long-term warming should be expected in response to a change in greenhouse gas concentrations. It is generally calculated in climate models by extrapolating global average temperatures to a point of where the planet is no longer a net absorber of energy. Here we show that some climate models experience energy leaks which change as the planet warms, undermining the standard approach and biasing some existing model estimates of ECS.
Jun Wang, John C. Moore, Liyun Zhao, Chao Yue, and Zhenhua Di
Earth Syst. Dynam., 13, 1625–1640, https://doi.org/10.5194/esd-13-1625-2022, https://doi.org/10.5194/esd-13-1625-2022, 2022
Short summary
Short summary
We examine how geoengineering using aerosols in the atmosphere might impact urban climate in the greater Beijing region containing over 50 million people. Climate models have too coarse resolutions to resolve regional variations well, so we compare two workarounds for this – an expensive physical model and a cheaper statistical method. The statistical method generally gives a reasonable representation of climate and has limited resolution and a different seasonality from the physical model.
Nidheesh Gangadharan, Hugues Goosse, David Parkes, Heiko Goelzer, Fabien Maussion, and Ben Marzeion
Earth Syst. Dynam., 13, 1417–1435, https://doi.org/10.5194/esd-13-1417-2022, https://doi.org/10.5194/esd-13-1417-2022, 2022
Short summary
Short summary
We describe the contributions of ocean thermal expansion and land-ice melting (ice sheets and glaciers) to global-mean sea-level (GMSL) changes in the Common Era. The mass contributions are the major sources of GMSL changes in the pre-industrial Common Era and glaciers are the largest contributor. The paper also describes the current state of climate modelling, uncertainties and knowledge gaps along with the potential implications of the past variabilities in the contemporary sea-level rise.
Changgui Lin, Erik Kjellström, Renate Anna Irma Wilcke, and Deliang Chen
Earth Syst. Dynam., 13, 1197–1214, https://doi.org/10.5194/esd-13-1197-2022, https://doi.org/10.5194/esd-13-1197-2022, 2022
Short summary
Short summary
This study endorses RCMs' added value on the driving GCMs in representing observed heat wave magnitudes. The future increase of heat wave magnitudes projected by GCMs is attenuated when downscaled by RCMs. Within the downscaling, uncertainties can be attributed almost equally to choice of RCMs and to the driving data associated with different GCMs. Uncertainties of GCMs in simulating heat wave magnitudes are transformed by RCMs in a complex manner rather than simply inherited.
Riccardo Silini, Sebastian Lerch, Nikolaos Mastrantonas, Holger Kantz, Marcelo Barreiro, and Cristina Masoller
Earth Syst. Dynam., 13, 1157–1165, https://doi.org/10.5194/esd-13-1157-2022, https://doi.org/10.5194/esd-13-1157-2022, 2022
Short summary
Short summary
The Madden–Julian Oscillation (MJO) has important socioeconomic impacts due to its influence on both tropical and extratropical weather extremes. In this study, we use machine learning (ML) to correct the predictions of the weather model holding the best performance, developed by the European Centre for Medium-Range Weather Forecasts (ECMWF). We show that the ML post-processing leads to an improved prediction of the MJO geographical location and intensity.
Nicola Maher, Robert C. Jnglin Wills, Pedro DiNezio, Jeremy Klavans, Sebastian Milinski, Sara C. Sanchez, Samantha Stevenson, Malte F. Stuecker, and Xian Wu
Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2022-26, https://doi.org/10.5194/esd-2022-26, 2022
Revised manuscript accepted for ESD
Short summary
Short summary
Understanding whether the El Niño–Southern Oscillation (ENSO) is likely to change in the future is important due to its widespread impacts. By using large ensembles, we can robustly isolate the time evolving response of ENSO variability in 14 climate models. We find that ENSO variability evolves in a non-linear fashion in many models and that there are large differences between models. These non-linear changes imply that ENSO impacts may vary dramatically throughout the 21st century.
Haicheng Zhang, Ronny Lauerwald, Pierre Regnier, Philippe Ciais, Kristof Van Oost, Victoria Naipal, Bertrand Guenet, and Wenping Yuan
Earth Syst. Dynam., 13, 1119–1144, https://doi.org/10.5194/esd-13-1119-2022, https://doi.org/10.5194/esd-13-1119-2022, 2022
Short summary
Short summary
We present a land surface model which can simulate the complete lateral transfer of sediment and carbon from land to ocean through rivers. Our model captures the water, sediment, and organic carbon discharges in European rivers well. Application of our model in Europe indicates that lateral carbon transfer can strongly change regional land carbon budgets by affecting organic carbon distribution and soil moisture.
Amber Boot, Anna S. von der Heydt, and Henk A. Dijkstra
Earth Syst. Dynam., 13, 1041–1058, https://doi.org/10.5194/esd-13-1041-2022, https://doi.org/10.5194/esd-13-1041-2022, 2022
Short summary
Short summary
Atmospheric pCO2 of the past shows large variability on different timescales. We focus on the effect of the strength of Atlantic Meridional Overturning Circulation (AMOC) on this variability and on the AMOC–pCO2 relationship. We find that climatic boundary conditions and the representation of biology in our model are most important for this relationship. Under certain conditions, we find internal oscillations, which can be relevant for atmospheric pCO2 variability during glacial cycles.
