Impact of Nocturnal Low-Level Jets on
Surface Turbulence and Fluxes
by
Henrique Ferro Duarte
(Under the direction of Monique Y. Leclerc)
Abstract
The effect of low-level jets (LLJs) on surface turbulence and fluxes in the nocturnal
stable boundary layer is investigated by using extensive sodar and tower observations from
two experimental sites in the United States. Surface turbulence and fluxes are found to be
typically stronger and more structured during LLJs, not corroborating the shear-sheltering
theory. Results from a turbulence kinetic energy budget analysis indicate a reasonable
contribution by the pressure transport term during LLJs, possibly related to an interaction
between LLJs, gravity waves, and turbulence. Turbulence statistics are found to follow
Monin-Obukhov similarity/z-less theory very well during LLJs, in general. Under very stable
conditions, however, the results indicate a departure from local similarity, possibly associated
with the input of non-local turbulence via pressure transport. The findings are of relevance
for observational and modeling studies of the nocturnal stable boundary layer, including
studies of surface-atmosphere exchange and pollutant dispersion.
Index words:
Low-level jets, Stable boundary layer, Turbulence and fluxes,
Eddy-covariance technique
Impact of Nocturnal Low-Level Jets on
Surface Turbulence and Fluxes
by
Henrique Ferro Duarte
B.Sc., Universidade Federal do Paraná, Brazil, 2004
M.Sc., Universidade Federal do Paraná, Brazil, 2006
A Dissertation Submitted to the Graduate Faculty
of The University of Georgia in Partial Fulfillment
of the
Requirements for the Degree
Doctor of Philosophy
Athens, Georgia
2014
c
2014
Henrique Ferro Duarte
All Rights Reserved
Impact of Nocturnal Low-Level Jets on
Surface Turbulence and Fluxes
by
Henrique Ferro Duarte
Approved:
Electronic Version Approved:
Maureen Grasso
Dean of the Graduate School
The University of Georgia
May 2014
Major Professor:
Monique Y. Leclerc
Committee:
David E. Stooksbury
Robert O. Teskey
Ian D. Flitcroft
Robert J. Kurzeja
Dedication
I dedicate this dissertation to my wife, Cristiane Barbosa de Lira, my parents, Carlos Augusto
Duarte and Maristela Barbosa Ferro, and sisters, Alice Barbosa Duarte and Daniela Ferro
Gil, for all the support during this journey.
iv
Acknowledgments
I would like to thank my advisor, Monique Leclerc, for have given me the opportunity to
pursue my Ph.D. at the University of Georgia. Working with her and her team was an
enriching experience in both professional and personal levels, and I am very grateful.
I would like to thank my advisory committee — Monique Leclerc, David Stooksbury,
Robert Teskey, Ian Flitcroft, and Robert Kurzeja — for their availability and feedback on
my research and dissertation.
Many thanks go to my lab friends David Durden, Gengsheng Zhang, Natchaya Pingintha,
Luciana Pires, Chompunut Chayawat, David Cotten, and Jasmine VanExel. I learned so
many things from them in the field, in the lab, and during seminars and classes... they made
this journey easier.
I would like to thank Robert Kurzeja, Matt Parker, and David Werth for the discussions
on my research and for the operational support during the experiment at the Savannah River
Site.
I would like to thank Nelson Dias for the discussions on my research and for all the
encouragement. I am very grateful.
I would like to thank the U.S. Department of Energy – TCP Program and the University
of Georgia for funding this research. I would like to specially thank Miguel Cabrera and
Monique Leclerc for the funding extension in my last year in the program, allowing me to
finalize this dissertation.
v
During my stay in the United States I had the help of many people. I would like to
thank my great friend David Durden and his wonderful family, and also Jerry and Marilyn
Johnson and Mahdi Gheysari for all their help and generosity. I also would like to thank my
friend Kranti Yemmireddy for being there when I needed the most.
Finally, I would like to thank my wife Cristiane Barbosa de Lira for being there throughout this whole journey and for being such a blessing in my life. I also would like to thank
my parents, Carlos Augusto Duarte and Maristela Barbosa Ferro, and sisters, Alice Barbosa Duarte and Daniela Ferro Gil, for all the love, support, and encouragement during my
studies away from my home land.
vi
Contents
Acknowledgments
v
List of Figures
ix
List of Tables
xii
1 Introduction and Literature Review
1
1.1
Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.2
Goal and Structure of This Dissertation . . . . . . . . . . . . . . . . . . . . .
12
2 Assessing the Shear-Sheltering Theory Applied to Low-Level Jets in the
Nocturnal Stable Boundary Layer
14
2.1
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
2.2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
2.3
Measurements and Signal Processing . . . . . . . . . . . . . . . . . . . . . .
18
2.4
Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
2.5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
2.6
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
3 Impact of Nocturnal Low-Level Jets on Surface Turbulence Kinetic Energy 44
3.1
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
45
3.2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
3.3
Measurements and Data Processing . . . . . . . . . . . . . . . . . . . . . . .
53
3.4
Low-Level Jet Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
3.5
Turbulence Kinetic Energy Budget . . . . . . . . . . . . . . . . . . . . . . .
61
3.6
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
3.7
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
4 Conclusions
77
References
80
viii
List of Figures
2.1
Experimental site and instrumentation overview: a eddy covariance tower, b
boundary layer sodar, and c general view of the site . . . . . . . . . . . . . .
2.2
20
Scatterplot of turbulence kinetic energy as a function of the Monin-Obukhov
stability parameter. Points are segregated in three groups: strong Sj , weak
Sj , and no LLJ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3
29
Scatterplot of friction velocity as a function of the Monin-Obukhov stability
parameter. Points are segregated in three groups: strong Sj , weak Sj , and no
LLJ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4
29
Scatterplot of sonic sensible heat flux as a function of the Monin-Obukhov
stability parameter. Points are segregated in three groups: strong Sj , weak
Sj , and no LLJ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5
30
Scatterplot of a turbulence kinetic energy, b friction velocity, c sonic sensible
heat flux, d CO2 flux, e shear-sheltering parameter using jet shear, and f
shear-sheltering parameter using wind shear between 5 and 10 m levels, as
a function of jet shear. Bullets and circles correspond to the strong- and
weak-Sj groups respectively . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
31
2.6
Comparison between shear-sheltering parameters Σj,a and Σj,b , calculated
using jet shear (Sj ) and local shear close to the surface (S10,5 ) in the denominator of Eq. 2.1, respectively. Bullets and circles correspond to the strongand weak-Sj groups, respectively . . . . . . . . . . . . . . . . . . . . . . . .
2.7
32
Mean spectra of a streamwise, b lateral, and c vertical velocity components,
d sonic temperature, and e CO2 concentration, and mean cospectra of vertical
velocity with f streamwise velocity, g sonic temperature, and h CO2 concentration. Bullets, circles, and crosses correspond to the groups of strong Sj ,
weak Sj , and no LLJ, respectively. The black line corresponds to the equations of Kaimal et al. (1972) for spectra and cospectra (Eqs. 2.6 and 2.7 in
the present paper) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
2.7
(cont) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.8
Mean streamwise velocity spectra obtained by Smedman et al. (2004, data
points extracted from their Fig. 7a). The LLJ spectrum (filled triangles) is
the mean of 118 half-hour spectra where a wind maximum was present at
low levels; the No-LLJ spectrum (open triangles) is the mean of 56 half-hour
spectra for cases without such wind maximum. The curve labeled Kaimal
correspond to the equation of Kaimal et al. (1972) for spectra (Eq. 2.6 in the
present paper) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
40
(a) Site location in the United States, (b) local topography map, and (c) local
satellite view (source: Google Earth; imagery date: 10/05/2010) showing land
use. The location of the tall tower (T) and the Remtech sodar (R) are indicated. 54
3.2
The Savannah River National Laboratory (SRNL) instrumented tall tower
used in the study. The two lowest eddy-covariance systems (34 and 68 m
levels) can be observed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
55
3.3
Histograms of (a) low-level jet height, (b) speed, and (c) direction for the
700 jet events (30-min profiles) observed during May–July/2009, 20:00 to
05:00 EST. These events are associated with continuous jet activity (minimum
duration of two hours) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4
59
Composite wind speed profile for all low-level jet events considered in this
study. LLJ speed and height are used as scaling parameters. Error bars
indicate ±1 standard deviation . . . . . . . . . . . . . . . . . . . . . . . . .
3.5
60
Normalized TKE budget terms as a function of stability for the LLJ group:
(a) shear production, (b) dissipation, (c) pressure transport, and (d) turbulent
transport. Blue points are bin averages, and error bars correspond to ±1
standard deviation. Purple curves correspond to least-square fitting for data
points up to ζ = 1
3.6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Normalized TKE budget terms for the LLJ group. Points correspond to the
bin averages shown in Fig. 3.5 . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7
63
64
Normalized TKE budget terms as a function of stability for both the LLJ
(green circles) and NO-LLJ (black circles) groups: (a) shear production, (b)
dissipation, (c) pressure transport, and (d) turbulent transport . . . . . . . .
3.8
66
Normalized TKE budget terms for the NO-LLJ group. Points correspond to
the bin averages of the data points shown in Fig. 3.7 . . . . . . . . . . . . .
xi
67
List of Tables
1.1
Observational and modeling studies reporting results on the pressure and turbulent transport terms (Tp and Tt respectively) of the TKE budget during
low-level jet conditions. Heights are given in meters above the surface. Shr
and D correspond to the shear production and dissipation terms, respectively.
8
1.1
(cont) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
2.1
Low-level jet statistics for the nocturnal periods considered (21:00 to 06:00
CDT). Hj , Uj , DIR, and Sj correspond to LLJ height, speed, direction, and
shear, respectively. N is the number of LLJ events (30-min profiles). Values
outside and inside the brackets are the averages and ranges within the periods,
respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
25
Statistics of eddy covariance and LLJ data are presented for the groups of
strong jet shear, weak jet shear, and no LLJ, in the format average±SD [range] 27
2.3
Approximate f /f0 interval corresponding to (co)spectral enhancement for the
strong-jet-shear group (Fig. 2.7) and corresponding f and eddy length scale
(λ) intervals, estimated based on the mean f0 values obtained for the group
(Table 2.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xii
38
3.1
Observational and modeling studies reporting results on the pressure and turbulent transport terms (Tp and Tt respectively) of the TKE budget during
low-level jet conditions. Heights are given in meters above the surface. Shr
and D correspond to the shear production and dissipation terms, respectively. 50
3.1
(cont) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2
Statistics of the low-level jet events (30-min profiles) observed in May–July/2009,
51
20:00 to 05:00 EST. Each event is associated with continuous jet activity (minimum duration of two hours). Number of continuous NO-LLJ runs is also shown. 58
3.3
Near-surface turbulence statistics (34 m data) for the LLJ and NO-LLJ groups,
for ζ[0 : 10]. N is the number of 30-min runs in each group . . . . . . . . . .
xiii
68
Chapter 1
Introduction and Literature Review
Low-level jets —hereafter also referred to as LLJ— are a common feature of the nocturnal
stable atmospheric boundary layer, consisting of a thin layer of strong winds located usually between 100 and 300 meters above ground level, with maximum wind speeds typically
between 10 and 20 m s−1 (Stull 1988).
The “low-level jet” term was first used by Means (1952), but so far there is no unique and
exact definition for the phenomenon, given the fact it can be originated from many different
atmospheric processes and may present a variety of characteristics. While some authors
prefer to classify a wind speed maximum as a LLJ based on the background atmospheric
conditions (i.e., based on the formation mechanisms) and the shape of the wind speed profile,
others have a more pragmatic way for classification. Bonner (1968), Stull (1988), and Banta
et al. (2002), for example, classify a given wind speed maximum as a LLJ if the difference
between this wind speed maximum and the adjacent wind speed minima exceeds a certain
value (∼ 2 m s−1 in their studies). Thresholds based on the speed and height of the wind
speed maximum are also imposed in some studies.
Several mechanisms have been associated with the low-level jet formation. During nighttime over land, LLJs are typically formed (at least in part) by the Blackadar (1957) mech-
1
anism: after the evening transition from a convective to a stable boundary layer, the atmospheric flow detaches from the surface and undergoes an inertial oscillation, reaching supergeostrophic speeds later in the night, with maximum jet speeds occurring during predawn
hours. Baroclinicity, katabatic flows, and fronts are some of the other many possible causes
of low-level jet formation (Stull 1988).
LLJs are not a local phenomenon. According to Freytag (1978), LLJs may reach lengths
of 2000 km and widths of 400 km. They have been observed over all continents: North
America (e.g., Banta et al. 2002; Mathieu et al. 2005; Karipot et al. 2009), South America
(e.g., Vera et al. 2006), Europe (e.g., Kraus et al. 1985; Corsmeier et al. 1997; Foken et al.
2012), Africa (e.g., Todd et al. 2008), Asia (e.g., Wang et al. 2013), Oceania (e.g., May
1995), and Antarctica (e.g., Buzzi et al. 1997). Also, as mentioned above, LLJs are not a
rare phenomenon. They were detected in 30% of the soundings done by Bonner (1968), for
example. Karipot et al. (2009) reported an even higher number for their site in Florida:
they observed jet activity on 62% of the nocturnal periods analyzed. More recently, Rife
et al. (2010) used NCAR’s CFDDA (Climate Four Dimensional Data Assimilation) mesoscale
reanalysis to study the global distribution and properties of the nocturnal LLJs in particular.
They were able to produce the first quantitative global maps of LLJ activity. The LLJs were
found to be more concentrated within the ±30◦ latitudes, with more intense activity in
the northern hemisphere likely due to its larger land mass and higher land-sea temperature
contrast. In each hemisphere, more intense activity was found to occur during the summer.
Given its typical meso/synoptic scale, a LLJ can promote coherent transport over very
long distances overnight. The phenomenon has been associated with the long-range transport
of trace gases including water vapor, CO2 , and pollutants such as ozone (e.g., Corsmeier et al.
1997; Wu and Raman 1998; Sogachev and Leclerc 2011; Hong et al. 2012). The northward
transport of large amounts of water vapor from the Gulf of Mexico by the Great Plains
LLJ, for instance, can trigger thunderstorms in the northern Great Plains (Wu and Raman
2
1998). The long-range transport of spores and insects by LLJs has also been reported in the
literature (e.g., Zhu et al. 2006; Pivonia et al. 2005), being often times linked to outbreaks
of agricultural pests and diseases. The release of large quantities of mineral dust from the
Sahara desert and subsequent long-range transport has also been linked to LLJ activity
(Todd et al. 2008).
Given the enhanced wind shear created in the subjet layer, low-level jets are often a
significant source of turbulence in the nocturnal stable boundary layer (e.g., Mahrt et al.
1979; Smedman 1988; Mahrt 1999; Mahrt and Vickers 2002; Banta et al. 2002, 2003, 2006;
Karipot et al. 2006, 2008). Their potential to transport trace gases over several hundreds of
kilometers overnight and modulate surface turbulence and fluxes, coupled with their ubiquitousness, underscores the relevance of low-level jets to both the air pollution and flux
communities (Corsmeier et al. 1997; Karipot et al. 2006, 2008; Sogachev and Leclerc 2011).
The high wind speeds and shear associated with LLJs also have implications to wind energy
applications (e.g., Storm et al. 2009), aviation safety (e.g., Madougou et al. 2014), and forest
fires (e.g., Simpson et al. 2013).
The impact of LLJs on surface turbulence and surface-atmosphere exchange is the focus
of the present study. A literature review is presented in Sec. 1.1, and the goals and the
structure of this dissertation are discussed in Sec. 1.2.
1.1
Literature Review
The enhanced wind shear associated with low-level jets is often a significant source of turbulence in the nocturnal stable boundary layer, and such connection was made by Mahrt et al.
(1979). Based on Richardson number (Ri) profiles (Ri used as an indicator of turbulence),
they found a strong-turbulence layer delimited by the surface and the jet core. They defined
it as the “momentum boundary layer”.
3
In a traditional boundary layer, the surface is the main source of turbulence and the
turbulence transport is upward. Smedman (1988) found, however, that the wind shear near
a LLJ may create layers of strong turbulence aloft. This configuration, in which the main
source of turbulence is elevated and downward transport of turbulence occurs, was coined
“upside-down boundary layer” by Mahrt (1999). The same configuration was also observed
during the CASES-99 experiment (Mahrt and Vickers 2002; Banta et al. 2002; Balsley et al.
2006).
Also based on CASES-99 data, Banta et al. (2003) showed the possibility of linking
low-level jet properties (e.g., jet height and speed) with turbulence kinetic energy (TKE)
measured near the surface. They introduced a “jet Richardson number” using the subjet layer wind shear in the denominator, and reported a correlation between the proposed
dimensionless number and surface turbulence.
Banta et al. (2006) and Banta (2008) further investigated the structure of the stable
boundary layer in the presence of LLJs. For strong LLJs, weakly stable boundary layer,
their measurements indicated the presence of a traditional boundary layer structure, with
turbulence maximum at the surface. For slightly increased stabilities (bulk/jet Ri), they
noticed the migration of the turbulence maximum from the surface to the layers above, i.e.,
upside-down structure. With a further increase in stability, they observed the occurrence of a
transitional regime, characterized by downward turbulence transport in intermittent bursts.
