RELATIONSHIP BETWEEN BRIGHTNESS TEMPERATURE
DIFFERENCE FIELD ABOVE CONVECTIVE STORMS AND OTHER
METEOROLOGICAL VARIABLES
1,2
Jindřich Šťástka
, Michaela Radová
1,2
1
Charles University in Prague, Faculty of Mathematics and Physics, Department of Meteorology and
Environment Protection, V Holešovičkách 2, 18000 Prague, Czech Republic.
2
Czech Hydrometeorological Institute, Na Šabatce 17, 14306 Prague, Czech Republic.
Abstract
Previous theoretical studies investigated influence of different moisture or temperature profiles on
simulated brightness temperature difference (BTD). This paper presents similar investigation using
satellite and sounding observations. We explore relationship of BTD field above convective storms
with two parameters obtained from proximity atmospheric soundings - inversion magnitude and mean
mixing ratio in 1 or 2 km above tropopause. The results show that the magnitude of temperature
inversion correlates with parameters describing BTD field better than the mean mixing ratio. The
positive correlation between the magnitude of temperature inversion and median as well as maximum
of the BTDs is in a good agreement with previous theoretical studies. Moreover, relationships between
the BTD field and other storm-related parameters are investigated. Significant positive correlation is
found between value of BTD median and distance of its occurrence from the satellite’s nadir in the
south-north direction which confirms our previous observation. Significant positive correlations are
also found between number of positive BTD pixels of the storm and BTD maximum as well as BTD
median. This finding indicates that larger storms exhibit higher BTD values more likely than the
smaller storms.
1. INTRODUCTION
Brightness temperature difference (BTD) between water vapor (WV) and infrared (IR) window
(approximately 10 to 12.5 μm) bands is often used in studies of cloud tops of convective storms (e.g.
Setvák et al., 2007). The BTD (defined as WV-IR) value is usually negative since the IR window band
can typically ”see” deeper into the warmer layers of the atmosphere than the WV band does.
However, above cloud tops of most of deep convective storms we observe that brightness
temperature (BT) in the WV band is often higher than BT in the IR window band. Positive BTDs are
discussed in several studies, e.g., in Fritz and Laszlo (1993), Ackerman (1996), Schmetz et al. (1997)
and Setvák et al. (2007, 2008 and 2010), but explanation of this phenomenon still remains unclear.
The most frequently offered explanations are presence of warmer water vapor in the lower
stratosphere, emissivity and scattering effects related to storm-top microphysics, presence of very thin
cirrus layer(s) above the storm top or some combination of the mentioned effects (e.g. Setvák, 2010;
Lattanzio et al., 2005).
Previous studies (Fritz and Laszlo, 1993; Lindsey and Grasso, 2007) used theoretical calculations to
determine what conditions are necessary for appearance of positive BTD. Fritz and Laszlo (1993)
examined different profiles of water vapor in the stratosphere, ranging from dry to moist. Their
calculations show BTD about 1.5 K for the dry stratospheric profile and about 3 K for the moistest one.
Based on their results, they assumed that warm water vapor in the lower stratosphere can explain
positive BTD values above convective storms. Lindsey and Grasso (2007) examined several different
moisture profiles and several temperature profiles which differ in temperature inversion magnitude.
Their results indicate that moist layer above the cloud and the larger magnitude of the temperature
inversion increase BTD values. They, however, discussed the importance of presence of
a temperature inversion and showed that the effect of the moist layer without a strong temperature
inversion is not sufficient for the explanation of the observed BTD values.
In our previous work (Šťástka and Radová, 2012) we described differences in evolution for a storm
close to the Earth’s limb, when observed from geostationary satellite, including the observation of
higher values of BTD in comparison with other studied storms (located further from the limb). We
discussed an influence of the storm’s proximity to the Earth’s limb on the BTD values measured by the
geostationary satellite. We suggested that for storms close to the Earth’s limb absorption and
subsequent re-emission of the outgoing radiation in the WV band could be more effective due to
longer pathlength through layer or layers of the warmer water vapor. This mechanism could, in
principle, result in occurrence of higher BTD values for storms located at latitudes or longitudes more
distant from nadir of geostationary satellites.
Our current work is inspired by mentioned theoretical studies and focuses on the relationship between
positive BTDs and two parameters retrieved from soundings – magnitude of temperature inversion
and water vapor amount above tropopause. The aim of this study is to verify the results of the
theoretical studies using satellite and sounding observations. Moreover, the observations we
described in Šťástka and Radová (2012) lead us to examination of relationship between BTD and
distance of storm from the sub-satellite position. In section 2 we describe used data and applied
processing. Section 3 focuses on investigation of relationships between parameters describing BTD
field and other mentioned characteristics. Results are summarized in section 4.