Aloïs Tilloy, Bruce D. Malamud, and Amélie Joly-Laugel
Earth Syst. Dynam., 13, 993–1020, https://doi.org/10.5194/esd-13-993-2022, https://doi.org/10.5194/esd-13-993-2022, 2022
Short summary
Short summary
Compound hazards occur when two different natural hazards impact the same time period and spatial area. This article presents a methodology for the spatiotemporal identification of compound hazards (SI–CH). The methodology is applied to compound precipitation and wind extremes in Great Britain for the period 1979–2019. The study finds that the SI–CH approach can accurately identify single and compound hazard events and represent their spatial and temporal properties.
Shruti Nath, Quentin Lejeune, Lea Beusch, Sonia I. Seneviratne, and Carl-Friedrich Schleussner
Earth Syst. Dynam., 13, 851–877, https://doi.org/10.5194/esd-13-851-2022, https://doi.org/10.5194/esd-13-851-2022, 2022
Short summary
Short summary
Uncertainty within climate model projections on inter-annual timescales is largely affected by natural climate variability. Emulators are valuable tools for approximating climate model runs, allowing for easy exploration of such uncertainty spaces. This study takes a first step at building a spatially resolved, monthly temperature emulator that takes local yearly temperatures as the sole input, thus providing monthly temperature distributions which are of critical value to impact assessments.
Linh N. Luu, Robert Vautard, Pascal Yiou, and Jean-Michel Soubeyroux
Earth Syst. Dynam., 13, 687–702, https://doi.org/10.5194/esd-13-687-2022, https://doi.org/10.5194/esd-13-687-2022, 2022
Short summary
Short summary
This study downscales climate information from EURO-CORDEX (approx. 12 km) output to a higher horizontal resolution (approx. 3 km) for the south of France. We also propose a matrix of different indices to evaluate the high-resolution precipitation output. We find that a higher resolution reproduces more realistic extreme precipitation events at both daily and sub-daily timescales. Our results and approach are promising to apply to other Mediterranean regions and climate impact studies.
Aine M. Gormley-Gallagher, Sebastian Sterl, Annette L. Hirsch, Sonia I. Seneviratne, Edouard L. Davin, and Wim Thiery
Earth Syst. Dynam., 13, 419–438, https://doi.org/10.5194/esd-13-419-2022, https://doi.org/10.5194/esd-13-419-2022, 2022
Short summary
Short summary
Our results show that agricultural management can impact the local climate and highlight the need to evaluate land management in climate models. We use regression analysis on climate simulations and observations to assess irrigation and conservation agriculture impacts on warming trends. This allowed us to distinguish between the effects of land management and large-scale climate forcings such as rising CO2 concentrations and thus gain insight into the impacts under different climate regimes.
Koffi Worou, Hugues Goosse, Thierry Fichefet, and Fred Kucharski
Earth Syst. Dynam., 13, 231–249, https://doi.org/10.5194/esd-13-231-2022, https://doi.org/10.5194/esd-13-231-2022, 2022
Short summary
Short summary
Over the Guinea Coast, the increased rainfall associated with warm phases of the Atlantic Niño is reasonably well simulated by 24 climate models out of 31, for the present-day conditions. In a warmer climate, general circulation models project a gradual decrease with time of the rainfall magnitude associated with the Atlantic Niño for the 2015–2039, 2040–2069 and 2070–2099 periods. There is a higher confidence in these changes over the equatorial Atlantic than over the Guinea Coast.
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.
Mickaël Lalande, Martin Ménégoz, Gerhard Krinner, Kathrin Naegeli, and Stefan Wunderle
Earth Syst. Dynam., 12, 1061–1098, https://doi.org/10.5194/esd-12-1061-2021, https://doi.org/10.5194/esd-12-1061-2021, 2021
Short summary
Short summary
Climate change over High Mountain Asia is investigated with CMIP6 climate models. A general cold bias is found in this area, often related to a snow cover overestimation in the models. Ensemble experiments generally encompass the past observed trends, suggesting that even biased models can reproduce the trends. Depending on the future scenario, a warming from 1.9 to 6.5 °C, associated with a snow cover decrease and precipitation increase, is expected at the end of the 21st century.
Benjamin Ward, Francesco S. R. Pausata, and Nicola Maher
Earth Syst. Dynam., 12, 975–996, https://doi.org/10.5194/esd-12-975-2021, https://doi.org/10.5194/esd-12-975-2021, 2021
Short summary
Short summary
Using the largest ensemble of a climate model currently available, the Max Planck Institute Grand Ensemble (MPI-GE), we investigated the impact of the spatial distribution of volcanic aerosols on the El Niño–Southern Oscillation (ENSO) response. By selecting three eruptions with different aerosol distributions, we found that the shift of the Intertropical Convergence Zone (ITCZ) is the main driver of the ENSO response, while other mechanisms commonly invoked seem less important in our model.