In this regime the LLJs are intermittent: the turbulence created reattaches the flow to the
surface causing the jet to dissipate; after stabilization the flow accelerates again, forming
the jet and restarting the cycle (cycle also demonstrated in the wind-tunnel experiment by
Ohya et al. 2008). With the bulk/jet Ri past the critical point, they observed a collapse of
the stable boundary layer. This strongly stable regime was characterized by weak winds and
weak/intermittent turbulence.
4
1.1.1
TKE Budget and Monin-Obukhov Similarity
The turbulence kinetic energy (TKE) budget in the surface layer has been studied within
the framework of Monin-Obukhov similarity theory (MOST) for many years (Wyngaard
and Coté 1971; Högström 1990; Oncley et al. 1996; Frenzen and Vogel 2001; Li et al. 2008).
However, as Li et al. (2008) pointed out, many uncertainties still remain, specifically on the
role of the transport terms. The classical assumption is that turbulence is locally balanced,
i.e. the transport terms are either negligible or they cancel each other (McBean and Elliot
1975). However, experimental results have challenged this assumption, showing evidence of
local imbalance and underscoring the role of the transport terms (e.g., Högström 1990, 1992;
Frenzen and Vogel 2001; Li et al. 2008). These studies have reported cases of either excess or
insufficient local dissipation, being associated with either TKE gain or loss via the transport
terms respectively. The reason for these differences is still an open question (Li et al. 2008).
This is especially true for stable conditions (Pahlow et al. 2001) where turbulence is sensitive
to stable boundary layer features such as low-level jets, gravity waves, density currents, and
Kelvin-Helmholtz shear instability (Cheng et al. 2005).
The TKE budget in the atmospheric boundary layer under the effect of LLJs was investigated in a few studies (Table 1.1). These studies were conducted for different sites, jet types,
and stability conditions. The majority of these studies points out that pressure transport
plays an important role in the budget near the surface, but at present, there does not appear
to be a consensus on whether the pressure transport term acts as a sink or source term.
Smedman et al. (1993, 1994) used aircraft slant profile data collected over the Baltic Sea
(near the southeastern Swedish coast) in their analysis. LLJs were present at heights from
500 to 1500 m, formed by frictional decoupling of the flow due to low sea surface temperatures
(a process analogous to the formation of a nocturnal LLJ over land), and stability was near
neutral. In Smedman et al. (1993), the pressure transport term was found to be an important
source term in the layers from the base to the top of the LLJ, with larger values at the base
5
of the LLJ, where shear production was a maximum. In the particular case analyzed by
Smedman et al. (1994), maximum shear production was also observed at the base of the
LLJ, but in the same layer the pressure transport term was a sink. At lower layers down to
the surface, the latter was a large source term. They suggested that the pressure transport
term was responsible for bringing TKE from the layer of maximum shear production (at the
jet base) down to the surface. They also suggested that the turbulence transported towards
the surface was “inactive” turbulence (large scale fluctuations – see Högström 1990), helping
to promote mixing in the subjet layer but not producing shear stress directly.
At a different site over the Baltic Sea (Stockholm archipelago), Smedman et al. (1995)
analyzed the TKE budget for cases characterized by weakly/moderately stable stratification
and much lower LLJs (core at 30 to 150 m ASL). Tower data collected at 8 and 31 m above
the surface were used. In this case, maximum shear production was found closer to the
surface (8 m level), and at the same level the pressure transport term was a sink. At the 31
m level the latter was a source term. They concluded that TKE was transported upwards
by the pressure transport term, away from the layer of maximum shear production (this idea
in agreement with Smedman et al. 1994).
Bergström and Smedman (1995) used data from the same site (Smedman et al. 1995)
and analyzed the TKE budget for cases with similar stability but without the presence of a
LLJ. They found the pressure transport term to be a source at the 8 m level, and suggested
that this was the result of the transport of “inactive” turbulence from upper layers in the
boundary layer towards the surface. Contrary to the pressure transport term, the turbulent
transport term was found to be small in the studies discussed so far (Smedman et al. 1993,
1994, 1995; Bergström and Smedman 1995).
Over land (SE Kansas, USA), Cuxart et al. (2002) also found important contributions
by the pressure transport term in the near-surface TKE budget for a night characterized by
strong stratification and LLJ activity (jet height from 100 to 200 m AGL). They observed
6
that, in a layer from 1.5 to 30 m AGL, the pressure transport was a relevant sink, coinciding
with maximum shear production. In a layer from 30 to 50 m AGL, the pressure transport
was a relevant source term. Their results, similarly to Smedman et al. (1995), indicate that
TKE was exported away from a layer of maximum shear production near the surface by
the pressure transport term. Cuxart et al. (2002) observed relevant contributions by the
turbulent transport term as well, but its behavior was not well defined (i.e., regarding the
orientation of the transport, away from or towards the surface).
The TKE budget under low-level jet conditions has also been studied based on numerical
simulation data. A coastal LLJ in northern Chile was modeled via MM5 by Muñoz and
Garreaud (2005), and a nocturnal LLJ in the Duero basin in Spain was simulated via a
single-column model by Conangla and Cuxart (2006) and also via large-eddy simulation
(LES) by Cuxart and Jiménez (2007) (see Table 1.1 for information on jet characteristics
and stability levels). The two transport terms in these studies were practically negligible at
layers below and above the jet, i.e., TKE was practically locally balanced.
Different LES results were obtained by Skyllingstad (2003) for katabatic flows (jet peak
a few meters away from the surface). He found relevant contributions by the pressure
transport term above and below the jet (no direct results for the turbulent transport were
shown). The pressure transport term was a sink above the jet and a source below the jet,
suggesting a transport of TKE towards the surface (similarly to Smedman et al. 1994).
According to Skyllingstad (2003), an upward transport also could be possible, with TKE
being transported away from the model domain by gravity wave activity. Axelsen and Dop
(2009) also studied katabatic flows using LES, and their results for the pressure transport
term are in general agreement with the results of Skyllingstad (2003). Axelsen and Dop
(2009) found the turbulent transport term to be a relevant term, typically a sink above and
below the jet and a source near the jet core.
7
8
Location
Baltic Sea, near
the Swedish SE
Coast
Baltic Sea, near
the Swedish SE
Coast
Baltic Sea,
Stockholm
archipelago
Baltic Sea,
Stockholm
archipelago
SE Kansas, USA
Coast of
north-central
Chile
Duero basin,
Spain
Duero basin,
Spain
Study
Smedman et al.
(1993)
Smedman et al.
(1994)
Smedman et al.
(1995)
Bergström and
Smedman
(1995)
Cuxart et al.
(2002)
Muñoz and
Garreaud
(2005)
Conangla and
Cuxart (2006)
Cuxart and
Jiménez (2007)
Frictional
decoupling at
nighttime;
katabatic flow;
baroclinicity
Frictional
decoupling at
nighttime;
katabatic flow;
baroclinicity
Topographic
barrier effect
Frictional
decoupling at
nighttime
no LLJ
Frictional
decoupling over
the cold sea
Frictional
decoupling over
the cold sea
Frictional
decoupling over
the cold sea
Jet Formation
Very stable
Near neutral
Moderately
stable
Moderately
stable
∼ 350
∼ 65
∼ 65
Weakly
stable to
very stable
100 to
200
—
Weakly–
moderately
stable
Near neutral
∼ 1500
30 to
150
Near neutral
Near-Surface
Stability
500 to
1200
Jet
Height
(m)
Model
(LES)
Model
(single
column)
Model
(MM5)
Tower
Tower
Tower
Aircraft
slant profile
+ tower
Aircraft
slant profile
Data Type
Very small (heights
above/below the jet)
Very small (heights
above/below the jet)
No direct result, but
Shr and D in close
equilibrium (heights
above/below the jet)
Loss at 1.5–30 m
layer (max Shr ) and
gain at 30–50 m layer
Gain at 8 m
Loss at 8 m (max
Shr ); Gain at 31 m
Loss at the base of
the jet (max Shr );
Gain at lower layers
down to the surface
Gain at the top and
base of the jet;
Larger values at the
base (max Shr )
Tp
Same as Tp
Relevant at 1.5–30 m
and 30–50 m layers,
but not well-defined
sign
Very small at 8 m
Very small at 8 and
31 m
Mostly small,
changing sign at
several heights
Very small (heights
above/below the jet)
Tt
Direct from
model
output
Very small (heights
above/below the jet)
Parameterized Very small (heights
together
above/below the jet)
with Tt
—
Direct
Residual
Residual
Residual
Residual
Tp
Calculation
Table 1.1: Observational and modeling studies reporting results on the pressure and turbulent transport terms (Tp and Tt
respectively) of the TKE budget during low-level jet conditions. Heights are given in meters above the surface. Shr and
D correspond to the shear production and dissipation terms, respectively.
9
Location
—
—
Study
Skyllingstad
(2003)
Axelsen and
Dop (2009)
Katabatic flow
Katabatic flow
Jet Formation
Stable
Stable
∼5
Near-Surface
Stability
∼ 2.5
Jet
Height
(m)
Model
(LES)
Model
(LES)
Data Type
Table 1.1: (cont)
Loss above the jet,
gain below the jet
Loss above the jet,
gain below the jet
Tp
Direct from
model
output
Direct from
model
output
Tp
Calculation
Loss above and
below the jet; Gain
at jet core
No direct result
shown
Tt
As mentioned previously, the classical assumption is that turbulence is locally balanced,
and therefore eventual gains or losses of TKE via the transport terms are expected to result
in deviations from MOST. As discussed above, this is a concern especially in the stable
boundary layer, given the presence of many non-local processes. The applicability of MOST
in the presence of LLJs has been discussed in a few studies. Smedman et al. (1995) observed
a significant departure from MOST for their dimensionless wind and temperature gradients
measured near the surface (8 m) during weakly/moderately stable conditions in the presence
of LLJs propagating at low heights (30–150 m) over the Baltic Sea. At the same site and
under similar stability, but in the absence of LLJs, Bergström and Smedman (1995) found
those dimensionless gradients to adhere to MOST. Smedman et al. (1995) pointed out that,
in their study, the flow was significantly governed by the proximity of the jet to the surface,
having some similarity to a laboratory wall jet. It is interesting to note that their results
show that TKE is not locally balanced at the 8 m level, with a large loss of TKE via pressure
transport.
In contrast with Smedman et al. (1995), Cheng et al. (2005) found dimensionless gradients
of wind and temperature near the surface (∼ 3 m) to follow MOST very well during the welldeveloped stage of a more typical type of LLJ over land (data from CASES-99 Great Plains
of the United States). The jet was observed at ∼ 150 m AGL and near-surface conditions
were weakly stable.
More recently, Banta et al. (2006) and Banta (2008) analyzed data from the CASES-99
and LAMAR-2003 experiments (strong wind nights weakly to moderately stable conditions)
and found results in apparent conflict with local similarity concepts, as jet speed was found
to be a better velocity scale than surface-layer friction velocity.
The studies discussed in this Section indicate that the behavior of the transport terms
(especially the pressure transport term) and the applicability of MOST are still an open
question in the stable boundary layer in the presence of LLJs. The results reported so far
10
are practically based on case studies. Further studies using larger data sets encompassing
a larger variety of jet and stability conditions are needed for a better understanding on the
impact LLJs have on surface turbulence.
1.1.2
Surface-Atmosphere Exchange
Trying to explain anomalous jumps of ozone concentration observed at the surface during
nighttime, Corsmeier et al. (1997) found that such jumps were associated with periods of
LLJ activity causing enhanced downward ozone fluxes. Temperature, wind speed and specific humidity also revealed the same jump pattern, indicating vertical mixing. Results by
Reitebuch et al. (2000) also showed a direct connection between LLJs and surface measurements, with the presence of turbulent mixing in the whole layer between the jet core and
the ground surface during episodes of elevated ozone concentration at nighttime.
The results of Corsmeier et al. (1997) also highlight the long-range transport potential of
LLJs, as their ozone concentration measurements were taken in a rural area with no apparent
sources in the surroundings. Following an example given in their study, assuming a LLJ of
12 m s−1 lasting for 12 hours, a trace gas released on its core could result in a horizontal
transport of 518 km during the night. Without LLJ, a typical wind speed of 2 m s−1 would
result in a transport six times smaller.
At a forest site in Florida, Karipot et al. (2006) reported enhanced shear and turbulence at the surface during intermittent low-level jet events, which were associated with
sporadic coupling between the canopy and the atmosphere, with intermittent accumulation
and venting of CO2 during the night. At the same location, Karipot et al. (2008) performed
a comparison of above-canopy turbulence statistics/fluxes for two groups, one characterized by strong low-level jets and the other by weak low-level jets. The strong low-level jet
group experienced weaker stability and larger turbulence kinetic energy, friction velocity,
and fluxes of CO2 and sensible heat. Karipot et al. (2008) also analyzed wind velocity and
11
CO2 spectra/cospectra and found that low-frequency contributions were more expressive in
the strong-LLJ group. These contributions were found to occur at scales comparable to LLJ
height.
Evidence of enhanced mixing and surface fluxes during LLJs was also presented by Foken
et al. (2012) for a forest site in Germany, based on measurements of trace gases including
CO2 , O3 , NO2 , and NO taken as part of the EGER project.
Despite the large number of studies reporting an enhancement of surface turbulence
and fluxes during during LLJ events, a few studies have pointed out to an opposite result.
Smedman et al. (2004) found a reduction of surface fluxes and an attenuation of low-frequency
turbulence energy for low-level jet events observed over the Baltic Sea. They explained their
results in light of the shear-sheltering theory (Hunt and Durbin 1999), which in this context
predicts that the enhanced vorticity below the jet can block the propagation of large eddies
from upper layers down to the surface. Prabha et al. (2008) also reported evidence of shear
sheltering for low-level jets observed over a forest site in Maine, USA. Further studies are
needed in order to shed light on these apparent discrepancies.
1.2
Goal and Structure of This Dissertation
The goal of the present study is to contribute to a better understanding of the impact of
nocturnal low-level jets on surface turbulence and fluxes by further investigating
• the applicability of the shear-sheltering theory,
• the TKE budget near the surface, with special attention to the pressure and turbulent
transport terms, and
• the applicability of MOST in light of the TKE transport terms.
12
In Chapter 2 the shear-sheltering theory is presented, discussed, and assessed using sodar
and eddy-covariance data collected during an intensive field campaign at a site in Oklahoma,
USA. This site was selected given its “simple” flat horizontally homogeneous surface and vast
repository of turbulence and low-level jet information. In Chapter 3 the TKE budget and
the applicability of MOST during LLJ activity are investigated using long-term sodar and
eddy-covariance data collected at a site in South Carolina, USA. The final conclusions are
presented in Chapter 4.
13
Chapter 2
Assessing the Shear-Sheltering Theory
Applied to Low-Level Jets in the
Nocturnal Stable Boundary Layer1
1
Duarte HF, Leclerc MY, Zhang G (2012) Theoretical and Applied Climatology 110:359–371
Reprinted here with kind permission from Springer Science and Business Media
14
2.1
Abstract
This paper investigates the existence of shear sheltering on turbulence data over a quasiideal experimental site in Oklahoma, USA. Originally developed for engineering flows, the
shear-sheltering theory is predicated upon the idea of low-level jets blocking large eddies
aloft, preventing them from propagating to the surface. In this scenario, suppression of
low-frequency turbulence energy and reduction of surface fluxes would be expected. Results
from the Oklahoma experiment show instead an enhancement of surface turbulence intensity
and of the relative contribution of large scales to total (co)variances for low-level jet cases
with strong shear, thus suggesting the absence of shear sheltering at the site. The results
underline the complexity of surface-atmosphere interactions in nocturnal stable conditions.
Atmospheric modeling of exchange using various scenarios of surface characteristics, flow
regimes, and low-level jet properties is suggested to further assess the potential applicability
of the shear-sheltering theory to atmospheric flows.
2.2
Introduction
This paper reports on the application of the theoretical results of Hunt and Durbin (1999)
based on rapid distortion theory (Townsend 1976) suggesting that free-stream eddies traveling from an external layer towards a shear layer can be fully blocked at the interfacial zone,
given that certain conditions regarding eddy size and horizontal velocity are met. Hunt and
Durbin (1999) coined the term shear sheltering to this blocking mechanism.
The mechanism has been well documented in engineering flows, where laminar boundary
layers can bypass transition given the input of free-stream turbulence, a process controlled
by shear sheltering. Direct numerical simulation studies have been performed (e.g., Jacobs
and Durbin 2001; Brandt et al. 2004; Zaki and Durbin 2005) to investigate the process. More
recently, Hernon et al. (2007) conducted a wind tunnel experiment considering a flow past a
15
flat plate, and the observed penetration of free-stream disturbances into the boundary layer
was found to agree with shear-sheltering theory.
