scholarly journals A delay equation model for the Atlantic Multidecadal Oscillation

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200659
Author(s):  
Swinda K. J. Falkena ◽  
Courtney Quinn ◽  
Jan Sieber ◽  
Henk A. Dijkstra
Keyword(s):  
Southern Oscillation ◽  
Atlantic Multidecadal Oscillation ◽  
Equation Model ◽  
Delay Equation ◽  
Memory Term ◽  
Extended Model ◽  
Differential Model ◽  
Delay Models ◽  
Spatially Extended ◽  
Delay Difference

A new technique to derive delay models from systems of partial differential equations, based on the Mori–Zwanzig (MZ) formalism, is used to derive a delay-difference equation model for the Atlantic Multidecadal Oscillation (AMO). The MZ formalism gives a rewriting of the original system of equations, which contains a memory term. This memory term can be related to a delay term in a resulting delay equation. Here, the technique is applied to an idealized, but spatially extended, model of the AMO. The resulting delay-difference model is of a different type than the delay differential model which has been used to describe the El Niño Southern Oscillation. In addition to this model, which can also be obtained by integration along characteristics, error terms for a smoothing approximation of the model have been derived from the MZ formalism. Our new method of deriving delay models from spatially extended models has a large potential to use delay models to study a range of climate variability phenomena.

scholarly journals Derivation of delay equation climate models using the Mori-Zwanzig formalism

2019 ◽  
Vol 475 (2227) ◽  
pp. 20190075 ◽  
Author(s):  
Swinda K. J. Falkena ◽  
Courtney Quinn ◽  
Jan Sieber ◽  
Jason Frank ◽  
Henk A. Dijkstra
Keyword(s):  
Ad Hoc ◽  
Climate Models ◽  
Conceptual Models ◽  
Southern Oscillation ◽  
Additional Term ◽  
Memory Term ◽  
Propagation Time ◽  
Delay Model ◽  
Delay Models ◽  
Nonlinear Delay

Models incorporating delay have been frequently used to understand climate variability phenomena, but often the delay is introduced through an ad hoc physical reasoning, such as the propagation time of waves. In this paper, the Mori-Zwanzig formalism is introduced as a way to systematically derive delay models from systems of partial differential equations and hence provides a better justification for using these delay-type models. The Mori-Zwanzig technique gives a formal rewriting of the system using a projection onto a set of resolved variables, where the rewritten system contains a memory term. The computation of this memory term requires solving the orthogonal dynamics equation, which represents the unresolved dynamics. For nonlinear systems, it is often not possible to obtain an analytical solution to the orthogonal dynamics and an approximate solution needs to be found. Here, we demonstrate the Mori-Zwanzig technique for a two-strip model of the El Niño Southern Oscillation (ENSO) and explore methods to solve the orthogonal dynamics. The resulting nonlinear delay model contains an additional term compared to previously proposed ad hoc conceptual models. This new term leads to a larger ENSO period, which is closer to that seen in observations.

A stochastic dynamical systems view of the Atlantic Multidecadal Oscillation

2008 ◽  
Vol 366 (1875) ◽  
pp. 2543-2558 ◽  
Author(s):  
H.A Dijkstra ◽  
L.M Frankcombe ◽  
A.S von der Heydt
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Normal Mode ◽  
Ocean Circulation ◽  
Southern Oscillation ◽  
Atlantic Multidecadal Oscillation ◽  
Equation Model ◽  
Stochastic Dynamical Systems ◽  
Multidecadal Variability ◽  
The North

We provide a dynamical systems framework to understand the Atlantic Multidecadal Oscillation and show that this framework is in many ways similar to that of the El Niño/Southern Oscillation. A so-called minimal primitive equation model is used to represent the Atlantic Ocean circulation. Within this minimal model, we identify a normal mode of multidecadal variability that can destabilize the background climate state through a Hopf bifurcation. Next, we argue that noise is setting the amplitude of the sea surface temperature variability associated with this normal mode. The results provide support that a stochastic Hopf bifurcation is involved in the multidecadal variability as observed in the North Atlantic.

scholarly journals The Life and Death of the Recent Global Surface Warming Hiatus Parsimoniously Explained

Climate ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 64 ◽  
Author(s):  
Kristoffer Rypdal
Keyword(s):  
Southern Oscillation ◽  
Thermal Inertia ◽  
Volcanic Eruptions ◽  
Atlantic Multidecadal Oscillation ◽  
Delayed Response ◽  
Small Contribution ◽  
Surface Warming ◽  
Life And Death ◽  
Model Driven ◽  
Warming Hiatus

The main features of the instrumental global mean surface temperature (GMST) are reasonably well described by a simple linear response model driven by anthropogenic, volcanic and solar forcing. This model acts as a linear long-memory filter of the forcing signal. The physical interpretation of this filtering is the delayed response due to the thermal inertia of the ocean. This description is considerably more accurate if El Niño Southern Oscillation (ENSO) and the Atlantic Multidecadal Oscillation (AMO) are regarded as additional forcings of the global temperature and hence subject to the same filtering as the other forcing components. By considering these as predictors in a linear regression scheme, more than 92% of the variance in the instrumental GMST over the period 1870–2017 is explained by this model, in particular, all features of the 1998–2015 hiatus, including its death. While the more prominent pauses during 1870–1915 and 1940–1970 can be attributed to clustering in time of strong volcanic eruptions, the recent hiatus is an unremarkable phenomenon that is attributed to ENSO with a small contribution from solar activity.

