Predictability as a function of scale

Abstract

The forecast skill of the Canadian Meteorological Centre (CMC) operational global forecast/analysis system is assessed as a function of scale for the traditional forecast variable of 500‐hPa geopotential height using results from January 2002. These results are compared to an earlier analysis of forecasts from the European Centre for Medium‐range Weather Forecasts (ECMWF) which indicated unexpectedly enhanced skill at high wavenumbers (small scales) especially in the mean forecast component identified with local topographical structures. The global rms error for the CMC forecasts is dominated by the transient component compared to the mean and continues to grow with time during the six days of the forecast. Geographically the transient error grows most rapidly in middle and high latitude regions of large natural variability. The relative error behaves differently and grows most rapidly initially in tropical regions and is inferred to exhibit both climatological and flow‐dependent error growth.

In terms of spherical harmonic two‐dimensional wavenumber n, low wavenumber (large scale) 500‐hPa geopotential height structures are dominated by the mean component but beyond wavenumber 10 to 15 the transient component dominates and exhibits an approximately n–5 spectral slope consistent with a quasi‐two dimensional turbulence enstrophy cascading subrange. Error grows slowly for the large scales dominated by mean climatological structures but these are not of interest for daily weather forecasting. Transient error grows rapidly at small scales and penetrates toward larger scales with time in keeping with the expected predictability behaviour. An expression of the form f(n, τ) = 1 – e–^τ/^τp(n) is fitted to the growth of relative error as a function of wavenumber and forecast range and gives a scale dependent predictability timescale for the transient component that varies as τ_p ? n^?3/2, although the generality of the relationship is not known.

The mean component at intermediate/high wavenumbers exhibits an apparent region of enhanced skill in the CMC system apparently connected to the topography. The result supports the possibility that some small‐scale mean flow structures, although containing only a minor amount of variance, are maintained in the face of errors in other scales. The results do not support the level of enhanced skill found in an earlier analysis of ECMWF results suggesting them to be an artefact of the analysis/forecast system in use at the time.     

On the average errors of an ensemble of forecasts 1

Abstract

The average error fields of an ensemble of 10‐day forecasts made with a global model at the European Centre for Medium Range Weather Forecasts, and first presented by Hollingsworth et al. (1980), are examined. The time evolution of the error fields is presented together with horizontal and vertical cross‐sections through the fields at fixed times to reveal some features of their three‐dimensional structure. The most striking deficiency of the model is seen to be its inability to maintain the amplitude of the quasi‐stationary zonal wavenumber 2 in the middle and upper troposphere.     

Aspects of wave behaviour in the mid‐ and upper troposphere of the southern Hemisphere

Abstract

The zonal wavenumber spectra of the geopotential heights of the 300‐ and 500‐mb surfaces in the Southern Hemisphere were determined for each month between May 1972 and November 1979 using daily operational analyses produced by the Australian Bureau of Meteorology. During over one‐quarter of the “summer” months (November through March) there are very prominent peaks at zonal wavenumber five in the region of the mid‐latitude jet (～35–60°S). Frequently wavenumber five totally dominates the eddy fields in individual daily maps so that height contours in mid‐latitudes take on virtually pentagonal shapes. During periods when wavenumber 5 is prominent, it is observed to propagate eastward in a very regular manner with a period of about eleven days. All these findings are consistent with Salby's (1982) earlier results concerning the Southern Hemisphere height fields during the first few months of the FGGE experiment.

There is little evidence for a similar phenomenon in the winter circulation of the Southern Hemisphere.     

Spectral analysis of the AVHRR sea surface temperature variability off the west coast of Vancouver Island

Abstract

From 16 AVHRR infrared satellite images of the west coast of Vancouver Island, British Columbia, collected during the five summers of 1984–1988, 4 alongshore temperature transects were sampled. Upon Fourier transforming the transect data, we found that the energy spectra of the temperature variance in alongshore wavenumber space in general followed a –2.1 power law, which agreed with previous observations from other parts of the world.

