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  • View in gallery

    (a) −yΘ, (b) σ(θ), (c) σ(v), and (d) υθ on the 850-mb surface within the Pacific storm track region.

  • View in gallery

    PDFs of (a) temperature fluctuations from 30-day running mean, (b) meridional velocity, and (c) heat flux at the points 40°N; 140°E, 180°, and 140°W. Note the log scale for the abscissa for (c).

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    Lagrangian meridional velocity autocorrelation for the points 40°N; 140°E, 180°, and 140°W as a function of lag time |tt0|.

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    Standard deviation of meridional particle displacements for the points 40°N; 140°E, 180°, and 140°W as a function of lag time.

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    Effective diffusivity DL (product of meridional position meridional velocity υ(t0)y(tt0) for the three reference points as a function of the lag time.

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    Observed mixing length calculated from the maximum value of the effective diffusivity DL.

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    Actual vs stochastic model meridional particle dispersal for the point 40°N, 180° as a function of lag time.

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    Variation of Lagrangian integral time T with longitude as obtained from the best fit of the Lagrangian particle dispersions calculated from the NMC analyzed wind fields to those predicted by the Langevin equation.

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    Variation of mixing length σ(υ)T with longitude along the Pacific storm track as obtained from the best fit of the Lagrangian integral time T.

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    Effect of varying τ/T on the temperature fluctuation / heat flux ratio.

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    Comparison of best fit value of mean meridional temperature gradient ∂yΘ for the stochastic model and the observed gradient ∂yΘ.

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    Best fit damping time τ for the stochastic model.

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    Comparison of observed, stochastic model best fit, and Lagrangian damped–advective model (a) temperature fluctuations and (b) heat flux using stochastic model fit parameters for the point 180°. Note the log scale for the abscissa in (b).

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Lower-Tropospheric Heat Transport in the Pacific Storm Track

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  • 1 Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois
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Abstract

The relative effects of dynamics and surface thermal interactions in determining the heat flux and temperature fluctuations within the lower-tropospheric portion of the Pacific storm track are quantified using the probability distribution functions (PDFs) of the temperature fluctuations and heat flux, Lagrangian passive tracer calculations, and a simple stochastic model. It is found that temperature fluctuations damp to the underlying oceanic temperature with a timescale of approximately 1 day but that dynamics still play the predominant role in determining atmospheric heat flux, due to eddy mixing lengths within the storm track of ≤ 5° latitude. These results are confirmed by the favorable comparison of the PDFs of the model-generated and observed temperature fluctuations and heat flux.

The implications of strong thermal damping in the lower troposphere are discussed and speculations are made regarding the effect of such damping upon baroclinic eddy life cycles and the general circulation.

* Current affiliation: Laboratoire de Meteorologie Dynamique, Université de Pierre et Marie Curie, Paris, France.

Corresponding author address: Dr. Kyle L. Swanson, Laboratoire de Météorologie Dynamique, Université de Pierre et Marie Curie, Tour 15, 4 Place Jussieu, 75252 Paris Cedex 05, France.

Email: swanson@lmd.ens.fr

Abstract

The relative effects of dynamics and surface thermal interactions in determining the heat flux and temperature fluctuations within the lower-tropospheric portion of the Pacific storm track are quantified using the probability distribution functions (PDFs) of the temperature fluctuations and heat flux, Lagrangian passive tracer calculations, and a simple stochastic model. It is found that temperature fluctuations damp to the underlying oceanic temperature with a timescale of approximately 1 day but that dynamics still play the predominant role in determining atmospheric heat flux, due to eddy mixing lengths within the storm track of ≤ 5° latitude. These results are confirmed by the favorable comparison of the PDFs of the model-generated and observed temperature fluctuations and heat flux.

The implications of strong thermal damping in the lower troposphere are discussed and speculations are made regarding the effect of such damping upon baroclinic eddy life cycles and the general circulation.

* Current affiliation: Laboratoire de Meteorologie Dynamique, Université de Pierre et Marie Curie, Paris, France.

Corresponding author address: Dr. Kyle L. Swanson, Laboratoire de Météorologie Dynamique, Université de Pierre et Marie Curie, Tour 15, 4 Place Jussieu, 75252 Paris Cedex 05, France.

Email: swanson@lmd.ens.fr

1. Introduction

From the standpoint of mixing, it is useful to decompose the midlatitudinal component of the general circulation into the isentropic mixing of Ertel potential vorticity (PV) in the interior of the troposphere and temperature mixing at the surface. While homogenization of potential vorticity in the interior of the troposphere provides an adequate representation of the effects of dynamical processes (Lindzen 1993; Sun and Lindzen 1994), dynamical transport clearly fails to homogenize temperature at the surface, as witnessed by the existence of strong climatological lower-tropospheric meridional temperature gradients (Peixoto and Oort 1992). The existence of such strong meridional temperature gradients is a challenge to our understanding of the role of synoptic eddies in the climate, as such gradients appear to be at odds with the simplest “baroclinic adjustment”-type arguments (Smagorinsky 1963; Stone 1972; Held 1978), which require sufficient temperature mixing and heat transport by synoptic eddies in the lower troposphere to render the mean flow neutral to baroclinic instability.

