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.

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 Estimates of the Water Vapor Climate Feedback during El Niño–Southern Oscillation

2009 ◽  
Vol 22 (23) ◽  
pp. 6404-6412 ◽  
Author(s):  
A. E. Dessler ◽  
S. Wong
Keyword(s):  
Global Warming ◽  
Water Vapor ◽  
El Niño ◽  
Climate Models ◽  
El Nino ◽  
Southern Oscillation ◽  
Specific Humidity ◽  
El Niño Southern Oscillation ◽  
El Nino Southern Oscillation ◽  
Water Vapor Feedback

Abstract The strength of the water vapor feedback has been estimated by analyzing the changes in tropospheric specific humidity during El Niño–Southern Oscillation (ENSO) cycles. This analysis is done in climate models driven by observed sea surface temperatures [Atmospheric Model Intercomparison Project (AMIP) runs], preindustrial runs of fully coupled climate models, and in two reanalysis products, the 40-yr European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-40) and the NASA Modern Era Retrospective-Analysis for Research and Applications (MERRA). The water vapor feedback during ENSO-driven climate variations in the AMIP models ranges from 1.9 to 3.7 W m−2 K−1, in the control runs it ranges from 1.4 to 3.9 W m−2 K−1, and in the ERA-40 and MERRA it is 3.7 and 4.7 W m−2 K−1, respectively. Taken as a group, these values are higher than previous estimates of the water vapor feedback in response to century-long global warming. Also examined is the reason for the large spread in the ENSO-driven water vapor feedback among the models and between the models and the reanalyses. The models and the reanalyses show a consistent relationship between the variations in the tropical surface temperature over an ENSO cycle and the radiative response to the associated changes in specific humidity. However, the feedback is defined as the ratio of the radiative response to the change in the global average temperature. Differences in extratropical temperatures will, therefore, lead to different inferred feedbacks, and this is the root cause of spread in feedbacks observed here. This is also the likely reason that the feedback inferred from ENSO is larger than for long-term global warming.

scholarly journals Interannual variability of the boreal summer tropical UTLS in observations and CCMVal-2 simulations

2016 ◽  
Vol 16 (13) ◽  
pp. 8695-8714 ◽  
Author(s):  
Markus Kunze ◽  
Peter Braesicke ◽  
Ulrike Langematz ◽  
Gabriele Stiller
Keyword(s):  
Climate Models ◽  
Southern Oscillation ◽  
Asian Summer Monsoon ◽  
Multiple Linear Regression Model ◽  
Transport Processes ◽  
Boreal Summer ◽  
Temperature Pattern ◽  
The Tibetan Plateau ◽  
Quasi Biennial Oscillation ◽  
Mixing Ratios

Abstract. During boreal summer the upper troposphere/lower stratosphere (UTLS) in the Northern Hemisphere shows a distinct maximum in water vapour (H2O) mixing ratios and a coincident minimum in ozone (O3) mixing ratios, both confined within the Asian monsoon anticyclone (AMA). This well-known feature has been related to transport processes emerging above the convective systems during the Asian summer monsoon (ASM), further modified by the dynamics of the AMA. We compare the ability of chemistry–climate models (CCMs) to reproduce the climatological characteristics and variability of H2O, O3, and temperature in the UTLS during the boreal summer with MIPAS satellite observations and ERA-Interim reanalyses. By using a multiple linear regression model the main driving factors, the strength of the ASM, the quasi-biennial oscillation (QBO), and the El Niño–Southern Oscillation (ENSO), are separated. The regression patterns related to ENSO show a coherent, zonally asymmetric signal for temperatures and H2O mixing ratios for ERA-Interim and the CCMs and suggest a weakening of the ASM during ENSO warm events. The QBO modulation of the lower-stratospheric temperature near the Equator is well represented as a zonally symmetric pattern in the CCMs. Changes in H2O and O3 mixing ratios are consistent with the QBO-induced temperature and circulation anomalies but less zonally symmetric than the temperature pattern. Regarding the ASM, the results of the regression analysis show for ERA-Interim and the CCMs enhanced H2O and reduced O3 mixing ratios within the AMA for stronger ASM seasons. The CCM results can further confirm earlier studies which emphasize the importance of the Tibetan Plateau/southern slope of the Himalayas as the main source region for H2O in the AMA. The results suggest that H2O is transported towards higher latitudes at the north-eastern edge of the AMA rather than towards low equatorial latitudes to be fed into the tropical pipe.