Summer images may be divided into 2 types: upwelling dominated and non‐upwelling dominated. When a strong upwelling‐induced alongshore cold front was observed, the regimes shoreward and seaward of the front had distinctly different spectra. Cross‐spectral analysis of transect data between images taken a day apart in the presence of strong upwelling events revealed significant coherence at the low wavenumber regime (wavelength 300 km and above, corresponding to the large eddies) and often at the high wavenumber regime (wavelength 30 km or below, corresponding to the fine structures of the eddies). The coherence dropped for images taken 2 or more days apart, suggesting a decorrelation time‐scale of about 2 days. In the absence of strong upwelling and associated eddies, summer transect temperature data from different years often showed a similar alongshore linear trend in addition to possible large differences in the mean temperature.     

Simulated Airborne Flux Measurements in a LES generated Convective Boundary Layer

One aim of past boundary-layer experiments with aircraft was the determination of areally averaged heat fluxes. In spite ofsophisticated instrumentation the measured fluxes extrapolated to the ground differed significantly from fluxes measured directly at ground stations. This studypresents simulated sensible heat flux measurements with aircraft flightsthrough a synthetic convective boundary layer created by a401 × 401 × 42 cubic-grid large eddy simulation (LES) with agrid spacing of 50 m. After some considerations with respect to necessary measurement lengths using results ofLenschow and Stankov (1986 – J. Atmos. Sci. 43, 1198–1209), simulated measurementcampaigns were carried out in three modelruns. During each model run five sets ofmeasurement runs were carried out successively.During each set of runs 10 aircraftflew at 10 altitudes with a ground speedof 100 m s^-1 simultaneously throughtime and space. In total, 150 legs were carried out, 15 at each flight level. The resulting`measured' heat fluxes were compared withthose of the `true' flux profiles obtaineddirectly from the ensemble-averagedLES-generated data. No significant systematic error between `measured' and `true' profiles was observed. Furthermore, the comparison of the resulting relative error with the theory ofLenschow and Stankov showed a good agreement at allmeasurement levels.     

On the efficiency of horizontal diffusion and numerical filtering in an Arakawa‐type model

Abstract

In a series of 5‐day forecasts with a 3‐layer/2.8° hemispheric model, horizontal diffusion schemes of the second and fourth degree are compared with a numericalfilter technique. The results, which are discussed mainly in terms of spectral energetics in zonal wavenumber space, indicate that fourth‐degree diffusion is more scale selective than second‐degree and equivalent to filtering. The seventh‐order filter applied only intermittently to the prognostic variables is superior to fourth‐degree diffusion from the viewpoint of computational economy. Excessive dissipation of the long waves may inhibit the production of eddy kinetic energy from eddy available potential energy.     

A diagnostic study of the southern hemisphere summer circulation of the CCC general circulation model

Abstract

The medium‐scale wave regime, consisting largely of zonal wavenumbers 5–7, frequently dominates the summer Southern Hemisphere tropospheric circulation. We perform a diagnostic study of this circulation as simulated by the Canadian Climate Centre (CCC) general circulation model (GCM). The analysis of Hövmöller diagrams, space‐time and zonal wavenumber spectra shows that the CCC GCM is able to simulate the observed medium‐scale wave regime.

The zonally averaged meridional eddy heat and momentum transports and the associated baroclinic and barotropic energy conversions are also examined. The distributions of the transports on the vertical plane agree well with the observations. After comparison with the observed December‐January‐February 1979 distributions, some quantitative differences remain: the heat transport is too weak aloft and too large near the surface, whereas the momentum transport tends to be too weak. The baroclinic and barotropic conversions show a maximum in the medium‐scale waves. The time evolution of the Richardson number of the mean flow suggests that the medium‐scale wave is due to a baroclinic instability.     

A global available potential energy‐kinetic energy budget in terms of the two‐dimensional wavenumber for the FGGE year

Abstract

A global vertically integrated available potential energy‐kinetic energy budget in terms of the two‐dimensional wavenumber is formulated using spherical harmonics. Results of the budget equations applied to the four mid‐season months of the FGGE year are given.     

