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- Author or Editor: Masahide Kimoto x
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Abstract
Construction and optimization methods of spherical hexagonal–pentagonal geodesic grids are investigated. The objective is to compare grid structures on common ground.
The distinction between two types of hexagonal–pentagonal grids is made. Three conventional grid optimization methods are summarized. In addition, three new optimization methods are proposed. Six desirable conditions for an ideal grid are described, and the grid optimization methods are organized in view of such conditions.
Interval uniformity, area uniformity, isotropy, and bisection of cell faces are systematically investigated for optimized grids. There are compensations of preferable grid features in each optimization method, and an optimal method cannot be decided based only on the research of grid features. It is suggested that grid optimization methods should be selected based on research of numerical schemes.
Abstract
Construction and optimization methods of spherical hexagonal–pentagonal geodesic grids are investigated. The objective is to compare grid structures on common ground.
The distinction between two types of hexagonal–pentagonal grids is made. Three conventional grid optimization methods are summarized. In addition, three new optimization methods are proposed. Six desirable conditions for an ideal grid are described, and the grid optimization methods are organized in view of such conditions.
Interval uniformity, area uniformity, isotropy, and bisection of cell faces are systematically investigated for optimized grids. There are compensations of preferable grid features in each optimization method, and an optimal method cannot be decided based only on the research of grid features. It is suggested that grid optimization methods should be selected based on research of numerical schemes.
Abstract
A detailed analysis of the bifurcation structure of a two-level, quasigeostrophic model is made by a combined use of a continuation algorithm and extensive time integrations. The model is formulated on a sphere with realistic Northern Hemisphere topography and is driven by Newtonian relaxation to axisymmetric radiative-equilibrium temperature that represents the equator-to-pole contrast of the diabatic heating. The strength of this heating contrast is varied as a primary control parameter. Bifurcations of not only stationary but also periodic, doubly periodic (quasi periodic), and chaotic solutions are followed for the model with triangular 15 (T15) horizontal resolution, corresponding to the number of (real) spherical harmonic coefficients, 240.
It is found that the model possesses multiple attractors for a fairly broad, but realistic, range in the parameter space. Characteristic oscillatory modes are associated with each one of these attractors. Two frequency bands, one in synoptic and the other in intraseasonal timescales, are dominant in such oscillations. These attractors keep their identity even when the system is perturbed by stochastic forcing of fairly large amplitude. Furthermore, when some parameters are changed to make the system more turbulent, it is observed that the system starts transiting among the ruins of attractors that used to be stable, a behavior reminiscent of the transitions among different flow regimes observed in the real atmosphere. Such behavior, called chaotic itinerancy, has recently attracted much attention as a characteristic of chaos in physical systems with many degrees of freedom. Chaotic itinerancy in the present model appears to be more complicated than the examples reported so far in that it consists of attractors with no obvious spatial symmetry and that preferred routes of transitions are observed. Evidences of multiple attractors and chaotic itinerancy are found in higher resolutions up to T21.
Discussions are made about implications of such model behavior to the understanding of observed low-frequency variability.
Abstract
A detailed analysis of the bifurcation structure of a two-level, quasigeostrophic model is made by a combined use of a continuation algorithm and extensive time integrations. The model is formulated on a sphere with realistic Northern Hemisphere topography and is driven by Newtonian relaxation to axisymmetric radiative-equilibrium temperature that represents the equator-to-pole contrast of the diabatic heating. The strength of this heating contrast is varied as a primary control parameter. Bifurcations of not only stationary but also periodic, doubly periodic (quasi periodic), and chaotic solutions are followed for the model with triangular 15 (T15) horizontal resolution, corresponding to the number of (real) spherical harmonic coefficients, 240.
