Infrared dynamics of decaying two-dimensional turbulence governed by the Charney-Hasegawa-Mima equation

The low wave number range of decaying turbulence governed by the Charney-Hasegawa-Mima (CHM) equation is examined theoretically and by direct numerical simulation. Here, the low wave number range is defined as values of the wave number k below the wave number kE corresponding to the peak of the energy spectrum, or alternatively the centroid wave number of the energy spectrum. The energy spectrum in the low wave number range in the infrared regime (k →0) is theoretically derived to be E(k) ∼k5, using a quasinormal Markovianized model of the CHM equation. This result is verified by direct numerical simulation of the CHM equation. The wave number triads (k,p,q) responsible for the formation of the low wave number spectrum are also examined. It is found that the energy flux Π(k) for k< kE can be entirely expressed by Π(-)(k), which is the total net input of energy to wave numbers k. Furthermore, the contribution of nonlocal triad interactions to the energy flux is found to be predominant in the range log (k/kE)<-0.5, where the nonlocal interactions are defined to be those triad interactions for which the ratio of the largest leg of the triad to the smallest leg is larger than four. ©2001 The Physical Society of Japan

Climatic control of the biomass-burning decline in the Americas after AD 1500

The significance and cause of the decline in biomass burning across the Americas after AD 1500 is a topic of considerable debate. We synthesized charcoal records (a proxy for biomass burning) from the Americas and from the remainder of the globe over the past 2000 years, and compared these with paleoclimatic records and population reconstructions. A distinct post-AD 1500 decrease in biomass burning is evident, not only in the Americas, but also globally, and both are similar in duration and timing to ‘Little Ice Age’ climate change. There is temporal and spatial variability in the expression of the biomass-burning decline across the Americas but, at a regional–continental scale, ‘Little Ice Age’ climate change was likely more important than indigenous population collapse in driving this decline.

How do plants respond to nutrient shortage by biomass allocation?

Plants constantly sense the changes in their environment; when mineral elements are scarce, they often allocate a greater proportion of their biomass to the root system. This acclimatory response is a consequence of metabolic changes in the shoot and an adjustment of carbohydrate transport to the root. It has long been known that deficiencies of essential macronutrients (nitrogen, phosphorus, potassium and magnesium) result in an accumulation of carbohydrates in leaves and roots, and modify the shoot-to-root biomass ratio. Here, we present an update on the effects of mineral deficiencies on the expression of genes involved in primary metabolism in the shoot, the evidence for increased carbohydrate concentrations and altered biomass allocation between shoot and root, and the consequences of these changes on the growth and morphology of the plant root system.

Is the Helmholtz equation really sign-indefinite?

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique at wavenumbers that correspond to eigenvalues of the Laplacian, and thus the variational problem cannot be sign-definite. However, even in cases where the solution is unique for all wavenumbers, the standard variational formulations of the Helmholtz equation are still indefinite when the wavenumber is large. This indefiniteness has implications for both the analysis and the practical implementation of finite element methods. In this paper we introduce new sign-definite (also called coercive or elliptic) formulations of the Helmholtz equation posed in either the interior of a star-shaped domain with impedance boundary conditions, or the exterior of a star-shaped domain with Dirichlet boundary conditions. Like the standard variational formulations, these new formulations arise just by multiplying the Helmholtz equation by particular test functions and integrating by parts.

Available potential energy density for a multicomponent Boussinesq fluid with arbitrary nonlinear equation of state

In this paper, the concept of available potential energy (APE) density is extended to a multicomponent Boussinesq fluid with a nonlinear equation of state. As shown by previous studies, the APE density is naturally interpreted as the work against buoyancy forces that a parcel needs to perform to move from a notional reference position at which its buoyancy vanishes to its actual position; because buoyancy can be defined relative to an arbitrary reference state, so can APE density. The concept of APE density is therefore best viewed as defining a class of locally defined energy quantities, each tied to a different reference state, rather than as a single energy variable. An important result, for which a new proof is given, is that the volume integrated APE density always exceeds Lorenz’s globally defined APE, except when the reference state coincides with Lorenz’s adiabatically re-arranged reference state of minimum potential energy. A parcel reference position is systematically defined as a level of neutral buoyancy (LNB): depending on the nature of the fluid and on how the reference state is defined, a parcel may have one, none, or multiple LNB within the fluid. Multiple LNB are only possible for a multicomponent fluid whose density depends on pressure. When no LNB exists within the fluid, a parcel reference position is assigned at the minimum or maximum geopotential height. The class of APE densities thus defined admits local and global balance equations, which all exhibit a conversion with kinetic energy, a production term by boundary buoyancy fluxes, and a dissipation term by internal diffusive effects. Different reference states alter the partition between APE production and dissipation, but neither affect the net conversion between kinetic energy and APE, nor the difference between APE production and dissipation. We argue that the possibility of constructing APE-like budgets based on reference states other than Lorenz’s reference state is more important than has been previously assumed, and we illustrate the feasibility of doing so in the context of an idealised and realistic oceanic example, using as reference states one with constant density and another one defined as the horizontal mean density field; in the latter case, the resulting APE density is found to be a reasonable approximation of the APE density constructed from Lorenz’s reference state, while being computationally cheaper.

