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  • View in gallery

    The first empirical orthogonal function (a) and first 90 days of the corresponding principal components (b) based on the observed 200-mb U field over the Pacific region. Units are nondimensional.

  • View in gallery

    The 200-mb U December–February climatology for (a) observations and (b) model simulation. The model bias (model minus observations) is shown in (c). Contour interval in (a) and (b) is 10 m s−1. Contour interval in (c) is 5 m s−1 with the zero contour omitted. Negative contours are dashed.

  • View in gallery

    DJF 6–30 day PKE for (a) observations and (b) model simulation. The percent difference between the two [(model minus observations)/observations] is shown in (c). The contour interval in (a) and (b) is 25 m2 s−2 and values greater than 25 m2 s−2 are shaded. The contour interval in (c) is 40% with dark (light) shading indicating regions greater than 20% (less than −20%).

  • View in gallery

    Total wavenumber K based on the observed 200-mb time-mean zonal wind for (a) stationary waves, (b) waves with phase speeds of 5 m s−1, and (c) waves with phase speeds of 10 m s−1. The contour interval is 2, with wavenumbers above 5 shaded. The critical line, where the zonal wind equals the phase speed, is indicated by the thickened contour.

  • View in gallery

    Same as Fig. 4 but for the model simulation.

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    The 200-mb streamfunction difference anomalies for the observed Pacific mode at (a) lag −4 days, (b) lag +2 days, (c) lag +0 days, and (d) lag +2 days. Contours at ±3, ±9, ±15, and ±21 × 106 m2 s−1 with positive (negative) values significant at the 95% level indicated by dark (light) shading. Negative contours are dashed. Thick contours represent the 0 m s−1 and 10 m s−1 contours of the 200-mb climatological zonal wind.

  • View in gallery

    The 200-mb streamfunction maximum (a) and minimum (b) anomalies for the observed Pacific mode at lag +0 days. Contours at ±1.5, ±4.5, ±7.5, and ±10.5 × 106 m2 s−1 with positive (negative) values significant at the 95% level indicated by dark (light) shading. Negative contours are dashed. Thick contours represent the 0 m s−1 and 10 m s−1 contours of the 200-mb climatological zonal wind.

  • View in gallery

    Same as Fig. 6 except for the modeled Pacific mode.

  • View in gallery

    The wave activity flux vectors (m2 s−2) corresponding to the lag +0 difference anomalies for observed (a) and modeled (b) Pacific modes, superimposed upon the 200-mb U winter climatology for (a) observations and (b) model simulation. The contour interval is 10 m s−1.

  • View in gallery

    The precipitation difference anomalies (shaded) and 200-mb divergence anomalies (thick contours) corresponding to the lag +0 Pacific mode for (a) observations and (b) model simulation. All precipitation anomalies greater than +0.15 cm day−1 (less than −0.15 cm day−1) indicated by dark (light) shading. The 200-mb divergence contours are at ±2.0 and ±6.0 m2 s−1 with negative contours dashed.

  • View in gallery

    The streamfunction difference anomalies based on the observed Pacific mode at lag +0 days at (a) 500 mb and (b) 850 mb. Contours for (a) at ±2, ±6, and ±10 × 106 m2 s−1 and contours for (b) at ±1, ±3, and ±5 × 106 m2 s−1 with positive (negative) values significant at the 95% level indicated by dark (light) shading. Negative contours dashed. Thick contours represent the 0 m s−1 and 10 m s−1 contours of the climatological zonal wind at the corresponding levels.

  • View in gallery

    Same as Fig. 11 except for the modeled Pacific mode.

  • View in gallery

    Same as Fig. 6 except for the observed Atlantic mode.

  • View in gallery

    Same as Fig. 6 except for the modeled Atlantic mode.

  • View in gallery

    Same as Fig. 9 except for observed (a) and modeled (b) Atlantic modes.

  • View in gallery

    The 200-mb streamfunction difference anomalies for (a) the observed east Asian mode and (b) the modeled east Asian mode at lag +2 days. Contours at ±3, ±9, ±15, and ±21 × 106 m2 s−1 with positive (negative) values significant at the 95% level indicated by dark (light) shading. Negative contours are dashed. Thick contours represent the 0 m s−1 and 10 m s−1 contours of the 200-mb climatological zonal wind.

  • View in gallery

    Same as Fig. 9 except for observed (a) and modeled (b) east Asian modes.

  • View in gallery

    The latitudinal distribution of perturbation energy density (m2 s−2) for (a) the Pacific modes, (b) the Atlantic modes, and (c) the east Asian modes. The thick solid lines denoted O − 2 and O + 0 are for the observed modes at lag −2 days and lag +0 days, respectively. The dot–dash lines denoted M − 2 and M + 0 are for the modeled modes at lag −2 days and lag +0 days, respectively. The thin solid line denotes the observed 95% confidence level. Units are m2 s−2.

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The Effect of Model Bias on the Equatorward Propagation of Extratropical Waves

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  • 1 Naval Research Laboratory, Monterey, California
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Abstract

The effect of model bias on the equatorward propagation of extratropical waves in a GCM simulation is assessed within the context of simple wave-guiding principles. The modes representing these waves are identified through the use of empirical orthogonal function analysis performed on the 200-mb zonal wind filtered to retain variations between 6 and 30 days. The temporal evolution and vertical structure of these modes are examined through the use of time-lagged composite analysis. The differences between observed and simulated wave propagation is examined in relationship to the theoretical wave-guiding properties associated with the observed and simulated time-mean flow. The utility of simple wave-guiding theory for describing the observed and modeled wave propagation is assessed.

The model bias in the time-mean flow is closely associated with the differences in the propagation of the transient waves. The excessively strong wave-guiding properties associated with the simulated Pacific jet appear to inhibit the proper meridional propagation of wave energy into the tropical central and eastern Pacific. In the simulation, waves that do propagate into the tropical Pacific either dissipate or are reflected near the equator, while in the observations, wave energy propagates into the Southern Hemisphere. On the other hand, the wave guiding by the subtropical and midlatitude jets over the Atlantic is weaker in the simulation than in the observations. In this region, wave energy propagates primarily into the Tropics in the simulation, while some of the observed wave energy is reflected toward the east and northeast over the Atlantic and northern Africa. The locations of the theoretical critical lines and wave guides of the time-mean flow, although based on many simplifying assumptions, are remarkably consistent with the propagation characteristics of these waves.

Corresponding author address: Dr. Carolyn Reynolds, Naval Research Laboratory, 7 Grace Hopper Avenue, Stop 2, Monterey, CA 93943-5502.