It is found that the model possesses multiple attractors for a fairly broad, but realistic, range in the parameter space. Characteristic oscillatory modes are associated with each one of these attractors. Two frequency bands, one in synoptic and the other in intraseasonal timescales, are dominant in such oscillations. These attractors keep their identity even when the system is perturbed by stochastic forcing of fairly large amplitude. Furthermore, when some parameters are changed to make the system more turbulent, it is observed that the system starts transiting among the ruins of attractors that used to be stable, a behavior reminiscent of the transitions among different flow regimes observed in the real atmosphere. Such behavior, called chaotic itinerancy, has recently attracted much attention as a characteristic of chaos in physical systems with many degrees of freedom. Chaotic itinerancy in the present model appears to be more complicated than the examples reported so far in that it consists of attractors with no obvious spatial symmetry and that preferred routes of transitions are observed. Evidences of multiple attractors and chaotic itinerancy are found in higher resolutions up to T21.
Discussions are made about implications of such model behavior to the understanding of observed low-frequency variability.
Abstract
Recurrent and persistent flow patterns are identified by examining multivariate probability density functions (PDFs) in the phase space of large-scale atmospheric motions. This idea is pursued systematically here in the hope of clarifying the extent to which intraseasonal variability can be described and understood in terms of multiple flow regimes.
Bivariate PDFs of the Northern Hemisphere (NH) wintertime anomaly heights at 700 mb are examined in the present paper, using a 37-year dataset. The two-dimensional phase plane is defined by the two leading empirical orthogonal functions (EOFs) of the anomaly fields. PDFs on this plane exhibit synoptically intriguing and statistically significant inhomogeneities on the periphery of the distribution. It is shown that these inhomogeneities are due to the existence of persistent and recurrent anomaly patterns, well-known as dominant teleconnection patterns; that is, the Pacific/North American (PNA) pattern, its reverse, and zonal and blocked phases of the North Atlantic Oscillation (NAO). It is argued that the inhomogeneities are obscured when PDFs are examined in a smaller-dimensional subspace than dynamically desired.
Abstract
Recurrent and persistent flow patterns are identified by examining multivariate probability density functions (PDFs) in the phase space of large-scale atmospheric motions. This idea is pursued systematically here in the hope of clarifying the extent to which intraseasonal variability can be described and understood in terms of multiple flow regimes.
Bivariate PDFs of the Northern Hemisphere (NH) wintertime anomaly heights at 700 mb are examined in the present paper, using a 37-year dataset. The two-dimensional phase plane is defined by the two leading empirical orthogonal functions (EOFs) of the anomaly fields. PDFs on this plane exhibit synoptically intriguing and statistically significant inhomogeneities on the periphery of the distribution. It is shown that these inhomogeneities are due to the existence of persistent and recurrent anomaly patterns, well-known as dominant teleconnection patterns; that is, the Pacific/North American (PNA) pattern, its reverse, and zonal and blocked phases of the North Atlantic Oscillation (NAO). It is argued that the inhomogeneities are obscured when PDFs are examined in a smaller-dimensional subspace than dynamically desired.
Abstract
This paper presents an observational analysis of recurrent flow patterns in the Northern Hemisphere (NH) winter, based on a 37-year series of daily 700-mb height anomalies. Large-scale anomaly patterns that appear repeatedly and persist beyond synoptic time scales are identified by searching for local maxima of probability density in a phase subspace, which is spanned by the leading empirical orthogenal functions (EOFs).
By using an angular probability density function (PDF), we focus on the shape, not magnitude, of the anomaly patterns. The PDF estimate is nonparametric; that is, our algorithm makes no a priori assumption on symmetry with respect to the climatological mean as in one-point correlation and rotated EOF analyses. The local density maxima are searched by iterative bump hunting.
Based on observed partial decoupling between the Pacific (PAC) and the Atlantic-Eurasian (ATL) sectors, the classification algorithm is applied separately to each of the two. Seven PAC and six ATL patterns are obtained. Anomaly maps that belong to the neighborhood of each PDF peak are associated with distinct flow regimes. These include regional blocked and zonal flows, and wave train-like anomaly patterns, some of them well known from previous studies, others revealed by our analysis for the first time.
Successive appearances of flow regimes are generally separated by unclassifiable, transient periods. A Markov chain describes transitions between different flow regimes; highly likely, as well as unlikely routes of transition exist. Chains of preferred transitions may be related to the existence of oscillatory modes in the NH extratropics.