There are several possible reasons why synoptic eddies do not mix temperature as strongly in the lower troposphere as simple baroclinic adjustment arguments would suggest. The most obvious reason is a dynamical one, namely, that the meridional scale of the synoptic eddies transporting heat is simply not large enough to remove the climatological meridional temperature gradients. The limitations of meridional mixing of temperature by synoptic eddies have been explored in several two-layer quasigeostrophic model studies (Panetta and Held 1989; Panetta 1993; Pavan and Held 1996), where it has been shown that as the meridional width of a baroclinically unstable region increases, the local eddy flux of heat asymptotes to a constant value rather than continues to increase indefinitely. Temperature variance under this scenario cascades to small scales where it is subsequently dissipated (Salmon 1980), and the most basic scaling arguments suggest that this dissipation of temperature variance can be represented by an eddy diffusivity. The coefficient of diffusivity is controlled by the largest scale eddies and is proportional to υ2τ, where τ is the Lagrangian velocity autocorrelation time and υ a typical velocity scale for the large-scale eddies. Pavan and Held (1996) have explored the applicability of eddy diffusivities for baroclinically unstable jet flows in the two-layer quasigeostrophic model and show that, for sufficiently wide jets, eddy diffusion of temperature provides an accurate description of the eddy dynamical transport.

However, there is another possibile reason why significant climatological meridional temperature gradients can exist in the face of seemingly vigorous synoptic-scale eddy activity. If the vertical exchange of sensible or latent heat between the lower troposphere and the underlying surface is strong, it will prevent temperature mixing by quickly damping out temperature anomalies. Such thermal damping will remove temperature variance equally at all scales and can be schematically represented by Newtonian relaxation of the temperature anomalies. In contrast with dynamically driven eddy diffusivity, however, the coefficient of damping would be independent of the properties of the eddies. Of course, strong thermal damping of temperature anomalies requires the surface to have a large enough heat capacity to maintain significant meridional temperature gradients in the face of vigorous synoptic eddy mixing. In the atmosphere, such thermal capacity could potentially be provided by the oceanic mixed layer, whose temperature remains roughly fixed on synoptic eddy timescales.

Our goal in this paper is to determine quantitatively whether the climatological meridional temperature gradients in the lower tropospheric portion of the Pacific storm track are the result of small dynamical eddy diffusivities or are the result of strong thermal interaction between the lower troposphere and the oceanic surface. The observations we examine are the NMC 850-mb temperature and wind fields for November–March 1972–86. Our data analysis is somewhat nonconventional, as in addition to examining the statistical moments of temperature and velocity fluctuations as a function of space within the storm track, we also examine the probability distribution functions (PDFs) of these quantities. The motivation for examining PDFs comes from recent results within the physics literature, where laboratory experiments of tracer mixing have shown that PDFs derived from a time series of tracer fluctuations and fluxes (where our tracer here is temperature) provide considerable information about the transport processes and underlying dynamics generating the fluctuations (Gollub et al. 1991). Examples of dynamical signatures within scalar PDFs include the prevalence of Gaussian distributions in the presence of weak mixing, where the advection by small eddies (in some suitable nondimensional sense) is conceptually the same from the Lagrangian standpoint as an uncorrelated random walk with a step size much smaller than the domain scale. On the other hand, the existence of extended tails of the PDF (i.e., higher than normal probability of large fluctuations) indicates strong mixing by eddies, where fluid from the boundary of the domain reaches points within the domain interior with little interaction with its surroundings (Pumir et al. 1991). Consideration of the entire PDF as opposed to a small number of its moments yields additional information with which to constrain simple models of temperature mixing and heat transport in the lower troposphere.

By themselves, however, PDFs of the analyzed temperature fluctuations and the heat flux are insufficient to quantify the relative effects of dynamical and thermal processes on lower-tropospheric heat transport. Hence, in order to isolate the role of dynamics in the observed heat transport, we construct a pointwise climatology of Lagrangian isobaric passive tracer mixing as a function of longitude for the lower-tropospheric Pacific storm track. Such a climatology allows pursuit of heat transport and temperature mixing as a problem in passive tracer transport, allowing consideration of the effect of the entire velocity field on transport without reference to the traditional synoptic eddy timescales of 2–6 days. The characteristics of passive tracer transport within this Lagrangian mixing climatology suggest that a simple stochastic model involving only one-dimensional advection and Newtonian relaxation to a specified temperature profile is sufficient to accurately understand and quantify the nature of lower-tropospheric heat transport.

