Energetics of Transient Eddies Related to the Midwinter Minimum of the North Pacific Storm-Track Activity

1. Introduction

Extratropical transient eddies largely regulate daily weather variations in midlatitudes, while interacting with the climatological-mean westerlies and low-frequency quasi-stationary circulation anomalies. These eddies play an important role in maintaining the time mean temperature field and hemispheric energy budget. Improved mechanistic understanding of these eddies is thus important for climate dynamics and regional weather forecasts. These transient eddies successively move eastward through a given midlatitude location, accounting locally for a major fraction of high-frequency fluctuations of a given atmospheric variable. Using a 10-yr atmospheric analysis data over the extratropical Northern Hemisphere, Blackmon (1976) decomposed the temporal variance of 500-hPa geopotential height locally into the contributions from high-pass-, bandpass-, and low-pass-filtered components, whose periods are less than 2 days, 2.5–6 days, and longer than 10 days, respectively. He suggested that maritime regions of large variance of the bandpass-filtered fluctuations closely correspond to those of frequent cyclone passage over the North Atlantic and Pacific basins, which were thus referred to as “storm tracks.” Blackmon et al. (1977) indicated that those storm tracks are characterized by strong lower-tropospheric poleward eddy heat flux based on the bandpass-filtered fluctuations, which is now commonly used as a measure of baroclinic eddy activity. In fact, poleward heat transport associated with high-frequency (sub-weekly) eddies are pronounced along the major storm tracks over the North Pacific (NP), North Atlantic, and south Indian Ocean. They tend to coincide closely with lower-tropospheric eddy-driven westerly jets and regions of strong near-surface baroclinicity anchored along major oceanic frontal zones (Nakamura et al. 2004).

Many studies have investigated climatological-mean, interannual or longer-scale variability, and seasonal evolution of storm-track activity based on similar techniques based on Eulerian statistics (e.g., Chang et al. 2002). Taking advantage of the Eulerian statistics, Lee and Kim (2003) and Nakamura et al. (2004) clarified the maintenance mechanisms for the westerly jets and storm tracks by separating eddy-driven, subpolar jets from the thermally driven subtropical jets. As argued by Nakamura et al. (2004), this clear separation holds over the North Atlantic throughout the cold season, while it holds over the NP only in the shoulder seasons (i.e., autumn and spring). Over the midwinter NP, a stronger subtropical jet is merged with a subpolar jet to form a hybrid jet.

According to linear theory of baroclinic instability, the stronger the vertical shear of zonal flow (equivalent to meridional temperature gradient through thermal wind balance) is, the larger the growth rate for most unstable eddies [$\sigma =0.31\left(f/N\right)\left(dU/dz\right)$; Eady 1949] becomes. Consistently, the climatological-mean North Atlantic storm-track activity measured by RMS of sub-weekly fluctuations of upper-tropospheric geopotential height is strongest in midwinter, when the upper-tropospheric westerly jet speed tends to maximize. Conversely, the corresponding NP storm-track activity exhibits its minimum in midwinter and becomes weaker than its Atlantic counterpart (Nakamura 1992). This is obviously inconsistent with baroclinic instability theory, since the westerly jet speed over the NP clearly maximizes in midwinter and is greater than over the midwinter Atlantic.

This counterintuitive phenomenon, referred to as the “midwinter minimum (MWM)” or “midwinter suppression” of the NP storm-track activity, has long been investigated from various viewpoints. Nakamura (1992) and Nakamura et al. (2002) argued that an excessive propagation speed of baroclinic eddies inhibits their development of eddies by reducing their residence time within the baroclinic zone over the western Pacific. It was suggested that the excessively strong lateral shear of the extremely strong westerly jet in midwinter may also lead to suppressed growth rate of eddies (Harnik and Chang 2004; Deng and Mak 2005). This is based on the “barotropic governor” mechanism proposed by James (1987), who showed that enhanced lateral shear of a westerly jet acts to suppress baroclinic eddy growth. The importance of the excessive strength of the westerlies has been substantiated by Afargan and Kaspi (2017), who observed a clear suppression of high-frequency eddy activity also over the North Atlantic during years of a particularly strong westerly jet. A similar result was obtained for a southward-shifted jet regime over the North Atlantic by Madonna et al. (2019).

Nakamura and Sampe (2002) pointed out that upper-tropospheric eddies propagating into the midwinter NP tend to be trapped into the southward and upward shifted westerly jet core and thus separated from the surface baroclinic zone, which is unfavorable for effective baroclinic growth of eddies (Nakamura et al. 2004). Vertical structure of the westerly Pacific jet varies between the stronger and more subtropical “merged” regime (Lachmy and Harnik 2014, 2016) in midwinter and the weaker eddy-driven regime in autumn and spring, which may be responsible for the MWM (Yuval et al. 2018; Yuval and Kaspi 2018). Following on this, by tracking upper and lower level eddies in the storm track region, Hadas and Kaspi (2021) showed that the baroclinic coupling of storms diminishes when the jet is enhanced, leading to reduced baroclinic eddy growth.

Furthermore, the effect of diabatic heating associated with low-level clouds in the cold sector of a cyclone was argued by Chang (2001) and Chang and Song (2006). Through a Lagrangian tracking method, Penny et al. (2010) focused on the “seeding effect” of upper-level cyclonic eddies propagating from the Asian Continent upstream of the Pacific storm track. They argued that fewer cyclonic eddies propagating from the upstream is responsible for the MWM, while no such clear relationship was found in an independent analysis by Chang and Guo (2012). Penny et al. (2013) argued that the discrepancies are partly due to different perspectives concerning whether cold seasons are viewed individually or as a single large dataset. In addition, Park et al. (2010) and Lee et al. (2013) suggested the potential importance of the upstream orography on the MWM.

