AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-9-841-2016Modeling the Zeeman effect in high-altitude SSMIS channels for numerical weather prediction profiles: comparing a fast model and a line-by-line modelLarssonRichardric.larsson@gmail.comhttps://orcid.org/0000-0001-6719-723XMilzMathiasRayerPeterSaundersRogerBellWilliamBootonAnnaBuehlerStefan A.https://orcid.org/0000-0001-6389-1160ErikssonPatrickhttps://orcid.org/0000-0002-8475-0479JohnViju O.Luleå University of Technology, Kiruna, SwedenMet Office, Exeter, UKUniversity of Hamburg, Hamburg, GermanyChalmers University of Technology, Gothenburg, SwedenEUMETSAT, Darmstadt, GermanyRichard Larsson (ric.larsson@gmail.com)3March2016928418579June20152October20158February201611February2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/9/841/2016/amt-9-841-2016.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/9/841/2016/amt-9-841-2016.pdf
We present a comparison of a reference and a fast radiative transfer model
using numerical weather prediction profiles for the Zeeman-affected high-altitude Special Sensor Microwave Imager/Sounder channels 19–22. We find that
the models agree well for channels 21 and 22 compared to the channels' system
noise temperatures (1.9 and 1.3 K, respectively) and the expected profile
errors at the affected altitudes (estimated to be around 5 K). For channel 22
there is a 0.5 K average difference between the models, with a standard
deviation of 0.24 K for the full set of atmospheric profiles. Concerning the same channel,
there is 1.2 K on average between the fast model and the sensor measurement,
with 1.4 K standard deviation. For channel 21 there is a 0.9 K average
difference between the models, with a standard deviation of 0.56 K. Regarding the same
channel, there is 1.3 K on average between the fast model and the sensor
measurement, with 2.4 K standard deviation. We consider the relatively small
model differences as a validation of the fast Zeeman effect scheme for these
channels. Both channels 19 and 20 have smaller average differences between
the models (at below 0.2 K) and smaller standard deviations (at below 0.4 K)
when both models use a two-dimensional magnetic field profile. However, when
the reference model is switched to using a full three-dimensional magnetic
field profile, the standard deviation to the fast model is increased to
almost 2 K due to viewing geometry dependencies, causing up to ±7 K
differences near the equator. The average differences between the two models
remain small despite changing magnetic field configurations. We are unable to
compare channels 19 and 20 to sensor measurements due to limited altitude
range of the numerical weather prediction profiles. We recommended that
numerical weather prediction software using the fast model takes the
available fast Zeeman scheme into account for data assimilation of the
affected sensor channels to better constrain the upper atmospheric temperatures.
Introduction
The main isotopologue of molecular oxygen's ground-state millimeter-wavelength band around 60 GHz is used by several satellites to remotely
measure temperature. This is because the band's radiometric signal is strong
due to molecular oxygen's high and fairly constant volume mixing ratio
(∼ 21 %) at all altitudes below about 80 km (see e.g., for the O2 volume mixing ratio in the US Standard Atmosphere).
Some examples of sensors utilizing this band for temperature soundings are
the Advanced Microwave Sounder Unit (AMSU-A), the Special Sensor Microwave
Imager/Sounder (SSMIS; ), and the Microwave Limb
Sounder (MLS; ). All the lines of the
millimeter band experience magnetic splitting and polarization from the
Zeeman effect . In the atmosphere of Earth,
this magnetic splitting is larger than the Doppler broadening, but only at
higher altitudes is the magnetic splitting larger than the pressure
broadening. As a simplistic and intuitive guideline for Earth, Doppler
broadening in the 60 GHz band is about 50 to 70 kHz, magnetic splitting is in
the range of 0.5 to 2 MHz, and pressure broadening by air is in the range of
10 to 20 kHz Pa-1see e.g.,for air pressure broadening.
Measured signals with significant weight at altitudes above what corresponds
to 25 to 200 Pa (around 60 to 45 km) are therefore altered by the magnetic
field. As a comparison, numerical weather prediction schemes usually profile
up to 2–10 Pa (around 80 to 65 km). The Zeeman effect must thus be taken into
account by the radiative transfer schemes used as forward models for
numerical weather prediction assimilations at the top of the modeled
profiles. This has been pointed out by ,
, , , , , and , among others.
The Radiative Transfer model for Television Infrared Observation Satellites
Operational Vertical Sounder (RTTOV) is designed for operational usage as a
fast radiative transfer scheme . In previous
versions (RTTOV-8 and older), the Zeeman effect was included as transmission
offsets based on but showed
that this scheme introduced unacceptable errors for retrievals of atmospheric
parameters. It was concluded that the old method for Zeeman effect
calculations in RTTOV is worse for assimilations than simply ignoring the
Zeeman effect altogether. This is problematic as the uppermost atmospheric
levels are the least constrained part of the numerical weather prediction
models. The errors at the uppermost regions of the numerical weather
prediction profiles can be ∼ 5 K, with the top of the profile having even
larger errors of up to 10 or 20 K, but the magnitude of the errors depends on
latitude and season. The variability of the upper atmosphere is also large
and depends on season and latitude. As a rough global estimate from available
data sets from experimental satellites from, the
variability between 65 and 80 km altitude (10 and 1 Pa) in the atmosphere is
around 15 K. Inaccurate modeling of the radiation from these parts of the
profile does not help to constrain the temperatures enough in the
assimilation schemes. A new and fast Zeeman effect radiative transfer scheme
designed by has been implemented in
RTTOV since version 10.