2. Observations

a. Distributions

To quantify the observed temperature fluctuations and heat transport within the North Pacific storm track region, which we roughly define as 30°–50°N latitude and 140°E–140°W longitude, we examine a 15-yr (1972–86) time series derived from the National Meteorological Center (NMC, now the National Centers for Environmental Prediction) gridpoint dataset of November–March temperatures and meridional velocities on the 850-mb pressure surface. We concentrate on the 850-mb surface as it is sufficiently far above the oceanic surface to be relatively free of boundary layer effects and is the approximate height of the maximum observed tropospheric heat flux (Peixoto and Oort 1992). The standard deviation of the temperature fluctuations σ(θ′), the meridional velocity deviation σ(υ), and the heat flux υ θ within the Pacific storm track region on the 850-mb surface are shown in Fig. 1, where (·) and σ(·) are the time mean and standard deviation of their arguments, respectively, and where the prime denotes deviations from a 30-day running mean. Use of a 30-day running mean to define fluctuations ensures that the assumption that heat transport and temperature mixing result primarily from synoptic-scale eddies and their associated timescales of 2–6 days is not explicitly built into the analysis, and removal of the trend from only the temperature field allows us to study the effect of the entire velocity field on heat transport.

The peak of the Pacific storm track is located at approximately 40°N, 170°W, where the heat flux and temperature fluctuations attain their respective maximum values of σ(θ′) = 4.2 K and υθ = 24 K m s−1. The variability in the meridional velocity peaks downstream of the largest temperature variability, with a maximum value of σ(υ) ≈ 10 m s−1 around 45°N, 170°W. The mean meridional temperature gradient on the 850-mb surface decreases in magnitude as one moves downstream through the storm track, with the largest magnitude gradient of ∂yΘ ≈ −1.2 K/degree latitude occurring at the far western edge of the storm track region (indicated by the farthest west plus sign in Fig. 1a), decreasing in magnitude to ∂yΘ ≈ −0.6 K/degree latitude at the far eastern edge. We focus on the latitude 40°N for the remainder of the paper, as we find that the heat transport and temperature fluctuations along this latitude are representative of those throughout the Pacific storm track region.

Examinaton of the PDFs of the temperature fluctuations, the meridional velocity, and the heat flux provides a different perspective on longitudinal variations within the Pacific storm track region. From the data, PDFs are readily estimated from the time series data by “binning,” that is, discretizing the sample space of the desired variable (e.g., temperature) into a number of bins, placing each data point from the time series into the appropriate bin, and finally, normalizing the PDF by dividing each bin by the total number of data points in the time series. Provided the discretization of the sample space is not too small, binning in this manner provides a robust estimate of a given PDF. We uniformly choose the discretization to be 0.1 times the standard deviation for the PDFs of the dynamical quantities examined herein.

Figure 2a shows the PDF of the temperature fluctuations at the points 40°N; 140°E, 140°W, and 180° as indicated by the plus signs in Fig. 1b. The temperature fluctuation PDFs are all quite symmetric, although there is a slight skew toward warmer temperature fluctuations for points at the upstream end of the storm track (140°E and 180°), in accord with the observed asymmetry between cyclonic and anticyclonic growth. The standard deviation of the temperature fluctuations is similar for the two upstream points, with σ(θ′) = 3.84 K and 4.14 K for 140°E and 180°, respectively, with a somewhat smaller value of 3.46 K at 140°W.

The nearly Gaussian PDFs for the temperature fluctuations suggest weak mixing, where weak here means that the mixing length of the eddies transporting heat is small compared to the length scale of the climatological meridional temperature gradients. Based solely on the structure of the temperature PDFs, dynamical incoherence of the eddy mixing emerges as the primary reason why these eddies fail to mix away the climatological lower tropospheric temperature gradients. However, such a conclusion based solely on the Gaussian structure of the temperature fluctuation PDFs is tenuous, as it is not clear from first principles what the signature of strong thermal interaction with the surface would be in the temperature fluctuation PDFs, regardless of the strength of the dynamical transport and mixing.

The meridional velocity PDFs in Fig. 2b reveal the dynamical underpinning for the storm track entrance warm temperature fluctuation skew, as the 140°E meridional velocity PDF exhibits a significant asymmetry between northward and southward meridional wind fluctuations. The velocity variability is similar to that of the temperature, increasing as one moves downstream within the storm track, from σ(υ) = 5.52 m s−1 at 140°E to 9.58 m s−1 at 180°, and then decreasing to σ(υ) = 6.9 m s−1 at 140°W. For reference, the means of the meridional velocity are ῡ = −1.69, 0.87, and 3.34 m s−1 for the points 40°N; 140°E, 180°, and 140°W, respectively.

