Continuous monitoring of atmospheric humidity profiles is important for many
applications, e.g., assessment of atmospheric stability and cloud formation.
Nowadays there are a wide variety of ground-based sensors for atmospheric
humidity profiling. Unfortunately there is no single instrument able to
provide a measurement with complete vertical coverage, high vertical and
temporal resolution and good performance under all weather conditions,
simultaneously. For example, Raman lidar (RL) measurements can provide water
vapor with a high vertical resolution, albeit with limited vertical coverage,
due to sunlight contamination and the presence of clouds. Microwave
radiometers (MWRs) receive water vapor information throughout the
troposphere, though their vertical resolution is poor. In this work, we present an MWR and
RL system synergy, which aims to overcome the specific sensor limitations.
The retrieval algorithm combining these two instruments is an optimal estimation method (OEM), which allows for an uncertainty analysis of the
retrieved profiles. The OEM combines measurements and a priori information,
taking the uncertainty of both into account. The measurement vector consists
of a set of MWR brightness temperatures and RL water vapor profiles. The
method is applied to a 2-month field campaign around Jülich (Germany),
focusing on clear sky periods. Different experiments are performed to analyze
the improvements achieved via the synergy compared to the individual
retrievals. When applying the combined retrieval, on average the
theoretically determined absolute humidity uncertainty is reduced above the
last usable lidar range by a factor of

Highly resolved, accurate and continuous measurements of water vapor are
required for a deeper understanding of many atmospheric phenomena

Some examples of ground-based synergies have been proposed by

Water vapor RL systems provide humidity profiles with high vertical
resolution. For this reason, such lidars have become a powerful tool in
active ground-based observations over recent years. New retrieval algorithms
optimally exploiting the information content have been developed

The MWR allows automated continuous data acquisition and is a robust
operational instrument

A method to combine RL and MWR was already proposed by

The method described in this document is a new approach based on an optimal estimation method (OEM), an iterative optimal and physically consistent
method that allows uncertainty assessment and provides the most probable
estimated atmospheric state together with its uncertainty description. The
aim of this study is to combine the information provided by the two
instruments in an OEM to retrieve atmospheric water vapor profiles. Note that
this flexible framework allows the retrieval of temperature once
corresponding RL and MWR data are available. The method was applied to the
2-month dataset collected during HOPE (HD(CP)

In this study we make use of the data collected during HOPE (HD(CP)2 Observational Prototype Experiment), which was a major field campaign in North Rhine-Westphalia, Germany, from April to June 2013. One main goal of HOPE was to provide information on subgrid variability (i.e., of water vapor) and microphysical properties on scales smaller than 1 km, which corresponds to the horizontal resolution of state-of-the-art operational mesoscale models. During the measurement period, three supersites were operating that were distributed within the 5–10 km surroundings of Forschungszentrum Jülich, Germany (50.905, 6.411944). Each supersite was composed of a rich variety of remote sensing instruments such as cloud radar, lidar and microwave radiometer instruments. A large set of more than 200 radiosondes (RSs) was launched only 4 km away from the JOYCE (Jülich ObservatorY for Cloud Evolution) site and at least twice a day.

At the permanent supersite JOYCE

The Raman lidar system BASIL

Signal selection is performed by means of narrowband interference filters,
whose specifications were reported in

During HOPE, BASIL was calibrated based on the comparison with the radiosondes launched approximately 4 km away from the instrument. A mean calibration coefficient was estimated by comparing BASIL and radiosonde data. Every clear sky radiosonde coincident with BASIL measurements (60 in total) is compared to the lidar profile in an altitude region with an extent of 1 km above the boundary layer. We choose this region to minimize the air mass differences related to the distance between the lidar station and the radiosonde launch facility station. For every profile comparison, a value for the calibration constant is calculated. From these 60 values, we calculate the mean value and use it as the calibration constant for the complete period of HOPE. The standard deviation of the mean calibration coefficient from the single values does not exceed 5 %.

In addition to the calibration constant uncertainty, other smaller systematic
uncertainty sources might affect the water vapor measurements. For example,
an additional uncertainty (

The statistical uncertainty of the water vapor mixing ratio is calculated
based on the application of the Poisson statistics

Note, the operation of BASIL has not been continuous during HOPE. The instrument collected a total of 430 h of measurements distributed over 44 days, which represents 30 % of the whole HOPE period.