Email: reynolds@nrlmry.navy.mil

Abstract

The effect of model bias on the equatorward propagation of extratropical waves in a GCM simulation is assessed within the context of simple wave-guiding principles. The modes representing these waves are identified through the use of empirical orthogonal function analysis performed on the 200-mb zonal wind filtered to retain variations between 6 and 30 days. The temporal evolution and vertical structure of these modes are examined through the use of time-lagged composite analysis. The differences between observed and simulated wave propagation is examined in relationship to the theoretical wave-guiding properties associated with the observed and simulated time-mean flow. The utility of simple wave-guiding theory for describing the observed and modeled wave propagation is assessed.

The model bias in the time-mean flow is closely associated with the differences in the propagation of the transient waves. The excessively strong wave-guiding properties associated with the simulated Pacific jet appear to inhibit the proper meridional propagation of wave energy into the tropical central and eastern Pacific. In the simulation, waves that do propagate into the tropical Pacific either dissipate or are reflected near the equator, while in the observations, wave energy propagates into the Southern Hemisphere. On the other hand, the wave guiding by the subtropical and midlatitude jets over the Atlantic is weaker in the simulation than in the observations. In this region, wave energy propagates primarily into the Tropics in the simulation, while some of the observed wave energy is reflected toward the east and northeast over the Atlantic and northern Africa. The locations of the theoretical critical lines and wave guides of the time-mean flow, although based on many simplifying assumptions, are remarkably consistent with the propagation characteristics of these waves.

Corresponding author address: Dr. Carolyn Reynolds, Naval Research Laboratory, 7 Grace Hopper Avenue, Stop 2, Monterey, CA 93943-5502.

Email: reynolds@nrlmry.navy.mil

1. Introduction

Many general circulation models (GCMs) exhibit significant deficiencies in the simulation of the tropical atmospheric state. This problem has significant implications not only for climate modeling, but also for weather forecasting. In the Tropics, forecast errors are dominated by model errors, while in the midlatitudes the model bias accounts for only a very small part of the total error (Palmer et al. 1990; Saha 1992; Reynolds et al. 1994). A common systematic error in GCMs is an easterly bias in the upper-tropospheric tropical wind field (White 1988; Palmer et al. 1990; Schubert et al. 1993). Most GCMs are also deficient in the simulation of tropical variability, particularly on intraseasonal timescales (Park et al. 1990; Schubert et al. 1993; Reynolds et al. 1996). A large part of the deficiency in tropical variability appears to be related to the failure of many models to reproduce the Madden–Julian oscillation (MJO; Madden and Julian 1972) with sufficient amplitude. However, it is also possible that the time-mean easterly bias exhibited by many GCMs inhibits the propagation of waves from the midlatitudes into the Tropics (Charney 1969). Of course, these processes may not be independent, as it has been suggested that extratropical forcing may serve as a triggering mechanism for the MJO (Hsu et al. 1990; Murakami 1988). There has been much work done on the influence of the background mean wind on wave propagation using both analytical and simple model studies (e.g., Hoskins and Karoly 1981; Webster and Holton 1982). In this paper we examine how well such simple wave-guiding principles describe the differences between observed and modeled wave propagation from the Northern Hemisphere midlatitudes into the Tropics.

Charney (1969) theorized that meridional propagation of Rossby waves occurs only in regions where the zonal phase speed of the wave has a larger easterly component than the background zonal wind speed. This would prohibit propagation of most waves from the midlatitudes into the easterly regime of the Tropics except for waves with the largest spatial scales, which carry little energy. However, there are two regions of the upper-tropospheric Tropics where the time-mean flow during the winter is westerly. Webster and Holton (1982) proposed that these regions would act as “ducts” for wave energy to propagate into the Tropics and from one hemisphere to the other. The effects of zonal asymmetry were studied using a nonlinear shallow-water model by Webster and Holton (1982) and linearized barotropic models by Karoly (1983) and Branstator (1983), who found increased equatorward propagation of wave energy in regions of equatorial westerlies. Hsu and Lin (1992) and Hoskins and Ambrizzi (1993) have shown that, according to the theoretical wave-guiding properties of the observed upper-tropospheric zonal flow, these westerly ducts should be regions of equatorward propagation of wave energy.

Consistent with the theory mentioned above, Arkin and Webster (1985) showed that the maximum perturbation kinetic energy in the upper-tropospheric Tropics is well correlated with the time-mean zonal wind. Since then, there has been observational support for the propagation of waves into the Tropics and Southern Hemisphere from the Northern Hemisphere midlatitudes in the central Pacific and Atlantic on the 6–30-day timescale (Hsu and Lin 1992; Kiladis and Weickmann 1992; Tomas and Webster 1994).

In this study, the ability of the atmospheric forecast model from the Navy Operational Global Atmospheric Prediction System (NOGAPS) to simulate the equatorward propagation of midlatitude waves on the 6–30-day timescale is assessed. Wave-guiding principles are applied to explain the differences between the observed and simulated wave propagation. The modes representing these waves are identified through the use of empirical orthogonal function (EOF) analysis performed on the 200-mb zonal wind. The temporal evolution and vertical structure of these modes are examined through the use of composite analysis. The wave-guiding properties of the observed and simulated time-mean flow are diagnosed using techniques based on the work of Hoskins and Karoly (1981) and Hoskins and Ambrizzi (1993). These wave-guiding properties were developed for nondivergent barotropic stationary Rossby plane waves where the WKB approximation is valid, and their applicability to conditions that do not strictly conform to these assumptions is examined. It is argued that model biases affecting the wave-guiding properties of the time-mean flow are closely related to biases in the propagation of wave energy into the Tropics. The usefulness of simple two-dimensional wave-guiding theory as a tool for linking model deficiencies in tropical variability with deficiencies in its simulation of the time-mean flow is examined.

The data and methodology used in this study are described in section 2. The time-mean, variance, and wave-guiding properties of the observed and simulated flow are presented in section 3. Section 4 contains the results based on the EOF analysis. A discussion of the results is presented in section 5.

2. Data and methodology

The technique used in this study is similar to that employed by Schubert et al. (1993) and Reynolds et al. (1996). To represent observed wind fields, twice-daily uninitialized analyses (averaged to daily means) from the European Centre for Medium-Range Weather Forecasts (ECMWF) for the eight winter seasons from 1985/86 through 1992/93 are used. To help mitigate the problem of uncertainty in these analyses, only data after November 1985 are used since the ECMWF analyses before this time were shown to have a poor representation of the tropical divergent wind field (Trenberth and Olson 1988). It should be noted however that a significant amount of uncertainty in the analyzed tropical divergent wind field after this time may still exist (Sardeshmukh and Liebmann 1993).

Microwave Sounding Unit (MSU)–derived daily averaged precipitation estimates (Spencer 1993) are used to represent observed precipitation values over the ocean. Spencer (1993) demonstrates that while there are significant discrepancies between MSU and global precipitation index monthly mean precipitation values, the pentad variability between the two indices is in good agreement.