The Atmospheric Radiative Transfer Simulator (ARTS) is designed to be a
reference radiative transfer model . The ARTS Zeeman
module implementation is described by and
has been validated by . This work focuses on comparing ARTS with
the new RTTOV scheme for the higher altitude SSMIS channels that are covered
by numerical weather prediction profiles, and it is partly based on previous
technical work presented by . SSMIS is a conical
scanner flying at an inclination of around 100∘ at about 800 km
altitude. It scans with a sensor zenith angle of ∼ 50∘
relative to the surface and covers a 2200 km wide swath ahead of the
satellite. For the upper atmospheric sounding channels that we are interested
in, the swath is divided into 30 pixels with approximately 25 ms integration
time each. Between scans, SSMIS uses what remains of its 1.9 s scan cycle
to calibrate against hot and cold loads. Model comparisons as this have
proven valuable in the past for other spectral regions
(see ),
as they allow us to quantify differences between the fast and the reference
model schemes. Besides for numerical weather prediction applications, it is
also important to quantify model discrepancies for climatological studies,
where statistical methods are used to identify trends that can be small
compared to an individual measurement's noise equivalent brightness temperature.
The next section describes the way both models treat the Zeeman effect, and
it also describes how we conduct our comparison. Later sections present the
model comparisons, and conclude this work with some remarks on future prospects.
Method
We focus our efforts on SSMIS channels 19 through 22, which are sensitive to
circular polarization of four O2 lines between 60 and 64 GHz, and have
weighting functions with peaks that range in altitudes between 40 and 80 km
(see ). These channels are described by
. Channel 19 has a local oscillator at 63.283248 GHz, with
an intermediate frequency of 285.271 MHz, and a 3 db passband width of
1.35 MHz. Channels 20–22 are all on the same local oscillator at 60.792668 GHz,
with the same first intermediate frequency of 357.892 MHz. Here the channels
start to differ. Channel 20 simply has a 3 db passband of 1.35 MHz, whereas
channel 21 has a secondary intermediate frequency of 2.0 MHz applied before
placing a 3 db passband of 1.3 MHz, and channel 22 has a secondary
intermediate frequency of 5.5 MHz applied before placing a 3 db passband of
2.6 MHz. For each channel we have prepared five sets of brightness
temperature data. One of these sets are measurements from SSMIS on board
DMSP-18 taken on 25 September 2013 between 00:00 and 06:00 (UTC).
The other four data sets are forward simulations in ARTS and RTTOV
using the atmospheric profiles derived from Met Office's numerical weather
prediction for the SSMIS measurements. The four simulated sets are (1) ARTS
with a three-dimensional magnetic field, (2) RTTOV with a two-dimensional
magnetic field (i.e., independent of altitude), (3) ARTS with the same
two-dimensional magnetic field as RTTOV, and (4) ARTS without any magnetic
field at all. The following subsections describe necessary components of our
forward simulations and discuss a few error sources when comparing the
data sets to one another.
Model descriptions
This subsection describes how the models treat the Zeeman effect. Sources to
the broader transfer schemes are cited, but not reviewed in detail.
RTTOV
RTTOV is a fast radiative transfer model used in numerical weather prediction
data assimilation schemes. It achieves its speed by precalculations of
coefficients for several predictors, based on a training set of monochromatic
transmittances, that translate the atmospheric profiles into polychromatic
transmission for select channels at some atmospheric profile levels.
Coefficients for these predictors have been determined for many operational
instruments, and the model is widely used. The transmission is used to
calculate the sensor-measured intensity using
I=∑inBTi,f0Δτi(⋯),
where the index i is for each simulated layer of the atmospheric profile,
n is the number of layers constructed from the profile, B(Ti, f0) is the
Planck function for the center of the polychromatic channel, Ti is the
temperature of the ith layer, and Δτi(⋯) is the difference
in the transmission to space across the layer. The triple dots indicate
inputs to the transmission prediction scheme. For more information on the
predictors, see .
There is no polarization in RTTOV as it models scalar radiative transfer.
However, in deriving the RTTOV coefficients, the polarized nature of the
Zeeman effect (and of other effects) is dealt with in monochromatic
calculations of the polarization state of the entire transmission. The output
of these calculations is the coefficient for the polarization component that
is relevant for the polychromatic channel. The effective transmission from a
level is thus
τx,i=Pi+1Pi+1†x,
where † indicates the conjugate transpose of the matrix, x indicates
evaluation for the transmission of the wanted polarization component, and,
counting upwards along the radiation path,
Pi=TnTn-1Tn-2⋯Ti,
where Ti is the polarized transmission across the ith level.
For Eq. (), Δτi=τi+1-τi. The
transmission from the n+ 1 level is taken as unity when considering
Δτn. The work by discusses the Zeeman
implementation in detail and gives the predictors (in their Table 2). RTTOV
uses a two-dimensional magnetic field consisting, for the entire radiation
path, of just one magnetic field magnitude and one angle relative to the
viewing direction of the instrument. These magnetic parameters are combined
with the layer temperature to form the predictors.
ARTS
ARTS is a monochromatic line-by-line radiative transfer model that calculates
absorption from a spectral line database for every level of the atmospheric
profile. The intensity as seen by a simulated sensor in ARTS is from solving
Iout=exp-KiriIin+1-exp-KiriBTi,f.
for each layer, where Ki is the polarized propagation matrix for
the ith layer, ri is the distance the radiation transfers through the
layer, Iin is the incoming polarized radiation, and
B(Ti, f) is the source function column vector (here
[B(Ti, f), 0, 0, 0]⊤, where B(Ti, f) is the Planck function). For
details on the ARTS calculations see .
The Zeeman module of ARTS calculates the Zeeman-affected propagation matrix
at every atmospheric level by splitting lines into their polarized components
as a function of the local magnetic field orientation. The propagation
matrices are then averaged over the layer and used in Eq. ().
