A Ducting Climatology derived from ECMWF Global Analysis

J. Geophys. Res., 109 (D18), D18104, doi:10.1029/2003JD004380, 2004
A Ducting Climatology derived from ECMWF Global Analysis
Fields
Axel von Engeln1 , João Teixeira2
Abstract. A global ducting climatology based on 6 years of ECMWF data is
presented. The ECMWF data has a resolution of 1.5◦ , 60 vertical levels, and a 6
hour daily frequency. Ducting probability, altitude, layer thickness, and magnitude
are calculated for different seasons and universal times by analyzing the refractivity
gradient with respect to altitude. Due to the limited ECMWF vertical resolution,
presented results are restricted to the lowest 2 km to 2.5 km of the atmosphere.
The climatology has mainly been generated for radio occultation data analysis,
where ducting events found at higher altitudes are generally not affecting the signal
acquisition. Since ducting is so much associated with boundary layer inversions
and in the subtropics with cloud-topped boundary layers, this study can also be
used as an inversion climatology. High ducting probabilities (≈ 100 %) are found
off the west coasts of the Americas, Africa, and Australia in typical stratocumulus
conditions. High probability is also observed over the Arabian Sea, with large
seasonal variations. Polar nights lead to high ducting probabilities, especially
visible over Antarctica but also over Greenland and Siberia. The daily cycle of
the probabilities shows the impact of radiative cooling during the night over desert
and tundra areas. Maximum mean ducting altitudes are found further off the west
coasts. Land based ducting events are generally near the surface. The mean ducting
layer thickness is higher over the sea, with maximum thicknesses of up to 250 m.
The mean magnitude of ducting is usually just below the critical gradient.
1. Introduction
good agreement of 1-2 K in the range of 5 to 25 km can
be achieved with the radio occultation measurement principle when compared to numerical weather prediction (NWP)
models, radiosondes, and satellite radiometers [Kursinski
et al., 1997; Rocken et al., 1997; Steiner et al., 1999; Wickert et al., 2001; Hajj et al., 2004; Gorbunov and Kornblueh,
2003]. Also, these studies generally show that an almost bias
free profiles of refractivity is provided by this measurement
principle in areas where water vapor is negligible.
Refractivity profiles in the lower, moist troposphere frequently show a negative bias, first reported by Rocken et al.
[1997]. This occurs mainly at mid and low latitudes, where
the water vapor distribution leads to large gradients in the refractivity field. These large gradients are often found at the
top of the planetary boundary layer (PBL) and can result in
multipath, or even the momentary disappearance of the occulted signal caused by atmospheric ducts [Hajj et al., 2004].
Several authors have focused on the causes for these negative refractivity biases [Sokolovskiy, 2000, 2001a; Ao et al.,
2003; Beyerle et al., 2003; Sokolovskiy, 2003], suggesting
that a combination of multipath, receiver tracking errors, and
ducting is responsible.
Especially the development of inversion methods that
Radio occultation is a fairly new remote sensing method
for obtaining profiles of refractivity by observing a GPS
satellite in occultation from a low-earth-orbit satellite. The
first proof-of-concept mission GPS/Met was launched 1995
and provided several thousand atmospheric profiles within
the following 2 years [Ware et al., 1996; Rocken et al., 1997].
In 2001, 2 further missions were started, the CHAMP [Reigber et al., 2000] and SAC-C satellites [Hajj et al., 2002].
Several other younger missions have also been launched, or
are currently being planned.
The use of GPS satellite signals by means of radio occultation has shown a great potential for the determination
of upper tropospheric and stratospheric refractivity profiles.
Temperature and pressure profiles can be calculated from
these refractivity profiles using the hydrostatic equation and
the ideal gas law [Kursinski et al., 1997]. Considerable
work has already been published, showing that statistically
1 Institute of Environmental Physics, University of Bremen, Bremen, Germany
2 UCAR/VSP at Naval Research Laboratory, Marine Meteorology Division, Monterey, CA, USA
1
VON ENGELN AND TEIXEIRA
2
correctly handle atmospheric multipath [Gorbunov, 2002;
Jensen et al., 2003] have led to a significant reduction in the
observed refractivity bias at altitudes above 2 km. Improved
open-loop receiver tracking techniques are expected to further reduce tracking errors [Sokolovskiy, 2001b; Ao et al.,
2003; Beyerle et al., 2003]. However, biases below 2 km
caused by atmospheric ducting are still present.
No global climatology on ducting exists currently, although such a dataset would be extremely useful for the processing of radio occultation data to access the probability and
the general characteristics of ducting at a certain location on
the Earth’s surface. But a global ducting climatology might
also prove useful for the radar community, or for the propagation of UHF or VHF TV and radio waves. It was already
shown in von Engeln et al. [2003] that the global analysis of
the European Center for Medium Range Weather Forecasts
(ECMWF) can be used to derive global ducting information.
However, this work focused only on a 10 day period in May
2001, no seasonal information is available. Also, the used
ECMWF fields had a very fine horizontal resolution of about
0.351◦, and no further analysis of the horizontal extent of
such a ducting event was performed. Ducting events stretching over large horizontal areas will cause severe disruptions
of the radio occultation signal.
We address these two limitations of von Engeln et al.
[2003] by looking at 6 years of ECMWF data to derive a
climatology, and by using a lower horizontal resolution of
the ECMWF global fields. This lower resolution will show
only ducts that cover an extended horizontal area, thus we focus on ducts that might cause severe disruptions of the radio
occultation signal. Our paper is structured as follows: Section 2 gives a brief introduction on ducting. Section 3 gives
an overview of the ECMWF data used, along with a validation of ECMWF ducting events using radiosondes. Section 4 presents the ducting probability results, Section 5 the
mean altitude, Section 6 the layer thickness, and Section 7
the magnitude of the ducting. The regions where ducting
should severely affect the radio occultation signal are presented in Section 8. Finally, a summary is presented in Section 9.