The model data come from nine winters of a 10-yr integration of NOGAPS (Hogan and Rosmond 1991; Hogan and Brody 1993) run at T47 horizontal resolution (which corresponds to a 2.5° gridpoint resolution) beginning with initial conditions from 1 January 1979. This 10-yr simulation is part of the Atmospheric Model Intercomparison Project (AMIP) sponsored by the World Climate Research Programme and the U.S. Department of Energy. Prescribed time-varying sea surface temperatures (SSTs) were used based on the observed monthly mean fields linearly interpolated to the forecast time. For this study winter corresponds to the three-month period from December through February. The intraseasonal variability on longer timescales from this same model simulation is discussed in detail in Reynolds et al. (1996). They find that tropical variability, especially in the Pacific, is too weak in the model, and that while modes of variability that are not related to tropical forcing are well simulated, modes that appear to be tropically forced, especially the MJO, are poorly simulated.

Empirical orthogonal function analysis was used to identify the primary modes of 6–30-day variability in the 200-mb winds. EOFs were computed for two regions in the Atlantic and Pacific based on the correlation matrix of the 200-mb zonal (U) wind fields filtered to retain only variations with periods between 6 and 30 days. Since the bandpass filter excludes variations longer than 30 days, the results shown here are almost identical to those where a mean annual cycle is removed before filtering. The 6–30-day period was chosen based on previous results showing meridional propagation of extratropical waves into the Tropics on these timescales (Tomas and Webster 1994; Kiladis and Weickmann 1992). The filter used is a recursive symmetric bandpassed filter described in Kaylor (1977). The Pacific region has longitudinal boundaries at 135°E and 90°W and latitudinal boundaries at 40°S and 70°N. The Atlantic region has longitudinal boundaries of 100°W and 35°E and latitudinal boundaries at 40°S and 70°N. The regions were chosen to include the areas around and upstream from the two regions of upper-tropospheric tropical westerlies where meridional propagation is expected.

The 2.5° model gridpoint data were interpolated to an equal area grid with horizontal resolution ranging from 2.5° at the equator to 5° at 60°N. The EOFs were orthogonally rotated using the varimax method in order to decrease the sensitivity of the EOFs to sampling errors (Richman 1986; Barnston and Livezey 1987). The number of modes retained (between 7 and 10) was determined by examination of the eigenvalues (O’Lenic and Livezey 1988). None of the remaining modes excluded from the rotation represented independent eigenvectors based on the criterion of North et al. (1982). Associated with each EOF is a principle component describing the time-varying amplitudes that correspond to the spatial patterns represented by the EOFs.

Composites were constructed by averaging a particular field, such as the 200-mb streamfunction, over all the days that corresponded to a relative maximum or minimum value of the principal component for a particular EOF. As an example, Fig. 1 shows the first EOF (Fig. 1a) and the first 90 days of the principal component time series (Fig. 1b) for the observed 200-mb U field over the Pacific region, which is discussed in detail in section 4. The spatial pattern of the EOF (Fig. 1a) indicates that a westerly anomaly centered at 30°N, 135°W would be accompanied by easterly anomalies centered at 50°N, 145°W and at 5°N, 130°W. The southwest to northeast phase tilt of the anomalies are suggestive of southeastward propagation of wave energy. Time-lagged composite analysis and wave activity flux diagnostics are used to investigate this possibility.

Composite fields for this EOF were constructed based on the principal component time series shown in Fig. 1b. Only dates corresponding to time series maxima and minima within the top and bottom 25% of all principal component values were included in the composites. A time series maximum (minimum) with a larger (smaller) value within five days was not included in the composite. In this case, the maximum composite would have included days 3, 17, 35, 63, and 78, while the minimum composite would have included days 13, 29, 46, and 71. Lagged composites were similarly calculated by averaging fields corresponding to a fixed number of days before or after the maxima or minima (i.e., the maximum composite for lag −2 days would include days 1, 15, 33, 61, and 76, etc.). Difference anomalies were formed by subtracting the composites based on the minima from the composites based on the maxima. There were approximately four maxima and minima per season, or between 30 and 40 dates in each composite. The significance of the anomalies was estimated based on 100 composites of randomly chosen dates with sample sizes of 32 and 36 for the observed and modeled data, respectively. The EOFs shown in this study are the EOFs that appear to exhibit the strongest wave energy propagation from the midlatitudes into the Tropics as determined from the location of the maximum strength of the time-lagged composites and from wave activity flux diagnostics (Plumb 1985).

3. Time-mean and variance fields

Figure 2 shows the 200-mb DJF climatological zonal wind for the observations, model simulation, and model bias, respectively. The east Asian jet in the model extends further north and west into the Pacific than the observed jet. In the Tropics, the longitudinal extent of westerlies in the central and eastern Pacific is similar in the observations and in the model; however, the magnitude of the westerlies is considerably larger in the observations, particularly between 0° and 10°S. The bias plot (Fig. 1c) clearly shows the northward displacement of the midlatitude jet over the Pacific, and to a lesser extent, the Atlantic, as well as the easterly bias throughout much of the Tropics. Note in particular that between 15°N and 30°N, the model has an easterly bias for most longitudes, with the exception of the western Atlantic region.

Figures 3a and 3b show the average 6–30-day perturbation kinetic energy (PKE) for the observation and the model, while Fig. 3c shows the percent difference between these two fields. PKE is defined as (u2 + υ2)/2, where u′ and υ′ are the 6–30-day filtered zonal and meridional 200-mb wind components. In Fig. 3c, areas with no stippling are where the modeled PKE is within 20% of the observed PKE, areas with light stippling are where the model has at most 20% less than the observed PKE, and areas with dark stippling are where the model has at least 20% more than the observed PKE. In the Tropics, the observed PKE maxima (values greater than or equal to 25 m2 s−2 in the central and eastern Pacific and Atlantic in Fig. 3a) coincide with the two regions of upper-tropospheric tropical westerlies (Fig. 2a), which is in agreement with Arkin and Webster (1985). Note also that the largest values of PKE in the Northern Hemisphere subtropics occur south of the exit regions of the Pacific and Atlantic midlatitude jets.

The model simulates the observed patterns of PKE to a large extent (Fig. 3b). However, the simulated PKE in the tropical and subtropical central and eastern Pacific is less than observed. The simulated PKE is less than 25 m2 s−2 throughout the tropical Pacific, while the observed PKE is between 25 and 50 m2 s−2. In the tropical and subtropical North Atlantic, the simulated PKE maximum is comparable to or even stronger than the observed PKE maximum. With the exception of the Atlantic region and the area around the maritime continent and the southern tropical Indian Ocean, the model subtropics and Tropics are very deficient in PKE. The relationship between the model bias and the simulated PKE is consistent with the theory that the modeled easterly bias in the eastern Pacific would inhibit meridional propagation of waves into the Tropics from the Northern Hemisphere midlatitudes, while the smaller modeled biases in the western Atlantic would allow meridional propagation of extratropical waves into the Tropics similar to what is observed (Charney 1969).