Despite these efforts, the governing mechanisms for the MWM of the NP storm-track activity have yet to be uncovered and are still under debate. The phenomenon becomes one of the most difficult issues remaining in extratropical atmospheric and climate dynamics. The MWM was successfully simulated in AGCM experiments (Christoph et al. 1997; Zhang and Held 1999), which has not led to full understanding of the detailed mechanisms though. Zhang and Held (1999) successfully simulated the MWM in a stochastic linear storm-track model, implying that it is mainly caused by linear dry dynamics. However, a similar effort by Whitaker and Sardeshmukh (1998) was unsuccessful. Using an atmospheric general circulation model (AGCM) with an idealized zonally symmetric setting, which reproduced the climatological conditions in the Pacific over the different seasons, Yuval et al. (2018) were able to reproduce the MWM demonstrating that zonal asymmetries are not essential for reproducing the MWM. Using a similar model with a seasonal dependent forcing, Novak et al. (2020) suggested the importance of the equatorward shift of the westerly jet in midwinter for the suppressed eddy activity.

Chang (2001) and Zhao and Liang (2019) examined the energetics of migratory eddies along the Pacific storm track as an attempt to understand dynamical processes underlying the MWM. Their arguments are, however, based largely on energy conversion/generation rates, which is, by definition, dependent on eddy amplitude and thus insufficient for fully explaining the mechanisms for the suppressed eddy activity. As a measure independent of eddy amplitude, Chang (2001) evaluated a local “growth rate” of a given process, defined as the related energy conversion divided by local eddy kinetic energy (EKE). Schemm and Rivière (2019) evaluated efficiency of the baroclinic conversion term, defined as the conversion normalized by the product of eddy amplitude and magnitude of background baroclinicity (Rivière and Joly 2006; Rivière et al. 2018). They suggested that the reduced efficiency of baroclinic conversion owing to an anomalous poleward tilt of eddies over the western NP poleward of ∼40°N contributes to MWM. Schemm et al. (2021) argued that more rapid development and decay of cyclones over the Kuroshio in midwinter is consistent with the reduction. Their evaluation is, however, conducted only for baroclinic conversion, and thus insufficient for full understanding of the mechanisms for MWM. Additionally, the NP storm track is zonally elongated rather than confined to the vicinity of the Kuroshio, and its MWM is therefore a basin-scale, nonlocal phenomenon. Therefore, a more comprehensive, three-dimensionally integrated energetics of eddies propagating along the NP storm track, which is independent of eddy amplitude, is required to clarify the mechanisms for the MWM, which is the main purpose of the present study.

This paper is organized as follows. Section 2 describes the data and analysis methods used in this study. Section 3 explores the climatological seasonal evolution of various Eulerian eddy statistics for the NP storm track. In section 4, the full energetics for the NP storm track are investigated, with particular focus on their seasonal evolution. Section 5 addresses long-term modulations of the MWM. Section 6 is for summary and discussion.

2. Data and analysis methods

b. Energetics

Eddy available potential energy (EAPE) and eddy kinetic energy (EKE) associated with sub-weekly synoptic-scale disturbances are defined as follows:

$\text{EAPE}=\frac{R}{p{S}_p}\left[\frac{{\left({T^{\prime }}^2\right)}_C}{2}\right],\text{ EKE}=\frac{{\left({u^{\prime }}^2+{{\upsilon }^{\prime }}^2\right)}_C}{2}\cdot$(1)

In (1), primes denote high-pass-filtered fields, subscripts “C” the climatological-mean fields, and $S_p \left(\equiv -\overline{T_c}\partial \text{ln}\overline{{\theta }_c}/\partial p\right)$ a stability parameter, where overbars denote horizontally averaged quantities over a specific domain. In (1), u, υ, T and R represent zonal and meridional wind components, temperature, and the gas constant for dry air, respectively. In taking the horizontal average, grid points below the surface are masked out, based on the climatological-mean surface pressure. The same set of grid points are used for horizontal averaging for a particular level at which S_p is calculated and the two adjacent levels, to minimize the effect of topography.

In the following equations, CK denotes the barotropic energy conversion (or KE conversion), CP the baroclinic energy conversion (or APE conversion), CQ the APE generation through diabatic processes, and ET the energy transfer from EAPE to EKE. Each of the energy conversion/generation terms is expressed as follows (cf. Tanaka et al. 2016):

$\text{CK}=\frac{{\left({{\upsilon }^{\prime }}^2-{u^{\prime }}^2\right)}_C}{2}\left(\frac{d{u}_c}{dx}-\frac{d{\upsilon }_c}{dy}\right)-{\left(u^{\prime }{\upsilon }^{\prime }\right)}_C\left(\frac{d{u}_c}{dy}+\frac{d{\upsilon }_c}{dx}\right),$(2a)

$\text{CP}=\frac{R}{p{S}_p}\left[-{\left(u^{\prime }{T}^{\prime }\right)}_C\frac{d{T}_c}{dx}-{\left({\upsilon }^{\prime }{T}^{\prime }\right)}_C\frac{d{T}_c}{dy}\right],$(2b)

$\text{CQ}=\frac{R}{p{S}_p}{\left(Q^{\prime }{T}^{\prime }\right)}_C,$(2c)

$\text{ET}=-\frac{R}{p}{\left({\omega }^{\prime }{T}^{\prime }\right)}_C,$(2d)

where Q denotes temperature tendency due to diabatic processes and ω is pressure velocity. In deriving (2), quasigeostrophic scaling is assumed and the tendency of horizontally averaged climatological-mean static stability is thus ignored.