The microwave radiometer profiler HATPRO

The absolute calibration of the instrument is performed roughly every 6
months, taking a cold and a hot load as reference, which are assumed to be
ideal black bodies. The cold black body is a liquid-nitrogen-cooled load at
approximately 77 K that is attached externally to the radiometer box. This
standard, together with an internal ambient black body load inside the
radiometer, is used for the absolute calibration procedure

The temporal resolution of this instrument is higher than for the RL: it is
able to provide one measurement every 1–3 s. Thus, a temporal
adaptation to the lidar time resolution is performed, averaging MWR
measurements in 5 min intervals. A major drawback of MWR water vapor
and temperature profile retrievals is the limited vertical resolution.
Typically, only two pieces of independent information for water vapor
profiles are contained in the measurements, whereby three–four are obtained for the
temperature profile

An optimal estimation method is applied which allows the state of
the atmosphere and its associated uncertainty to be estimated. Using this scheme requires a
set of measurements (with their uncertainty specification), a forward model,
which relates the atmospheric state to the instrument measurements and some
a priori information. In the following, a short description of the
scheme is presented. More details can be found in

Given the

The iterative equation described in Eq. (

The a priori information is calculated from the set of radiosondes launched
during HOPE. A total of 217 sondes have been considered. Generally, at least
two of them are available for every day of the campaign, typically one around
noon and the other at midnight. From these data, the average profile of
absolute humidity

For the same set of radiosondes, the correlation (corr) and
covariance (cov) matrices are calculated according to

Both covariance and correlation matrices have been calculated as in Eq. (

The measurement vector

Correlation matrix derived from 217 radiosondes launched during HOPE. Correlation is shown for absolute humidity as a function of the altitude (from 0 to 10 km above the ground).

The size of

In effect, the observation vector

The error covariance matrix associated with the MWR measurement (with
dimensions

The part of

The forward model for the lidar is straightforward because in our retrieval
approach we consider WVMR as part of the measurements vector. Therefore, the
lidar FM for water vapor simply performs the conversion from absolute
humidity to mixing ratio. However, the implementation of a more complex lidar
forward model, e.g., the approach implemented by

The retrieval vertical grid is defined for every profile. It varies, as well as the observation vector, depending on the amount of available lidar information for every given profile. In the atmospheric regions where lidar data are available, the vertical grid of the retrieval product is 30 m (same as the lidar). Above the point where the RL signal is lost, and since the MWR cannot provide such high resolution, the algorithm retrieves only one value every 1 km.

In a first approach, the OEM is implemented for the combination of the two
instruments to retrieve atmospheric absolute humidity. The setup is designed
such that the OEM can work with input from a single instrument as well. This
aspect allows us to compare the performance of each sensor working alone in
contrast to the combination of the both. In the following, we demonstrate the
algorithm presenting the results corresponding to 24 April at 11:00 UTC, where a collocated RS is used only as reference (Fig.

At first, we only introduce the portion of profile in the OEM where RL data
are considered to be valid (i.e., from 180 m to 2.5 km,

The OEM uncertainty of the combined retrieval is calculated as the square
root of the main diagonal elements in

The profile obtained with the RL-MWR combination best fits the RS (shown as
reference), launched at the same time 4 km away. The combined retrieval
reveals absolute humidity values closer to the radiosonde at 3 km than single
instrument retrievals. This is due to both the additional microwave
radiometer observations as well as propagated lidar information (via the a
priori covariance matrix). It is interesting to pay attention to the lower
part of the atmosphere, close to the ground. In Fig.

Absolute humidity profiles for a priori (yellow), only-RL (red), only-MWR (green) and MWR+RL (blue). The horizontal blue lines correspond to the theoretical retrieval error for the MWR+RL case. The RS is used as reference (black). The dashed horizontal gray lines enclose the region where the lidar data are used. The inset is a zoom for the region close to the ground, between 0 and 250 m.

We can additionally evaluate the quality of our retrieval by calculating the

Vertical resolution for the only-RL (red), only-MWR (green) and MWR+RL (blue). The dashed lines enclose the area where RL data have been considered.

From left to right and top to bottom, absolute humidity (g m

The combined retrieval is now applied to more than one profile. An example of
this is shown in Fig.

One can see clearly how the RL zero overlap region does not allow
any information from the lowest 180 m to be received. In addition, the lidar signal is
strongly affected by the background daytime radiation from around 2.5 km
above. Note that following the explanation in Sect.