An examination of the wave-guiding properties of these time-mean flows is useful for examining the impact of model bias on wave propagation. Following Hoskins and Karoly (1981), the total wavenumber K is calculated based on the dispersion relationship for barotropic Rossby plane waves in westerly flow
i1520-0493-125-12-3249-e1
where
i1520-0493-125-12-3249-e2
and K = (k2 + l2)1/2. If c = ω/k is the eastward phase speed of the wave, then
i1520-0493-125-12-3249-e3
Here, K is calculated based on the WKB approximation applied to a Mercator projection as described in Hoskins and Karoly (1981), where the mercator coordinate equivalent of β∗ is given by
i1520-0493-125-12-3249-e4
where ϕ is latitude and a and Ω the radius and rotation rate of the earth, respectively. As explained in Hoskins and Ambrizzi (1993; their Fig. 2), stationary waves will be refracted away from regions of lower K (turning latitudes) and toward regions of higher K. Waves will be absorbed at critical latitudes, where U = c.

Figure 4 shows K based on the observed 200-mb zonal wind for (a) stationary waves (c = ω = 0) and for waves with eastward phase speeds of (b) 5 and (c) 10 m s−1. Areas with K > 5 are shaded in Fig. 4. Since waves will be refracted toward regions of higher K, meridional propagation of waves with zonal wavenumber 5 or greater should be confined to these shaded regions. Critical latitudes, where U = c, are denoted by heavy contours in Fig. 4 and indicate regions of wave absorption. Inside these heavy contours, where U < c, K is undefined. As pointed out by Branstator (1983), Hoskins and Ambrizzi (1993), Hsu and Lin (1992), and others, the midlatitude jets act as wave guides since their flanks are regions where the gradient of absolute vorticity, and therefore K, is small. For waves with eastward phase speeds (Fig. 4b,c), the critical latitudes shift poleward and the westerly ducts through which cross-hemispheric propagation is possible shrink considerably in the Pacific and disappear altogether in the Atlantic.

Figure 5 shows K based on the 200-mb zonal wind from the model simulation. A comparison of Figs. 4 and 5 indicates that the wave guide from the southeastern United States to Europe is stronger in the observations than in the simulation, while the wave guide over the Pacific is stronger in the simulation than in the observations. In the simulation there appears to be a stronger barrier to meridional propagation in the subtropical central Pacific in the vicinity of Hawaii than in the observations. (Even though, in fact, the westerly duct in the Pacific is approximately the same width in the simulation and the observations.) Also, in the simulation, stationary waves that do propagate into the Tropics would be reflected just south of the equator in the region of low K (Fig. 5a), while waves with eastward phase speeds would be absorbed at a critical line in this region (Fig. 5b,c). In the observations, waves with an eastward phase speed of 5 m s−1 and zonal wavenumber 5 or 6 should be able to propagate into the Southern Hemisphere midlatitudes (Fig. 4b), and even stationary waves would not be reflected until the waves were at approximately 20°S (Fig. 4a).

4. EOF results

a. The Pacific

Results are presented based on the EOFs that appear to represent the strongest propagation of wavelike disturbances from the northern midlatitudes into the Tropics. Wave energy propagation is inferred through the change in location of the maximum strength of the anomaly in the time-lagged composite sequence. Figure 6 shows the 200-mb streamfunction difference anomalies from (a) lag −4 days to (d) lag +2 days for the observed Pacific mode. This mode represents approximately 11% of the 6–30-day variance and 5% of the total variance over the domain used to calculate the EOFs. The period spectral density analysis of the principal components of this mode shows an energy peak at a period of 25 days. It should be noted that the period spectral density plot will be influenced not only by the phase propagation speed of each event but also the average time between each event. The time interval between peaks in the time series shown in Fig. 1b varies from 14 to 27 days, and the spectral peak at 25 days probably indicates that this is the average interval between events. Changes in the phase propagation speed for different events will result in the strength of the time-lagged difference anomalies becoming weaker as the time lag is increased. The climatological positions of the 0 m s−1 and 10 m s−1 200-mb zonal wind contours are also included in this figure and are denoted by the thickened contours. Recall that these contours would represent critical lines for stationary waves and waves with eastward phase speeds of 10 m s−1, respectively.

The positive anomaly with the largest strength at lag +0 days is located at 20°N, 135°W. At lag −4 days this anomaly is centered on 30°N, 160°W and at lag +2 days is centered on 15°N, 130°W, indicating a southeastward phase propagation with time. Note also that the relative strength of the anomalies to the west of this feature weakens as the lag time increases, while the relative strength of the anomalies to the east and south of this feature increases with time, indicating a southeastward energy propagation. This is consistent with the southwest to northeast orientation of the difference anomalies. The eastward phase propagation, based on the time-lagged difference anomalies, is greater than 10 m s−1 poleward of 30°N and approximately 6 m s−1 at 15°N. The anomalies in the Southern Hemisphere Tropics appear to be approximately stationary. Even though the midlatitude anomalies centered over the Pacific extend northeastward along their major axes to North America and the eastern Atlantic, wave energy, as inferred from the strength of the difference anomalies, fails to propagate southeastward over the region of easterly winds over South America. South of the equator, the anomalies lose their southwest to northeast phase tilt and become oriented east to west, which is consistent with the low values of K indicating a turning latitude at about 20°S in Fig. 4a. The similarity between this observed mode and those found by Tomas and Webster (1994, their Fig. 8) and Kiladis and Weickmann (1992, their Fig. 2) using different statistical techniques gives us confidence that the technique employed here is capable of identifying physically significant phenomena. The maximum and minimum composite anomalies for the observed Pacific mode are shown in Fig. 7. The fairly high degree of antisymmetry exhibited for this mode is indicative of all the difference anomalies shown in this study.

