The project MUSICA (MUlti-platform remote Sensing of Isotopologues for
investigating the Cycle of Atmospheric water) has shown that the sensor IASI
aboard the satellite MetOp can measure the free tropospheric
{H

The retrieval simulation method is based on the physical principles of
radiative transfer and we show that the uncertainty of the simulations is
within the uncertainty of the MUSICA MetOp/IASI products, i.e. the retrieval
simulations are reliable enough. We demonstrate the working principle of the
simulator by applying it to ECHAM5-wiso model data. The few case studies
clearly reveal the large potential of the MUSICA MetOp/IASI
{H

A major challenge for climate system modelling is the
insufficient understanding of tropospheric moisture pathways and their
coupling to atmospheric circulation

Particularly informative is the distribution of pairs of the humidity
concentration and the ratios between different isotopologues

Recently, there has been large progress in measuring and modelling
tropospheric water vapour isotopologues

Many aspects of the complex nature of the remote sensing data are captured by
the averaging kernel matrix

However, for any comparison of remote sensing data with atmospheric model
data, we need the averaging kernels that correspond to the modelled
atmospheric state and not to the atmospheric state observed by the satellite.
The reason is that atmospheric humidity fields strongly vary on small spatial
and temporal scales. We cannot expect that the averaging kernel obtained for
a remote sensing observation made at a certain location (often an area
smaller than 100 km

In order to produce model {H

A retrieval simulator for the TES HDO product has been proposed by

In this paper, we present a physics-based method for simulating the MUSICA
MetOp/IASI {H

A remote sensor measures radiances that inform about the conditions where the radiation has been emitted and about the conditions during radiative transfer. In order to simulate remote sensing retrievals the respective radiative transfer has to be understood. In this section we give a brief overview on the principles of radiative transfer of thermal nadir radiances and outline its relation to the sensitivity of the remote sensing system.

The radiances

Equation (

Using these approximations, there remain two contributions. The term

The term

For understanding the remote sensing system's sensitivity the Jacobians
(

We can separately calculate the Jacobians for the two contribution terms
(

A retrieval algorithm works with discretised vertical profiles (atmospheric
trace gas concentrations and temperatures at

The averaging kernel (

Reliable water isotopologue ratio retrievals are possible by a
logarithmic-scale retrieval of H

However, the retrievals are generally performed in the
{

Example of an averaging kernel for an observation over the tropical ocean. Shown are the row entries of the four
blocks of the MetOp/IASI full averaging kernel matrix in the {H

A full averaging kernel matrix (

Figure

The two blocks along the diagonal describe the direct responses, i.e. they
represent the averaging kernels for H

For the Type 1 product we observe that H

With the help of the a posteriori processing we can overcome this problem.
The Type 2 product are the a posteriori processed data. For this data product
H

For a given atmospheric state the averaging kernels can be calculated
according to Eq. (

There are many different atmospheric trace gases that interact with infrared
radiation. For simplification we only consider H

The cross-section

Further simplifications are that we calculate the Planck function (

Even with these simplifications there are still a lot of calculations
necessary to get the Jacobian matrix

H

We make the simplified calculations for all cloud-free MUSICA IASI (IASI-A
and IASI-B) retrievals of 10 August 2014. These are about 300 000 individual
observation, i.e. we calculated

Figure

The term

Relation between the Jacobians (

For the weak line there is a certain anti-correlation between the
contribution terms

The two lines with different line strength give complementary information
about the atmospheric state. This is shown in Fig.

Figures

According to Eq. (

The function that performs the simulations are freely available in the Supplement of this paper. We provide this function as routines for MATLAB (AVKsimulator.m) and Python (AVKsimulator.py) platforms. The routines read information from the directory regularisation, which has to be copied to the same path as the routines.

The routine needs as input the model data of surface altitude (in m. a.s.l.), surface emissivity (unitless) and surface temperature (skin
temperature in K). Further required inputs are the vertical profiles of
altitude (in m. a.s.l.), pressure (in hPa), temperature (in K)
and humidity mixing ratios (in

The output of the routine is the {H

The Supplement of this paper contains also a netcdf file
example_ECHAM5wiso_20140212hh00.nc with selected ECHAM5-wiso

Simulated averaging kernels for the surface and atmospheric
conditions corresponding to the averaging kernels of Fig.

