Dynamics of the Intertropical Convergence Zone

Previous studies have shown that the latitude of the Intertropical Convergence Zone (ITCZ) is negatively correlated with cross-equatorial atmospheric energy transport and that the ITCZ shifts southward as the northern hemisphere cools and the northward cross-equatorial energy transport strengthens. However, it has remained unclear what controls the sensitivity of the ITCZ position to cross-equatorial energy transport, and what other factors may lead to shifts of the ITCZ position. In this thesis, it is shown how an energetic perspective using the vertically-integrated moist static energy balance of the atmosphere can be used to address this question. Climate states with a double-ITCZ around the equator also occur, for example, seasonally over the eastern Pacific, and frequently in climate models. Here it is shown how the ITCZ position is connected to the energy balance near the equator under a wide range of circumstances, including states with single and double ITCZs and using a Taylor expansion of the meridional energy transport around the equator quantitative estimates for the ITCZ location are derived. Simulations with an idealized aquaplanet general circulation model (GCM) confirm the quantitative adequacy of these relations. Using these ideas, an idealized precipitation model for the tropics is presented that is able to capture variations of paleoclimatological precipitation records on orbital time scales. The results provide a framework for assessing and understanding causes of common climate model biases and for interpreting tropical precipitation changes, such as those evident in records of climates of the past

The Equatorial Energy Balance, ITCZ Position, and Double-ITCZ Bifurcations

The intertropical convergence zone (ITCZ) migrates north–south on seasonal and longer time scales. Previous studies have shown that the zonal-mean ITCZ displacement off the equator is negatively correlated with the energy flux across the equator; when the ITCZ lies in the Northern Hemisphere, energy flows southward across the equator, and vice versa. The hemisphere that exports energy across the equator is the hemisphere with more net energy input, and it is usually the warmer hemisphere. But states with a double ITCZ straddling the equator also occur, for example, seasonally over the eastern Pacific and frequently in climate models. Here it is shown how the ITCZ position is connected to the energy balance near the equator in a broad range of circumstances, including states with single and double ITCZs. Taylor expansion of the variation of the meridional energy flux around the equator leads to the conclusion that for large positive net energy input into the equatorial atmosphere, the ITCZ position depends linearly on the cross-equatorial energy flux. For small positive equatorial net energy input, the dependence of the ITCZ position on the cross-equatorial energy flux weakens to the third root. When the equatorial net energy input or its curvature become negative, a bifurcation to double-ITCZ states occurs. Simulations with an idealized aquaplanet general circulation model (GCM) confirm the quantitative adequacy of these relations. The results provide a framework for assessing and understanding causes of common climate model biases and for interpreting tropical precipitation changes, such as those evident in records of climates of the past

Order-disorder transitions in a sheared many body system

Motivated by experiments on sheared suspensions that show a transition between ordered and disordered phases, we here study the long-time behavior of a sheared and overdamped 2-d system of particles interacting by repulsive forces. As a function of interaction strength and shear rate we find transitions between phases with vanishing and large single-particle diffusion. In the phases with vanishing single-particle diffusion, the system evolves towards regular lattices, usually on very slow time scales. Different lattices can be approached, depending on interaction strength and forcing amplitude. The disordered state appears in parameter regions where the regular lattices are unstable. Correlation functions between the particles reveal the formation of shear bands. In contrast to single particle densities, the spatially resolved two-particle correlation functions vary with time and allow to determine the phase within a period. As in the case of the suspensions, motion in the state with low diffusivity is essentially reversible, whereas in the state with strong diffusion it is not.Comment: 12 pages, 13 figures; Supplemental Movies: https://youtu.be/oFcrWo9Vs6E, https://youtu.be/tcowb7o05JQ, https://youtu.be/GkEUwycn7V4, https://youtu.be/k-XCo8CWFU

Energetic Constraints on the Position of the Intertropical Convergence Zone

The intertropical convergence zone (ITCZ) can shift meridionally on seasonal and longer time scales. Previous studies have shown that the latitude of the ITCZ is negatively correlated with cross-equatorial atmospheric energy transport. For example, the ITCZ shifts southward as the Northern Hemisphere cools and the northward cross-equatorial energy transport strengthens in response. It has remained unclear what controls the sensitivity of the ITCZ position to cross-equatorial energy transport and what other factors may lead to shifts of the ITCZ position. Here it is shown that the sensitivity of the ITCZ position to cross-equatorial energy transport depends on the net energy input to the equatorial atmosphere: the net radiative energy input minus any energy uptake by the oceans. Changes in this energy input can also lead to ITCZ shifts. The cross-equatorial energy transport is related through a series of approximations to interhemispheric asymmetries in the near-surface temperature distribution. The resulting theory of the ITCZ position is tested in idealized general circulation model simulations with a slab ocean as lower boundary condition. In the simulations, cross-equatorial energy transport increases under global warming (primarily because extratropical latent energy fluxes strengthen), and this shifts the ITCZ poleward. The ITCZ shifts equatorward if primarily the tropics warm in response to an increased net energy input to the equatorial atmosphere. The results have implications for explaining the varied response of the ITCZ to global or primarily tropical changes in the atmospheric energy balance, such as those that occur under global warming or El Niño

