| 1. |
- Bonfils, Anthony F., 1994-, et al.
(författare)
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Asymptotic interpretation of the Miles mechanism of wind-wave instability
- 2022
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Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 944
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Tidskriftsartikel (refereegranskat)abstract
- When wind blows over water, ripples are generated on the water surface. These ripples can be regarded as perturbations of the wind field, which is modelled as a parallel inviscid flow. For a given wavenumber k, the perturbed streamfunction of the wind field and the complex phase speed are the eigenfunction and the eigenvalue of the so-called Rayleigh equation in a semi-infinite domain. Because of the small air-water density ratio, rho(a)/rho(w) epsilon << 1, the wind and the ripples are weakly coupled, and the eigenvalue problem can be solved perturbatively. At the leading order, the eigenvalue is equal to the phase speed c(0) of surface waves. At order epsilon, the eigenvalue has a finite imaginary part, which implies growth. Miles (J. Fluid Mech., vol. 3, 1957, pp. 185-204) showed that the growth rate is proportional to the square modulus of the leading-order eigenfunction evaluated at the so-called critical level z = z
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| 2. |
- Bonfils, Anthony, 1994-, et al.
(författare)
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Flow driven interfacial waves: an asymptotic study
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We use asymptotic methods to study the evolution of short wavelength interfacial waves driven by the combined action of wind and current. We solve the Rayleigh equation for the stability of the shear flow, and construct a uniformly valid approximation for the perturbed streamfunction, or eigenfunction. We then expand the real part of the eigenvalue, the phase speed, in a power series of the inverse wavenumber and show that the imaginary part is exponentially small. We give expressions for the growth rates of the Miles (1957) and rippling (e.g., Young & Wolfe 2013) instabilities that are valid for an arbitrary shear flow. The accuracy of the results is demonstrated by a comparison with the exact solution of the eigenvalue problem in the case when both the wind and the current have an exponential profile.
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| 3. |
- Bonfils, Anthony, 1994-
(författare)
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Waves and instabilities through the lens of asymptotic analysis
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Understanding the interaction of water waves with winds and marine currents is a fundamental problem in geophysical fluid dynamics. From the point of view of hydrodynamic stability, surface waves are regarded as perturbations of an inviscid parallel shear flow modeling the wind in the air and the current in the water. For small two-dimensional perturbations, the linearization of the Euler equation of motion yields an eigenvalue problem to be solved for a given wavenumber k. The eigenfunction is a streamfunction obeying the so-called Rayleigh equation. The eigenvalue is a complex phase speed, c, whose real part is the actual phase speed of sheared waves while the imaginary part of kc is the growth rate of the wave amplitude. Using the smallness of the air/water density ratio and assuming no flow in the water, Miles solved this eigenvalue problem perturbatively in 1957. He uncovered an instability of the wind field due to a critical layer in the air, where the wind speed equals the phase speed of free surface waves, and showed that the growth rate of wind-waves is proportional to the square modulus of the solution of the Rayleigh equation at the critical level. This level is a regular singular point, which makes the resolution of the Rayleigh equation challenging. For that reason, an explicit expression of the growth rate of the Miles instability as a function of the wavenumber was lacking. Firstly, I designed a numerical scheme to solve the Rayleigh equation for an arbitrary monotonic wind profile. Secondly, I solved it analytically using asymptotic methods for long and short waves.In physical oceanography, a standard model for the mean turbulent wind field is the logarithmic profile, which contains only one length scale: the roughness length, z0 ~1 mm, accounting for the presence of waves on the water surface. I am interested in waves propagating due to gravity and surface tension, which have wavelengths ranging from a few millimeters to hundreds of meters. Hence, a natural small parameter is kz0, which I used to obtain long wave solutions of the Rayleigh equation, and subsequently the growth rate of the Miles instability. The comparison with both numerical and measured growth rates is excellent. Furthermore, I approximated the maximum growth rate in the strong wind limit, and inferred that the fastest growing wave is such that the aerodynamic pressure is in phase with the wave slope.I also considered the short wave limit of the eigenvalue problem. Using 1/(kL) as a small parameter, where L is a characteristic length scale of the shear, I found general asymptotic solutions for interfacial waves in presence of a wind and