The shear-sheltering theory was first tested in atmospheric flows by Smedman et al.
(2004), where the strong enhancement of vorticity in the layers below a low-level jet (hereafter, referred to as LLJ) would block the propagation of large eddies aloft towards the
surface. From wind profile and eddy covariance data collected at two marine sites in the
Baltic Sea, they noted that during periods characterized by LLJ events, the measured surface sensible heat flux was approximately 50% smaller than in the absence of an LLJ, all
other conditions being similar. They observed a significant suppression of low-frequency
turbulence energy in the spectral analysis of horizontal and vertical wind components, in
agreement with the theory that predicts the blocking of large eddies due to the enhanced
vorticity in the layer below the LLJ.
The application of the shear-sheltering theory to LLJs as in Smedman et al. (2004) may
seem contradictory at first, since an enhancement of turbulence at the surface would be
expected due to the shear created below a low-level jet. Karipot et al. (2006), for instance,
reported from data collected at a forest site in Florida that intermittent nocturnal jet activity was able to generate shear and turbulence at the surface, causing bursts of the CO2
accumulated near the ground during strong stable conditions. Karipot et al. (2008), using
turbulence data (wind velocity components and scalars) from the same site in Florida, observed actually an enhancement of low-frequency contributions to variances and covariances
at scales up to jet core height, in contrast with the findings of Smedman et al. (2004). Furthermore, their results do not show any significant decrease of low-frequency contributions to
(co)variances at larger scales (i.e., greater than LLJ height), suggesting the lack of evidence
of shear sheltering.
Hunt and Durbin (1999), however, were clear that exceptions do occur. According to
the theory, the disturbances above the shear layer (i.e., large eddies above the LLJ shear
16
layer in this case) must have an “appropriate size” (see Hunt and Durbin 1999) and must
propagate with horizontal velocity close to that of the mean flow in order to the shear
sheltering phenomenon be observed. While the propagation velocity is likely to be close to
that of the mean wind, there is no information at present on the eddy size above the jet in
any of the papers related to the topic.
Smedman et al. (2004) proposed a pragmatic way to measure the overall strength of the
phenomenon, using a shear-sheltering parameter (Σj ) defined as:
Σj =
(Uj /Hj2 )u∗
,
(dU/dz)2
(2.1)
where Uj and Hj are the low-level jet speed and height above ground level, u∗ is the friction
velocity, and dU/dz is the wind shear. It is important to note that Smedman et al. (2004)
did not specify clearly which shear layer should be considered in the calculation of dU/dz.
This issue will be further discussed in Section 2.4.3.
Using wind profile and eddy covariance data from a forest site in Maine, USA, Prabha
et al. (2008) also documented periods where shear sheltering was present. Strong low-level
jets and high wind shear events were associated with high shear sheltering. On the other
hand, cases of low wind shear and weak low-level jets were associated with turbulent bursts
at the surface, i.e., low or no shear sheltering was observed. For the calculation of Σj ,
Prabha et al. (2008) used u∗ values measured at 9 m above the forest canopy and wind
shear calculated from the difference between wind speeds at the jet core and at 20 m height
(canopy top). They were also able to correlate Σj with the gradient of CO2 concentration
measured within the forest canopy: higher gradients (i.e., high stratification, low mixing)
were associated with higher Σj .
Smedman et al. (2004) and Prabha et al. (2008) appear to be so far the two leading
studies investigating the role of low-level jets on the theoretical existence of shear-sheltering
17
phenomenon, with their experimental results supporting the theory. Other studies, however,
while not discussing explicitly the shear-sheltering topic, point out to opposite results when
spectral analyses and statistics of surface turbulence in the presence of jets are examined
(e.g., Karipot et al. 2006, 2008).
The literature and availability of coincident surface turbulence and low-level jet data are
rather sparse preventing a more conclusive assessment and additional insight on the subject. In an effort to shed light on these apparent discrepancies, the present study further
investigates the applicability of the theory of Hunt and Durbin (1999) to low-level jets in
the nocturnal stable boundary layer, by analyzing wind profile and turbulence data collected at an experimental site in Oklahoma, USA. The site was selected given its “simple”
flat horizontally homogeneous surface and vast repository of turbulence and low-level jet
information.
In the sequence, Section 2.3 presents information about the experimental site, instrumentation used, and data measured. The methodology adopted is also described, including
information on the selection of runs, data quality control, LLJ selection criterion, and processing of turbulence data. Section 2.4 presents the results obtained, including statistics of
the LLJs at the study site, information about surface turbulence and fluxes, and spectral
analysis results. The conclusions are presented in Section 2.5.
2.3
2.3.1
Measurements and Signal Processing
Experimental Site and Instrumentation
The field experiment was performed at the US Department of Energy’s Atmospheric Radiation Measurement Program - Cloud and Radiation Testbed central facility site in Lamont,
Oklahoma (36.605 N, 97.488 W, 315 m altitude) during September 10-24, 2007. The site is
18
flat and homogeneous, with several kilometers of fetch along the predominant wind direction.
The site was covered with short grass at the time of the experiment.
Three eddy covariance systems were deployed on a triangular tower at 2, 5, and 10
m AGL. Each system consisted of a three-dimensional sonic anemometer (model CSAT3,
Campbell Sci., Logan, UT, USA) and an open-path CO2 /H2 O gas analyzer (model Li-7500,
Li-Cor Inc., Lincoln, NE, USA). A datalogger (model CR5000, Campbell Sci., Logan, UT,
USA) was programmed for 20-Hz sampling of the three wind velocity components, sonic
temperature, CO2 and H2 O concentrations, atmospheric pressure, and CSAT3 diagnostic
parameter, from the three eddy covariance systems. Statistics of 30 min were also calculated.
A phased-array boundary-layer Doppler sodar (model PA2, Remtech Inc., Paris, France)
operating with a central frequency of 2 kHz was deployed approximately 250 m away from
the eddy covariance tower, providing profiles of the mean wind velocity components (u , v ,
w), their variances (σu2 , σv2 , σw2 ) and covariances (u0 v 0 , u0 w0 , v 0 w0 ), and mean echo strength.
The sodar configuration was adjusted based on the results obtained in the first few days of
campaign. In its final configuration, the sodar was programmed to retrieve 30-min mean
profiles, from 20 to 905 m AGL at 15-m increments. Figure 2.1 shows the instrumentation
setup and a general view of the experimental site.
2.3.2
Data Selection and Quality Control
The data used in this study correspond to the period between September 15 and 23, 2007,
where the configuration of both sodar and eddy covariance systems was kept unchanged
and data from both systems were continuously available. Only nighttime data (21:00–06:00
CDT) were considered.
The high-frequency eddy covariance data used in this study correspond to the instruments
deployed at the highest level of the tower (10 m). Exceptionally, wind speed data from the
sonic anemometer at 5 m were used to calculate the mean wind shear between 10 and 5 m
19
Figure 2.1: Experimental site and instrumentation overview: a eddy covariance tower, b
boundary layer sodar, and c general view of the site
levels. The data were divided in 30-min runs, and the quality of each one was assessed with
the aid of CSAT3/LI7500 diagnostic parameters. Runs with poor data quality, usually due
to accumulation of dew on the sensors optical/sonic paths, were rejected.
The sodar processing unit performs internally a data quality control, rejecting poor quality measurements caused by fixed echoes, background acoustic noise, and other adverse
environmental factors. The output 30-min profiles were further assessed visually, and the
ones presenting abnormal spikes and/or significant gaps were rejected.
20
2.3.3
Low-Level Jet Selection Criterion
The “low-level jet” term was first introduced by Means (1952), but so far there is no unique
and exact definition for such phenomenon, once it can be originated from many different
atmospheric processes and may present a variety of characteristics.
Pragmatic ways of classifying a given wind speed maximum as a LLJ have been used
in the literature (e.g., Bonner 1968; Stull 1988; Whiteman et al. 1997; Andreas et al. 2000;
Banta et al. 2002). These methods are generally based on thresholds for the wind speed
maximum and falloff values between the maximum and the next wind speed minima above
and below the correspondent height.
For this study, LLJs were defined following a criterion similar to the one used by Andreas
et al. (2000), with no thresholds for the wind speed maximum and with a falloff value of
2 m s−1 . Andreas et al. (2000) used the falloff criterion for the next wind speed minima
above and below the height of wind speed maximum. In this study, however, the falloff was
required only towards the next wind speed minimum above, as done by Whiteman et al.
(1997). The first wind speed maximum from the surface which meets those requirements
was selected as the low-level jet.
Following the extraction of the relevant jet information from the dataset, namely core
height, speed, and direction, three groups were defined for the subsequent eddy covariance
data analysis, based on jet shear values (Sj , calculated from the mean wind speed at the
jet core and at 20 m height). A strong-shear group and a weak-shear group were created,
gathering 30-min runs where Sj > 0.03 and Sj ≤ 0.03 s−1 , respectively. This threshold for Sj
was chosen in order to create two contrasting groups with approximately the same number of
runs. A third group was created including all runs where no LLJ was found. Only runs with
the MoninObukhov stability parameter (ζ) between 0 and 0.5 (slightly stable to moderately
stable conditions) were considered, as in Smedman et al. (2004).
21
2.3.4
Turbulence Data
Signal Processing
As mentioned in Section 2.3.2, 30-min runs were used for calculations. In order to align
the instrumentation in the streamwise direction in the signal processing, a three-dimensional
coordinate rotation was applied to the sonic anemometer raw data, forcing v and w (mean
lateral and vertical wind velocities, respectively) to zero.
After obtaining the 30-min average for each variable, the raw data were linearly detrended
(Rannik and Vesala 1999) and the resulting fluctuations were used to calculate variances
and covariances. Fluxes and ζ were then calculated. Density correction was applied for
calculating the CO2 flux (Webb et al. 1980).
In order to avoid contaminated data due to flow distortion by the eddy covariance tower,
the angle of attack of the 30-min mean wind vector on the sonic transducers was verified for
each run. Even considering a conservative rejection zone of 60◦ behind the sonic anemometer,
no mean wind vector fell into that region, and therefore no run was discarded because of
this issue.
Fourier Spectra and Cospectra
Following the coordinate rotation and the linear detrending, the 30-min runs containing
high-frequency data were used to obtain Fourier spectra of u, v, w, Ts , and c (streamwise,
lateral, and vertical wind velocity components, sonic temperature, and CO2 concentration,
respectively), and Fourier cospectra of u−w, w−Ts , and w−c.
The raw spectra were nondimensionalized by multiplying the spectral densities Sxx (n)
by n/σx2 , where x = (u, v, w, Ts , c), n is the natural frequency, and σx2 is the corresponding
variance. The same was done for the raw cospectra, but multiplying the cospectral densities
Cxy (n) by n/x0 y 0 , where x0 y 0 is the covariance between the variables x and y. The natural
22
frequency on the abscissa was nondimensionalized as f = nz/u, where z is the measurement
height and u is the mean streamwise wind speed at z (10 m). No displacement length was
considered given the surface characteristics of the experimental site.
Each raw, nondimensionalized (co)spectrum was then smoothed by dividing the data into
64 non-overlapping f classes of logarithmically increasing width and averaging the nondimensionalized (co)spectral densities inside each class. Having the abscissa in logarithmic
scale, the classes within a particular (co)spectrum present the same width, and the central
f is used to represent the nondimensionalized frequency of the respective class.
In a plot nSxx (n)/σx2 vs. f , the inertial subrange (ins) can be represented as
nSxx (n) σx2 = αf −2/3 ,
(2.2)
ins
and for the cospectrum analog (u−w, w−Ts , w−c), as
nCxy (n) x0 y 0 = βf −4/3 ,
(2.3)
ins
where α and β are constants for a given run. Those constants were fitted for each 30min smooth spectrum and cospectrum via a Levenberg–Marquardt nonlinear least squares
algorithm, using data within the interval 1 ≤ f ≤ 10 (for the data collected in this study, it
was found that the inertial subrange could be reasonably delimited by such interval). Having
the constants α and β, the nondimensionalized frequency f for each smooth spectrum and
cospectrum was normalized by f0 = α3/2 and f0 = β 3/4 , respectively. f0 is defined as the
nondimensionalized frequency at the intersection of the extrapolated inertial subrange and
the nSxx (n)/σx2 = 1 (or nCxy (n)/x0 y 0 = 1) line. This normalization, originally proposed by
Kaimal et al. (1972), makes all (co)spectra coincide in the inertial subrange.
23
As discussed previously, the runs were separated into three different groups according to
Sj (LLJ shear) values. For a given variable, u for instance, a mean spectrum was obtained for
each group, by averaging individual smoothed spectra. For that, the shortest f /f0 interval
including all data points from all individual spectra in a given group was divided into 32 nonoverlapping classes of logarithmically increasing width. The mean spectrum was obtained
by averaging all the points (from all individual spectra) in each class. The central f /f0
(given the abscissa in log scale) was used to represent each class. The mean cospectra were
obtained following exactly the same procedure.
2.4
2.4.1
Results and Discussion
Low-Level Jet Statistics
Statistics of the low-level jet events observed during the campaign is shown in Table 2.1.
Average, minimum and maximum values of LLJ height, speed, direction, and shear and
number of LLJ events (30-min profiles) are presented for each night. Overall statistics are
also shown.
Considering that the total number of 30-min wind profiles within each nocturnal period
analyzed is 19, it can be seen from the number of LLJ events in Table 2.1 that at least 47%
of each night presented LLJ activity, ratio reaching 84% in nights 15/16 and 16/17. The
exception is the night 22/23, with almost negligible jet activity (3 LLJ events only).
It can be seen that the classical southerly Great Plains LLJ dominated the nocturnal
periods analyzed. Overall average LLJ height, speed, and shear were approximately 300 m,
16 m s−1 , and 0.03 s−1 . The strongest LLJs were observed in the nights 16/17 and 17/18,
with mean Uj above ∼ 19 m s−1 (maximum ∼ 21 m s−1 ) and mean Sj exceeding 0.035 s−1 .
Nights 15/16 and 20/21 presented LLJs with intermediate strength, and the remaining nights
24
Table 2.1: Low-level jet statistics for the nocturnal periods considered (21:00 to 06:00 CDT).
Hj , Uj , DIR, and Sj correspond to LLJ height, speed, direction, and shear, respectively. N
is the number of LLJ events (30-min profiles). Values outside and inside the brackets are
the averages and ranges within the periods, respectively
Day
Hj (m)
Uj (m s−1 )
DIR (deg)
Sj (s−1 )
N
15/16
16/17
17/18
18/19
19/20
20/21
21/22
22/23
343
317
324
303
297
234
291
275
[260–440]
[200–395]
[230–440]
[200–470]
[215–410]
[170–290]
[230–380]
[230–320]
Overall
305 [170–470]
15.8
19.4
18.9
13.3
13.2
14.3
11.9
12.2
[13.9–17.2] 183 [148–209]
[17.5–21.3] 187 [168–204]
[10.0–20.8] 188 [165–349]
[11.3–14.1] 174 [159–193]
[12.5–13.6] 176 [159–197]
[11.0–16.8] 173 [147–194]
[8.3–14.2] 192 [157–221]
[11.3–13.4] 157 [156–158]
15.6 [8.3–21.3]
181 [147–349]
0.029
0.037
0.035
0.025
0.025
0.030
0.026
0.020
[0.021–0.035]
[0.030–0.047]
[0.011–0.042]
[0.017–0.030]
[0.017–0.031]
[0.017–0.037]
[0.017–0.032]
[0.019–0.021]
16
16
14
9
12
11
10
3
0.030 [0.011–0.047]
91
were characterized by relatively weak LLJs, with mean Uj below ∼ 13 m s−1 and mean Sj
below 0.026 s−1 .
The values found in this campaign are comparable with results obtained in previous
climatological studies of the Great Plains LLJ. Whiteman et al. (1997) performed a 2-year
climatology study based on wind profile data taken at the same location used in the present
study, and found that southerly LLJs are predominant, occurring most frequently at 300–600
m AGL. For the warm season (April–September), they reported a mean Uj of 16.0 m s−1 . In
a more recent work, Song et al. (2005) performed a 6-year climatological study at the same
region and found that 72% of the nights were characterized by southerly LLJs, with mean
Uj equal to 18 m s−1 in the warm season. They also reported that Hj was most frequently
at 200–400 m AGL.
Inertial oscillation of the ageostrophic wind as frictional decoupling takes place at sunset
(Blackadar (1957) mechanism) is pointed out as the main agent in the formation of the
25
nocturnal Great Plains LLJ (Parish et al. 1988; Zhong et al. 1996; Parish and Oolman
2010).
2.4.2
Surface Turbulence and Fluxes
Table 2.2 presents statistics of eddy covariance and LLJ data for the groups considered
(strong Sj (LLJ shear), weak Sj , and no LLJ). In Table 2.2, Hs , Fc , TKE, and S10,5 are sonic
sensible heat flux, CO2 flux, turbulence kinetic energy, and wind shear calculated from wind
speeds at 10 and 5 m AGL, respectively. Σj,a and Σj,b correspond to the shear-sheltering
parameter calculated using Sj and S10,5 in the denominator of Eq. 2.1, respectively.
