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- Author or Editor: R. Vautard x
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Abstract
A critical examination of the foundations of the slow manifold concept is presented. We study the behavior of the simple Lorenz truncated primitive equation model and show that free gravity modes exist for large forcing. For small forcing, the flow is dominated by geostrophic motion and quasi-invariant manifolds are found. However, we present arguments against the existence of a strictly invariant manifold. We show that the bounded derivative conditions are generally not satisfied, even when an invariant manifold exists; smooth functions always possess fast transients. We present a new initialization method based on the analytic expansion of local invariant manifolds and compare it with Machenhauer's method on a simple example.
Abstract
A critical examination of the foundations of the slow manifold concept is presented. We study the behavior of the simple Lorenz truncated primitive equation model and show that free gravity modes exist for large forcing. For small forcing, the flow is dominated by geostrophic motion and quasi-invariant manifolds are found. However, we present arguments against the existence of a strictly invariant manifold. We show that the bounded derivative conditions are generally not satisfied, even when an invariant manifold exists; smooth functions always possess fast transients. We present a new initialization method based on the analytic expansion of local invariant manifolds and compare it with Machenhauer's method on a simple example.
Abstract
The algorithm developed by Vautard and Legras is applied to a series of 37 winter of 700 mb geopotential height observations, in order to identify quasi-stationary patterns occurring over the extratropical North Atlantic area. Weather regimes are obtained as solutions of a act of nine nonlinear statistical equations, giving the balance of the large-scale average tendency. Four regime patterns are found. The first one exhibits the typical European blocking dipole. The second one is an enhanced zonal flow. The third one consists of a positive anomaly over Greenland, and the last one is characterized by a ridge over the eastern Atlantic Ocean. The role played by the transient small scales in the maintenance of thew four regimes is discussed.
Next, the backward and forward memory times of the different weather regimes are established. Evidence is brought that the atmosphere keeps its memory of regime occurrences into the medium range (10–20 days). Backward memory times are shorter (5–10 days), showing that the onsets of the regimes are rather sudden. Preferred precursor and successor patterns are identified as the maxima of the composite probability densities of the anomalies occurring before the onsets and after the breaks. Some transitions between regimes are quite smooth, while others consist of a dramatic change, within a couple of days, of the weather pattern. For instance, blocking is often preceeded by a positive anomaly in the mid-Atlantic together with a trough over Europe.
The preferred transitions between regimes are examined. It is shown, in particular, that zonal flows am likely to become blocked flows, and that the Greenland Anticyclone regime (third regime) is likely to succeed blocking events. All statistics are tested against climatology. The systematic aspect of this study gives rise to multiple applications, especially for case and composite studies on model prediction errors.
Abstract
The algorithm developed by Vautard and Legras is applied to a series of 37 winter of 700 mb geopotential height observations, in order to identify quasi-stationary patterns occurring over the extratropical North Atlantic area. Weather regimes are obtained as solutions of a act of nine nonlinear statistical equations, giving the balance of the large-scale average tendency. Four regime patterns are found. The first one exhibits the typical European blocking dipole. The second one is an enhanced zonal flow. The third one consists of a positive anomaly over Greenland, and the last one is characterized by a ridge over the eastern Atlantic Ocean. The role played by the transient small scales in the maintenance of thew four regimes is discussed.
Next, the backward and forward memory times of the different weather regimes are established. Evidence is brought that the atmosphere keeps its memory of regime occurrences into the medium range (10–20 days). Backward memory times are shorter (5–10 days), showing that the onsets of the regimes are rather sudden. Preferred precursor and successor patterns are identified as the maxima of the composite probability densities of the anomalies occurring before the onsets and after the breaks. Some transitions between regimes are quite smooth, while others consist of a dramatic change, within a couple of days, of the weather pattern. For instance, blocking is often preceeded by a positive anomaly in the mid-Atlantic together with a trough over Europe.