Finally, the PDFs for the heat flux υθ′ are shown in Fig. 2c for the three points 40°N; 140°E, 180°, and 140°W. The means of these distributions respectively are υθ = 13.9, 22.1, and 13.64 K m s−1. For the latter two points, the correlation resulting in the nonzero mean shows up primarily in the asymmetric extended tail on the positive side of the distribution, with significant noise imposed upon the correlated behavior comprising much of the structure of the distribution. It is this asymmetry that contains the essence of the dynamical processes and that must be quantified if we are to understand how dynamics and thermal forcing interact to determine the observed atmospheric heat flux. Note that the extended tails of the heat flux indicate large sensitivity to extreme events. For example, removing from the 180° heat flux PDF of Fig. 2c all events with υθ′ > 125 K m s−1 reduces the mean heat flux by 20%, even though these events make up only 2% of the heat flux sample.

b. Lagrangian mixing climatology

While the PDFs provide some hints as to the relative roles of dynamics and thermal effects in determining the lower-tropospheric temperature fluctuations and heat flux within the Pacific storm track, it is desirable to understand the role of dynamical processes in isolation. Hence, we construct a Lagrangian mixing climatology for the points along 40°N within the Pacific storm track. This mixing climatology is constructed by passively advecting particles originating at points within the Pacific storm track region in the analyzed 850-mb NMC zonal and meridional velocity fields. While this approach neglects the constraints on the vertical motion of individual parcels of air enforced by hydrostatic and geostrophic balance, to the extent that parcel motion in the lower troposphere is quasi-isobaric and/or for sufficiently short timescales, such an isobaric mixing climatology will be representative of the true isentropic mixing climatology.

On time and spatial scales associated with large-scale meteorological phenomena, it is conceptually useful to consider dynamical transport as a problem in chaotic advection (Aref 1984; Pierrehumbert 1991a b; Pierrehumbert and Yang 1993). The fundamental principle behind chaotic advection is that although the large-scale advecting velocity field (or in our case, its representation in the NMC analyzed data) may be quite smooth on spatial and temporal scales of interest, the Lagrangian motion of individual parcels can be very complicated. For the study of lower-tropospheric mixing using the NMC analyzed velocity fields, this implies that although the large-scale velocity field may be dominated by synoptic-scale eddies with spatial scales of O(2000 km) and temporal scales of O(1 week) within the Pacific storm track, the mixing lengths and Lagrangian autocorrelation times may respectively be much smaller than these Eulerian spatial and temporal scales would suggest. Pierrehumbert (1991a) provides an example of the difference between Eulerian and Lagrangian time and spatial scales in chaotic advective transport. In that study, a time periodic perturbation to a single Rossby wave yields a flow with an essentially infinite Eulerian correlation time, but the Lagrangian velocity autocorrelation times for individual passive particles are quite small, due to the chaotic wandering of the particle trajectories.