The average jet shear observed was 0.035 and 0.024 s−1 for the strong- and weak-Sj
groups, respectively. While the height of the LLJ did not change significantly between the
two groups, the enhanced jet speed was the primary cause of the high jet shear values in
the first group, with average Uj approximately 4 m s−1 higher than the value for the second
group.
Comparing the statistics for the weak-Sj and no-LLJ groups, it can be seen that the
values are reasonably close, except the results for σc2 . In general, the averages indicate a
slightly increased turbulence activity and reduced stability for the weak-Sj group, except
the local shear S10,5 , whose average was slightly smaller in comparison with the value in the
no-LLJ group. The variances σc2 and σT2s and covariances w0 Ts0 and w0 c0 were slightly smaller
in the weak-Sj group. This suggests intermittent turbulence activity in the no-LLJ group
(higher stability) and associated bursts, increasing the variance of sonic temperature and
CO2 concentration and related fluxes. The weak-Sj group results suggest a less stratified
surface layer with more continuous turbulence.
Comparing the averages for the weak-Sj and strong-Sj groups, the latter is characterized
by a significant increase of turbulence and reduction of stability. u goes from 3.7 to 5.9
m s−1 , and variances σu2 , σv2 , and σw2 and TKE more than double. ζ decreases (∼ 50%)
26
27
3.6±0.7 [2.7 to 5.1]
0.28±0.14 [0.09 to 0.72]
0.18±0.08 [0.06 to 0.35]
0.10±0.05 [0.03 to 0.19]
0.030±0.014 [0.014 to 0.075]
6.9±7.9 [1.0 to 32.9]
−0.070±0.031 [−0.130 to −0.021]
−0.020±0.004 [−0.026 to −0.010]
0.23±0.06 [0.15 to 0.39]
−24.7±5.5 [−32.4 to −12.9]
0.26±0.06 [0.15 to 0.36]
0.18±0.06 [0.10 to 0.34]
0.28±0.13 [0.09 to 0.63]
0.20±0.13 [0.06 to 0.46]
–
–
–
0.161±0.015 [0.136 to 0.191]
–
–
0.11±0.02 [0.06 to 0.14]
0.20±0.03 [0.15 to 0.25]
0.28±0.03 [0.23 to 0.35]
0.16±0.02 [0.12 to 0.20]
0.16±0.02 [0.08 to 0.19]
0.16±0.05 [0.09 to 0.27]
0.23±0.04 [0.14 to 0.32]
0.21±0.04 [0.13 to 0.32]
u (m s−1 )
σu2 (m2 s−2 )
σv2 (m2 s−2 )
2
σw
(m2 s−2 )
2
σTs (K2 )
σc2 (mg2 m−6 )
u0 w0 (m2 s−2 )
w0 Ts0 (m K s−1 )
w0 c0 (mg m−2 s−1 )
Hs (W m−2 )
u∗ (m s−1 )
Fc (mg m−2 s−1 )
TKE (m2 s−2 )
ζ (–)
Hj (m)
Uj (m s−1 )
Sj (s−1 )
S10,5 (s−1 )
Σj,a (–)
Σj,b (–)
f0,u (–)
f0,v (–)
f0,w (–)
f0,Ts (–)
f0,c (–)
f0,uw (–)
f0,wTs (–)
f0,wc (–)
N is the number of 30-min runs in each group
No LLJ shear
30
N
3.7±0.9 [2.8 to 8.0]
0.33±0.23 [0.10 to 1.40]
0.20±0.12 [0.06 to 0.70]
0.11±0.07 [0.03 to 0.37]
0.022±0.008 [0.010 to 0.046]
3.2±2.1 [0.6 to 11.9]
−0.074±0.048 [−0.273 to −0.017]
−0.017±0.005 [−0.027 to −0.007]
0.18±0.04 [0.11 to 0.28]
−21.4±6.1 [−32.9 to −8.4]
0.26±0.08 [0.13 to 0.52]
0.14±0.03 [0.09 to 0.24]
0.32±0.20 [0.10 to 1.24]
0.17±0.11 [0.02 to 0.48]
321±72 [185 to 470]
13.7±1.6 [10.0 to 17.2]
0.024±0.005 [0.011 to 0.030]
0.155±0.014 [0.134 to 0.189]
0.0707±0.0410 [0.0248 to 0.2046]
0.0017±0.0009 [0.0004 to 0.0048]
0.09±0.02 [0.05 to 0.13]
0.18±0.03 [0.09 to 0.24]
0.27±0.03 [0.21 to 0.35]
0.16±0.02 [0.13 to 0.20]
0.15±0.02 [0.09 to 0.20]
0.14±0.05 [0.07 to 0.25]
0.22±0.04 [0.17 to 0.33]
0.21±0.05 [0.14 to 0.33]
Weak LLJ shear
32
5.9±1.7 [2.5 to 8.9]
0.76±0.41 [0.11 to 1.72]
0.42±0.20 [0.07 to 0.88]
0.24±0.12 [0.03 to 0.49]
0.024±0.007 [0.011 to 0.037]
1.6±1.1 [0.6 to 6.6]
−0.156±0.084 [−0.352 to −0.021]
−0.026±0.008 [−0.042 to −0.007]
0.19±0.04 [0.10 to 0.25]
−32.6±10.3 [−52.1 to −9.1]
0.38±0.11 [0.15 to 0.60]
0.13±0.03 [0.08 to 0.20]
0.71±0.36 [0.11 to 1.53]
0.09±0.08 [0.02 to 0.37]
297±54 [170 to 395]
17.9±2.5 [13.0 to 21.3]
0.035±0.004 [0.030 to 0.047]
0.162±0.015 [0.126 to 0.192]
0.0657±0.0272 [0.0217 to 0.1585]
0.0031±0.0012 [0.0010 to 0.0070]
0.08±0.02 [0.05 to 0.11]
0.16±0.02 [0.10 to 0.23]
0.24±0.03 [0.19 to 0.33]
0.14±0.02 [0.11 to 0.18]
0.11±0.02 [0.08 to 0.18]
0.09±0.05 [0.01 to 0.23]
0.18±0.04 [0.11 to 0.27]
0.16±0.04 [0.11 to 0.28]
Strong LLJ shear
45
Table 2.2: Statistics of eddy covariance and LLJ data are presented for the groups of strong jet shear, weak jet shear, and
no LLJ, in the format average ± SD [range]
towards slightly stable conditions (ζ ∼ 0.1). The magnitude of the sonic sensible heat
flux and the friction velocity increases approximately 50%. σc2 drops approximately 50%,
indicating more mixing and continuous turbulence. The CO2 flux (Fc ) remains almost the
same, slightly smaller for the strong-Sj group. The local shear, S10,5 , has a slight increase.
The average of σT2s , and mainly the averages of σc2 and Fc were smaller for the strongSj group in relation to the no-LLJ group. This suggests that intermittent turbulence and
associated CO2 bursts occurred for the runs in the no-LLJ group, and that runs in the strongSj group were characterized by a more continuous turbulent activity and less stratified surface
layer.
Scatterplots of TKE, u∗ , and Hs as a function of ζ, distinguishing the points according
to the three different groups, are displayed in Figs. 2.2, 2.3, and 2.4, respectively. These
figures illustrate that LLJs with strong shear are able to significantly enhance turbulence and
fluxes and reduce stability close to the surface (cf. Table 2.2). The points associated with
the no-LLJ and weak-Sj groups form a second cluster, corresponding to weaker turbulence,
smaller fluxes, and increased stability. No clear difference can be seen between the latter
two groups. Similar results were obtained by Karipot et al. (2008), where reduced stability
and enhanced turbulence and fluxes were observed during strong-LLJ cases, in comparison
to weak-LLJ cases.
Figure 2.5 presents scatterplots of TKE, u∗ , Hs , Fc , Σj,a , and Σj,b as a function of Sj .
It can be seen that TKE and the magnitude of the fluxes of momentum, sonic sensible
heat, and CO2 display approximately a linear increase with jet shear for the strong-Sj group
(Sj > 0.03 s−1 ). As the jet shear goes below 0.03 s−1 , its relationship with TKE and fluxes
becomes murkier, mainly for Fc . As seen in Table 2.2, the average CO2 flux for the weak-Sj
and strong-Sj groups are practically the same.
28
1.6
Strong Sj
Weak Sj
No LLJ
1.4
TKE (m2 s-2)
1.2
1
0.8
0.6
0.4
0.2
0
0
0.05
0.1
0.15
0.2
0.25
ζ
0.3
0.35
0.4
0.45
0.5
Figure 2.2: Scatterplot of turbulence kinetic energy as a function of the Monin-Obukhov
stability parameter. Points are segregated in three groups: strong Sj , weak Sj , and no LLJ
0.6
Strong Sj
Weak Sj
No LLJ
0.55
0.5
u* (m s-1)
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0
0.05
0.1
0.15
0.2
0.25
ζ
0.3
0.35
0.4
0.45
0.5
Figure 2.3: Scatterplot of friction velocity as a function of the Monin-Obukhov stability
parameter. Points are segregated in three groups: strong Sj , weak Sj , and no LLJ
29
10
Strong Sj
Weak Sj
No LLJ
0
Hs (W m-2)
-10
-20
-30
-40
-50
-60
0
0.05
0.1
0.15
0.2
0.25
ζ
0.3
0.35
0.4
0.45
0.5
Figure 2.4: Scatterplot of sonic sensible heat flux as a function of the Monin-Obukhov
stability parameter. Points are segregated in three groups: strong Sj , weak Sj , and no LLJ
2.4.3
Shear-Sheltering Parameter
As seen in Table 2.2, the average Σj,b approximately doubles for the strong-Sj group, comparing to the weak-Sj group. This is what one would expect: an increase of the sheltering
effect associated with increasing jet shear. Figure 2.5f illustrates a clear linear relationship
between jet shear and Σj,b , with a slight change in slope for Sj below 0.03 s−1 .
On the other hand, the relationship between Sj and Σj,a (jet shear used in the denominator of Eq. 2.1) is not as clear, especially for Sj below 0.03 s−1 (Fig. 2.5e). A linear
relationship can be seen above this value. The mean Σj,a for the two Sj groups are similar, and the one for the strong-Sj group is slightly smaller, the opposite of what one would
expect.
A comparison between the magnitude of both shear-sheltering parameters and their relation with jet shear are illustrated in Fig. 2.6. The total range of Σj,a , considering the two
30
1.6
0.6
(a)
(b)
0.55
1.4
0.5
1.2
1
-1
u* (m s )
TKE (m2 s-2)
0.45
0.8
0.6
0.4
0.35
0.3
0.25
0.4
0.2
0.2
0
0.01
0.15
Strong Sj
Weak Sj
0.015
0.02
0.025
0.03 0.035
Sj (s-1)
0.04
0.045
0.05
0.1
0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055
Sj (s-1)
0.055
-5
0.24
(c)
(d)
-10
0.22
-15
0.2
-2 -1
Fc (mg m s )
Hs (W m-2)
-20
-25
-30
-35
-40
0.18
0.16
0.14
0.12
-45
0.1
-50
0.08
-55
0.01
0.015
0.02
0.025
0.03 0.035
Sj (s-1)
0.04
0.045
0.05
0.06
0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055
Sj (s-1)
0.055
0.22
0.007
(e)
(f)
0.2
0.006
0.18
0.005
0.16
0.004
Σj,b
Σj,a
0.14
0.12
0.003
0.1
0.08
0.002
0.06
0.001
0.04
0.02
0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055
Sj (s-1)
0
0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055
Sj (s-1)
Figure 2.5: Scatterplot of a turbulence kinetic energy, b friction velocity, c sonic sensible
heat flux, d CO2 flux, e shear-sheltering parameter using jet shear, and f shear-sheltering
parameter using wind shear between 5 and 10 m levels, as a function of jet shear. Bullets
and circles correspond to the strong- and weak-Sj groups respectively
31
0.22
Strong Sj
Weak Sj
0.2
0.18
0.16
Σj,a
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0.001
0.002
0.003
0.004
Σj,b
0.005
0.006
0.007
Figure 2.6: Comparison between shear-sheltering parameters Σj,a and Σj,b , calculated using
jet shear (Sj ) and local shear close to the surface (S10,5 ) in the denominator of Eq. 2.1,
respectively. Bullets and circles correspond to the strong- and weak-Sj groups, respectively
Sj groups is [0.0217–0.2046]. For Σj,b , [0.0004–0.0070]. The Σj,a values are on average ∼ 30
times larger than the Σj,b values, given the fact that the shear used in the denominator of
Eq. 2.1 was Sj , significantly smaller than the shear S10,5 used in the calculation of Σj,b . Note
that shear is raised to the power of two in the denominator.
According to the results in Smedman et al. (2004, their Fig. 5, for instance), their
calculated shear-sheltering parameter was concentrated within the [0.001–0.01] interval, with
only few points in the [0.01–0.1] range. Not considering the latter, the values found for Σj,b in
this study are comparable with the shear-sheltering parameter values reported by Smedman
et al. (2004), even though generally smaller. This suggests that Smedman et al. (2004) used
a local wind shear close to the surface (similar to S10,5 ) and not jet shear in their calculations.
However, it is difficult to say exactly how they calculated wind shear, i.e., which bulk layer
was considered. This information was not given in their article, and therefore one should
32
be careful when comparing the magnitude of the shear-sheltering parameter found in both
studies.
Prabha et al. (2008), using Sj in the calculation of the shear-sheltering parameter, found
Σj,a values approximately within a range of [0.03–2.00] according to their Fig. 2. In this
study, Σj,a was within the [0.0217–0.2046] range. Approximately half of the values of Prabha
et al. (2008) were in the [0.2–2.0] range, which would indicate stronger shear-sheltering
activity in their study. In addition to inherent differences in LLJ properties between the two
studies, such difference in magnitude could be related to u∗ . In this study, u∗ was measured
over a grass surface at 10 m AGL. In the study of Prabha et al. (2008), u∗ was measured
over a coniferous forest canopy at 29 m AGL (canopy height = 20 m). It is important to
note, however, that the use of jet shear to obtain the shear-sheltering parameter is less than
ideal.
Smedman et al. (2004) derived the shear-sheltering parameter starting with the definition
of a nondimensional group relevant to measure the phenomenon:
Σj =
Lx d2 u/dz 2
,
du/dz
(2.4)
where Lx is a horizontal eddy length scale. Assuming the curvature of the mean wind profile
d2 u/dz 2 ∼ Uj /Hj2 and a local estimated value of Lx ∼ u∗ /(du/dz), they obtained
Σj ∼
(Uj /Hj2 )u∗
.
(du/dz)2
(2.5)
For the calculation of Lx , we believe the local wind shear at the location where u∗ is
measured or vicinity should be used instead of jet shear, and therefore Σj,b seems more
appropriate for measuring shear sheltering than Σj,a . Using jet shear in the denominator
implies in (du/dz)2 ≈ (Uj /Hj )2 , resulting in a shear-sheltering parameter of the order of
u∗ /Uj , with no jet height in play.
33
As seen in Section 2.4.2, turbulence and fluxes for the strong-Sj group (corresponding to
higher Σj,b values) are reasonably stronger than the values observed for the no-LLJ group, in
contrast to the findings of Smedman et al. (2004). Sensible heat fluxes reported by Smedman
et al. (2004) for LLJ cases were 50% smaller than fluxes corresponding to no-LLJ cases. The
results in Section 2.4.2 do not contradict necessarily shear-sheltering theory, provided that
the turbulence added due to the shear below the LLJ overcomes the decrease in turbulence
due to a hypothetical shear-sheltering phenomenon blocking eddies with length scales larger
than Hj .
2.4.4
Spectral Analysis
Results
Figure 2.7a–e presents the mean spectra of u, v, w, Ts , and c, respectively, for the three
groups analyzed. The mean cospectra of u−w, w−Ts , and w−c are presented in Fig. 2.7f–h.
The equations proposed by Kaimal et al. (1972) for spectra (their Eq. 23)
0.16(f /f0 )
1 + 0.16(f /f0 )5/3
(2.6)
nCxy (n)
0.88(f /f0 )
=
1 + 1.5(f /f0 )2.1
x0 y 0
(2.7)
nSxx (n)
x0 2
=
and cospectra (their Eq. 33)
were also plotted as reference.
The statistics of the f0 values obtained for all spectra and cospectra analyzed is reported
in Table 2.2. It can be seen that the average values systematically decrease with decreasing
stability (as shown in Kaimal (1973)), with higher averages for the no-LLJ group (ζ ∼ 0.2)
and smaller averages for the strong-Sj group (ζ ∼ 0.1).