a current, where the density ratio does not need to be small. One application concerns the mixing of elements at the surface of white dwarfs. Moreover, short wave asymptotics provide insights on another instability. When waves have a phase speed that matches the current speed, there is another critical layer, in the water, which is responsible for the so-called rippling instability. I obtained a general asymptotic formula for the growth rate of this instability.Finally, I used my experience in solving eigenvalue problems to study, in collaboration with other researchers, wrinkles in thin elastic sheets floating on a liquid foundation. We had to solve a fourth order eigenvalue problem where the eigenvalue is the compressive load imposed on the sheet and the eigenfunction is the vertical displacement. For homogeneous sheets, the bending stiffness of the sheet is constant and the eigenvalue problem could be solved analytically. We found that the buckling shape has a symmetric and an antisymmetric mode. The mode associated with the minimum compressive load depends on the size of the confined sheet. Hence, there are changes of symmetry at certain confinement sizes for which the buckling shape is degenerate. We numerically showed that this degeneracy disappears for composite sheets, whose bending stiffness depends on space due to the presence of liquid inclusions.
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| 4. |
- Giorgini, Ludovico T., et al.
(författare)
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Analytical Survival Analysis of the Ornstein-Uhlenbeck Process
- 2020
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Ingår i: Journal of statistical physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 181:6, s. 2404-2414
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Tidskriftsartikel (refereegranskat)abstract
- We use asymptotic methods from the theory of differential equations to obtain an analytical expression for the survival probability of an Ornstein-Uhlenbeck process with a potential defined over a broad domain. We form a uniformly continuous analytical solution covering the entire domain by asymptotically matching approximate solutions in an interior region, centered around the origin, to those in boundary layers, near the lateral boundaries of the domain. The analytic solution agrees extremely well with the numerical solution and takes into account the non-negligible leakage of probability that occurs at short times when the stochastic process begins close to one of the boundaries. Given the range of applications of Ornstein-Uhlenbeck processes, the analytic solution is of broad relevance across many fields of natural and engineering science.
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| 5. |
- Giorgini, Ludovico Theo, 1994-, et al.
(författare)
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Modeling the El Niño Southern Oscillation with Neural Differential Equations
- 2021
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Konferensbidrag (refereegranskat)abstract
- We use a Neural Ordinary Differential Equation to model and predict the seasonal to interannual variability of El Niño Southern Oscillation (ENSO). We train our neural network model using partial observations involving only sea surface temperature data. Our approach is computationally inexpensive, it reproduces the main seasonal features of ENSO, and exhibits robust predictions skills.
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| 6. |
- Giorgini, Ludovico Theo, et al.
(författare)
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Non-Gaussian stochastic dynamical model for the El Niño southern oscillation
- 2022
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Ingår i: Physical Review Research. - : American Physical Society (APS). - 2643-1564. ; 4:2
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Tidskriftsartikel (refereegranskat)abstract
- A nonautonomous stochastic dynamical model approach is developed to describe the seasonal to interannual variability of the El Niño southern oscillation (ENSO). We determine the model coefficients by systematic statistical estimations using partial observations involving only sea surface temperature data. Our approach reproduces the observed seasonal phase locking and its uncertainty, as well as the highly non-Gaussian statistics of ENSO. Finally, we recover the intermittent time series of the hidden processes, including the thermocline depth and the wind bursts.
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| 7. |
- Guarnieri, F., et al.
(författare)
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Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum
- 2017
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 58:9
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with a negative constant drift, described by a Fokker-Planck equation with a potential V(x) = -[b ln(x) + a x], for b > 0 and a < 0. The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process that has been extensively studied for its applications in physics, biology, and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schrodinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a constant negative drift. We conclude with a comparison to other analytical methods and with numerical solutions.