Both three-dimensional and two-dimensional magnetic fields are
accepted as input. If the magnetic field is three-dimensional this means that
there is a unique magnetic vector per level, whereas the two-dimensional
magnetic field is similar to the RTTOV definition. In either case, ARTS keeps
the polarization of the propagation matrices stored throughout the modeled
transfer. By the end of the simulation, the polarized polychromatic sensor
response is calculated from the monochromatic simulations and the channels'
spectral responses. For more details on the ARTS Zeeman module see the work
by . recently and successfully
simulated ground-based observations of molecular oxygen microwave radiation
using the ARTS Zeeman module for several observational directions at high
spectral resolution, which validates the ARTS implementation of the Zeeman
effect for linear polarization.
The atmospheric profiles used in this study. The horizontal lines
are profile levels and color scale is normalized per profile level: darker
regions in the figure indicate more profiles with that temperature.
The atmospheric profile inputs
There were a total of 8300 atmospheric profiles used for the simulations in
this work. The profiles are derived from Met Office's numerical weather
prediction model. For a description of the Met Office numerical weather
prediction profiles at high altitude and a list of assimilated data, see
. The profiles are abstractly shown in Fig. .
Note that there is an unfortunate visual illusion in Fig.
that there is a discontinuity between the temperature at the 10 Pa
level (65 km) and the temperature at higher pressure levels. One major
problem we encounter is that the channels of SSMIS are sensitive to altitudes
that are above the numerical weather prediction profiles' top at 10 Pa. The
weighting functions of channels 21 and 22 are mostly covered by the 10 Pa
level but the weighting functions of channels 19 and 20 are not covered. To
work around the problem of insufficiently high-reaching pressure levels of
the Met Office profiles, we assume that all higher altitude pressure levels
have the same temperature as the 10 Pa level. This assumption is simple and
inaccurate, as the lapse rates at high altitudes are generally large, but it
is another work altogether to define how to deal with the temperature field
above the top of the numerical prediction profiles in a way that minimizes
errors. One reason to use a constant temperature extrapolation for this work
follows from the fact that RTTOV predicts optical depths on preset coefficient
levels. When presented with an atmosphere that has insufficiently high-reaching
pressure levels, RTTOV does this after assigning the temperature of the
supplied atmospheric top to all the overlying coefficient levels, which is an
extrapolation at constant temperature across the overlying layer of gas. The
radiative transfer integration is performed subsequently on the supplied
levels, but includes the source function and the absorption for the overlying
layer of gas by, in effect, moving the supplied top at fixed temperature
across this layer to represent the space boundary. Since the radiation of
both channels 21 and 22 is mostly emitted at an altitude range covered by the
Met Office atmospheric profiles, forcing a constant temperature above the top
emulates the behavior of RTTOV when it is directly supplied by the Met
Office profiles for these channels. This still means that the simulated
results of channels 19 and 20 are unrealistic. We therefore favor the low-altitude channels 21 and 22 in this comparison work but include a brief
discussion on how the models differ for the higher channels 19 and 20. This
discussion focus on qualitative differences between the models that are
apparent for the channels despite the otherwise unrealistic simulations. As
one more note on the atmospheric profiles, we assume, for simplicity, that
there is a constant molecular oxygen volume mixing ratio for the entire
profile even though this is not the case above ∼ 80 km.
Version 11 of the International Geomagnetic Reference Field
IGRF-11; is used for the ARTS simulations with a
three-dimensional magnetic field. The two-dimensional magnetic field values
at the altitude corresponding to 5 Pa (around 70 km) have been extracted from
IGRF-11 for both ARTS and RTTOV for those simulations. These extracted values
are mapped in Fig. , which also shows the global
coverage of the data sets. The argument for using a two-dimensional magnetic
field is that the magnetic field does not change much along the path of a
transfer. If this argument is good for SSMIS observations, then the
difference in brightness temperature as a function of magnetic field
extraction altitude will be small for the simulations.
Mean and standard deviations of our comparison for the four SSMIS
channels. The left two columns with data are a direct comparison between
the SSMIS data set and the corresponding full model simulations. The rightmost
column shows the Zeeman effect by turning the effect on and off in ARTS. The
remaining columns compare RTTOV simulations with ARTS simulations using
three-dimensional and two-dimensional magnetic fields. SD denotes standard deviation. n/a denotes data that are not applicable. Noise levels are from
.
The RTTOV simulations have been performed with the prediction coefficients
derived by in this study. ARTS uses line center
frequencies from the Jet Propulsion Laboratory spectroscopy database
(http://spec.jpl.nasa.gov/). There is a mismatch between the input line
centers to ARTS and RTTOV by exactly 8.4, 8.1, 8.9, and 8.2 kHz referring to
Table 1 in for the 7+, 9+, 15+, and 17+ O2
lines, respectively. ARTS always uses the higher frequency. The line centers
given by, e.g., are 2.2, 1.9, 5.1, and
7.4 kHz below the line centers used by ARTS, but were derived for use at low
altitudes where pressure broadening is more important than exactness of line
centers. Nevertheless the model input spectroscopy is similar and should be
compared with the frequency stability of SSMIS reported by
(80 kHz for channels 19, 20, and 21; 120 kHz for
channel 22). Since the frequency instabilities are larger than differences in
the lines' central frequencies between the models, we do not think that line
center accuracy is crucial for the comparison with SSMIS data, but it can
still introduce biases between the models. The channels' spectral response
and a few examples of the simulated spectra from ARTS can be seen in
Fig. . (Note that from code review at the
Met Office for the derivation of RTTOV's coefficients, we find that it
appears that round-off levels of 100 kHz have been used for the line centers.
The resulting differences in line centers between ARTS and RTTOV are still
small compared to SSMIS frequency stability. They are instead 16, 32, 14, and
-26 kHz for the 7+, 9+, 15+, and 17+ lines, respectively.)