In addition to those energy conversion terms from the climatological-mean background state, barotropic and baroclinic energy conversion rates from low-frequency variabilities, in which sub-weekly transient eddies are embedded, are also evaluated. In the following two equations, CKLF and CPLF denote the barotropic and baroclinic energy conversion rates from the low-frequency variability, respectively:

$\text{CKLF}=\left[\left(\frac{{{\upsilon }^{\prime }}^2-{u^{\prime }}^2}{2}\right)\left(\frac{\partial u_L}{\partial x}-\frac{\partial {\upsilon }_L}{\partial y}\right)-\left(u^{\prime }{\upsilon }^{\prime }\right)\left(\frac{\partial u_L}{\partial y}+\frac{\partial {\upsilon }_L}{\partial x}\right)\right]-\left(u_L\frac{\partial \text{EKE}}{\partial x}+{\upsilon }_L\frac{\partial \text{EKE}}{\partial y}\right)-(u^{\prime }{u}_L\frac{\partial u_L}{\partial x}+u^{\prime }{\upsilon }_L\frac{\partial u_L}{\partial y}+{\upsilon }^{\prime }{u}_L\frac{\partial {\upsilon }_L}{\partial x}+{\upsilon }^{\prime }{\upsilon }_L\frac{\partial {\upsilon }_L}{\partial y}),$(2e)

$\text{CPLF}=\frac{R}{p{S}_p}\left[-\left(u^{\prime }{T}^{\prime }\right)\frac{d{T}_L}{dx}-\left({\upsilon }^{\prime }{T}^{\prime }\right)\frac{d{T}_L}{dy}\right]-\left(u_L\frac{\partial \text{EAPE}}{\partial x}+{\upsilon }_L\frac{\partial \text{EAPE}}{\partial y}\right)+\frac{R}{p{S}_p}\left(-T^{\prime }{u}_L\frac{\partial T_L}{\partial x}-T^{\prime }{\upsilon }_L\frac{\partial T_L}{\partial y}\right),$(2f)

where subscript “L” represents low-pass-filtered anomalies as deviations from the climatological mean. CKLF and CPLF are calculated every 6 h based on (2e) and (2f), and their climatological-mean values indicate the climatological seasonal evolutions of energy conversions from the low-frequency variability. The derivation of these terms is described in appendix A. Note that, by this definition, “low-frequency variability” includes even interannual fluctuations, but the results are qualitatively similar when low-frequency variability is defined as low-pass-filtered subseasonal deviations from the 31-day running mean fields.

The energy conversion/generation terms were integrated vertically from the surface to the 100-hPa level and then integrated horizontally within a specified domain. This study focuses on the energetics of sub-weekly eddies along the NP storm track within the domain (20°–65°N, 130°E–130°W). When the energetics within a local domain is discussed, energy inflow or outflow by energy fluxes through its lateral boundaries (EF) needs to be estimated. The flux may be expressed as follows:

$\text{EF}={\displaystyle {\int }_{p_s}^{p_{\text{top}}}\left[{\left({\text{Φ}}^{\prime }{v}^{\prime }\right)}_C+\left(\text{EAPE}+\text{EKE}\right)v_c\right]}dp,$(3)

where Φ is geopotential, p_s denotes surface pressure, and p_top is set to be 100 hPa.

For more quantitative discussion on the energetics based on (1), (2), and (3), the normalized rate ¹ of each of the conversion, generation and flux terms is evaluated by dividing it by the total energy of transient eddies defined as the sum of EAPE and EKE:

$\text{normalized rate}\equiv \frac{\langle \text{energy conversion}/\text{generation term}\rangle }{\langle \text{EAPE}+\text{EKE}\rangle }\cdot$(4)

Hereafter, we signify the normalized rate simply as “λ,” and a subscript as listed in Table 1 is added in referring to a specific conversion/generation process. The unit of this normalized energy conversion (or generation) rate is day⁻¹, and its reciprocal thus gives a time scale of how long it would take to replenish the total eddy energy within the storm-track domain solely by a given conversion/generation process. Because the energy conversion/generation rates, by definition, depend on eddy amplitude, it is essential to evaluate the conversion/generation as its normalized rate, which is independent of eddy amplitude, for the eddy energetics for storm tracks. In the following, a negative value of λ means that eddies are transferring energy to the mean flow or low-frequency variability.

Table 1

List of the symbols for the normalized rates used in this study. All quantities are expressed in the unit of day⁻¹.

View Table

3. Climatology of the North Pacific storm-track activity

We begin our analysis with exploring the seasonal evolution of the climatological activity of the NP storm track based on the atmospheric reanalysis that covers a longer period than in previous studies. Figure 1 shows the climatological-mean seasonal evolution of meridionally averaged eddy statistics around the axes of their local maxima at individual longitudes.

Climatological seasonality in storm-track activity measured as RMS of sub-weekly fluctuations in meridional wind velocity (m s⁻¹) at the (a) 300-hPa level ($V^{\prime }{V^{\prime }}_{300}$) and (b) 850-hPa level ($V^{\prime }{V^{\prime }}_{850}$). These statistics are meridionally averaged for 9 grids whose center is at the maximum of a given quantity in 20°–60°N at each longitude. Contours denote the climatological westerly wind speed (m s⁻¹) at the respective levels. (c) As in (b), but for 850-hPa poleward heat flux by sub-weekly transients ($V^{\prime }{T^{\prime }}_{850}$). Contours represent 850-hPa Eady growth rate (day⁻¹) of the background state averaged meridionally around the $V^{\prime }{T^{\prime }}_{850}$ maxima at individual longitudes. Climatological seasonality in (d) averaged over 180°–150°W, (e) $V^{\prime }{V^{\prime }}_{850}$ over 160°E–170°W, and (f) $V^{\prime }{T^{\prime }}_{850}$ (black) and the Eady growth rate (red) averaged over 150°E–180° based on (a)–(c), respectively, as function of latitude. The values are indicated as the fractions (%) of their climatological maxima.

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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Climatological seasonality in storm-track activity measured as RMS of sub-weekly fluctuations in meridional wind velocity (m s⁻¹) at the (a) 300-hPa level ($V^{\prime }{V^{\prime }}_{300}$) and (b) 850-hPa level ($V^{\prime }{V^{\prime }}_{850}$). These statistics are meridionally averaged for 9 grids whose center is at the maximum of a given quantity in 20°–60°N at each longitude. Contours denote the climatological westerly wind speed (m s⁻¹) at the respective levels. (c) As in (b), but for 850-hPa poleward heat flux by sub-weekly transients ($V^{\prime }{T^{\prime }}_{850}$). Contours represent 850-hPa Eady growth rate (day⁻¹) of the background state averaged meridionally around the $V^{\prime }{T^{\prime }}_{850}$ maxima at individual longitudes. Climatological seasonality in (d) averaged over 180°–150°W, (e) $V^{\prime }{V^{\prime }}_{850}$ over 160°E–170°W, and (f) $V^{\prime }{T^{\prime }}_{850}$ (black) and the Eady growth rate (red) averaged over 150°E–180° based on (a)–(c), respectively, as function of latitude. The values are indicated as the fractions (%) of their climatological maxima.