2. Ducting
Ducting is caused by a strong gradient in refractivity N
with respect to altitude. Refractivity itself is calculated following the formula given by Smith and Weintraub [1953],
valid at GPS frequencies:
pi
ei
Ni = 77.6 + 3.73 × 105 2
(1)
Ti
Ti
where pi is the atmospheric pressure at level i (with radius
ri ) in [hPa], Ti the atmospheric temperature at level i in [K],
and ei the water vapor partial pressure at level i in [hPa].
The refractivity gradient dN/dr with respect to altitude r
is used to characterize the atmospheric conditions. A region
with a positive gradient is called subrefractive. These conditions lead to radio waves being refracted away from the
Earth’s surface. Regions with a gradient between -76 km−1
and 0 km−1 show normal refraction. Regions with dN/dr
between -76 km−1 and about -160 km−1 are called super refractive [Almond and Clarke, 1973]. Critical refraction occurs when the radius of curvature of the ray is equal to the
radius of curvature of the atmosphere and the ray will propagate at a fixed height above the surface. Ducts appear when
dN/dr leads to rays that curve down into the surface at low
altitudes, which is given when:
dN
−106
≤
dr
Rc
(2)
where Rc is the radius of curvature of the atmosphere in
[km]. This condition is fulfilled when dN/dr is less than
-160 km−1 for a mean value of Rc [Kursinski et al., 1997].
0
Performing the derivative dN/dr = N results in 4 contributing terms:
N
0
0
= 77.6 · p ·
1
T
0
−77.6 · T ·
p
T2
1
T2
0
e
(3)
−3.73 × 105 · T · 3
T
The first term represents the hydrostatic variations of pressure with altitude, it is about -30 km−1 in the lowest few km
of the atmosphere. The second term will be more important
closer to the surface where higher pressures are found. The
third term will generally contribute to ducting at altitudes
where strong gradients in e are found. The fourth term is
negligible.
Ducting is often associated with the existence of boundary layer inversions in temperature and moisture. The thickness of these inversions can vary between a few tens of meters close to the surface or the top of stratocumulus (e.g.
[Duynkerke et al., 1999]) and values of around 400 m in cumulus regions [e.g. [Siebesma et al., 2003]), or even higher
in dry PBL convection over land. Because of this variety of
values, the vertical resolution needed to capture such gradients depends on the type of inversions. It is indeed due to the
different types of inversions possible in the PBL that models such as ECMWF have much higher resolution close to
the ground (usually between 10 m and 30 m) changing with
height to values (in this particular case) of about 300 m at
1.5 km height. It is not possible to say with certainty what
resolution is necessary to resolve ducting, but in von Engeln
et al. [2003] we have shown that the ECMWF data is probably good enough in order to capture a substantial part of the
ducting events.
Ducting has been observed in radiosonde data at altitudes
up to around 4 km but most ducting events are found below
2 km [Patterson, 1982; Kursinski et al., 1997]. The maximum altitude for ducting was estimated by Kursinski et al.
[2000] to be around 5 km. An introduction into the occurrence of ducts is for example given in Hsu [1988]. Ducting
0
+3.73 × 105 · e ·
DUCTING CLIMATOLOGY
events over the sea are traditionally separated into evaporation and elevated ducts. Evaporation ducts are caused by
the rapidly decreasing water vapor with height, they occur
within about 30 m above the surface and are found over relatively warm water. Elevated ducts can be caused by temperature and moisture inversions aloft, usually associated with
the subsidence of air masses, as for example off the western coasts of the continents, particularly in areas with cold
upwelling water. Another cause is the diurnal warming and
cooling of the PBL. Diurnal variations of the PBL are much
smaller over the sea than over the land, due to the large heat
capacity of water. Consequently, large temporal and spatial variability exists in the PBL height across the coastal
zone. von Engeln et al. [2003] presented a study based on
ECMWF data for 10 days in May 2001, which showed that
ducting can also occur at low altitudes over land, where the
temperature profile is mainly responsible for the occurrence
of ducting. These conditions were often found over Antarctica and desert areas.
The following ducting characteristics are presented in
this study (ducting layer: layer where dN/dr is less than
-160 km−1 ):
Ducting Probability Percentage of observations affected by
ducting
Ducting Altitude Mean altitude of ducting layer, averaged
over all ducts at location
Ducting layer thickness Thickness of the ducting layer, averaged over all ducts at location
Ducting Magnitude Either mean gradient of the ducting
layer, averaged over all ducts at location (total magnitude), or mean gradient of the ducting layer when
humidity is removed from the refractivity calculation
(dry magnitude)
Several types of ducts could also coexist at a certain location. We focus in this study on the first duct observed by
a downward scan through the atmosphere, which could either be an elevated, an evaporation, or a dry duct. Although
evaporation ducts should not affect radio occultation data,
magnitude and position of these ducts might still be useful
for research focusing on reflected GPS signals.
3. ECMWF Data
ECMWF data used here is a combination of the ERA40 reanalysis project [Simmons and Gibson, 2000] and for
more recent times the operational analysis of the ECMWF
center. Everything before November 21, 2001 is taken from
the ERA-40 reanalysis, afterward, the operational analysis
is used. A time span of 6 years is used: 1998 – 2003. All
data is available on a 1.5◦ by 1.5◦ latitude/longitude grid and
on the 60 operational vertical model levels of the ECMWF
center (original Gaussian grid: T159L60) [Teixeira, 1999b;
Jakob et al., 2000]. Four analysis times (at Universal Time
3
(UT) UT 00, UT 06, UT 12, UT 18) are used for each day.
The vertical resolution is roughly 10 m, 150 m, 200 m, and
300 m around 0.0 km, 0.5 km, 1.0 km, and 1.5 km altitude
respectively. In total, there are 18 levels between 0 km and
about 3 km.