Magnetic field used in our simulation mapped on a two-dimensional
surface showing the strength of the field in the left panel. The right
panel contains the angle between the magnetic field vector and the
radiation's propagation path. (This figure appears in and is
republished with rights from EUMETSAT.)
Channel configurations for SSMIS. The colors represent polar
simulations (60∘ N 0∘ E; teal and red lines) and equatorial
simulations (0∘ N 0∘ E; blue and green lines). The different
colors also denote the simulations' azimuthal angle; blue and red responses
show SSMIS facing towards the east (75∘), whereas green and teal show it
facing towards the west (-75∘). The channels are indicated by black
boxes of different line styles as seen in the legends. The simulated
measurement responses are assumed to be the average of the spectra within the
frequency ranges.
From Fig. , we see that channels 19 and 20
are in the center of the broadened lines, and that channels 21 and 22 are in
the line shape's wings near the equator (weak magnetic field strengths), but
that channel 21 is on the edge of the strongly Zeeman-affected part of the
line when the magnetic field is stronger (i.e., near the poles). It is clear
from this figure in combination with Fig. that the
increased magnetic field strength at higher latitudes causes a stronger
broadening of the line. Since the SSMIS channels measure so close to the line
centers, resulting errors from line center mismatches have been studied using
the same simulations as shown in Fig. .
The results of these tests are in Fig. , which shows
ARTS simulations with uniformly shifted line centers (emulating a channel
frequency shift). We see that the effect of the channel frequency shift is
large for channels 19 and 20 near the equator (ΔTb≈±2 K at
±50 kHz shift looking westward) and that the effect here strongly depends
on the observational geometry (ΔTb≈±2 K at 50 kHz shift when
instead looking eastward). Closer to the North Pole, the effect is still
noticeable but is fairly constant with observational geometry
(ΔTb≈-0.1 K at ±50 kHz). There is a noticeable effect on channel 21
of ΔTb≈±0.5 K at ±50 kHz for the polar simulations and
ΔTb≈±0.2 K at ±50 kHz for equatorial simulations.
Channel 22 is only weakly affected by a shifting channel center, with
|ΔTb|< 0.05 K even at ±150 kHz shift. Note that
Figs. and only represent two
locations on the globe and that the absolute effect of a shifting channel
center changes over the globe.
Changes in brightness temperatures introduced by an offset in
channel frequency for a single atmospheric scenario. This figure shows the
changes in channel brightness temperatures for the simulations in
Fig. ; both legends and line colors represent the cases in Fig. . The 0 kHz
brightness temperature has been used as reference (hence 0 K at 0 kHz). The
title of each subplot shows the channel.
Weighting functions for SSMIS from ARTS with a three-dimensional
magnetic field for an example of one orbit for channels 19 to 22. Color shows the
change in transmissions per kilometer of atmospheric altitude traversed by
the radiation. The y axis is the altitude range and the x axis shows the
latitude of the sensor as a function of time. For all four channels, two swath
positions are shown. Position no. 15 points downward along the orbit of the sensor.
Position no. 1 points westward as the sensor travels northward, and it points
eastward as the sensor travels southward.
Finally, we have prepared weighting functions for an example of one orbit (the
orbit is from 1 January 2012 around 13:30 UTC) and for two
measurement pixels (or observational geometries that are relative to the
motion of the satellite). These are shown in Fig. . With respect to each
channel, the weighting function of channel 22 is almost constant over the
orbit and observational geometry is not important. Channel 21 is similarly
little influenced by observational geometry but in the polar region
(the reader should be reminded that this is where the magnetic field is stronger) the weighting function is
“smeared” and the channel is influenced by much greater altitudes (though the
influence is not very strong). Both of the weighting functions of channels 19
and 20 change with geographical location and with observational geometry.
It can be seen that the observational geometry is important by the broadened
weighting function in the westward-facing pixel as compared to the
along-the-track pixel around the first pass at -30∘ latitude, which is not as evident during the second pass (comparing the then
eastward-facing pixel to the along-the-track pixel). Again, remember that
Fig. only shows an example of one orbit and that the weighting
function will be different for other orbits and for other observational geometries.
Are there layering issues?
Since ARTS averages optical properties and RTTOV averages atmospheric
properties to create the layer transfer, we must quantify the errors
introduced by this model discrepancy. We do this by artificially decreasing
the maximum layer thickness (ri of Eq. ) for
ARTS. We find that using an atmospheric layering of 50 m for a few of the
profiles instead of using the same layering thickness as RTTOV only changes our
results by ∼ 2 × 10-4 K. The layering thickness is therefore
not an issue for ARTS. We cannot test this for RTTOV directly without
altering the predictor coefficients, but it is shown by
that using a sparsely layered approach or using a
1 km altitude grid does not alter the simulated brightness temperature much. From these observations we argue that there is no issue with the layers
in the present study.
Results and discussions
The results of our comparison are summarized in Table .
Channel-by-channel, the table shows the mean differences between the compared
data sets, their corresponding standard deviations, and the channels' noise
equivalent temperatures. Figures to
show the data sets in spread plots and as global distribution maps for
channels 19 to 22. Figure shows SSMIS measurements
cf. the simulations for channel 21, and Fig. shows SSMIS
measurements cf. the simulations for channel 22. Figure has
been prepared to show the Zeeman effect in ARTS for all channels and
Fig. has been prepared to interpret equatorial results more easily.
Model to model
Before comparing RTTOV and ARTS we will discuss Fig. . The
figure shows the model effect of turning the magnetic field on and off in
ARTS. By comparing to Fig. , we see that there is an
anti-correlation between magnetic field strength and brightness temperature
change for channels 19, 20, and 22. The correlation for channel 21 is instead
positive. On a channel-by-channel basis, channel 22 experiences minimal
Zeeman effect. In the extreme polar regions, the channel is only up to 0.4 K
Tb warmer when the Zeeman effect is considered, but most of the rest of
the planet experiences a Zeeman effect that is less than 0.1 K Tb.