流依赖球面小波背景误差协方差模型设计和初步试验

基于资料同化集合设计了流依赖球面小波背景场误差协方差模型中背景误差方差和局地垂直相关协方差的统计计算方法。为了提高背景误差方差的估计精度,采用客观滤波技术来减少因集合样本个数不足而引入的随机取样噪声。最后在银河四维变分同化业务系统(YH4DVar)上设计了集合资料同化的试验系统,以流依赖背景误差方差为重点验证了模型的有效性。结果表明:基于流依赖球面小波背景误差协方差模型能够有效估计出随天气状态变化的背景场误差方差,对台风等剧烈变化的天气过程的同化分析和预报都具有一定的正效果。      

Possible Sources of Forecast Errors Generated by the Global/Regional Assimilation and Prediction System for Landfalling Tropical Cyclones. Part Ⅱ: Model Uncertainty

This paper investigates the possible sources of errors associated with tropical cyclone (TC) tracks forecasted using the Global/Regional Assimilation and Prediction System (GRAPES). In Part I, it is shown that the model error of GRAPES may be the main cause of poor forecasts of landfalling TCs. Thus, a further examination of the model error is the focus of Part II. Considering model error as a type of forcing, the model error can be represented by the combination of good forecasts and bad forecasts. Results show that there are systematic model errors. The model error of the geopotential height component has periodic features, with a period of 24 h and a global pattern of wavenumber 2 from west to east located between 60°S and 60°N. This periodic model error presents similar features as the atmospheric semidiurnal tide, which reflect signals from tropical diabatic heating, indicating that the parameter errors related to the tropical diabatic heating may be the source of the periodic model error. The above model errors are subtracted from the forecast equation and a series of new forecasts are made. The average forecasting capability using the rectified model is improved compared to simply improving the initial conditions of the original GRAPES model. This confirms the strong impact of the periodic model error on landfalling TC track forecasts. Besides, if the model error used to rectify the model is obtained from an examination of additional TCs, the forecasting capabilities of the corresponding rectified model will be improved.     

ERS‐1 and Almaz estimates of directional ocean wave spectra conditioned by simultaneous aircraft SAR and buoy measurements

Abstract

The European Space Agency ERS‐1 C‐band V‐V polarization synthetic aperture radar (SAR) and the Russian Almaz S‐band H‐H polarization SAR are compared for their wavenumber response to ocean wave fields existing on 23 November 1991 at the Grand Banks site of the North American ERS‐1 SAR Wave Spectra Validation Experiment. Two‐dimensional wave spectra from two Wavec heave, pitch and roll buoys and a Canadian CV‐580 aircraft C‐band V‐V polarization SAR are used to condition a linear modulation transfer model of wave imaging with SAR. A model of hydrodynamic modulation is included with the velocity bunching and tilt imaging mechanisms to better understand wind and wave interactions. Krogstad's quasi‐linear formulation of Hasselmann's ocean‐SAR integral transform is applied to model SAR velocity bunching and azimuth smearing. Narrow and broad bandwidth components of azimuth wavenumber response for the aircraft SAR are associated with, respectively, non‐linear and incoherent velocity smearing during Doppler resolution of the radar scene. The stationary resolutions of the SAR systems are compared for homogeneous scenes of wind‐roughened, but fetch‐limited, sea surfaces. This comparison is conducted in the Chesapeake Bay of Maryland using ERS‐1 and Almaz satellite imagery collected on 9 May 1992 and 14 May 1991, respectively. The results confirm that SAR imaging of ocean waves can be improved by flying platforms with low R/V (range/velocity) ratios to alleviate the azimuth velocity smear, and near‐nadir incidence angles to increase the effect of tilt modulation.     

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.     

