Simulations and mechanisms of subtropical low-cloud response to climate change

This thesis focuses on improving the simulation skills and the theoretical understanding of the subtropical low cloud response to climate change.

First, an energetically consistent forcing framework is designed and implemented for the large eddy simulation (LES) of the low-cloud response to climate change. The three representative current-day subtropical low cloud regimes of cumulus (Cu), cumulus-over-stratocumulus, and stratocumulus (Sc) are all well simulated with this framework, and results are comparable to the conventional fixed-SST approach. However, the cumulus response to climate warming subject to energetic constraints differs significantly from the conventional approach with fixed SST. Under the energetic constraint, the subtropics warm less than the tropics, since longwave (LW) cooling is more efficient with the drier subtropical free troposphere. The surface latent heat flux (LHF) also increases only weakly subject to the surface energetic constraint. Both factors contribute to an increased estimated inversion strength (EIS), and decreased inversion height. The decreased Cu-depth contributes to a decrease of liquid water path (LWP) and weak positive cloud feedback. The conventional fixed-SST approach instead simulates a strong increase in LHF and deepening of the Cu layer, leading to a weakly negative cloud feedback. This illustrates the importance of energetic constraints to the simulation and understanding of the sign and magnitude of low-cloud feedback.

Second, an extended eddy-diffusivity mass-flux (EDMF) closure for the unified representation of sub-grid scale (SGS) turbulence and convection processes in general circulation models (GCM) is presented. The inclusion of prognostic terms and the elimination of the infinitesimal updraft fraction assumption makes it more flexible for implementation in models across different scales. This framework can be consistently extended to formulate multiple updrafts and downdrafts, as well as variances and covariances. It has been verified with LES in different boundary layer regimes in the current climate, and further development and implementation of this closure may help to improve our simulation skills and understanding of low-cloud feedback through GCMs.

Constraints on the carbon cycle and climate during the early evolution of animals

One of the greatest challenges in science lies in disentangling causality in complex, coupled systems. This is illustrated no better than in the dynamic interplay between the Earth and life. The early evolution and diversification of animals occurred within a backdrop of global change, yet reconstructing the potential role of the environment in this evolutionary transition is challenging. In the 200 million years from the end-Cryogenian to the Ordovician, enigmatic Ediacaran fauna explored body plans, animals diversified and began to biomineralize, forever changing the ocean's chemical cycles, and the biological community in shallow marine ecosystems transitioned from a microbial one to an animal one.

In the following dissertation, a multi-faceted approach combining macro- and micro-scale analyses is presented that draws on the sedimentology, geochemistry and paleontology of the rocks that span this transition to better constrain the potential environmental changes during this interval.

In Chapter 1, the potential of clumped isotope thermometry in deep time is explored by assessing the importance of burial and diagenesis on the thermometer. Eocene- to Precambrian-aged carbonates from the Sultanate of Oman were analyzed from current burial depths of 350-5850 meters. Two end-member styles of diagenesis independent of burial depth were observed.

Chapters 2, 3 and 4 explore the fallibility of the Ediacaran carbon isotope record and aspects of the sedimentology and geochemistry of the rocks preserving the largest negative carbon isotope excursion on record---the Shuram Excursion. Chapter 2 documents the importance of temperature, fluid composition and mineralogy on the delta 18-O min record and interrogates the bulk trace metal signal. Chapter 3 explores the spatial variability in delta 13-C recorded in the transgressive Johnnie Oolite and finds a north-to-south trend recording the onset of the excursion. Chapter 4 investigates the nature of seafloor precipitation during this excursion and more broadly. We document the potential importance of microbial respiratory reactions on the carbonate chemistry of the sediment-water interface through time.

Chapter 5 investigates the latest Precambrian sedimentary record in carbonates from the Sultanate of Oman, including how delta 13-C and delta 34-S CAS vary across depositional and depth gradients. A new model for the correlation of the Buah and Ara formations across Oman is presented. Isotopic results indicate delta 13-C varies with relative eustatic change and delta 34-S CAS may vary in absolute magnitude across Oman.

Chapter 6 investigates the secular rise in delta 18-Omin in the early Paleozoic by using clumped isotope geochemistry on calcitic and phosphatic fossils from the Cambrian and Ordovician. Results do not indicate extreme delta 18-O seawater depletion and instead suggest warmer equatorial temperatures across the early Paleozoic.