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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Climatological seasonality in storm-track activity measured as RMS of sub-weekly fluctuations in meridional wind velocity (m s⁻¹) at the (a) 300-hPa level ($V^{\prime }{V^{\prime }}_{300}$) and (b) 850-hPa level ($V^{\prime }{V^{\prime }}_{850}$). These statistics are meridionally averaged for 9 grids whose center is at the maximum of a given quantity in 20°–60°N at each longitude. Contours denote the climatological westerly wind speed (m s⁻¹) at the respective levels. (c) As in (b), but for 850-hPa poleward heat flux by sub-weekly transients ($V^{\prime }{T^{\prime }}_{850}$). Contours represent 850-hPa Eady growth rate (day⁻¹) of the background state averaged meridionally around the $V^{\prime }{T^{\prime }}_{850}$ maxima at individual longitudes. Climatological seasonality in (d) averaged over 180°–150°W, (e) $V^{\prime }{V^{\prime }}_{850}$ over 160°E–170°W, and (f) $V^{\prime }{T^{\prime }}_{850}$ (black) and the Eady growth rate (red) averaged over 150°E–180° based on (a)–(c), respectively, as function of latitude. The values are indicated as the fractions (%) of their climatological maxima.

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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The variance of sub-weekly fluctuations in 300-hPa meridional wind ($V^{\prime }{V^{\prime }}_{300}$) as a measure of the upper-level storm-track activity exhibits its prominent MWM under the extremely strong westerly jet (Fig. 1a), while its counterpart for the 850-hPa wind variance ($V^{\prime }{V^{\prime }}_{850}$) is less clear and its early-winter peak is more distinct (Fig. 1b). The two peaks in $V^{\prime }{V^{\prime }}_{300}$ seem to accompany weak secondary maxima of the 300-hPa westerly wind speed (U₃₀₀) in the eastern NP (see 30 m s⁻¹ contour in Fig. 1a). The corresponding maxima of the 850-hPa westerly intensity (U₈₅₀) are more evident, as an indication of an eddy-driven jet. In early winter, the peak of $V^{\prime }{V^{\prime }}_{850}$ is stronger and extends farther eastward than in spring. To examine their seasonal evolutions more quantitatively, those Eulerian statistics are averaged within longitudinal sectors that correspond to the storm-track core regions. The MWM is distinct in $V^{\prime }{V^{\prime }}_{300}$ with a reduction by more than 20% from its spring peak (Fig. 1d). By contrast, $V^{\prime }{V^{\prime }}_{850}$ peaks in early winter, then weakens slightly in midwinter and retains its intensity into spring (Fig. 1e). Such a distinct MWM in the storm-track activity as above is not observed over the North Atlantic for the period 1958/59–2016/17 (not shown), as pointed out by previous studies (e.g., Nakamura 1992).

Poleward eddy heat flux (V′T′) is a measure of baroclinic development of eddies and related to the baroclinic energy conversion (CP in section 2). We focus on the lower troposphere, where V′T′ is prominent throughout the cold season. At the 850-hPa, $V^{\prime }{T^{\prime }}_{850}$ is largest around 40°N in the western NP, where a prominent oceanic frontal zone is located. Unlike $V^{\prime }{V^{\prime }}_{850}$, $V^{\prime }{T^{\prime }}_{850}$ shows a distinct MWM (Fig. 1c). In contrast, the climatological-mean 850-hPa Eady growth rate [EGR; $\sigma \hspace{0.17em}=\hspace{0.17em}0.31\left(f/N\right)\left(dU/dz\right)$] exhibits a distinct midwinter maximum in the western NP (black contours in Fig. 1c), in agreement with Nakamura (1992). A close examination reveals, however, that the climatological-mean EGR is enhanced (suppressed) to the south (north) of the storm-track axis in midwinter (Yuval et al. 2018), which corresponds to the modulated vertical structure of the Pacific jet. Nevertheless, the net enhancement of EGR in midwinter maximizes around the axis. In theory, the growth rate of baroclinic eddies is therefore supposed to maximize in midwinter, but in reality, the eddy activity is somehow suppressed. Specifically, $V^{\prime }{T^{\prime }}_{850}$ in midwinter is ∼85% of its peak value in spring, whereas the EGR in midwinter is ∼20% larger than in spring (Fig. 1f).

To investigate the typical structure of transient eddies, the local correlation in high-pass-filtered 850-hPa fluctuations between meridional wind and temperature is calculated as $\text{Corr}\left(V^{\prime }, T^{\prime }\right)=V^{\prime }{T}^{\prime }/\sqrt{V^{\prime }{V}^{\prime }\times T^{\prime }{T}^{\prime }}$. The correlation can be viewed as a measure of baroclinic structure of eddies. The western NP is a region of particularly high positive correlation and the correlation peaks in midwinter (Figs. 2a,b), when $V^{\prime }{T^{\prime }}_{850}$ exhibits its distinct minimum. This means that eddy baroclinic structure does not contribute to the distinct MWM of $V^{\prime }{T^{\prime }}_{850}$. Rather, the MWM of $V^{\prime }{T^{\prime }}_{850}$ is contributed primarily by high-pass-filtered temperature fluctuations (Fig. 2c). Actually, the fluctuations measured as RMS of $T^{\prime }{T^{\prime }}_{850}$ are particularly strong over the western NP with a distinct MWM (Fig. 2c). Its midwinter variance is less than 80% of those at the autumn/spring peaks (Fig. 2d), yielding more prominent suppression than its counterpart in $V^{\prime }{T^{\prime }}_{850}$.