Matthias Gröger, Christian Dieterich, Jari Haapala, Ha Thi Minh Ho-Hagemann, Stefan Hagemann, Jaromir Jakacki, Wilhelm May, H. E. Markus Meier, Paul A. Miller, Anna Rutgersson, and Lichuan Wu
Earth Syst. Dynam., 12, 939–973, https://doi.org/10.5194/esd-12-939-2021, https://doi.org/10.5194/esd-12-939-2021, 2021
Short summary
Short summary
Regional climate studies are typically pursued by single Earth system component models (e.g., ocean models and atmosphere models). These models are driven by prescribed data which hamper the simulation of feedbacks between Earth system components. To overcome this, models were developed that interactively couple model components and allow an adequate simulation of Earth system interactions important for climate. This article reviews recent developments of such models for the Baltic Sea region.
Halima Usman, Thomas A. M. Pugh, Anders Ahlström, and Sofia Baig
Earth Syst. Dynam., 12, 857–870, https://doi.org/10.5194/esd-12-857-2021, https://doi.org/10.5194/esd-12-857-2021, 2021
Short summary
Short summary
The study assesses the impacts of climate change on forest productivity in the Hindu Kush Himalayan region. LPJ-GUESS was simulated from 1851 to 2100. In first approach, the model was compared with observational estimates. The comparison showed a moderate agreement. In the second approach, the model was assessed for the temporal and spatial trends of net biome productivity and its components along with carbon pool. Increases in both variables were predicted in 2100.
Kerstin Hartung, Ana Bastos, Louise Chini, Raphael Ganzenmüller, Felix Havermann, George C. Hurtt, Tammas Loughran, Julia E. M. S. Nabel, Tobias Nützel, Wolfgang A. Obermeier, and Julia Pongratz
Earth Syst. Dynam., 12, 763–782, https://doi.org/10.5194/esd-12-763-2021, https://doi.org/10.5194/esd-12-763-2021, 2021
Short summary
Short summary
In this study, we model the relative importance of several contributors to the land-use and land-cover change (LULCC) flux based on a LULCC dataset including uncertainty estimates. The uncertainty of LULCC is as relevant as applying wood harvest and gross transitions for the cumulative LULCC flux over the industrial period. However, LULCC uncertainty matters less than the other two factors for the LULCC flux in 2014; historical LULCC uncertainty is negligible for estimates of future scenarios.
Fransje van Oorschot, Ruud J. van der Ent, Markus Hrachowitz, and Andrea Alessandri
Earth Syst. Dynam., 12, 725–743, https://doi.org/10.5194/esd-12-725-2021, https://doi.org/10.5194/esd-12-725-2021, 2021
Short summary
Short summary
The roots of vegetation largely control the Earth's water cycle by transporting water from the subsurface to the atmosphere but are not adequately represented in land surface models, causing uncertainties in modeled water fluxes. We replaced the root parameters in an existing model with more realistic ones that account for a climate control on root development and found improved timing of modeled river discharge. Further extension of our approach could improve modeled water fluxes globally.
Manuela I. Brunner, Eric Gilleland, and Andrew W. Wood
Earth Syst. Dynam., 12, 621–634, https://doi.org/10.5194/esd-12-621-2021, https://doi.org/10.5194/esd-12-621-2021, 2021
Short summary
Short summary
Compound hot and dry events can lead to severe impacts whose severity may depend on their timescale and spatial extent. Here, we show that the spatial extent and timescale of compound hot–dry events are strongly related, spatial compound event extents are largest at
sub-seasonal timescales, and short events are driven more by high temperatures, while longer events are more driven by low precipitation. Future climate impact studies should therefore be performed at different timescales.
Francisco José Cuesta-Valero, Almudena García-García, Hugo Beltrami, and Joel Finnis
Earth Syst. Dynam., 12, 581–600, https://doi.org/10.5194/esd-12-581-2021, https://doi.org/10.5194/esd-12-581-2021, 2021
Short summary
Short summary
The current radiative imbalance at the top of the atmosphere is increasing the heat stored in the oceans, atmosphere, continental subsurface and cryosphere, with consequences for societies and ecosystems (e.g. sea level rise). We performed the first assessment of the ability of global climate models to represent such heat storage in the climate subsystems. Models are able to reproduce the observed atmosphere heat content, with biases in the simulation of heat content in the rest of components.
Francesco Piccioni, Céline Casenave, Bruno Jacques Lemaire, Patrick Le Moigne, Philippe Dubois, and Brigitte Vinçon-Leite
Earth Syst. Dynam., 12, 439–456, https://doi.org/10.5194/esd-12-439-2021, https://doi.org/10.5194/esd-12-439-2021, 2021
Short summary
Short summary
Small lakes are ecosystems highly impacted by climate change. Here, the thermal regime of a small, shallow lake over the past six decades was reconstructed via 3D modelling. Significant changes were found: strong water warming in spring and summer (0.7 °C/decade) as well as increased stratification and thermal energy for cyanobacteria growth, especially in spring. The strong spatial patterns detected for stratification might create local conditions particularly favourable to cyanobacteria bloom.