34
0.3
0.25
nSvv/σv2
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
10-3
10-2
10-1
100
101
102
(b)
0.25
Strong Sj
Weak Sj
No LLJ
Kaimal
0.2
nSuu/σu2
0.3
(a)
103
0
10-3
104
10-2
10-1
100
f/f0
102
103
0.3
(c)
0.25
0.25
0.2
0.2
nSTsTs/σTs2
nSww/σw2
0.3
0.15
0.1
0.05
0
10-3
101
104
f/f0
(d)
0.15
0.1
0.05
10-2
10-1
100
101
102
103
0
10-3
104
10-2
10-1
f/f0
100
101
102
103
104
f/f0
0.3
0.4
(e)
(f)
0.35
0.25
0.3
nCuw/<u’w’>
nScc/σc2
0.2
0.15
0.1
0.25
0.2
0.15
0.1
0.05
0.05
0
0
10-3
10-2
10-1
100
101
102
103
-0.05
10-3
104
f/f0
10-2
10-1
100
f/f0
101
102
103
Figure 2.7: Mean spectra of a streamwise, b lateral, and c vertical velocity components, d
sonic temperature, and e CO2 concentration, and mean cospectra of vertical velocity with
f streamwise velocity, g sonic temperature, and h CO2 concentration. Bullets, circles, and
crosses correspond to the groups of strong Sj , weak Sj , and no LLJ, respectively. The black
line corresponds to the equations of Kaimal et al. (1972) for spectra and cospectra (Eqs. 2.6
and 2.7 in the present paper)
35
0.4
0.4
(g)
0.3
0.3
0.25
0.25
0.2
0.15
0.1
0.2
0.15
0.1
0.05
0.05
0
0
-0.05
10-3
(h)
0.35
nCwc/<w’c’>
nCwTs/<w’Ts’>
0.35
10-2
10-1
100
f/f0
101
102
-0.05
10-3
103
10-2
10-1
100
f/f0
101
102
103
Figure 2.7: (cont)
As it can be seen in Fig. 2.7, in general, the mean (co) spectra were reasonably close
to the curves proposed by Kaimal et al. (1972). It is worth to remember that the data
used in this study were collected at a site located in the same region of the famous Kansas
experiments.
As seen in Section 2.4.2 for the turbulence parameters and fluxes, the difference between
the mean no-LLJ and weak-Sj (co)spectra is minimal, with slightly increased separation for
the Suu and Svv spectra. Even though the difference is minimal, it still can be seen that the
mean weak-Sj (co)spectra have higher values at low frequencies.
The (co)spectral curves corresponding to the strong-Sj group show generally a significant
increase in the relative contribution of large scales to the total (co)variance. Such increase
is compensated by a decrease in the relative contribution of scales around the (co)spectral
peak. Note that the area below the (co)spectral curves in Fig. 2.7 is preserved, given the
variables plotted and the linear and log scales used for the ordinate and abscissa, respectively.
The relative contribution of eddy scales in the inertial subrange is practically unaltered.
Of all mean spectra and cospectra, the w spectrum is the only one that does not display
significant differences between the strong-Sj and weak-Sj /no-LLJ groups, even though a
36
slightly increase in the contribution of large scales to the total variance can be seen. Such
small difference for the w spectrum in relation to the differences observed in the (co)spectrum
of other variables is also reported by Smedman et al. (2004), Prabha et al. (2008), and Karipot
et al. (2008). It is important to note that Smedman et al. (2004) compared mean spectra for
LLJ and no-LLJ groups; Karipot et al. (2008) compared results for strong- and weak-LLJ
groups (regarding Uj magnitude), and Prabha et al. (2008) used strong- and weak-Σj groups.
All those groups, however, can be approximately translated to strong- and weak-Sj groups.
As afore mentioned, in general, all mean spectra and cospectra obtained here are reasonably close to the curves proposed by Kaimal et al. (1972). Looking closer, it can be seen
that the curves corresponding to the strong-Sj group are more separated from the curves of
Kaimal et al. in comparison to the results for the no-LLJ and weak-Sj groups. The exception
is the v spectrum, where the strong-Sj curve is closer to Kaimal et al.’s.
The f /f0 intervals presenting an enhancement of (co)spectral amplitudes for the strongSj curves in relation to the no-LLJ and weak-Sj curves are approximately delimited in Table
2.3. Given the average values of f0 for the strong Sj group (Table 2.2), an approximation
for the f range was made. From the latter, the approximate eddy length scale (λ) range,
corresponding to the enhancement of (co)spectral amplitudes, was obtained by λ = z/f ,
where z is the measurement height (10 m).
Table 2.3 shows that increased relative contributions to the total (co)variances are occurring at scales not only smaller, but also larger than LLJ height (from Table 2.2, the average
jet height for the strong-Sj group is ∼ 300 m, with values within the [170–395 m] range).
The λ range is very similar for the u, v, and Ts spectra. The λ upper limit for the w spectrum is a little lower, 417 m, value close to the largest LLJ height observed in the strong-Sj
group. With regards to the c spectrum, the λ upper limit was a little higher (909 m). For
the cospectra, relative contributions to the total covariances were increased at scales larger
than ∼ 200 m (CwTs , Cwc ) and 370 m (Cuw ).
37
Table 2.3: Approximate f /f0 interval corresponding to (co)spectral enhancement for the
strong-jet-shear group (Fig. 2.7) and corresponding f and eddy length scale (λ) intervals,
estimated based on the mean f0 values obtained for the group (Table 2.2)
Mean (co)spectrum (strong Sj group)
f /f0
f0
f
λ (m)
Suu
Svv
Sww
STs Ts
Scc
Cuw
CwTs
Cwc
[0.2 to 2.0] 0.08 [0.016 to 0.160] [63 to 625]
[0.1 to 2.0] 0.16 [0.016 to 0.320] [31 to 625]
[0.1 to 1.0] 0.24 [0.024 to 0.240] [42 to 417]
[0.1 to 1.0] 0.14 [0.014 to 0.140] [71 to 714]
[0.1 to 1.0] 0.11 [0.011 to 0.110] [91 to 909]
[— to 0.3] 0.09 [— to 0.027]
[370 to —]
[— to 0.3] 0.18 [— to 0.054]
[185 to —]
[— to 0.3] 0.16 [— to 0.048]
[208 to —]
Discussion
Given the approximately linear relationship found between Sj and Σj,b , the strong-Sj and
weak-Sj curves can be also interpreted as strong- and weak-shear-sheltering curves, respectively. The results found in the spectral analysis seem opposite of what one would expect
assuming that a shear-sheltering mechanism is present due to LLJ activity. A decrease of
the relative contributions to the total (co)variances at lower frequencies would be expected
for the strong-Sj (also strong-Σj,b ) (co)spectra. In other words, some large eddies of scales
superior to LLJ height would be expected to be totally or partially blocked from propagating
towards the surface due to the strong shear layer created by the LLJ. However, the λ values
indicated in Table 2.3 show that the relative contribution of some eddies with length scales
larger than Hj is even higher.
If the enhancement of contributions were observed only at large scales below Hj (considering the eddies created below the LLJ), the authors believe that no conflict would necessarily
exist with the shear-sheltering theory. In this study, however, not only the enhancement
occurs at scales smaller than LLJ height, but also at some scales larger than Hj , where a
38
decrease of the contributions would be expected. For the mean cospectra, the contributions
from all scales larger than 300 m (approximated mean LLJ height for the strong-Sj group)
were enhanced.
Smedman et al. (2004) did a Fourier spectral analysis of u and w wind velocity components for two groups (no LLJ and LLJ), and found a significant and systematic decrease
of contributions from scales left to the spectral peak for the LLJ mean u spectrum, while
the decrease in the LLJ mean w spectrum, as previously mentioned, was modest. The data
points from their LLJ/no-LLJ mean u spectra were extracted from their Fig. 7a and replotted in Fig. 2.8, using linear scale for the y-axis. An intriguing fact is that the area below
the curves plotted for each group is not conserved, which may indicate some inconsistency
in the results. The area below the LLJ spectrum shows to be significantly smaller than
the area below the No-LLJ spectrum. Also, their results suggest that even the contribution
from large eddies with λ smaller than Hj are suppressed, not only the contribution from
eddies with scales larger than Hj . The present authors would expect enhancement of the
contributions from some λ < Hj , even in a shear-sheltering scenario.
Karipot et al. (2008) performed a Fourier spectral analysis segregating the measurement
runs into two groups: strong LLJ and weak LLJ. Their mean strong-LLJ (co) spectra presented enhanced relative contributions to the total (co)variances at frequencies (f ) between
0.025 and 0.1, corresponding to length scales up to LLJ height. In this study, as can be
seen in Table 2.3, the frequency (f ) intervals corresponding to spectral enhancement for the
strong-jet-shear group were reasonably close to the one found by Karipot et al. (2008). However, the associated length scales also included values above Hj . As in Karipot et al. (2008),
no significant decrease in the contribution of scales >> Hj was observed in this study.
Prabha et al. (2008) obtained mean wavelet variance spectra of wind velocity components
and scalars (temperature and CO2 concentration) for two groups: strong Σj,a and weak Σj,a .
In the former group, an enhancement of contributions from a range of large scales left to
39
Points extracted from Fig. 7a in Smedman et al. (2004)
0.6
0.5
No LLJ
LLJ
Kaimal
nSuu/σu
2
0.4
0.3
0.2
0.1
0
10-3
10-2
10-1
100
101
102
103
104
f/f0
Figure 2.8: Mean streamwise velocity spectra obtained by Smedman et al. (2004, data points
extracted from their Fig. 7a). The LLJ spectrum (filled triangles) is the mean of 118 halfhour spectra where a wind maximum was present at low levels; the No-LLJ spectrum (open
triangles) is the mean of 56 half-hour spectra for cases without such wind maximum. The
curve labeled Kaimal correspond to the equation of Kaimal et al. (1972) for spectra (Eq. 2.6
in the present paper)
40
the spectral peak can be noted (especially for u and v spectra) in their Fig. 6, similar to
the results obtained in the present study for the strong-Sj (strong-Σj,b ) group. However,
they also observed a substantial decrease of contributions from larger scales, closer to the
low-frequency end of the spectra, being considered an evidence of shear sheltering.
Assuming the theory is valid, the absence of shear sheltering in this study could be
related to the magnitude of Σj,b (or Σj,a ) observed. As discussed in Section 2.4.3, the values
found in this study were in general smaller than those of Prabha et al. (2008) and Smedman
et al. (2004). The strong Σj,b values reported here are called “strong” in a relative basis.
In an absolute basis, it is possible that they could be considered “weak”. However, it is
noteworthy to highlight that the difference of magnitude observed among the studies may
be partially related to the different possible ways to calculate Σj (choice of heights for u∗
and shear calculation).
Even assuming that the Σj,b values for the strong-Sj group were small in an absolute basis,
the observed enhancement of the contribution to the total (co)variances at scales larger than
Hj seems to be inconsistent with shear-sheltering theory. A no change or at least a slight
decrease would be expected.
The absence of shear sheltering could be explained by the nature of the large eddies above
the jet shear layer during the field campaign. According to Hunt and Durbin (1999), shear
sheltering strongly depends on the size and horizontal velocity of those eddies, and may be
limited or not occur at all.
2.5
Conclusions
This study has shown an important enhancement of both turbulence kinetic energy and
surface fluxes in strong jet shear conditions. In the same conditions, this study has shown
also an enhancement of relative contributions to total (co)variances at scales of the order
41
of LLJ height and larger. These results suggest that shear sheltering is not present at the
site. The authors believe it is also possible that the theory of shear sheltering, corroborated
elsewhere in other physical systems, is not one that is normally applicable in studies of
terrestrial surface-atmosphere interactions.
Assuming the application of shear-sheltering theory to low-level jets is valid, the absence
of the mechanism in this study may be attributed to properties of large eddies above the jet
shear layer: according to Hunt and Durbin (1999), maximum shear sheltering occurs when
those eddies present an “appropriate” size and travel with horizontal velocity equal to that
of the mean flow. If these conditions are not met, shear sheltering is limited or does not
occur at all. This could be the case of the present study.
Large eddies aloft propagating with the same horizontal velocity of the mean flow may
be more likely to occur at sites such as the one used by Smedman et al. (2004, Baltic Sea):
flat, homogeneous, and with large fetch (> 100 km in their study). However, despite the fact
that near-ideal site conditions were present in Oklahoma, no evidence of shear sheltering was
found, further reducing the likelihood of such phenomenon over real, non-ideal terrestrial
surfaces, typically characterized by inhomogeneities and limited fetch. Furthermore, the
spectral results of Karipot et al. (2008) also do not suggest the presence of shear sheltering
at their study site in Florida. The study of Prabha et al. (2008) so far appears to be the
only evidence of shear sheltering over a terrestrial site. It may be possible that the type of
LLJ (regarding its formation mechanism and the associated shape of wind profile) has some
influence on the occurrence of shear sheltering (different LLJs may present the same jet speed
and height). In this study, as in the study of Karipot et al. (2008), the LLJ formation was
attributed mainly to the nocturnal frictional decoupling and subsequent inertial oscillation
(Blackadar mechanism). The same was observed by Smedman et al. (2004), but in their case
the frictional decoupling was caused by the development of a thermal inversion due to the
42
transport of warm air from mainland to a colder Baltic Sea. In Prabha et al. (2008), the jets
were attributed mainly to katabatic winds.
While shear-sheltering theory applied to engineering flows has been well documented,
its application to atmospheric low-level jets has been under-reported; this is because the
application to atmospheric physical systems is far more complex than previously anticipated.
Atmospheric modeling of exchange using various scenarios of surface characteristics, flow
regimes, and low-level jet properties is likely to be the ideal method to gain a more definitive
insight into the applicability of shear-sheltering theory to nocturnal atmospheric flows.
2.6
Acknowledgments
This study was funded by the US Department of Energy, Terrestrial Carbon Processes Program, grant ER64321. The authors wish to thank Nelson Luı́s Dias, Carmen Nappo, David
Durden, Robert Kurzeja, Matthew Parker, and David Werth for their comments and suggestions, and Jinkyu Hong, Natchaya Pingintha, Chompunut Chayawat, and Xiaofeng Guo
for the help in the field experiment. We also thank Brad Orr, Dan Rusk, and Dan Nelson
(US Department of Energy’s ARM-SGP site) for the operational support provided during
the campaign.
43
Chapter 3
Impact of Nocturnal Low-Level Jets
on Surface Turbulence Kinetic
Energy1
1
Duarte HF, Leclerc MY, Zhang G, Durden D, Kurzeja R, Parker M, Werth D.
To be submitted to Boundary-Layer Meteorology
44
3.1
Abstract
This paper reports on the role of low-level jets (LLJs) on the modulation of surface turbulence
in the stable boundary layer, focusing on the behavior of the transport terms of the turbulence
kinetic energy (TKE) budget. It also examines the applicability of Monin-Obukhov similarity
theory (MOST) in light of these terms. Using coincident surface turbulence and LLJ data
collected over a three-month period in South Carolina, this paper shows that turbulence
during LLJ periods is typically stronger and more well developed in comparison with periods
without a LLJ. Surface turbulence is found to be locally imbalanced. Gain of non-local
TKE is found to occur primarily via pressure transport. The latter is found to be nearly
in balance with buoyant consumption, suggesting a connection with gravity waves. The
behavior of the pressure transport term is found to be better delineated in the presence of
LLJs, likely due to a modulation of wave activity by the jets. Shear production is found to
adhere to MOST remarkably well during LLJs, except under very stable conditions. Gain
of non-local TKE via pressure transport, likely consisted of large-scale fluctuations, is the
probable cause of the observed deviation from the MOST/z-less prediction. The fact that this
deviation is observed for periods with Kolmogorov turbulence (i.e., well-developed turbulence
with inertial subrange slope close to −5/3, used in the analysis) indicates that Kolmogorov
turbulence is not a sufficient condition to guarantee the applicability of the MOST/z-less
concept, as recently suggested in the literature. Implications of these results are discussed.
3.2
Introduction
Low-level jets are a common feature of the nocturnal stable boundary layer (Song et al. 2005;
Karipot et al. 2009). They have been observed at numerous locations over all continents (e.g.,
Banta et al. 2002; Karipot et al. 2009; Vera et al. 2006; Foken et al. 2012; Todd et al. 2008;
Wang et al. 2013; May 1995). During nighttime over land, low-level jets are typically formed
45
(at least in part) by the Blackadar (1957) mechanism. Baroclinicity, katabatic flows, and
fronts are some of the other possible causes of low-level jet formation (Stull 1988).
Low-level jets have been associated with long-range transport of scalars (e.g., Corsmeier
et al. 1997; Sogachev and Leclerc 2011; Hong et al. 2012). They are often a significant source
of turbulence in the nocturnal stable boundary layer given the enhanced shear created in
the subjet layer (e.g., Mahrt et al. 1979; Mahrt 1999; Mahrt and Vickers 2002; Banta et al.
2002, 2003, 2006; Karipot et al. 2006, 2008; Duarte et al. 2012). Their potential to transport
scalars (e.g., CO2 , H2 O, O3 , and pollutants) over several hundreds of kilometers in one night
and modulate surface turbulence and fluxes, coupled with their ubiquitousness, underscores
the relevance of low-level jets to both the air pollution and flux communities (Corsmeier
et al. 1997; Karipot et al. 2006, 2008; Sogachev and Leclerc 2011).