(a) As in Fig. 1c, but for the correlation (%) between V′ and T′ at 850 hPa within 150°E–180° around $V^{\prime }{T^{\prime }}_{850}$ maxima at individual longitudes. Contours indicate climatological-mean $V^{\prime }{T^{\prime }}_{850}$. (b) As in Fig. 1f, but for the correlations between V′ and T′ at 850 (black), 600 (green), and 400 hPa (blue) within 150°E–180°. (c) As in (a), but for climatological-mean RMS of $T^{\prime }{T^{\prime }}_{850}$ (color; K) and U₃₀₀ (m s⁻¹). (d) As in (b), but for $T^{\prime }{T^{\prime }}_{850}$. (e) As in (c), but for RMS of $Q^{\prime }{Q^{\prime }}_{850}$ (K day⁻¹). (f) As in (b), but for $Q^{\prime }{Q^{\prime }}_{850}$ around the Q′Q′ axis within 140°–170°E.

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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(a) As in Fig. 1c, but for the correlation (%) between V′ and T′ at 850 hPa within 150°E–180° around $V^{\prime }{T^{\prime }}_{850}$ maxima at individual longitudes. Contours indicate climatological-mean $V^{\prime }{T^{\prime }}_{850}$. (b) As in Fig. 1f, but for the correlations between V′ and T′ at 850 (black), 600 (green), and 400 hPa (blue) within 150°E–180°. (c) As in (a), but for climatological-mean RMS of $T^{\prime }{T^{\prime }}_{850}$ (color; K) and U₃₀₀ (m s⁻¹). (d) As in (b), but for $T^{\prime }{T^{\prime }}_{850}$. (e) As in (c), but for RMS of $Q^{\prime }{Q^{\prime }}_{850}$ (K day⁻¹). (f) As in (b), but for $Q^{\prime }{Q^{\prime }}_{850}$ around the Q′Q′ axis within 140°–170°E.

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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(a) As in Fig. 1c, but for the correlation (%) between V′ and T′ at 850 hPa within 150°E–180° around $V^{\prime }{T^{\prime }}_{850}$ maxima at individual longitudes. Contours indicate climatological-mean $V^{\prime }{T^{\prime }}_{850}$. (b) As in Fig. 1f, but for the correlations between V′ and T′ at 850 (black), 600 (green), and 400 hPa (blue) within 150°E–180°. (c) As in (a), but for climatological-mean RMS of $T^{\prime }{T^{\prime }}_{850}$ (color; K) and U₃₀₀ (m s⁻¹). (d) As in (b), but for $T^{\prime }{T^{\prime }}_{850}$. (e) As in (c), but for RMS of $Q^{\prime }{Q^{\prime }}_{850}$ (K day⁻¹). (f) As in (b), but for $Q^{\prime }{Q^{\prime }}_{850}$ around the Q′Q′ axis within 140°–170°E.

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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The distinct MWM in $T^{\prime }{T^{\prime }}_{850}$ is likely to be contributed by diabatic heating. In fact, the background meridional temperature gradient also peaks in midwinter as seen in EGR and $V^{\prime }{V^{\prime }}_{850}$ exhibits no distinct MWM (Fig. 1), suggesting that meridional temperature advection associated with sub-weekly eddies should become strongest in midwinter. Actually, diabatic heating fluctuations measured as RMS of $Q^{\prime }{Q^{\prime }}_{850}$ exhibit their distinct early-winter peak and a clear MWM along its axis (Figs. 2e,f), which is located slightly to the south (∼36°N) of the low-level storm-track axis marked by $V^{\prime }{T^{\prime }}_{850}$ maxima at individual longitudes. In the midwinter western NP, enhanced heat exchange with the underlying ocean and latent heat release both occurring under the strong cold advection behind individual cyclones can act to suppress lower-tropospheric temperature fluctuations (Chang 2001; Nakamura et al. 2004).

The poleward eddy heat flux is closely related to the upward wave-activity flux and thus the vertical structure of the MWM signature. Figure 3 shows zonal sections of the wave-activity flux defined by Takaya and Nakamura (2001) on 4 December, 24 January, and 19 March, which climatologically correspond to the first peak, MWM, and second peak, respectively, of the NP storm-track activity. The flux plotted does not include the contribution of the term proportional to eddy phase speed. The eastward component of the flux in the upper troposphere therefore represents the downstream development of transient eddies pointed out by Chang (1993), and the flux is indeed dominantly eastward (Fig. 3). In addition, the flux is strongly upward from the lower- to midtroposphere over the western and central NP. In this region, eddy baroclinic growth is prominent as marked by high positive V′–T′ correlation (Fig. 2a), and abundant heat release from the ocean occurs in the cold season around the oceanic frontal zone to maintain near-surface baroclinicity (bottom panels in Fig. 3; Hotta and Nakamura 2011). In the lower half of the troposphere, the upward wave-activity flux is strongest in midwinter (Fig. 3b), owing partly to the reduction of the stability parameter under the enhanced heat supply from the ocean (not shown). However, the upward flux at ∼400-hPa is weaker in midwinter than in the shoulder seasons, when the flux exhibits a deeper structure and the strong flux reaches above the 400-hPa level (in color). In early winter, the strongest upward flux at ∼400-hPa is consistent with a peak of $V^{\prime }{T^{\prime }}_{400}$ (not shown), which may contribute to the distinct upper-tropospheric MWM in $V^{\prime }{V^{\prime }}_{300}$ despite the unclear MWM in $V^{\prime }{V^{\prime }}_{850}$. In spring, the midtropospheric upward flux is rather confined to the upstream portion of the storm track (∼160°E), which is consistent with the westward-extended maxima of $V^{\prime }{V^{\prime }}_{300}$ and EKE (contours in Fig. 3) into the Asian continent.