scholarly journals Overview and sample applications of SMILES and Odin-SMR retrievals of upper tropospheric humidity and cloud ice mass

2014 ◽  
Vol 14 (23) ◽  
pp. 12613-12629 ◽  
Author(s):  
P. Eriksson ◽  
B. Rydberg ◽  
H. Sagawa ◽  
M. S. Johnston ◽  
Y. Kasai
Keyword(s):  
Climate Models ◽  
Southern Oscillation ◽  
A Priori ◽  
Global Climate Models ◽  
Monte Carlo Integration ◽  
Data Sets ◽  
Upper Troposphere ◽  
Retrieval Scheme ◽  
Cloud Ice ◽  
Ice Water

Abstract. Retrievals of cloud ice mass and humidity from the Superconducting Submillimeter-Wave Limb-Emission Sounder (SMILES) and the Odin-SMR (Sub-Millimetre Radiometer) limb sounder are presented and example applications of the data are given. SMILES data give an unprecedented view of the diurnal variation of cloud ice mass. Mean regional diurnal cycles are reported and compared to some global climate models. Some improvements in the models regarding diurnal timing and relative amplitude were noted, but the models' mean ice mass around 250 hPa is still low compared to the observations. The influence of the ENSO (El Niño–Southern Oscillation) state on the upper troposphere is demonstrated using 12 years of Odin-SMR data. The same retrieval scheme is applied for both sensors, and gives low systematic differences between the two data sets. A special feature of this Bayesian retrieval scheme, of Monte Carlo integration type, is that values are produced for all measurements but for some atmospheric states retrieved values only reflect a priori assumptions. However, this "all-weather" capability allows a direct statistical comparison to model data, in contrast to many other satellite data sets. Another strength of the retrievals is the detailed treatment of "beam filling" that otherwise would cause large systematic biases for these passive cloud ice mass retrievals. The main retrieval inputs are spectra around 635/525 GHz from tangent altitudes below 8/9 km for SMILES/Odin-SMR, respectively. For both sensors, the data cover the upper troposphere between 30° S and 30° N. Humidity is reported as both relative humidity and volume mixing ratio. The vertical coverage of SMILES is restricted to a single layer, while Odin-SMR gives some profiling capability between 300 and 150 hPa. Ice mass is given as the partial ice water path above 260 hPa, but for Odin-SMR ice water content, estimates are also provided. Besides a smaller contrast between most dry and wet cases, the agreement with Aura MLS (Microwave Limb Sounder) humidity data is good. In terms of tropical mean humidity, all three data sets agree within 3.5 %RHi. Mean ice mass is about a factor of 2 lower compared to CloudSat. This deviation is caused by the fact that different particle size distributions are assumed, combined with saturation and a priori influences in the SMILES and Odin-SMR data.

A NONLINEAR DELAY MODEL DESCRIBING THE GROWTH OF TUMOR CELLS UNDER IMMUNE SURVEILLANCE AGAINST CANCER AND ITS STABILITY ANALYSIS

2012 ◽  
Vol 05 (03) ◽  
pp. 1260017 ◽  
Author(s):  
LING CHEN ◽  
WANBIAO MA
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Tumor Cells ◽  
Local Stability ◽  
Immune Surveillance ◽  
Delay Model ◽  
Existence Of Periodic Solutions ◽  
Growth Of Tumor ◽  
Nonlinear Delay

In this paper, based on some biological meanings and a model which was proposed by Lefever and Garay (1978), a nonlinear delay model describing the growth of tumor cells under immune surveillance against cancer is given. Then, boundedness of the solutions, local stability of the equilibria and Hopf bifurcation of the model are discussed in details. The existence of periodic solutions explains the restrictive interactions between immune surveillance and the growth of the tumor cells.

scholarly journals Northern winter stratospheric temperature and ozone responses to ENSO inferred from an ensemble of Chemistry Climate Models

2009 ◽  
Vol 9 (22) ◽  
pp. 8935-8948 ◽  
Author(s):  
C. Cagnazzo ◽  
E. Manzini ◽  
N. Calvo ◽  
A. Douglass ◽  
H. Akiyoshi ◽  
...  
Keyword(s):  
Climate Models ◽  
Southern Oscillation ◽  
Polar Vortex ◽  
Atmospheric Modeling ◽  
Residual Circulation ◽  
Model Simulations ◽  
Enso Events ◽  
Stratospheric Temperature ◽  
The Mean ◽  
Column Ozone

