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Abstract
A primitive equations dry atmospheric model is used to investigate the atmospheric response to a tropical diabatic forcing pattern and explore how the atmospheric response changes as a function of the amplitude of the forcing. The forcing anomaly represents a linear fit of the model forcing to a tropical SST pattern of an El Niño/La Niña type. The time-averaged 500-hPa geopotential height anomaly responses of two long integrations, with forcing anomalies of equal amplitudes but opposite signs, show an asymmetric feature that is similar to observations and to previous modeling results related to El Niño and La Niña. Ensemble experiments with 61 different amplitudes of this forcing pattern are conducted. An EOF analysis of the ensemble mean of the 90-day-averaged 500-hPa height for different amplitudes of forcings shows that the leading mode of the forced variability resembles the Pacific–North American (PNA) pattern, while the second mode is a wave train across the North Atlantic to Eurasia. The relationship between the amplitude of the PNA mode and the amplitude of the forcing is linear, while the amplitude of the Atlantic/Eurasian mode has a nearly parabolic relationship with the amplitude of the forcing. A set of linear experiments with forcing perturbations and eddy flux anomalies associated with the positive and negative amplitudes of forcing conditions indicates that the nonlinearity of the extratropical response primarily results from the modification of the “basic state” caused by the large-amplitude forcing and the subsequent sensitivity of the response to that modified basic flow. A La Niña–type basic state yields a stronger response in the North Atlantic to the tropical Pacific forcing than does an El Niño–type basic state.
Abstract
A primitive equations dry atmospheric model is used to investigate the atmospheric response to a tropical diabatic forcing pattern and explore how the atmospheric response changes as a function of the amplitude of the forcing. The forcing anomaly represents a linear fit of the model forcing to a tropical SST pattern of an El Niño/La Niña type. The time-averaged 500-hPa geopotential height anomaly responses of two long integrations, with forcing anomalies of equal amplitudes but opposite signs, show an asymmetric feature that is similar to observations and to previous modeling results related to El Niño and La Niña. Ensemble experiments with 61 different amplitudes of this forcing pattern are conducted. An EOF analysis of the ensemble mean of the 90-day-averaged 500-hPa height for different amplitudes of forcings shows that the leading mode of the forced variability resembles the Pacific–North American (PNA) pattern, while the second mode is a wave train across the North Atlantic to Eurasia. The relationship between the amplitude of the PNA mode and the amplitude of the forcing is linear, while the amplitude of the Atlantic/Eurasian mode has a nearly parabolic relationship with the amplitude of the forcing. A set of linear experiments with forcing perturbations and eddy flux anomalies associated with the positive and negative amplitudes of forcing conditions indicates that the nonlinearity of the extratropical response primarily results from the modification of the “basic state” caused by the large-amplitude forcing and the subsequent sensitivity of the response to that modified basic flow. A La Niña–type basic state yields a stronger response in the North Atlantic to the tropical Pacific forcing than does an El Niño–type basic state.
Abstract
The stability of free and forced planetary waves in a β plane channel is investigated with a barotropic model. The equilibrium flows that are considered have the gravest possible scale in the meridional direction and a zonal wavenumber of either 1 or 2. The equilibrium-forced waves are the result of the interaction of a constant mean zonal wind over finite-amplitude surface orography.
The frequency of all possible small-amplitude perturbations to the equilibrium flows are calculated as a function of the strength of the mean zonal wind and of the amplitude of the orography. The forced zonal-wavenumber-1 flow is found to have three major regions of instability in parameter space, two of which have stationary growing perturbations. The free Rossby wave of that scale is stable for all amplitudes. The forced zonal-wavenumber-2 wave has two adjacent instability domains one on each side of the resonant mean zonal wind. The free wave becomes unstable for sufficiently large amplitudes. The results are interpreted through the use of a severely truncated spectral model and are related to those of previous studies with infinite β-planes. We also report the existence of a traveling subresonant topographic instability, which seems to have gone unnoticed in previous studies.
Abstract
The stability of free and forced planetary waves in a β plane channel is investigated with a barotropic model. The equilibrium flows that are considered have the gravest possible scale in the meridional direction and a zonal wavenumber of either 1 or 2. The equilibrium-forced waves are the result of the interaction of a constant mean zonal wind over finite-amplitude surface orography.