The modeled Pacific mode (Fig. 8) represents approximately 11% of the 6–30-day variance and 6% of the total variance in this region. Since the total variance in the model over this region is only about 75% of the total variance in the observations, in absolute terms this mode represents about 25% less variance than the observed Pacific mode. The modeled Pacific mode shares some characteristics with the observed Pacific mode. Both modes exhibit southeastward phase and energy propagation, as inferred from the strength of the time-lagged difference anomalies, and the eastward phase propagation for the simulated mode is also approximately 10 m s−1 in the midlatitudes and slows to approximately 5 m s−1 in the subtropics. However, there are also significant differences between these two modes. Period spectral density analysis based on the principal components of this mode shows a broad spectral peak between 8 and 30 days. This broad peak may indicate significant variations in the time between events. The strong anomalies over Canada and the United States at lag −2 days and after suggest a secondary direction of westward energy propagation at higher latitudes (Figs. 8b–d). The modeled difference anomalies are also much weaker than the observed difference anomalies south and east of Hawaii. Both of these differences are consistent with stronger wave guiding by the Pacific jet in the simulation (Fig. 5) than in the observations (Fig. 4). The modeled mode has very little energy near the equator, inferred from the weak difference anomalies here, with some weak evidence of wave energy reflection toward the east at low latitudes west of Mexico (Figs. 8c). These characteristics are also consistent with the simulated wave guides in Fig. 5, which indicate that wave energy would either be reflected or absorbed at this latitude, depending on the eastward phase speed of the wave.

In an effort to identify more objectively directions of wave energy propagation, the stationary wave activity flux vectors for the observed and modeled Pacific modes are shown for the lag +0 time in Fig. 9. Although this diagnostic was developed for stationary waves, the slow phase propagation relative to the energy propagation of these modes allows for useful information to be gained from this tool. The horizontal components of the stationary wave activity flux F were computed following Plumb (1985); that is,
i1520-0493-125-12-3249-eq1
where u′, υ′, and Φ′ are the zonally asymmetric parts of the difference anomaly 200-mb geostrophic wind components and geopotential fields, respectively; p is the pressure ratio, 200 mb/1000 mb; Ω is the earth’s rotation rate; a is the earth’s radius; ϕ is latitude; and λ is longitude. The flux vectors indicate the horizontal direction and strength of stationary wave energy propagation. The divergence and convergence of these vectors indicate wave energy source and sink regions, respectively. The wave activity flux vectors are not computed for the deep Tropics (there is a singularity in the formula for these vectors at the equator).

The observed wave activity flux vectors (Fig. 9a) indicate a source region (divergence) of wave energy in the vicinity of the north flank of the east Asian jet and, consistent with the time-lagged difference anomalies, a southeastward propagation from there. The location of the source region may indicate that barotropic instability is acting as a source of wave energy. The strongest equatorward energy propagation occurs in the exit region of the Pacific jet (see Fig. 2). This is also the region where the zonal wind shear on the flank of the jet weakens and where southward energy propagation is expected according to Fig 4. The strongest wave energy propagation in the subtropics occurs northwest of the strongest tropical westerlies. The modeled wave activity flux vectors (Fig. 9b) also indicate a source region of wave energy on the north flank of the jet and southeastward propagation from there. However, the southeastward propagation is significantly weaker south and east of Hawaii than in the observations. The convergence of the flux vectors in the general vicinity of Hawaii may indicate a wave energy sink in this region, which would be consistent with wave energy absorption here. This region is slightly farther south than the theoretical region of wave-energy reflection and absorption indicated by Fig. 5. There is also a secondary direction of westward wave energy propagation in the midlatitudes that extends across the North Pacific to North America, consistent with the stronger waveguide in that region (see Fig. 5).

The modeled and observed upper-level divergence and precipitation difference anomalies contemporaneous with Figs. 6c and 8c are shown in Fig. 10 (note, only ocean precipitation estimates are available from this MSU dataset). All precipitation anomalies greater than 0.15 cm day−1 are shaded, unlike the streamfunction anomalies, which are only shaded in regions where the anomalies are significant at the 95% level. More than half of the precipitation anomalies over the midlatitudes and the central and eastern tropical Pacific are not significant at this level, and none of the anomalies over the western Pacific or SPCZ are significant. The relationships found are very similar in the modeled and observed modes and are consistent with the results found in Kiladis and Weickmann (1992) for their composites and case studies. Midlatitude upper-level divergence and positive precipitation anomalies are associated with regions of southwesterly flow, and upper-level convergence and negative precipitation anomalies are associated with regions of northeasterly flow. Away from regions of high topography, centers of lower-level convergence (divergence, not shown) are slightly southeast of centers of upper-level divergence (convergence) and in quadrature with the low-level circulation anomalies. The northwest phase tilt with height and the phase quadrature between the divergence and circulation anomalies is similar to that expected for quasigeostrophic midlatitude systems.

The existence of significant streamfunction anomalies over the tropical easterlies in the observed Pacific mode for lag +0 days (Fig. 6c) suggests that the tropical anomalies may be due to some tropical forcing mechanism. While there are precipitation anomalies over the warm pool and the SPCZ (Fig. 10a), these anomalies are of small spatial scale, not statistically significant, and are presumably due to sampling error. Neither are these anomalies accompanied by a coherent or strong signal in the upper-level tropical divergence. The largest anomalies in the upper-level divergence occur at or north of 20°N. This suggests that the streamfunction anomalies in the tropical central and eastern Pacific are not forced by remote convective heating in the Tropics. The fact that the minimum composite of the streamfunction anomaly (Fig. 7a) shows significant tropical anomalies in the upper-level westerlies, but not in the upper-level easterlies, also suggests that these anomalies are not the result of forcing originating in other regions of the Tropics. Time-lagged difference anomalies of the precipitation (not shown) suggest that the tropical anomalies in the central Pacific occur concurrently with the streamfunction anomalies. Although it appears from this work that the tropical streamfunction anomalies are not being initiated by tropical convection, it is certainly possible that tropical convection associated with these anomalies may interact with, and perhaps reinforce, these circulation anomalies.

Figures 11 and 12 show the 500-mb and 850-mb streamfunction difference anomalies based on the observed and modeled Pacific modes superimposed upon the 0 m s−1 and 10 m s−1 zonal wind contours at those levels. These difference anomalies are contemporaneous with the 200-mb streamfunction difference anomalies shown in Figs. 6c and 8c (note that the contour intervals in the figures are different, as the strength of the anomalies are smaller at lower levels). In the midlatitudes, the observed anomalies (Fig. 11) are very similar at all three levels and exhibit a slight northwest phase tilt with height (between 5° and 10° longitude). The mid- and lower-level anomalies become less coherent and are of weaker strength at lower latitudes, consistent with the results of Tomas and Webster (1994). However, the anomalies at 850 mb do extend significantly into the easterly trade wind regime in the subtropics. These plots, and time-lagged difference anomalies (not shown) indicate that, although the upper-level anomalies appear to dissipate at or near critical latitudes, the lower-level anomalies exist in regions where their phase speed is greater than the local zonal wind. However, they do not propagate as far south as the upper-level anomalies.