Abstract. The connection between the El Niño Southern Oscillation (ENSO) and the Northern polar stratosphere has been established from observations and atmospheric modeling. Here a systematic inter-comparison of the sensitivity of the modeled stratosphere to ENSO in Chemistry Climate Models (CCMs) is reported. This work uses results from a number of the CCMs included in the 2006 ozone assessment. In the lower stratosphere, the mean of all model simulations reports a warming of the polar vortex during strong ENSO events in February–March, consistent with but smaller than the estimate from satellite observations and ERA40 reanalysis. The anomalous warming is associated with an anomalous dynamical increase of column ozone north of 70° N that is accompanied by coherent column ozone decrease in the Tropics, in agreement with that deduced from the NIWA column ozone database, implying an increased residual circulation in the mean of all model simulations during ENSO. The spread in the model responses is partly due to the large internal stratospheric variability and it is shown that it crucially depends on the representation of the tropospheric ENSO teleconnection in the models.

scholarly journals Transient climate simulations of the deglaciation 21–9 thousand years before present; PMIP4 Core experiment design and boundary conditions

2015 ◽  
Vol 8 (10) ◽  
pp. 9045-9102 ◽  
Author(s):  
R. F. Ivanovic ◽  
L. J. Gregoire ◽  
M. Kageyama ◽  
D. M. Roche ◽  
P. J. Valdes ◽  
...  
Keyword(s):  
Working Group ◽  
Ad Hoc ◽  
Climate Models ◽  
Ice Sheet ◽  
Before Present ◽  
Last Deglaciation ◽  
Transient Simulations ◽  
The Last Deglaciation ◽  
Set Up ◽  
Core Simulation

Abstract. The last deglaciation, which marked the transition between the last glacial and present interglacial periods, was punctuated by a series of rapid (centennial and decadal) climate changes. Numerical climate models are useful for investigating mechanisms that underpin the events, especially now that some of the complex models can be run for multiple millennia. We have set up a Paleoclimate Modelling Intercomparison Project (PMIP) working group to coordinate efforts to run transient simulations of the last deglaciation, and to facilitate the dissemination of expertise between modellers and those engaged with reconstructing the climate of the last 21 thousand years. Here, we present the design of a coordinated Core simulation over the period 21–9 thousand years before present (ka) with time varying orbital forcing, greenhouse gases, ice sheets, and other geographical changes. A choice of two ice sheet reconstructions is given, but no ice sheet or iceberg meltwater should be prescribed in the Core simulation. Additional focussed simulations will also be coordinated on an ad-hoc basis by the working group, for example to investigate the effect of ice sheet and iceberg meltwater, and the uncertainty in other forcings. Some of these focussed simulations will focus on shorter durations around specific events to allow the more computationally expensive models to take part.

scholarly journals On the Dynamical Mechanisms Governing El Niño–Southern Oscillation Irregularity

2018 ◽  
Vol 31 (20) ◽  
pp. 8401-8419 ◽  
Author(s):  
Judith Berner ◽  
Prashant D. Sardeshmukh ◽  
Hannah M. Christensen
Keyword(s):  
El Niño ◽  
Time Scale ◽  
Climate Models ◽  
El Nino ◽  
Southern Oscillation ◽  
El Niño Southern Oscillation ◽  
El Nino Southern Oscillation ◽  
Short Time Scale ◽  
Time Step ◽  
Climate System Model

This study investigates the mechanisms by which short time-scale perturbations to atmospheric processes can affect El Niño–Southern Oscillation (ENSO) in climate models. To this end a control simulation of NCAR’s Community Climate System Model is compared to a simulation in which the model’s atmospheric diabatic tendencies are perturbed every time step using a Stochastically Perturbed Parameterized Tendencies (SPPT) scheme. The SPPT simulation compares better with ECMWF’s twentieth-century reanalysis in having lower interannual sea surface temperature (SST) variability and more irregular transitions between El Niño and La Niña states, as expressed by a broader, less peaked spectrum. Reduced-order linear inverse models (LIMs) derived from the 1-month lag covariances of selected tropical variables yield good representations of tropical interannual variability in the two simulations. In particular, the basic features of ENSO are captured by the LIM’s least damped oscillatory eigenmode. SPPT reduces the damping time scale of this eigenmode from 17 to 11 months, which is in better agreement with the 8 months obtained from reanalyses. This noise-induced stabilization is consistent with perturbations to the frequency of the ENSO eigenmode and explains the broadening of the SST spectrum (i.e., the greater ENSO irregularity). Although the improvement in ENSO shown here was achieved through stochastic physics parameterizations, it is possible that similar improvements could be realized through changes in deterministic parameterizations or higher numerical resolution. It is suggested that LIMs could provide useful insight into model sensitivities, uncertainties, and biases also in those cases.

