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Seasonality and Synoptic Support of Stratiform Clouds in the Northeastern Pacific

Eyal Goldmann Division of Natural Sciences

El Camino College March 2017

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1. Introduction

On average, approximately 34% of earth’s oceanic surface is covered by low stratiform

clouds (i.e. stratus + stratocumulus + fog) (Warren, 1988). As these clouds have high albedos

while also radiating at near-surface temperatures, they have a strong cooling effect on earth’s

climate, and have thus been the subject of much modeling and observational study.

As shown in Figure 1 (Klein and Hartmann, 1993), oceanic stratiform coverage is highly

dependent on season and region. Especially strong stratiform coverage in the JJA seasonal average

(Figure 1a) occurs in the North Atlantic, and in eastern oceanic regions near the coasts of southern

Africa and South America. In the North Pacific, the JJA plot shows a strong stratiform band

covering nearly the entire midlatitude ocean, and a protruding band reaching southward along the

west coast of North America. As we shall see later, this protruding region coincides roughly with

the northerly branch of the semipermanent North Pacific anticyclonic circulation.

Figure 1: Seasonal mean global cloud amounts (a) JJA (b) DJF (Klein and Hartmann, 1993)

Comparison of the JJA and DJF plots in Figure 1 also reveals striking seasonal variation.

In the Northern Hemisphere, winter cloud amounts in the dominant stratiform regions decrease by

about one-third from summer to winter. (The Peruvian and Namibian stratiform regions peak in

the Southern spring (Klein and Hartmann, 1993).)

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In this article we will study the seasonality of marine clouds in the northeastern Pacific,

with particular attention to the “Californian stratus region” (Klein and Hartmann, 1993) abutting

the midlatitude and subtropical North American coast. A long history of observational studies and

modeling efforts focused on this region (e.g. Kloesel, 1992) makes it, in my view, a natural

starting point for understanding stratiform clouds in general, and their seasonality in particular.

We will begin our study in Section 2 with an overview of marine boundary layer (MBL)

thermodyanmic structure and low clouds in the northeastern Pacific, with a focus on their seasonal

variation. Then in Section 3 we will explore how MBL clouds are supported by and interact with

MBL thermodynamic structure. In Section 4, we tie these threads together by demonstrating that

the seasonal thermodynamics of the northeastern Pacific’s MBL, and thus its seasonal cloud

coverage, may be understood as consequences of synoptic-level seasonal variation in the Northern

Pacific and continental North America.

2. Seasonal Cycles in Northeastern Pacific Marine Boundary Layer Clouds

We begin our study by examining the seasonality of both MBL clouds and MBL

thermodynamic structure in the northeast Pacific.

Figure 2(a,b) (Lin et al., 2009) compares summer and winter cloud cover and in-cloud

liquid water path in this region. A striking seasonal contrast is clearly evident: While winter cloud

amount is mostly less than 65%, the summer cloud amount exceeds 75% over much of the area

shown. In-cloud water in summer exceeds that in winter by 50-100%.

Figure 2 (c), a cross-section along the line shown in Figure 2 (a), compares summer and

winter low cloud amount and in-cloud water as a function of distance from the coast. We see

clearly that the low-cloud seasonality of coastal California extends well into the ocean.

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Figure 2 (d,e), also from Lin et al., compares the summer and winter heights of the

boundary layer capping inversion. The winter inversion is relatively high, greater than 1000 m

over most of the plot area, and shows relatively weak spatial structure. By contrast, the summer

inversion height starts at about 500 m near the coast, and increases steeply, reaching 1000 m about

100 km from the coast, then increasing more gradually, reaching about 2000 m near the Hawaiian

islands outside of the plot area (Neiburger, 1960).

The rightmost two columns in Figure 2 offer seasonal comparisons of two stability

indicators: lower tropospheric stability (LTS), the potential temperature difference between 700

and 1000 hPa; and inversion strength (IS), the temperature difference between the top and bottom

of the inversion. Of the two, LTS shows a more pronounced seasonal variation, being

substantially stronger in summer than in winter (by about 5K near the coast and as much as 8K

over the ocean). The summer LTS also shows a clear gradient structure absent in the winter. The

IS is rather less seasonal that the LTS, being at most about 2K greater in the summer than in the

winter, with this difference gradually decreasing to zero with distance from the coast.

For another perspective, vertical profiles of several lower-tropospheric thermodynamic

properties measured in summertime coastal California in the presence of a thin cloud layer just

beneath the inversion are shown in Figure 3(Albrecht et al., 1985). These include profiles of

potential temperature θ, water vapor mixing ratio q, and equivalent potential temperature θe. As we

might expect, θ increases and q decreases going upward through the inversion. The decrease of θe

upward through the inversion is a result of the decrease in q.