The anomalies for the modeled mode (Fig. 12) also indicate a northwestward phase tilt with height in the midlatitudes (between 10° and 20° longitude). The modeled 850-mb anomalies are stronger than the observed 850-mb anomalies. The difference pattern also exhibits significant strength in the easterly trade-wind regime, but the cyclonic anomaly centered at 150°W just north of the equator at 200 mb is not apparent at the 500-mb or 850-mb levels. Thus, both observed and modeled modes exhibit a baroclinic structure in the midlatitudes, whereas in the Tropics, the anomalies at the lower levels become considerably less coherent and weaker. The close correspondence between the waveguides and the propagation characteristics of these waves at 200 mb is not apparent in the middle and lower troposphere. Thus, the propagation paths of these waves appear to be determined by the upper-tropospheric basic state, and the inconsistencies between the lower-tropospheric anomalies and the theoretical wave-guiding properties of the flow at those levels illustrates the inadequacies of applying simple two-dimensional theory to three-dimensional waves.

b. The Atlantic

Figures 13 and 14 show the 200-mb streamfunction difference anomalies associated with observed and modeled modes that propagate into the Atlantic at lags −4 days to +2 days. As in Figs. 6 and 8, the 200-mb DJF climatological positions of the 0 m s−1 and 10 m s−1 zonal wind contours have been superimposed. These modes each represent about 10% of the 6–30-day 200-mb zonal wind field variance and about 5% of the full zonal wind field variance in the Atlantic region. The modeled mode represents about 12% less variance than the observed mode in an absolute sense. Period spectral density analysis based on the principal components of these modes indicates a spectral peak between 15 and 25 days for the observed mode and a spectral peak at 25 days for the modeled mode. As in the Pacific region, both observed and modeled modes exhibit a southeastward energy and phase propagation, as inferred from the relative strength and positions of the time-lagged difference anomalies, in this case into the equatorial Atlantic region from over North America and the North Pacific. The eastward phase propagation is about 7.5 m s−1 at 30°N slowing to 6 m s−1 at 10°N for both modes. At lag −4 days (Fig. 13a), the observed mode shows some indication of a poleward reflection of wave energy, inferred from the northwest to southeast phase orientation, in the mid-Atlantic at approximately 30°N. This mode also shows wave energy propagation, inferred from the strength of the time-lagged difference anomalies, into northern Africa at lag +0 and +2 days (Figs. 13c and 13d). These two regions of apparent wave reflection coincide with regions of low K in Fig. 4. It should be noted that the northwest to southeast phase tilt at lag −4 days could also be suggestive of poleward energy propagation away from a tropical heating anomaly centered over South America. Unfortunately, the MSU precipitation estimates are only for ocean areas; however, the upper-level divergence at this time (not shown) does not show a strong anomaly over South America.

The modeled Atlantic mode (Fig. 14) is very similar to the observed mode over North America but shows no evidence of wave reflection either over the Atlantic or North Africa. These differences are consistent with the differences in the theoretical wave guiding by the mean flow (Fig. 5), which indicates much weaker wave guiding by the Atlantic and subtropical African jet in the simulation than in the observations. Neither mode appears to exhibit significant cross-hemispheric energy propagation, (the observed positive anomaly over southern Africa in Figs. 13c,d does not appear to be related to the wave pattern over the North Atlantic). This is consistent with Fig. 5b, which indicates wave absorption in the deep Tropics for waves with eastward phase speeds of 5 m s−1.

Figure 15 shows the wave activity flux vectors for the observed and modeled Atlantic modes. Both the observed and modeled modes indicate a wave energy source region (divergence) over the northeast Pacific and southeastward wave energy propagation toward the tropical Atlantic. The two plots are far more similar than the corresponding plots for the Pacific modes (Fig. 9); however, there are some minor differences. For instance, the observed mode (Fig. 15a) indicates a weak secondary westward propagation of wave energy across the North Atlantic, consistent with a stronger midlatitude waveguide in the observations than in the model (Figs. 4 and 5).

The 500-mb and 850-mb streamfunction difference anomalies associated with these modes (not shown) indicate that the vertical structure of the Atlantic modes has many characteristics in common with the vertical structure of the Pacific modes. In the midlatitudes, the anomalies indicate a northwestward phase tilt with height. The mid- and low-level anomalies do not propagate as far equatorward as the upper-level anomalies. The tropical anomalies over the central Atlantic and Africa do not occur at the 500-mb level, whereas at the 850-mb level, there are no strong anomalies over the Atlantic south of 20°N in either the observations or the simulation. The 850-mb anomalies do extend into the easterly trades in the Atlantic but are weaker than the anomalies in the Pacific at similar latitudes. The Atlantic modes also exhibit a similar relationship for upper-level divergence and precipitation as the Pacific modes.

c. East Asia

EOFs were calculated based on the 200-mb zonal wind for several domains. The only locations where there appeared to be propagation from the midlatitudes into the Tropics were the Atlantic and central and eastern Pacific, discussed above. In other regions, modes that originated in the midlatitudes did not propagate into the Tropics. For comparison, examples of eastward-propagating modes in the midlatitudes over Asia are presented. These modes are based on EOFs calculated using the observed and modeled 200-mb U field over the domain of 60°E–165°W and 40°S–70°N. Figure 16 shows the 200-mb streamfunction difference anomalies associated with these modes for lag +2 days for both the observations and the model (propagation into the Tropics would be most apparent at this lag time). Even though the anomalies have a strong southwest to northeast phase tilt indicative of southeastward energy propagation, the significant anomalies are confined to the midlatitude and subtropical westerlies and do not occur in the easterly regime of the deep Tropics. The observed anomalies (Fig. 16a) are consistent with a reflection of wave energy back toward the north at a turning latitude at about 20°N, consistent with the low values of K on the south flank of the jet in this region (Fig. 4). As with the observed mode, the modeled mode (Fig. 16b) shows no significant propagation of the anomalies into the tropical easterlies, although the evidence for wave reflection is weaker. The wave activity flux vectors (Fig. 17) do not indicate energy propagation south of the southern flank of the east Asian jet in either case, and the shift in direction of the vectors from southeastward to eastward is also consistent with wave energy reflection, particularly for the observed mode.

To facilitate a comparison of the amount of wave energy that reaches the Tropics for the different observed and modeled modes, the perturbation energy density E′ = (u2 + υ2)/2 is calculated, where u′ and υ′ are the 200-mb U and V difference anomalies associated with the observed and modeled modes discussed above. Figure 18 shows E′ at different lag times for the observed (heavy solid) and modeled (broken) modes over the Pacific (averaged from 120°E to 60°W at each latitude), Atlantic (averaged from 150°W to 30°E), and east Asian (averaged from 60°E to 120°W) regions. These are the same areas shown in the steamfunction difference anomaly figures. The thin solid line indicates the 95% confidence level for the observed anomalies (the 95% confidence level for the simulated anomalies is qualitatively similar but of smaller value in the tropics). For the Pacific region (Fig. 18a) the observed and modeled modes share certain characteristics. Both modes show an increase in energy in the Northern Hemisphere subtropics from lag −2 days to lag +0 days. Both modes also show a sharp latitudinal gradient in energy between 20°N and 10°N at lag +0 days, which indicates that wave energy is either being absorbed or reflected at this latitude (the energy levels at lag +2 days, not shown, are smaller than those for lag +0 days at all latitudes). However, only the observed mode has a significant amount of energy in both the northern and southern subtropics and Tropics.

