Levi G. Silvers

Shallow Water Quasi‐Geostrophic Theory on the Sphere

[1]xa0Quasi-geostrophic theory forms the basis for much of our understanding of mid-latitude atmospheric dynamics. The theory is typically presented in either its f-plane form or its β-plane form. However, for many applications, including diagnostic use in global climate modeling, a fully spherical version would be most useful. Such a global theory does in fact exist and has for many years, but few in the scientific community seem to have ever been aware of it. In the context of shallow water dynamics, it is shown that the spherical version of quasigeostrophic theory is easily derived (re-derived) based on a partitioning of the flow between nondivergent and irrotational components, as opposed to a partitioning between geostrophic and ageostrophic components. In this way, the invertibility principle is expressed as a relation between the streamfunction and the potential vorticity, rather than between the geopotential and the potential vorticity. This global theory is then extended by showing that the invertibility principle can be solved analytically using spheroidal harmonic transforms, an advancement that greatly improves the usefulness of this “forgotten” theory. When the governing equation for the time evolution of the potential vorticity is linearized about a state of rest, a simple Rossby-Haurwitz wave dispersion relation is derived and examined. These waves have a horizontal structure described by spheroidal harmonics, and the Rossby-Haurwitz wave frequencies are given in terms of the eigenvalues of the spheroidal harmonic operator. Except for sectoral harmonics with low zonal wavenumber, the quasi-geostrophic Rossby-Haurwitz frequencies agree very well with those calculated from the primitive equations. One of the many possible applications of spherical quasi-geostrophic theory is to the study of quasi-geostrophic turbulence on the sphere. In this context, the theory is used to derive an anisotropic Rhines barrier in three-dimensional wavenumber space.

Radiative convective equilibrium as a framework for studying the interaction between convection and its large-scale environment

An uncertain representation of convective clouds has emerged as one of the key barriers to our understanding of climate sensitivity. The large gap in resolved spatial scales between General Circulation Models (GCMs) and high resolution models has made a systematic study of convective clouds across model configurations difficult. It is shown here that the simulated atmosphere of a GCM in Radiative Convective Equilibrium (RCE) is sufficiently similar across a range of domain sizes to justify the use of RCE to study both a GCM and a high resolution model on the same domain with the goal of improved constraints on the parameterized clouds. Simulations of RCE with parameterized convection have been analyzed on domains with areas spanning more than two orders of magnitude ( 0.80−204×106km2), all having the same grid spacing of 13 km. The simulated climates on different domains are qualitatively similar in their degree of convective organization, the precipitation rates, and the vertical structure of the clouds and water vapor, with the similarity increasing as the domain size increases. Sea surface temperature perturbation experiments are used to estimate the climate feedback parameter for the differently configured experiments, and the cloud radiative effect is computed to examine the role which clouds play in the response. Despite the similar climate states between the domains the feedback parameter varies by more than a factor of two; the hydrological sensitivity parameter is better behaved, varying by a factor of 1.4. The sensitivity of the climate feedback parameter to domain size is related foremost to a nonsystematic response of low-level clouds as well as an increasingly negative longwave feedback on larger domains.

A Filtered Model of Tropical Wave Motions

[1]xa0Large-scale tropical phenomena such as the Madden-Julian Oscillation (MJO) and El Nino-Southern Oscillation (ENSO) are often studied using the longwave approximation to equatorial β-plane theory. This approximation involves the neglect of the (∂v/∂t) term in the meridional momentum equation. The approximation does not distort Kelvin waves, completely filters inertia-gravity waves, is reasonably accurate for long Rossby waves, but greatly distorts short Rossby waves. Here we present an improvement of the long wave model, based on an approximation of the (∂v/∂t) term rather than its complete neglect. The new model is similar to the longwave model in the sense that it does not distort Kelvin waves and completely filters inertia-gravity waves. However, it differs from the long wave model in the sense that it accurately describes Rossby waves of all wavelengths, thus making it a useful tool for the study of a wider range of tropical phenomena than just the MJO and ENSO. Although most of the mathematical analysis performed here is in the context of equatorial β-plane theory, we briefly discuss how the ideas can be generalized to spherical geometry.

Double and single ITCZs with and without clouds

AbstractA major bias in tropical precipitation over the Pacific in climate simulations stems from the models’ tendency to produce two strong distinct intertropical convergence zones (ITCZs) too often. Several mechanisms have been proposed that may contribute to the emergence of two ITCZs, but current theories cannot fully explain the bias. This problem is tackled by investigating how the interaction between atmospheric cloud-radiative effects (ACREs) and the large-scale circulation influences the ITCZ position in an atmospheric general circulation model. Simulations are performed in an idealized aqua-planet setup and the longwave and the shortwave ACREs are turned off individually or jointly. The low-level moist static energy (MSE) is shown to be a good predictor of the ITCZ position. Therefore, a mechanism is proposed that explains the changes in MSE and thus ITCZ position due to ACREs consistently across simulations. The mechanism implies that the ITCZ moves equatorward if the Hadley circulation strengt...