The implications of these profiles will be explored in the next section, when we discuss

theoretical work which attempts to explain the connections between MBL thermodynamic

structure and MBL cloud structure.

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distance (km) distance (km)

(j)

(i)

(h)

(g)

(f) (d)

(e)

(c) (k)

Figure 3 : Lower troposphere profiles of potential temperature, mixing ratio, and equivalent potential temperature. Data taken June 5, 1976. From Albrecht et al. (1985).

Figure 2: Upper row: JJA mean; middle row: DJF mean; bottom row: cross section through segment in (a), with origin at coast. (a,b,c) low cloud amount (d,e) inversion height (f,g,h) lower-tropospheric stability, uses upper color scale (i,j,k) inversion strength, uses lower color scale. Assembled from several figures in Lin et al., 2009.

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3. Modeling of the Cloud-topped MBL

The basic physical processes driving MBL stratiform cloud development were described in

a landmark paper by Lilly (1968), whose work has been a basis for essentially all subsequent

modeling of this problem. The essential elements follow:

1. Moisture from the ocean evaporates into the boundary layer, and is carried up towards the inversion by turbulence-driven mixing.

2. In the initial stages of cloud formation, moisture carried upward is deposited directly beneath the

inversion. Thus, the cloud layer begins to form just beneath the inversion and grows downward. 3. Once the cloud layer has begun to form, radiative cooling of the cloud top destabilizes the mixed layer,

and drives continued mixing and cloud growth.

Lilly also describes a mechanism for destabilizing the cloud layer, which has come to be

known as Cloud-Top Entrainment Instability (CTEI) (Deardorff, 1980). CTEI is initiated when a

parcel of dry air above the cloud layer is mixed downward into the cloud. Initially, the mixed

parcel is unsaturated, and thus cools as liquid water mixed into the parcel evaporates. If the mixed

parcel then sinks due to the cooling – i.e. “buoyancy reversal” – the cloud layer is expected to

continue entraining the dry air above until the cloud has evaporated completely. A strong

inversion is expected to prevent CTEI by stabilizing the cloud against entrainment of the overlying

air.

Much subsequent work has been invested in developing quantitative criteria which predict

whether a particular inversion structure will be sufficient to prevent CTEI. These criteria are

usually expressed in terms of a stability parameter κ, defined as

𝜅𝜅 = 𝑐𝑐𝑝𝑝∆𝜃𝜃𝑒𝑒𝐿𝐿Δ𝑞𝑞𝑡𝑡

≅ 1 + 𝑐𝑐𝑝𝑝∆𝜃𝜃𝑙𝑙𝐿𝐿Δ𝑞𝑞𝑡𝑡

, (1)

which must be less than a critical value κc, i.e.

𝜅𝜅 < 𝜅𝜅c. (2)

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In Eq. (1), ∆𝜃𝜃𝑒𝑒, ∆𝜃𝜃𝑙𝑙 and Δ𝑞𝑞𝑡𝑡 are, respectively, the inversion-bottom to inversion-top

changes in equivalent potential temperature, liquid water potential temperature, and total (i.e.

liquid + vapor) water mixing ratio across the inversion; 𝑐𝑐𝑝𝑝 is the constant-pressure specific heat;

and L is the latent heat of vaporization. (𝜃𝜃𝑙𝑙 is the potential temperature attained by compressing a

parcel adiabatically until all of its liquid water content has evaporated (Betts, 1973).) This

standard form of the stability criterion was first introduced by Kuo and Schubert (1988), closely

following earlier work by Deardorff (1980) and Randall (1980)). Recall from Figure 3 that across

a stable inversion, ∆𝜃𝜃𝑒𝑒 < 0, ∆𝜃𝜃 > 0, and Δ𝑞𝑞𝑡𝑡 < 0. We may infer that ∆𝜃𝜃𝑙𝑙 > 0 across a stable

version, as ∆𝜃𝜃𝑙𝑙 ≈ ∆𝜃𝜃 (Wood, 2012). See also Stevens et al. (2007) for a typical vertical profile of

∆𝜃𝜃𝑙𝑙 in a cloudy MBL.

