A theoretical framework for energy and momentum consistency in subgrid-scale parameterization for climate models

A theoretical framework for the joint conservation of energy and momentum in the parameterization of subgrid-scale processes in climate models is presented. The framework couples a hydrostatic resolved (planetary scale) flow to a nonhydrostatic subgrid-scale (mesoscale) flow. The temporal and horizontal spatial scale separation between the planetary scale and mesoscale is imposed using multiple-scale asymptotics. Energy and momentum are exchanged through subgrid-scale flux convergences of heat, pressure, and momentum. The generation and dissipation of subgrid-scale energy and momentum is understood using wave-activity conservation laws that are derived by exploiting the (mesoscale) temporal and horizontal spatial homogeneities in the planetary-scale flow. The relations between these conservation laws and the planetary-scale dynamics represent generalized nonacceleration theorems. A derived relationship between the wave-activity fluxes-which represents a generalization of the second Eliassen-Palm theorem-is key to ensuring consistency between energy and momentum conservation. The framework includes a consistent formulation of heating and entropy production due to kinetic energy dissipation.

Interactions between shallow and deep convection under a finite departure from convective quasi–equilibrium

The present paper presents a simple theory for the transformation of non-precipitating, shallow convection into precipitating, deep convective clouds. In order to make the pertinent point a much idealized system is considered, consisting only of shallow and deep convection without large–scale forcing. The transformation is described by an explicit coupling between these two types of convection. Shallow convection moistens and cools the atmosphere, whereas deep convection dries and warms, leading to destabilization and stabilization respectively. Consequently, in their own stand–alone modes, shallow convection perpetually grows, whereas deep convection simply damps: the former never reaches equilibrium, and the latter is never spontaneously generated. Coupling the modes together is the only way to reconcile these undesirable separate tendencies so that the convective system as a whole can remain in a stable periodic state under this idealized setting. Such coupling is a key missing element in current global atmospheric models. The energy–cycle description as originally formulated by Arakawa and Schubert, and presented herein is suitable for direct implementation into models using a mass–flux parameterization, and would alleviate the current problems with the representation of these two types of convection in numerical models. The present theory also provides a pertinent framework for analyzing large–eddy simulations and cloud–resolving modelling.

Estimating the volume of tephra deposits: a new simple strategy

Volume determination of tephra deposits is necessary for the assessment of the dynamics and hazards of explosive volcanoes. Several methods have been proposed during the past 40 years that include the analysis of crystal concentration of large pumices, integrations of various thinning relationships, and the inversion of field observations using analytical and computational models. Regardless of their strong dependence on tephra-deposit exposure and distribution of isomass/isopach contours, empirical integrations of deposit thinning trends still represent the most widely adopted strategy due to their practical and fast application. The most recent methods involve the best fitting of thinning data using various exponential seg- ments or a power-law curve on semilog plots of thickness (or mass/area) versus square root of isopach area. The exponential method is mainly sensitive to the number and the choice of straight segments, whereas the power-law method can better reproduce the natural thinning of tephra deposits but is strongly sensitive to the proximal or distal extreme of integration. We analyze a large data set of tephra deposits and propose a new empirical method for the deter- mination of tephra-deposit volumes that is based on the integration of the Weibull function. The new method shows a better agreement with observed data, reconciling the debate on the use of the exponential versus power-law method. In fact, the Weibull best fitting only depends on three free parameters, can well reproduce the gradual thinning of tephra deposits, and does not depend on the choice of arbitrary segments or of arbitrary extremes of integration.

Simple and effective technical procedures for the packing and application of nanospray PicoFrit HPLC columns for proteomic analyses

A simple procedure was developed for packing PicoFrit HPLC columns with chromatographic stationary phase using a reservoir fabricated from standard laboratory HPLC fittings. Packed columns were mounted onto a stainless steel ultra-low volume precolumn filter assembly containing a 0.5-mu m pore size steel frit. This format provided a conduit for the application of the nanospray voltage and protected the column from obstruction by sample material. The system was characterised and operational performance assessed by analysis of a range of peptide standards (n = 9).

Relaxation of surface tension in the free-surface boundary layers of simple Lennard-Jones liquids

In this paper we use molecular dynamics to answer a classical question: how does the surface tension on a liquid/gas interface appear? After defining surface tension from the first principles and performing several consistency checks, we perform a dynamic experiment with a single simple liquid nanodroplet. At time zero, we remove all molecules of the interfacial layer of molecules, creating a fresh bare interface with the bulk arrangement of molecules. After that the system evolves towards equilibrium, and the expected surface tension is re-established. We found that the system relaxation consists of three distinct stages. First, the mechanical balance is quickly re-established. During this process the notion of surface tension is meaningless. In the second stage, the surface tension equilibrates, and the density profile broadens to a value which we call “intrinsic” interfacial width. During the third stage, the density profile continues to broaden due to capillary wave excitations, which does not however affect the surface tension.We have observed this scenario for monatomic Lennard-Jones (LJ) liquid as well as for binary LJ mixtures at different temperatures, monitoring a wide range of physical observables.

