Errors near the poles generated by a semi‐Lagrangian integration scheme in a global spectral model

Abstract

When a semi‐Lagrangian integration scheme was introduced into a global spectral model by Ritchie (1988), large errors developed in the neighbourhood of the poles. It took approximately 6 months of effort to diagnose the problem and find an appropriate correction. The method that was used to diagnose the source of error was quite tedious, but it was successful. Furthermore, it seems that this method could be used to diagnose other sources of error that occasionally show up in numerical integrations. For this reason, it was felt that this method should be described in a separate article. This is the main objective of the presentation that follows.

An integration is carried out with the original version of the model and some results are presented in order to illustrate these errors. In order to identify their exact cause, the model is stripped down in two steps. At each step, some checks are made to ensure that the errors are stillpresent in the degraded version of the model. In the end, the remaining equations are sufficiently simple to ensure that the cause of the errors becomes obvious. The diagnosis immediately suggests some alternative computational designs. A modification that completely eliminates these errors is then proposed and tested. An integration with the modified spectral model is carried out and results are presented to show that the errors have disappeared.     

The application of non‐linear normal mode initialization to an operational forecast model

Abstract

The non‐linear normal mode initialization technique used in shallow water equation models by Baer (1977) and Machenhauer (1977) is now applied to a full baroclinic primitive equations forecast model. The initialization procedure is shown to be capable of completely removing high frequency oscillations from model integrations, even in the presence of topography. The procedure also produces a consistent and physically realistic initial vertical motion field.     

Effects of variable wind shear on the mesoscale circulation forced by slab‐symmetric diabatic heating

Abstract

We examine the response of stably stratified airflow to a slab‐symmetric diabatic forcing associated with condensation in long‐lasting precipitation bands. The steady‐state linearized Boussinesq equations are used to model the diagnostic relationship between the vertical motion field, the heating source and the ambient flow. The basic‐state flow is assumed to be horizontally uniform and non‐rotating, but the static stability and wind vary in the vertical. Linear theory shows that the speed of the along‐band wind component is unimportant for slab‐symmetric heating since it cannot contribute towards the advection of buoyancy or vertical motion.

For typical atmospheric stratification and a moving heating source associated with a cloud band, the Taylor‐Goldstein equation is solved numerically. The numerical results show that the cross‐band wind shear tilts the updraft core and broadens it. While the magnitude of the shear is increased, the circulation becomes stronger. The details of the wind profile are also important in determining the intensity and structure of the circulation. When the wind profile indicates a convex bulge (i.e. the low‐level shear is weaker than the upper‐level shear), the circulation becomes slightly weaker in comparison with the linear wind profile. Conversely, the circulation becomes stronger when the wind profile has a concave shape. Increasing the concave bulge tends to enhance the circulation but not in a monotonic fashion. This non‐monotonic relation between the vertical motion and the parabolic wind profile is interpreted in terms of kinetic energy changes of parcels that interchange their altitudes.     

Promoting renewable energies under the CDM: combining national quotas in Europe and the CDM

Abstract

In the context of combating climate change, renewable energies are considered to play an important role. As these energies are currently not fully competitive compared with conventional power generation technologies, (minimum) quotas have been proposed as one means of overcoming this problem. However, when implementing any instruments at the national level, one should bear in mind that the efficiency of most types of renewable energies is dependent on the location. Thus, leaving the national perspective and investing abroad may result in improved efficiency. Against this background, the integration of the CDM into the European renewable energy policy is proposed.     

On modelling geophysical flows having low rossby numbers

Abstract

New, fourth‐order “c” grid Coriolis term treatments are compared with widely used second‐order treatments. Their improved accuracy is demonstrated by a grid convergence study for a relevant linear problem. Such an accuracy improvement is relatively easy and costs little for low Rossby number flows compared with high Rossby number flows, because one must consider only the Coriolis and pressure gradient terms in low Rossby number flows. The “c” grid is favourable for the latter, but the Coriolis terms benefit greatly by the higher order treatments analysed herein.     

GRAPES全球模式静力平衡奇异向量改进及应用试验

采用线性化物理过程方案的GRAPES全球模式奇异向量在进行非线性模式积分时会有部分奇异向量出现崩溃问题,这说明奇异向量结构可能存在扰动变量之间不协调之处,需要对奇异向量扰动的计算方法优化,进而改进基于奇异向量的集合预报初值扰动,提高GRAPES全球集合预报效果.基于原有的GRAEPS全球奇异向量计算方法,在求解奇异向量...     