Pablo Ortega, Jon I. Robson, Matthew Menary, Rowan T. Sutton, Adam Blaker, Agathe Germe, Jöel J.-M. Hirschi, Bablu Sinha, Leon Hermanson, and Stephen Yeager
Earth Syst. Dynam., 12, 419–438, https://doi.org/10.5194/esd-12-419-2021, https://doi.org/10.5194/esd-12-419-2021, 2021
Short summary
Short summary
Deep Labrador Sea densities are receiving increasing attention because of their link to many of the processes that govern decadal climate oscillations in the North Atlantic and their potential use as a precursor of those changes. This article explores those links and how they are represented in global climate models, documenting the main differences across models. Models are finally compared with observational products to identify the ones that reproduce the links more realistically.
Calum Brown, Ian Holman, and Mark Rounsevell
Earth Syst. Dynam., 12, 211–231, https://doi.org/10.5194/esd-12-211-2021, https://doi.org/10.5194/esd-12-211-2021, 2021
Short summary
Short summary
The variety of human and natural processes in the land system can be modelled in many different ways. However, little is known about how and why basic model assumptions affect model results. We compared two models that represent land use in completely distinct ways and found several results that differed greatly. We identify the main assumptions that caused these differences and therefore key issues that need to be addressed for more robust model development.
Johannes Vogel, Pauline Rivoire, Cristina Deidda, Leila Rahimi, Christoph A. Sauter, Elisabeth Tschumi, Karin van der Wiel, Tianyi Zhang, and Jakob Zscheischler
Earth Syst. Dynam., 12, 151–172, https://doi.org/10.5194/esd-12-151-2021, https://doi.org/10.5194/esd-12-151-2021, 2021
Short summary
Short summary
We present a statistical approach for automatically identifying multiple drivers of extreme impacts based on LASSO regression. We apply the approach to simulated crop failure in the Northern Hemisphere and identify which meteorological variables including climate extreme indices and which seasons are relevant to predict crop failure. The presented approach can help unravel compounding drivers in high-impact events and could be applied to other impacts such as wildfires or flooding.
Peter Pfleiderer, Aglaé Jézéquel, Juliette Legrand, Natacha Legrix, Iason Markantonis, Edoardo Vignotto, and Pascal Yiou
Earth Syst. Dynam., 12, 103–120, https://doi.org/10.5194/esd-12-103-2021, https://doi.org/10.5194/esd-12-103-2021, 2021
Short summary
Short summary
In 2016, northern France experienced an unprecedented wheat crop loss. This crop loss was likely due to an extremely warm December 2015 and abnormally high precipitation during the following spring season. Using stochastic weather generators we investigate how severe the metrological conditions leading to the crop loss could be in current climate conditions. We find that December temperatures were close to the plausible maximum but that considerably wetter springs would be possible.
Jelle van den Berk, Sybren Drijfhout, and Wilco Hazeleger
Earth Syst. Dynam., 12, 69–81, https://doi.org/10.5194/esd-12-69-2021, https://doi.org/10.5194/esd-12-69-2021, 2021
Short summary
Short summary
A collapse of the Atlantic Meridional Overturning Circulation can be described by six parameters and Langevin dynamics. These parameters can be determined from collapses seen in climate models of intermediate complexity. With this parameterisation, it might be possible to estimate how much fresh water is needed to observe a collapse in more complicated models and reality.
Jakob Zscheischler, Philippe Naveau, Olivia Martius, Sebastian Engelke, and Christoph C. Raible
Earth Syst. Dynam., 12, 1–16, https://doi.org/10.5194/esd-12-1-2021, https://doi.org/10.5194/esd-12-1-2021, 2021
Short summary
Short summary
Compound extremes such as heavy precipitation and extreme winds can lead to large damage. To date it is unclear how well climate models represent such compound extremes. Here we present a new measure to assess differences in the dependence structure of bivariate extremes. This measure is applied to assess differences in the dependence of compound precipitation and wind extremes between three model simulations and one reanalysis dataset in a domain in central Europe.
Christian B. Rodehacke, Madlene Pfeiffer, Tido Semmler, Özgür Gurses, and Thomas Kleiner
Earth Syst. Dynam., 11, 1153–1194, https://doi.org/10.5194/esd-11-1153-2020, https://doi.org/10.5194/esd-11-1153-2020, 2020
Short summary
Short summary
In the warmer future, Antarctica's ice sheet will lose more ice due to enhanced iceberg calving and a warming ocean that melts more floating ice from below. However, the hydrological cycle is also stronger in a warmer world. Hence, more snowfall will precipitate on Antarctica and may balance the amplified ice loss. We have used future climate scenarios from various global climate models to perform numerous ice sheet simulations to show that precipitation may counteract mass loss.