The meaning of Eqs. (1) and (2) is perhaps most transparent when we consider the second

expression in Eq. (1), i.e. 𝜅𝜅 ≈ 1 + 𝑐𝑐𝑝𝑝∆𝜃𝜃𝑙𝑙𝐿𝐿Δ𝑞𝑞𝑡𝑡

. Since Δ𝑞𝑞𝑡𝑡 < 0, an increase in ∆𝜃𝜃𝑙𝑙, i.e. greater inversion

strength, reduces 𝜅𝜅 and thus increases the likelihood that the criterion in Eq. (2) is met.

3.1. Experimental tests of CTEI criteria and subsequent revision

A substantial literature of (attempted) verification, falsification, and modification has

grown up around the ideas in Lilly’s 1968 study.

To begin with, a number of studies have shown strong correlation between lower-

tropospheric thermodynamic structure and cloud coverage. Klein and Hartmann’s (1993)

benchmark result plotting stratiform cloud amount vs. LTS, using data from a number of global

stratiform cloud regions, is shown in Figure 4(a). As the figure itself points out, r2 = 0.88 indicates

a strong correlation between these quantities.

Klein and Hartmann’s concept was further developed by Wood and Bretherton (2006), who

introduce as a stability parameter the “estimated inversion strength”,

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EIS = LTS − 𝛤𝛤𝑚𝑚850(𝑧𝑧700 − LCL), (3)

which estimates the inversion strength in terms of LTS, the moist adiabatic lapse rate at 850 hPa

𝛤𝛤𝑚𝑚850, the 700-hPa height 𝑧𝑧700, and the lifting condensation level (LCL).

Wood and Bretherton’s regression of EIS with cloud coverage using global data, shown in

Figure 4, has a correlation coefficient of 0.92.

Figure 4: (a) Low-cloud amount vs. lower-tropospheric stability (Klein and Hartmann, 1993) (b) Low-cloud amount vs. estimated inversion strength. Low cloud regions indicated include Peruvian(P), Namibian(N), Californian(C), Australian(A), Canarian(Ca), North Pacific(Pa), North Atlantic(At), China(Ch) (Wood and Bretherton, 2006).

The story becomes more complicated when we try to understand why inversion strength is

connected to low-cloud structure. The usual narrative that inversion strength protects against

CTEI has its standard quantitative expression in Eqs. (1) and (2). And yet, the evaluation and

even appropriateness of these has been a longstanding source of angst in the literature.

Initially, Kuo and Schubert (1988) found 𝜅𝜅𝑐𝑐 = 0.23. However, they also found that this

criterion is overly restrictive, as observed stratiform MBL clouds often have 𝜅𝜅 > 0.23 (see also

Stevens et al., 2003).

The earliest responses to this failure of Eqs. (1) and (2) included attempts to recalculate 𝜅𝜅𝑐𝑐

as well as to formulate qualitatively different stability criteria. MacVean and Mason (1990), for

instance, stipulate that turbulence generated by buoyancy reversal distributes itself through the

cloud layer rather than remaining at the inversion where it can generate more turbulence. Their

(a) (b)

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analysis leads to 𝜅𝜅𝑐𝑐 ≅ 0.70, which appears to be an overly weak stability criterion, as observed

stratiform clouds rarely have values of κ this large (e.g. Duynkerke, 1993).

Another weakened stability criterion is due to Duynkerke (1993), who argues that an

entrained parcel will gradually change its properties as more of the cloudy air mixes into it, and

thus formulates a stability criterion based on an integral of the parcel buoyancy during the mixing

process. This too leads to a stability criterion less restrictive than 𝜅𝜅𝑐𝑐 = 0.23.

Several recent modeling studies suggest that 𝜅𝜅 ≈ 0.23 marks a gradual transition to

reduced cloudiness rather than an absolute existence criterion. For example, Yamaguchi and

Randall (2008), using large-eddy simulations, find that the stability criterion of Eqs. (1) and (2)

with 𝜅𝜅𝑐𝑐 = 0.23 is indeed an excellent predictor of CTEI. However, CTEI so predicted may

require several hours to evaporate the cloud, and can be offset by cloud-building processes. Other

studies (e.g. Moeng (2000), Lock (2009), Yue (2013)) find that a transition from complete cloud

cover to gradually decreasing cloud cover occurs when 𝜅𝜅 ≈ 0.2, with cloud cover having largely

vanished when 𝜅𝜅 ≈ 0.4.

This is but a partial recounting of attempts to reconcile the CTEI concept with observation,

and active study continues in the literature. See e.g. Wood (2012) for a recent review.