Simulations of the 14 July 1987 squall line using a fully compressible model

Abstract

Numerical simulations of the severe squall line of 14 July 1987 are discussed within the context of semi‐Lagrangian and semi‐implicit integrations. The fully compressible non‐hydrostatic Euler set of equations constitutes the basic dynamical framework of the numerical model. With elementary precipitation physics and with a generalized treatment of lateral boundary conditions, nested integrations simulate the observed structure of the squall line. The numerical solution and observations show a well organized precipitation system including a mesoscale fast‐propagating prefrontal squall line and a slow‐propagating system moving with the synoptic wave. The prefrontal squall line is seen to be a manifestation of the organization of an inertia‐gravity wave and has characteristics of a wave‐CISK mechanism. Owing to the interaction between the upper jet stream dynamics and moisture, the prefrontal perturbation is initiated locally and subsequently irradiates away from its point source. The high computational efficiency and the accuracy of the model emphasize its potential and demonstrate its value as an interesting tool for mesoscale modelling.     

Sensitivity experiments for polar low forecasting with the CMC mesoscale finite‐element model

Abstract

High‐resolution versions of the Canadian operational regional finite‐element model (RFE) have been developed to assess their potential in simulating mesoscale, difficult‐to‐forecast and potentially dangerous weather systems commonly referred to as polar lows. The operational (1989) 100‐km version and a 50‐km version of the model have been run for two different polar low cases: one over Hudson Bay and one over Davis Strait. More integrations have also been performed on the Hudson Bay event both at 50 and 25 km to assess the model sensitivity to ice cover. As expected, the reduction in spatial truncation errors provided by the increase in resolution results in a better simulation of the systems. Moreover, when run at higher resolutions the model shows a significant sensitivity to ice cover. The results of the ice‐cover experiments also put into perspective the interaction between the heat and moisture fluxes at the surface, the low‐level wind structure, and the relation of these to the development of the polar low. This study suggests that the improved forecast accuracy obtained from increased resolution is limited by the correctness of the analysis of the ice cover, which acts as a stationary forcing for the entire forecast period.     

On the influence of stratospheric conditions on forced tropospheric waves in a steady‐state primitive equation model

Abstract

The structure of a forced planetary wave is computed by means of a linearized steady‐state primitive equation model on a hemisphere. The vertical velocity in pressure coordinates is specified at the lower boundary to simulate orographie forcing. The vertical finite differences are on equally spaced pressure levels with a moderately high vertical resolution. The upper boundary condition dp/dt = 0 is applied at p =0 in the model. Numerical experiments show that the tropospheric structure of forced planetary waves is sensitive to the stratospheric background conditions in the model.     

Carbon dioxide capture and storage: a status report

Abstract

Fossil fuel combustion is the largest source of anthropogenic greenhouse gas (GHG) emissions. As a result of combustion, essentially all of the fuel carbon is emitted to the atmosphere as carbon dioxide (CO₂), along with small amounts of methane and, in some cases, nitrous oxide. It has been axiomatic that reducing anthropogenic GHG emissions requires reducing fossil-fuel use. However, that relationship may no longer be as highly coupled in the future. There is an emerging understanding that CO₂ capture and storage (CCS) technology offers a way of using fossil fuels while reducing CO₂ emissions by 85% or more. While CCS is not the ‘silver bullet’ that in and of itself will solve the climate change problem, it is a powerful addition to the portfolio of technologies that will be needed to address climate change. The goal of this Commentary is to describe CCS technology in simple terms: how it might be used, how it might fit into longer term mitigation strategies, and finally, the policy issues that its emergence creates. All of these topics are discussed in much greater detail in the recently published Intergovernmental Panel on Climate Change (IPCC) Special Report on Carbon Dioxide Capture and Storage (SRCCS) (IPCC, 2005).     

Optimal estimation of Eddy viscosity and friction coefficients for a Quasi‐three‐dimensional numerical tidal model

Abstract

It is shown that the parameters in a quasi‐three‐dimensional numerical tidal model can be estimated accurately by assimilation of data from current meters and tide gauges. The tidal model considered is a semi‐linearized one in which advective nonlinearities are neglected but nonlinear bottom friction is included. The parameters estimated are the eddy viscosity, bottom friction coefficient, water depth and wind drag coefficient, the first three of which are allowed to be position‐dependent. The adjoint method is used to construct the gradient of a cost function defined as a certain norm of the difference between computed and observed current and surface elevations. On the basis of a number of tests, it is shown that very effective estimation of the nodal values of the parameters can be achieved using the current data either alone or in combination with elevation data. When random errors are introduced into the data, the estimated parameters are quite sensitive to the magnitude of the errors, and in particular the eddy viscosity is unstably sensitive. The sensitivity of the viscosity can be stabilized by incorporating an appropriate penalty term in the cost function or alternatively by reducing the number of estimated viscosity values via a finite element approximation. Once stabilized, the sensitivity of the estimates to data errors is significantly reduced by assimilating a longer data record.     