Measuring variation in potato roots in both field and glasshouse: the search for useful yield predictors and a simple screen for root traits

Aims Potatoes have an inadequate rooting system for efficient acquisition of water and minerals and use disproportionate amounts of irrigation and fertilizer. This research determines whether significant variation in rooting characteristics of potato exists, which characters correlate with final yield and whether a simple screen for rooting traits could be developed. Methods Twenty-eight genotypes of Solanum tuberosum groups Tuberosum and Phureja were grown in the field; eight replicate blocks to final harvest, while entire root systems were excavated from four blocks. Root classes were categorised and measured. The same measurements were made on these genotypes in the glasshouse, 2 weeks post emergence. Results In the field, total root length varied from 40 m to 112 m per plant. Final yield was correlated negatively with basal root specific root length and weakly but positively with total root weight. Solanum tuberosum group Phureja genotypes had more numerous roots and proportionally more basal than stolon roots compared with Solanum tuberosum, group Tuberosum genotypes. There were significant correlations between glasshouse and field measurements. Conclusions Our data demonstrate that variability in rooting traits amongst commercially available potato genotypes exists and a robust glasshouse screen has been developed. By measuring potato roots as described in this study, it is now possible to assess rooting traits of large populations of potato genotypes.

Emission: a simple new technique to correct rainfall estimates from attenuation due to both the radome and heavy rainfall

We present a new technique for correcting errors in radar estimates of rainfall due to attenuation which is based on the fact that any attenuating target will itself emit, and that this emission can be detected by the increased noise level in the radar receiver. The technique is being installed on the UK operational network, and for the first time, allows radome attenuation to be monitored using the increased noise at the higher beam elevations. This attenuation has a large azimuthal dependence but for an old radome can be up to 4 dB for rainfall rates of just 2–4 mm/h. This effect has been neglected in the past, but may be responsible for significant errors in rainfall estimates and in radar calibrations using gauges. The extra noise at low radar elevations provides an estimate of the total path integrated attenuation of nearby storms; this total attenuation can then be used as a constraint for gate-by-gate or polarimetric correction algorithms.

Simulated variations in atmospheric CO2 over a Wisconsin forest using a coupled ecosystem-atmosphere model

Ecosystem fluxes of energy, water, and CO2 result in spatial and temporal variations in atmospheric properties. In principle, these variations can be used to quantify the fluxes through inverse modelling of atmospheric transport, and can improve the understanding of processes and falsifiability of models. We investigated the influence of ecosystem fluxes on atmospheric CO2 in the vicinity of the WLEF-TV tower in Wisconsin using an ecophysiological model (Simple Biosphere, SiB2) coupled to an atmospheric model (Regional Atmospheric Modelling System). Model parameters were specified from satellite imagery and soil texture data. In a companion paper, simulated fluxes in the immediate tower vicinity have been compared to eddy covariance fluxes measured at the tower, with meteorology specified from tower sensors. Results were encouraging with respect to the ability of the model to capture observed diurnal cycles of fluxes. Here, the effects of fluxes in the tower footprint were also investigated by coupling SiB2 to a high-resolution atmospheric simulation, so that the model physiology could affect the meteorological environment. These experiments were successful in reproducing observed fluxes and concentration gradients during the day and at night, but revealed problems during transitions at sunrise and sunset that appear to be related to the canopy radiation parameterization in SiB2.

Determination of tube theory parameters using a simple grid model as an example

Although the tube theory is successful in describing entangled polymers qualitatively, a more quantitative description requires precise and consistent definitions of its parameters. Here we investigate the simplest model of entangled polymers, namely a single Rouse chain in a cubic lattice of line obstacles, and illustrate the typical problems and uncertainties of the tube theory. In particular we show that in general one needs 3 entanglement related parameters, but only 2 combinations of them are relevant for the long-time dynamics. Conversely, the plateau modulus can not be determined from these two parameters and requires a more detailed model of entanglements with explicit entanglement forces, such as the slipsprings model. It is shown that for the grid model the Rouse time within the tube is larger than the Rouse time of the free chain, in contrast to what the standard tube theory assumes.