A synoptic characterization of onsets and breaks for the flow regimes obtained is given by compositing. In situ evolutions of anomaly patterns, slow westward shifts of high-latitude anomaly centers, and successive down-stream increase of anomaly magnitudes are the typical signatures of such events.
Abstract
This paper presents an observational analysis of recurrent flow patterns in the Northern Hemisphere (NH) winter, based on a 37-year series of daily 700-mb height anomalies. Large-scale anomaly patterns that appear repeatedly and persist beyond synoptic time scales are identified by searching for local maxima of probability density in a phase subspace, which is spanned by the leading empirical orthogenal functions (EOFs).
By using an angular probability density function (PDF), we focus on the shape, not magnitude, of the anomaly patterns. The PDF estimate is nonparametric; that is, our algorithm makes no a priori assumption on symmetry with respect to the climatological mean as in one-point correlation and rotated EOF analyses. The local density maxima are searched by iterative bump hunting.
Based on observed partial decoupling between the Pacific (PAC) and the Atlantic-Eurasian (ATL) sectors, the classification algorithm is applied separately to each of the two. Seven PAC and six ATL patterns are obtained. Anomaly maps that belong to the neighborhood of each PDF peak are associated with distinct flow regimes. These include regional blocked and zonal flows, and wave train-like anomaly patterns, some of them well known from previous studies, others revealed by our analysis for the first time.
Successive appearances of flow regimes are generally separated by unclassifiable, transient periods. A Markov chain describes transitions between different flow regimes; highly likely, as well as unlikely routes of transition exist. Chains of preferred transitions may be related to the existence of oscillatory modes in the NH extratropics.
A synoptic characterization of onsets and breaks for the flow regimes obtained is given by compositing. In situ evolutions of anomaly patterns, slow westward shifts of high-latitude anomaly centers, and successive down-stream increase of anomaly magnitudes are the typical signatures of such events.
Abstract
The dynamical basis of extratropical low-frequency variability (LFV) is investigated using a quasigeostrophic model on a sphere with realistic Northern Hemisphere topography. The model is driven by Newtonian relaxation to an axisymmetric radiative equilibrium temperature. Two versions of the model are used: one with two vertical levels and horizontal T15 resolution and the other with five levels and T21 resolution. In previous investigations, by the authors, the former model has been found to possess multiple attractors in a stable range of the model parameters and to wander irregularly among attractor ruins for unstable parameter sets. A similar behavior is found for the higher-resolution model as well.
Three aspects of LFV are considered in this paper. The first two are intermittent appearances of quasi-stationary weather regimes and low-frequency oscillations. The third is the dominance of a few principal patterns of variability that show red noise–like temporal behavior. In the real atmosphere, the first two can be found by careful examinations in the general predominance of the last aspect. The model is able to simulate these aspects with a certain level of realism.
It is found that the first two are associated with the existence of multiple attractors and oscillations intrinsic to them. As for the two-level model, attractors that used to be confined to small regions in phase space correspond to quasi-stationary weather regimes and those located in regions where the phase space structure is flat support the oscillations with sizable amplitudes at a more turbulent stage. The five-level model shows a more complicated behavior, but the relevance of multiple attractors and associated oscillations has been confirmed as well.
It is found in the realistic range of parameters that singular modes of linearized equations with time-mean basic states form the basis of principal spatial patterns for which low-frequency temporal variations dominate. The singular vector with the smallest singular value roughly coincides with the first mode of empirical orthogonal function (EOF) for the lower-resolution model. The smallness of the singular value guarantees the small rate of time change so that the system spends a long time along the linear axis in phase space. The singular vector is found to be relatively insensitive to the changes in the basic state for the linearization. The relevance of the singular vector is more controversial in the higher-resolution model. The similarity with the leading EOFs is lost considerably. However, it is found that leading singular vectors still play a role in determining a low-dimensional linear subspace with which most of the low-frequency variance is associated. The interaction between singular modes and forcing due to transients is suggested to be responsible for the deviation of the principal patterns from singular modes.