The preferred transitions between regimes are examined. It is shown, in particular, that zonal flows am likely to become blocked flows, and that the Greenland Anticyclone regime (third regime) is likely to succeed blocking events. All statistics are tested against climatology. The systematic aspect of this study gives rise to multiple applications, especially for case and composite studies on model prediction errors.
Abstract
The description of clouds in mesoscale models has progressed significantly during recent years by improving microphysical schemes with more physical parameterizations deduced from observations. Recently, the first lidar in space, the Ice, Cloud, and Land Elevation Satellite (ICESat)/Geosciences Laser Altimeter System, has collected a valuable dataset that improves the knowledge of occurrence and macrophysical properties of clouds, and particularly high-altitude clouds, which are usually optically thin. This study evaluates the capability of the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) to reproduce optically thin clouds using the ICESat October–November 2003 dataset. Initial and boundary conditions are prescribed from NCEP products and MM5 run over the European continent with a 40-km spatial resolution. Spaceborne lidar profiles are diagnosed from model outputs and compared with the observed ones at the same location and time. One month of simulations–observations comparisons shows that the model correctly reproduces cloud structures on average, but underestimates the thinnest clouds (by 0%–20%) and overestimates less thin clouds in the upper troposphere (altitude >6 km). The total low-level water cloud amount (altitude <6 km) appears fairly well reproduced, although the masking effect of higher clouds does not allow for a firm conclusion. The clouds are rarely simulated and observed simultaneously, 50% for high clouds and 20% for low clouds. The lack of high-altitude very thin clouds is possibly due to dry biases in the upper-troposphere humidity fields used to force the model. The overestimation of optically less thin cloud may be due to an overestimation of the cloud lifetime or water vapor supersaturation around ice clouds that is not taken into account in the model. When the upper troposphere and low warm clouds appear in the model at the same time and location as in the observations, they are optically too thick, likely because their water/ice content and particle concentration are overestimated simultaneously.
Abstract
The description of clouds in mesoscale models has progressed significantly during recent years by improving microphysical schemes with more physical parameterizations deduced from observations. Recently, the first lidar in space, the Ice, Cloud, and Land Elevation Satellite (ICESat)/Geosciences Laser Altimeter System, has collected a valuable dataset that improves the knowledge of occurrence and macrophysical properties of clouds, and particularly high-altitude clouds, which are usually optically thin. This study evaluates the capability of the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) to reproduce optically thin clouds using the ICESat October–November 2003 dataset. Initial and boundary conditions are prescribed from NCEP products and MM5 run over the European continent with a 40-km spatial resolution. Spaceborne lidar profiles are diagnosed from model outputs and compared with the observed ones at the same location and time. One month of simulations–observations comparisons shows that the model correctly reproduces cloud structures on average, but underestimates the thinnest clouds (by 0%–20%) and overestimates less thin clouds in the upper troposphere (altitude >6 km). The total low-level water cloud amount (altitude <6 km) appears fairly well reproduced, although the masking effect of higher clouds does not allow for a firm conclusion. The clouds are rarely simulated and observed simultaneously, 50% for high clouds and 20% for low clouds. The lack of high-altitude very thin clouds is possibly due to dry biases in the upper-troposphere humidity fields used to force the model. The overestimation of optically less thin cloud may be due to an overestimation of the cloud lifetime or water vapor supersaturation around ice clouds that is not taken into account in the model. When the upper troposphere and low warm clouds appear in the model at the same time and location as in the observations, they are optically too thick, likely because their water/ice content and particle concentration are overestimated simultaneously.
Abstract
The ability of four-dimensional variational (4DVAR) assimilation of data to reduce various observational error structures in a quasigeostrophic model is studied. It is found that 4DVAR with assimilation periods on the order of a week is very efficient at reducing error in phase space directions that have not amplified in the past, that is, those phase space directions that do not lie on the unstable manifold of the system. This is particularly true for observational errors that project in rapidly growing singular vector phase space directions.