2. METHODOLOGY
2.1 Dataset and processing
MSG Spinning Enhanced Visible and InfraRed Imager (SEVIRI; Schmetz et al. 2002) WV 6.2 μm and
IR 10.8 μm Rapid Scan data (5 minutes repeat cycle) are used as the primary inputs to the following
analysis. These data were received through the EUMETCast (EUMETSAT Multicast Distribution
System) stream at Czech Hydrometeorological Institute (CHMI). Selected cases were processed by
SCISYS Space 2met! Software. Upper-air data were obtained from the University of Wyoming
sounding archive. The additional analyses and visualizations were made by our own python routines.
2.2 Processing of satellite data
In the initial step of the satellite data processing we identify pixels representing individual storms. Each
storm is defined as a compact set of pixels with IR 10.8 BTs smaller than 225 K. This value was
determined on the basis of observations of mid-latitude storms as a threshold which allows
investigation of behavior of almost each satellite-observed storm-cell separately. An example of
detected storms is shown in Fig. 1. In the second step, median and maximum of BTD is computed for
each detected storm in each time of its evolution. For each storm, maxima of these two characteristics
are computed. These maximal values will be referred as “BTD maximum” and “BTD median” further in
the text.
Figure 1: Illustration of detection of individual storms shown for situation above Europe on 12 September 2008 13:45
UTC. Numbers denote positions of detected objects. a) MSG color enhanced IR 10.8 image, b) MSG BTD (WV 6.2 – IR
10.8) image – only positive values are shown.
2.3 Processing of sounding data
In this study, we use radiosonde data from stations around the whole Europe. To select appropriate
sounding for investigation of conditions for each studied storm we follow definition of proximity
soundings used in Groenemeijer and Delden (2005) for the area of the Netherlands and its close
vicinity. They require the sounding to be within 100 km from the investigated event. As in some parts of
Europe the spatial density of upper air stations is not sufficient for using such strict criterion, we
increase the maximum distance to 150 km and hence the following criteria are used. The mutual
position of the sounding and the BTD event must fulfill:


The BTD event occurred within 150 km of a point advected with the 0-3 km mean wind from
the sounding location.
The BTD event occurred within a time period starting 4 h before sounding was released until
4 h after that time.
For each studied storm, magnitude (strength) of temperature inversion and mean of mixing ratio in 1
and 2 km above the tropopause are calculated from assigned sounding data. This calculation is based
on interpolated data (linearly with respect to height) of temperature and mixing ratio. Linear regression
is used to determine magnitude of temperature inversion. An example of sounding with the
demonstration of retrieving the magnitude of temperature inversion is shown in Fig. 2.
Figure 2: Sounding from Prague-Libus, 31 May 2008 1800 UTC, with demonstration of linear interpolation (red curve),
which was used to quantify the lower stratospheric temperature inversion. Corresponding values of inversion
magnitude and mean mixing ratio in 1 km above the tropopause are stated in the figure.
3. RESULTS
We have analyzed two convective seasons (May – October) 2008 and 2009. Our dataset includes 123
convective storms with different extent (Fig. 3.) and magnitude of BTDs. The geographical distribution
of analyzed cases is shown in Fig. 4.
Figure 3: Histogram of number of positive BTD pixels corresponding to analyzed cases.
The aim of this study is to verify the results of the theoretical studies (Fritz and Laszlo, 1993; Lindsey
and Grasso, 2007). Therefore, we examine relationships between BTD parameters (BTD median and
BTD maximum) and the sounding-derived parameters. Results are shown in scatterplots in Fig. 5a, b
and Fig. 6a, b. In all scatterplots in Fig. 5 and Fig. 6 there are stated Spearman’s rank correlation
coefficients and p-values between corresponding parameters.
While there is only very weak or no correlation between mean mixing ratio and both BTD parameters
as shown in Fig. 5b and 6b, the magnitude of temperature inversion correlates with both BTD
parameters significantly better (Fig. 5a and 6a). The latter correlation is higher when it is calculated in
2 km above the tropopause than in 1 km.
Figure 4: The geographical distribution of analyzed cases. Red (blue) circles denote positions of occurrence of BTD
maximum (BTD median) for all studied storms. Size of each circle corresponds to the number of positive BTD pixels in
the storm.