The frequency of all possible small-amplitude perturbations to the equilibrium flows are calculated as a function of the strength of the mean zonal wind and of the amplitude of the orography. The forced zonal-wavenumber-1 flow is found to have three major regions of instability in parameter space, two of which have stationary growing perturbations. The free Rossby wave of that scale is stable for all amplitudes. The forced zonal-wavenumber-2 wave has two adjacent instability domains one on each side of the resonant mean zonal wind. The free wave becomes unstable for sufficiently large amplitudes. The results are interpreted through the use of a severely truncated spectral model and are related to those of previous studies with infinite β-planes. We also report the existence of a traveling subresonant topographic instability, which seems to have gone unnoticed in previous studies.
Abstract
The interactions between low-frequency transients and synoptic-scale eddies are examined. The 300-mb data from 1981 to 1986 analyzed by the ECMWF are used to calculate the height tendency of the slow transients due to vorticity forcing by synoptic-scale eddies. It is found that the low-frequency transients are correlated with the forcing by the synoptic-scale eddies, most notably in the eastern part of the Pacific and Atlantic basins, where a significant portion of the time variance of the slow transient height field can be explained by the forcing. The lag correlation coefficients between the forcing and the slow transients indicate that the former leads the latter by a small phase difference (about one day).
The structure of the forcing is studied by an EOF analysis. The leading EOF mode in both oceanic sectors has a dipole structure. The pattern of the geopotential height field associated with each EOF mode of the forcing is also identified. The height pattern associated with the first Pacific forcing mode has a wave train structure, and the one associated with the first Atlantic forcing mode is a localized dipole. The correlation between the height pattern and the corresponding EOF mode in each sector is then examined, and no significant time phase shift can be found between the two.
Finally, a simple theoretical explanation is proposed to account for the phase relationship between the slow transients and their forcing by the synoptic-scale eddies.
Abstract
The interactions between low-frequency transients and synoptic-scale eddies are examined. The 300-mb data from 1981 to 1986 analyzed by the ECMWF are used to calculate the height tendency of the slow transients due to vorticity forcing by synoptic-scale eddies. It is found that the low-frequency transients are correlated with the forcing by the synoptic-scale eddies, most notably in the eastern part of the Pacific and Atlantic basins, where a significant portion of the time variance of the slow transient height field can be explained by the forcing. The lag correlation coefficients between the forcing and the slow transients indicate that the former leads the latter by a small phase difference (about one day).
The structure of the forcing is studied by an EOF analysis. The leading EOF mode in both oceanic sectors has a dipole structure. The pattern of the geopotential height field associated with each EOF mode of the forcing is also identified. The height pattern associated with the first Pacific forcing mode has a wave train structure, and the one associated with the first Atlantic forcing mode is a localized dipole. The correlation between the height pattern and the corresponding EOF mode in each sector is then examined, and no significant time phase shift can be found between the two.
Finally, a simple theoretical explanation is proposed to account for the phase relationship between the slow transients and their forcing by the synoptic-scale eddies.
Abstract
The output of two global atmospheric models participating in the second phase of the Canadian Historical Forecasting Project (HFP2) is utilized to assess the forecast skill of the Madden–Julian oscillation (MJO). The two models are the third generation of the general circulation model (GCM3) of the Canadian Centre for Climate Modeling and Analysis (CCCma) and the Global Environmental Multiscale (GEM) model of Recherche en Prévision Numérique (RPN). Space–time spectral analysis of the daily precipitation in near-equilibrium integrations reveals that GEM has a better representation of the convectively coupled equatorial waves including the MJO, Kelvin, equatorial Rossby (ER), and mixed Rossby–gravity (MRG) waves. An objective of this study is to examine how the MJO forecast skill is influenced by the model’s ability in representing the convectively coupled equatorial waves.
The observed MJO signal is measured by a bivariate index that is obtained by projecting the combined fields of the 15°S–15°N meridionally averaged precipitation rate and the zonal winds at 850 and 200 hPa onto the two leading empirical orthogonal function (EOF) structures as derived using the same meridionally averaged variables following a similar approach used recently by Wheeler and Hendon. The forecast MJO index, on the other hand, is calculated by projecting the forecast variables onto the same two EOFs.