Figure

We can measure H

The Type 2 kernels show the situation after applying the a posteriori
correction to the actual and the simulated kernels, respectively. The a
posteriori correction assures that H

The reasonable agreement between actual and simulated kernels for the
tropical ocean example situation is encouraging (seen by comparing
Figs.

Comparison of the DOFS values obtained from the actual and the simulated averaging kernels. Left for the Type 1 product and right for the Type 2 product.

The DOFS (degree of freedom of signal) value is a measure for the information
content in a remote sensing product. The higher the DOFS value the more
independent is the product from the a priori assumptions. The DOFS value is
calculated as the trace of the averaging kernel matrix. We evaluate the trace
of the matrix block

Figure

Our simulations capture the actual sensitivity of the remote sensing system reasonably well. The dependency of the sensitivity on the surface and atmospheric conditions seems to be well understood. The simulation allow the separation of conditions leading to low sensitivity from conditions leading to high sensitivity.

We focus on the Type 2 averaging kernels, because this is the product type of
choice for {H

Variations over broad layers can be captured by a covariance matrix

Furthermore, we decouple the boundary layer (the first 500–800 m above
surface) from the free atmosphere by assuming a correlation length of only
500 m between the boundary layer and higher altitudes. Figure

We are interested in the errors caused by the limited sensitivity of the
remote sensing system for observing the broad vertical structures described
by the covariance matrix

Covariances used for estimating the quality of the simulated averaging kernels.

Evaluation of the simulated sensitivity error matrix

In the following we focus on analysing the square root values of the diagonal
elements of

Figure

The simulated kernels correctly identify the altitudes around 5 km a.s.l. as
the tropospheric region where

The remaining three panels (left panels in the middle and bottom row of
panels of Fig.

We observe a good correlation between the

The leftmost panel in the middle row of panels and the central panel in the
bottom row of panels compare differences of

The error we make by using the simulated kernel instead of the actual kernel
for the interpretation of broad vertical structures can be estimated as

Cumulative occurrences of the

Figure

Example of the daily geographical distribution of

Example of the daily geographical distribution of

The black dots show the cumulative occurrences for those situations where the
remote sensing system is actually sensitive for atmospheric
{H

In this context we would like to note that for the altitude of
5 km a.s.l. the sensitivity criterion of

In this section we examine the geographical patterns of

Figure

The

Interferences in

Figure

Largest (

As discussed in the context of Eqs. (

We assume uncertainties in the parameters that describe the surface and
atmospheric conditions according to the second column of Table

We observe that the interferences due to uncertainties in surface conditions
(emissivity and temperature) are generally smaller than 3 ‰ (even the
95 %-percentiles are smaller than 3 ‰). This means that even an error of
10 % or 5 K in the surface emissivity or temperature, respectively, do not
significantly affect the simulation error. This is an important finding and
means that our model–measurement comparisons will only be very weakly
affected by uncertain model surface conditions. We observe the strongest
interference due to uncertainty in the free tropospheric humidity levels.
This is good, because it is the parameter that is most strongly linked with
the {H

We also estimate the interference due to using a constant satellite viewing
angle of

In this section we give some application examples of the retrieval simulator
for validating the {H

The following case studies will identify differences between the model and
the observations thereby revealing the potential of the {H

Since the MUSICA MetOp/IASI {H

Latitudinal- and seasonal-scale signals in the {H

For our first case study we investigate the {H

Figure

The top row of panels show the ECHAM5-wiso data for a broad layer around 5 km a.s.l. We calculate the signals for this broad layer by convolving the ECHAM5-wiso profiles with a normalised Gauss function with the peak at 5 km a.s.l. and a FWHM (full width at half maximum) value of 5 km. These contour lines are calculated by considering all situations where the clear sky criterion is fulfilled.