The variations and climatic significance of D/H ratios in the carbon-bound hydrogen of cellulose in trees

The σD values of nitrated cellulose from a variety of trees covering a wide geographic range have been measured. These measurements have been used to ascertain which factors are likely to cause σD variations in cellulose C-H hydrogen.

It is found that a primary source of tree σD variation is the σD variation of the environmental precipitation. Superimposed on this are isotopic variations caused by the transpiration of the leaf water incorporated by the tree. The magnitude of this transpiration effect appears to be related to relative humidity.

Within a single tree, it is found that the hydrogen isotope variations which occur for a ring sequence in one radial direction may not be exactly the same as those which occur in a different direction. Such heterogeneities appear most likely to occur in trees with asymmetric ring patterns that contain reaction wood. In the absence of reaction wood such heterogeneities do not seem to occur. Thus, hydrogen isotope analyses of tree ring sequences should be performed on trees which do not contain reaction wood.

Comparisons of tree σD variations with variations in local climate are performed on two levels: spatial and temporal. It is found that the σD values of 20 North American trees from a wide geographic range are reasonably well-correlated with the corresponding average annual temperature. The correlation is similar to that observed for a comparison of the σD values of annual precipitation of 11 North American sites with annual temperature. However, it appears that this correlation is significantly disrupted by trees which grew on poorly drained sites such as those in stagnant marshes. Therefore, site selection may be important in choosing trees for climatic interpretation of σD values, although proper sites do not seem to be uncommon.

The measurement of σD values in 5-year samples from the tree ring sequences of 13 trees from 11 North American sites reveals a variety of relationships with local climate. As it was for the spatial σD vs climate comparison, site selection is also apparently important for temporal tree σD vs climate comparisons. Again, it seems that poorly-drained sites are to be avoided. For nine trees from different "well-behaved" sites, it was found that the local climatic variable best related to the σD variations was not the same for all sites.

Two of these trees showed a strong negative correlation with the amount of local summer precipitation. Consideration of factors likely to influence the isotopic composition of summer rain suggests that rainfall intensity may be important. The higher the intensity, the lower the σD value. Such an effect might explain the negative correlation of σD vs summer precipitation amount for these two trees. A third tree also exhibited a strong correlation with summer climate, but in this instance it was a positive correlation of σD with summer temperature.

The remaining six trees exhibited the best correlation between σD values and local annual climate. However, in none of these six cases was it annual temperature that was the most important variable. In fact annual temperature commonly showed no relationship at all with tree σD values. Instead, it was found that a simple mass balance model incorporating two basic assumptions yielded parameters which produced the best relationships with tree σD values. First, it was assumed that the σD values of these six trees reflected the σD values of annual precipitation incorporated by these trees. Second, it was assumed that the σD value of the annual precipitation was a weighted average of two seasonal isotopic components: summer and winter. Mass balance equations derived from these assumptions yielded combinations of variables that commonly showed a relationship with tree σD values where none had previously been discerned.

It was found for these "well-behaved" trees that not all sample intervals in a σD vs local climate plot fell along a well-defined trend. These departures from the local σD VS climate norm were defined as "anomalous". Some of these anomalous intervals were common to trees from different locales. When such widespread commonalty of an anomalous interval occurred, it was observed that the interval corresponded to an interval in which drought had existed in the North American Great Plains.

Consequently, there appears to be a combination of both local and large scale climatic information in the σD variations of tree cellulose C-H hydrogen.

Storm track response to perturbations in climate

This thesis advances our understanding of midlatitude storm tracks and how they respond to perturbations in the climate system. The midlatitude storm tracks are regions of maximal turbulent kinetic energy in the atmosphere. Through them, the bulk of the atmospheric transport of energy, water vapor, and angular momentum occurs in midlatitudes. Therefore, they are important regulators of climate, controlling basic features such as the distribution of surface temperatures, precipitation, and winds in midlatitudes. Storm tracks are robustly projected to shift poleward in global-warming simulations with current climate models. Yet the reasons for this shift have remained unclear. Here we show that this shift occurs even in extremely idealized (but still three-dimensional) simulations of dry atmospheres. We use these simulations to develop an understanding of the processes responsible for the shift and develop a conceptual model that accounts for it.