A correct representation of the PBL within the ECMWF
model is especially important as noted above. The following physical parameterizations in the ECMWF model can
have a profound impact on the temperature and humidity
structure of the PBL: the prognostic cloud scheme [Tiedtke,
1993], the moist convection scheme [Tiedtke, 1989], the vertical diffusion parameterization [Beljaars and Betts, 1993;
Louis et al., 1981] and the soil/surface scheme [Viterbo and
Beljaars, 1995; Viterbo et al., 1999].
Following von Engeln et al. [2003], the ECMWF data is
spline fitted to a vertical grid with 20 m resolution. Refractivity gradients are calculated on this grid. Also, topographic
effects have been removed from the data, all altitudes are
with respect to the Earth surface at that particular location.
3.1. Validation
Only the ECMWF PBL height representation was validated using radiosondes in von Engeln et al. [2003]. Results
presented over there show that the ECMWF model reproduces the mean PBL height with a bias of about 20 m, leading to the conclusion that ECMWF analysis fields can be
used for ducting studies.
A further validation of ducting altitude, thickness, and total magnitude is performed here by using upper air soundings from the research vessel Polarstern [König-Langlo and
Marx, 1997] of the Alfred Wegener Institute (AWI). Starting
late 1982, VAISALA RS80 radiosondes were launched during research cruises of the ship. Cruises were mostly within
the polar regions and the Atlantic. Measurements were prescanned to remove observations with erroneous water vapor
observations, leaving a total of more than 6000 profiles. The
vertical resolution is around 30 m. Only radiosondes that
fall within the years 1998 to 2003 are considered, leaving almost 2000 profiles. In order to compare them to ECMWF,
the resulting profiles were smoothed with boxcar averages
of 200 m. This will generally decrease the number of ducts
found at a particular location, since thin ducting layers are
removed.
Figure 1 shows a comparison of the ducting characteristics of the ECMWF data with the AWI radiosondes. Ducting layer mean altitude, thickness, and mean gradient of the
ECMWF data are calculated at the nearest time and location
of the corresponding AWI radiosonde. The ECMWF values
are calculated by averaging over the surrounding pixel of the
radiosonde that shows ducting.
Figure 1 shows that in general the ECMWF data reproduces relatively well the results based on the radiosondes.
The location of the radiosondes are in regions of the Atlantic
where a substantial number of ducts have been reported due
to strong inversions associated with boundary layer clouds.
VON ENGELN AND TEIXEIRA
4
2.0
60
1.5
0 -120
-60
0
60
AWI layer altitude [km]
30
120
-30
1.0
0.5
-60
0.0
0.0
0.4
0.5
1.0
ECMWF layer altitude [km]
1.5
2.0
-150
-200
AWI layer gradient [1/km]
AWI layer thickness [km]
0.3
0.2
-250
-300
0.1
-350
0.0
0.0
0.1
0.2
ECMWF layer thickness [km]
0.3
0.4
-400
-400
-350
-300
-250
ECMWF layer gradient [1/km]
-200
-150
Figure 1. Comparison of AWI radiosonde ducts to closest ECMWF ducts: map of radiosonde locations (upper left), mean
altitude of duct layer (upper right), thickness of duct layer (bottom left), and mean total magnitude of duct (bottom right). A
linear least-square fit to the data is also shown. AWI data is smoothed over a 200 m interval.
DUCTING CLIMATOLOGY
It can be seen that the mean ducting layer altitude, in spite
of a negative bias of about 150 m in the ECMWF data, compares relatively well with the radiosonde data in terms of the
duct height. This results are similar to the ones presented in
von Engeln et al. [2003] where a comparison of the ECMWF
PBL height against a totally different set of radiosondes allowed us to justify the confidence in the ECMWF data for
the ducting studies. The negative bias means that in the
ECMWF model the PBL has a tendency of not growing
enough, which confirms previous studies with the ECMWF
model [Holm et al., 2002].
Holm et al. [2002] shows that for stratocumulus situations
the ECMWF model does underestimate the PBL height.
Since the PBL height is the result of a delicate balance between the large-scale subsidence and the cloud-top entrainment, it is not straightforward to find the exact reason for this
underestimation. But it is a well known fact that cloud-top
entrainment is in general not represented accurately in largescale models caused by both, numerical (lack of vertical
resolution) and physical (unrealistic parameterization of the
turbulent vertical mixing in stratocumulus-topped boundary layers) reasons. These problems are common to most
NWP and climate models and are in no way specific of the
ECMWF model. However, results presented by Duynkerke
and Teixeira [2001], using much more observations than the
study mentioned above do not show such an obvious underestimation in PBL height in California stratocumulus regions.
Hence, although the PBL height results show a negative
bias in PBL height of the ECMWF model, it is difficult to
argue for certain that there is a clear negative bias in the
ECMWF model. This may well be the case for some situations; the different studies discussed above are not necessarily conclusive in this respect. A major issue is that there are
no global observations on the PBL height. Over the oceans
radiosondes are scarce and current satellite remote sensing
observations do not have the vertical resolution that would
allow them to detect PBL inversions.
The thickness results in Figure 1 illustrate the reason why
we believe that the vertical resolution of the ECMWF data
may well be good enough for our studies. Note that in terms
of layer thickness the ECMWF results have a negative bias
when compared with the radiosondes, which means that in
general ducting layer thicknesses are thinner in the ECMWF
data. So, although ECMWF does not reproduce the AWI
data perfectly, this cannot be due to the lack of vertical resolution otherwise the bias should be of opposite sign. An
analysis of the mean total magnitude leads to similar conclusions: the ECMWF data overestimates the gradient when
compared to radiosondes. If the vertical resolution was too
low in the ECMWF model this would lead to the opposite
result [von Engeln et al., 2003].