Abstract
The dynamical basis of extratropical low-frequency variability (LFV) is investigated using a quasigeostrophic model on a sphere with realistic Northern Hemisphere topography. The model is driven by Newtonian relaxation to an axisymmetric radiative equilibrium temperature. Two versions of the model are used: one with two vertical levels and horizontal T15 resolution and the other with five levels and T21 resolution. In previous investigations, by the authors, the former model has been found to possess multiple attractors in a stable range of the model parameters and to wander irregularly among attractor ruins for unstable parameter sets. A similar behavior is found for the higher-resolution model as well.
Three aspects of LFV are considered in this paper. The first two are intermittent appearances of quasi-stationary weather regimes and low-frequency oscillations. The third is the dominance of a few principal patterns of variability that show red noise–like temporal behavior. In the real atmosphere, the first two can be found by careful examinations in the general predominance of the last aspect. The model is able to simulate these aspects with a certain level of realism.
It is found that the first two are associated with the existence of multiple attractors and oscillations intrinsic to them. As for the two-level model, attractors that used to be confined to small regions in phase space correspond to quasi-stationary weather regimes and those located in regions where the phase space structure is flat support the oscillations with sizable amplitudes at a more turbulent stage. The five-level model shows a more complicated behavior, but the relevance of multiple attractors and associated oscillations has been confirmed as well.
It is found in the realistic range of parameters that singular modes of linearized equations with time-mean basic states form the basis of principal spatial patterns for which low-frequency temporal variations dominate. The singular vector with the smallest singular value roughly coincides with the first mode of empirical orthogonal function (EOF) for the lower-resolution model. The smallness of the singular value guarantees the small rate of time change so that the system spends a long time along the linear axis in phase space. The singular vector is found to be relatively insensitive to the changes in the basic state for the linearization. The relevance of the singular vector is more controversial in the higher-resolution model. The similarity with the leading EOFs is lost considerably. However, it is found that leading singular vectors still play a role in determining a low-dimensional linear subspace with which most of the low-frequency variance is associated. The interaction between singular modes and forcing due to transients is suggested to be responsible for the deviation of the principal patterns from singular modes.
Abstract
Historical wintertime sea surface temperature (SST) data show that a sandwich pattern dominates on the decadal timescales in the North Atlantic, at least after the 1970s. The authors investigated how such decadal SST anomalies can survive against local thermal feedback, which acts to dampen them rapidly. At the surface, winter SST anomalies have a negligible projection with the subsequent summer anomalies while they show a significant projection with the SST anomalies in the next winter. On the other hand, observed summer temperature anomalies below the mixed layer tend to have the same sign as the previous winter SST anomalies, although the magnitude of the former is roughly one-third of the latter. This suggests that a reemergence mechanism of SST anomalies associated with the seasonal cycle of the mixed layer depth (MLD), which has been verified by Alexander and Deser, helps maintain the decadal SST anomalies. In order to examine this scenario, a mixed layer model driven by daily atmospheric data generated by a T42 atmospheric general circulation model was used. The mixed layer model well reproduces the climatology of both SST and MLD in the North Atlantic. An experiment in which a thermal forcing having the observed decadal pattern is added only for the initial winter shows that the SST anomalies disappear until July but reappear in the subsequent winters. This result supports the inference based on the observational evidence, and is explained as follows: (i) SST anomalies are partly detrained to deeper levels in spring when the mixed layer shoals rapidly, (ii) temperature anomalies beneath the shallow mixed layer are preserved during summer, (iii) they are entrained into the surface in the succeeding fall and winter when the mixed layer is again deepened. The recurrence of SST anomalies was found in two centers of the decadal anomaly pattern (30°–45°N, 80°–50°W and 45°–60°N, 50°–20°W), but not in another center in the subtropics (10°–25°N, 40°–10°W) where the MLD reveals only a small seasonality. The magnitude of recurrent SST anomalies is affected by two factors: MLD difference between winter and summer and the persistence of SST anomalies from winter to spring as they determine the amount and the magnitude of detrained temperature anomalies into the mixed layer, respectively.