Easing Color Shifts in Score-Based Diffusion Models

Generated images of score-based models can suffer from errors in their spatial means, an effect, referred to as a color shift, which grows for larger images. This paper introduces a computationally inexpensive solution to mitigate color shifts in score-based diffusion models. We propose a simple nonlinear bypass connection in the score network, designed to process the spatial mean of the input and to predict the mean of the score function. This network architecture substantially improves the resulting spatial means of the generated images, and we show that the improvement is approximately independent of the size of the generated images. As a result, our solution offers a comparatively inexpensive solution for the color shift problem across image sizes. Lastly, we discuss the origin of color shifts in an idealized setting in order to motivate our approach

Seasonal and Interannual Variations of the Energy Flux Equator and ITCZ. Part I: Zonally Averaged ITCZ Position

In the zonal mean, the ITCZ lies at the foot of the ascending branch of the tropical mean meridional circulation, close to where the near-surface meridional mass flux vanishes. The ITCZ also lies near the energy flux equator (EFE), where the column-integrated meridional energy flux vanishes. This latter observation makes it possible to relate the ITCZ position to the energy balance, specifically the atmospheric net energy input near the equator and the cross-equatorial energy flux. Here the validity of the resulting relations between the ITCZ position and energetic quantities is examined with reanalysis data for the years 1979–2014. In the reanalysis data, the EFE and ITCZ position indeed covary on time scales of seasons and longer. Consistent with theory, the ITCZ position is proportional to the cross-equatorial atmospheric energy flux and inversely proportional to atmospheric net energy input at the equator. Variations of the cross-equatorial energy flux dominate seasonal variations of the ITCZ position. By contrast, variations of the equatorial net energy input, driven by ocean energy uptake variations, dominate interannual variations of the ITCZ position (e.g., those associated with ENSO)

The stability of stratified spatially periodic shear flows at low Péclet number

This work addresses the question of the stability of stratified, spatially periodic shear flows at low Péclet number but high Reynolds number. This little-studied limit is motivated by astrophysical systems, where the Prandtl number is often very small. Furthermore, it can be studied using a reduced set of “low-Péclet-number equations” proposed by Lignières [“The small-Péclet-number approximation in stellar radiative zones,” Astron. Astrophys. 348, 933–939 (1999)]. Through a linear stability analysis, we first determine the conditions for instability to infinitesimal perturbations. We formally extend Squire’s theorem to the low-Péclet-number equations, which shows that the first unstable mode is always two-dimensional. We then perform an energy stability analysis of the low-Péclet-number equations and prove that for a given value of the Reynolds number, above a critical strength of the stratification, any smooth periodic shear flow is stable to perturbations of arbitrary amplitude. In that parameter regime, the flow can only be laminar and turbulent mixing does not take place. Finding that the conditions for linear and energy stability are different, we thus identify a region in parameter space where finite-amplitude instabilities could exist. Using direct numerical simulations, we indeed find that the system is subject to such finite-amplitude instabilities. We determine numerically how far into the linearly stable region of parameter space turbulence can be sustained

Seasonal and Interannual Variations of the Energy Flux Equator and ITCZ. Part II: Zonally Varying Shifts of the ITCZ

The ITCZ lies at the ascending branch of the tropical meridional overturning circulation, where near-surface meridional mass fluxes vanish. Near the ITCZ, column-integrated energy fluxes vanish, forming an atmospheric energy flux equator (EFE). This paper extends existing approximations relating the ITCZ position and EFE to the atmospheric energy budget by allowing for zonal variations. The resulting relations are tested using reanalysis data for 1979–2014. The zonally varying EFE is found as the latitude where the meridional component of the divergent atmospheric energy transport (AET) vanishes. A Taylor expansion of the AET around the equator relates the ITCZ position to derivatives of the AET. To a first order, the ITCZ position is proportional to the divergent AET across the equator; it is inversely proportional to the local atmospheric net energy input (NEI) that consists of the net energy fluxes at the surface, at the top of the atmosphere, and zonally across longitudes. The first-order approximation captures the seasonal migrations of the ITCZ in the African, Asian, and Atlantic sectors. In the eastern Pacific, a third-order approximation captures the bifurcation from single- to double-ITCZ states that occurs during boreal spring. In contrast to linear EFE theory, during boreal winter in the eastern Pacific, northward cross-equatorial AET goes along with an ITCZ north of the equator. EFE and ITCZ variations driven by ENSO are characterized by an equatorward (poleward) shift in the Pacific during El Niño (La Niña) episodes, which are associated with variations in equatorial ocean energy uptake