Channel 21 experiences the absolute strongest Zeeman effect out of all channels of
just above 8 K Tb at the strongest sources of magnetic fields. The weaker
magnetic field regions only experience around 1 or 2 K Tb. The simulations
for channels 19 and 20 change a lot when the Zeeman effect is considered.
Channel 20 gets 2 K Tb warmer at strong magnetic sources with the Zeeman
effect considered. The same value for channel 19 is higher, at 5 K Tb.
Both channels are around 7 K Tb colder at the equator. One interesting
feature to note is the angular dependencies of the Zeeman effect near the
equator. Especially clear perhaps above the Atlantic between Brazil and
western Africa, the center of the measurement swaths around the equator is
less influenced by the Zeeman effect than the surrounding swath positions.
Channels 19 and 20
Figure shows the channel 19 comparison of RTTOV with
ARTS, which was run using both a full three-dimensional magnetic field and an
identical two-dimensional magnetic field setup as used by RTTOV. From
Table , it can be seen that the mean brightness temperature
differences between the models are small on average regardless of magnetic
field setup, with both comparisons' mean difference showing |ΔTb|< 0.34 K.
This is about the same size as the average Zeeman effect in
ARTS at ΔTb≈-0.44 K. There is a large increase in the standard
deviation of the differences from 0.33 K in the two-dimensional magnetic
field comparison to the three-dimensional magnetic field comparison, which
has a standard deviation of 1.8 K. There is a still larger increase in standard
deviation to 2.9 K if the Zeeman effect is ignored.
From the global distribution maps shown in Fig. , we
see that the largest discrepancies for channel 19 between RTTOV and ARTS with
a three-dimensional magnetic field are located all across the equator, with a
brightness temperature differences of up to 7 K systematically distributed in
higher and lower brightness temperature regions; most warmer regions are located to
the south of the equator and most colder regions are located to the north of the
equator when the satellite is moving southward. When the satellite is moving
northward, the resulting warm–cold region distribution seems to change across
the swath. By remembering Fig. , which shows the
two-dimensional magnetic field, we can by eye correlate these larger
brightness temperature differences with areas of relatively weak magnetic
field strength and with a magnetic field angle that is close to being parallel with
the radiation path. We use Fig. to focus on
equatorial differences between the channels in this study. For channel 19,
this figure shows that the differences between three-dimensional ARTS and
RTTOV range over 7 K near the equator, but that the same range for
differences between two-dimensional ARTS and RTTOV is only around 1 K. We
note that a large change over the swath is consistent with the changing
weighting functions of channel 19 in Fig. , which close to the
equator can be quite broadened by changing the observational geometry. Thus,
if the satellite had been moving northward over Eurasia, instead of over
the Pacific Ocean, we cannot expect to see the same type of regional
discrepancies since the magnetic field angle is changed by the viewing
geometry. Looking only at the comparison of RTTOV and ARTS simulations with a
two-dimensional magnetic field for channel 19, we find brightness temperature
differences between the models of up to 1 K. There appears to be a weak
positive bias of around 0.3 K in the equatorial regions and a weak negative
bias of around 0.6 K closer to the poles. We cannot identify the reason for
these discrepancies clearly but the line center frequency differences of
around 20 kHz between the models can explain some of these differences.
Channel 19 comparison of RTTOV and ARTS simulations. The upper row
contains spread plots for RTTOV simulations on the y axis and for ARTS
simulations on the x axis. The lower row contains the above spread plots
mapped onto the surface of Earth to where the corresponding SSMIS measurement
was done. In these maps, the magnitudes of the difference between the
simulations are shown in color. The color corresponds to ARTS minus RTTOV.
The left column shows RTTOV compared to ARTS simulations with a three-dimensional
magnetic field and the right column shows RTTOV compared to ARTS simulations
with a two-dimensional magnetic field. It is important to note that the color
scale changes between the maps; this has been done to highlight all model
differences, which are discussed in the text.
Channel 20 comparison of RTTOV and ARTS simulations as for
Fig. .
Channel 21 comparison of RTTOV and ARTS simulations as for
Fig. but with a fixed color scale.
Channel 22 comparison of RTTOV and ARTS simulations as for
Fig. but with a fixed color scale.
Comparison of model simulations and SSMIS measurements for
channel 21. Similar to Fig. with some changes. The left
column spread plot still shows RTTOV simulations on the y axis but SSMIS
measurements on the x axis; the corresponding scatter map represents SSMIS
minus RTTOV. The right column spread plot shows ARTS simulations with a
three-dimensional magnetic field on the y axis and SSMIS measurements on
the x axis; the corresponding scatter map is for SSMIS minus
ARTS.
For channel 20 in Fig. , most of the same features are
available as for channel 19 in Fig. , with a few
modifications. From Table , the average brightness
temperature differences between models are small, with both comparisons
showing a mean of |ΔTb|< 0.17 K. The average model to model
difference is thus much smaller than the average Zeeman effect in ARTS, which
is ΔTb≈-2.2 K. The standard deviation of the model to model
differences changes in the same way for channel 20 as it does for channel 19.
RTTOV simulations minus ARTS simulations with a three-dimensional magnetic
field have a much larger standard deviation of 1.7 K than the standard
deviation of 0.27 K for RTTOV simulations minus ARTS simulations with a
two-dimensional magnetic field. For channel 20 the ARTS Zeeman effect
standard deviation of 2.0 K is relatively close to the three-dimensional
model to model standard deviation. From Fig. , it can be seen that the
equatorial differences between three- and two-dimensional ARTS and RTTOV are
similar to the differences for channel 19. One interesting difference is that
while channel 19 has a fairly even equatorial bias when it compares
two-dimensional ARTS to RTTOV simulations, this is not the case for channel 20. Instead,
the eastern hemisphere experiences a positive bias of about 0.5 to 0.7 K and
the western hemisphere sees close to no biases.