The linear fit to the data, as shown in Figure 1, was also
used to evaluate different interpolation schemes and boxcar
smoothing intervals of the AWI data. Table 1 shows the linear fit coefficients for the applied and several other smooth-
5
ing intervals. Also shown is the impact of a linear interpolation in ln(N) instead of a spline fit of the ECMWF data.
A smoothing interval of 100 m clearly shows that the
ECMWF data is not able to reproduce the ducting found in
the AWI dataset. A 200 m smoothing interval already shows
very good agreement and almost 70 % of matches. Radiosondes represent a point measurement, while the ECMWF
fields cover an area of 1.5◦ by 1.5◦ , hence especially ducts
with higher thicknesses cover large horizontal areas. The
agreement is best in altitude, duct thickness and duct magnitude show less good agreement with a 200 m smoothing.
Thus the altitude of the duct is rather stable over a large
horizontal area, thicknesses and magnitude show larger variation. Judging from Figure 1, thicker ducting layers show
better agreement between the AWI and ECMWF data than
thinner layers, which is expected given the resolution of the
ECMWF data.
The applied interpolation scheme has an impact on the
linear fit coefficients. Refractivity was generally spline fitted, but results obtained by a linear fit in ln(N) are very similar, as can be seen in Table 1. And although a spline or linear
interpolation assumes knowledge about the refractivity profile inbetween the sampling points, results with no interpolation applied show worse results.
A further analysis of the AWI radiosonde dataset shows
ducts at altitudes of up to about 6 km. Smoothing with a
200 m vertical interval will remove almost all ducts found
at altitudes above about 2 km, hence these duct thicknesses
are below 200 m. Running calculations with a wave optics simulator [Beyerle et al., 2003] and varying the ducting
layer thicknesses shows an impact of ducting on the simulated measurement at about 200 m layer thickness, only very
strong ducting events with magnitudes below -250 km−1 already show an impact with a 100 m thick layer (personal
communication, G. Beyerle, GeoForschungsZentrum Potsdam, Germany, 2003). Hence the application of a 200 m
smoothing interval to the ECMWF data will in general not
remove ducts critical to the radio occultation measurement,
and the less sharp ECMWF model inversion as compared to
the observed one, mentioned in Holm et al. [2002], is also
considered to be uncritical.
Separated by latitude, ducts in the AWI radiosonde dataset
at low latitudes show thicknesses of around 200 m to 300 m
in the lowest 2 km, these are captured well with the ECMWF
vertical resolution. Above, layer thicknesses are around
50 m to 150 m. These layer thicknesses are also found for
mid latitude ducts above 2 km. Between about 0.8 km and
2 km altitude about 60 % of mid latitude ducts show ducting
thicknesses around 100 m to 200 m, thus generally uncritical for radio occultation. Hence mid latitude ducts sufficient
to disrupt the radio occultation data acquisition are mostly
found below 0.8 km. High latitude ducts are at all altitudes
below 200 m thickness, thus uncritical for radio occultation
signals.
VON ENGELN AND TEIXEIRA
6
Table 1. Least-square linear fit coefficients (y = ax + b) for different radiosonde smoothing intervals. Spline (SP) and linear
interpolation (LI) of ECMWF fields are shown. Numbers in brackets give the percentage of matches found.
100 m
200 m
300 m
400 m
Parameter
a
b
a
b
a
b
a
b
Altitude SP
Altitude LI
Thickness SP
Thickness LI
Magnitude SP
Magnitude LI
0.71 (38%)
0.68 (34%)
0.25
0.22
0.03
-0.01
0.59
0.64
0.06
0.07
-199.3
-206.7
0.97 (68%)
1.02 (59%)
0.40
0.23
0.50
0.45
0.17
0.16
0.11
0.14
-96.9
-107.9
0.96 (84%)
1.01 (78%)
0.53
0.40
0.75
0.67
0.16
0.15
0.11
0.13
-65.2
-80.8
1.06 (92%)
1.06 (89%)
0.62
0.44
1.17
1.00
0.08
0.09
0.07
0.11
-20.2
-46.6
4. Ducting Probability
Figure 2 shows the percentage of ducting occurrence separated by season at each latitude, longitude grid point. Seasons start with the Northern Hemisphere winter scenario,
covering the months December, January, February (DJF).
High ducting probability throughout the year is found off
the western coasts of the Americas, and Africa. These areas roughly correspond to the regions where stratocumulus
clouds are prevalent [Klein and Hartmann, 1993]. The variability of these high probability regions is associated with
the stratocumulus boundary layers.
Seasonal variations are present in both Hemisphere, Northern (NH) and Southern (SH). NH spring and summer months
(MAM, JJA) off the west coast of California show higher
ducting probability than during autumn and winter times
(SON, DJF) reflecting the higher frequency of stratocumulus during the NH summer. There is also a spatial shift visible with the annual cycle in this area, the maximum in the
summer months (JJA) is found about 5◦ further north following the migration of the inter-tropical convergence zone
(ITCZ) to the north during NH summer. The NH west coast
of Africa shows similar variability, the autumn season shows
a visible decrease in ducting probability, where the spring
season (MAM) shows largest probabilities just off the coast.
The northward shift is also visible in this area.
SH ducting probability off the coast of Africa and South
America show their maximum during the SH winter and
spring months (JJA, SON). This also coincides with the peak
season for stratocumulus in the SH [Klein and Hartmann,
1993]. A band of enhanced ducting probability follows the
trade winds off the coast of South America, mainly during
the season SON, but still present in DJF. Ducting is also observed off the north-west coast of Australia, mainly during
SH spring and summer (SON, DJF).
High ducting probability is also found during the SH autumn and winter (MAM, JJA) over the Antarctic continent,
as already shown in von Engeln et al. [2003]. These are
mainly based on dry ducting, i.e. the strong surface temperature inversions due to surface radiative cooling, leads to
a strong gradient in the refractivity profile. Similar patterns
but with lower probability can be observed over Greenland
and Siberia during NH winter (DJF) times. Hence ducting
generation over the polar latitudes is most common near or
during the polar night, only very low ducting probabilities
are found during local summer.