The above results indicate that the effective damping time for the winter SST anomalies is much longer than the local damping time of several months.
Abstract
Historical wintertime sea surface temperature (SST) data show that a sandwich pattern dominates on the decadal timescales in the North Atlantic, at least after the 1970s. The authors investigated how such decadal SST anomalies can survive against local thermal feedback, which acts to dampen them rapidly. At the surface, winter SST anomalies have a negligible projection with the subsequent summer anomalies while they show a significant projection with the SST anomalies in the next winter. On the other hand, observed summer temperature anomalies below the mixed layer tend to have the same sign as the previous winter SST anomalies, although the magnitude of the former is roughly one-third of the latter. This suggests that a reemergence mechanism of SST anomalies associated with the seasonal cycle of the mixed layer depth (MLD), which has been verified by Alexander and Deser, helps maintain the decadal SST anomalies. In order to examine this scenario, a mixed layer model driven by daily atmospheric data generated by a T42 atmospheric general circulation model was used. The mixed layer model well reproduces the climatology of both SST and MLD in the North Atlantic. An experiment in which a thermal forcing having the observed decadal pattern is added only for the initial winter shows that the SST anomalies disappear until July but reappear in the subsequent winters. This result supports the inference based on the observational evidence, and is explained as follows: (i) SST anomalies are partly detrained to deeper levels in spring when the mixed layer shoals rapidly, (ii) temperature anomalies beneath the shallow mixed layer are preserved during summer, (iii) they are entrained into the surface in the succeeding fall and winter when the mixed layer is again deepened. The recurrence of SST anomalies was found in two centers of the decadal anomaly pattern (30°–45°N, 80°–50°W and 45°–60°N, 50°–20°W), but not in another center in the subtropics (10°–25°N, 40°–10°W) where the MLD reveals only a small seasonality. The magnitude of recurrent SST anomalies is affected by two factors: MLD difference between winter and summer and the persistence of SST anomalies from winter to spring as they determine the amount and the magnitude of detrained temperature anomalies into the mixed layer, respectively.
The above results indicate that the effective damping time for the winter SST anomalies is much longer than the local damping time of several months.
Abstract
The impact of tropical instability waves (TIWs) on El Niño–Southern Oscillation (ENSO) characteristics is investigated by introducing a new parameterization of TIWs into an atmosphere–ocean general circulation model (AOGCM), the Model for Interdisciplinary Research on Climate (MIROC), with a medium-resolution (~1.4°) ocean model (known as MIROCmedres). Because this resolution is not sufficient to reproduce eddies at the spatial scale of TIWs, this approach isolates TIW effects from other factors that can affect ENSO characteristics. The parameterization scheme represents the effect of baroclinic eddy heat transport by TIWs. A 100-yr integration reveals a significant role of TIWs in observed ENSO asymmetry. Asymmetric heat transport associated with TIWs that are active (inactive) during La Niña (El Niño) generates a significant asymmetric negative feedback to ENSO and explains the observed asymmetric feature of a stronger-amplitude El Niño and weaker-amplitude La Niña. Furthermore, the parameterized eddy heat flux also affects the mean subsurface heat balance via the shallowing and steepening thermocline. This change in subsurface stratification induces a stronger thermocline feedback and a longer ENSO period.
Abstract
The impact of tropical instability waves (TIWs) on El Niño–Southern Oscillation (ENSO) characteristics is investigated by introducing a new parameterization of TIWs into an atmosphere–ocean general circulation model (AOGCM), the Model for Interdisciplinary Research on Climate (MIROC), with a medium-resolution (~1.4°) ocean model (known as MIROCmedres). Because this resolution is not sufficient to reproduce eddies at the spatial scale of TIWs, this approach isolates TIW effects from other factors that can affect ENSO characteristics. The parameterization scheme represents the effect of baroclinic eddy heat transport by TIWs. A 100-yr integration reveals a significant role of TIWs in observed ENSO asymmetry. Asymmetric heat transport associated with TIWs that are active (inactive) during La Niña (El Niño) generates a significant asymmetric negative feedback to ENSO and explains the observed asymmetric feature of a stronger-amplitude El Niño and weaker-amplitude La Niña. Furthermore, the parameterized eddy heat flux also affects the mean subsurface heat balance via the shallowing and steepening thermocline. This change in subsurface stratification induces a stronger thermocline feedback and a longer ENSO period.