We demonstrate that changes in the convective static stability in the deep tropics alone can drive remote shifts in the midlatitude storm tracks. Through simulations with a dry idealized general circulation model (GCM), midlatitude storm tracks are shown to be located where the mean available potential energy (MAPE, a measure of the potential energy available to be converted into kinetic energy) is maximal. As the climate varies, even if only driven by tropical static stability changes, the MAPE maximum shifts primarily because of shifts of the maximum of near-surface meridional temperature gradients. The temperature gradients shift in response to changes in the width of the tropical Hadley circulation, whose width is affected by the tropical static stability. Storm tracks generally shift in tandem with shifts of the subtropical terminus of the Hadley circulation.

We develop a one-dimensional diffusive energy-balance model that links changes in the Hadley circulation to midlatitude temperature gradients and so to the storm tracks. It is the first conceptual model to incorporate a dynamical coupling between the tropical Hadley circulation and midlatitude turbulent energy transport. Numerical and analytical solutions of the model elucidate the circumstances of when and how the storm tracks shift in tandem with the terminus of the Hadley circulation. They illustrate how an increase of only the convective static stability in the deep tropics can lead to an expansion of the Hadley circulation and a poleward shift of storm tracks.

The simulations with the idealized GCM and the conceptual energy-balance model demonstrate a clear link between Hadley circulation dynamics and midlatitude storm track position. With the help of the hierarchy of models presented in this thesis, we obtain a closed theory of storm track shifts in dry climates. The relevance of this theory for more realistic moist climates is discussed.

Free algebras in Von Neumann-Bernays-Gӧdel set theory and positive elementary inductions in reasonable structures

This thesis consists of two independent chapters. The first chapter deals with universal algebra. It is shown, in von Neumann-Bernays-Gӧdel set theory, that free images of partial algebras exist in arbitrary varieties. It follows from this, as set-complete Boolean algebras form a variety, that there exist free set-complete Boolean algebras on any class of generators. This appears to contradict a well-known result of A. Hales and H. Gaifman, stating that there is no complete Boolean algebra on any infinite set of generators. However, it does not, as the algebras constructed in this chapter are allowed to be proper classes. The second chapter deals with positive elementary inductions. It is shown that, in any reasonable structure ᶆ, the inductive closure ordinal of ᶆ is admissible, by showing it is equal to an ordinal measuring the saturation of ᶆ. This is also used to show that non-recursively saturated models of the theories ACF, RCF, and DCF have inductive closure ordinals greater than _ω.

Structure-Function Studies of Nicotinic Acetylcholine Receptors Using Selective Agonists and Positive Allosteric Modulators

This dissertation primarily describes chemical-scale studies of nicotinic acetylcholine receptors (nAChRs) in order to better understand ligand-receptor selectivity and allosteric modulation influences during receptor activation. Electrophysiology coupled with canonical and non-canonical amino acids mutagenesis is used to probe subtle changes in receptor function.

The first half of this dissertation focuses on differential agonist selectivity of α4β2-containing nAChRs. The α4β2 nAChR can assemble in alternative stoichiometries as well as assemble with other accessory subunits. Chapter 2 identifies key structural residues that dictate binding and activation of three stoichiometry-dependent α4β2 receptor ligands: sazetidine-A, cytisine, and NS9283. These do not follow previously suggested hydrogen-bonding patterns of selectivity. Instead, three residues on the complementary subunit strongly influence binding ability of a ligand and receptor activation. Chapter 3 involves isolation of a α5α4β2 receptor-enriched population to test for a potential alternative agonist binding location at the α5 α4 interface. Results strongly suggest that agonist occupation of this site is not necessary for receptor activation and that the α5 subunit only incorporates at the accessory subunit location.

The second half of this dissertation seeks to identify residue interactions with positive allosteric modulators (PAMs) of the α7 nAChR. Chapter 4 focuses on methods development to study loss of potentiation of Type I PAMs, which indicate residues vital to propagation of PAM effects and/or binding. Chapter 5 investigates α7 receptor modulation by a Type II PAM (PNU 120596). These results show that PNU 120596 does not alter the agonist binding site, thus is relegated to influencing only the gating component of activation. From this, we were able to map a potential network of residues from the agonist binding site to the proposed PNU 120596 binding site that are essential for receptor potentiation.

Theory of the positive column of a gas discharge

An attempt is made to provide a theoretical explanation of the effect of the positive column on the voltage-current characteristic of a glow or an arc discharge. Such theories have been developed before, and all are based on balancing the production and loss of charged particles and accounting for the energy supplied to the plasma by the applied electric field. Differences among the theories arise from the approximations and omissions made in selecting processes that affect the particle and energy balances. This work is primarily concerned with the deviation from the ambipolar description of the positive column caused by space charge, electron-ion volume recombination, and temperature inhomogeneities.

