Synchronicity in predictive modelling: a new view of data assimilation

International audienceThe problem of data assimilation can be viewed as one of synchronizing two dynamical systems, one representing "truth" and the other representing "model", with a unidirectional flow of information between the two. Synchronization of truth and model defines a general view of data assimilation, as machine perception, that is reminiscent of the Jung-Pauli notion of synchronicity between matter and mind. The dynamical systems paradigm of the synchronization of a pair of loosely coupled chaotic systems is expected to be useful because quasi-2D geophysical fluid models have been shown to synchronize when only medium-scale modes are coupled. The synchronization approach is equivalent to standard approaches based on least-squares optimization, including Kalman filtering, except in highly non-linear regions of state space where observational noise links regimes with qualitatively different dynamics. The synchronization approach is used to calculate covariance inflation factors from parameters describing the bimodality of a one-dimensional system. The factors agree in overall magnitude with those used in operational practice on an ad hoc basis. The calculation is robust against the introduction of stochastic model error arising from unresolved scales

On the physical nudging equations

In this work we show how it is possible to derive a new set of nudging equations, a tool still used in many data assimilation problems, starting from statistical physics considerations and availing ourselves of stochastic parameterizations that take into account unresolved interactions. The fluctuations used are thought of as Gaussian white noise with zero mean. The derivation is based on the conditioned Langevin dynamics technique. Exploiting the relation between the Fokker-Planck and the Langevin equations, the nudging equations are derived for a maximally observed system that converges towards the observations in finite time. The new nudging term found is the analog of the so called quantum potential of the Bohmian mechanics. In order to make the new nudging equations feasible for practical computations, two approximations are developed and used as bases from which extending this tool to non-perfectly observed systems. By means of a physical framework, in the zero noise limit, all the physical nudging parameters are fixed by the model under study and there is no need to tune other free ad-hoc variables. The limit of zero noise shows that also for the classical nudging equations it is necessary to use dynamical information to correct the typical relaxation term. A comparison of these approximations with a 3DVar scheme, that use a conjugate gradient minimization, is then shown in a series of four twin experiments that exploit low order chaotic models

Sensitivity of Aerosol Distribution and Climate Response to Stratospheric SO_2 Injection Locations

Injection of SO_2 into the stratosphere has been proposed as a method to, in part, counteract anthropogenic climate change. So far, most studies investigated injections at the equator or in a region in the tropics. Here we use Community Earth System Model version 1 Whole Atmosphere Community Climate Model (CESM1(WACCM)) to explore the impact of continuous single grid point SO_2 injections at seven different latitudes and two altitudes in the stratosphere on aerosol distribution and climate. For each of the 14 locations, 3 different constant SO_2 emission rates were tested to identify linearity in aerosol burden, aerosol optical depth, and climate effects. We found that injections at 15°N and 15°S and at 25 km altitude have equal or greater effect on radiation and surface temperature than injections at the equator. Nonequatorial injections transport SO_2 and sulfate aerosols more efficiently into middle and high latitudes and result in particles of smaller effective radius and larger aerosol burden in middle and high latitudes. Injections at 15°S produce the largest increase in global average aerosol optical depth and increase the change in radiative forcing per Tg SO_2/yr by about 15% compared to equatorial injections. High-altitude injections at 15°N produce the largest reduction in global average temperature of 0.2° per Tg S/yr for the last 7 years of a 10 year experiment. Injections at higher altitude are generally more efficient at reducing surface temperature, with the exception of large equatorial injections of at least 12 Tg SO_2/yr. These findings have important implications for designing a strategy to counteract global climate change

The Climate Response to Stratospheric Aerosol Geoengineering Can Be Tailored Using Multiple Injection Locations

By injecting different amounts of SO_2 at multiple different latitudes, the spatial pattern of aerosol optical depth (AOD) can be partially controlled. This leads to the ability to influence the climate response to geoengineering with stratospheric aerosols, providing the potential for design. We use simulations from the fully coupled whole-atmosphere chemistry climate model CESM1(WACCM) to demonstrate that by appropriately combining injection at just four different locations, 30°S, 15°S, 15°N, and 30°N, then three spatial degrees of freedom of AOD can be achieved: an approximately spatially uniform AOD distribution, the relative difference in AOD between Northern and Southern Hemispheres, and the relative AOD in high versus low latitudes. For forcing levels that yield 1–2°C cooling, the AOD and surface temperature response are sufficiently linear in this model so that the response to different combinations of injection at different latitudes can be estimated from single-latitude injection simulations; nonlinearities associated with both aerosol growth and changes to stratospheric circulation will be increasingly important at higher forcing levels. Optimized injection at multiple locations is predicted to improve compensation of CO_2-forced climate change relative to a case using only equatorial aerosol injection (which overcools the tropics relative to high latitudes). The additional degrees of freedom can be used, for example, to balance the interhemispheric temperature gradient and the equator to pole temperature gradient in addition to the global mean temperature. Further research is needed to better quantify the impacts of these strategies on changes to long-term temperature, precipitation, and other climate parameters

Stratospheric Dynamical Response and Ozone Feedbacks in the Presence of SO_2 Injections