An historical perspective on the development of the thermodynamic equation of seawater - 2010

Oceanography is concerned with understanding the mechanisms controlling the movement of seawater and its contents. A fundamental tool in this process is the characterization of the thermophysical properties of seawater as functions of measured temperature and electrical conductivity, the latter used as a proxy for the concentration of dissolved matter in seawater. For many years a collection of algorithms denoted the Equation of State 1980 (EOS-80) has been the internationally accepted standard for calculating such properties. However, modern measurement technology now allows routine observations of temperature and electrical conductivity to be made to at least one order of magnitude more accurately than the uncertainty in this standard. Recently, a new standard has been developed, the Thermodynamical Equation of Seawater 2010 (TEOS-10). This new standard is thermodynamically consistent, valid over a wider range of temperature and salinity, and includes a mechanism to account for composition variations in seawater. Here we review the scientific development of this standard, and describe the literature involved in its development, which includes many of the articles in this special issue.

Vertical distribution and radiative effects of mineral dust and biomass burning aerosol over West Africa during DABEX

This paper presents measurements of the vertical distribution of aerosol extinction coefficient over West Africa during the Dust and Biomass-burning Aerosol Experiment (DABEX)/African Monsoon Multidisciplinary Analysis dry season Special Observing Period Zero (AMMA-SOP0). In situ aircraft measurements from the UK FAAM aircraft have been compared with two ground-based lidars (POLIS and ARM MPL) and an airborne lidar on an ultralight aircraft. In general, mineral dust was observed at low altitudes (up to 2 km), and a mixture of biomass burning aerosol and dust was observed at altitudes of 2–5 km. The study exposes difficulties associated with spatial and temporal variability when intercomparing aircraft and ground measurements. Averaging over many profiles provided a better means of assessing consistent errors and biases associated with in situ sampling instruments and retrievals of lidar ratios. Shortwave radiative transfer calculations and a 3-year simulation with the HadGEM2-A climate model show that the radiative effect of biomass burning aerosol was somewhat sensitive to the vertical distribution of aerosol. In particular, when the observed low-level dust layer was included in the model, the absorption of solar radiation by the biomass burning aerosols increased by 10%. We conclude that this absorption enhancement was caused by the dust reflecting solar radiation up into the biomass burning aerosol layer. This result illustrates that the radiative forcing of anthropogenic absorbing aerosol can be sensitive to the presence of natural aerosol species.

The influence of vegetation, fire spread and fire behaviour on biomass burning and trace gas emissions: results from a process-based model

A process-based fire regime model (SPITFIRE) has been developed, coupled with ecosystem dynamics in the LPJ Dynamic Global Vegetation Model, and used to explore fire regimes and the current impact of fire on the terrestrial carbon cycle and associated emissions of trace atmospheric constituents. The model estimates an average release of 2.24 Pg C yr−1 as CO2 from biomass burning during the 1980s and 1990s. Comparison with observed active fire counts shows that the model reproduces where fire occurs and can mimic broad geographic patterns in the peak fire season, although the predicted peak is 1–2 months late in some regions. Modelled fire season length is generally overestimated by about one month, but shows a realistic pattern of differences among biomes. Comparisons with remotely sensed burnt-area products indicate that the model reproduces broad geographic patterns of annual fractional burnt area over most regions, including the boreal forest, although interannual variability in the boreal zone is underestimated.