(top) Zonal sections of climatological-mean wave-activity flux associated with sub-weekly transient eddies (vectors) defined by Takaya and Nakamura (2001) without the term proportional to eddy phase speed for (a) 4 Dec, (b) 24 Jan, and (c) 19 Mar. Colors indicate its vertical component (Pa m s⁻²). Black contours denote climatological-mean EKE (m² s⁻²). Purple dotted lines denote levels at which the climatological-mean westerly wind speed is 10 m s⁻¹ as an approximate measure of transient eddy phase speed. Quantities shown are meridionally averaged over 30°–55°N. (bottom) Horizontal maps of climatological-mean sensible heat flux from the ocean (W m⁻²).

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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(top) Zonal sections of climatological-mean wave-activity flux associated with sub-weekly transient eddies (vectors) defined by Takaya and Nakamura (2001) without the term proportional to eddy phase speed for (a) 4 Dec, (b) 24 Jan, and (c) 19 Mar. Colors indicate its vertical component (Pa m s⁻²). Black contours denote climatological-mean EKE (m² s⁻²). Purple dotted lines denote levels at which the climatological-mean westerly wind speed is 10 m s⁻¹ as an approximate measure of transient eddy phase speed. Quantities shown are meridionally averaged over 30°–55°N. (bottom) Horizontal maps of climatological-mean sensible heat flux from the ocean (W m⁻²).

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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(top) Zonal sections of climatological-mean wave-activity flux associated with sub-weekly transient eddies (vectors) defined by Takaya and Nakamura (2001) without the term proportional to eddy phase speed for (a) 4 Dec, (b) 24 Jan, and (c) 19 Mar. Colors indicate its vertical component (Pa m s⁻²). Black contours denote climatological-mean EKE (m² s⁻²). Purple dotted lines denote levels at which the climatological-mean westerly wind speed is 10 m s⁻¹ as an approximate measure of transient eddy phase speed. Quantities shown are meridionally averaged over 30°–55°N. (bottom) Horizontal maps of climatological-mean sensible heat flux from the ocean (W m⁻²).

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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The covariance between high-pass-filtered diabatic heating and temperature (Q′T′) contributes to diabatic energy generation of eddies (CQ in section 2). We focus on the midtroposphere, where Q′T′ is large mainly due to condensational heating. As evident in Fig. 4a, meridionally averaged $Q^{\prime }{T^{\prime }}_{600}$ around its local maxima is strongest over the western NP and peaks in early winter. When averaged zonally over 150°E–180°, it is suppressed in midwinter slightly (∼90% of the early winter peak, not shown), but its midwinter reduction is weaker than its counterpart of $V^{\prime }{T^{\prime }}_{850}$ or $T^{\prime }{T^{\prime }}_{850}$.

(a) As in Fig. 1c, but for the covariance (K² day⁻¹) between high-pass-filtered diabatic heating associated with precipitation (Q′) and temperature (T′) at 600 hPa. Contours denote climatological-mean U₃₀₀ (m s⁻¹). (b) As in Fig. 2b, but for $Q^{\prime }{T^{\prime }}_{850}$ (black), $Q^{\prime }{T^{\prime }}_{600}$ (green), and $Q^{\prime }{T^{\prime }}_{400}$ (blue). (c) As in (a), but for the covariance between high-pass-filtered (sign-reversed) pressure velocity (−ω′) and temperature (T′) at 600 hPa (Pa K s⁻¹). (d) As in (b), but for $-{\omega }^{\prime }{T^{\prime }}_{850}$, $-{\omega }^{\prime }{T^{\prime }}_{600}$, and $-{\omega }^{\prime }{T^{\prime }}_{400}$.

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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(a) As in Fig. 1c, but for the covariance (K² day⁻¹) between high-pass-filtered diabatic heating associated with precipitation (Q′) and temperature (T′) at 600 hPa. Contours denote climatological-mean U₃₀₀ (m s⁻¹). (b) As in Fig. 2b, but for $Q^{\prime }{T^{\prime }}_{850}$ (black), $Q^{\prime }{T^{\prime }}_{600}$ (green), and $Q^{\prime }{T^{\prime }}_{400}$ (blue). (c) As in (a), but for the covariance between high-pass-filtered (sign-reversed) pressure velocity (−ω′) and temperature (T′) at 600 hPa (Pa K s⁻¹). (d) As in (b), but for $-{\omega }^{\prime }{T^{\prime }}_{850}$, $-{\omega }^{\prime }{T^{\prime }}_{600}$, and $-{\omega }^{\prime }{T^{\prime }}_{400}$.

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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(a) As in Fig. 1c, but for the covariance (K² day⁻¹) between high-pass-filtered diabatic heating associated with precipitation (Q′) and temperature (T′) at 600 hPa. Contours denote climatological-mean U₃₀₀ (m s⁻¹). (b) As in Fig. 2b, but for $Q^{\prime }{T^{\prime }}_{850}$ (black), $Q^{\prime }{T^{\prime }}_{600}$ (green), and $Q^{\prime }{T^{\prime }}_{400}$ (blue). (c) As in (a), but for the covariance between high-pass-filtered (sign-reversed) pressure velocity (−ω′) and temperature (T′) at 600 hPa (Pa K s⁻¹). (d) As in (b), but for $-{\omega }^{\prime }{T^{\prime }}_{850}$, $-{\omega }^{\prime }{T^{\prime }}_{600}$, and $-{\omega }^{\prime }{T^{\prime }}_{400}$.

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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The covariance between high-pass-filtered (sign-reversed) pressure velocity and temperature (−ω′T′) contributes to the transfer from EAPE to EKE (ET in section 2). The covariance −ω′T′ is prominent in the midtroposphere. Similar to $Q^{\prime }{T^{\prime }}_{600}$, meridionally averaged 600-hPa −ω′T′ around its local maxima is strongest over the western NP and again peaks in early winter (Fig. 4c). Its midwinter amplitude is 90%–95% of the early winter peak (not shown), although this slight suppression is insufficient to account for a distinct minimum like that in $V^{\prime }{T^{\prime }}_{850}$.