Renate Anna Irma Wilcke, Erik Kjellström, Changgui Lin, Daniela Matei, Anders Moberg, and Evangelos Tyrlis
Earth Syst. Dynam., 11, 1107–1121, https://doi.org/10.5194/esd-11-1107-2020, https://doi.org/10.5194/esd-11-1107-2020, 2020
Short summary
Short summary
Two long-lasting high-pressure systems in summer 2018 led to heat waves over Scandinavia and an extended summer period with devastating impacts on both agriculture and human life. Using five climate model ensembles, the unique 263-year Stockholm temperature time series and a composite 150-year time series for the whole of Sweden, we found that anthropogenic climate change has strongly increased the probability of a warm summer, such as the one observed in 2018, occurring in Sweden.
Jeemijn Scheen and Thomas F. Stocker
Earth Syst. Dynam., 11, 925–951, https://doi.org/10.5194/esd-11-925-2020, https://doi.org/10.5194/esd-11-925-2020, 2020
Short summary
Short summary
Variability of sea surface temperatures (SST) in 1200–2000 CE is quite well-known, but the history of deep ocean temperatures is not. Forcing an ocean model with these SSTs, we simulate temperatures in the ocean interior. The circulation changes alter the amplitude and timing of deep ocean temperature fluctuations below 2 km depth, e.g. delaying the atmospheric signal by ~ 200 years in the deep Atlantic. Thus ocean circulation changes are shown to be as important as SST changes at these depths.
Sebastian Milinski, Nicola Maher, and Dirk Olonscheck
Earth Syst. Dynam., 11, 885–901, https://doi.org/10.5194/esd-11-885-2020, https://doi.org/10.5194/esd-11-885-2020, 2020
Short summary
Short summary
Initial-condition large ensembles with ensemble sizes ranging from 30 to 100 members have become a commonly used tool to quantify the forced response and internal variability in various components of the climate system, but there is no established method to determine the required ensemble size for a given problem. We propose a new framework that can be used to estimate the required ensemble size from a model's control run or an existing large ensemble.
Yu Huang, Lichao Yang, and Zuntao Fu
Earth Syst. Dynam., 11, 835–853, https://doi.org/10.5194/esd-11-835-2020, https://doi.org/10.5194/esd-11-835-2020, 2020
Short summary
Short summary
We investigate the applicability of machine learning (ML) on time series reconstruction and find that the dynamical coupling relation and nonlinear causality are crucial for the application of ML. Our results could provide insights into causality and ML approaches for paleoclimate reconstruction, parameterization schemes, and prediction in climate studies.
Anna Louise Merrifield, Lukas Brunner, Ruth Lorenz, Iselin Medhaug, and Reto Knutti
Earth Syst. Dynam., 11, 807–834, https://doi.org/10.5194/esd-11-807-2020, https://doi.org/10.5194/esd-11-807-2020, 2020
Short summary
Short summary
Justifiable uncertainty estimates of future change in northern European winter and Mediterranean summer temperature can be obtained by weighting a multi-model ensemble comprised of projections from different climate models and multiple projections from the same climate model. Weights reduce the influence of model biases and handle dependence by identifying a projection's model of origin from historical characteristics; contributions from the same model are scaled by the number of members.
James D. Annan, Julia C. Hargreaves, Thorsten Mauritsen, and Bjorn Stevens
Earth Syst. Dynam., 11, 709–719, https://doi.org/10.5194/esd-11-709-2020, https://doi.org/10.5194/esd-11-709-2020, 2020
Short summary
Short summary
In this paper we explore the potential of variability for constraining the equilibrium response of the climate system to external forcing. We show that the constraint is inherently skewed, with a long tail to high sensitivity, and that while the variability may contain some useful information, it is unlikely to generate a tight constraint.
Andrea Böhnisch, Ralf Ludwig, and Martin Leduc
Earth Syst. Dynam., 11, 617–640, https://doi.org/10.5194/esd-11-617-2020, https://doi.org/10.5194/esd-11-617-2020, 2020
Short summary
Short summary
North Atlantic air pressure variations influencing European climate variables are simulated in coarse-resolution global climate models (GCMs). As single-model runs do not sufficiently describe variations of their patterns, several model runs with slightly diverging initial conditions are analyzed. The study shows that GCM and regional climate model (RCM) patterns vary in a similar range over the same domain, while RCMs add consistent fine-scale information due to their higher spatial resolution.
György Károlyi, Rudolf Dániel Prokaj, István Scheuring, and Tamás Tél
Earth Syst. Dynam., 11, 603–615, https://doi.org/10.5194/esd-11-603-2020, https://doi.org/10.5194/esd-11-603-2020, 2020
Short summary
Short summary
We construct a conceptual model to understand the interplay between the atmosphere and the ocean biosphere in a climate change framework, including couplings between extraction of carbon dioxide by phytoplankton and climate change, temperature and carrying capacity of phytoplankton, and wind energy and phytoplankton production. We find that sufficiently strong mixing can result in decaying global phytoplankton content.