Wave attenuation in the marginal ice zone during LIMEX

Abstract

During the Labrador Ice Margin Experiments, LIMEX ‘87 in March 1987 and LIMEX ‘89 in March and April 1989, the Canada Centre for Remote Sensing (CCRS) CV‐580 aircraft collected synthetic aperture radar (SAR) image data over the marginal ice zone off the east coast of Newfoundland, Canada. One aspect of these experimental programs was the observation of ocean waves penetrating into the marginal ice zone (MIZ). Based upon directional wavenumber spectra derived from SAR image data, the wave attenuation rate is estimated using SAR image spectra and compared with predictions from a model developed by Liu and Mollo‐Christensen (1988). The wave and ice conditions were considerably different in LIMEX ‘87 and LIMEX ‘89. However, the model‐data comparisons are very good for all ice conditions observed. Both the model and the SAR‐derived wave attenuation rates show a characteristic roll‐over at high wavenumbers. A model for the eddy viscosity is proposed, using dimensional analysis, as a simple function of ice roughness and wave‐induced velocity. Eddy viscosities derived from SAR and wave buoy data for the wave attenuation rate show a trend that is consistent with the proposed model.     

Dynamics and predictability of a low-order wind-driven ocean–atmosphere coupled model

The dynamics of a low-order coupled wind-driven ocean–atmosphere system is investigated with emphasis on its predictability properties. The low-order coupled deterministic system is composed of a baroclinic atmosphere for which 12 dominant dynamical modes are only retained (Charney and Straus in J Atmos Sci 37:1157–1176, 1980) and a wind-driven, quasi-geostrophic and reduced-gravity shallow ocean whose field is truncated to four dominant modes able to reproduce the large scale oceanic gyres (Pierini in J Phys Oceanogr 41:1585–1604, 2011). The two models are coupled through mechanical forcings only. The analysis of its dynamics reveals first that under aperiodic atmospheric forcings only dominant single gyres (clockwise or counterclockwise) appear, while for periodic atmospheric solutions the double gyres emerge. In the present model domain setting context, this feature is related to the level of truncation of the atmospheric fields, as indicated by a preliminary analysis of the impact of higher wavenumber (“synoptic” scale) modes on the development of oceanic gyres. In the latter case, double gyres appear in the presence of a chaotic atmosphere. Second the dynamical quantities characterizing the short-term predictability (Lyapunov exponents, Lyapunov dimension, Kolmogorov–Sinaï (KS) entropy) displays a complex dependence as a function of the key parameters of the system, namely the coupling strength and the external thermal forcing. In particular, the KS-entropy is increasing as a function of the coupling in most of the experiments, implying an increase of the rate of loss of information about the localization of the system on its attractor. Finally the dynamics of the error is explored and indicates, in particular, a rich variety of short term behaviors of the error in the atmosphere depending on the (relative) amplitude of the initial error affecting the ocean, from polynomial (at ² + bt ³ + ct ⁴) up to exponential-like evolutions. These features are explained and analyzed in the light of the recent findings on error growth (Nicolis et al. in J Atmos Sci 66:766–778, 2009).     

Some effects of vertical resolution on modelling forced planetary waves with a time‐dependent model

Abstract

Previous studies by Nakamura (1976) and Kirkwood and Derome (1977) have shown that the use of a relatively low vertical resolution in a numerical model of the atmosphere can lead to a poor representation of the forced stationary planetary waves. In the present study the consequences of this result on short‐term numerical forecasts are investigated. This is done by performing forecast experiments using a low resolution linear β‐plane model that is initialized with data extracted from the steady forced solution of the high resolution (reference) version of the model. The deviation of the low resolution forecast from the initial state, which can be interpreted as the forecast error due to insufficient vertical resolution, is examined as a function of time.

It is shown that the short‐range forecast error is dominated by a westward propagating external mode and that in time some of the eastward moving internal modes gain in importance.     

A study of planetary wave errors in a spectral numerical weather prediction model

Abstract

A series of fifteen 96‐h forecasts made with a spectral numerical weather prediction model is studied with reference to errors in the planetary wavelengths. The major contributor to the short (less than 48‐h) range forecast error is identified as an external mode. The medium range forecast error (96 h) is internal in character and reflects a deficiency in the simulation of the quasi‐stationary components.     