With the HFP2 hindcast output spanning 35 yr, for the first time the MJO forecast skill of dynamical models is assessed over such a long time period with a significant and robust result. The result shows that the GEM model produces a significantly better level of forecast skill for the MJO in the first 2 weeks. The difference is larger in Northern Hemisphere winter than in summer, when the correlation skill score drops below 0.50 at a lead time of 10 days for GEM whereas it is at 6 days for GCM3. At lead times longer than about 15 days, GCM3 performs slightly better. There are some features that are common for the two models. The forecast skill is better in winter than in summer. Forecasts initialized with a large amplitude for the MJO are found to be more skillful than those with a weak MJO signal in the initial conditions. The forecast skill is dependent on the phase of the MJO at the initial conditions. Forecasts initialized with an MJO that has an active convection in tropical Africa and the Indian Ocean sector have a better level of forecast skill than those initialized with a different phase of the MJO.
Abstract
The output of two global atmospheric models participating in the second phase of the Canadian Historical Forecasting Project (HFP2) is utilized to assess the forecast skill of the Madden–Julian oscillation (MJO). The two models are the third generation of the general circulation model (GCM3) of the Canadian Centre for Climate Modeling and Analysis (CCCma) and the Global Environmental Multiscale (GEM) model of Recherche en Prévision Numérique (RPN). Space–time spectral analysis of the daily precipitation in near-equilibrium integrations reveals that GEM has a better representation of the convectively coupled equatorial waves including the MJO, Kelvin, equatorial Rossby (ER), and mixed Rossby–gravity (MRG) waves. An objective of this study is to examine how the MJO forecast skill is influenced by the model’s ability in representing the convectively coupled equatorial waves.
The observed MJO signal is measured by a bivariate index that is obtained by projecting the combined fields of the 15°S–15°N meridionally averaged precipitation rate and the zonal winds at 850 and 200 hPa onto the two leading empirical orthogonal function (EOF) structures as derived using the same meridionally averaged variables following a similar approach used recently by Wheeler and Hendon. The forecast MJO index, on the other hand, is calculated by projecting the forecast variables onto the same two EOFs.
With the HFP2 hindcast output spanning 35 yr, for the first time the MJO forecast skill of dynamical models is assessed over such a long time period with a significant and robust result. The result shows that the GEM model produces a significantly better level of forecast skill for the MJO in the first 2 weeks. The difference is larger in Northern Hemisphere winter than in summer, when the correlation skill score drops below 0.50 at a lead time of 10 days for GEM whereas it is at 6 days for GCM3. At lead times longer than about 15 days, GCM3 performs slightly better. There are some features that are common for the two models. The forecast skill is better in winter than in summer. Forecasts initialized with a large amplitude for the MJO are found to be more skillful than those with a weak MJO signal in the initial conditions. The forecast skill is dependent on the phase of the MJO at the initial conditions. Forecasts initialized with an MJO that has an active convection in tropical Africa and the Indian Ocean sector have a better level of forecast skill than those initialized with a different phase of the MJO.
Abstract
In the second phase of the Canadian Historical Forecasting Project (HFP2), four global atmospheric general circulation models (GCMs) were used to perform seasonal forecasts over the period of 1969–2003. Little predictive skill was found from the uncalibrated GCM ensemble seasonal predictions for the Canadian winter precipitation. This study is an effort to improve the precipitation forecasts through a postprocessing approach.
Canadian winter precipitation is significantly influenced by two of the most important atmospheric large-scale patterns: the Pacific–North American pattern (PNA) and the North Atlantic Oscillation (NAO). The time variations of these two patterns were found to be significantly correlated with those of the leading singular value decomposition (SVD) modes that relate the ensemble mean forecast 500-mb geopotential height over the Northern Hemisphere and the tropical Pacific SST in the previous month (November). A statistical approach to correct the ensemble forecasts was formulated based on the regression of the model’s leading forced SVD patterns and the observed seasonal mean precipitation. The performance of the corrected forecasts was assessed by comparing its cross-validated skill with that of the original GCM ensemble mean forecasts. The results show that the corrected forecasts predict the Canadian winter precipitation with statistically significant skill over the southern prairies and a large area of Québec–Ontario.