4. Energetics for the North Pacific storm track

With the Eulerian statistics for sub-weekly transient eddies discussed above, we examine the climatological energetics for the NP storm track in the framework described in section 2b. As a typical midwinter case, distributions of vertically integrated climatological-mean energy and conversion/generation terms are shown in Fig. 5 for the 24 January, when the storm-track activity shows its minimum climatologically. Vertically integrated climatological EKE and EAPE both exhibit their maxima along the NP storm track (Figs. 5a,b). The EAPE maximum is located upstream of the EKE maximum with smaller magnitude.

Climatological energetics of sub-weekly eddies for 24 Jan. Vertically integrated climatological-mean (a) EKE and (b) EAPE (10⁵ J m⁻²). (c) Vertically integrated climatological-mean CK term (color; W m⁻²), extended E–P flux at 300 hPa (vectors; m² s⁻²), and U₃₀₀ (purple contours; m s⁻¹). (d) Vertically integrated climatological-mean CP (color), $V^{\prime }{T^{\prime }}_{850}$ (black contour, m K s⁻¹), and T₈₅₀ (red contours; every 4K). (e) Vertically integrated climatological-mean CQ (color) and Q₇₀₀ (Black contours; every 1 K day⁻¹). (f) Vertically integrated climatological-mean ET from EAPE to EKE. (g) Vertically integrated climatological-mean energy flux (vector; 10⁷ J m s⁻¹) and its amplitude (color; 10⁷ J m s⁻¹).

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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Climatological energetics of sub-weekly eddies for 24 Jan. Vertically integrated climatological-mean (a) EKE and (b) EAPE (10⁵ J m⁻²). (c) Vertically integrated climatological-mean CK term (color; W m⁻²), extended E–P flux at 300 hPa (vectors; m² s⁻²), and U₃₀₀ (purple contours; m s⁻¹). (d) Vertically integrated climatological-mean CP (color), $V^{\prime }{T^{\prime }}_{850}$ (black contour, m K s⁻¹), and T₈₅₀ (red contours; every 4K). (e) Vertically integrated climatological-mean CQ (color) and Q₇₀₀ (Black contours; every 1 K day⁻¹). (f) Vertically integrated climatological-mean ET from EAPE to EKE. (g) Vertically integrated climatological-mean energy flux (vector; 10⁷ J m s⁻¹) and its amplitude (color; 10⁷ J m s⁻¹).

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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Climatological energetics of sub-weekly eddies for 24 Jan. Vertically integrated climatological-mean (a) EKE and (b) EAPE (10⁵ J m⁻²). (c) Vertically integrated climatological-mean CK term (color; W m⁻²), extended E–P flux at 300 hPa (vectors; m² s⁻²), and U₃₀₀ (purple contours; m s⁻¹). (d) Vertically integrated climatological-mean CP (color), $V^{\prime }{T^{\prime }}_{850}$ (black contour, m K s⁻¹), and T₈₅₀ (red contours; every 4K). (e) Vertically integrated climatological-mean CQ (color) and Q₇₀₀ (Black contours; every 1 K day⁻¹). (f) Vertically integrated climatological-mean ET from EAPE to EKE. (g) Vertically integrated climatological-mean energy flux (vector; 10⁷ J m s⁻¹) and its amplitude (color; 10⁷ J m s⁻¹).

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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The barotropic energy conversion (CK) is negative around the jet exit region (Fig. 5c), where eddies are giving up EKE to the background westerlies. This is consistent with the westerly acceleration through vorticity flux by transient eddies represented as the diverging extended E–P flux (Trenberth 1986). In agreement with previous studies (e.g., Schemm and Rivière 2019), the baroclinic energy conversion (CP) is prominent in the storm-track core just east of Japan (Fig. 5d). This is due to the collocation of strongest poleward eddy heat flux and distinct meridional gradient of climatological-mean temperature (or large EGR) in the presence of the NP oceanic frontal zone (Hotta and Nakamura 2011) and the prominent Pacific jet. The CP maximum is located slightly upstream of the EAPE maximum. The amplitude of CP is much greater than that of CK. The APE generation through diabatic heating (CQ) is overall positive along the NP storm track (Fig. 5e), reflecting the positive Q′–T′ correlation in the free troposphere. The region of the positive CQ roughly collocates with the region of positive diabatic heating in the midtroposphere. The energy transfer (ET) from EAPE to EKE is largest in the western NP between the CP and EAPE maxima. The maximum value of ET is comparable to that of CP (Fig. 5f), indicating that most of the converted APE (CP) is transferred into EKE. The eastward energy flux (EF) is strongest along the storm track and deflected northward over the eastern NP (Fig. 5g), consistent with the distributions of EKE and EAPE (Figs. 5a,b).

Those energy conversion/generation terms are integrated horizontally over the NP domain (20°–65°N, 130°W–130°E) and vertically from the surface to 100 hPa, to evaluate the comprehensive energy budget for the NP storm track. Figure 6a shows the seasonal evolution of the three-dimensionally integrated EKE and EAPE. Both the integrated EKE and EAPE are reduced slightly in midwinter between their peaks in early winter and spring, in a manner consistent with the seasonality of $V^{\prime }{V^{\prime }}_{300}$ and $T^{\prime }{T^{\prime }}_{850}$ (Figs. 1a and 2d). This result verifies that spatially integrated eddy energy shows seasonal evolution similar to that of eddy statistics around the core region of the NP storm track.

(a) Climatological-mean seasonal evolution of EKE (blue), EAPE (red), and EKE + EAPE (black) integrated three-dimensionally over the NP (10¹⁸ J). A tick mark on the abscissa represents the first day of a given calendar month. (b) As in (a), but for three-dimensionally integrated power of CK (solid blue), CKLF (dashed blue), CP (solid red), CPLF (dashed red), CQ (solid green), CQ associated only with precipitation (dashed green), EF (light blue), and ET (purple). Units: 10¹³ W. (c) As in (b), but for λ_CK (solid blue), λ_CKLF (dashed blue), λ_CP (solid red), λ_CPLF (dashed red), λ_CQ (solid green), λ_CQ associated only with precipitation (dashed green), λ_EF (light blue), and λ_ET (purple). Black line denotes λ_Tot relevant to the budget of EKE + EAPE (viz., CK + CP + CQ + EF + CKLF + CPLF). Units: day⁻¹.