To construct the Lagrangian mixing climatology from the observations, short time back trajectories are calculated from the twice daily 850-mb NMC analyzed wind fields. The backward time evolution [x(t), y(t)] (where x and y are longitude and latitude, respectively) from t = t0 to t = t0 − 8 days of particles originating at a given point is computed according to the equations
i1520-0469-54-11-1533-e1
where the velocity fields are bilinearly interpolated in space and time and the geometric factors for motion on the sphere are implicitly assumed in (1). For each point along 40°N within the Pacific storm track, back trajectories are calculated twice each day, with individual trajectories starting at 0000 and 1200 UTC. This procedure yields a Lagrangian climatology for each point along 40°N within the storm track region, which is the composite of 4540 individual particle back trajectories, spanning the 1972–86 November–March NMC analysis time period used in the construction of the PDFs in the previous section.
The first quantity of interest derived from this mixing climatology is the meridional velocity autocorrelation, defined for each starting point x0 along 40°N within the Pacific storm track region as
i1520-0469-54-11-1533-e2
where υ̃(x, t) ≡ υ(x, t) − ῡ(x), the overline indicates time average, and the subscript ranges over the starting times of the 4540 individual particle Lagrangian back trajectories. The autocorrelation gives the effective timescale over which fluid parcels can tap into the mean temperature gradient and, when multiplied by the standard deviation of the meridional velocity field, yields the mixing length for the fluid. As shown in Fig. 3, the autocorrelation decay is approximately exponential for the three reference points within the Pacific storm track. Fitting this decay to an exponential yields decay times of approximately 1.3 days for the point 140°E and 0.75 days for 180° and 140°W. Given typical velocity fluctuation magnitudes O(≤ 10 m s−1), this implies mixing lengths of O(≤ 600 km). Note that the Lagrangian mixing lengths and autocorrelation times within the Pacific storm track are significantly smaller than their Eulerian counterparts, which, respectively, have values of 2000 km and 3–4 days (Chang 1993; Lim and Wallace 1991), as expected from the chaotic nature of Lagrangian particle trajectories.
The meridional dispersion of particles σ(y) as a function of time from the Lagrangian back trajectories provides insight into the nature of eddy transport (Taylor 1921). This quantity, shown as a function of t0t in Fig. 4 for the three storm track reference points, grows at an initial rate of about 5° latitude per day, with this initial growth rate increasing as one moves from west to east within the storm track. This is an intriguing result, for if temperature is mixed isobarically along a mean temperature gradient ∂yΘ, one expects the standard deviation of the temperature fluctuations to be
σθσyτy
where τ is some damping time. Given a typical magnitude for temperature fluctuations of 4 K and a typical meridional temperature gradient of ∂yΘ = −1 K/degree latitude, this implies a damping time τO(1 day), much smaller than typically assumed radiative damping times of 10–20 days within the interior of the troposphere (Peixoto and Oort 1992). Of course, there is another possible explanation for the small temperature fluctuations, namely that the temperature is mixed along a surface much closer to the time mean isentropic surface than the time mean isobaric surface. Unfortunately, information contained in the intrinsically two-dimensional Lagrangian mixing climatology cannot distinguish isobaric and isentropic mixing. However, combining the information contained within the Lagrangian mixing climatology with that contained within the temperature and heat flux PDFs allows for the differentiation of quasi-isobaric and quasi-isentropic mixing of temperature, which shall be explored in the next section.
A final quantity of interest derived from the Lagrangian mixing climatology is the effective eddy diffusivity due to transport by the large-scale eddies. If temperature variance is removed at small scales and if temperature is mixed along the 850-mb isobaric surface, then the quantity
DLυ(t0)y(t0t)
should be proportional to the heat flux with constant of proportionality the mean meridional temperature gradient ∂yΘ. The variation with t0t of DL is shown in Fig. 5. The effective diffusivity DL attains its maximum value for times between 1 and 2 days, as expected from the observed velocity autocorrelations. However, DL also increases strongly in magnitude from west to east within the storm track. Multiplying the maximum value of DL for each of the three points 140°W, 180°, and 140°E by the respective local mean meridional temperature gradient yields heat flux values of 30.66, 28.93, and 28.53 K m s−1. These values overestimate the observed 850-mb heat flux by as much as a factor of 2 at the extreme up- and downstream ends of the storm track.

An upper bound on the mixing length can be obtained by dividing the maximum value of DL by the standard deviation of the velocity at each of the points within the storm track. This mixing length, shown in Fig. 6, has a value of between 4 and 5° latitude throughout the storm track region, with a minimum occurring near 175°W, near the maximum value of the observed heat flux (Fig. 1d). Given that this mixing length is small compared to the length scales of about 30° latitude associated with the mean meridional temperature gradients, the conclusion that the strong climatological temperature gradients are the result of inefficient dynamical transport is inescapable.

While the Lagrangian mixing climatology highlights the role of dynamics as a limiting factor in lower tropospheric heat transport, it provides no insight into the role of thermal interaction with the surface. For example, it is of interest to understand whether the inclusion of thermal effects allows differentiation of quasi-isobaric and quasi-isentropic mixing in generating temperature fluctuations. Additionally, there remains a significant discrepancy between the value of the heat flux derived from purely Lagrangian mixing considerations and the observed values of heat flux. To examine what role nonconservative thermal processes play in lower tropospheric heat transport, we now consider a simple stochastic model that captures the essence of the passive transport contained within the Lagrangian mixing climatology but that allows for thermal interactions.