Abstract
In the second phase of the Canadian Historical Forecasting Project (HFP2), four global atmospheric general circulation models (GCMs) were used to perform seasonal forecasts over the period of 1969–2003. Little predictive skill was found from the uncalibrated GCM ensemble seasonal predictions for the Canadian winter precipitation. This study is an effort to improve the precipitation forecasts through a postprocessing approach.
Canadian winter precipitation is significantly influenced by two of the most important atmospheric large-scale patterns: the Pacific–North American pattern (PNA) and the North Atlantic Oscillation (NAO). The time variations of these two patterns were found to be significantly correlated with those of the leading singular value decomposition (SVD) modes that relate the ensemble mean forecast 500-mb geopotential height over the Northern Hemisphere and the tropical Pacific SST in the previous month (November). A statistical approach to correct the ensemble forecasts was formulated based on the regression of the model’s leading forced SVD patterns and the observed seasonal mean precipitation. The performance of the corrected forecasts was assessed by comparing its cross-validated skill with that of the original GCM ensemble mean forecasts. The results show that the corrected forecasts predict the Canadian winter precipitation with statistically significant skill over the southern prairies and a large area of Québec–Ontario.
Abstract
A statistical postprocessing approach is applied to seasonal forecasts of surface air temperatures (SAT) over North America in fall, when the original uncalibrated predictions have little skill. The data used are ensemble-mean seasonal forecasts from four atmospheric general circulation models (GCMs) in the Canadian Historical Forecasting Project (HFP2) during the period 1969–2001. The statistical postprocessing uses the relationship between the predicted 500-hPa geopotential height (Z500) and the observed SAT to calibrate the SAT forecasts. The dimensions of the predicted Z500 fields are reduced to three modes with fixed spatial structures but time-dependent amplitudes. The latter are obtained through a singular value decomposition (SVD) analysis linking the variability of the ensemble-mean predicted Z500 to the tropical Pacific sea surface temperatures (SSTs). Results show that the postprocessing significantly improves the predictive skill of North American SAT in fall. The distributions of the SAT temporal standard deviation and the skill of the postprocessed ensemble forecasts are consistent among the GCMs, indicating that the approach is effective in reducing the model-dependent part of the errors associated with GCMs.
Abstract
A statistical postprocessing approach is applied to seasonal forecasts of surface air temperatures (SAT) over North America in fall, when the original uncalibrated predictions have little skill. The data used are ensemble-mean seasonal forecasts from four atmospheric general circulation models (GCMs) in the Canadian Historical Forecasting Project (HFP2) during the period 1969–2001. The statistical postprocessing uses the relationship between the predicted 500-hPa geopotential height (Z500) and the observed SAT to calibrate the SAT forecasts. The dimensions of the predicted Z500 fields are reduced to three modes with fixed spatial structures but time-dependent amplitudes. The latter are obtained through a singular value decomposition (SVD) analysis linking the variability of the ensemble-mean predicted Z500 to the tropical Pacific sea surface temperatures (SSTs). Results show that the postprocessing significantly improves the predictive skill of North American SAT in fall. The distributions of the SAT temporal standard deviation and the skill of the postprocessed ensemble forecasts are consistent among the GCMs, indicating that the approach is effective in reducing the model-dependent part of the errors associated with GCMs.
Abstract
A multivariable linear regression model is constructed based on the status of the Madden–Julian oscillation (MJO) and persistence in order to forecast wintertime surface air temperature anomalies over North America out to 4 pentads (20 days). The current and previous states of the MJO are utilized as predictors, based on the Real-time Multivariate (RMM) indices of Wheeler and Hendon. Beyond the persistence-driven first pentad, potentially useful skill is mainly observed during strong MJO events in phases 3, 4, 7, and 8, which correspond to a dipole diabatic heating anomaly in the tropical Indian Ocean and western Pacific. This skill is largely centered over the eastern United States and the Great Lakes region during pentads 2 and 3.