The turbulence kinetic energy (TKE) budget in the surface layer has been studied within
the framework of Monin-Obukhov similarity theory (MOST) for many years (e.g., Wyngaard
and Coté 1971; Högström 1990; Oncley et al. 1996; Frenzen and Vogel 2001; Li et al. 2008).
However, as Li et al. (2008) pointed out, many uncertainties still remain, specifically on the
role of the transport terms. The classical assumption is that turbulence is locally balanced,
i.e. the transport terms are either negligible or they cancel each other (McBean and Elliot
1975). However, experimental results have challenged this assumption, showing evidence of
local imbalance and underscoring the role of the transport terms (e.g., Högström 1990, 1992;
Frenzen and Vogel 2001; Li et al. 2008). These studies have reported cases of either excess or
insufficient local dissipation, being associated with either TKE gain or loss via the transport
terms respectively. The reason for these differences is still an open question (Li et al. 2008).
This is especially true for stable conditions (Pahlow et al. 2001) where turbulence is sensitive
to stable boundary layer features such as low-level jets, gravity waves, density currents, and
Kelvin-Helmholtz shear instability (Cheng et al. 2005).
46
The TKE budget in the atmospheric boundary layer under the effect of LLJs was investigated in a few studies (Table 3.1). These studies were conducted for different sites, jet types,
and stability conditions. The majority of these studies points out that pressure transport
plays an important role in the budget near the surface, but at present, there does not appear
to be a consensus on whether the pressure transport term acts as a sink or source term.
Smedman et al. (1993, 1994) used aircraft slant profile data collected over the Baltic Sea
(near the southeastern Swedish coast) in their analysis. LLJs were present at heights from
500 to 1500 m, formed by frictional decoupling of the flow due to low sea surface temperatures
(a process analogous to the formation of a nocturnal LLJ over land), and stability was near
neutral. In Smedman et al. (1993) the pressure transport term was found to be an important
source term in the layers from the base to the top of the LLJ, with larger values at the base
of the LLJ, where shear production was a maximum. In the particular case analyzed by
Smedman et al. (1994), maximum shear production was also observed at the base of the
LLJ, but in the same layer the pressure transport term was a sink. At lower layers down to
the surface, the latter was a large source term. They suggested that the pressure transport
term was responsible for bringing TKE from the layer of maximum shear production (at the
jet base) down to the surface. They also suggested that the turbulence transported towards
the surface was “inactive” turbulence (large scale fluctuations – see Högström 1990), helping
to promote mixing in the subjet layer but not producing shear stress directly.
At a different site over the Baltic Sea (Stockholm archipelago), Smedman et al. (1995)
analyzed the TKE budget for cases characterized by weakly/moderately stable stratification
and much lower LLJs (core at 30 to 150 m ASL). Tower data collected at 8 and 31 m above
the surface were used. In this case, maximum shear production was found closer to the
surface (8 m level), and at the same level the pressure transport term was a sink. At the 31
m level the latter was a source term. They concluded that TKE was transported upwards
47
by the pressure transport term, away from the layer of maximum shear production (this idea
in agreement with Smedman et al. 1994).
Bergström and Smedman (1995) used data from the same site (Smedman et al. 1995)
and analyzed the TKE budget for cases with similar stability but without the presence of a
LLJ. They found the pressure transport term to be a source at the 8 m level, and suggested
that this was the result of the transport of “inactive” turbulence from upper layers in the
boundary layer towards the surface. Contrary to the pressure transport term, the turbulent
transport term was found to be small in the studies discussed so far (Smedman et al. 1993,
1994, 1995; Bergström and Smedman 1995).
Over land (SE Kansas, USA), Cuxart et al. (2002) also found important contributions
by the pressure transport term in the near-surface TKE budget for a night characterized by
strong stratification and LLJ activity (jet height from 100 to 200 m AGL). They observed
that, in a layer from 1.5 to 30 m AGL, the pressure transport was a relevant sink, coinciding
with maximum shear production. In a layer from 30 to 50 m AGL, the pressure transport
was a relevant source term. Their results, similarly to Smedman et al. (1995), indicate that
TKE was exported away from a layer of maximum shear production near the surface by
the pressure transport term. Cuxart et al. (2002) observed relevant contributions by the
turbulent transport term as well, but its behavior was not well defined (i.e., regarding the
orientation of the transport, away from or towards the surface).
The TKE budget under low-level jet conditions has also been studied based on numerical
simulation data. A coastal LLJ in northern Chile was modeled via MM5 by Muñoz and
Garreaud (2005), and a nocturnal LLJ in the Duero basin in Spain was simulated via a
single-column model by Conangla and Cuxart (2006) and also via large-eddy simulation
(LES) by Cuxart and Jiménez (2007) (see Table 3.1 for information on jet characteristics
and stability levels). The two transport terms in these studies were practically negligible at
layers below and above the jet, i.e., TKE was practically locally balanced.
48
Different LES results were obtained by Skyllingstad (2003) for katabatic flows (jet peak
a few meters away from the surface). He found relevant contributions by the pressure
transport term above and below the jet (no direct results for the turbulent transport were
shown). The pressure transport term was a sink above the jet and a source below the jet,
suggesting a transport of TKE towards the surface (similarly to Smedman et al. 1994).
According to Skyllingstad (2003), an upward transport also could be possible, with TKE
being transported away from the model domain by gravity wave activity. Axelsen and Dop
(2009) also studied katabatic flows using LES, and their results for the pressure transport
term are in general agreement with the results of Skyllingstad (2003). Axelsen and Dop
(2009) found the turbulent transport term to be a relevant term, typically a sink above and
below the jet and a source near the jet core.
As mentioned previously, the classical assumption is that turbulence is locally balanced,
and therefore eventual gains or losses of TKE via the transport terms are expected to result
in deviations from MOST. As discussed above, this is a concern especially in the stable
boundary layer, given the presence of many non-local processes. The applicability of MOST
in the presence of LLJs has been discussed in a few studies. Smedman et al. (1995) observed
a significant departure from MOST for their dimensionless wind and temperature gradients
measured near the surface (8 m) during weakly/moderately stable conditions in the presence
of LLJs propagating at low heights (30–150 m) over the Baltic Sea. At the same site and
under similar stability, but in the absence of LLJs, Bergström and Smedman (1995) found
those dimensionless gradients to adhere to MOST. Smedman et al. (1995) pointed out that,
in their study, the flow was significantly governed by the proximity of the jet to the surface,
having some similarity to a laboratory wall jet. It is interesting to note that their results
show that TKE is not locally balanced at the 8 m level, with a large loss of TKE via pressure
transport.
49
50
Location
Baltic Sea, near
the Swedish SE
Coast
Baltic Sea, near
the Swedish SE
Coast
Baltic Sea,
Stockholm
archipelago
Baltic Sea,
Stockholm
archipelago
SE Kansas, USA
Coast of
north-central
Chile
Duero basin,
Spain
Duero basin,
Spain
Study
Smedman et al.
(1993)
Smedman et al.
(1994)
Smedman et al.
(1995)
Bergström and
Smedman
(1995)
Cuxart et al.
(2002)
Muñoz and
Garreaud
(2005)
Conangla and
Cuxart (2006)
Cuxart and
Jiménez (2007)
Frictional
decoupling at
nighttime;
katabatic flow;
baroclinicity
Frictional
decoupling at
nighttime;
katabatic flow;
baroclinicity
Topographic
barrier effect
Frictional
decoupling at
nighttime
no LLJ
Frictional
decoupling over
the cold sea
Frictional
decoupling over
the cold sea
Frictional
decoupling over
the cold sea
Jet Formation
Very stable
Near neutral
Moderately
stable
Moderately
stable
∼ 350
∼ 65
∼ 65
Weakly
stable to
very stable
100 to
200
—
Weakly–
moderately
stable
Near neutral
∼ 1500
30 to
150
Near neutral
Near-Surface
Stability
500 to
1200
Jet
Height
(m)
Model
(LES)
Model
(single
column)
Model
(MM5)
Tower
Tower
Tower
Aircraft
slant profile
+ tower
Aircraft
slant profile
Data Type
Very small (heights
above/below the jet)
Very small (heights
above/below the jet)
No direct result, but
Shr and D in close
equilibrium (heights
above/below the jet)
Loss at 1.5–30 m
layer (max Shr ) and
gain at 30–50 m layer
Gain at 8 m
Loss at 8 m (max
Shr ); Gain at 31 m
Loss at the base of
the jet (max Shr );
Gain at lower layers
down to the surface
Gain at the top and
base of the jet;
Larger values at the
base (max Shr )
Tp
Same as Tp
Relevant at 1.5–30 m
and 30–50 m layers,
but not well-defined
sign
Very small at 8 m
Very small at 8 and
31 m
Mostly small,
changing sign at
several heights
Very small (heights
above/below the jet)
Tt
Direct from
model
output
Very small (heights
above/below the jet)
Parameterized Very small (heights
together
above/below the jet)
with Tt
—
Direct
Residual
Residual
Residual
Residual
Tp
Calculation
Table 3.1: Observational and modeling studies reporting results on the pressure and turbulent transport terms (Tp and Tt
respectively) of the TKE budget during low-level jet conditions. Heights are given in meters above the surface. Shr and
D correspond to the shear production and dissipation terms, respectively.
51
—
Upper coastal
plain of South
Carolina, USA
Current study
—
Skyllingstad
(2003)
Axelsen and
Dop (2009)
Location
Study
Frictional
decoupling at
nighttime;
baroclinicity
Katabatic flow
Katabatic flow
Jet Formation
120 to
560
∼5
∼ 2.5
Jet
Height
(m)
Weakly
stable to
very stable
Stable
Stable
Near-Surface
Stability
Tower
Model
(LES)
Model
(LES)
Data Type
Table 3.1: (cont)
Gain at 34–68 m
layer
Loss above the jet,
gain below the jet
Loss above the jet,
gain below the jet
Tp
Residual
Direct from
model
output
Direct from
model
output
Tp
Calculation
Very small at 34–68
m layer
Loss above and
below the jet; Gain
at jet core
No direct result
shown
Tt
In contrast with Smedman et al. (1995), Cheng et al. (2005) found dimensionless gradients
of wind and temperature near the surface (∼ 3 m) to follow MOST very well during the welldeveloped stage of a more typical type of LLJ over land (data from CASES-99 – Great Plains
of the United States). The jet was observed at ∼ 150 m AGL and near-surface conditions
were weakly stable.
More recently, Banta et al. (2006) and Banta (2008) analyzed data from the CASES-99
and LAMAR-2003 experiments (strong wind nights weakly to moderately stable conditions)
and found results in apparent conflict with local similarity concepts, as jet speed was found
to be a better velocity scale than surface-layer friction velocity.
The studies discussed in the paragraphs above indicate that the behavior of the transport
terms (especially the pressure transport term) and the applicability of MOST are still an
open question in the stable boundary layer in the presence of LLJs. The results reported so
far are practically based on case studies. Further studies using larger data sets encompassing
a larger variety of jet and stability conditions are needed for a better understanding on the
impact LLJs have on surface turbulence.
Addressing the question above, the goal of this study is to investigate the role of LLJs on
the modulation of surface turbulence in the stable boundary layer, focusing on the behavior of
the transport terms of the TKE budget. This paper also aims at examining the applicability
of MOST in light of those terms. Tower and acoustic remote sensing data collected over a
three-month period in South Carolina, USA are used in the analysis.
Section 3.3 presents information about the experimental site and the instrumentation,
data selection, and processing of the turbulence and acoustic remote sensing data. The
characteristics of low-level jets observed at the experimental site are presented in Sec. 3.4.
The results of the analysis of the TKE budget and the applicability of MOST are presented
and discussed in Sec. 3.5. Conclusions are presented in Sec. 3.6.
52
3.3
3.3.1
Measurements and Data Processing
Experimental Site and Instrumentation
Turbulence data were collected on a tall tower near Beech Island, SC (33.406N, 81.834W,
alt. 117 m) in 2009/2010. The region is characterized by a mosaic of broken forests (mixed
pine) and agricultural lands, with urban, suburban, and industrial areas within 20 km (Fig.
3.1). Eddy-covariance measurements (three wind velocity components and concentrations of
CO2 and water vapor) were made at 34, 68, and 329 m AGL on the tall tower (Fig. 3.2)
with three-dimensional sonic anemometers (Applied Technologies Inc., model Sx at 34 m,
model A at 68 and 329 m; Longmont, CO, USA) and CO2 /H2 O gas analyzers (Li-Cor Inc.,
model Li-7500, Lincoln, NE, USA) at a frequency of 10 Hz.
Vertical profiles of mean wind speed and direction, vertical wind velocity, echo strength,
and the standard deviations of wind direction and velocity components were measured by
a phased-array boundary-layer Doppler sodar (Remtech Inc., model PA2, Paris, France)
operating with a central frequency of 2 kHz. The sodar was operated with a maximum
vertical range of 1200 m, a vertical resolution of 20 m, and was programmed to retrieve
15-min averaged profiles. The sodar was deployed at the Savannah River Site (33.340N,
81.564W, alt. 87 m), near Aiken, SC, approximately 26 km from the tall tower mentioned
above (Fig. 3.1). The sodar site is surrounded by mixed forest spanning several kilometers.
3.3.2
Data Selection
We selected the months of May, June, and July, 2009 for the present study, and considered
only nighttime data (20:00 to 05:00 EST). Several nights during these months presented lowlevel jet activity lasting for multiple hours, with a high incidence of southwesterly winds.
Continuous low-level jet activity, formed by (or facilitated by) the stabilization of the atmospheric boundary layer on the regional scale, is a desired feature given the fact that the sodar
53
85˚W
80˚W
(a)
35˚N
35˚N
30˚N
30˚N
85˚W
80˚W
(b)
(c)
Figure 3.1: (a) Site location in the United States, (b) local topography map, and (c) local
satellite view (source: Google Earth; imagery date: 10/05/2010) showing land use. The
location of the tall tower (T) and the Remtech sodar (R) are indicated.
54
Figure 3.2: The Savannah River National Laboratory (SRNL) instrumented tall tower used
in the study. The two lowest eddy-covariance systems (34 and 68 m levels) can be observed.
and tall tower were separated by 26 km. Southwesterly winds are also a desired feature, given
the orientation of the sonic anemometers on the tall tower (210◦ azimuth). Winter months
were avoided due to the predominance of northeasterly winds (direction in which turbulence
is most disturbed by the tower structure).
3.3.3
Turbulence Data Processing
We processed the turbulence data using 30-min blocks. We used the despiking method described in Vickers and Mahrt (1997) and applied the planar-fit coordinate rotation described
by Wilczak et al. (2001) to wind velocity components. The data were then linearly detrended
(Rannik and Vesala 1999). Resulting fluctuations were used to calculate variances and covariances. Only runs with average wind direction between 70◦ and 350◦ were considered to
avoid flow distortion due to the tower structure (sonic anemometers were pointed to 210◦ ).
55
We calculated the dissipation rate of TKE () by using the inertial dissipation method,
based on Kolmogorov’s hypothesis:
3/2
2π f 5/3 Suu (f )
,
=
u
αu
(3.1)
where u is the average streamwise wind velocity, Suu (f ) is the power spectrum of u as a
function of natural frequency f , and αu is the associated Kolmogorov constant, here taken
as 0.5 (Batchelor 1953). In the inertial subrange, f 5/3 Suu (f ) is assumed to be constant,
where Suu ∝ f −5/3 (Kolmogorov’s −5/3 power law). This method was also used in the
Baltic Sea LLJ studies discussed in Sec. 3.2 (Smedman et al. 1993, 1994, 1995; Bergström
and Smedman 1995).
The power spectrum of u was calculated for each 30-min run, and bin averaging was
employed to smooth the spectra (64 non-overlapping f classes of logarithmically increasing
width were used). We then used the frequency band f [0.5 : 2.0] Hz to calculate the average
of f 5/3 Suu (f ) and consequently via Eq. 3.1 (this frequency band was also used by Piper
and Lundquist (2004) to calculate from similar sonic anemometer data).
Turbulence runs without a well-formed inertial subrange (i.e., presenting non-Kolmogorov
turbulence) were removed from the analysis of the TKE budget terms and applicability of
MOST. For being considered in the analysis, a given run was required to have an inertial
subrange slope within the interval −1.69 ± 0.14 (note that −5/3 = −1.67), defined based
on the average slope ± 2 standard deviations considering data from the 34 and 68 m levels
during LLJs.
3.3.4
Sodar Data Processing and LLJ Criteria
The sodar data were averaged to 30-min profiles in order to allow the comparison with the
tall tower data. Those 30-min profiles were used for selecting low-level jet events.