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| 8. |
- Jüling, André, et al.
(författare)
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Multidecadal variability in the climate system : phenomena and mechanisms
- 2020
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Ingår i: The European Physical Journal Plus. - : Springer Science and Business Media LLC. - 2190-5444. ; 135:6
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Forskningsöversikt (refereegranskat)abstract
- An open and fundamental issue in climate dynamics is the origin of multidecadal variability in the climate system. Resolving this issue is essential for adequate attribution of human-induced climate change. The purpose of this paper is to provide a perspective on multidecadal variability from the analysis of observations and results from model simulations. Data from the instrumental record indicate the existence of large-scale coherent patterns of multidecadal variability in sea surface temperature. Combined with long time series of proxy data, these results provide ample evidence for the existence of multidecadal sea surface temperature variations. Results of a hierarchy of climate models have provided several mechanisms of this variability, ranging from pure atmospheric forcing, via internal ocean processes to coupled ocean-atmosphere interactions. An important problem is that current state-of-the-art climate models underestimate multidecadal variability. We argue that these models miss important processes in their representation of ocean eddies and focus on a robust mechanism of multidecadal variability which is found in multi-century simulations with climate models having a strongly eddying ocean component.
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| 9. |
- Kim, Hye-Jin, et al.
(författare)
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Subseasonal relationship between Arctic and Eurasian surface air temperature
- 2021
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Ingår i: Scientific Reports. - : Springer Science and Business Media LLC. - 2045-2322. ; 11:1
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Tidskriftsartikel (refereegranskat)abstract
- The subseasonal relationship between Arctic and Eurasian surface air temperature (SAT) is re-examined using reanalysis data. Consistent with previous studies, a significant negative correlation is observed in cold season from November to February, but with a local minimum in late December. This relationship is dominated not only by the warm Arctic-cold Eurasia (WACE) pattern, which becomes more frequent during the last two decades, but also by the cold Arctic-warm Eurasia (CAWE) pattern. The budget analyses reveal that both WACE and CAWE patterns are primarily driven by the temperature advection associated with sea level pressure anomaly over the Ural region, partly cancelled by the diabatic heating. It is further found that, although the anticyclonic anomaly of WACE pattern mostly represents the Ural blocking, about 20% of WACE cases are associated with non-blocking high pressure systems. This result indicates that the Ural blocking is not a necessary condition for the WACE pattern, highlighting the importance of transient weather systems in the subseasonal Arctic-Eurasian SAT co-variability.
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| 10. |
- Kim, Joo-Hong, et al.
(författare)
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Salinity Control of Thermal Evolution of Late Summer Melt Ponds on Arctic Sea Ice
- 2018
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Ingår i: Geophysical Research Letters. - 0094-8276 .- 1944-8007. ; 45:16, s. 8304-8313
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Tidskriftsartikel (refereegranskat)abstract
- The thermal evolution of melt ponds on Arctic sea ice was investigated through a combination of autonomous observations and two-dimensional high-resolution fluid dynamics simulations. We observed one relatively fresh pond and one saline pond on the same ice floe, with similar depth. The comparison of observations and simulations indicates that thermal convection dominates in relatively fresh ponds, but conductive heat transfer dominates in salt-stratified ponds. Using a parameterized surface energy balance, we estimate that the heat flux to the ice is larger under the saline pond than the freshwater pond when averaged over the observational period. The deviation is sensitive to assumed wind, varying between 3 and 14 W/m(2) for winds from 0 to 5 m/s. If this effect persists as conditions evolve through the melt season, our results suggest that this imbalance potentially has a climatologically significant impact on sea-ice evolution. Plain Language Summary Sea ice provides key feedbacks on polar and global climate, with melt ponds being particularly significant. Melt ponds darken the ice surface, thereby increasing the absorption of sunlight and accelerating ice melt. This study provides a new perspective on melt-pond salinity, its previously unrecognized significance in controlling the thermal properties of ponds, and the potential impact on ice melting as we transition toward a younger sea ice cover. Many state-of-the-art sea ice models represent melt ponds as a freshwater layer with a surface temperature of 0 degrees C, consistent with a past Arctic ocean dominated by desalinated perennial ice and relatively fresh ponds. However, perennial ice has diminished in recent decades, with increasing prevalence of young saline ice. This leads to ponds with a wider range of salinities and temperatures. We show that salinity strongly impacts pond temperatures, using observations of adjacent freshwater and saline melt ponds on Arctic sea ice. Combining this data with model simulations, we find that melt-pond salinity impacts heat transfer to the ice below and the resulting melting rate. Our study reveals that melt-pond salinity and salt stratification are key variables influencing heat transfer in melt ponds, which need to be considered in future model development.