The Atlantic modes (Fig. 18b) also indicate a southward extension of wave energy from lag −2 days to lag +0 days and an abrupt decrease in wave energy between 20°N and 10°N for both the observed and modeled modes at lag +0 days. There is a significant amount of perturbation energy in the deep Tropics for the observed Atlantic mode, although it is considerably less than for the observed Pacific mode. The modeled Pacific and Atlantic modes are quite similar at lag +0 days, and neither indicates a significant amount of energy south of 5°N.

The latitudinal distributions of perturbation energy for the extratropical modes over east Asia (Fig. 18c) clearly show a more northerly cutoff of wave energy than the Atlantic and Pacific modes. There is no significant wave energy south of 25°N, which indicates that there is essentially no propagation of wave energy into the region of strong tropical easterlies over the maritime continent and the west Pacific from east Asia for these modes.

The latitudinal distributions of energy for these modes share some similarities with the latitudinal distributions of perturbation energy density calculated by Waugh et al. (1994) who use contour surgery to examine the nonlinear response of barotropic, nondivergent flow to northern midlatitude topographic forcing. Waugh et al. (1994) find a sharp latitudinal cutoff in energy south of 10°N for experiments based on an easterly tropical regime for both weak (linear) and strong (nonlinear) forcing. This is very similar to results presented here for the three modeled modes and the observed east Asian mode (except for shifts in latitude). For experiments with tropical westerlies and weak forcing, Waugh et al. (1994) show uninhibited wave propagation across the equator and approximately equal amounts of energy in the Northern and Southern Hemispheres. However, when the magnitude of the forcing is increased, Waugh et al. (1994) find that a “surf zone” develops near the equator in which the Rossby waves break and deform into small-scale eddies. The latitudinal energy distribution for this case of strong forcing and tropical westerlies exhibits both a sharp latitudinal gradient in wave energy north of the equator, similar to the easterly experiments, as well as some wave energy in the deep Tropics and Southern Hemisphere (though much less than for the weak forcing westerly case). Similar latitudinal energy distributions for the observed Pacific mode, and to a lesser extent the observed Atlantic mode, shown here may indicate that similar “surf zones” exist in the observations, allowing only a small portion of wave energy to propagate through this region, or perhaps allowing energy to propagate only intermittently. Unfortunately, the composite technique used here tends to filter out the random small-scale anomalies associated with wave breaking and therefore cannot provide more direct information about surf zones.

5. Discussion

In this study, the ability of a GCM to simulate observed wave propagation from the Northern Hemisphere midlatitudes into the Tropics is examined. Overall, NOGAPS simulates many aspects of the observed waves quite well. The propagation speed and vertical structure of the simulated modes are very similar to those of the observed modes. The model also simulates well the propagation of wave energy into the tropical Atlantic. However, the model does not adequately simulate the propagation of wave energy into the tropical eastern Pacific, a region where the model has a significant tropical and subtropical easterly bias in the upper-tropospheric wind field.

The above results indicate that, to a large degree, the propagation of upper-level circulation anomalies in the Pacific and Atlantic in both the observations and the simulation is consistent with theoretical wave-guiding principles developed for barotropic plane waves under the WKB approximation (Hoskins and Karoly 1981). Differences in the critical lines and wave-guiding properties of the time-mean flow between the observations and the simulation are very consistent with differences in the propagation characteristics of the upper-tropospheric modes identified here, as well as differences in the 6–30-day variance in the subtropical and tropical central and eastern Pacific and Atlantic. Specifically, the stronger wave-guiding characteristics of the midlatitude jet and weaker tropical westerly duct in the model simulation over the Pacific result in weaker variance in this area. Similarly, weaker wave guiding by the Atlantic and subtropical African jets in the simulation leads to stronger variability in the tropical Atlantic.

The theoretical wave-guiding properties of the background flow discussed in Hoskins and Ambrizzi (1993) were developed for nondivergent barotropic stationary Rossby plane waves in an environment where the zonal variations in the background flow change slowly enough so that the WKB approximation is valid. Many of these assumptions are not strictly applicable to the waves discussed in this paper. These modes are not barotropic, exhibiting a northwest tilt with height, and are not nondivergent, exhibiting the relationship between the divergence and circulation anomalies similar to that associated with midlatitude quasigeostrophic systems. In many regions, particularly in regions close to the westerly ducts, the scale separation between the zonal variations in the background flow and the transients is quite small, so that the WKB approximation does not hold. Although these modes are approximately stationary in the deep Tropics and Southern Hemisphere, they exhibit eastward phase velocities of up to 11 m s−1 in the Northern Hemisphere midlatitudes. Also, the wave-guiding theory presented here assumes that the meridional background flow is zero, while previous studies point out the possibility that even small meridional flows can have a strong impact on the existence and location of critical lines and meridional wave propagation (e.g., Schneider and Warterson 1984; Farrell and Waterson 1985; Watterson and Schneider 1987) and a strong impact on the location of the Rossby wave surf zone (Held and Phillips 1990). It is interesting to note that the model bias in the 200-mb velocity has a northerly component over the southeastern United States and Caribbean and a southerly component along 10°N in the central and eastern Pacific. These meridional biases may help to promote meridional energy propagation into the Atlantic while inhibiting it in the eastern Pacific. (It should be noted that Arkin and Webster 1985 did not find a strong relationship between perturbation kinetic energy and the meridional wind.)

Despite its inherent simplifying assumptions, the wave-guiding theory presented in Hoskins and Ambrizzi (1993) is very consistent with the propagation characteristics of the modes identified here in the upper troposphere, even in the Tropics. This may be surprising given the highly nonlinear and divergent nature of many phenomena in the deep Tropics. However, the identification of the upper-tropospheric westerlies as regions of enhanced tropical, and even interhemispheric, propagation has been found not only in studies of nondivergent systems (Karoly 1983; Branstator 1983) but also in theoretical studies of divergent systems (Webster and Holton 1982) as well as in the several observational studies mentioned in the introduction. Branstator (1983) points out that the similarities of his results and those of Webster and Holton for cross-hemispheric propagation through westerlies indicate that nonlinearities and divergence are not necessary for describing this behavior. Although the tropical atmosphere in general is highly divergent, the anomalies shown here actually exhibit the largest divergence in the extratropics. Waugh et al. (1994) indicate that nonlinearities can result in a Rossby wave surf zone near the equator that can significantly decrease cross-hemispheric energy propagation. This may explain the relative weakness of the anomalies at the equator compared to those in the subtropics, even in the absence of linearly diagnosed wave absorption or reflection regions. Overall, however, the differences in the wave-guiding properties of the mean flow due to the bias in the modeled time-mean state are very consistent with the differences between the observed and simulated wave propagation and variance plots.