In general, long period 4DVAR changes the forecast error growth rates to rates similar to the leading Lyapunov exponents for the system. However, error structures that grow significantly faster than the leading Lyapunov vector and are not readily reduced by long period 4DVAR can be constructed by doing a singular vector decomposition in the subspace of growing backward Lyapunov vectors. This procedure is an approximation to calculating the singular vectors using an appropriate analysis error covariance metric for the assimilation technique. 4DVAR acting on observational errors constructed in this manner yields forecast error growth a factor of 5 larger than that of the leading Lyapunov vector over a 4-day forecast period.
The addition of model error places limits on the application of long assimilation period 4DVAR. Model error adds a background level of error to the assimilated solution that cannot be reduced, and also limits how far into the past the assimilation period can be extended. These effects combine to reduce the quality of the optimal assimilated state that can obtained by applying 4DVAR. However, model error does not diminish the ability of long assimilation period 4DVAR to reduce rapidly growing singular vector–type error components. Since long assimilation periods can potentially produce large analysis errors if model error exists, the relative benefit of extending the assimilation period to reduce forecast error growth rates must be weighed in a given situation.
Abstract
The ability of four-dimensional variational (4DVAR) assimilation of data to reduce various observational error structures in a quasigeostrophic model is studied. It is found that 4DVAR with assimilation periods on the order of a week is very efficient at reducing error in phase space directions that have not amplified in the past, that is, those phase space directions that do not lie on the unstable manifold of the system. This is particularly true for observational errors that project in rapidly growing singular vector phase space directions.
In general, long period 4DVAR changes the forecast error growth rates to rates similar to the leading Lyapunov exponents for the system. However, error structures that grow significantly faster than the leading Lyapunov vector and are not readily reduced by long period 4DVAR can be constructed by doing a singular vector decomposition in the subspace of growing backward Lyapunov vectors. This procedure is an approximation to calculating the singular vectors using an appropriate analysis error covariance metric for the assimilation technique. 4DVAR acting on observational errors constructed in this manner yields forecast error growth a factor of 5 larger than that of the leading Lyapunov vector over a 4-day forecast period.
The addition of model error places limits on the application of long assimilation period 4DVAR. Model error adds a background level of error to the assimilated solution that cannot be reduced, and also limits how far into the past the assimilation period can be extended. These effects combine to reduce the quality of the optimal assimilated state that can obtained by applying 4DVAR. However, model error does not diminish the ability of long assimilation period 4DVAR to reduce rapidly growing singular vector–type error components. Since long assimilation periods can potentially produce large analysis errors if model error exists, the relative benefit of extending the assimilation period to reduce forecast error growth rates must be weighed in a given situation.
Abstract
A 25-year dataset of potential vorticity on the 315-K isentropic surface is built from the National Meteorological Center (NMC) final analysis archive. Potential vorticity is calculated from the nonlinear gradient wind balance using temperature and geopotential fields, since the wind field is not available in the early part of the archive.
The validity of this calculation is assessed by comparing the results with potential vorticity obtained directly from European Centre for Medium-Range Weather Forecasts (ECMWF) analyzed winds. The error due to the nonlinear balance approximation turns out to be smaller than the difference between ECMWF and NMC analysis.
The possibility of studying diabatic forcing as a residual of the equation of potential vorticity conservation is examined. The average potential vorticity forcing found in this way is consistent with the authors knowledge of the mean diabatic heating. The amplitude of the residual decreases through the analysis period, reflecting the improvement in the observational network and in the analysis schemes.
Next the authors demonstrate that this dataset can be used for studies of transient-mean flow interactions. The authors present diagnostics of the transient feedback by separating the contribution of vortical and thermal terms on the isentropic surface. Also, the contribution of high-frequency (periods less than 10 days) and low-frequency (periods greater than 10 days) transients is examined. On the 315-K surface, transients act mostly in reducing the potential vorticity gradient through thermal terms and accelerate the zonal flow through vortical forcing.
Finally, these diagnostics are also applied to a long ensemble of blocking events, and the authors study the anomaly of transient feedback during these events. It is found that transients have primarily an advective effect, forcing the dipole structure to retrograde westward. Thermal and vortical terms have a very distinct action on the blocking anomaly. Vortical forcing is constructive and advective, whereas thermal forcing is dissipative and makes the dipole rotate clockwise.