scholarly journals Recurrence Analysis of Vegetation Indices for Highlighting the Ecosystem Response to Drought Events: An Application to the Amazon Forest

2020 ◽  
Vol 12 (6) ◽  
pp. 907 ◽  
Author(s):  
Teodoro Semeraro ◽  
Andrea Luvisi ◽  
Antonio O. Lillo ◽  
Roberta Aretano ◽  
Riccardo Buccolieri ◽  
...  
Keyword(s):  
Time Series ◽  
Land Surface ◽  
Vegetation Index ◽  
Southern Oscillation ◽  
Vegetation Indices ◽  
Atlantic Multidecadal Oscillation ◽  
Enso Event ◽  
Amazon Forest ◽  
Ecosystem Response ◽  
Water Index

Forests are important in sequestering CO2 and therefore play a significant role in climate change. However, the CO2 cycle is conditioned by drought events that alter the rate of photosynthesis, which is the principal physiological action of plants in transforming CO2 into biological energy. This study applied recurrence quantification analysis (RQA) to describe the evolution of photosynthesis-related indices to highlight disturbance alterations produced by the Atlantic Multidecadal Oscillation (AMO, years 2005 and 2010) and the El Niño-Southern Oscillation (ENSO, year 2015) in the Amazon forest. The analysis was carried out using Moderate Resolution Imaging Spectroradiometer (MODIS) images to build time series of the enhanced vegetation index (EVI), the normalized difference water index (NDWI), and the land surface temperature (LST) covering the period 2001–2018. The results did not show significant variations produced by AMO throughout the study area, while a disruption due to the global warming phase linked to the extreme ENSO event occurred, and the forest was able to recover. In addition, spatial differences in the response of the forest to the ENSO event were found. These findings show that the application of RQA to the time series of vegetation indices supports the evaluation of the forest ecosystem response to disruptive events. This approach provides information on the capacity of the forest to recover after a disruptive event and, therefore is useful to estimate the resilience of this particular ecosystem.

scholarly journals Dynamic wavelet correlation analysis for multivariate climate time series

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Josué M. Polanco-Martínez ◽  
Javier Fernández-Macho ◽  
Martín Medina-Elizalde
Keyword(s):  
Time Series ◽  
Tropical Cyclone ◽  
North Atlantic ◽  
Large Scale ◽  
Southern Oscillation ◽  
Atlantic Multidecadal Oscillation ◽  
Last Millennium ◽  
Climate Data ◽  
The North ◽  
Climate Time Series

AbstractThe wavelet local multiple correlation (WLMC) is introduced for the first time in the study of climate dynamics inferred from multivariate climate time series. To exemplify the use of WLMC with real climate data, we analyse Last Millennium (LM) relationships among several large-scale reconstructed climate variables characterizing North Atlantic: i.e. sea surface temperatures (SST) from the tropical cyclone main developmental region (MDR), the El Niño-Southern Oscillation (ENSO), the North Atlantic Multidecadal Oscillation (AMO), and tropical cyclone counts (TC). We examine the former three large-scale variables because they are known to influence North Atlantic tropical cyclone activity and because their underlying drivers are still under investigation. WLMC results obtained for these multivariate climate time series suggest that: (1) MDRSST and AMO show the highest correlation with each other and with respect to the TC record over the last millennium, and: (2) MDRSST is the dominant climate variable that explains TC temporal variability. WLMC results confirm that this method is able to capture the most fundamental information contained in multivariate climate time series and is suitable to investigate correlation among climate time series in a multivariate context.

scholarly journals A Spatially Extended Model for Residential Segregation

2007 ◽  
Vol 2007 ◽  
pp. 1-20 ◽  
Author(s):  
Antonio Aguilera ◽  
Edgardo Ugalde
Keyword(s):  
Residential Segregation ◽  
Control Parameter ◽  
Housing Prices ◽  
Dynamical Process ◽  
Extended Model ◽  
The Status ◽  
Spatially Extended ◽  
Segregation Phenomenon ◽  
Virtual City ◽  
The Cost

We analyze urban spatial segregation phenomenon in terms of the income distribution over a population, and an inflationary parameter weighting the evolution of housing prices. For this, we develop a discrete spatially extended model based on a multiagent approach. In our model, the mobility of socioeconomic agents is driven only by the housing prices. Agents exchange location in order to fit their status to the cost of their housing. On the other hand, the price of a particular house depends on the status of its tenant, and on the neighborhood mean lodging cost weighted by a control parameter. The agent's dynamics converges to a spatially organized configuration, whose regularity is measured by using an entropy-like indicator. This simple model provides a dynamical process organizing the virtual city, in a way that the population inequality and the inflationary parameter determine the degree of residential segregation in the final stage of the process, in agreement with the segregation-inequality thesis put forward by Douglas Massey.

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