Benefits from increased cooperation and energy trade under CO2 commitments—The Nordic case

Abstract

In this paper, benefits from increasing cross-border cooperation under future CO₂ commitments in the Nordic countries are examined and evaluated. Four cooperative strategies are analyzed and valued separately: cross-border electricity trade, cross-border emission-permit trade, the introduction of a trans-Nordic natural gas transmission grid, and, finally, utilization of all these three strategies simultaneously. The valuation is done under varying CO₂ commitments and under three different scenarios for future energy demand and technological development. In conducting this analysis, the energy-systems model-generator MARKAL (MARKet ALlocation) was used to model the Nordic energy system. It is shown that all cooperative strategies do lower the abatement costs considerably, especially if the strategy including full cooperation is utilized. In this case, additional costs from meeting CO₂ targets may be at least halved for commitments less than 10% reduction until 2050 based on emissions in 1995. No significant difference between low and high CO₂ commitments could be observed in the size of the benefits from cooperation, expressed in billions (10⁹) of Swedish crowns. Benefits from cooperation are generally larger for scenarios including relatively higher future energy demand.     

An efficient optimum interpolation analysis scheme

Abstract

One of the characteristics of the optimum interpolation analysis scheme is that a matrix problem that depends on the number of observations has to be solved for each grid‐point value that is calculated. In data‐rich regions, this matrix can be quite large and in general, a limit on its size has to be imposed in order to avoid an excessive amount of computation.

In the proposed univariate analysis scheme, the autocorrelation function has been approximated by the second‐order and fourth‐order Taylor series expansion of the Gaussian Hill function. It is shown that the weights given to the observations can then be evaluated analytically by resolving associated systems of order 4 and 9, respectively.

When 24 pieces of data are used, the proposed schemes are, respectively, 6 and 3 times faster than an optimum interpolation analysis scheme using the Gaussian autocorrelation function. Furthermore, the analyses produced by those 3 schemes are almost identical. The search radius being limited, the proposed schemes are useful and worth while only over data‐dense areas.     

Fractal properties of whitecaps

Abstract

Images of a field of breaking waves over the ocean obtained using a line‐scanner on an aircraft are analyzed for a possible fractal geometry. The cumulative probability function of the intensity is shown to be self‐similar for sufficiently large intensities occupying about 10% of an imaged area. This structure is invariant to successive averaging over successively larger boxes. A box‐counting technique was applied to images of one representative flight. The estimated fractal dimension decreases from about 2.25 for a 10% a real coverage to about 1.7 for 0.1% coverage. It is concluded that the spatial distribution of the scattered light from foam and whitecaps is not monofractal, but is instead multifractal.     

A numerical model of the internal tide in knight inlet,British Columbia

Abstract

A two‐dimensional, hydrostatic numerical model of the tides in Knight Inlet is compared with observations of velocity and density obtained from three cyclesonde moorings. The observations from a fourth cyclesonde mooring were used to provide boundary data at the open end of the model. The time period in the fjord that the model simulates was a period of high, freshwater runoff, so that the fjord had a distinct, surface layer. The use of high, vertical resolution was avoided by attaching a homogeneous, fresh, surface layer to the top of the model. The density equation was linearized about a mean, fixed density field, and the mixing of density was not allowed.

The model reproduces the semidiurnal (M₂, S₂ and N₂) and diurnal (K₁ and O₁) velocity and density signals in the inlet. The shallow‐water constituents (M₄ and MK₃) are reproduced even though the density equation has been linearized. The fortnightly constituent (MSf) is poorly simulated. When the advection terms in the momentum equation are set to zero, the basic features of the semidiurnal and diurnal constituents are still reproduced, but the shallow‐water constituents are poorly simulated.

The energy flux along the inlet of the M₂ internal tide is insensitive to the advective terms in the momentum equation. The total rate of dissipation of M₂ energy is similar to the energy flux in the M₂ internal tide near the sill, which implies that, according to the model, most of the energy removed from the barotropic tide is fed into the internal tide. The majority of the energy in the M₂ internal tide is dissipated close to the sill of the inlet, but enough of the energy makes its way to the head of the inlet to reflect and set up a recognizable standing wave pattern.     

Changes in Snow Mass Balance in the Canadian Rocky Mountains Caused by CO2 Rise: Regional Atmosphere Model Results

Abstract

This study investigates snow mass balance in the Canadian Rockies under a relatively conservative Intergovernmental Panel on Climate Change emission scenario for the twenty-first century through the use of regional atmosphere modelling. We dynamically downscale results from five 10-year subsets of general circulation model integrations to 6?km resolution to produce a physically consistent representation of the atmosphere at high elevations. Regional model results make evident greater warming with increasing elevation at low to mid-levels of the atmosphere, and a simple thermodynamic explanation of this process is presented. Simulated increases in atmospheric water vapour result in increases in cloud cover and precipitation at high elevations, which temporarily offset the effects of rising temperatures, but by 2100 all model elevations experience reductions in snow mass balance. A simple energy balance model produces reasonable estimates of changes in the elevation of equilibrium net snow accumulation, with increases between 185 and 197?m under an approximate 1.5°C rise in surface temperatures by 2100.     