The APE atlas

This Atlas presents statistical analyses of the simulations submitted to the Aqua-Planet Experiment (APE) data archive. The simulations are from global Atmospheric General Circulation Models (AGCM) applied to a water-covered earth. The AGCMs include ones actively used or being developed for numerical weather prediction or climate research. Some are mature, application models and others are more novel and thus less well tested in Earth-like applications. The experiment applies AGCMs with their complete parameterization package to an idealization of the planet Earth which has a greatly simplified lower boundary that consists of an ocean only. It has no land and its associated orography, and no sea ice. The ocean is represented by Sea Surface Temperatures (SST) which are specified everywhere with simple, idealized distributions. Thus in the hierarchy of tests available for AGCMs, APE falls between tests with simplified forcings such as those proposed by Held and Suarez (1994) and Boer and Denis (1997) and Earth-like simulations of the Atmospheric Modeling Intercomparison Project (AMIP, Gates et al., 1999). Blackburn and Hoskins (2013) summarize the APE and its aims. They discuss where the APE fits within a modeling hierarchy which has evolved to evaluate complete models and which provides a link between realistic simulation and conceptual models of atmospheric phenomena. The APE bridges a gap in the existing hierarchy. The goals of APE are to provide a benchmark of current model behaviors and to stimulate research to understand the cause of inter-model differences., APE is sponsored by the World Meteorological Organization (WMO) joint Commission on Atmospheric Science (CAS), World Climate Research Program (WCRP) Working Group on Numerical Experimentation (WGNE). Chapter 2 of this Atlas provides an overview of the specification of the eight APE experiments and of the data collected. Chapter 3 lists the participating models and includes brief descriptions of each. Chapters 4 through 7 present a wide variety of statistics from the 14 participating models for the eight different experiments. Additional intercomparison figures created by Dr. Yukiko Yamada in AGU group are available at http://www.gfd-dennou.org/library/ape/comparison/. This Atlas is intended to present and compare the statistics of the APE simulations but does not contain a discussion of interpretive analyses. Such analyses are left for journal papers such as those included in the Special Issue of the Journal of the Meteorological Society of Japan (2013, Vol. 91A) devoted to the APE. Two papers in that collection provide an overview of the simulations. One (Blackburn et al., 2013) concentrates on the CONTROL simulation and the other (Williamson et al., 2013) on the response to changes in the meridional SST profile. Additional papers provide more detailed analysis of the basic simulations, while others describe various sensitivities and applications. The APE experiment data base holds a wealth of data that is now publicly available from the APE web site: http://climate.ncas.ac.uk/ape/. We hope that this Atlas will stimulate future analyses and investigations to understand the large variation seen in the model behaviors.

Sensitivity of simulated climate to conservation of momentum in gravity wave drag parameterization

The Canadian Middle Atmosphere Model is used to examine the sensitivity of simulated climate to conservation of momentum in gravity wave drag parameterization. Momentum conservation requires that the parameterized gravity wave momentum flux at the top of the model be zero and corresponds to the physical boundary condition of no momentum flux at the top of the atmosphere. Allowing momentum flux to escape the model domain violates momentum conservation. Here the impact of momentum conservation in two sets of model simulations is investigated. In the first set, the simulation of present-day climate for two model-lid height configurations, 0.001 and 10 hPa, which are identical below 10 hPa, is considered. The impact of momentum conservation on the climate with the model lid at 0.001 hPa is minimal, which is expected because of the small amount of gravity wave momentum flux reaching 0.001 hPa. When the lid is lowered to 10 hPa and momentum is conserved, there is only a modest impact on the climate in the Northern Hemisphere; however, the Southern Hemisphere climate is more adversely affected by the deflection of resolved waves near the model lid. When momentum is not conserved in the 10-hPa model the climate is further degraded in both hemispheres, particularly in winter at high latitudes, and the impact of momentum conservation extends all the way to the surface. In the second set of simulations, the impact of momentum conservation and model-lid height on the modeled response to ozone depletion in the Southern Hemisphere is considered, and it is found that the response can display significant sensitivity to both factors. In particular, both the lower-stratospheric polar temperature and surface responses are significantly altered when the lid is lowered, with the effect being most severe when momentum is not conserved. The implications with regard to the current round of Intergovernmental Panel on Climate Change model projections are discussed.