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| 11. |
- Lim, Soon Hoe, et al.
(författare)
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Predicting critical transitions in multiscale dynamical systems using reservoir computing
- 2020
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Ingår i: Chaos. - : AIP Publishing. - 1054-1500 .- 1089-7682. ; 30:12
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Tidskriftsartikel (refereegranskat)abstract
- We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and induces critical transitions. By taking advantage of recent advances in reservoir computing, we present a data-driven method to predict the future evolution of the state. We show that our method is capable of predicting a critical transition event at least several numerical time steps in advance. We demonstrate the success as well as the limitations of our method using numerical experiments on three examples of systems, ranging from low dimensional to high dimensional. We discuss the mathematical and broader implications of our results.
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| 12. |
- Moon, Woosok, et al.
(författare)
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Analytical solution of stochastic resonance in the nonadiabatic regime
- 2021
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Ingår i: Physical review. E. - : American Physical Society (APS). - 2470-0045 .- 2470-0053. ; 104:4
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Tidskriftsartikel (refereegranskat)abstract
- We generalize stochastic resonance to the nonadiabatic limit by treating the double-well potential using two quadratic potentials. We use a singular perturbation method to determine an approximate analytical solution for the probability density function that asymptotically connects local solutions in boundary layers near the two minima with those in the region of the maximum that separates them. The validity of the analytical solution is confirmed numerically. Free from the constraints of the adiabatic limit, the approach allows us to predict the escape rate from one stable basin to another for systems experiencing a more complex periodic forcing.
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| 13. |
- Moon, Woosok, et al.
(författare)
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Baroclinic instability and large-scale wave propagation in a planetary-scale atmosphere
- 2022
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Ingår i: Quarterly Journal of the Royal Meteorological Society. - : Wiley. - 0035-9009 .- 1477-870X. ; 148:743, s. 809-825
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Tidskriftsartikel (refereegranskat)abstract
- Midlatitude atmospheric variability is dominated by the dynamics of the baroclinically unstable jet stream, which meanders and sheds eddies at the scale of the Rossby deformation radius. The eddies interact with each other and with the jet, affecting the variability on a wide range of scales, but the mechanisms of planetary-scale fluctuations of the jet are not well understood. Here, we develop a theoretical framework to explore the stability of planetary-scale motions in an idealized two-layer model of the atmosphere. The model is based on a combination of vertical shear and the Sverdrup relation, providing the dynamic link between the two layers, with meridional eddy heat fluxes parameterized as a diffusive process with the memory of past baroclinicity of the jet. We find that a planetary-scale instability exists if the vertical shear of the jet does not exceed a particular threshold. The inclusion of the eddy-memory effect enables westward or eastward propagation of planetary waves relative to the barotropic mean flow. Importantly, we find growing planetary waves that propagate slowly westward or are stationary, which could have important implications for the formation of atmospheric blocking events. Our theoretical results suggest that, with ongoing polar amplification due to global warming and the corresponding reduction of the vertical shear of the mean wind, the background conditions for the growth of planetary-scale waves via planetary-scale baroclinic instability are becoming more favorable.