3. Stochastic model

Consider a simple model consisting only of advection in the meridional direction, with the advecting velocity given by a stochastic model of the form
i1520-0469-54-11-1533-e5
where Δt is the time step and T is a characteristic timescale, which we shall call the Lagrangian integral time. We uniformly set Δt = T/100 for considerations herein. The stochastic forcing ξ is considered to be white in time with unit magnitude; under this assumption, (5) yields the scalar velocity υ with the properties
i1520-0469-54-11-1533-e6
where, following the notation of section 2, C(tt0) is the velocity autocorrelation. Hence, the velocity in this model is given by a simple time-correlated random walk. The continuous time version of (5) is the so-called Langevin equation and is widely applied in the study of stochastic processes as well as in Lagrangian closure theories for 3D turbulence (Pope 1994; Lasota and Mackey 1994). Note that the velocity in (5) is that following a particle, as we seek to retain the Lagrangian perspective of the mixing climatology of the previous section.
The Langevin equation predicts that the statistical variance of a Lagrangian particle evolving in the velocity field (5) as a function of time is given by the expression
y(t)2V2TtTe−|t|/T
which can be compared immediately to the meridional particle dispersions calculated as part of Lagrangian mixing climatology in the previous section. Performing a least-squares fit for T in (8) to the observed particle dispersions, it is found that (8) provides an excellent fit to the observed particle dispersion throughout the heart of the Pacific storm track region (160°E to 160°W), with the fit somewhat less satisfactory outside of this region. An example of the quality of this fit is shown in Fig. 7 for the point 180°, where (8) is found to differ from the back trajectory calculated Lagrangian variance by at most 0.2° for the Lagrangian integral time T = .58 days over the 8-day back trajectory statistics. Examination of the best fit of (8) for T over the longitudinal range of the Pacific storm track (Fig. 8) reveals that T decays from east to west within the track, from 1.6 days at 140°E to 0.35 days at 140°W. If the particle dispersion were governed by the Langevin equation, the Lagrangian integral time T and the velocity autocorrelation time defined in the previous section would be identical, as the Langevin equation predicts velocity autocorrelations will decay like e−|tt0|/T. However, we find that fitting the Lagrangian integral time T to the particle variance provides a more robust fit to the observations than the more traditionally applied method of fitting the velocity autocorrelation to an exponential as was done in the previous section. Hence we shall use T as our mixing timescale for the remainder of this work.

Once T is known, multiplication by the standard deviation of the meridional velocity fluctuations yields a mixing length, shown in Fig. 9. As expected from the agreement of expression (8) with the observed particle dispersion in the heart of the storm track (160°E to 160°W), this mixing length agrees with the observed mixing length (Fig. 6) within this region but overestimates the observed length at the upstream end and underestimates it at the downstream end of the storm track.

Given the ability of the stochastic model to reproduce the observed meridional transport within the Pacific storm track region, we now proceed to use the model-generated stochastic velocity field to drive a Lagrangian damped–advective model describing the evolution of temperature fluctuations. This model has the form
θttθttθytyτ
where y(t) is simply the passively advected particle position
yttytt
and υ(t) is given by (5). This Lagrangian temperature evolution equation has two free parameters, τ and ∂yΘ, which are chosen so that the model reproduces the observed standard deviation of the temperature fluctuations and the mean of the heat flux for the points within the storm track. Before applying the stochastic model to the NMC analyzed data, it is useful to understand how variations in τ are reflected in the temperature fluctuations and heat flux. As shown in Fig. 10, the ratio τ/T determines the relative efficiency of the heat flux relative to the temperature fluctuations, as measured by the ratio of υθ to σ(υ′)σ(θ′). Since this ratio decreases monotonically as the damping time increases relative to the Lagrangian integral time, the heat flux efficiency relative to its optimal value decreases as the damping decreases. Note that this is a relative measurement; σ(θ′) increases quite strongly with increasing τ/T, yielding a corresponding increase in the absolute value of the heat flux.

Since the ratio of the temperature fluctuations to the heat flux decreases monotonically with τ/T, a unique fit to the observed temperature fluctuations and heat flux can be obtained, allowing unambiguous application of the stochastic temperature fluctuation model to the NMC analysis time series. The variation of the best fit ∂yΘ and τ to the observed heat flux and temperature fluctuations within the Pacific storm track region is shown in Figs. 11 and 12, respectively.

The best fit mean temperature gradient ∂yΘ is smaller in magnitude than the observed gradient in the western end of the storm track but is quite comparable to the observed gradient throughout most of the storm track. However, we claim that the failure of the model to reproduce the observed temperature gradient at the upstream end of the storm track is not spurious, but has a dynamically feasible explanation. Note that the portion of the storm track where the model gradient is smaller than the observed gradient is confined to the region where the meridional velocity variance is strongly amplifying downstream (cf. Fig. 2b). Such an increase in velocity variance within the storm track region signifies baroclinic conversion of mean flow potential energy to eddy kinetic energy. However, strong baroclinic conversion requires that energy-extracting particle trajectories must have a three-dimensional character, with meridional/vertical particle trajectory slopes lying somewhere between the time mean isentropic and isobaric surfaces, as in the traditional “wedge of instability” arguments (Eady 1949; Pedlosky 1987; Thorpe et. al. 1989). The three-dimensional character of the particle trajectories means that temperature will be mixed along an “effective” mean temperature gradient ∂yΘ, which is smaller than the observed mean isobaric gradient, just as indicated by the stochastic model results. Thus, we do not consider the failure of the model to fit the observed isobaric temperature gradients at the upstream end of the storm track to be a weakness but rather a strength, as the model errs in precisely the region where vertical motion should be important. Finally, as shown in Fig. 12, the damping time τ hovers around 1 day, with stronger damping near the peak observed heat flux and temperature fluctuations at 170°E and weaker damping at the upstream and downstream ends of the storm track.