The presentation is divided into three parts, the first of which involved the derivation of the final macroscopic equations from kinetic theory. The final equations are obtained by taking the first three moments of the Boltzmann equation for each of the three species in the plasma. Although the method used and the equations obtained are not novel, the derivation is carried out in detail in order to appraise the validity of numerous approximations and to justify the use of data from other sources. The equations are applied to a molecular hydrogen discharge contained between parallel walls. The applied electric field is parallel to the walls, and the dependent variables—electron and ion flux to the walls, electron and ion densities, transverse electric field, and gas temperature—vary only in the direction perpendicular to the walls. The mathematical description is given by a sixth-order nonlinear two-point boundary value problem which contains the applied field as a parameter. The amount of neutral gas and its temperature at the walls are held fixed, and the relation between the applied field and the electron density at the center of the discharge is obtained in the process of solving the problem. This relation corresponds to that between current and voltage and is used to interpret the effect of space charge, recombination, and temperature inhomogeneities on the voltage-current characteristic of the discharge.

The complete solution of the equations is impractical both numerically and analytically, and in Part II the gas temperature is assumed uniform so as to focus on the combined effects of space charge and recombination. The terms representing these effects are treated as perturbations to equations that would otherwise describe the ambipolar situation. However, the term representing space charge is not negligible in a thin boundary layer or sheath near the walls, and consequently the perturbation problem is singular. Separate solutions must be obtained in the sheath and in the main region of the discharge, and the relation between the electron density and the applied field is not determined until these solutions are matched.

In Part III the electron and ion densities are assumed equal, and the complicated space-charge calculation is thereby replaced by the ambipolar description. Recombination and temperature inhomogeneities are both important at high values of the electron density. However, the formulation of the problem permits a comparison of the relative effects, and temperature inhomogeneities are shown to be important at lower values of the electron density than recombination. The equations are solved by a direct numerical integration and by treating the term representing temperature inhomogeneities as a perturbation.

The conclusions reached in the study are primarily concerned with the association of the relation between electron density and axial field with the voltage-current characteristic. It is known that the effect of space charge can account for the subnormal glow discharge and that the normal glow corresponds to a close approach to an ambipolar situation. The effect of temperature inhomogeneities helps explain the decreasing characteristic of the arc, and the effect of recombination is not expected to appear except at very high electron densities.

Reggeization of some unequal mass processes involving higher spins : the reactions pion-nucleon going to (V,Nucleon), pion-nucleon going to (V,delta-hyperon), and photon-proton going to (positive pion,neutron)

Recent theoretical developments in the reggeization of inelastic processes involving particles with high spin are incorporated into a model of vector meson production. A number of features of experimental differential cross sections and density matrices are interpreted in terms of this model.

The method chosen for reggeization of helicity amplitudes first separates kinematic zeros and singularities from the parity-conserving amplitudes and then applies results of Freedman and Wang on daughter trajectories to the remaining factors. Kinematic constraints on helicity amplitudes at t = 0 and t = (M – M_Δ)² are also considered.

It is found that data for reactions of types πN→VN and πN→VΔ are consistent with a model of this type in which all kinematic constraints at t = 0 are satisfied by evasion (vanishing of residue functions). As a quantitative test of the parametrization, experimental differential cross sections of vector meson production reactions dominated by pion trajectory exchange are compared with the theory. It is found that reduced residue functions are approximately constant, once the kinematic behavior near t = (M – M_Δ)² has been removed.

The alternative possibility of conspiracy between amplitudes is also discussed; and it is shown that unless conspiracy is present, some amplitudes allowed by angular momentum conservation will not contribute with full strength in the forward direction. An example, γp→π⁺n in which the data for dσ/dt indicate conspiracy, is studied in detail.

Stationary Eddies and Zonal Variations of the Global Hydrological Cycle in a Changing Climate

This thesis advances our physical understanding of the sensitivity of the hydrological cycle to global warming. Specifically, it focuses on changes in the longitudinal (zonal) variation of precipitation minus evaporation (P - E), which is predominantly controlled by planetary-scale stationary eddies. By studying idealized general circulation model (GCM) experiments with zonally varying boundary conditions, this thesis examines the mechanisms controlling the strength of stationary-eddy circulations and their role in the hydrological cycle. The overarching goal of this research is to understand the cause of changes in regional P - E with global warming. An understanding of such changes can be useful for impact studies focusing on water availability, ecosystem management, and flood risk.