The errors that remain in the comparison with RTTOV and ARTS simulations with
a two-dimensional magnetic field for channel 20 are similar to those for
channel 19 of up to ∼ 1.5 K. Because both line centers for channel 20 are
shifted in frequency with the same sign, we can compare the remaining
discrepancies in Fig. to the channel frequency shift
presented in Fig. . As a test not presented in any
figures of this work, we ran ARTS with changed line center frequencies of
30 kHz for the lines influencing channel 20. This altered spectroscopy
reduces the mean difference between the models by half, but the standard deviation
still remains fairly unchanged. This means that there are still unidentified
discrepancies between the models for channel 20.
Comparison of model simulations and SSMIS measurements for
channel 22 as for Fig. .
The Zeeman effect in ARTS for all four channels. Colors correspond
to ARTS without any magnetic field minus ARTS with a three-dimensional
magnetic field.
The swath dependencies around the equatorial crossings of this
study. The first row shows the map of the data. Color-coding is the same in
this map as in the other plots where the swath from one orbit has its own
colors; black circles are not used because they are more than 5∘ from
the equator (5∘ was just arbitrarily chosen as the limit). The y axis
label in the other plots overlap with labels in Figs.
to . Channels are named in the plot titles. Linear regression
for brightness temperature differences was performed over longitude and the
best-fit line is drawn between ±20 % of the longitude range of
the data from each orbit. The first two rows of the regression plots
represent the model comparison and the last row represents the comparison between the models and
SSMIS measurements.
Channels 21 and 22
Common to both the lower peaking channels 21 and 22 is that the reduction to
a two-dimensional magnetic field in ARTS is numerically noticeable but much
smaller than for channels 19 and 20. It is possible in Fig. ,
for channel 21, to see this difference qualitatively in the global
distributions near magnetically strong regions. One example is above Siberia
where there is a region with two-dimensional ARTS simulations that are
ΔTb≈ 0.1 K warmer than RTTOV. The three-dimensional ARTS
simulations are instead ΔTb≈-0.2 K to RTTOV. It is also
possible to see a systematic 1 K gradient over the swaths near the equator in
the comparison of RTTOV and three-dimensional ARTS in Fig.
for channel 21. This systematic gradient is reduced to a fraction
of a Kelvin for differences between two-dimensional ARTS and RTTOV. Similarly to channels 19 and 20, these swath discrepancies should change when SSMIS is
scanning northward or southward. Still, since the Zeeman effect is weak for
channel 21 at the equator, most model differences there (the average bias is
around 1.7 K in Fig. ) are due to other reasons than
the Zeeman effect.
Focusing only on two-dimensional magnetic field simulations for channel 21
(Fig. ; right column), the polar regions agree fairly
well between ARTS and RTTOV, with |ΔTb|< 0.6 K, barring a -1 K
region above Antarctica close to 0∘ E longitude. These < 0.6 K
differences are possible to understand from the 30 kHz line shifts identified
for channel 20 above. Similarly to channel 20, however, introducing the line center
shifts only reduces the model to model discrepancies, without much change in
the standard deviation. (We remind the reader that channels 20, 21, and 22
measure the same two lines as are shown in
Fig. ; therefore, effects on one of the channels should be similar
to the others.) Since channel 21 weighting functions of Fig. are
stretched to higher altitudes near the poles, it is possible that some model
differences have been missed or exaggerated in our study due to our constant
temperature profiles at these higher altitudes. It is deemed unlikely that
this has had a big impact on our results because the largest differences
between the models are found across the equator, where the channel 21 weighting
function is covered by our physical profile. Also, the standard deviation of
the model to model difference is about 0.56 K. In relation to the sensor
noise equivalent temperature of 1.9 K, the model to model standard deviation
is small, so any effect of the stretched weighting function on our comparison
is also small. From Fig. , the Zeeman effect is up to 8 K
Tb at the strong magnetic regions for channel 21, whereas the models
compare to within 0.6 K in these regions. This means that the models are
still fairly close to one another in the strong magnetic field regions
compared to the size of the Zeeman effect. Instead of at the poles, the
largest model differences are found close to the equator, where differences
of almost 3 K appear. We cannot explain these large differences from the
channel shifts of Fig. .
For channel 22, there seems to be no correlation between magnetic field
parameters and model to model differences. This is not surprising considering
that the Zeeman effect is not very important for channel 22, with an average
effect of ΔTb= 0.13 K that has a standard deviation of only 0.088 K.
The mean differences between the models are ΔTb≈-0.53 K with a
standard deviation of 0.24 K, regardless of magnetic field setup in ARTS. Concerning channel 21, we find from Fig. that near the
equator there is a larger than average negative bias. For channel 22 it
averages at ΔTb≈-0.75 K. Another region of interest is the
South Pole, where the largest model to model differences occur – it is not shown
in any plots that Antarctica is the warmest region in our simulations
with atmospheric temperature of around 280 K for channel 22. From the scatter
plots of Fig. , we see that there are beginnings of
deviation between the models at higher temperatures, which show the
Antarctica deviations. One potential cause for these discrepancies is
therefore that the RTTOV coefficients were derived using transmission
coefficients from simulations with an atmospheric training set that also had
highest temperatures around 280 K at the peak of the weighting function of
channel 22. It has previously been identified as a problem by
for
water spectroscopy models that RTTOV coefficients derived for atmospheric input close to
the limits of the training set can cause accuracy issues in RTTOV. In other regions, the model to model differences
are small and appear to oscillate around 0 K.