Model-measurement comparison of mesospheric temperature inversions, and a simple theory for their occurrence

Mesospheric temperature inversions are well established observed phenomena, yet their properties remain the subject of ongoing research. Comparisons between Rayleigh-scatter lidar temperature measurements obtained by the University of Western Ontario's Purple Crow Lidar (42.9°N, 81.4°W) and the Canadian Middle Atmosphere Model are used to quantify the statistics of inversions. In both model and measurements, inversions occur most frequently in the winter and exhibit an average amplitude of ∼10 K. The model exhibits virtually no inversions in the summer, while the measurements show a strongly reduced frequency of occurrence with an amplitude about half that in the winter. A simple theory of mesospheric inversions based on wave saturation is developed, with no adjustable parameters. It predicts that the environmental lapse rate must be less than half the adiabatic lapse rate for an inversion to form, and it predicts the ratio of the inversion amplitude and thickness as a function of environmental lapse rate. Comparison of this prediction to the actual amplitude/thickness ratio using the lidar measurements shows good agreement between theory and measurements.

Angular momentum conservation and gravity wave drag parameterization: implications for climate models

The robustness of the parameterized gravity wave response to an imposed radiative perturbation in the middle atmosphere is examined. When momentum is conserved and for reasonable gravity wave drag parameters, the response to a polar cooling induces polar downwelling above the region of the imposed cooling, with consequent adiabatic warming. This response is robust to changes in the gravity wave source spectrum, background flow, gravity wave breaking criterion, and model lid height. When momentum is not conserved, either in the formulation or in the implementation of the gravity wave drag parameterization, the response becomes sensitive to the above-mentioned factors—in particular to the model lid height. The spurious response resulting from nonconservation is found to be nonnegligible in terms of the total gravity wave drag–induced downwelling.

Introductory remarks

The very first numerical models which were developed more than 20 years ago were drastic simplifications of the real atmosphere and they were mostly restricted to describe adiabatic processes. For prediction of a day or two of the mid tropospheric flow these models often gave reasonable results but the result deteriorated quickly when the prediction was extended further in time. The prediction of the surface flow was unsatisfactory even for short predictions. It was evident that both the energy generating processes as well as the dissipative processes have to be included in numerical models in order to predict the weather patterns in the lower part of the atmosphere and to predict the atmosphere in general beyond a day or two. Present-day computers make it possible to attack the weather forecasting problem in a more comprehensive and complete way and substantial efforts have been made during the last decade in particular to incorporate the non-adiabatic processes in numerical prediction models. The physics of radiational transfer, condensation of moisture, turbulent transfer of heat, momentum and moisture and the dissipation of kinetic energy are the most important processes associated with the formation of energy sources and sinks in the atmosphere and these have to be incorporated in numerical prediction models extended over more than a few days. The mechanisms of these processes are mainly related to small scale disturbances in space and time or even molecular processes. It is therefore one of the basic characteristics of numerical models that these small scale disturbances cannot be included in an explicit way. The reason for this is the discretization of the model's atmosphere by a finite difference grid or the use of a Galerkin or spectral function representation. The second reason why we cannot explicitly introduce these processes into a numerical model is due to the fact that some physical processes necessary to describe them (such as the local buoyance) are a priori eliminated by the constraints of hydrostatic adjustment. Even if this physical constraint can be relaxed by making the models non-hydrostatic the scale problem is virtually impossible to solve and for the foreseeable future we have to try to incorporate the ensemble or gross effect of these physical processes on the large scale synoptic flow. The formulation of the ensemble effect in terms of grid-scale variables (the parameters of the large-scale flow) is called 'parameterization'. For short range prediction of the synoptic flow at middle and high latitudes, very simple parameterization has proven to be rather successful.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part II: combined effects of gravity waves and equatorial planetary waves

This study examines the effect of combining equatorial planetary wave drag and gravity wave drag in a one-dimensional zonal mean model of the quasi-biennial oscillation (QBO). Several different combinations of planetary wave and gravity wave drag schemes are considered in the investigations, with the aim being to assess which aspects of the different schemes affect the nature of the modeled QBO. Results show that it is possible to generate a realistic-looking QBO with various combinations of drag from the two types of waves, but there are some constraints on the wave input spectra and amplitudes. For example, if the phase speeds of the gravity waves in the input spectrum are large relative to those of the equatorial planetary waves, critical level absorption of the equatorial planetary waves may occur. The resulting mean-wind oscillation, in that case, is driven almost exclusively by the gravity wave drag, with only a small contribution from the planetary waves at low levels. With an appropriate choice of wave input parameters, it is possible to obtain a QBO with a realistic period and to which both types of waves contribute. This is the regime in which the terrestrial QBO appears to reside. There may also be constraints on the initial strength of the wind shear, and these are similar to the constraints that apply when gravity wave drag is used without any planetary wave drag. In recent years, it has been observed that, in order to simulate the QBO accurately, general circulation models require parameterized gravity wave drag, in addition to the drag from resolved planetary-scale waves, and that even if the planetary wave amplitudes are incorrect, the gravity wave drag can be adjusted to compensate. This study provides a basis for knowing that such a compensation is possible.