56
We used the same criterion used by Banta et al. (2002) for the identification of LLJs,
where the first wind speed maximum above ground level with speed at least 1.5 m s−1 larger
than the adjacent minima above and below is classified as a low-level jet. With this criterion,
we extracted the relevant low-level jet information – height (Zj ), speed (Uj ), and direction
(DIRj ) – for the period of interest. Intermittent jets were not considered in this study (see
discussion in Sec. 3.3.2). Only low-level jets with duration equal to or greater than two
hours (i.e., for a minimum of four consecutive 30-min profiles) were included in the “LLJ
group”. Similarly, continuous periods (two or more hours of duration) without LLJ activity
were also determined, providing a contrasting “NO-LLJ group” for comparison.
3.4
Low-Level Jet Statistics
Table 3.2 presents the statistics for the observed low-level jets. The period of interest in this
study spans from April 30, 20:00 EST to August 1, 05:00 EST, 2009. It only considers the
30-min blocks between 20:00 and 05:00 EST. The total number of 30-min blocks associated
with this period is 1767. The number of 30-min sodar profiles used in the analysis was 1489
(i.e., ∼84% coverage).
Results show a high occurrence rate of low-level jets at the experimental site. Continuous
jet activity was observed in ∼47% of the profiles analyzed. Interestingly, Karipot et al. (2009)
also reported in their climatological study a 47% jet occurrence rate for their site also in SE
United States (northern Florida) for the months of June to August. It is important to note,
however, that continuous jets and intermittent jets were computed in their statistics, while
in the present study only continuous jets were considered. The results therefore suggest a
higher occurrence rate of jets at the South Carolina site.
Fig. 3.3 shows histograms of jet height, speed, and direction. For jet height, we can
see higher frequencies in the 300-400 m range, especially at 380 m, while jet speed presents
57
Table 3.2: Statistics of the low-level jet events (30-min profiles) observed in May–July/2009,
20:00 to 05:00 EST. Each event is associated with continuous jet activity (minimum duration
of two hours). Number of continuous NO-LLJ runs is also shown.
Uj (m s−1 ) Uj /Zj (s−1 )
Zj (m)
Mean
Std dev
Minimum
Maximum
326
79
120
560
11.2
2.6
4.6
19.3
Number of events (LLJ)
Number of events (NO-LLJ)
Number of profiles used in
the analysis
Number of 30-min blocks in
the period of interest
0.035
0.007
0.018
0.058
700
376
1489
1767
a frequency peak in the 10-13 m s−1 range. Regarding jet direction, we can see a higher
occurrence in the S-W quadrant, especially between SW and W. These results are in general
agreement with the climatological results reported by Karipot et al. (2009) for their northern
Florida site.
In order to illustrate the general shape of the LLJs analyzed in this study, Fig. 3.4
presents a composite wind speed profile for all selected cases (see Table 3.2). Note the welldefined linear behavior in the subjet layer, with less scatter, and the relatively narrow LLJ
core.
Given the location of our experimental site in the upper coastal plain of South Carolina, and considering the proximity of the Appalachian Mountains and the Atlantic Ocean,
terrain-induced baroclinicity along with inertial accelerations likely plays an important role
in the development of the southwesterly jets observed in this study. Pibal observations of
the Carolina LLJ by Sjostedt et al. (1990) show a predominance of LLJs with direction
58
140
(A)
20
140
20
80
10
60
40
5
20
15
100
80
10
%
15
100
Number of events
120
%
Number of events
120
(B)
60
40
5
20
0
0
0
100
200
300 400
zJ (m)
500
600
0
700
0
0
2
140
4
6
(C)
8 10 12 14 16 18 20 22 24
UJ (m s-1)
20
15
100
80
10
%
Number of events
120
60
40
5
20
0
0
0
60
120
180
240
DIRJ (deg)
300
360
Figure 3.3: Histograms of (a) low-level jet height, (b) speed, and (c) direction for the 700 jet
events (30-min profiles) observed during May–July/2009, 20:00 to 05:00 EST. These events
are associated with continuous jet activity (minimum duration of two hours)
59
3
2.5
z/ZJ
2
1.5
1
0.5
0
0
0.2
0.4
0.6
u/UJ
0.8
1
1.2
Figure 3.4: Composite wind speed profile for all low-level jet events considered in this study.
LLJ speed and height are used as scaling parameters. Error bars indicate ±1 standard
deviation
parallel to the coastline, with a higher frequency of northeasterly jets during autumn and
southwesterly/westerly jets during spring and summer (the case of the present study). Doyle
and Warner (1993) investigated the structure and dynamics of the northeasterly Carolina
coastal plain LLJ using a mesoscale model, and found that the jet was formed due to strong
baroclinicity in the region between the Appalachian Mountains and the Atlantic Ocean, and
that its strength was modulated by strong inertial accelerations. Observations from a site in
Maryland (mid-Atlantic state) during the warm season (Zhang et al. 2006) also indicate the
predominance of southwesterly/westerly LLJs. Zhang et al. (2006) investigated the dynamics of the southwesterly LLJ using a mesoscale model, and similarly to Doyle and Warner
(1993), they found that baroclinicity (due to the Appalachians Mountains and the Atlantic
Ocean) and inertial accelerations played an important role in the development of the LLJ.
60
3.5
3.5.1
Turbulence Kinetic Energy Budget
Formulation
Assuming horizontal homogeneity and neglecting subsidence, the TKE budget equation for
a coordinate system aligned with the mean wind is given by (Stull 1988):
g
∂u ∂w0 e 1 ∂w0 p0
∂e
−
−
= w0 θv0 −u0 w0
−
∂t
∂z} | {z
∂z } ρ ∂z |{z}
θv
{z
|{z}
|
|
{z
}
| {z }
D
Stg
B
Shr
Tt
(3.2)
Tp
where
Stg = storage term
B = buoyant production/consumption term
Shr = shear production term
Tt = turbulent transport term
Tp = pressure transport term
D = dissipation term
Variables e, t, g, θv , w, u, z, ρ, p, and correspond to instantaneous TKE, time, acceleration
of gravity, virtual potential temperature, vertical wind velocity, streamwise wind velocity,
height above the surface, air density, atmospheric pressure, and dissipation rate of TKE,
respectively. Overbars indicate averaging, and primes indicate fluctuations from the mean.
The instantaneous TKE is calculated from the fluctuations of the streamwise (u), lateral (v),
and vertical (w) wind velocities as e = 0.5(u0 2 + v 0 2 + w0 2 ).
A dimensionless version of Eq. 3.2 can be obtained by multiplying it by κ(z − d)/u3∗ ,
where κ is the Von Kármán constant and d is the displacement height:
+
+
Stg
= B + + Shr
+ Tt+ + Tp+ + D+ .
61
(3.3)
Note that with this nondimensionalization the buoyant production/consumption term becomes the negative of the Monin-Obukhov stability parameter, i.e. B + ≡ κ(z−d)B/u3∗ = −ζ.
There is no consensus yet on the relative contribution of each term in Eqs. 3.2 and 3.3
in the stable boundary layer. According to Wyngaard (2010), for the TKE budget under
stable conditions, “both turbulent and pressure transport are found to be negligible, so that
shear production is essentially balanced by buoyant destruction and viscous dissipation” (i.e.,
local balance assumption). However, experimental results have challenged this assumption,
showing evidence of local imbalance and underscoring the role of the transport terms (e.g.,
Högström 1990, 1992; Frenzen and Vogel 2001; Li et al. 2008). Li et al. (2008) defined an
imbalance coefficient ψ ≡ −D+ (ζ = 0), where D+ (0) is the dimensionless dissipation under
+
neutral conditions. Under local balance, Shr
(0) = −D+ (0) = ψ = 1. However, ψ values
greater than 1 (“excess dissipation”) and smaller than 1 (“insufficient dissipation”) have
been reported (see review by Li et al. 2008, Table 2). The results from the LLJ studies by
Smedman et al. (1993, 1994), for instance, correspond to the former group (ψ > 1), where
the excess dissipation was associated with the energy gain via the pressure transport term.
3.5.2
Results and Discussion
Except for the pressure transport term, we calculated all the budget terms directly (Eq. 3.2)
for a layer between 34 and 68 m AGL. For the calculation of Stg , B, and Shr , we averaged
the values of e, θv , w0 θv0 , and u0 w0 observed at 34 and 68 m. The dissipation rate of TKE
was calculated using Eq. 3.1, and the average between 34 and 68 m was used to calculate
D in Eq. 3.2. In the last step, the pressure transport term was calculated as the residual
term of the budget:
Tp = Stg − B − Shr − Tt − D.
62
(3.4)
20
25
1 + 4.11x
20
10
15
-D+
Shr+
15
1.24 + 4.18x
5
10
0
5
-5
0.01
(A)
0.1
1
0
0.01
10
(B)
0.1
-B+ = ζ
20
1
10
-B+ = ζ
20
0.31 + 0.96x
15
10
10
Tt+
Tp +
15
-0.07
5
5
0
0
-5
0.01
(C)
0.1
1
-5
0.01
10
-B+ = ζ
(D)
0.1
1
10
-B+ = ζ
Figure 3.5: Normalized TKE budget terms as a function of stability for the LLJ group: (a)
shear production, (b) dissipation, (c) pressure transport, and (d) turbulent transport. Blue
points are bin averages, and error bars correspond to ±1 standard deviation. Purple curves
correspond to least-square fitting for data points up to ζ = 1
Each term was then nondimensionalized according to Eq. 3.3, using κ = 0.4, d = 13.2 m,
z = 51 m (34–68 m layer midpoint), and the average u∗ between 34 and 68 m. According to
MOST, these terms are expected to be a function of ζ.
Figure 3.5(a–d) presents the normalized TKE budget terms as a function of ζ (i.e., the
negative of the normalized buoyant production/consumption term, −B + , calculated for the
34–68 m layer) for the selected LLJ events. The bin averages for each term are plotted
together in Fig. 3.6.
63
20
Shr+
D+
Tp+
Tt+
B+
10
0
-10
-20
0.01
0.1
1
10
+
-B = ζ
Figure 3.6: Normalized TKE budget terms for the LLJ group. Points correspond to the
bin averages shown in Fig. 3.5
It can be seen that shear production and dissipation are the dominant terms of the
budget, as expected in the stable boundary layer (Wyngaard 2010). The general result
does not support, however, the concept of local balance of TKE. Dissipation is found to be
approximately of the same magnitude of shear production. The total local losses, i.e., D +B,
therefore exceed the local production, indicating that non-local TKE is gained in the layer
via transport. As shown in Fig. 3.6, the turbulent transport is found to be virtually zero,
therefore the observed energy gain is attributed to the pressure transport term. The storage
term is found to be negligible (data not shown).
The higher scatter observed for the pressure transport term in Fig. 3.5c is attributed to
the fact that, since Tp+ is calculated as a residual, it contains accumulated errors from the
other terms in addition to any advective term which is assumed to be negligible in Eq. 3.2.
Despite the presence of several high positive values, we can see from the bin averaged values
64
that, on average, Tp is approximately in balance with buoyant destruction. The general
+
result of Shr
≈ −D+ , Tt+ ≈ 0, and Tp+ ≈ −B + is in agreement with the discussions in
Kaimal and Finnigan (1994) regarding the TKE budget in the stable boundary layer.
+
The results show that Shr
and D+ follow MOST (local scaling formulation) remarkably
well up to ζ ∼ 1, corroborating earlier findings by Cheng et al. (2005). This result is in
agreement with the concept of z-less stratification (i.e., turbulence statistics assumed to
be independent of z). The latter predicts a linear behavior of those terms with ζ (Hong
2010; Grachev et al. 2013). The observed near-zero turbulent transport term is consistent
with the concept of local TKE equilibrium (c.f. Sec. 3.5.1) and z-less stratification, while
the non-zero pressure transport is not (Tp+ ≈ −B + ). Note that Tt+ and Tp+ represent the
vertical divergence (∂/∂z) of the terms −w0 e and −w0 p0 /ρ respectively (c.f. Eq. 3.2) and are
expected to be null in z-less conditions. Further discussion on Tp+ and the observed z-less
breakdown will be presented at the end of this Section.
Figure 3.7 shows a comparison between the normalized TKE budget terms (as a function
of ζ) for the LLJ group with the ones for the NO-LLJ group, and Fig. 3.8 shows the
respective bin averages for the NO-LLJ group. We can observe that the normalized TKE
budget terms in both groups follow practically the same behavior, but more scatter is present
for the NO-LLJ points. In this group, even with the filtering method based on the inertial
subrange slope values (c.f. Sec. 3.3.3), some scatter still persists.
The near-surface turbulence statistics in Table 3.3 shows that for the LLJ group, average
TKE and friction velocity (u∗ ) are 30 and 39% greater than for the NO-LLJ group, respectively, and average Monin-Obukhov stability parameter (ζ) is 49% smaller. The differences
of the median values between both groups are even more pronounced. Table 3.3 also shows
larger standard deviations in the turbulence statistics observed for the NO-LLJ group. We
also found the inertial subrange slopes (Suu ) for the LLJ group to be very close to the expected −5/3, while more scatter was observed for the NO-LLJ group (data not shown),
65
25
15
20
10
15
LLJ
NO-LLJ
-D+
Shr+
20
5
10
0
5
-5
0.01
(A)
0.1
1
0
0.01
10
(B)
0.1
-B+ = ζ
1
10
-B+ = ζ
20
15
15
10
10
Tt+
Tp +
20
5
5
0
0
-5
0.01
(C)
0.1
1
-5
0.01
10
-B+ = ζ
(D)
0.1
1
10
-B+ = ζ
Figure 3.7: Normalized TKE budget terms as a function of stability for both the LLJ
(green circles) and NO-LLJ (black circles) groups: (a) shear production, (b) dissipation,
(c) pressure transport, and (d) turbulent transport
66
20
Shr+
Tp+
D+
Tt+
B+
10
0
-10
-20
0.01
0.1
1
10
+
-B = ζ
Figure 3.8: Normalized TKE budget terms for the NO-LLJ group. Points correspond to
the bin averages of the data points shown in Fig. 3.7
with a reasonably larger amount of runs being rejected by the filter described in Sec. 3.3.3.
These results indicate that the NO-LLJ cases are more susceptible to nonstationarity issues
associated with weaker turbulence, while the LLJ cases tend to present stronger and more
well-developed turbulence.
Focusing on the results for the LLJ group, we fitted the following curves to the data in
Fig. 3.5:
+
= 1 + c1 ζ,
Shr
(3.5)
D+ = c2 + c3 ζ,
(3.6)
Tt+ = c4 ,
(3.7)
where c1 , c2 , c3 , and c4 are constants. Eq. 3.5 is the classical Businger-Dyer relation (Businger
et al. 1971; Dyer 1974) for the dimensionless shear production term in stable conditions, and
67
Table 3.3: Near-surface turbulence statistics (34 m data) for the LLJ and NO-LLJ groups,
for ζ[0 : 10]. N is the number of 30-min runs in each group
ζ (–)
TKE (m2 s−2 )
u∗ (m s−1 )
N
LLJ
avg ± std dev [min:max], median
NO-LLJ
avg ± std dev [min:max], median
0.46 ± 0.63[0.004 : 8.00], 0.29
0.35 ± 0.30[0.01 : 1.96], 0.26
0.25 ± 0.13[0.02 : 0.72], 0.23
0.91 ± 1.11[0.004 : 8.29], 0.53
0.27 ± 0.46[0.01 : 2.78], 0.12
0.18 ± 0.15[0.02 : 0.77], 0.13
591
240
Eq. 3.6 corresponds to the typical form used for the dimensionless dissipation under the
same conditions (Li et al. 2008). We only used data up to ζ = 1 for the curve fitting, given
the higher uncertainties at higher stabilities. The results were:
+
Shr
= 1 + 4.11ζ,
(3.8)
D+ = −1.24 − 4.18ζ, and
(3.9)
Tt+ = −0.07.
(3.10)
With the results above, Tp+ (0) must equal 0.31 in order to close the budget. We therefore
fitted the following curve to the data in Fig. 3.5c:
Tp+ = 0.31 + c5 ζ,
(3.11)
Tp+ = 0.31 + 0.96ζ.
(3.12)
and obtained
The dimensionless shear production term in our study is reasonably close to the prediction
(c1 = 4.11 vs 4.7 in Businger et al. (1971); we actually observed an even closer result when
68
limiting the curve fitting to the data up to ζ = 0.5 (results not shown)). Our results also show
an excess of dissipation, with the imbalance coefficient greater than 1 (ψ = −D+ (0) = 1.24),
being associated with the energy input via the pressure transport term.
Similar results based on observations over land were reported by Högström (1990). For
weakly stable conditions, he found
+
Shr
= 1 + 4.8ζ,
(3.13a)
D+ = −1.24 − 4.7ζ,
(3.13b)
Tt+ = −0.25, and
(3.13c)
Tp+ = 0.49 + 0.9ζ,
(3.13d)
with higher accuracy for ζ up to 0.2, given the available data. Note that, in his study,
the contribution of the pressure transport term was slightly higher. In a following study,
Högström (1992) found that, for neutral conditions D+ (0) = −1.24, Tt+ (0) = 0, and Tp+ (0) =
0.24. These values are closer to the ones found in the present study. The value we found for
D+ (0) is exactly the same as the one reported by Högström (1990, 1992).