The middle row of panels shows the ECHAM5-wiso data for 5 km a.s.l. after
passing through the retrieval simulator, i.e. we applied
Eq. (

The bottom row of panels shows the contour plots as obtained from the MUSICA
MetOp/IASI retrievals. These data are for clear sky situations (determined by
EUMETSAT cloud filter and MUSICA MetOp/IASI retrieval fit quality filter) and
fulfil the sensitivity criterion (we only work with data where we estimate a

We observe that the humidity concentrations are well predicted by the model.
For the different seasons and latitudes the model and observation cover very
similar humidity ranges. There is no significant difference between the
modelled humidity and the humidity as observed by IASI. There is also some
agreement concerning the latitudinal and seasonal variation of the
{H

However, for humid situations (for H

Diurnal-scale signals in the {H

In the second case study we investigate diurnal-scale signals in the
{H

The study is made for the tropics (February and August, latitudinal belt from
10

The comparison of the first two rows of panels gives insight into the effect
of the retrieval simulator. There are only a few moderately dry situations
that are removed by the sensitivity filter (

The plots in the middle and bottom row of panels are for data that have the
same characteristics and they can be compared in a meaningful way. There are
several similarities to the comparison made in the context of the previous
figure: (a) again the slopes of the {H

However, the subtropical summertime atmosphere of the Sahara desert is
significantly moister in the model than in the IASI data (compare the
greenish contours in the right panels). Interestingly, the Sahara is also the
region where IASI observes a very strong diurnal signal. While IASI observes
rather similar humidity concentrations for morning and evening, the

The left panels show that for tropical ocean scenarios model and satellite
consistently find no diurnal signal. However, there seems to be a weak
diurnal cycle over land, where the MUSICA MetOp/IASI morning data show
slightly higher humidity concentrations than the evening data with at the
same time almost unchanged

The case study comparisons as shown in Figs.

It is unlikely that tropical water masses have no ocean source corresponding
to temperatures above 20–25

Our interpretation of the weak diurnal cycle as seen in the IASI data over
tropical land (bottom left panel of Fig.

The MUSICA MetOp/IASI retrieval scheme can generate reliable
free tropospheric {H

However, remote sensing {H

The retrieval simulator is based on the physical principles of atmospheric radiative transfer. It is shown that a consideration of these physical principles is necessary in order to understand the remote sensing measurement and thus in order to be able to simulate the averaging kernels.

The quality of the retrieval simulations is empirically assessed. It is shown
that the simulator reasonably well identifies the situations in which the
remote sensing system is sensitive with respect to {H

We give a few examples of the working principle of the simulator and apply it
to ECHAM5-wiso data. We document that model data that have been processed
with the simulator can be compared to the MUSICA MetOp/IASI
{H

Now that more and more atmospheric models have the isotopologues included, it
is time to think in detail about the kind of atmospheric moisture processes
that can be investigated with such models. For such investigations the model
data need to be combined with reliable reference measurements. Our retrieval
simulator allows such combination and can be easily adopted to any model
data. The characteristics of the MUSICA MetOp/IASI {H

The retrieval simulator is available in the supplement of this article in the form of MATLAB and Python routines. Figures 11 and 12 show examples with MUSICA MetOp/IASI data and ECHAM5-wiso data. The dissemination of MUSICA MetOp/IASI data via a database is currently in preparation and this work is still ongoing. At the moment the data are only available by request from Matthias Schneider (KIT, IMK-ASF). Examples of ECHAM5-wiso data are provided in the supplement of this article and more ECHAM5-wiso data are available by request from Martin Werner (AWI).

Christian Borger, Andreas Wiegele, Omaira E. García and Eliezer Sepúlveda worked on the MUSICA MetOp/IASI retrievals and contributed to the analyses of the retrieval products. Frank Hase developed the PROFFIT-nadir retrieval code. Martin Werner developed the ECHAM water isotopologue products and provided ECHAM5-wiso data. Matthias Schneider coordinated and designed the MUSICA project, developed the retrieval simulator and prepared the paper with contributions from all co-authors.

The authors declare that they have no conflict of interest.

This study has been conducted in the framework of the project MUSICA, which is funded by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement number 256961.

Eliezer Sepúlveda is supported by EUMETSAT (Fellowship Programme, project VALIASI).

We acknowledge the support by the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the Karlsruhe Institute of Technology. Edited by: J. Worden Reviewed by: two anonymous referees