Models to measurements
Direct comparison of simulated measurements with the SSMIS data set is only
possible for channels 21 and 22 because the higher altitude channels 19 and 20
are not covered by the altitude levels of the numerical weather prediction
profiles. We want to remind the reader that the Met Office numerical weather
prediction model profiles are believed to be inaccurate at higher altitudes.
All such inaccuracies are retained in the following comparisons of models to measurements.
The comparisons for channel 21 between SSMIS measurements, with regards to
RTTOV simulations and with regards to ARTS simulations with a three-dimensional
magnetic field, are found in Fig. . We find that the
mean value of SSMIS measurements minus RTTOV simulations is -1.3 K, and the
mean value of SSMIS measurements minus ARTS simulations is -0.34 K. ARTS
agrees better than RTTOV with SSMIS. Both comparisons have a standard
deviation of around 2.4 K, and the noise equivalent temperature of the sensor
is 1.9 K . So even if ARTS appears to be better,
RTTOV simulations are close to SSMIS measurements given the sensor's noise
and RTTOV is close to ARTS given the simulations to measurement standard deviations.
One key point that we want to take note of is that the noise of channel 21 is
a lot smaller than the standard deviation of simulations to measurement. This
is a similarity between our study and the one performed by
. They found that RTTOV agrees with SSMIS at a root
mean square of 2.3 K at a mean difference of -0.95 K for channel 21.
use retrieved temperature profiles by the
limb-scanning SABER instrument on board the TIMED satellite. This should mean
that their temperature profiles are reasonably accurate, since limb scanners
have a high signal-to-noise ratio. Still, they found, as we do, that the
standard deviation of the simulations to measurement are consistently larger
than the noise of the sensor.
Looking in more details at the global distribution maps, we see that the
largest discrepancies for both models are available closer to the poles, with
a tendency for warmer brightness temperature differences (up to about 7 K) in
the south and colder brightness temperature differences in the north (down to
about -7 K). The weighting function of channel 21 is shifted upwards for
stronger magnetic field (see Fig. at high absolute
latitudes). This upwards shift places a significant part of the weighting
function at pressure levels where we have set the temperature to a constant
value (above the 10 Pa/65 km level). Clearly a better method for extending
the temperatures above 10 Pa is required. Across the equator the models are
closer to SSMIS measurements. RTTOV agrees better with SSMIS measurements
near the equator, with an average difference of around -1 K, than ARTS
simulations, which has an average difference of 2 K to the SSMIS
measurements. Looking at the equator in more details in Fig. ,
we cannot determine if ARTS or RTTOV equatorial behavior is best
there for channel 21. Both models compare to SSMIS with much larger effects
over the swath at the equator than how the models compare to one another.
Swath effects are about 3 K large between models and measurements. We remind
the reader that these swath effects are 1 K between three-dimensional ARTS
and RTTOV. ARTS has on average slightly smaller swath effects – reduced by
about 20 % judging by differences in the absolute averages of the
a regression coefficient in the linear fit of y=ax+b that is
plotted – than RTTOV but there is a large variation in these swath effects.
There are some similarities between the channel 21 and the channel 22
comparisons of model simulations and SSMIS measurements as found in
Fig. . In average, ARTS still agrees better than RTTOV
with SSMIS measurements, with the respective differences to measurements
being ΔTb≈-0.63 K for ARTS and ΔTb≈-1.3 K for
RTTOV as seen in Table . Both models have approximately
1.4 K standard deviation to the measurements, which is similar to the sensor
equivalent noise temperature of 1.3 K . Since the
model-to-measurement standard deviation retains atmospheric input errors,
this means that the models have a good agreement with the measurements. There
are still a few dominating features visible in the global distribution maps.
These features are all in the Southern Hemisphere, with a region above West
Antarctica that has a -7.5 K bias compared to both models, and two regions
with a 3 K bias to the observations, one located just north of the cold
Antarctica anomaly and another located towards the east of it.
We note that RTTOV and SSMIS agree better for channel 22 in our study than in
the study by . They found approximately the same
average difference between RTTOV and SSMIS as we did
(ΔTb≈-1.3 K), but the standard deviation in their test was much larger
at 2.2 K compared to 1.4 K in ours. The temperature profiles are more
accurate for limb sounding, so their uncertainties should reasonably be below
or similar to ours. One possible explanation is that there are measurements
with colder brightness temperatures included in the study by
than compared to our study. These lower brightness
temperatures were consistently underestimated by RTTOV, which should increase
the standard deviation.
Summary, conclusions, and outlook
We have presented a comparative study showing how well the fast RTTOV agrees
with reference model ARTS for the high-altitude channels 19–22 of SSMIS using
globally distributed numerical weather prediction model profiles from Met
Office. This study shows that the RTTOV Zeeman effect scheme for SSMIS
implemented by works well. The agreement between the
forward simulations and the corresponding SSMIS measurements is generally
good but there are some discrepancies; quantitative values of the comparison
are summarized in Table .