Of course, the ability of the stochastic model to fit the observed temperature fluctuations and heat flux is not surprising, as a two-parameter model should be able to accommodate two constraints. However, there is a dynamical “constraint” of which the model has no knowledge, namely the structure of the heat flux and temperature fluctuation PDFs. As discussed in the introduction, the primary reason for introducing PDFs into the data analysis is the additional information they contain on the underlying dynamical processes. Figure 13b shows a comparison of the modeled and observed heat flux PDF for the point 180°; similar agreement is found for other points within the storm track. The ability of the simple model to reproduce without explicit consideration the PDFs is evidence that the stochastic model correctly represents the relative effects of both the dynamical and thermal processes occurring in the NMC analysis. Thus, in addition to weak synoptic eddy mixing of temperature on the pole–equator spatial scale of the mean meridional temperature gradient inferred from the Lagrangian mixing climatology, strong thermal damping of lower-tropospheric temperature fluctuations is also playing a role in determining lower-tropospheric heat flux and temperature fluctuations.

These stochastic model results can be tested by coupling a temperature advection–Newtonian cooling scheme to the Lagrangian back trajectories calculated in section 2, where the temperature fluctuations are taken to damp to the observed spatially varying time mean temperature field Θ(x, y) with the stochastic model predicted damping time τ. The PDF of the temperature fluctuations and heat flux from such a calculation are shown in Figs. 13a,b for the point 180°. These PDFs, with respective values of σ(θ′) = 3.83 K and υθ = 22.8 K m s−1 for the temperature fluctuations and heat flux, are not only consistent with the statistics of the observed temperature fluctuations and heat flux values of σ(θ′) = 4.14 K and υθ = 21.8 K m s−1, respectively, but also appear to reproduce finer-scale structures within the observed PDFs. Equivalent agreement throughout the storm track region confirms that strong thermal damping of lower-tropospheric temperature fluctuations is playing an important role in the determination of the lower-tropospheric heat flux.

4. Discussion and conclusions

The primary results of this work are that, within the NMC analysis, lower-tropospheric heat transport is characterized by mixing lengths of approximately 5° latitude, as well as by strong thermal damping of temperature anomalies back to the underlying oceanic surface temperature with characteristic timescales of one day. The primary effect of this thermal damping is to reduce the heat flux by as much as a factor of approximately 2 over what it would be under the action of temperature mixing alone.

However, it is the loss of velocity correlation from the Lagrangian standpoint that limits lower tropospheric heat flux within the Pacific storm track. Mixing lengths of order 5° latitude as calculated both directly from the observations (Fig. 6) as well as from the stochastic model best fits (Fig. 9) are simply too small on the spatial scale of the climatological mean meridional temperature gradients to effectively homogenize temperature in the lower troposphere. However, the strength of the thermal interaction with the underlying oceanic surface plays a significant role in maintaining the strong observed meridional temperature gradients. This is most apparent upon comparing the relative gradients of isentropic potential vorticity within the troposphere with temperature gradients at the ground. While both quantities are presumably mixed by eddies with similar mixing lengths and timescales, potential vorticity becomes nearly homogenized along isentropic surfaces (Sun and Lindzen 1993) while temperature at the surface does not. The only reason why the time mean gradients of these two quantities should differ is that potential vorticity is damped on interior tropospheric radiative timescales of 10–20 days, while lower-tropospheric temperature is damped on timescales of order 1 day.

The question naturally arises as to whether the strong thermal damping required by the intrinsically two-dimensional analysis applied herein could instead be the result of features neglected in the model, such as 3D particle trajectory effects (Thorpe et al. 1989). The results herein suggest that this is not the case, as the quasi-isobaric mixing indicated by the stochastic model in Fig. 11 appears to be necessary to properly account for the heat flux–temperature fluctuation ratio. Perhaps even stronger evidence of the validity of the analysis herein is provided by the structure of the heat flux PDFs of Fig. 2c. These PDFs, which are accurately reproduced by the stochastic model, constrain the effects of dynamical processes in the observed temperature fluctuations and heat flux sufficiently, allowing the effects of thermal processes to be understood by the application of simple models and/or Lagrangian mixing information. Of course, this statement is true only insofar as the NMC analyzed fields provide an accurate representation of the lower tropospheric temperature and meridional velocity fields. While it goes beyond the analysis here, the relationship between temperature fluctuations and heat flux could be tested by examining time series of radiosonde measurements at a single point within the Pacific storm track, as construction of the PDFs requires only data from a single point.