The Arabian Sea area shows high ducting probability
throughout the year, although the largest area covered is
found during NH spring (MAM) times. A combination
of warm water temperatures during spring [Reynolds and
Smith, 1994] with dry air from the deserts aloft leads to
higher ducting probability [Brooks et al., 1999]. During
summer times (JJA), the water temperature decreases. This
cooling in summer is produced by the south-west Monsoon,
which causes southwest winds that generate an upwelling of
cold water [Tomczak and Godfrey, 2003]. Increased winds
will lead to more mixing, thus reducing the ducting probability.
A strong seasonal variation is also observed over the
Mediterranean Sea. Only very low ducting probability is
present during NH winter (DJF), while the maximum occurs during NH summer (JJA). Ducting probability increases
toward the south of the Mediterranean Sea, caused by dry
African winds, similar to the Arabian Sea region.
Besides Antarctica and Greenland, ducting probability
over land can reach up to 50 % with complex regional patterns. As already mentioned in von Engeln et al. [2003],
ducting can occur over the African deserts, but also over the
tropical rainforests. Generally, most of these ducting events
are found at low latitudes.
A band with no ducting events is persistent at about 60◦
through all seasons, mainly in the SH. There has also been
an enhanced number of ocean reflected data observed by radio occultation in this area and south of it [Beyerle et al.,
2002]. In order to explain the frequent observation of ocean
reflected radio occultation signals in this region and the low
probability for ducting, two things have to be kept in mind:
(i) on the one hand, the sea surface is considerably cold, leading to low values of humidity in the atmosphere, (ii) on the
other hand, this area is characterized by sub-polar lows with
DUCTING CLIMATOLOGY
7
Season: DJF
Season: MAM
60
60
30
30
-120 -60
0
60
120
-120 -60
0
-30
-30
-60
-60
100.0 %
60
120
80.0 %
60.0 %
Season: JJA
Season: SON
60
60
30
30
40.0 %
-120 -60
0
60
120
-120 -60
0
-30
-30
-60
-60
60
120
20.0 %
0.0 %
Figure 2. Ducting probability per season at each latitude, longitude grid point. White areas indicate no ducting occurrence.
8
the frontal lifting of subtropical air masses over polar air,
leading to a well mixed water vapor content. These lows
form an almost continuous zone of low pressure in the SH at
a latitude of between 50◦ and 70◦ .
Little or no ducting over the oceans is found in the NH
winter (DJF) in the mid-latitudes. However, some ducting is
observed in NH summer (e.g. off the east coast of Asia and
America), since fog development during the warmer seasons
may lead to a higher probability of ducting events in these
areas [Pettersen, 1969; Warren et al., 1986; Hsu, 1988]. It
has been shown that the ECMWF model is capable of reproducing the main characteristics of the global fog climatology
[Teixeira, 1999a].
While Figure 2 summarizes the ducting probability over
the seasons of the year, daily variations are shown in Figure 3
over the available ECMWF universal times.
Ducting disappears over desert and tundra areas during
the day, since there is a substantial diurnal cycle over land.
Only during the night is radiative cooling leading to the development of a strong surface inversion. Thus no ducting
is observed in the east of China, Russia at 06 UT, moving
west within increasing UT. At 12 UT, desert and grass areas
in Africa show no ducting, while this pattern has moved over
the Americas at 18 UT, mainly visible on the west coast of
South America.
No daily variations are visible in the ducting probability over Greenland, Siberia and Antarctica, where ducting
mainly occurs during the polar night, as mentioned above.
Ducting over the sea is only marginally affected by the daily
cycle, very similar ducting probability is observed throughout the day off the west coast of the Americas, Africa, and
the north-west coast of Australia. The same applies to the
Arabian Sea region.
As mentioned in the introduction, there is also a probability for an upper and a lower duct appearing at the same
time. These are mainly found off the west coasts of North
America, North Africa, around the Persian Gulf area, and
in NH summer (JJA) above the Mediterranean Sea. Maximum probabilities found over here do not exceed 20 % (not
shown).
5. Ducting Altitude
The mean altitude of ducting per season is shown in Figure 4. As mentioned above, the decreasing resolution with
altitude of the ECMWF data renders the ducting information
above about 2.5 km mostly useless.
The mean altitude of the duct increases with distance
from the western coasts of the Americas, Africa, and the
north-west coast of Australia. These ducting events are
caused by the sharp gradient of humidity and temperature
associated with stratocumulus clouds in the PBL [Klein and
Hartmann, 1993; Duynkerke et al., 1999]. The events further to the west and toward the Equator are at higher altitudes, and are associated with trade wind cumulus [Hsu,
1988; Teixeira and Hogan, 2002; Siebesma, 1998]. Sea-
VON ENGELN AND TEIXEIRA
sonal variations are mainly observed in the Northern Atlantic, where higher mean ducting altitudes are observed in
NH autumn and winter (SON, DJF) over large areas, probably due to frontal convection. The band with no ducting
events at about 60◦ in the SH shows the frontal lifting of
subtropical air masses over polar air, with higher mean altitudes north of this band, and lower ones south of it. Events
over the Mediterranean and Arabian Sea are found at lower
altitudes.
Ducting events over the sea are generally at a higher altitude than those over land. Most land events are close to the
surface, as already found in von Engeln et al. [2003]. Events
over the polar regions are near the surface, as are most events
within the Eurasian continent. Over land, seasonal patterns
are relatively pronounced, with the mean altitude increasing
during local summer. This is due to the fact that during summer a substantial part of the ducting that occurs over land
may be happening at the top of the dry convective boundary
layer.
In an analysis of the daily variations of the mean ducting altitude (not shown) it can be seen that over land, high
mean altitudes are found at 06 UT on the east coasts of Asia,
and Australia over land. These high mean altitudes are observed over land at 12 UT over Africa, and at 18 UT over
South America. As mentioned above, this is due to daytime
dry convection over land (particularly during local summer).