Kira Rehfeld, Raphaël Hébert, Juan M. Lora, Marcus Lofverstrom, and Chris M. Brierley
Earth Syst. Dynam., 11, 447–468, https://doi.org/10.5194/esd-11-447-2020, https://doi.org/10.5194/esd-11-447-2020, 2020
Short summary
Short summary
Under continued anthropogenic greenhouse gas emissions, it is likely that global mean surface temperature will continue to increase. Little is known about changes in climate variability. We analyze surface climate variability and compare it to mean change in colder- and warmer-than-present climate model simulations. In most locations, but not on subtropical land, simulated temperature variability up to decadal timescales decreases with mean temperature, and precipitation variability increases.
Eirik Myrvoll-Nilsen, Sigrunn Holbek Sørbye, Hege-Beate Fredriksen, Håvard Rue, and Martin Rypdal
Earth Syst. Dynam., 11, 329–345, https://doi.org/10.5194/esd-11-329-2020, https://doi.org/10.5194/esd-11-329-2020, 2020
Short summary
Short summary
This paper presents efficient Bayesian methods for linear response models of global mean surface temperature that take into account long-range dependence. We apply the methods to the instrumental temperature record and historical model runs in the CMIP5 ensemble to provide estimates of the transient climate response and temperature projections under the Representative Concentration Pathways.
Lea Beusch, Lukas Gudmundsson, and Sonia I. Seneviratne
Earth Syst. Dynam., 11, 139–159, https://doi.org/10.5194/esd-11-139-2020, https://doi.org/10.5194/esd-11-139-2020, 2020
Short summary
Short summary
Earth system models (ESMs) are invaluable to study the climate system but expensive to run. Here, we present a statistical tool which emulates ESMs at a negligible computational cost by creating stochastic realizations of yearly land temperature field time series. Thereby, 40 ESMs are considered, and for each ESM, a single simulation is required to train the tool. The resulting ESM-specific realizations closely resemble ESM simulations not employed during training at point to regional scales.
Yu Sun and Riccardo E. M. Riva
Earth Syst. Dynam., 11, 129–137, https://doi.org/10.5194/esd-11-129-2020, https://doi.org/10.5194/esd-11-129-2020, 2020
Short summary
Short summary
The solid Earth is still deforming because of the effect of past ice sheets through glacial isostatic adjustment (GIA). Satellite gravity observations by the Gravity Recovery and Climate Experiment (GRACE) mission are sensitive to those signals but are superimposed on the redistribution effect of water masses by the hydrological cycle. We propose a method separating the two signals, providing new constraints for forward GIA models and estimating the global water cycle's patterns and magnitude.
Mareike Schuster, Jens Grieger, Andy Richling, Thomas Schartner, Sebastian Illing, Christopher Kadow, Wolfgang A. Müller, Holger Pohlmann, Stephan Pfahl, and Uwe Ulbrich
Earth Syst. Dynam., 10, 901–917, https://doi.org/10.5194/esd-10-901-2019, https://doi.org/10.5194/esd-10-901-2019, 2019
Short summary
Short summary
Decadal climate predictions are valuable to society as they allow us to estimate climate conditions several years in advance. We analyze the latest version of the German MiKlip prediction system (https://www.fona-miklip.de) and assess the effect of the model resolution on the skill of the system. The increase in the resolution of the system reduces the bias and significantly improves the forecast skill for North Atlantic extratropical winter dynamics for lead times of two to five winters.
Calum Brown, Bumsuk Seo, and Mark Rounsevell
Earth Syst. Dynam., 10, 809–845, https://doi.org/10.5194/esd-10-809-2019, https://doi.org/10.5194/esd-10-809-2019, 2019
Short summary
Short summary
Concerns are growing that human activity will lead to social and environmental breakdown, but it is hard to anticipate when and where such breakdowns might occur. We developed a new model of land management decisions in Europe to explore possible future changes and found that decision-making that takes into account social and environmental conditions can produce unexpected outcomes that include societal breakdown in challenging conditions.
Francine Schevenhoven, Frank Selten, Alberto Carrassi, and Noel Keenlyside
Earth Syst. Dynam., 10, 789–807, https://doi.org/10.5194/esd-10-789-2019, https://doi.org/10.5194/esd-10-789-2019, 2019
Short summary
Short summary
Weather and climate predictions potentially improve by dynamically combining different models into a
supermodel. A crucial step is to train the supermodel on the basis of observations. Here, we apply two different training methods to the global atmosphere–ocean–land model SPEEDO. We demonstrate that both training methods yield climate and weather predictions of superior quality compared to the individual models. Supermodel predictions can also outperform the commonly used multi-model mean.