Abstract
This study newly developed the interactively nested climate model (INCL) using a general circulation model (GCM) interactively nested with a regional atmospheric model (RAM). One interactive experiment with finer RAM topography and another with coarser topography, as well as offline versions of each experiment, were performed to investigate the effects of subsynoptic-scale eddies and subsynoptic-scale mountains in northeast Asia on the larger-scale climate, using the GCM with T42 atmosphere and the RAM with 40-km mesh size in the INCL system. The subsynoptic-scale eddy effect restrictively increased synoptic-scale eddy activity within the RAM domain. In contrast, subsynoptic-scale mountains had the effect of robust anticyclonic circulation around the Sea of Japan and effectively forced larger-scale circulation. The effect was positively fed back to the mean field and amplified the anticyclonic circulation accompanied by suppressed storm activity in northeast Asia. The results suggest that subsynoptic-scale mountains affect not only subsynoptic-scale eddies but also the global climate.
Abstract
This study newly developed the interactively nested climate model (INCL) using a general circulation model (GCM) interactively nested with a regional atmospheric model (RAM). One interactive experiment with finer RAM topography and another with coarser topography, as well as offline versions of each experiment, were performed to investigate the effects of subsynoptic-scale eddies and subsynoptic-scale mountains in northeast Asia on the larger-scale climate, using the GCM with T42 atmosphere and the RAM with 40-km mesh size in the INCL system. The subsynoptic-scale eddy effect restrictively increased synoptic-scale eddy activity within the RAM domain. In contrast, subsynoptic-scale mountains had the effect of robust anticyclonic circulation around the Sea of Japan and effectively forced larger-scale circulation. The effect was positively fed back to the mean field and amplified the anticyclonic circulation accompanied by suppressed storm activity in northeast Asia. The results suggest that subsynoptic-scale mountains affect not only subsynoptic-scale eddies but also the global climate.
Abstract
An objective analysis of monthly ocean subsurface temperatures from 1950 to 1998 is carried out. The analysis scheme and the results with estimated analysis errors are presented.
The analysis domain is global with a horizontal grid of 1° × 1° and 14 vertical levels in the upper 500 m. Subsurface temperature observations used in the objective analysis are archived by the National Ocean Data Center of the National Oceanic and Atmospheric Administration, together with those collected through the global telecommunication system and domestic communication lines in Japan. All the observations are preprocessed by quality control and data selection procedures developed in this study. Together with these observations, three-dimensional fields of the upper-ocean temperature are optimally estimated using a variational technique. To ensure smooth and continuous vertical temperature profiles, a constraint term is introduced to the cost function that is minimized in the analysis. In addition, the analysis scheme is formulated to constrain mixed layer temperatures to become close to sea surface temperatures produced by the Met Office.
The three-dimensional structure of thermal anomalies is represented by the objective analysis. Interannual variations of temperature anomalies in the northern and tropical Pacific are presented and examined with the estimated errors. For the purpose of verification against independent observations of the objective analysis, dynamical heights estimated from the analyzed temperatures and climatological salinity are compared with tide gauge and sea surface height observations.
An investigation of analysis errors and signal-to-noise (S–N) ratio reveals that the reliability increases in the tropical Pacific since the 1970s and the S–N ratio for seasonally averaged temperatures in a 3° latitude × 6° longitude box at 100-m depth is 2.5 in the 1990s. This is not only due to the increase in data sampling but also to an increase in interannual variances of subsurface temperature. At midlatitudes of the Northern (Southern) Hemisphere, the S–N ratio is above (below) unity over the whole period of the objective analysis. The changes are very small in these 50 yr, although recent observational networks cover the global oceans better and the observations are more homogeneously distributed than those of the previous decades.