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| 14. |
- Moon, Woosok, et al.
(författare)
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Coupling functions in climate
- 2019
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Ingår i: Philosophical Transactions. Series A. - : The Royal Society. - 1364-503X .- 1471-2962. ; 377:2160
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Tidskriftsartikel (refereegranskat)abstract
- We examine how coupling functions in the theory of dynamical systems provide a quantitative window into climate dynamics. Previously, we have shown that a one-dimensional periodic non-autonomous stochastic dynamical system can simulate the monthly statistics of surface air temperature data. Here, we expand this approach to two-dimensional dynamical systems to include interactions between two subsystems of the climate. The relevant coupling functions are constructed from the covariance of the data from the two sub-systems. We demonstrate the method on two tropical climate indices, the El-Nino-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD), to interpret the mutual interactions between these two air-sea interaction phenomena in the Pacific and Indian Oceans. The coupling function reveals that the ENSO mainly controls the seasonal variability of the IOD during its mature phase. This demonstrates the plausibility of constructing a network model for the seasonal variability of climate systems based on such coupling functions. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.
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| 15. |
- Moon, Woosok, et al.
(författare)
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Eddy memory as an explanation of intraseasonal periodic behaviour in baroclinic eddies
- 2021
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Ingår i: Quarterly Journal of the Royal Meteorological Society. - : Wiley. - 0035-9009 .- 1477-870X. ; 147:737, s. 2395-2408
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Tidskriftsartikel (refereegranskat)abstract
- The baroclinic annular mode (BAM) is a leading-order mode of the eddy kinetic energy in the Southern Hemisphere exhibiting oscillatory behaviour at intraseasonal time-scales. The oscillation mechanism has been linked to transient eddy–mean flow interactions which remain poorly understood. Here we demonstrate that the finite memory effect in eddy-heat flux dependence on the large-scale flow can explain the origin of the BAM's oscillatory behaviour. We represent the eddy memory effect by a delayed integral kernel that leads to a generalized Langevin equation for the planetary-scale heat equation. Using a mathematical framework for the interactions between planetary- and synoptic-scale motions, we derive a reduced dynamical model of the BAM – a stochastically forced oscillator with a period proportional to the geometric mean between the eddy memory time-scale and the diffusive eddy equilibration time-scale. Our model provides a formal justification for the previously proposed phenomenological model of the BAM and could be used to explicitly diagnose the memory kernel and improve our understanding of transient eddy–mean flow interactions in the atmosphere.
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| 16. |
- Moon, Woosok, et al.
(författare)
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Intrinsic Pink-Noise Multidecadal Global Climate Dynamics Mode
- 2018
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Ingår i: Physical Review Letters. - : American Physical Society. - 0031-9007 .- 1079-7114. ; 121:10
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Tidskriftsartikel (refereegranskat)abstract
- Understanding multidecadal variability is an essential goal of climate dynamics. For example, the recent phenomenon referred to as the "global warming hiatus" may reflect a coupling to an intrinsic, preindustrial, multidecadal variability process. Here, using a multifractal time-series method, we demonstrate that 42 data sets of 79 proxies with global coverage exhibit pink-noise characteristics on multidecadal timescales. To quantify the persistence of this behavior, we examine high-resolution ice core and speleothem data to find pink noise in both pre- and postindustrial periods. We examine the spatial structure with an empirical orthogonal function analysis of the monthly averaged surface temperature from 1901 to 2012. The first mode clearly shows the distribution of ocean heat flux sinks located in the eastern Pacific and the Southern Ocean and has pink-noise characteristics on a multidecadal timescale. We hypothesize that this pink-noise multidecadal spatial mode may resonate with externally driven greenhouse gas forcing, driving large-scale climate processes.