Abstract
A multivariable linear regression model is constructed based on the status of the Madden–Julian oscillation (MJO) and persistence in order to forecast wintertime surface air temperature anomalies over North America out to 4 pentads (20 days). The current and previous states of the MJO are utilized as predictors, based on the Real-time Multivariate (RMM) indices of Wheeler and Hendon. Beyond the persistence-driven first pentad, potentially useful skill is mainly observed during strong MJO events in phases 3, 4, 7, and 8, which correspond to a dipole diabatic heating anomaly in the tropical Indian Ocean and western Pacific. This skill is largely centered over the eastern United States and the Great Lakes region during pentads 2 and 3.
Abstract
Data for 39 winters are used to compute the potential vorticity (PV) budget on the θ = 315 K isentropic surface over the Northern Hemisphere. The object is to compare the mechanisms that maintain the PV balance during normal winters with those that maintain the balance during winters with anomalies of the North Atlantic Oscillation (NAO) and Pacific–North American (PNA) types. On an isentropic surface that does not intersect the ground, which is usually the case for the 315 K surface, the mean seasonal flow must be such as to maintain a simple local balance between the diabatic and frictional sources/sinks of PV, the isentropic advection of PV by the mean seasonal flow, and the mean seasonal PV advection by the subseasonal transients.
The climatology over the 39 winters shows that the main positive PV centers over the east coasts of Asia and Canada are maintained through a three-way balance among the upstream diabatic/frictional sources of PV, the PV advection by the mean seasonal flow, and that by the subseasonal transients. The transients with periods between 2 and 10 days and those with periods between 10 and 90 days are found to contribute about equally to the PV balance. The PV balance of NAO and PNA winter anomalies reveals that the PV advection by the subseasonal transients more systematically opposes the advection by the seasonal mean flow, so that the local PV source term is proportionately much less important than it is in the maintenance of climatological PV centers.
The calculations were also made on the θ = 350 K and 450 K isentropes. The results are presented only briefly to highlight the main similarities and differences with those obtained at 315 K.
Abstract
Data for 39 winters are used to compute the potential vorticity (PV) budget on the θ = 315 K isentropic surface over the Northern Hemisphere. The object is to compare the mechanisms that maintain the PV balance during normal winters with those that maintain the balance during winters with anomalies of the North Atlantic Oscillation (NAO) and Pacific–North American (PNA) types. On an isentropic surface that does not intersect the ground, which is usually the case for the 315 K surface, the mean seasonal flow must be such as to maintain a simple local balance between the diabatic and frictional sources/sinks of PV, the isentropic advection of PV by the mean seasonal flow, and the mean seasonal PV advection by the subseasonal transients.
The climatology over the 39 winters shows that the main positive PV centers over the east coasts of Asia and Canada are maintained through a three-way balance among the upstream diabatic/frictional sources of PV, the PV advection by the mean seasonal flow, and that by the subseasonal transients. The transients with periods between 2 and 10 days and those with periods between 10 and 90 days are found to contribute about equally to the PV balance. The PV balance of NAO and PNA winter anomalies reveals that the PV advection by the subseasonal transients more systematically opposes the advection by the seasonal mean flow, so that the local PV source term is proportionately much less important than it is in the maintenance of climatological PV centers.
The calculations were also made on the θ = 350 K and 450 K isentropes. The results are presented only briefly to highlight the main similarities and differences with those obtained at 315 K.
Abstract
It is desirable to filter the unpredictable components from a medium-range forecast. Such a filtered forecast can be obtained by averaging an ensemble of predictions that started from slightly different initial atmospheric states. Different strategies have been proposed to generate the initial perturbations for such an ensemble. “Optimal” perturbation give the largest error at a prespecified forecast time. “Bred” perturbations have grown during a period prior to the analysis. “OSSE-MC” perturbations are obtained using a Monte Carlo-like observation system simulation experiment (OSSE).
In the current pilot study, the properties of the different strategies are compared. A three-level quasigeostrophic model is used to describe the evolution of the errors. The tangent linear version of this model and its adjoint version are used to generate the optimal perturbations, while bred perturbations are generated using the full nonlinear model. In the OSSE-MC method, random perturbations of model states are used in the simulation of radiosonde and satellite observations. These observations are then assimilated using an optimal interpolation (OI) assimilation system. A large OSSE-MC ensemble is obtained using such input and the OI system, which then provides the ground truth for the other ensembles. Its observed statistical properties are also used in the construction of the optimal and the bred perturbations.