4. Relation between synoptic-level seasonality and low-cloud seasonality in the northeastern

Pacific

In the previous two sections, we have laid substantial groundwork for understanding the

seasonality of low clouds in the northeastern Pacific. In Section 2, we discussed the seasonality of

this region’s MBL clouds and MBL thermodynamic structure. In Section 3, we discussed work

which attempts to explain, in general, the connection between MBL clouds and MBL

thermodynamic structure. Ideally, the next step would be to connect the seasonality of MBL

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thermodynamic structure in the northeastern Pacific to the region’s synoptic seasonality,

completing chain of causality connecting low-cloud seasonality to the larger seasonal cycle.

There does, however, appear to be a missing link in the literature. It is frequently asserted

(e.g. Kloesel 1992) that synoptic-level subsidence strengthens boundary-layer inversions by

supplying adiabatically compressed and heated air to the inversion top, thus promoting cloud

coverage. However, explicit demonstrations of this, or references to such, do not seem to appear

in the low-cloud literature. Rather, the subsidence-inversion strength connection is inferred from a

large body of observational work (e.g. Lau and Crane 1997; Norris and Klein 2000) demonstrating

correlation between regions of upper-level subsidence and low-cloud fraction, with inversion

strength inferred as an intermediary. (For an illustration of the complexities associated with this,

see Myers and Norris (2013), who argue that cloud coverage anticorrelates with subsidence when

inversion strength is controlled for!) Consider for instance Kubar et al.’s (2012) global

comparison of 500-hPa subsidence with low-cloud fraction, shown in Figure 5. Of the five major

subsidence regions apparent in Figure 5(a), only the eastern North Atlantic near the west African

coast is not associated with a major low-cloud area. Conversely, each of the major low-cloud

regions occurs in a region of strong subsidence. Accepting then, perhaps skeptically, the usual

assumed connection between subsidence and inversion strength, we proceed to examine synoptic-

level drivers of subsidence in the northeast Pacific.

4.1. Synoptic structure of the northeastern Pacific stratiform cloud region

As previously discussed, marine low cloud structure is associated with synoptically driven

subsidence which (presumably) maintains and strengthens the capping inversion atop the MBL. In

this subsection we will examine both surface-level divergence and 500 hPa vertical velocity as

indicators of subsidence in the northeastern Pacific, and connect these with MBL clouds in the

following subsection.

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Figure 5: Notice the coincidence between regions of upper-level subsidence and low cloud fraction (a) 8-year mean 𝜔𝜔500 (Pa/s) (b) 8-year mean low-cloud fraction. (Kubar et al., 2012)

The main driver of low-level circulation in the summertime northeastern Pacific is the

semipermanent North Pacific High (NPH), which is itself strongly seasonal, weakening

substantially and moving southward in the winter (e.g. Bograd et al., 2002). Summertime

circulation around the NPH, shown in Figure 6(a) (Klein et al., 1995) includes northerly flow

which closely follows the California coast, and then turns to merge with the easterly trade winds.

Seasonally-averaged streamlines and surface divergence (Neiburger, 1960) are also

included in Figure 6(b,c). Notice that the strongest surface divergence occurs near the U.S. coast,

towards the north end of the protruding band of low marine clouds shown in Figure 1(a).

500 hPa circulation in the summertime northeastern Pacific lacks a clear dominant feature

such as the surface-level NPH. Consider however, Figure 7(a) (Adams and Comrie, 1997), which

shows the summertime 500 hPa surface over both the eastern Pacific and western North America.

Key features in this Figure include a trough situated near the U.S. west coast, and an anticyclonic

circulation, known as the North American Monsoon, centered over northern Mexico. In Figure

7(b) (Higgins et al., 1997), we see that merging of the southerly flow west of the anticyclone

center with the midlatitude westerlies results in substantial convergence off the U.S. west coast.

Figure 7(c) (ibid) shows a strong center of downward 500 hPa vertical velocity in the same region,

only slightly to the north of the center of surface divergence in Figure 6(c). It seems plausible that

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the continental anticyclone acts as an upper-level driver of subsidence, consistent with the

observation of Stevens et al. (2007) of a positive correlation between the continental anticyclone

strength and low-level marine clouds.

Figure 6: Mean (a) surface pressure, temperature and winds (b) streamlines (c) surface divergence associated with North Pacific High. (a) is June-September mean (Klein et al. 1995), (b,c) are July mean (Neiburger, 1960).