Equilibrium Climate Sensitivity Obtained From Multimillennial Runs of Two GFDL Climate Models

Equilibrium climate sensitivity (ECS), defined as the long‐term change in global mean surface air temperature in response to doubling atmospheric CO₂, is usually computed from short atmospheric simulations over a mixed layer ocean, or inferred using a linear regression over a short‐time period of adjustment. We report the actual ECS from multimillenial simulations of two Geophysical Fluid Dynamics Laboratory (GFDL) general circulation models (GCMs), ESM2M, and CM3 of 3.3 K and 4.8 K, respectively. Both values are ~1 K higher than estimates for the same models reported in the Fifth Assessment Report of the Intergovernmental Panel on Climate Change obtained by regressing the Earths energy imbalance against temperature. This underestimate is mainly due to changes in the climate feedback parameter (−α) within the first century after atmospheric CO₂ has stabilized. For both GCMs it is possible to estimate ECS with linear regression to within 0.3 K by increasing CO₂ at 1% per year to doubling and using years 51–350 after CO₂ is constant. We show that changes in −α differ between the two GCMs and are strongly tied to the changes in both vertical velocity at 500 hPa (ω500) and estimated inversion strength that the GCMs experience during the progression toward the equilibrium. This suggests that while cloud physics parametrizations are important for determining the strength of −α, the substantially different atmospheric state resulting from a changed sea surface temperature pattern may be of equal importance.

The Diversity of Cloud Responses to Twentieth Century Sea Surface Temperatures

Low-level clouds are shown to be the conduit between the observed sea surface temperatures (SST) and large decadal fluctuations of the top of the atmosphere radiative imbalance. The influence of low-level clouds on the climate feedback is shown for global mean time series as well as particular geographic regions. The changes of clouds are found to be important for a midcentury period of high sensitivity and a late century period of low sensitivity. These conclusions are drawn from analysis of amip-piForcing simulations using three atmospheric general circulation models (AM2.1, AM3, and AM4.0). All three models confirm the importance of the relationship between the global climate sensitivity and the eastern Pacific trends of SST and low-level clouds. However, this work argues that the variability of the climate feedback parameter is not driven by stratocumulus-dominated regions in the eastern ocean basins, but rather by the cloudy response in the rest of the tropics.

A Theory of Topographically Bound Balanced Motions and Application to Atmospheric Low-Level Jets

AbstractThe subject of this study is topographically bound low-level jets, such as the South American summertime low-level jet on the eastern side of the Andes and its companion, the Chilean low-level jet on the western side of the Andes. These jets are interpreted as balanced flows that obey the potential vorticity invertibility principle. This invertibility principle is expressed in isentropic coordinates, and the mathematical issue of isentropes that intersect the topography is treated by the method of a massless layer. In this way, the low-level jets on the western and eastern sides of the Andes can both be attributed to the infinite potential vorticity that lies in the infinitesimally thin massless layer on the topographic feature. To obtain a cyclonic flow centered on the topographic feature, the mountain crest must have been heated enough to draw down the overlying isentropic surfaces; otherwise, isentropic surfaces bend upward at the mountain crest and an anticyclonic flow is produced. Both anticy...

The GFDL Global Atmosphere and Land Model AM4.0/LM4.0: 1. Simulation Characteristics With Prescribed SSTs

In this two-part paper, a description is provided of a version of the AM4.0/LM4.0 atmosphere/ land model that will serve as a base for a new set of climate and Earth system models (CM4 and ESM4) under development at NOAA’s Geophysical Fluid Dynamics Laboratory (GFDL). This version, with roughly 100 km horizontal resolution and 33 levels in the vertical, contains an aerosol model that generates aerosol fields from emissions and a ‘‘light’’ chemistry mechanism designed to support the aerosol model but with prescribed ozone. In Part 1, the quality of the simulation in AMIP (Atmospheric Model Intercomparison Project) mode—with prescribed sea surface temperatures (SSTs) and sea-ice distribution—is described and compared with previous GFDL models and with the CMIP5 archive of AMIP simulations. The model’s Cess sensitivity (response in the top-of-atmosphere radiative flux to uniform warming of SSTs) and effective radiative forcing are also presented. In Part 2, the model formulation is described more fully and key sensitivities to aspects of the model formulation are discussed, along with the approach to model tuning.

The GFDL Global Atmosphere and Land Model AM4.0/LM4.0: 2. Model Description, Sensitivity Studies, and Tuning Strategies

In Part II of this two-part paper, documentation is provided of key aspects of a version of the AM4.0/LM4.0 atmosphere/land model that will serve as a base for a new set of climate and Earth system models (CM4 and ESM4) under development at NOAAs Geophysical Fluid Dynamics Laboratory (GFDL). The quality of the simulation in AMIP (Atmospheric Model Intercomparison Project) mode has been provided in Part I. Part II provides documentation of key components and some sensitivities to choices of model formulation and values of parameters, highlighting the convection parameterization and orographic gravity wave drag. The approach taken to tune the models clouds to observations is a particular focal point. Care is taken to describe the extent to which aerosol effective forcing and Cess sensitivity have been tuned through the model development process, both of which are relevant to the ability of the model to simulate the evolution of temperatures over the last century when coupled to an ocean model.

Accounting for Changing Temperature Patterns Increases Historical Estimates of Climate Sensitivity

Eight atmospheric general circulation models (AGCMs) are forced with observed historical (1871–2010) monthly sea surface temperature and sea ice variations using the Atmospheric Model Intercomparison Project II data set. The AGCMs therefore have a similar temperature pattern and trend to that of observed historical climate change. The AGCMs simulate a spread in climate feedback similar to that seen in coupled simulations of the response to CO2 quadrupling. However, the feedbacks are robustly more stabilizing and the effective climate sensitivity (EffCS) smaller. This is due to a pattern effect, whereby the pattern of observed historical sea surface temperature change gives rise to more negative cloud and longwave clear‐sky feedbacks. Assuming the patterns of long‐term temperature change simulated by models, and the radiative response to them, are credible; this implies that existing constraints on EffCS from historical energy budget variations give values that are too low and overly constrained, particularly at the upper end. For example, the pattern effect increases the long‐term Otto et al. (2013, https://doi.org/10.1038/ngeo1836) EffCS median and 5–95% confidence interval from 1.9 K (0.9–5.0 K) to 3.2 K (1.5–8.1 K).