The above results demonstrate the applicability of the simplified wave-guiding principles developed in Hoskins and Karoly (1981) and Hoskins and Ambrizzi (1993) in describing the propagation of observed and modeled waves on the 6–30-day timescale. These diagnostic wave guides also provide a useful tool for understanding the deficiencies in model variability in relationship to the model time-mean bias. These results also point out the necessity of properly simulating subtle aspects of the time-mean flow such as the meridional gradient of absolute vorticity in order to simulate adequately cross-hemispheric propagation and tropical variability in GCMs.

Acknowledgments

The 10-yr model simulation studied here was part of the AMIP project sponsored by the World Climate Research Programme and the Department of Energy and is being conducted at the Naval Research Laboratory by Dr. Tim Hogan and Dr. Tom Rosmond. The ECMWF analyses were obtained through the National Center for Atmospheric Research. The authors would like to thank Dr. Tom Murphree for valuable contributions during a preceding study and Dr. Patrick Harr for valuable discussions. Support of the sponsor, Office of Naval Research, and the program manager, Naval Research Laboratory, program element 0601153N, is gratefully acknowledged. Computing support was provided by the Department of Defense High-Performance Computing program.

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Fig. 1.
Fig. 1.

The first empirical orthogonal function (a) and first 90 days of the corresponding principal components (b) based on the observed 200-mb U field over the Pacific region. Units are nondimensional.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 2.
Fig. 2.

The 200-mb U December–February climatology for (a) observations and (b) model simulation. The model bias (model minus observations) is shown in (c). Contour interval in (a) and (b) is 10 m s−1. Contour interval in (c) is 5 m s−1 with the zero contour omitted. Negative contours are dashed.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 3.
Fig. 3.

DJF 6–30 day PKE for (a) observations and (b) model simulation. The percent difference between the two [(model minus observations)/observations] is shown in (c). The contour interval in (a) and (b) is 25 m2 s−2 and values greater than 25 m2 s−2 are shaded. The contour interval in (c) is 40% with dark (light) shading indicating regions greater than 20% (less than −20%).

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 4.
Fig. 4.

Total wavenumber K based on the observed 200-mb time-mean zonal wind for (a) stationary waves, (b) waves with phase speeds of 5 m s−1, and (c) waves with phase speeds of 10 m s−1. The contour interval is 2, with wavenumbers above 5 shaded. The critical line, where the zonal wind equals the phase speed, is indicated by the thickened contour.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 5.
Fig. 5.

Same as Fig. 4 but for the model simulation.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 6.
Fig. 6.

The 200-mb streamfunction difference anomalies for the observed Pacific mode at (a) lag −4 days, (b) lag +2 days, (c) lag +0 days, and (d) lag +2 days. Contours at ±3, ±9, ±15, and ±21 × 106 m2 s−1 with positive (negative) values significant at the 95% level indicated by dark (light) shading. Negative contours are dashed. Thick contours represent the 0 m s−1 and 10 m s−1 contours of the 200-mb climatological zonal wind.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 7.
Fig. 7.

The 200-mb streamfunction maximum (a) and minimum (b) anomalies for the observed Pacific mode at lag +0 days. Contours at ±1.5, ±4.5, ±7.5, and ±10.5 × 106 m2 s−1 with positive (negative) values significant at the 95% level indicated by dark (light) shading. Negative contours are dashed. Thick contours represent the 0 m s−1 and 10 m s−1 contours of the 200-mb climatological zonal wind.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 8.
Fig. 8.

Same as Fig. 6 except for the modeled Pacific mode.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 9.
Fig. 9.

The wave activity flux vectors (m2 s−2) corresponding to the lag +0 difference anomalies for observed (a) and modeled (b) Pacific modes, superimposed upon the 200-mb U winter climatology for (a) observations and (b) model simulation. The contour interval is 10 m s−1.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 10.
Fig. 10.

The precipitation difference anomalies (shaded) and 200-mb divergence anomalies (thick contours) corresponding to the lag +0 Pacific mode for (a) observations and (b) model simulation. All precipitation anomalies greater than +0.15 cm day−1 (less than −0.15 cm day−1) indicated by dark (light) shading. The 200-mb divergence contours are at ±2.0 and ±6.0 m2 s−1 with negative contours dashed.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 11.
Fig. 11.

The streamfunction difference anomalies based on the observed Pacific mode at lag +0 days at (a) 500 mb and (b) 850 mb. Contours for (a) at ±2, ±6, and ±10 × 106 m2 s−1 and contours for (b) at ±1, ±3, and ±5 × 106 m2 s−1 with positive (negative) values significant at the 95% level indicated by dark (light) shading. Negative contours dashed. Thick contours represent the 0 m s−1 and 10 m s−1 contours of the climatological zonal wind at the corresponding levels.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 12.
Fig. 12.

Same as Fig. 11 except for the modeled Pacific mode.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 13.
Fig. 13.

Same as Fig. 6 except for the observed Atlantic mode.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 14.
Fig. 14.

Same as Fig. 6 except for the modeled Atlantic mode.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 15.
Fig. 15.

Same as Fig. 9 except for observed (a) and modeled (b) Atlantic modes.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 16.
Fig. 16.

The 200-mb streamfunction difference anomalies for (a) the observed east Asian mode and (b) the modeled east Asian mode at lag +2 days. Contours at ±3, ±9, ±15, and ±21 × 106 m2 s−1 with positive (negative) values significant at the 95% level indicated by dark (light) shading. Negative contours are dashed. Thick contours represent the 0 m s−1 and 10 m s−1 contours of the 200-mb climatological zonal wind.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 17.
Fig. 17.

Same as Fig. 9 except for observed (a) and modeled (b) east Asian modes.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

Fig. 18.
Fig. 18.

The latitudinal distribution of perturbation energy density (m2 s−2) for (a) the Pacific modes, (b) the Atlantic modes, and (c) the east Asian modes. The thick solid lines denoted O − 2 and O + 0 are for the observed modes at lag −2 days and lag +0 days, respectively. The dot–dash lines denoted M − 2 and M + 0 are for the modeled modes at lag −2 days and lag +0 days, respectively. The thin solid line denotes the observed 95% confidence level. Units are m2 s−2.

Citation: Monthly Weather Review 125, 12; 10.1175/1520-0493(1997)125<3249:TEOMBO>2.0.CO;2

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