Injections of sulfur dioxide into the stratosphere are among several proposed methods of solar radiation management. Such injections could cool the Earth's climate. However, they would significantly alter the dynamics of the stratosphere. We explore here the stratospheric dynamical response to sulfur dioxide injections ∼5 km above the tropopause at multiple latitudes (equator, 15°S, 15°N, 30°S and 30°N) using a fully coupled Earth system model, Community Earth System Model, version 1, with the Whole Atmosphere Community Climate Model as its atmospheric component (CESM1(WACCM)). We find that in all simulations, the tropical lower stratosphere warms primarily between 30°S and 30°N, regardless of injection latitude. The quasi-biennial oscillation (QBO) of the tropical zonal wind is altered by the various sulfur dioxide injections. In a simulation with a 12 Tg yr^(−1) equatorial injection, and with fully interactive chemistry, the QBO period lengthens to ∼3.5 years but never completely disappears. However, in a simulation with specified (or noninteractive) chemical fields, including O_3 and prescribed aerosols taken from the interactive simulation, the oscillation is virtually lost. In addition, we find that geoengineering does not always lengthen the QBO. We further demonstrate that the QBO period changes from 24 to 12–17 months in simulations with sulfur dioxide injections placed poleward of the equator. Our study points to the importance of understanding and verifying of the complex interactions between aerosols, atmospheric dynamics, and atmospheric chemistry as well as understanding the effects of sulfur dioxide injections placed away from the Equator on the QBO

Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise

The Primitive Equations are a basic model in the study of large scale Oceanic and Atmospheric dynamics. These systems form the analytical core of the most advanced General Circulation Models. For this reason and due to their challenging nonlinear and anisotropic structure the Primitive Equations have recently received considerable attention from the mathematical community. In view of the complex multi-scale nature of the earth's climate system, many uncertainties appear that should be accounted for in the basic dynamical models of atmospheric and oceanic processes. In the climate community stochastic methods have come into extensive use in this connection. For this reason there has appeared a need to further develop the foundations of nonlinear stochastic partial differential equations in connection with the Primitive Equations and more generally. In this work we study a stochastic version of the Primitive Equations. We establish the global existence of strong, pathwise solutions for these equations in dimension 3 for the case of a nonlinear multiplicative noise. The proof makes use of anisotropic estimates, $L^{p}_{t}L^{q}_{x}$ estimates on the pressure and stopping time arguments.Comment: To appear in Nonlinearit

Stratospheric Response in the First Geoengineering Simulation Meeting Multiple Surface Climate Objectives

We describe here changes in stratospheric dynamics and chemistry in a first century‐long sulfate aerosol geoengineering simulation in which the mean surface temperature and the interhemispheric and equator‐to‐pole surface temperature gradients were kept near their 2020 levels despite the RCP8.5 emission scenario. Simulations were carried out with the Community Earth System Model, version 1 with the Whole Atmosphere Community Climate Model as its atmospheric component [CESM1(WACCM)] coupled to a feedback algorithm controlling the magnitude of sulfur dioxide (SO_2) injections at four injection latitudes. We find that, throughout the entire geoengineering simulation, the lower stratospheric temperatures increase by ∼0.19 K per Tg SO_2 injection per year or ∼10 K with ∼40 Tg SO_2/year total SO_2 injection. These temperature changes are associated with a strengthening of the polar jets in the stratosphere and weakening of the mean zonal wind in the lower stratosphere subtropics and throughout the troposphere, associated with weaker storm track activity. In the geoengineering simulation the quasi‐biennial oscillation of the tropical lower stratospheric winds remains close to the presently observed quasi‐biennial oscillation, even for large amounts of SO2 injection. Water vapor in the stratosphere increases substantially: by 25% with ∼20 Tg SO_2/year annual injection and by up to 90% with a ∼40 Tg SO_2/year injection. Stratospheric column ozone in the geoengineering simulation is predicted to recover to or supersede preozone hole conditions by the end of the century

Effects of Different Stratospheric SO_2 Injection Altitudes on Stratospheric Chemistry and Dynamics

Strategically applied geoengineering is proposed to reduce some of the known side effects of stratospheric aerosol modifications. Specific climate goals could be reached depending on design choices of stratospheric sulfur injections by latitude, altitude, and magnitude. Here we explore in detail the stratospheric chemical and dynamical responses to injections at different altitudes using a fully coupled Earth System Model. Two different scenarios are explored that produce approximately the same global cooling of 2°C over the period 2042–2049, a high‐altitude injection case using 24 Tg SO_2/year at 30 hPa (≈25‐km altitude) and a low‐altitude injection case using 32 Tg SO_2/year injections at 70 hPa (between 19‐ and 20‐km altitude), with annual injections divided equally between 15°N and 15°S. Both cases result in a warming of the lower tropical stratosphere up to 10 and 15°C for the high‐ and low‐altitude injection case and in substantial increases of stratospheric water vapor of up to 2 and 4 ppm, respectively, compared to no geoengineering conditions. Polar column ozone in the Northern Hemisphere is reduced by up to 18% in March for the high‐altitude injection case and up to 8% for the low‐altitude injection case. However, for winter middle and high northern latitudes, low‐altitude injections result in greater column ozone values than without geoengineering. These changes are mostly driven by dynamics and advection. Antarctic column ozone in 2042–2049 does not recover from present‐day (2002–2009) values for both cases

Dynamics of Decadal Climate Variability and Implications for its Prediction

The temperature record of the last 150 years is characterized by a long-term warming trend, with strong multidecadal variability superimposed. The multidecadal variability is also seen in other (societal important) parameters such as Sahel rainfall or Atlantic hurricane activity. The existence of the multidecadal variability makes climate change detection a challenge, since Global Warming evolves on a similar timescale. The ongoing discussion about a potential anthropogenic signal in the Atlantic hurricane activity is an example. A lot of work was devoted during the last years to understand the dynamics of the multidecadal variability, and external as well as internal mechanisms were proposed. This White Paper focuses on the internal mechanisms relevant to the Atlantic Multidecadal Oscillation/Variability (AMO/V) and the Pacific Decadal Oscillation/Variability (PDO/V). Specific attention is given to the role of the Meridional Overturning Circulation (MOC) in the Atlantic. The implications for decadal predictability and prediction are discussed