Figure 7: Mean 500 hPa (a) geopotential height (b) wind field (specific humidity is not discussed in this article) (c) vertical velocity. (a) is July/August mean (Adams and Comrie, 1997) (b) is JJA mean (Higgins et al., 1997) 4.2. Connection between Synoptic Structure and Low Clouds in the Northeastern Pacific

Several observational studies focused on the northeast Pacific have examined correlations

between synoptic motion and low cloud structure. Klein (1997) composited sea level pressure and

surface wind fields associated with nighttime observations of low-level clouds at ocean weather

station November (30ºN 140ºW). Figure 8 (a,b) shows the composited surface fields when

nighttime low cloud amounts are respectively < 0.55 and > 0.90, and Figure 8 (c) shows “(cloudy

surface divergence) minus (not-cloudy surface divergence).” Panels (a) and (b) show a clear

(a)

(b) (c)

(a)

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strengthening of the NPH in association with increased cloudiness, and panel (c) shows a clear

increase in the associated surface divergence towards the north end of the coastal low-cloud

region.

Figure 8: (a) Surface pressure and wind for low-cloud amount < 0.55 (b) for low-cloud amount > 0.90 (c) (surface divergence when low--cloud amount > 0.90) minus (surface divergence when low-cloud amount < 0.55). Composited from multiyear June-September data (Klein, 1997).

Figure 9: Mean LCF on days when (a) 𝜔𝜔500 >(b) , when 𝜔𝜔500 < 0. (c) 15-day correlation between 𝜔𝜔500 and low-cloud fraction. (Kubar et al., 2012)

Turning now to upper-level synoptic structure, consider Kubar et al.’s (2012) global

comparison of low-cloud fraction (LCF) associated with 500-hPa sinking motion vs. 500-hPa

rising motion, shown in Figure 9. We see that nearly everywhere, the LCF is greater in the

presence of upper-level descent. The decrease between these cases is greater in the Californian

low-cloud region than in any other major low-cloud region. On shorter time scales of one, five,

and 15 days however, Kubar et al. find that correlations between 500-hPa vertical pressure velocity

(a) (b) (c)

(a) (b)

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ω500 and LCF tend to be weaker in several major low-cloud regions, including near California,

than over most of the ocean. They attribute this to the inversion typically being so low in these

regions that additional subsidence may push the inversion beneath the LCL. The 15-day

correlation result is shown in Figure 9(c).

Figure 10: Correlation between LCF and 𝜔𝜔500 near the Washington-Oregon coast. (a) Scatter plot relating monthly means of these values with an exponential fit (b) Time series relating 3-month running means. (Kubar et al., 2012)

Finally, consider Kubar et al.’s examination of the correlation between LCF and 𝜔𝜔500 near

the Oregon and Washington coast (125-135W, 40-50N), just north of the coastal low-cloud center

near California. Figure 10(a) plots monthly-mean LCF as a function of monthly-mean 𝜔𝜔500 for

this region. A simple exponential fit matches the scatter plot with r = 0.91. (Similar anlyses for

three other major low cloud regions also show strong correlations.) Additionally, a time series of

the three-month running means of these quantities, shown in Figure 10(b), shows a close

coincidence between the seasonal cycling of LCF and 𝜔𝜔500.

In sum, the surface- and upper-level studies reasonably demonstrate that low cloud

structure in the northeast Pacific is supported and strengthened by synoptically driven subsidence.

By the usual inference, the intermediary between these is the boundary layer inversion, which is

strengthened by the subsidence and in turn supports low-cloud development.

(a) (b)

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5. Discussion

Taken as a whole, the studies reviewed in this paper demonstrate a causal connection

between large-scale seasonal cycles and the seasonality of low marine clouds in the northeastern

Pacific: Seasonal changes in North Pacific and North American synoptic structure drive

subsidence over the Pacific Ocean near the U.S. and Mexican west coasts. Increasing subsidence

during the summer is presumed to strengthen the inversion atop the MBL, which in turn stabilizes

and supports cloud development.

Of the various steps in this causal chain, the relationship between subsidence and inversion

strength is most poorly understood. The persisting uncertainty in this issue appears to stem from

difficulty measuring and modeling the entrainment velocity, i.e. the rate at which subsiding air is

incorporated into the cloud top. Although observational studies have made some progress in

measuring the entrainment velocity (Wood and Bretherton, 2004), numerical models obtain widely

varying values of the entrainment velocity, even when the models are identically initialized

(Moeng, 1996; Stevens 2002).

In general, the long-term development of MBL cloud science evinces a remarkable

contrast: The overall conceptual framework has been largely stable since Lilly’s 1968 study, but

turbulence persists in the understanding of many crucial details, such as the mechanism by which

the cloud destabilizes, for which CTEI has long been a leading, if controversial candidate; and the

modeling of the entrainment velocity, which is a prerequisite for properly understanding synoptic

driving of the cloud system. Given the importance of marine low-cloud systems, climatological

and otherwise, work on these problems will surely continue.

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