Modelling Extreme Storm-Induced Currents over the Grand Banks

Abstract

The wind climate of the mountainous terrain in the southern Yukon is simulated using the Wind Energy Simulation Toolkit (WEST) developed by the Recherche en Prévision Numérique (RPN) group of Environment Canada and is compared to measurements in the field. WEST combines two models that operate at different spatial scales. The Mesoscale Compressible Community (MC2) model is a mesoscale numerical weather prediction model that produces simulations over large domains of the order of a thousand kilometres. The MC2 model uses long‐term synoptic scale wind climate data from the analysis of radiosonde and other observations to simulate mean wind fields at tens of metres above the ground using a horizontal resolution of a few kilometres. The mesoscale results are used as input to MS‐Micro/3 (Mason and Sykes (1979) version of the Jackson and Hunt (1975) model version for microcomputers/3‐dimensional; MS‐Micro hereafter), a more computer‐efficient, microscale model with simpler linearized momentum equations and a domain restricted to a few tens of kilometres with horizontal grid sizes of tens or hundreds of metres. MS‐Micro provides wind field results at specific wind generator hub heights (typically 30 to 50 m above ground level (AGL)) which are of interest to researchers and developers of wind farms.

WEST shows relatively strong correlations between its simulated long‐term mean wind speed and the measurements from ten wind energy monitoring stations. However, in the mountainous terrain of the Yukon, WEST tends to predict wind speeds which are about 40% too high. The model also produces erroneous wind directions and some were perpendicular to valley orientations. The most likely cause of the wind speed and direction errors is the substantially modified 5‐km grid‐spaced mesoscale terrain used in MC2. The WEST simulation was also found to double the wind speeds observed at airport stations and there was poor correlation between the simulated and observed wind speeds.

The bias in the model could be attributed to a number of factors, including the use of smoothed topography by the model, the discrepancy between the neutral atmosphere assumed in MS‐Micro and the normally observed stable atmosphere, the application of MS‐Micro to every third grid point of the MC2 output, abnormally high sea level wind speeds in the input climate data for MC2, and a certain degree of disagreement between the land surface characteristics used in the model and those found in the field.

At comparatively low computer cost, WEST predicts a wind climate map that compares favourably to the wind measurements made in several locations in the Yukon. However, the problem of the modified terrain in the mountainous regions is the most pressing problem and needs to be addressed before WEST is used in the mountainous regions of Canada.     

A review of analytical models of sea‐ice growth

Abstract

The modelling of sea‐ice growth is a classical problem in geophysics, which has been traditionally treated as one‐dimensional, considering only the vertical heat transfer. The modelling work commenced in the 1800s with analytic methods. These are very effective tools for examining the sea‐ice growth problem, providing a clear insight into the physical mechanisms and producing simple first‐order approximations for the ice thickness in various conditions. This paper describes the physical problem of sea‐ice growth, presents an analytical modelling framework for the problem and provides analytic solutions for different environmental conditions.     

考虑背景风压场影响的边界层数值模式

本文提出一个在中性情况下边界层数值模式中考虑背景风压场影响的方法。背景风压场的水平非均匀影响了边界层运动方程中的惯性力项及边界层的上界风速。本文把三维问题用一种线性化方法简化为一维问题，只要知道背景气压场的空间分布，即可求出考虑了背景场影响的边界层风场。     

Future restrictions for sinks in the CDM How about a cap on supply?

Abstract

The first commitment period of the Kyoto Protocol is expected to result in only a small role for the Clean Development Mechanism (CDM), including afforestation and reforestation projects. Wide ranging concerns regarding sinks in the CDM have been reflected in the Marrakech Accords capping the total amount of emission offsets from sinks projects to be used by Annex I countries. Decisions about the second commitment period and beyond are likely to be of far greater importance for these projects.

This paper contributes to the discussion on how caps on sinks under the CDM could be used to obtain overall improved outcomes for developing countries. We examine two distinctive ways in which quantitative caps on sinks in the CDM can be implemented: one, restricting the use of sinks CERs to meet targets, as under the Marrakech Accords (a cap on demand); and two, restricting supply of sink CERs using a quota system. We argue in favour of a supply side cap, if Parties are to preserve the idea of limiting sinks in the CDM. Limiting the supply of credits could lead to better financial outcomes for developing countries as a whole, make higher-cost projects viable which may have better sustainability impacts, and provide an alternative to deal with equity concerns between developing countries.