We conclude, when comparing ARTS to RTTOV, that using a three-dimensional
magnetic field in ARTS gives an increased standard deviation compared to
using a two-dimensional magnetic field in ARTS for channels 19 and 20; this
increase is from 0.3 to 1.8 K for channel 19 and from 0.27 to 1.7 K for
channel 20. The brightness temperature differences by a three-dimensional
magnetic field for these channels are found to be up to ±7 K across the
equator, whereas ARTS with a two-dimensional magnetic field is in the range
±1 K from RTTOV. Since we follow the numerical weather prediction profile
top (and emulate the behavior of RTTOV above this top), we cannot be sure
that these are the model differences for a proper atmosphere. Despite this
limitation, our comparisons still suggest that the dimensionality of the
magnetic field is important for the higher altitude channels. The natural top
of the mesosphere variability is around 15 K, so potential modeling errors of
up to 7 K is a lot; however, we have not yet tested how this translates to
numerical weather prediction model errors at these altitudes. Today, the
estimated numerical weather prediction model errors are about 10 K at these
altitudes. These errors will be reduced by using RTTOV with two-dimensional
magnetic fields and the information available in the higher altitude SSMIS
channels, but we cannot estimate by how much – this must be tested using
the present version of RTTOV in trial operational settings. Still, it would
be better to use a three-dimensional magnetic field in RTTOV than a
two-dimensional magnetic field but a fast Zeeman scheme using a
three-dimensional magnetic fields is not yet available. It is difficult to update RTTOV for
three-dimensional magnetic fields but it should be possible. The
coefficients used in RTTOV are generated from a large set of calculations
that fits the effective scalar line-by-line transmission to space
(Eq. ) to a predetermined set of predictors.
The polarized transmission from a level to space depends on the polarized
transmission across all levels closer to the sensor (through the
Ts of Eq. ). Therefore, using a
three-dimensional magnetic field with the present set of predictors will not
work, since changes at higher altitudes change the effective scalar
transmission to space. We have not attempted to extend the present set of
predictors to account for perturbations at higher altitudes and further study
will be necessary on how to achieve this. Since the magnetic field is fairly
slow changing (see Fig. for an estimate), a
level-by-level set of perturbations might be applied to transmittances on the
right in Eq. (), and predictors
incorporated into RTTOV to simulate the effect of the perturbations on the
left of Eq. (). This would allow the user to
perturb a fixed input field, as presently expected by RTTOV, into a field
that varies along the radiation path.
Similar brightness temperature differences as for channels 19 and 20 between
two- and three-dimensional magnetic fields are present for channel 21 but
these differences are much smaller in magnitude. In regions where the
magnetic field is strong (closer to the poles), the dimensionality of the
magnetic field can give differences of about 0.5 K in local regions. The
Zeeman effect is up to 8 K in these high magnetic field strength
regions, so the Zeeman effect treatment in the models still agrees fairly well
for a strong magnetic field. Near the equator, the differences over a swath of
measurement are found to be about 1 K large due to the dimensionality of the
magnetic field, whereas the Zeeman effect itself is only 1 to 2 K large.
However, there are other effects than the Zeeman effect that are important in
the comparisons of the models. The model difference at the equator is on average 3 K, and this is larger than the difference between using a three-
or two-dimensional magnetic field. We cannot identify the reason for these
3 K model differences. In comparing models to measurements, the range of
error is about ±7 K Tb for channel 21. The errors of Met Office
profiles are expected to be large at higher altitudes, so we do not expect
models and measurements to agree better than this for now.
Channel 22 is unaffected by the dimensionality of the magnetic field because
it is mostly unaffected by the Zeeman effect; the channel experience at most
only a few tenths of a Kelvin of the Zeeman effect. Other differences
dominate model to model differences. As regard to channel 21, there is an
unexplained brightness temperature difference across the equator. For channel 22
this difference averages to around -0.75 K. Also, there seems to be a
limit in the temperature range for RTTOV's training data that lowers RTTOV
accuracy at the highest atmospheric temperatures. This is seen above
Antarctica, creating a model to model bias of about 1 K for regions with the
highest atmospheric temperature in this study. Except for localized large
differences between models and measurement, the modeled channel 22 shows a
good agreement with the measurements. Since channel 22 measures at lower
altitude than channel 21, the Met Office profiles are more accurate and this
is reflected in the better agreement with SSMIS measurements.
Our results imply that RTTOV, with the new Zeeman scheme by
, models the SSMIS data set with acceptable accuracy
compared to sensor noise parameters of channels 21 and 22. This in turn shows
that the concerns raised on using RTTOV's past Zeeman
capabilities for data assimilation schemes are addressed in newer versions.
We recommend that future iterations of numerical weather prediction software
start using versions of RTTOV from version 10 and onwards for the
assimilation of SSMIS channels 21 and 22. This would not improve much over
using an older RTTOV version for channel 22, but it would greatly improve
agreements for channel 21. If SSMIS channel 21 is modeled well by RTTOV it
can be assimilated into the numerical weather prediction scheme and consequently help improve middle mesospheric temperatures. It is likely that
model to model discrepancies for channel 21 can be reduced even more if the
model top levels reached higher altitudes, since high-latitude weighting
functions of channel 21 reach much higher altitudes than equatorial weighting
functions; a level top at 0.01 Pa/100 km is also necessary for channels 19
and 20 to be modeled. The lack of a three-dimensional magnetic field in RTTOV
is not ideal for channel 21 but neither is it a huge issue. Models and measurements differ by 7 K at the equator currently and three-dimensional
magnetic field makes only about 1 K difference for this channel. An option to
work around the dimensionality problem currently is to apply biases, similar to
those we find between ARTS and RTTOV in this work, to correct the simulated
measurements in the assimilation schemes. Especially regional biases have to
be described for the inversions to apply these biases. Uncertainties in the
atmospheric temperature field of the numerical weather prediction model
levels at high altitude are nevertheless currently large and consideration of the
higher altitude SSMIS channels can help mitigate these uncertainties.
As regards to an outlook, there is an ongoing effort to use ARTS for retrievals of
atmospheric temperature profiles using all of the high-altitude SSMIS
channels. The results of these efforts will be reported upon in future work.
Acknowledgements
This work was partly funded by EUMETSAT grant number NWP_VS13_02, with
report number NWPSAF-MO-VS-049. The writing of this article mainly took place
in Hamburg under a CliSAP stipend. The authors also want to acknowledge the
communities that support, both by usage and development, the two radiative
transfer simulators.
Edited by: D. Cimini
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