Solar radiation warms the land surface generating dry convective motions leading to the growth of the boundary layer
and consequently of the boundary layer inversion. Thus
the higher mean ducting altitudes observed during summer
months in Figure 4 are generated during the day.
6. Thickness of Ducting Layer
The impact of ducting on radio occultation signals depends on the vertical extent of the ducting layer, and the total
magnitude of the ducting [Kursinski et al., 1997]. Kursinski
et al. [2000] state that a minimum ducting layer thickness
of about 100 m is capable of producing extinction of radio
occultation signals, although this appears as a very conservative estimate, where 150 m are more realistic (see above).
Figure 5 shows the mean thickness of the ducting layer separated by season.
Several campaigns (ASTEX, ATEX, BOMEX) dedicated
to the study of the PBL already found that the inversion
thickness at the PBL top varies between about 100 m and
400 m, varying with distance from the coast [Duynkerke
et al., 1999; Stevens et al., 2001; Siebesma et al., 2003].
Mean ducting thicknesses found here generally agree with
these values. The mean thickness is higher over the sea, land
based events are usually less than 100 m thick.
Sea based events can reach mean thicknesses of about
250 m, the ducting thickness is highest where high ducting
probability is found. The events at higher mean altitudes off
the west coasts show thicknesses around 150 m, but these
thicknesses might be too low as discussed in connection with
DUCTING CLIMATOLOGY
9
Time: UT00
Time: UT06
60
60
30
30
-120 -60
0
60
120
-120 -60
0
-30
-30
-60
-60
100.0 %
60
120
80.0 %
60.0 %
Time: UT12
Time: UT18
60
60
30
30
40.0 %
-120 -60
0
60
120
-120 -60
0
-30
-30
-60
-60
60
120
20.0 %
0.0 %
Figure 3. Ducting probability per universal time at each latitude, longitude grid point. White areas indicate no ducting
occurrence.
VON ENGELN AND TEIXEIRA
10
Season: DJF
Season: MAM
60
60
30
30
-120 -60
0
60
120
-120 -60
0
-30
-30
-60
-60
2.5 km
60
120
2.0 km
1.5 km
Season: JJA
Season: SON
1.0 km
-120 -60
60
60
30
30
0
60
120
-120 -60
0
-30
-30
-60
-60
60
120
0.5 km
0.0 km
Figure 4. Mean ducting altitude of ducting layer per season at each latitude, longitude grid point. White areas indicate no
ducting occurrence.
DUCTING CLIMATOLOGY
11
Season: DJF
Season: MAM
60
60
30
30
-120 -60
0
60
120
-120 -60
0
-30
-30
-60
-60
250.0 m
60
120
200.0 m
150.0 m
Season: JJA
Season: SON
60
60
30
30
100.0 m
-120 -60
0
60
120
-120 -60
0
-30
-30
-60
-60
60
120
50.0 m
0.0 m
Figure 5. Mean thickness of ducting layer per season at each latitude, longitude grid point. White areas indicate no ducting
occurrence.
12
Figure 1.
Small seasonal effects can be distinguished. The mean
thickness of events over the Antarctic continent tends to
be slightly higher during seasons that also show a higher
ducting probability (see Figure 2), which means that surface
inversions are stronger during local winters. Events over
Greenland and Siberia show a similar correlation. The mean
ducting thickness in the Indian Ocean / Arabian Sea shows
a large seasonal dependency caused by the south-west Monsoon. A large area covered with high mean ducting thicknesses is found in NH spring (MAM), decreasing to a very
small area in NH summer (JJA). Also, the thickness on the
north-west coast of Australia is reduced during this period.
The daily cycle of the mean ducting thickness does not
vary significantly over sea, but land events tend to be thicker
around noon local time (not shown) because of increased
boundary layer convection at those times. The main reason
for this is connected to the strong diurnal cycle of surface
temperature over land, as opposed to a quasi-steady state situation over the oceans.
VON ENGELN AND TEIXEIRA
possible based mostly on the dry component of the refractivity. The mean dry magnitude per season is shown in Figure 7.
The mean dry magnitudes show a larger seasonal variability than the total ones. In particular, the polar regions show
large dry magnitudes that are close to the total ones as shown
in Figure 6, the low humidity has almost no impact on the
gradient of the refractivity. The largest dry magnitudes are
observed near or during the polar night, especially significant during JJA over Antarctica and DJF over the high northern latitudes. High dry magnitudes are observed as South as
the Sahara desert in the NH winter (DJF), covering most of
Russia and parts of China. Northern America shows similar
features, but not stretching that far south.
Since events over the ocean are caused by the humidity,
dry magnitudes are very low for all seasons. Most events
within ± 30◦ around the Equator are humidity based, except
for the Sahara area.
Daily variations (not shown) are generally low for the
mean dry magnitude over sea. Over land, similar patterns
as with the mean magnitude can be found, i.e. higher mean
dry magnitudes during local night times.
7. Magnitude of Ducting
As mentioned above, the total magnitude of the ducting
also influences the impact on radio occultation data. We investigate the total magnitude, including the temperature and
humidity profile, and the dry magnitude. The latter has been
calculated by first removing the humidity term (second term
on the rhs) from Eq. 1 and then calculating the gradient for
the layer where ducting was found in the total magnitude.
The mean total magnitude over the layer is shown in Figure 6.
Total magnitudes are very uniform over the globe, generally just below the required -160 km−1 for ducting, with
some exceptions. The events near the west coasts of the
Americas, Africa, and north-west coast of Australia have
slightly lower ducting magnitudes, but these lower magnitudes are not found further west, where high ducting altitudes occur, meaning that inversions are strong in stratocumulus regions. The lowest magnitudes are found around the
Red Sea, Persian Gulf during NH spring (MAM), when dry
air moves over the humid air above the warm sea [Brooks
et al., 1999]. These strong magnitudes are significantly reduced with the Monsoon in JJA.