Based on a moisture-budget analysis of ERA-Interim data, we establish an approximation for zonally anomalous P - E in terms of surface moisture content and stationary-eddy vertical motion in the lower troposphere. Part of the success of this approximation comes from our finding that transient-eddy moisture fluxes partially cancel the effect of stationary-eddy moisture advection, allowing divergent circulations to dominate the moisture budget. The lower-tropospheric vertical motion is related to horizontal motion in stationary eddies by Sverdrup and Ekman balance. These moisture- and vorticity-budget balances also hold in idealized and comprehensive GCM simulations across a range of climates.

By examining climate changes in the idealized and comprehensive GCM simulations, we are able to show the utility of the vertical motion P - E approximation for splitting changes in zonally anomalous P - E into thermodynamic and dynamic components. Shifts in divergent stationary-eddy circulations dominate changes in zonally anomalous P - E. This limits the local utility of the "wet gets wetter, dry gets drier” idea, where existing P - E patterns are amplified with warming by the increase in atmospheric moisture content, with atmospheric circulations held fixed. The increase in atmospheric moisture content manifests instead in an increase in the amplitude of the zonally anomalous hydrological cycle as measured by the zonal variance of P - E. However, dynamic changes, particularly the slowdown of divergent stationary-eddy circulations, limit the strengthening of the zonally anomalous hydrological cycle. In certain idealized cases, dynamic changes are even strong enough to reverse the tendency towards "wet gets wetter, dry gets drier” with warming.

Motivated by the importance of stationary-eddy vertical velocities in the moisture budget analysis, we examine controls on the amplitude of stationary eddies across a wide range of climates in an idealized GCM with simple topographic and ocean-heating zonal asymmetries. An analysis of the thermodynamic equation in the vicinity of topographic forcing reveals the importance of on-slope surface winds, the midlatitude isentropic slope, and latent heating in setting the amplitude of stationary waves. The response of stationary eddies to climate change is determined primarily by the strength of zonal surface winds hitting the mountain. The sensitivity of stationary-eddies to this surface forcing increases with climate change as the slope of midlatitude isentropes decreases. However, latent heating also plays an important role in damping the stationary-eddy response, and this damping becomes stronger with warming as the atmospheric moisture content increases. We find that the response of tropical overturning circulations forced by ocean heat-flux convergence is described by changes in the vertical structure of moist static energy and deep convection. This is used to derive simple scalings for the Walker circulation strength that capture the monotonic decrease with warming found in our idealized simulations.

Through the work of this thesis, the advances made in understanding the amplitude of stationary-waves in a changing climate can be directly applied to better understand and predict changes in the zonally anomalous hydrological cycle.

Matrices whose hermitian part is positive definite

We are concerned with the class ∏_n of nxn complex matrices A for which the Hermitian part H(A) = A+A*/2 is positive definite.

Various connections are established with other classes such as the stable, D-stable and dominant diagonal matrices. For instance it is proved that if there exist positive diagonal matrices D, E such that DAE is either row dominant or column dominant and has positive diagonal entries, then there is a positive diagonal F such that FA ϵ ∏_n.

Powers are investigated and it is found that the only matrices A for which A^m ϵ ∏_n for all integers m are the Hermitian elements of ∏_n. Products and sums are considered and criteria are developed for AB to be in ∏_n.

Since ∏_n n is closed under inversion, relations between H(A)^-1 and H(A^-1) are studied and a dichotomy observed between the real and complex cases. In the real case more can be said and the initial result is that for A ϵ ∏_n, the difference H(adjA) - adjH(A) ≥ 0 always and is ˃ 0 if and only if S(A) = A-A*/2 has more than one pair of conjugate non-zero characteristic roots. This is refined to characterize real c for which cH(A^-1) - H(A)^-1 is positive definite.

The cramped (characteristic roots on an arc of less than 180°) unitary matrices are linked to ∏_n and characterized in several ways via products of the form A ^-1A*.

Classical inequalities for Hermitian positive definite matrices are studied in ∏_n and for Hadamard's inequality two types of generalizations are given. In the first a large subclass of ∏_n in which the precise statement of Hadamardis inequality holds is isolated while in another large subclass its reverse is shown to hold. In the second Hadamard's inequality is weakened in such a way that it holds throughout ∏_n. Both approaches contain the original Hadamard inequality as a special case.