Abstract
An objective analysis of monthly ocean subsurface temperatures from 1950 to 1998 is carried out. The analysis scheme and the results with estimated analysis errors are presented.
The analysis domain is global with a horizontal grid of 1° × 1° and 14 vertical levels in the upper 500 m. Subsurface temperature observations used in the objective analysis are archived by the National Ocean Data Center of the National Oceanic and Atmospheric Administration, together with those collected through the global telecommunication system and domestic communication lines in Japan. All the observations are preprocessed by quality control and data selection procedures developed in this study. Together with these observations, three-dimensional fields of the upper-ocean temperature are optimally estimated using a variational technique. To ensure smooth and continuous vertical temperature profiles, a constraint term is introduced to the cost function that is minimized in the analysis. In addition, the analysis scheme is formulated to constrain mixed layer temperatures to become close to sea surface temperatures produced by the Met Office.
The three-dimensional structure of thermal anomalies is represented by the objective analysis. Interannual variations of temperature anomalies in the northern and tropical Pacific are presented and examined with the estimated errors. For the purpose of verification against independent observations of the objective analysis, dynamical heights estimated from the analyzed temperatures and climatological salinity are compared with tide gauge and sea surface height observations.
An investigation of analysis errors and signal-to-noise (S–N) ratio reveals that the reliability increases in the tropical Pacific since the 1970s and the S–N ratio for seasonally averaged temperatures in a 3° latitude × 6° longitude box at 100-m depth is 2.5 in the 1990s. This is not only due to the increase in data sampling but also to an increase in interannual variances of subsurface temperature. At midlatitudes of the Northern (Southern) Hemisphere, the S–N ratio is above (below) unity over the whole period of the objective analysis. The changes are very small in these 50 yr, although recent observational networks cover the global oceans better and the observations are more homogeneously distributed than those of the previous decades.
Abstract
Properties of the local predictability in the Lorenz system of three variables are investigated as a first step to develop a dynamical method for the skill prediction in the numerical weather forecasts instead of conventional statistical and empirical methods. As a measure of the local predictability, we adopt Lorenz's index which gives the amplification rate of the root-mean-square error during a prescribed time interval. In particular, we exert ourselves to understand a role of the quasi-stationary state in determining the variation of the Lorenz index.
In an intermittent chaos regime, the Lorenz index determined for a time interval of the one return in the Poincaré section has a minimum value at the onset of the laminar phase, gradually increases during the laminar phase, and abruptly attains a large value at the break of the laminar phase. If we consider the laminar phase as a quasi-stationary state generated by a local minimum point in the one-dimensional Poincaré map, this characteristic evolution of the Lorenz index is directly connected with the local dynamics of the local minimum point.
The fine phase–spatial distribution of the Lorenz index for a short time interval on the Lorenz attractor is also discussed in connection with the role of the unstable stationary point in organizing the local predictability.
Abstract
Properties of the local predictability in the Lorenz system of three variables are investigated as a first step to develop a dynamical method for the skill prediction in the numerical weather forecasts instead of conventional statistical and empirical methods. As a measure of the local predictability, we adopt Lorenz's index which gives the amplification rate of the root-mean-square error during a prescribed time interval. In particular, we exert ourselves to understand a role of the quasi-stationary state in determining the variation of the Lorenz index.
In an intermittent chaos regime, the Lorenz index determined for a time interval of the one return in the Poincaré section has a minimum value at the onset of the laminar phase, gradually increases during the laminar phase, and abruptly attains a large value at the break of the laminar phase. If we consider the laminar phase as a quasi-stationary state generated by a local minimum point in the one-dimensional Poincaré map, this characteristic evolution of the Lorenz index is directly connected with the local dynamics of the local minimum point.
The fine phase–spatial distribution of the Lorenz index for a short time interval on the Lorenz attractor is also discussed in connection with the role of the unstable stationary point in organizing the local predictability.