Similar mechanisms are also responsible for the low magnitudes found over the Mediterranean Sea during NH summer (JJA). The strongest magnitudes are observed near the
African continent, on the southern side of the Mediterranean
Sea. The radiative cooling during polar nights also leads to
stronger magnitudes of the ducting. This can be seen over
the Antarctic continent, but also over Greenland.
Daily variations of the ducting magnitude (not shown) are
generally small over the sea. Land events show higher mean
magnitudes during local night times, due to temperature inversions generated by radiative cooling.
As pointed out in von Engeln et al. [2003], ducting is also
8. Most affected Region
Figures 2 to 7 give an overview of areas where ducting
occurs in general. For a duct to affect the radio occultation
signal, it has to be around 100 m thick. Thin ducting layers
do not introduce additional errors in the radio occultation
processing [Sokolovskiy, 2003]. Following Kursinski et al.
[1997] we calculate a modified thickness ∆r. It depends on
the thickness of the event ∆z, and the ratio η of dN/dr to
-160 km−1:
∆r ≈ η∆z
(4)
∆r is the actually observed vertical interval of ducting. We
assume that all locations where the modified ducting thickness is less than 100 m are not affected. Figure 8 shows the
ducting probability of the remaining areas.
Almost all high latitude areas will in general not affect the
directly received radio occultation signal, although reflected
signals from the ground might show a signature. The highest
impact can still be found off the west coast of the Americas,
Africa, and Australia. Also still affected is the Persian Gulf
region. Events over the continents are mostly removed, although seasonal and local time variations do lead to localized
ducting. The eastern US still shows low ducting probability during summer. The transport of moist air from the gulf
of Mexico region northward together with daily convective
activity are probably responsible for these events. Ducting
events over south America, the Indian sub-continent, Africa,
and Australia also follow similar diurnal patterns, but show
weaker seasonal signatures.
Figure 8 uses a 100 m criteria to assess whether ducting is critical to the radio occultation acquisition, following
Kursinski et al. [1997]. Our calculations using a wave optic simulator show that modified ducting thicknesses around
DUCTING CLIMATOLOGY
13
Season: DJF
Season: MAM
60
60
30
30
-120 -60
0
60
120
-120 -60
0
-30
-30
-60
-60
-600.0 km-1
60
120
-480.0 km-1
-360.0 km-1
Season: JJA
Season: SON
-240.0 km-1
-120 -60
60
60
30
30
0
60
120
-120 -60
0
-30
-30
-60
-60
60
120
-120.0 km-1
-0.0 km-1
Figure 6. Mean total magnitude of ducting layer per season at each latitude, longitude grid point. White areas indicate no
ducting occurrence.
VON ENGELN AND TEIXEIRA
14
Season: DJF
Season: MAM
60
60
30
30
-120 -60
0
60
120
-120 -60
0
-30
-30
-60
-60
-600.0 km-1
60
120
-480.0 km-1
-360.0 km-1
Season: JJA
Season: SON
-240.0 km-1
-120 -60
60
60
30
30
0
60
120
-120 -60
0
-30
-30
-60
-60
60
120
-120.0 km-1
-0.0 km-1
Figure 7. Mean dry magnitude of ducting layer per season at each latitude, longitude grid point. White areas indicate no
ducting occurrence.
DUCTING CLIMATOLOGY
15
Season: DJF
Season: MAM
60
60
30
30
-120 -60
0
60
120
-120 -60
0
-30
-30
-60
-60
100.0 %
60
120
80.0 %
60.0 %
Season: JJA
Season: SON
40.0 %
-120 -60
60
60
30
30
0
60
120
-120 -60
0
-30
-30
-60
-60
60
120
20.0 %
0.0 %
Figure 8. Ducting probability per season at each latitude, longitude grid point. Areas with a modified thickness of less than
100 m are assumed to show no ducting (shown as white areas).
16
150 m (see above) are more likely to be critical to the signal
acquisition, thus results shown over here present a conservative estimate. A 150 m modified thickness would restrict
Figure 8 to regions where high probability is found.
The modified thickness as calculated from Eq. 4 shows a
very small area with maximum values of up to about 650 m
in the Persian Gulf for the JJA season. The MAM season shows a larger area covered with modified thicknesses
around 500 m here. All other areas show only a small modification of the thicknesses of Figure 5, since magnitudes are
generally just above the required ducting threshold (see Figure 6).
9. Conclusion
Global ECMWF ERA-40 reanalysis and operational analysis fields of temperature, water vapor, pressure, and geopotential have been used to compile a climatology of ducting. The global fields cover the years 1998 to 2003. They
have 60 vertical levels, a 1.5◦ longitude, latitude resolution,
and are available at 4 universal times: 00, 06, 12, 18. The
presented climatology is mainly generated to help identifying areas with high ducting probabilities in radio occultation
data and thus allow to study the negative refractivity bias at
low latitudes and altitudes. But since ducting is very much
associated with the boundary layer inversions, this study can
also be used as a climatology of inversions.
Refractivity profiles have been calculated at each longitude, latitude point, along with the gradient of refractivity
with respect to altitude. Ducting happens when this gradient is below about -160 km−1 . Ducting probability, altitude,
thickness of layer, total, and dry magnitude have been calculated. Ducting events have been first validated using radiosonde profiles and then analyzed for the four seasons and
the four universal times.
A validation of the ECMWF fields with AWI radiosonde
data obtained from cruises of the Polarstern vessel was performed first. The ECMWF fields have a vertical resolution
of 10 m at the surface which degrades with altitude. The average resolution is about 200 m in the lowest 2 km, thus the
AWI radiosonde profiles have been smoothed over 200 m intervals for this comparison. This generally removes all ducting events in the radiosonde dataset at altitudes above about
2 km. Also, events at mid and high latitudes are partly removed, while low latitude events in the lowest 2 km are captured well with the applied smoothing.