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| 17. |
- Moon, Woosok, et al.
(författare)
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Nonadiabatic escape and stochastic resonance
- 2020
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Ingår i: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 53:9
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Tidskriftsartikel (refereegranskat)abstract
- We analyze the fluctuation-driven escape of particles from a metastable state under the influence of a weak periodic force. We develop an asymptotic method to solve the appropriate Fokker-Planck equation with mixed natural and absorbing boundary conditions. The approach uses two boundary layers flanking an interior region; most of the probability is concentrated within the boundary layer near the metastable point of the potential and particles transit the interior region before exiting the domain through the other boundary layer, which is near the unstable maximal point of the potential. The dominant processes in each region are given by approximate time-dependent solutions matched to construct the approximate composite solution, which gives the rate of escape with weak periodic forcing. Using reflection we extend the method to a double well potential influenced by white noise and weak periodic forcing, and thereby derive a two-state stochastic model-the simplest treatment of stochastic resonance theory-in the nonadiabatic limit.
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| 18. |
- Moon, Woosok, et al.
(författare)
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Physical length scales of wind-blown snow redistribution and accumulation on relatively smooth Arctic first-year sea ice
- 2019
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Ingår i: Environmental Research Letters. - : IOP Publishing. - 1748-9326. ; 14:10
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Tidskriftsartikel (refereegranskat)abstract
- Snow thickness measurements over relatively smooth Arctic first-year sea ice, obtained near Cambridge Bay in the Canadian Arctic (2014, 2016 and 2017) and near Elson Lagoon in the Alaskan Arctic (2003 and 2006), are analyzed to quantify physical length-scales and their relevant scaling behaviors. We use the multi-fractal temporally weighted detrended fluctuation analysis method to detect two major physical length-scales from the two independent study locations. Our results suggest that physical processes underlying the formation of snow dunes are consistent and that the wind is the main process shaping the snow thickness variability and redistribution. One scale, around 10 m, appears to be related to the formation of the snow 'dunes', while the other scale, between 30 and 100 m, is likely associated with the various interactions of the snow dunes such as merging, calving and lateral linking. Results imply that snow on level sea ice shows self-organized characteristics.
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| 19. |
- Moon, Woosok, et al.
(författare)
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River Nile discharge, the Pacific Ocean and world climate - a seasonal synchronization perspective
- 2021
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Ingår i: Tellus. Series A, Dynamic meteorology and oceanography. - : Stockholm University Press. - 0280-6495 .- 1600-0870. ; 73:1, s. 1-12
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Tidskriftsartikel (refereegranskat)abstract
- The Nile is the longest river in Africa stretching over around 6650 km through 11 countries. From the times of the ancient Egyptian Pharaonic civilization, the Nile is known to be a blessing, which provides major resources including water and fertile soil for agriculture, and facilitates transportations and international trades in nearby countries. Due to its invaluable importance to local economy and agriculture, it is undoubtedly of paramount importance to know how the variability of the Nile is controlled by local and global climate and its morphological characteristics. Here, we utilize a newly developed time-series analysis method applied to monthly Nile river inflow data to reveal various factors changing the river inflow from seasonal to inter-annual, decadal and beyond. On seasonal time-scales a positive feedback, associated mostly with river's morphological change driven by summer precipitation, is identified as a main mechanism for maximal variability in September leading to major flooding or drought. In particular, the positive feedback is quite similar in its mechanism to major climate feedbacks observed, e.g. with ice albedo and Bjerknes feedbacks. The slow time-evolution of the positive feedback explains human endeavour history to control nature, such as the control of the Nile annual flooding through dam construction. The analysis of climate association reveals clear link with large-scale and low-frequency forcing. Decadal and multi-decadal timescales of local precipitation and associated teleconnection with atmospheric and oceanic circulation can be traced back to the Pacific Ocean, and involve mostly the El-Nino Southern Oscillation and the Pacific Decadal Oscillation.
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