Abstract
A 25-year dataset of potential vorticity on the 315-K isentropic surface is built from the National Meteorological Center (NMC) final analysis archive. Potential vorticity is calculated from the nonlinear gradient wind balance using temperature and geopotential fields, since the wind field is not available in the early part of the archive.
The validity of this calculation is assessed by comparing the results with potential vorticity obtained directly from European Centre for Medium-Range Weather Forecasts (ECMWF) analyzed winds. The error due to the nonlinear balance approximation turns out to be smaller than the difference between ECMWF and NMC analysis.
The possibility of studying diabatic forcing as a residual of the equation of potential vorticity conservation is examined. The average potential vorticity forcing found in this way is consistent with the authors knowledge of the mean diabatic heating. The amplitude of the residual decreases through the analysis period, reflecting the improvement in the observational network and in the analysis schemes.
Next the authors demonstrate that this dataset can be used for studies of transient-mean flow interactions. The authors present diagnostics of the transient feedback by separating the contribution of vortical and thermal terms on the isentropic surface. Also, the contribution of high-frequency (periods less than 10 days) and low-frequency (periods greater than 10 days) transients is examined. On the 315-K surface, transients act mostly in reducing the potential vorticity gradient through thermal terms and accelerate the zonal flow through vortical forcing.
Finally, these diagnostics are also applied to a long ensemble of blocking events, and the authors study the anomaly of transient feedback during these events. It is found that transients have primarily an advective effect, forcing the dipole structure to retrograde westward. Thermal and vortical terms have a very distinct action on the blocking anomaly. Vortical forcing is constructive and advective, whereas thermal forcing is dissipative and makes the dipole rotate clockwise.
Abstract
The ability of the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) to simulate midlatitude ice clouds is evaluated. Model outputs are compared to long-term meteorological measurements by active (radar and lidar) and passive (infrared and visible fluxes) remote sensing collected at an atmospheric observatory near Paris, France. The goal is to understand which of four microphysical schemes is best suited to simulate midlatitude ice clouds. The methodology consists of simulating instrument observables from the model outputs without any profile inversion, which allows the authors to use fewer assumptions on microphysical and optical properties of ice particles.
Among the four schemes compared in the current study, the best observation-to-simulations scores are obtained with Reisner et al. provided that the particles’ sedimentation velocity from Heymsfield and Donner is used instead of that originally proposed. For this last scheme, the model gives results close to the measurements for clouds with medium optical depth of typically 1 to 3, whatever the season. In this configuration, MM5 simulates the presence of midlatitude ice clouds in more than 65% of the authors’ selection of observed cloud cases. In 35% of the cases, the simulated clouds are too persistent whatever the microphysical scheme and tend to produce too much solid water (ice and snow) and not enough liquid water.
Abstract
The ability of the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) to simulate midlatitude ice clouds is evaluated. Model outputs are compared to long-term meteorological measurements by active (radar and lidar) and passive (infrared and visible fluxes) remote sensing collected at an atmospheric observatory near Paris, France. The goal is to understand which of four microphysical schemes is best suited to simulate midlatitude ice clouds. The methodology consists of simulating instrument observables from the model outputs without any profile inversion, which allows the authors to use fewer assumptions on microphysical and optical properties of ice particles.
Among the four schemes compared in the current study, the best observation-to-simulations scores are obtained with Reisner et al. provided that the particles’ sedimentation velocity from Heymsfield and Donner is used instead of that originally proposed. For this last scheme, the model gives results close to the measurements for clouds with medium optical depth of typically 1 to 3, whatever the season. In this configuration, MM5 simulates the presence of midlatitude ice clouds in more than 65% of the authors’ selection of observed cloud cases. In 35% of the cases, the simulated clouds are too persistent whatever the microphysical scheme and tend to produce too much solid water (ice and snow) and not enough liquid water.