The positive correlation of the magnitude of temperature inversion and BTD median or BTD maximum
is in a good agreement with previous theoretical studies (Lindsey and Grasso, 2007). Lindsey and
Grasso (2007) also suggested that increased amount of water vapor can cause not negligible changes
in BTD values only in presence of a strong temperature inversion. Such behavior could be one of the
reasons of the very low correlations found between BTD parameters and mean mixing ratio (Fig. 5b,
Fig. 6b). We note here that our results can be influenced by the fact that there are higher uncertainties
in humidity measurements than in temperature measurements in the lower stratosphere. The
uncertainty of relative humidity measurements is estimated by Vömel et al. (2007) to be increasing
with height to 9 % of the measured relative humidity in the tropopause region and no more than 10 %
in the stratosphere. The accuracy of temperature measurements in the tropopause region seems to be
1
more stable. For example Vaisala specifies the accuracy about 0.3 °C for the radiosonde RS92 which
is often used in Europe.
Figure 5: Scatterplot of BTD median vs a) inversion magnitude in 1 km (blue) and 2 km (red) above the tropopause,
b) mean mixing ratio in 1 km (blue) and 2 km (red) above the tropopause, c) number of positive BTD pixels, d) E-W
distance (brown) and S-N distance (green). Values of the Spearman’s rank correlation coefficient rs and p-value are
stated in each scatterplot.
As was already mentioned in the introduction, our previous work Šťástka and Radová (2012) leads us
to examination of relationship between BTD parameters and distance of storm from the sub-satellite
position. We investigate the relationship with distance in the south-north direction (S-N distance) and
in the east-west direction (E-W distance) separately. We found strong positive correlation (rs = 0.63)
between the BTD median and the S-N distance while almost no correlation was found with the E-W
distance (Fig. 5d). The former correlation confirms our previous observations (Šťástka and Radová,
2012). Difference between correlations with the S-N and E-W distance could be explained by the fact
that there are greater distances from satellite’s nadir in the south-north direction than in the east-west
direction for the studied area (Fig. 4). The nadir of the used satellite (Meteosat 8) is located at 0°
latitude and 9.5° E longitude. Fig. 6d shows that the correlation between the S-N distance and the
BTD maximum is not as significant as for the BTD median.
At last we examine relationships between BTD parameters and number of positive BTD pixels of
storm. The corresponding scatterplots, Fig. 5c and Fig. 6c, show significant correlation for BTD
maximum (rs = 0.64) as well as BTD median (rs = 0.48). As the extent of positive BTD pixels usually
corresponds to the storm size, this result indicates that larger storms can produce higher BTD values
more likely than the smaller storms.
Figure 6: Same as in Fig. 5 but for BTD maximum.
4. DISCUSSION AND CONCLUSIONS
In our study we investigated the relationship between BTD field and several other parameters. Based
on previous theoretical studies, we selected two parameters obtainable from soundings: inversion
magnitude and mean mixing ratio in 1 and 2 km above tropopause. Other investigated parameters
were E-W distance, S-N distance and number of positive BTD pixels of the storms. The links between
these parameters and BTD median as well as BTD maximum were investigated on dataset of 123
cases above Europe from convective seasons 2008 and 2009.
The results show a very low correlation between both examined BTD parameters and the mean
mixing ratio. Stronger correlations were obtained for the inversion magnitude. The positive correlation
between the magnitude of temperature inversion and the BTD median as well as the BTD maximum is
in a good agreement with the previous theoretical studies (e.g. Lindsey and Grasso, 2007).
Our results also show quite strong positive correlations between the extent of positive BTD pixels of
storm and both BTD parameters. This finding indicates that the larger storms exhibit higher BTD
values more likely than the smaller storms. Significant correlation (rs = 0.63) was found also between
the BTD median and the S-N distance while there is almost no correlation with the E-W distance. The
correlation between the BTD median and the S-N distance is in a good agreement with our previous
observation described in Šťástka and Radová (2012). We explain the difference between correlations
for the S-N and E-W distance by the fact that there are greater distances from satellite’s nadir in the
south-north direction than in the east-west direction for the studied area (Fig. 4) and Meteosat 8
satellite.
In our future study we plan to categorize the storms according to their IR window brightness
temperatures, extent and/or position to quantify investigated relationships for different types of storms
separately.
ACKNOWLEDGEMENTS
The work was partially supported by the Grant Agency of the Charles University, project Study of tops
of convective storms by means of remote sensing methods, No. 604812. The authors also
acknowledge EUMETSAT and CHMI for data used in this paper.
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