It is of interest to discuss which processes can cause such strong damping of temperature variance within the lower troposphere. There are two candidates, namely latent and sensible heat exchange with the surface. Of these two, sensible heat exchange is more likely the culprit, as there is no observed asymmetry between the cold and warm temperature fluctuations (Fig. 2a) that one would expect from the release of latent heat. Needless to say, the effectiveness of sensible heat transport in damping lower-tropospheric temperature fluctuations will be strongly dependent on the heat capacity of the underlying oceanic mixed layer, which is sufficiently large to render the surface temperature fixed on synoptic timescales.

Finally, the effect of strong thermal damping of lower-tropospheric temperature anomalies to the underlying surface temperature is unexplored territory with regard to our current understanding of the linear and nonlinear growth and equilibration of synoptic-scale eddies as well larger questions dealing with the nature of large-scale baroclinic turbulence. The effects of such damping have been traditionally neglected in simple quasigeostrophic modeling of baroclinic turbulence, as the typically used Ekman layer boundary conditions only parameterize mechanical damping. Presumably, strong surface temperature perturbation damping reduces linear baroclinic eddy growth rates but to what extent and what the effect on the vertical structure of the eddies would be is unclear. Such an exploration, unfortunately, must be relegated to future work, as it necessarily requires extensive application of numerical models in order to yield a quantitative understanding of the effects of surface fluxes on large-scale atmospheric dynamics. However, given the strong sensible heat flux driven damping of lower-tropospheric temperature anomalies, it appears that the only remaining route to synoptic eddy-driven baroclinic adjustment is through the interior homogenization of potential vorticity, as proposed by Lindzen (1993). States neutral to the growth of synoptic-scale eddies requiring sufficient temperature homogenization in the lower troposphere appear to simply be unattainable, given the strong thermal coupling between the lower troposphere and the oceanic surface.

Acknowledgments

This work was supported by the National Science Foundation under Grant ATM 89-20589. Comments on earlier versions of this work by Isaac Held as well as comments on the final version by an anonymous reviewer are gratefully acknowledged.

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Fig. 1.
Fig. 1.

(a) −yΘ, (b) σ(θ), (c) σ(v), and (d) υθ on the 850-mb surface within the Pacific storm track region.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1533:LTHTIT>2.0.CO;2

Fig. 2.
Fig. 2.

PDFs of (a) temperature fluctuations from 30-day running mean, (b) meridional velocity, and (c) heat flux at the points 40°N; 140°E, 180°, and 140°W. Note the log scale for the abscissa for (c).

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1533:LTHTIT>2.0.CO;2

Fig. 3.
Fig. 3.

Lagrangian meridional velocity autocorrelation for the points 40°N; 140°E, 180°, and 140°W as a function of lag time |tt0|.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1533:LTHTIT>2.0.CO;2

Fig. 4.
Fig. 4.

Standard deviation of meridional particle displacements for the points 40°N; 140°E, 180°, and 140°W as a function of lag time.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1533:LTHTIT>2.0.CO;2

Fig. 5.
Fig. 5.

Effective diffusivity DL (product of meridional position meridional velocity υ(t0)y(tt0) for the three reference points as a function of the lag time.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1533:LTHTIT>2.0.CO;2

Fig. 6.
Fig. 6.

Observed mixing length calculated from the maximum value of the effective diffusivity DL.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1533:LTHTIT>2.0.CO;2

Fig. 7.
Fig. 7.

Actual vs stochastic model meridional particle dispersal for the point 40°N, 180° as a function of lag time.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1533:LTHTIT>2.0.CO;2

Fig. 8.
Fig. 8.

Variation of Lagrangian integral time T with longitude as obtained from the best fit of the Lagrangian particle dispersions calculated from the NMC analyzed wind fields to those predicted by the Langevin equation.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1533:LTHTIT>2.0.CO;2

Fig. 9.
Fig. 9.

Variation of mixing length σ(υ)T with longitude along the Pacific storm track as obtained from the best fit of the Lagrangian integral time T.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1533:LTHTIT>2.0.CO;2

Fig. 10.
Fig. 10.

Effect of varying τ/T on the temperature fluctuation / heat flux ratio.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1533:LTHTIT>2.0.CO;2

Fig. 11.
Fig. 11.

Comparison of best fit value of mean meridional temperature gradient ∂yΘ for the stochastic model and the observed gradient ∂yΘ.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1533:LTHTIT>2.0.CO;2

Fig. 12.
Fig. 12.

Best fit damping time τ for the stochastic model.

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1533:LTHTIT>2.0.CO;2

Fig. 13.
Fig. 13.

Comparison of observed, stochastic model best fit, and Lagrangian damped–advective model (a) temperature fluctuations and (b) heat flux using stochastic model fit parameters for the point 180°. Note the log scale for the abscissa in (b).

Citation: Journal of the Atmospheric Sciences 54, 11; 10.1175/1520-0469(1997)054<1533:LTHTIT>2.0.CO;2

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