Canonical description of the perspective projections

A unique parameterization of the perspective projections in all whole-numbered dimensions is reported. The algorithm for generating a perspective transformation from parameters and for recovering parameters from a transformation is a modification of the Givens orthogonalization algorithm. The algorithm for recovering a perspective transformation from a perspective projection is a modification of Roberts' classical algorithm. Both algorithms have been implemented in Pop-11 with call-out to the NAG Fortran libraries. Preliminary monte-carlo tests show that the transformation algorithm is highly accurate, but that the projection algorithm cannot recover magnitude and shear parameters accurately. However, there is reason to believe that the projection algorithm might improve significantly with the use of many corresponding points, or with multiple perspective views of an object. Previous parameterizations of the perspective transformations in the computer graphics and computer vision literature are discussed.

Design of an active arm support for assisting arm movements

In this paper we have explored areas of application for health care manipulators and possible user groups. We have shown the steps in the design approach to the conceptual mechanism from the AAS. The future work will be measurement from properties of the muscle with the elbow parameterization test-bed to get a database to design one part of the control area from the AAS. More work on the mechanical design is required before a functional prototype can be built.

Spin-up and adjustment of the Antarctic Circumpolar Current and global pycnocline

A theory is presented for the adjustment of the Antarctic Circumpolar Current (ACC) and global pycnocline to a sudden and sustained change in wind forcing. The adjustment timescale is controlled by the mesoscale eddy diffusivity across the ACC, the mean width of the ACC, the surface area of the ocean basins to the north, and deep water formation in the North Atlantic. In particular, northern sinking may have the potential to shorten the timescale and reduce its sensitivity to Southern Ocean eddies, but the relative importance of northern sinking and Southern Ocean eddies cannot be determined precisely, largely due to limitations in the parameterization of northern sinking. Although it is clear that the main processes that control the adjustment timescale are those which counteract the deepening of the global pycnocline, the theory also suggests that the timescale can be subtly modified by wind forcing over the ACC and global diapycnal mixing. Results from calculations with a reduced-gravity model compare well with the theory. The multidecadal-centennial adjustment timescale implies that long observational time series will be required to detect dynamic change in the ACC due to anthropogenic forcing. The potential role of Southern Ocean mesoscale eddy activity in determining both the equilibrium state of the ACC and the timescale over which it adjusts suggests that the response to anthropogenic forcing may be different in coupled ocean-atmosphere climate models that parameterize and resolve mesoscale eddies.

Biotic carbon feedbacks in a materially-closed soil-vegetation-atmosphere system

The magnitude and direction of the coupled feedbacks between the biotic and abiotic components of the terrestrial carbon cycle is a major source of uncertainty in coupled climate–carbon-cycle models1, 2, 3. Materially closed, energetically open biological systems continuously and simultaneously allow the two-way feedback loop between the biotic and abiotic components to take place4, 5, 6, 7, but so far have not been used to their full potential in ecological research, owing to the challenge of achieving sustainable model systems6, 7. We show that using materially closed soil–vegetation–atmosphere systems with pro rata carbon amounts for the main terrestrial carbon pools enables the establishment of conditions that balance plant carbon assimilation, and autotrophic and heterotrophic respiration fluxes over periods suitable to investigate short-term biotic carbon feedbacks. Using this approach, we tested an alternative way of assessing the impact of increased CO2 and temperature on biotic carbon feedbacks. The results show that without nutrient and water limitations, the short-term biotic responses could potentially buffer a temperature increase of 2.3 °C without significant positive feedbacks to atmospheric CO2. We argue that such closed-system research represents an important test-bed platform for model validation and parameterization of plant and soil biotic responses to environmental changes.

The influence of eddy parameterizations on the transport of the Antarctic Circumpolar Current in coupled climate models

The transport of the Antarctic Circumpolar Current (ACC) varies strongly across the coupled GCMs (general circulation models) used for the IPCC AR4. This note shows that a large fraction of this across-model variance can be explained by relating it to the parameterization of eddy-induced transports. In the majority of models this parameterization is based on the study by Gent and McWilliams (1990). The main parameter is the quasi-Stokes diffusivity kappa (often referred to less accurately as ’’thickness diffusion’’). The ACC transport and the meridional density gradient both correlate strongly with kappa across those models where kappa is a prescribed constant. In contrast, there is no correlation with the isopycnal diffusivity jiso across the models. The sensitivity of the ACC transport to kappa is larger than to the zonal wind stress maximum. Experiments with the fast GCM FAMOUS show that changing kappa directly affects the ACC transport by changing the density structure throughout the water column. Our results suggest that this limits the role of the wind stress magnitude in setting the ACC transport in FAMOUS. The sensitivities of the ACC and the meridional density gradient are very similar across the AR4 GCMs (for those models where kappa is a prescribed constant) and among the FAMOUS experiments. The strong sensitivity of the ACC transport to kappa needs careful assessment in climate models.

Vertical propagation of information in a middle atmosphere data assimilation system by gravity-wave drag feedbacks

The mesospheric response to the 2002 Antarctic Stratospheric Sudden Warming (SSW) is analysed using the Canadian Middle Atmosphere Model Data Assimilation System (CMAM-DAS), where it represents a vertical propagation of information from the observations into the data-free mesosphere. The CMAM-DAS simulates a cooling in the lowest part of the mesosphere which is accomplished by resolved motions, but which is extended to the mid- to upper mesosphere by the response of the model's non-orographic gravity-wave drag parameterization to the change in zonal winds. The basic mechanism is that elucidated by Holton consisting of a net eastward wave-drag anomaly in the mesosphere during the SSW, although in this case there is a net upwelling in the polar mesosphere. Since the zonal-mean mesospheric response is shown to be predictable, this demonstrates that variations in the mesospheric state can be slaved to the lower atmosphere through gravity-wave drag.