Adria K. Schwarber, Steven J. Smith, Corinne A. Hartin, Benjamin Aaron Vega-Westhoff, and Ryan Sriver
Earth Syst. Dynam., 10, 729–739, https://doi.org/10.5194/esd-10-729-2019, https://doi.org/10.5194/esd-10-729-2019, 2019
Short summary
Short summary
Simple climate models (SCMs) underlie many important scientific and decision-making endeavors. This illustrates the need for their use to be rooted in a clear understanding of their fundamental responses. In this study, we provide a comprehensive assessment of model performance by evaluating the fundamental responses of several SCMs. We find biases in some responses, which have implications for decision science. We conclude by recommending a standard set of validation tests for any SCM.
Cited articles
Atangana, A.: Drawdown in prolate spheroidal–spherical coordinates obtained via Green's function and perturbation methods, Commun. Nonlin. Sci. Numer. Simul., 19, 1259–1269, 2014.
Atangana, A. and Baleanu, D.: Modelling the advancement of the impurities and the melted oxygen concentration within the scope of fractional calculus, Int. J. Non-Lin. Mech., 67, 278–284, 2014.
Atangana, A. and Bildik, N.: The use of fractional order derivative to predict the groundwater flow, Math. Probl. Eng., 2013, 543026, https://doi.org/10.1155/2013/543026, 2013.
Atangana, A. and Vermeulen, P.: Analytical solutions of a space-time fractional derivative of groundwater flow equation, Abstr. Appl. Anal., 2014, 381753, https://doi.org/10.1155/2014/381753, 2014.
Baeumer, B. and Meerschaert, M.: Fractional diffusion with two time scales, Physica A, 373, 237–251, 2007.
Baeumer, B., Benson, D. A., and Meerschaert, M. M.: Advection and dispersion in time and space, Physica A, 350, 245–262, 2005.
Bear, J.: Groundwater hydraulics, McGraw, New York, 1979.
Benson, D. A., Wheatcraft, S. W., and Meerschaert, M. M.: Application of a fractional advection-dispersion equation, Water Resour. Res., 36, 1403–1412, 2000a.
Benson, D. A., Wheatcraft, S. W., and Meerschaert, M. M.: The fractional-order governing equation of Lévy motion, Water Resour. Res., 36, 1413–1423, 2000b.
Black, J. H., Barker, J. A., and Noy, D. J.: Crosshole investigations – the method, theory and analysis of crosshole sinusoidal pressure tests in fissured rock, Stripa Proj., Int. Rep. 86-03, SKB, Stockholm, 1986.
Cloot, A. and Botha, J.: A generalised groundwater flow equation using the concept of non-integer order derivatives, Water SA, 32, 1–7, 2006.
Ercan, A. and Kavvas, M. L.: Fractional governing equations of diffusion wave and kinematic wave open-channel flow in fractional time-space. II. Numerical simulations, J. Hydrol. Eng., 20, 04014097, https://doi.org/10.1061/(ASCE)HE.1943-5584.0001081, 2014.
Ercan, A. and Kavvas, M. L.: Numerical Solution and Application of Time-Space Fractional Governing Equations of One-Dimensional Unsteady Open Channel Flow Process, Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2016-364, 2016.
Freeze, R. A. and Cherry, J. A.: Groundwater, Prentice Hall International, Hemel Hempstead, 1979.
Kang, P. K., Le Borgne, T., Dentz, M., Bour, O., and Juanes, R.: Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model, Water Resour. Res., 51, 940–959, 2015.
Kavvas, M. L. and Ercan, A.: Time-Space Fractional Governing Equations of Unsteady Open Channel Flow, J. Hydrol. Eng., 22, 04016052, https://doi.org/10.1061/(ASCE)HE.1943-5584.0001460, 2016.
Kavvas, M. L., Kim, S., and Ercan, A.: Fractional ensemble average governing equations of transport by time-space nonstationary stochastic fractional advective velocity and fractional dispersion. I: Theory, J. Hydrol. Eng., 20, 04014039, https://doi.org/10.1061/(ASCE)HE.1943-5584.0000992, 2014.
Kavvas, M. L., Ercan, A., and Polsinelli, J.: Governing equations of transient soil water flow and soil water flux in multi-dimensional fractional anisotropic media and fractional time, Hydrol. Earth Syst. Sci., 21, 1547–1557, h https://doi.org/10.5194/hess-21-1547-2017, 2017.
Khalil, R., Al Horani, M., Yousef, A., and Sababheh, M.: A new definition of fractional derivative, J. Comput. Appl. Math., 264, 65–70, 2014.
Kim, S., Kavvas, M., and Ercan, A.: Fractional ensemble average governing equations of transport by time-space nonstationary stochastic fractional advective velocity and fractional dispersion. II: Numerical investigation, J. Hydrol. Eng., 20, 04014040, https://doi.org/10.1061/(ASCE)HE.1943-5584.0000994, 2014.
Levy, M. and Berkowitz, B.: Measurement and analysis of non-Fickian dispersion in heterogeneous porous media, J. Contam. Hydrol., 64, 203–226, 2003.