Drivers of Twenty-First Century U.S. Winter Precipitation Trends in CMIP6 Models: A Storyline-Based Approach

2021 ◽  
pp. 1-48
Author(s):  
Daniel F. Schmidt ◽  
Kevin M. Grise
Keyword(s):  
Climate Models ◽  
Southern Oscillation ◽  
Global Climate ◽  
The United States ◽  
Winter Precipitation ◽  
Global Climate Models ◽  
First Century ◽  
Precipitation Trend ◽  
Twenty First Century ◽  
Precipitation Trends

AbstractClimate change during the twenty-first century has the potential to substantially alter geographic patterns of precipitation. However, regional precipitation changes can be very difficult to project, and in some regions, global climate models do not even agree on the sign of the precipitation trend. Since some of this uncertainty is due to internal variability rather than model bias, models cannot be used to narrow the possibilities to a single outcome, but they can usefully quantify the range of plausible outcomes and identify the combination of dynamical drivers that would be likely to produce each.This study uses a storylines approach—a type of regression-based analysis—to identify some of the key dynamical drivers that explain the variance in 21st century U.S. winter precipitation trends across CMIP6 models under the SSP3-7.0 emissions scenario. This analysis shows that the spread in precipitation trends is not primarily driven by differences in modeled climate sensitivity. Key drivers include global-mean surface temperature, but also tropical upper-troposphere temperature, the El Niño-Southern Oscillation (ENSO), the Pacific-North America (PNA) pattern, and the East Pacific (EP) dipole (a dipole pattern in geopotential heights over North America’s Pacific coast). Combinations of these drivers can reinforce or cancel to produce various high- or low-impact scenarios for winter precipitation trends in various regions of the United States. For example, the most extreme winter precipitation trends in the southwestern U.S. result from opposite trends in ENSO and EP, whereas the wettest winter precipitation trends in the midwestern U.S. result from a combination of strong global warming and a negative PNA trend.

scholarly journals Connecting regional aerosol emissions reductions to local and remote precipitation responses

2018 ◽  
Author(s):  
Daniel M. Westervelt ◽  
Andrew J. Conley ◽  
Arlene M. Fiore ◽  
Jean-François Lamarque ◽  
Drew T. Shindell ◽  
...  
Keyword(s):  
Sulfur Dioxide ◽  
Climate Models ◽  
Southern Oscillation ◽  
The United States ◽  
Carbonaceous Aerosol ◽  
Geophysical Fluid Dynamics Laboratory ◽  
Emissions Reductions ◽  
Control Simulation ◽  
Precipitation Response ◽  
Aerosol Emissions

Abstract. The unintended climatic implications of aerosol and precursor emission reductions implemented to protect public health are poorly understood. We investigate the precipitation response to regional changes in aerosol emissions using three coupled chemistry-climate models: NOAA Geophysical Fluid Dynamics Laboratory Coupled Model 3 (GFDL-CM3), NCAR Community Earth System Model (CESM1), and NASA Goddard Institute for Space Studies ModelE2 (GISS-E2). Our approach contrasts a long present-day control simulation from each model (up to 400 years with perpetual year 2000 or 2005 emissions) with fourteen individual aerosol emissions perturbation simulations (160–240 years each). We perturb emissions of sulfur dioxide and/or carbonaceous aerosol within six world regions and assess the significance of precipitation responses relative to internal variability determined by the control simulation and across the models. Global and regional precipitation mostly increases when we reduce regional aerosol emissions in the models, with the strongest responses occurring for sulfur dioxide emissions reductions from Europe and the United States. Precipitation responses to aerosol emissions reductions are largest in the tropics and project onto the El Niño-Southern Oscillation (ENSO). Regressing precipitation onto an Indo-Pacific zonal sea level pressure gradient index (a proxy for ENSO) indicates that the ENSO component of the precipitation response to regional aerosol removal can be as large as 20 % of the total simulated response. Precipitation increases in the Sahel in response to aerosol reductions in remote regions because an anomalous interhemispheric temperature gradient alters the position of the Intertropical Convergence Zone (ITCZ). This mechanism holds across multiple aerosol reduction simulations and models.

Sign in / Sign up

Export Citation Format

Share Document