Instantaneous gelation in Smoluchowski’s coagulation equation revisited

We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, M. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initial data, the regularized gelation time decreasesas M increases, consistent with the expectation that the gelation time is zero in the unregularized system. This decrease appears to be a logarithmically slow function of M, indicating that instantaneously gelling kernels may still be justifiable as physical models despite the fact that they are highly singular in the absence of a cutoff. We also study the case when a source of monomers is introduced in the regularized system. In this case a stationary state is reached. We present a complete analytic description of this regularized stationary state for the model kernel, K(m1,m2)=max{m1,m2}ν, which gels instantaneously when M→∞ if ν>1. The stationary cluster size distribution decays as a stretched exponential for small cluster sizes and crosses over to a power law decay with exponent ν for large cluster sizes. The total particle density in the stationary state slowly vanishes as [(ν−1)logM]−1/2 when M→∞. The approach to the stationary state is nontrivial: Oscillations about the stationary state emerge from the interplay between the monomer injection and the cutoff, M, which decay very slowly when M is large. A quantitative analysis of these oscillations is provided for the addition model which describes the situation in which clusters can only grow by absorbing monomers.

How body mass and lifestyle affect juvenile biomass production in placental mammals

In mammals, the mass-specific rate of biomass production during gestation and lactation, here called maternal productivity, has been shown to vary with body size and lifestyle. Metabolic theory predicts that post-weaning growth of offspring, here termed juvenile productivity, should be higher than maternal productivity, and juveniles of smaller species should be more productive than those of larger species. Furthermore because juveniles generally have similar lifestyles to their mothers, across species juvenile and maternal productivities should be correlated. We evaluated these predictions with data from 270 species of placental mammals in 14 taxonomic/lifestyle groups. All three predictions were supported. Lagomorphs, perissodactyls and artiodactyls were very productive both as juveniles and as mothers as expected from the abundance and reliability of their foods. Primates and bats were unproductive as juveniles and as mothers, as expected as an indirect consequence of their low predation risk and consequent low mortality. Our results point the way to a mechanistic explanation for the suite of correlated life-history traits that has been called the slow–fast continuum.

The elliptic sine-Gordon equation: a nonlinear elliptic integrable PDE

In this paper, we summarise this recent progress to underline the features specific to this nonlinear elliptic case, and we give a new classification of boundary conditions on the semistrip that satisfy a necessary condition for yielding a boundary value problem can be effectively linearised. This classification is based on formulation the equation in terms of an alternative Lax pair.

Estimating Lorenz's reference state in an ocean with a nonlinear equation of state for seawater

The study of the mechanical energy budget of the oceans using Lorenz available potential energy (APE) theory is based on knowledge of the adiabatically re-arranged Lorenz reference state of minimum potential energy. The compressible and nonlinear character of the equation of state for seawater has been thought to cause the reference state to be ill-defined, casting doubt on the usefulness of APE theory for investigating ocean energetics under realistic conditions. Using a method based on the volume frequency distribution of parcels as a function of temperature and salinity in the context of the seawater Boussinesq approximation, which we illustrate using climatological data, we show that compressibility effects are in fact minor. The reference state can be regarded as a well defined one-dimensional function of depth, which forms a surface in temperature, salinity and density space between the surface and the bottom of the ocean. For a very small proportion of water masses, this surface can be multivalued and water parcels can have up to two statically stable levels in the reference density profile, of which the shallowest is energetically more accessible. Classifying parcels from the surface to the bottom gives a different reference density profile than classifying in the opposite direction. However, this difference is negligible. We show that the reference state obtained by standard sorting methods is equivalent, though computationally more expensive, to the volume frequency distribution approach. The approach we present can be applied systematically and in a computationally efficient manner to investigate the APE budget of the ocean circulation using models or climatological data.

A traceable physical calibration of the vertical advection-diffusion equation for modelling ocean heat uptake

The classic vertical advection-diffusion (VAD) balance is a central concept in studying the ocean heat budget, in particular in simple climate models (SCMs). Here we present a new framework to calibrate the parameters of the VAD equation to the vertical ocean heat balance of two fully-coupled climate models that is traceable to the models’ circulation as well as to vertical mixing and diffusion processes. Based on temperature diagnostics, we derive an effective vertical velocity w∗ and turbulent diffusivity k∗ for each individual physical process. In steady-state, we find that the residual vertical velocity and diffusivity change sign in mid-depth, highlighting the different regional contributions of isopycnal and diapycnal diffusion in balancing the models’ residual advection and vertical mixing. We quantify the impacts of the time-evolution of the effective quantities under a transient 1%CO2 simulation and make the link to the parameters of currently employed SCMs.