The quality of the different ensemble mean medium-range forecasts is compared for forecast lengths of up to 15 days and ensembles of 2, 8, and 32 members. Before 6 days the control performs almost as well as any ensemble mean. Bred and OSSE-MC ensembles of only two members are of marginal quality. For all three methods an ensemble size of 8 is sufficient to obtain the main part of the possible improvement over the control, and all perform well for 32-member ensembles. Still better results are obtained from a weighted mean of the climate and the ensemble mean.
Abstract
It is desirable to filter the unpredictable components from a medium-range forecast. Such a filtered forecast can be obtained by averaging an ensemble of predictions that started from slightly different initial atmospheric states. Different strategies have been proposed to generate the initial perturbations for such an ensemble. “Optimal” perturbation give the largest error at a prespecified forecast time. “Bred” perturbations have grown during a period prior to the analysis. “OSSE-MC” perturbations are obtained using a Monte Carlo-like observation system simulation experiment (OSSE).
In the current pilot study, the properties of the different strategies are compared. A three-level quasigeostrophic model is used to describe the evolution of the errors. The tangent linear version of this model and its adjoint version are used to generate the optimal perturbations, while bred perturbations are generated using the full nonlinear model. In the OSSE-MC method, random perturbations of model states are used in the simulation of radiosonde and satellite observations. These observations are then assimilated using an optimal interpolation (OI) assimilation system. A large OSSE-MC ensemble is obtained using such input and the OI system, which then provides the ground truth for the other ensembles. Its observed statistical properties are also used in the construction of the optimal and the bred perturbations.
The quality of the different ensemble mean medium-range forecasts is compared for forecast lengths of up to 15 days and ensembles of 2, 8, and 32 members. Before 6 days the control performs almost as well as any ensemble mean. Bred and OSSE-MC ensembles of only two members are of marginal quality. For all three methods an ensemble size of 8 is sufficient to obtain the main part of the possible improvement over the control, and all perform well for 32-member ensembles. Still better results are obtained from a weighted mean of the climate and the ensemble mean.
Abstract
Numerical experiments have been performed to determine whether it is possible to improve the quality of atmospheric forecasts by using the average of two predictions starting from slightly perturbed initial conditions. The predictions are made with a T21 quasi-nondivergent three-level model and a “perfect model” approach is used, so that all prediction errors are due to the uncertainty in the initial conditions. The two perturbed predictions are initialized by adding to and subtracting from the control initial state a small-amplitude disturbance called a “bred” mode, obtained as the fastest-growing small-amplitude perturbation of the model over a 20-day period preceding the beginning of the forecast.
The results indicate that for initial states that contain very small analysis errors the two-member ensemble yields a mean forecast of lower quality than the control forecast. For larger-amplitude analysis error fields, however, the ensemble prediction outperforms the control forecast. When a statistical distribution of possible analysis errors is considered, it is found that on average the mean of the two perturbed predictions is of higher quality than the control forecast.
The study has also shown that the spread between the two perturbed predictions is correlated with the magnitude of the forecast error for every day of the forecast period from day 1 to day 10.
The same approach has been applied to Lorenz's three-component model and similar results have been obtained.
Abstract
Numerical experiments have been performed to determine whether it is possible to improve the quality of atmospheric forecasts by using the average of two predictions starting from slightly perturbed initial conditions. The predictions are made with a T21 quasi-nondivergent three-level model and a “perfect model” approach is used, so that all prediction errors are due to the uncertainty in the initial conditions. The two perturbed predictions are initialized by adding to and subtracting from the control initial state a small-amplitude disturbance called a “bred” mode, obtained as the fastest-growing small-amplitude perturbation of the model over a 20-day period preceding the beginning of the forecast.
The results indicate that for initial states that contain very small analysis errors the two-member ensemble yields a mean forecast of lower quality than the control forecast. For larger-amplitude analysis error fields, however, the ensemble prediction outperforms the control forecast. When a statistical distribution of possible analysis errors is considered, it is found that on average the mean of the two perturbed predictions is of higher quality than the control forecast.
The study has also shown that the spread between the two perturbed predictions is correlated with the magnitude of the forecast error for every day of the forecast period from day 1 to day 10.
The same approach has been applied to Lorenz's three-component model and similar results have been obtained.