The validation showed that the ducting layer mean altitude is reproduced relatively well in ECMWF data with a
negative bias of about 150 m. ECMWF data underestimates
the layer thickness of the smoothed AWI data, which shows
that the vertical resolution seems not to be the limiting factor
in this study.
Note that this ECMWF derived ducting climatology will
underestimate the number of ducts with thicknesses below
about 200 m, especially at mid and high latitudes and at altitudes above about 2 km. But ducts with thicknesses below
VON ENGELN AND TEIXEIRA
about 200 m are generally found to be uncritical for the radio
occultation signal acquisition in simulated data.
The climatology shows high ducting probability mainly
off the western coasts of the Americas, Africa and Australia,
and over the Red, Arabian and Mediterranean seas. Northern
hemisphere spring and summer months show a higher ducting probability near the west coast of California than autumn
and winter months. A northward shift with summer months
can be observed here and on the north-west coast of Africa.
Southern Hemisphere ducting off the coast of South America
and Africa have their maximum during the Northern Hemisphere summer and autumn months, while Australia has a
maximum during Northern Hemisphere winter.
Polar nights in the respective hemispheres lead to high
ducting probability over the Antarctic continent, Greenland
and Siberia. These events are caused by surface radiative
cooling which shows that the surface temperature inversion
is responsible for ducting.
Large scale meteorological patterns can also have an impact on the ducting probability, e.g. the summer Monsoon
in the Arabian Sea, or the subpolar low belt in the Southern
Hemisphere. Also visible is the mid-latitude fog development in Northern Hemisphere summer.
An analysis of ducting probability over the available universal times shows that land based ducting events over desert
or tundra areas are not observed during local noon. Radiative cooling effects cause ducting in these areas during the
night time.
The maximum mean ducting altitudes are found off the
west coast of the Americas, Africa, and north-west coast of
Australia, west of the probability maximum, along the trade
winds. Lower altitudes are found closer to the coastline, basically following the planetary boundary layer top. Land
events are close to the surface during the Northern Hemisphere winter, but in summer the ducting altitude shows an
increase during the day, caused by the inversion at the top of
the dry convective boundary layer.
The mean thickness of the ducting layer is generally
higher over the sea than over land. Sea events can be up to
250 m thick, while the extent of the ducting layer is generally
below 100 m over land. The thickest sea events are generally
found along the planetary boundary layer off the west coasts
of the Americas, Africa, and Australia. But maximum layer
thicknesses are also found around the Arabian Sea, Persian
Gulf, especially during Northern Hemisphere spring.
The mean total magnitude of the ducting layer is generally just below the required -160 km−1 for ducting, with
some exceptions. Events off the west coasts of the Americas, Africa, and Australia show slightly lower mean total
magnitudes. The minimum total magnitudes are found during Northern Hemisphere spring in the Arabian Sea/Persian
Gulf area. Slightly lower magnitudes are also found during
the polar night over Antarctica’s and Greenland’s land ice.
The mean dry magnitude of the found ducting layer has
also been calculated, neglecting the impact of water vapor
DUCTING CLIMATOLOGY
on the refractivity. Mean dry magnitudes show a larger variability, polar dry magnitudes over land are close to the corresponding total magnitudes. Hence, the low humidity over
the polar regions has almost no impact on ducting conditions. Dry magnitudes increase during the polar night of the
corresponding hemisphere.
Daily variations of the dry and total magnitude are generally small over sea, but over land they show maxima during local night time. Radiative cooling leads to an increased
surface based temperature inversion during the night, thus
generating higher refractivity gradients.
Areas where severe disruptions of the radio occultation
signal might occur are identified by calculating a modified
ducting layer thickness that takes into account the found
mean refractivity gradient. All areas with modified thicknesses below 100 m are then assumed to show no ducting.
This filter removes almost all high latitude ducting events,
and most of the events occurring over land. High ducting
probability is still found off the west coast of the Americas,
Africa, Australia, and in the Persian Gulf region. The modified thicknesses of 100 m is likely to be a conservative estimate, where 150 m to 200 m are more realistic. Using this
criteria, only events which are in areas with high ducting
probability are found to be critical to the signal acquisition.
Future work will focus on the identification of ducting
events in radio occultation data, which will on the one hand
allow the study of the PBL, and on the other hand could also
help to remove the present refractivity bias at low altitudes
and latitudes.
Acknowledgments. A. von Engeln was partly funded by the
German Federal Ministry of Education and Research (BMBF),
within the AFO2000 project UTH-MOS (Grant 07ATC04), and
the Visitor Support Program of the Office of Naval Research International Field Office in London (Grant Number: N00014-04-14020). J. Teixeira acknowledges the support of the Office of Naval
Research under Program Element 062345N. The authors wish to
thank Dr. N. Kreitz (ECMWF, Reading, UK), V. Oommen-John, P.
Mills, and Dr. J. Meyer-Arnek (Institute of Environmental Physics,
University of Bremen, Germany) for support with the ECMWF and
AWI radiosonde data extraction, as well as Dr. G. Beyerle (GeoForschungsZentrum Potsdam, Germany) for providing simulated
radio occultation data.
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A. von Engeln, University of Bremen, Institute of Environmental Physics, Otto-Hahn-Allee 1, D-28359 Bremen,
Germany. (e-mail : engeln@uni-bremen.de)
J. Teixeira, Naval Research Laboratory, Marine Meteorology Division, 7 Grace Hopper Avenue STOP 2, Monterey
CA 93943, USA (email: teixeira@nrlmry.navy.mil)
This preprint was prepared with AGU’s LATEX macros v5.01, with the
extension package ‘AGU++ ’ by P. W. Daly, version 1.6b from 1999/08/19.