Li, M.-F., Ren, J.-R., and Zhu, T.: Series expansion in fractional calculus and fractional differential equations, arXiv preprint arXiv:0910.4819, 2009.
Li, Z. and Zhang, Y.-K.: Quantifying fractal dynamics of groundwater systems with detrended fluctuation analysis, J. Hydrol., 336, 139–146, 2007.
Meerschaert, M. M., Benson, D. A., and Bäumer, B.: Multidimensional advection and fractional dispersion, Phys. Rev. E, 59, 5026, https://doi.org/10.1103/PhysRevE.59.5026, 1999.
Meerschaert, M. M., Benson, D. A., Scheffler, H.-P., and Baeumer, B.: Stochastic solution of space-time fractional diffusion equations, Phys. Rev. E, 65, 041103, https://doi.org/10.1103/PhysRevE.65.041103, 2002.
Meerschaert, M. M., Mortensen, J., and Wheatcraft, S. W.: Fractional vector calculus for fractional advection–dispersion, Physica A, 367, 181–190, 2006.
Metzler, R. and Klafter, J.: The random walk's guide to anomalous diffusion: a fractional dynamics approach, Phys. Rep., 339, 1–77, 2000.
Odibat, Z. M. and Shawagfeh, N. T.: Generalized Taylor's formula, Appl. Math. Comput., 186, 286–293, 2007.
Peaudecerf, P. and Sauty, J.: Application of a mathematical-model to characterization of dispersion effects on groundwater quality, Prog. Water Technol., 10, 443–454, 1978.
Podlubny, I.: Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Academic Press, Boston, USA, 1998.
Rakhshandehroo, G. R. and Amiri, S. M.: Evaluating fractal behavior in groundwater level fluctuations time series, J. Hydrol., 464, 550–556, 2012.
Schumer, R., Benson, D. A., Meerschaert, M. M., and Wheatcraft, S. W.: Eulerian derivation of the fractional advection–dispersion equation, J. Contam. Hydrol., 48, 69–88, 2001.
Schumer, R., Meerschaert, M. M., and Baeumer, B.: Fractional advection-dispersion equations for modeling transport at the Earth surface, J. Geophys. Res.-Ea. Surf., 114, F00A07, https://doi.org/10.1029/2008JF001246, 2009.
Sidle, R. C., Nilsson, B., Hansen, M., and Fredericia, J.: Spatially varying hydraulic and solute transport characteristics of a fractured till determined by field tracer tests, Funen, Denmark, Water Resour. Res., 34, 2515–2527, 1998.
Silliman, S. and Simpson, E.: Laboratory evidence of the scale effect in dispersion of solutes in porous media, Water Resour. Res., 23, 1667–1673, 1987.
Sudicky, E., Cherry, J., and Frind, E.: Migration of contaminants in groundwater at a landfill: A case study: 4. A natural-gradient dispersion test, J. Hydrol., 63, 81–108, 1983.
Tu, T., Ercan, A., and Kavvas, M. L.: Fractal Scaling Analysis of Groundwater Dynamics in Confined Aquifers, Earth Syst. Dynam. Discuss., https://doi.org/10.5194/esd-2017-27, in review, 2017.
Usero, D.: Fractional Taylor series for Caputo fractional derivatives, Construction of numerical schemes, http://www.fdi.ucm.es/profesor/lvazquez/calcfrac/docs/paper_usero.pdf (last access: February 2017), 2008.
Van Tonder, G., Botha, J., Chiang, W.-H., Kunstmann, H., and Xu, Y.: Estimation of the sustainable yields of boreholes in fractured rock formations, J. Hydrol., 241, 70–90, 2001.
Wang, H. F. and Anderson, M. P.: Introduction to groundwater modeling: finite difference and finite element methods, Academic Press, San Diego, California, 1995.
Wheatcraft, S. W. and Meerschaert, M. M.: Fractional conservation of mass, Adv. Water Resour., 31, 1377–1381, 2008.
Yu, X., Ghasemizadeh, R., Padilla, I. Y., Kaeli, D., and Alshawabkeh, A.: Patterns of temporal scaling of groundwater level fluctuation, J. Hydrol., 536, 485–495, 2016.
Zhang, Y. and Benson, D. A.: Lagrangian simulation of multidimensional anomalous transport at the MADE site, Geophys. Res. Lett., 35, L07403, https://doi.org/10.1029/2008GL033222, 2008.
Zhang, Y., Benson, D. A., Meerschaert, M. M., and LaBolle, E. M.: Space-fractional advection-dispersion equations with variable parameters: Diverse formulas, numerical solutions, and application to the Macrodispersion Experiment site data, Water Resour. Res., 43, W05439, https://doi.org/10.1029/2006WR004912, 2007.
Zhang, Y., Benson, D. A., and Reeves, D. M.: Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications, Adv. Water Resour., 32, 561–581, 2009.
Short summary
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.
A dimensionally consistent governing equation of transient, saturated groundwater flow in...
Special issue
Altmetrics
Final-revised paper
Preprint