Högström (1990) suggested that such positive contribution from Tp+ was related to “inactive” turbulence (large scale fluctuations which do not promote the transport of momentum)
being injected to the surface layer from the upper parts of the boundary layer. Smedman
et al. (1994) found the same result at a different site and observed that the TKE input at
the surface was from a LLJ, i.e., TKE was transported away from a layer of strong shear
production underneath a LLJ to the surface via pressure transport.
As alluded earlier, other studies have also reported results indicating important contributions by Tp in the near-surface TKE budget during LLJ conditions (c.f. Table 3.1).
These studies were associated with different sites, LLJ types, and stability levels. The role
of the pressure transport term as a sink or a source term varied in each study. Before inter69
comparing the results, it is important to note that, as Tp is a smaller term in the budget,
the relative role of error in this term is greater than in the dominant terms (Shr and D).
The differences observed could be at least in part related to different approaches used in the
calculation of Tp , as discussed below.
Out of the experimental studies cited in Table 3.1, all of them (except Cuxart et al.
2002) calculated the pressure transport term as a residual. Note that this term may include
advection (assumed negligible, but may vary from site to site) and accumulated errors from
the calculation of other budget terms. Different choices of ∆z for the calculation of the gradients, measurement types (tower vs aircraft), and screening methods to remove unsuitable
periods for the calculation of the dissipation term are some of the factors that may lead to
different levels of error and therefore to differences in Tp . On the other hand, Cuxart et al.
(2002) calculated Tp directly, i.e., they used data from sonic anemometers and collocated
microbarographs to obtain w0 p0 . This approach, however, is known to be problematic due
to the limitation of the available technology to measure small static pressure fluctuations
of interest (Li et al. 2008). Regarding modeling studies cited in Table 3.1, differences in
Tp could be at least in part associated with different modeling approaches and associated
parameterizations and simplifications used.
The general result seen in Table 3.1 is that TKE is exported away from a layer of maximum shear production via pressure transport. This layer of maximum shear production can
be near the surface (Smedman et al. 1995; Cuxart et al. 2002) or aloft near the base of the
LLJ (Smedman et al. 1994), depending on the jet characteristics and stratification in the
boundary layer. The former scenario corresponds to a traditional boundary layer, while the
latter corresponds to an upside-down boundary layer (Mahrt and Vickers 2002). The LES
results for katabatic jets by Skyllingstad (2003) and Axelsen and Dop (2009) are consistent
with the idea of TKE transport away from a layer of maximum shear production via Tp .
Despite the fact that a peak in shear production was observed at the shallow layer between
70
the surface and the jet core, strong shear production of the same magnitude was observed
at layers above the jet core. TKE was found to be exported away from this layer via Tp ,
with energy gain being observed close to the surface. It is important to note, however, that
the results obtained by Smedman et al. (1993) and Bergström and Smedman (1995) seem to
not align with the general result discussed in this paragraph. Smedman et al. (1993) found
Tp to be consistently positive at the top and base of LLJs. Bergström and Smedman (1995)
found Tp to be positive near the surface in the absence of LLJs. These results indicate that
the energy gain via Tp may be associated with a different process.
Three possible explanations for our positive Tp in the 34–68 m layer during LLJ events
are: i ) maximum shear production occurs at the surface, and TKE is transported upwards
by Tp into the layer; ii ) maximum shear production occurs close to the LLJ, and TKE is
transported downwards by Tp ; and iii ) energy from the upper layers in the boundary layer is
transported towards the surface layer, regardless if the maximum shear production occurs at
the surface or aloft near the LLJ, in a process not necessarily associated with low-level jets.
Our results indicate typically higher turbulence intensities near the surface and decreasing
magnitudes with height (not shown), suggesting the presence of a traditional boundary layer
and supporting (i) instead of (ii ). Explanation (iii ) also seems to have value. The fact
that we obtained similar results for the NO-LLJ group reinforces (i) and (iii ). As discussed
earlier, the observed pressure transport term tends to balance the buoyant destruction term,
on average. It is possible that gravity waves are responsible for the observed energy gain near
the surface via Tp . Bergström and Smedman (1995), for instance, found Tp+ > 0 near the
surface for stable, no-LLJ conditions that coincided with evidence of gravity wave activity
for most of the events analyzed.
Even though our results show a similar behavior of Tp for both NO-LLJ and LLJ groups,
typically presenting positive values, the results for Tp for the LLJ group indicate a better
relationship with ζ. While the results in both groups could be possibly linked with gravity
71
waves —which are a common phenomenon in the stable boundary layer—, we hypothesize
that the LLJs could trigger the formation of gravity waves given the enhanced wind shear
adjacent to their cores, resulting in more organized wave activity and more organized behavior of Tp . However, it is important to note that the less organized behavior of Tp for the
NO-LLJ group is at least in part related to uncertainties due to the impact of nonstationarity
on the calculation of the other TKE budget terms. Further investigation on the relationship
between LLJs, gravity waves, and Tp is suggested.
Z-less Breakdown and Tp
As discussed in the previous Section, the shear production term is found to adhere to MOST
remarkably well up to ζ ∼ 1 (Fig. 3.5a), in agreement with the linear z-less prediction.
+
Above ζ ∼ 1, Shr
is found to be typically smaller than the linear prediction, suggesting a
breakdown of the z-less concept. This behavior has also been reported in other studies (see
review by Hong 2010; Grachev et al. 2013), and there is a persisting debate on the validity
of the z-less stratification assumption (Yagüe et al. 2001; Grachev et al. 2005; Mahrt 2007;
Hong 2010; Grachev et al. 2013).
Using extensive observations over the Arctic pack ice, Grachev et al. (2013) reported
that deviations from z-less theory were associated with non-Kolmogorov turbulence (i.e.,
turbulence without a well-defined inertial subrange), not expected to adhere to MOST in first
place. They suggested Rif (flux Richardson number) = 0.20–0.25 as a primary threshold for
the applicability of MOST, as they found inertial subrange slopes of wind velocity spectra to
depart from −5/3 for Rif above 0.20–0.25. After filtering out the periods with Rif above the
threshold, their results showed adherence to the z-less limit of MOST, and they concluded
that this approach ends the controversy on the subject. In other words, the use of data
periods characterized by non-Kolmogorov turbulence may explain why previous studies have
72
found MOST/z-less breakdown, but those periods are not supposed to follow MOST in first
place (note that different screening/selection of periods may lead to different conclusions).
We used the Rif -based screening method in a first attempt (Rif < 0.2 specifically), and
our results for Shr and D indicated a close agreement with the linear MOST/z-less prediction
(even for ζ > 1; results not shown), in agreement with the results of Grachev et al. (2013).
However, note that this filtering method is justified only if the inertial subrange slope values
depart from −5/3 for Rif > 0.2. The inertial subrange slope values we obtained for Suu ,
differently from the results in Grachev et al. (2013), did not display a clear relationship
with Rif (data not shown). Many periods with Kolmogorov turbulence were observed for
Rif > 0.2, and their removal was not justified. A different screening method was then
adopted, based directly on the departure of the inertial subrange slope values from −5/3
+
(c.f. Sec. 3.3.3). After using this more robust approach for our data set, our results for Shr
(Fig. 3.5a) indicate z-less breakdown. Our results indicate that the presence of Kolmogorov
turbulence is not a sufficient criterion to guarantee the applicability of the MOST/z-less
concept, as suggested by Grachev et al. (2013).
Our results suggest that the near-surface TKE gain via the pressure transport term is
+
responsible for the z-less breakdown observed for Shr
at high stabilities. Obviously, Tp+ 6= 0,
per se, is already a sign of z-less breakdown. It is possible that such turbulence has an
“inactive” nature (Högström 1990), i.e., consisted of large scale fluctuations contributing to
the increasing of mixing (standard deviations) but not to the transport of momentum (u∗ ).
+
and Tp+ increase linearly with ζ up to ζ ∼ 1. Above that, Tp+ increases faster
Both Shr
+
with ζ, and Shr
increases at a slower rate. The increase of mixing due to “inactive” turbulence
+
could lead to a decrease in the wind speed gradient and therefore to the decrease of Shr
in
relation to the linear z-less prediction, observed for ζ greater than ∼ 1. It is interesting
to observe that the dissipation term (Fig. 3.5b), calculated based on spectral densities in
the inertial subrange (small eddy scales), seems to approximately follow the linear z-less
73
prediction for ζ > 1. This implies that the total energy gain in the considered layer (i.e., via
+
Shr
and Tp+ ) should be linear with ζ.
3.6
Conclusions
The behavior of surface turbulence during nocturnal low-level jet events was investigated
using a combination of sodar and turbulence/flux tower data collected in the upper coastal
plain of South Carolina, USA over a three-month period. The analysis focused on the TKE
budget, with special attention to the pressure transport term, and also on the applicability
of MOST in light of this term. Cases with well-developed turbulence were selected for the
analysis.
Near-surface TKE was found to be locally imbalanced, opposing the classic view of the
TKE budget in the stable boundary layer. The total local energy losses (buoyant consumption and dissipation) were found to typically exceed local shear production. As the turbulent
transport term was found to be practically negligible, the observed additional TKE was attributed to pressure transport. The latter was found to be in approximate balance with
buoyant consumption.
Previous findings on the near-surface TKE budget during LLJs also indicate that the
turbulent transport is very small, but results for the pressure transport varied (c.f. Table
3.1). It is important to note first that, as Tp is a smaller term in the budget, the relative
role of error in this term is greater than in the dominant terms (Shr and D). The differences
observed across studies could be at least in part related to different approaches used in the
calculation of Tp . The general view in previous studies is that TKE is transported away from
layers of maximum shear production (at the surface or close to the LLJ core) via Tp , but
results from studies including Högström (1990), Smedman et al. (1993), and Bergström and
Smedman (1995) indicate that TKE may be brought down from upper layers in the boundary
74
layer, in a process not necessarily associated with LLJs. In the present study, the behavior of
Tp was generally similar for periods with and without LLJs, suggesting an upward transport
of TKE from a layer of maximum shear production near the surface (as in Smedman et al.
1995; Cuxart et al. 2002), or more likely, a downward transport from upper layers in the
boundary layer. The close relationship observed between pressure transport and buoyant
destruction may suggest that the former is associated with gravity wave activity. Under LLJ
conditions, the behavior of Tp was found to be more defined. The authors hypothesize that
this could be a reflection of the modulation of gravity wave activity by LLJs.
The shear production and dissipation terms during LLJs were found to conform well to
the MOST local-zless predictions in general, corroborating earlier findings by Cheng et al.
(2005), with the support of a more extensive data set. Under very stable conditions, however, shear production was found to depart from the linear prediction. This result indicate
that the presence of Kolmogorov turbulence (i.e., well-developed turbulence with inertial
subrange slope close to −5/3) is not a sufficient condition to guarantee the applicability of
the MOST/z-less concept, as suggested by Grachev et al. (2013).
The results suggest that non-local TKE gain via pressure transport (per se an indication
+
of conflict with the z-less concept) could be the cause of the observed behavior for Shr
under
very stable conditions (values smaller than the z-less prediction). Such energy, likely of an
“inactive” nature, would impact mixing (by increasing the variance of the wind velocity
components) but not directly u∗ , as discussed in Högström (1990). The enhanced mixing
+
would reduce the wind speed gradient, and therefore Shr
.
Of relevance to numerical modeling studies of the stable boundary layer, the present
study shows experimental evidence that pressure transport cannot be neglected in the TKE
budget. The processes controlling this term remain uncertain, but as discussed above, LLJs
could possibly play a role. Further studies on the relationship between LLJs, gravity waves,
and Tp are suggested.
75
The present study also found that turbulence during LLJ periods was typically stronger
and more stationary, with a more well-defined inertial subrange in comparison with periods
without a LLJ. This result has an important implication to flux calculations during nighttime
stable conditions. It suggests that the use of a u∗ threshold criterion (a common approach
in the flux community – see Aubinet et al. 2012) most likely would result in a selection of
periods under the influence of LLJs (average u∗ was found to be 39% larger for the LLJ
group). Studies have shown that LLJs are able to transport scalars over long distances (in
the order of hundreds of km) during nighttime (e.g., Corsmeier et al. 1997; Sogachev and
Leclerc 2011; Hong et al. 2012), which means they could impact the measurement of the
local net ecosystem exchange (NEE) with a flux tower.
In other words, the LLJs may provide the turbulent conditions necessary for calculating
fluxes via the eddy covariance technique, but that does not guarantee that the advection
terms of the NEE equation are negligible (also pointed out by Hong et al. 2012). In fact,
the LLJs may actually do the opposite with the advection terms. Neglecting those terms in
that case could result in significant errors in the NEE measurements. This approximation is
done in most studies, given the extreme difficulties of measuring advection in the field.
Wind profile measurements —allowing the detection of LLJs beyond the height of the
flux measurements— can have a great value in the interpretation of local surface-atmosphere
flux measurements during nighttime conditions.
3.7
Acknowledgments
This study was funded by the U.S. Department of Energy, Terrestrial Carbon Processes
Program, grant ER64321. The work performed by SRNL was supported, in part, from
funding also provided by the DOE Office of Science Terrestrial Carbon Processes Program
and was performed under contract no. DE-AC09-08SR22470.
76
Chapter 4
Conclusions
The effect of low-level jets on surface turbulence and fluxes in the nocturnal stable boundary
layer was investigated by using extensive sodar and tower observations from two experimental
sites in the United States.
In the Oklahoma experiment, surface turbulence and fluxes were found to be reasonably enhanced in the presence of low-level jets. This enhancement was found to occur at
large scales, not corroborating the shear-sheltering theory and underlining the complexity
of surface-atmosphere interactions in nocturnal stable conditions. Atmospheric modeling of
exchange using various scenarios of surface characteristics, flow regimes, and low-level jet
properties is suggested to further assess the potential applicability of the shear-sheltering
theory to atmospheric flows.
In the South Carolina study, surface turbulence during LLJ periods was found to be
typically stronger and more stationary, with a more well-defined inertial subrange in comparison with periods without a LLJ. Contrary to the classic view of the TKE budget in the
stable boundary layer, surface TKE was found to be locally imbalanced, with a relevant gain
of non-local energy via pressure transport. The latter was found to be in approximate balance with buoyant consumption, suggesting a possible connection with gravity wave activity.
77
Under LLJ conditions, the behavior of the pressure transport term was found to be more
defined. It is hypothesized that this could be a reflection of the modulation of gravity wave
activity by LLJs. Further studies on the relationship between LLJs, gravity waves, and the
pressure transport term are suggested.
Also in the South Carolina study, the shear production and dissipation terms of the
TKE budget during LLJs were found to conform well to the Monin-Obukhov/z-less theory
in general, corroborating earlier findings by Cheng et al. (2005) with the support of a more
extensive data set. Under very stable conditions, however, shear production was found to
depart from the linear prediction. An interesting aspect is that the periods used in the
analysis were characterized by Kolmogorov turbulence (i.e., well-developed turbulence with
inertial subrange slope close to −5/3), which according to the recent results of Grachev et al.
(2013) are expected to follow the z-less prediction. The present results indicate, however,
that the presence of Kolmogorov turbulence is not a sufficient condition to guarantee the
applicability of the MOST/z-less concept. They also suggest that the gain of non-local TKE
(likely consisted of large scale fluctuations) via pressure transport is a possible cause of the
departure from z-less observed for the shear production term.
The presented results are of relevance to observational and modeling studies of processes
in the nocturnal stable boundary layer, including studies of surface-atmosphere exchange
and pollutant dispersion. Of particular relevance to numerical modeling studies, the present
study shows experimental evidence that pressure transport cannot be neglected in the TKE
budget. The processes controlling this term remain uncertain, but as discussed above, LLJs
could possibly play a role. Further investigation is encouraged.
The results from the Oklahoma and South Carolina experiments show that turbulence
is typically stronger and more well-developed during LLJ conditions. These results have an
important implication to flux calculations during nighttime stable conditions. They suggest
that the use of a u∗ threshold criterion (a common approach in the flux community – see
78
Aubinet et al. 2012) most likely would result in a selection of periods under the influence of
LLJs. Studies have shown that LLJs are able to transport scalars over long distances (in the
order of hundreds of km) during nighttime (e.g., Corsmeier et al. 1997; Sogachev and Leclerc
2011; Hong et al. 2012), which means they could impact the measurement of the local net
ecosystem exchange (NEE) with a flux tower.
In other words, LLJs may provide the turbulent conditions necessary for calculating fluxes
via the eddy covariance technique, but that does not guarantee that the advection terms of
the NEE equation are negligible (also pointed out by Hong et al. 2012). In fact, LLJs may
actually do the opposite with the advection terms. Neglecting those terms in that case could
result in significant errors in the NEE measurements. This approximation is done in most
studies, given the extreme difficulties of measuring advection in the field.
Wind profile measurements —allowing the detection of LLJs beyond the height of the
flux measurements— can have a great value in the interpretation of local surface-atmosphere
flux measurements during nighttime conditions.
79
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