Potential Predictability of Sea Surface Temperature in a Coupled Ocean--Atmosphere GCM

Using the Flexible Global Ocean--Atmosphere--Land System model (FGOALS) version g1.11, a group of seasonal hindcasting experiments were carried out. In order to investigate the potential predictability of sea surface temperature (SST), singular value decomposition (SVD) analyses were applied to extract dominant coupled modes between observed and predicated SST from the hindcasting experiments in this study. The fields discussed are sea surface temperature anomalies over the tropical Pacific basin (20^oS--20^oN, 120^oE--80^oW), respectively starting in four seasons from 1982 to 2005. On the basis of SVD analysis, the simulated pattern was replaced with the corresponding observed pattern to reconstruct SST anomaly fields to improve the ability of the simulation. The predictive skill, anomaly correlation coefficients (ACC), after systematic error correction using the first five modes was regarded as potential predictability. Results showed that: 1) the statistical postprocessing approach was effective for systematic error correction; 2) model error sources mainly arose from mode 2 extracted from the SVD analysis---that is, during the transition phase of ENSO, the model encountered the spring predictability barrier; and 3) potential predictability (upper limits of predictability) could be high over most of the tropical Pacific basin, including the tropical western Pacific and an extra 10-degrees region of the mid and eastern Pacific.     

Calculation of solar irradiances for inclined surfaces: Validation of selected hourly and daily models

Abstract

Irradiance data obtained over a long period at Vancouver and Toronto, Canada, and covering a range of slope orientations are used to validate four models that estimate either the direct or diffuse solar irradiances for inclined surfaces. Evaluations are initially performed for daily and hourly time integrals. A simple parametrization of the diffuse sky radiance dramatically improves estimates of the diffuse irradiance. Both of the direct irradiance models have difficulty accommodating the diurnal characteristics of the irradiance, and consequently modelling errors are substantial for slopes not directly facing the equator. For equator‐facing slopes a saving in data requirements and computational effort through the use of daily integrals can be achieved with little additional error. A substantial portion of the differences between the measured and estimated irradiances is non‐systematic in nature and is therefore reduced through temporal averaging.     

Sensitivity of ADOM dry deposition velocities to input parameters: A comparison with measurements for SO2 and NO2 over three land use types

Abstract

Dry deposition velocity measurements of SO₂ and NO₂ over a deciduous forest, a carrot field and a snow surface are compared with estimates obtained from the dry deposition module in the regional Eulerian Acid Deposition and Oxidant Model (ADOM). The comparison with measurements taken in the fall and winter shows large model overestimates, sometimes as large as a factor of 5. The NO₂ estimates are particularly poor and support existing evidence that models that employ the constant flux assumption for NO₂ are inadequate. The canopy and the snow surface resistances are the largest contributors to the total resistances for SO₂ and NO₂, except for situations in which some of the snow turns into liquid water, when the aerodynamic resistance becomes important.

Increasing the magnitudes, taken from measurements, of the ADOM original values for the stomatal, cuticle, ground and snow resistances and decreasing the NO₂ mesophyll resistance and the Leaf Area Index (LAI) yield improved model results, particularly for SO₂, reducing the error by almost a factor of 5 at times. The new estimates compare favourably with those from a model that includes Wesely's canopy resistance parametrization. Over snow the NO₂ estimates are improved by as much as a factor of 6. Observed deposition velocities for SO₂ vary from 0 to 0.65 cm s^?2 over a deciduous forest, 0 to 0.60 cm s^?2 over a carrot field and are generally less than 0.05 cm s^?2 over snow.     

Cross‐equatorial error propagation: Research note

Abstract

Numerical simulation experiments published in 1974 by Daley have been repeated with a much higher resolution, spectral, shallow water model. With a forecast period extending toll d, it is shown that a global model in which only the largest scales are used at initial time in the Southern Hemisphere yields a more accurate forecast for the Northern Hemisphere than a hemispheric model does. Compared with a uniform high‐resolution, global model, the error in the Northern Hemisphere forecast is high in the ultra‐long waves but decreases rather rapidly while the resolution of the initial Southern Hemispheric data is increased.