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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(a) Climatological-mean seasonal evolution of EKE (blue), EAPE (red), and EKE + EAPE (black) integrated three-dimensionally over the NP (10¹⁸ J). A tick mark on the abscissa represents the first day of a given calendar month. (b) As in (a), but for three-dimensionally integrated power of CK (solid blue), CKLF (dashed blue), CP (solid red), CPLF (dashed red), CQ (solid green), CQ associated only with precipitation (dashed green), EF (light blue), and ET (purple). Units: 10¹³ W. (c) As in (b), but for λ_CK (solid blue), λ_CKLF (dashed blue), λ_CP (solid red), λ_CPLF (dashed red), λ_CQ (solid green), λ_CQ associated only with precipitation (dashed green), λ_EF (light blue), and λ_ET (purple). Black line denotes λ_Tot relevant to the budget of EKE + EAPE (viz., CK + CP + CQ + EF + CKLF + CPLF). Units: day⁻¹.

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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(a) Climatological-mean seasonal evolution of EKE (blue), EAPE (red), and EKE + EAPE (black) integrated three-dimensionally over the NP (10¹⁸ J). A tick mark on the abscissa represents the first day of a given calendar month. (b) As in (a), but for three-dimensionally integrated power of CK (solid blue), CKLF (dashed blue), CP (solid red), CPLF (dashed red), CQ (solid green), CQ associated only with precipitation (dashed green), EF (light blue), and ET (purple). Units: 10¹³ W. (c) As in (b), but for λ_CK (solid blue), λ_CKLF (dashed blue), λ_CP (solid red), λ_CPLF (dashed red), λ_CQ (solid green), λ_CQ associated only with precipitation (dashed green), λ_EF (light blue), and λ_ET (purple). Black line denotes λ_Tot relevant to the budget of EKE + EAPE (viz., CK + CP + CQ + EF + CKLF + CPLF). Units: day⁻¹.

Citation: Journal of Climate 35, 4; 10.1175/JCLI-D-21-0123.1

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Among the energy conversion/generation terms, CP and ET are much larger than the others (Fig. 6b), reflecting the baroclinic nature of sub-weekly eddies. Those terms peak in early winter before suppressed slightly in midwinter. The larger CP in winter than in autumn is consistent with both Chang (2001) and Zhao and Liang (2019). The most enhanced downstream extension of $V^{\prime }{T^{\prime }}_{850}$ in early winter (Fig. 1c) may be responsible for the early-winter peak of the spatially integrated CP. As shown later, CP is dominated by the component related to poleward eddy heat flux.

The climatological-mean barotropic conversion CK is systematically negative (Fig. 6b), indicating that EKE is converted into the mean westerlies, which is consistent with the acceleration of the midlatitude westerlies by transient eddies. More destructive (negative) CK in midwinter indicates stronger upper-tropospheric jet acceleration by transient eddies. The stronger negative feedback by eddies acting on a stronger westerly jet is consistent with results obtained through a dry quasigeostrophic model experiment by Robert et al. (2017).

The barotropic and baroclinic energy conversions from low-frequency variability to sub-weekly transients (CKLF and CPLF) are systematically negative and positive, respectively (Fig. 6b), yielding the slightly negative net energy conversion. Though relatively small, the magnitude of negative CKLF weakens around midwinter, acting to attenuate the midwinter suppression of the storm-track activity. The offsetting contributions between CKLF and CPLF are consistent with Lau and Nath (1991), who found that transient eddies along storm tracks act to reinforce monthly-mean circulation anomalies mainly through eddy vorticity fluxes while acting to weaken monthly-mean thermal anomalies. Differences in the relative amplitude of CKLF compared to CPLF between the present study and theirs can be attributable to different definitions of low-frequency variabilities.

The flux term EF is also negative throughout the cold season, indicating that eddy energy as a net is transported out of the NP storm track. It should be noted that there is still a relatively large positive remainder (∼10¹⁴ W in winter) in the energy budget of transient eddies, which is consistent with the previous studies (e.g., Chang et al. 2002). The remainder may be primarily due to dissipation associated with surface friction and gravity waves induced by orography, which was found to be quite effective (with time scale of less than 1 day) in the planetary boundary layer (Klinker and Sardeshmukh 1992).²

By definition, the energy conversion/generation terms are proportional to the squared amplitude of transient eddies. To avoid the dependence of those terms on eddy amplitude, it is vitally important to evaluate their normalized rates (λ) based on (4). Figure 6c indicates that λ_CP (red line) is much higher than λ_CK, λ_CQ, λ_EF, λ_CKLF, and λ_CPLF. We thus confirm that baroclinic eddy growth, especially through the poleward eddy heat flux (Fig. 7a), is of primary importance for maintaining the NP storm-track activity. The λ_CP is highest in early winter and then reduced somewhat in midwinter and further into early spring, which is consistent with the early-winter peak of the V′–T′ correlation in the mid and upper troposphere (Fig. 2b). Interestingly, λ_ET (purple line) maximizes in January, indicating that the internal conversion from EAPE to EKE is most effective in midwinter. It is mainly contributed to by the lower and midtropospheric ET, as seen in the ω′–T′ correlation (Fig. 4d). By contrast, λ_ET (light blue line) and λ_CK (blue line) are more destructive in early and midwinter than in spring, while λ_CQ (green line) is nearly constant throughout the cold season. The midtropospheric Q′–T′ correlation exhibits its midwinter maximum (green line in Fig. 4b), but its effect is offset by the MWM of the corresponding correlation in the upper troposphere (blue line) and autumn peak of the lower-tropospheric counterpart (black line) as well as the effect by vertical diffusion and radiative processes, as shown below.