Tropical cyclone climatology in a 10-km global atmospheric GCM: toward weather-resolving climate modeling

Northern Hemisphere tropical cyclone (TC) activity is investigated in multiyear global climate simulations with theECMWFIntegrated Forecast System (IFS) at 10-km resolution forced by the observed records of sea surface temperature and sea ice. The results are compared to analogous simulationswith the 16-, 39-, and 125-km versions of the model as well as observations. In the North Atlantic, mean TC frequency in the 10-km model is comparable to the observed frequency, whereas it is too low in the other versions. While spatial distributions of the genesis and track densities improve systematically with increasing resolution, the 10-km model displays qualitatively more realistic simulation of the track density in the western subtropical North Atlantic. In the North Pacific, the TC count tends to be too high in thewest and too low in the east for all resolutions. These model errors appear to be associated with the errors in the large-scale environmental conditions that are fairly similar in this region for all model versions. The largest benefits of the 10-km simulation are the dramatically more accurate representation of the TC intensity distribution and the structure of the most intense storms. The model can generate a supertyphoon with a maximum surface wind speed of 68.4 m s21. The life cycle of an intense TC comprises intensity fluctuations that occur in apparent connection with the variations of the eyewall/rainband structure. These findings suggest that a hydrostatic model with cumulus parameterization and of high enough resolution could be efficiently used to simulate the TC intensity response (and the associated structural changes) to future climate change.

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.

A global perspective on Langmuir turbulence in the ocean surface boundary layer.

The turbulent mixing in thin ocean surface boundary layers (OSBL), which occupy the upper 100 m or so of the ocean, control the exchange of heat and trace gases between the atmosphere and ocean. Here we show that current parameterizations of this turbulent mixing lead to systematic and substantial errors in the depth of the OSBL in global climate models, which then leads to biases in sea surface temperature. One reason, we argue, is that current parameterizations are missing key surface-wave processes that force Langmuir turbulence that deepens the OSBL more rapidly than steady wind forcing. Scaling arguments are presented to identify two dimensionless parameters that measure the importance of wave forcing against wind forcing, and against buoyancy forcing. A global perspective on the occurrence of waveforced turbulence is developed using re-analysis data to compute these parameters globally. The diagnostic study developed here suggests that turbulent energy available for mixing the OSBL is under-estimated without forcing by surface waves. Wave-forcing and hence Langmuir turbulence could be important over wide areas of the ocean and in all seasons in the Southern Ocean. We conclude that surfacewave- forced Langmuir turbulence is an important process in the OSBL that requires parameterization.

Impact of melt ponds on Arctic sea ice simulations from 1990 to 2007

The extent and thickness of the Arctic sea ice cover has decreased dramatically in the past few decades with minima in sea ice extent in September 2007 and 2011 and climate models did not predict this decline. One of the processes poorly represented in sea ice models is the formation and evolution of melt ponds. Melt ponds form on Arctic sea ice during the melting season and their presence affects the heat and mass balances of the ice cover, mainly by decreasing the value of the surface albedo by up to 20%. We have developed a melt pond model suitable for forecasting the presence of melt ponds based on sea ice conditions. This model has been incorporated into the Los Alamos CICE sea ice model, the sea ice component of several IPCC climate models. Simulations for the period 1990 to 2007 are in good agreement with observed ice concentration. In comparison to simulations without ponds, the September ice volume is nearly 40% lower. Sensitivity studies within the range of uncertainty reveal that, of the parameters pertinent to the present melt pond parameterization and for our prescribed atmospheric and oceanic forcing, variations of optical properties and the amount of snowfall have the strongest impact on sea ice extent and volume. We conclude that melt ponds will play an increasingly important role in the melting of the Arctic ice cover and their incorporation in the sea ice component of Global Circulation Models is essential for accurate future sea ice forecasts.

Predictability and uncertainty in a regional climate model

The evaluation of the quality and usefulness of climate modeling systems is dependent upon an assessment of both the limited predictability of the climate system and the uncertainties stemming from model formulation. In this study a methodology is presented that is suited to assess the performance of a regional climate model (RCM), based on its ability to represent the natural interannual variability on monthly and seasonal timescales. The methodology involves carrying out multiyear ensemble simulations (to assess the predictability bounds within which the model can be evaluated against observations) and multiyear sensitivity experiments using different model formulations (to assess the model uncertainty). As an example application, experiments driven by assimilated lateral boundary conditions and sea surface temperatures from the ECMWF Reanalysis Project (ERA-15, 1979–1993) were conducted. While the ensemble experiment demonstrates that the predictability of the regional climate varies strongly between different seasons and regions, being weakest during the summer and over continental regions, important sensitivities of the modeling system to parameterization choices are uncovered. In particular, compensating mechanisms related to the long-term representation of the water cycle are revealed, in which summer dry and hot conditions at the surface, resulting from insufficient evaporation, can persist despite insufficient net solar radiation (a result of unrealistic cloud-radiative feedbacks).

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.

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.

Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

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.