The MWR+RL time series reveals a successful synergy between RL and MWR, making use of the TB and a priori information to complete the profile where RL measurements are not available (i.e., in the blind region below 180 m and at regions of too high a lidar noise level).

The absolute humidity algorithm has been applied to all the clear sky periods with simultaneous availability of MWR and RL. The MWR measured continuously, so this selection is restricted to lidar availability. There are 4201 lidar profiles in total (30 % of the total campaign). Of these, 717 profiles are considered as clear sky (around 17 % of the total). Of the clear sky profiles, the convergence of the OEM is found in 95.8 % of the cases, that is, 687 profiles. In the rest of the cases, the convergence is not reached because the algorithm cannot find a profile which is simultaneously consistent with the measurements of the two instruments and the a priori information, within their uncertainties.

Another key atmospheric parameter that we can evaluate after applying the OEM
is the IWV. The independent measurements of IWV from the Global Position
Satellite (GPS) ground station

Figure

Figure

As explained above, the retrieval grid of each profile depends on how much
data from the RL can be taken into account, which will depend on the
atmospheric conditions, day/night, background noise, etc. In order to clearly
assess the benefits of the sensor synergy, a different retrieval strategy is
used for the subsequent tests: the algorithm is applied using only the RL
profiles up to a fixed altitude in order to retrieve all profiles using the
same vertical grid. Thus, all RL profiles have been capped at an altitude of
2.5 km. In the case that a given lidar profile gets too noisy before this
altitude, the profile is discarded and not taken into account for the
statistics. This cutoff altitude is chosen in order to keep at least 75 % of
the profiles within the statistics (only 23 % of the considered RL profiles
reach 100 % relative uncertainty at a height lower than 2.5 km). This
strategy simplifies the separate study of three atmospheric regions, defined
as follows.

Region (a) from ground to 180 m: no lidar data are available

Region (b) from 180 m to 2.5 km: this is the only domain where there are lidar data.
It is enclosed inside the dashed horizontal lines in Fig.

Region (c) from 2.5 km to 10 km: no lidar data are considered.

At first, a comparison of the absolute humidity profiles to the
radiosonde profiles is performed. Unfortunately, only 18 valid clear sky
radiosondes have been found during the periods where BASIL measured. In Fig.

Region (a) exhibits the largest standard deviations (SDs) and biases, with
similar values for the three cases. In addition to the fact that no lidar
data are available here, this result may be due to different surface-related
local effects at the site where the RS was launched (

In region (b), bias and standard deviation for the only-RL and RL+MWR are
very similar, whereby only-MWR reveals the largest values. The similarity
between only-RL and the combination is again explained by the small
uncertainty associated to the lidar measurements. The product of the
combination tends to the lidar data when available, as seen in Sect.

In region (c) all the three values for the different retrievals are similar. The only-MWR seems to perform best when comparing to the RS, because both its bias and SD are the smallest. The only-RL case presents the largest bias and SD because in this region only information from the a priori is provided. The combination of the two sensors presents intermediate values, however, more similar to the only-MWR case.

Mean and standard deviation of the difference between the 18 clear sky radiosondes: MWR (in green), RL (in red) and the combination of both (blue). The dashed horizontal lines enclose the region where the lidar data are used.

Unfortunately, this set of only 18 radiosondes does not allow a significant
assessment of the synergy benefits. In addition, when interpreting the
results in Fig.

As already mentioned in Sect.

In order to investigate the algorithm performance during day- and nighttime
separately, Fig.

Figure

Left: mean theoretical error over the 636 clear sky cases during the complete HOPE period, separated into daytime (solid) and nighttime (dashed) measurements. In black: a priori uncertainty (lowest 3 km are out of margins). Red: only-RL. Green: only MWR. In blue: the MWR+RL. Right: number of RL profiles reaching each altitude, corresponding to the number of profiles used to calculate the average in the left panel.

Another theoretical error analysis is performed clipping all lidar
measurements at 2.5 km, following the same argumentation as in Sect.

Figure

However, when the combination of RL+MWR is performed, the resulting error is
the smallest for all the altitudes. In region (b), the error is almost the
same as for the only-RL case. Outside this region, the MWR contribution plays
an important role in reducing the uncertainty. In region (c), from average
uncertainty values of 0.17 and 0.22 g m

One can quantify the relative error reduction err

Mean theoretical error over 636 clear sky cases during the complete HOPE period. The lidar data have been artificially cut off at 2.5 km. In black: a priori uncertainty. Red: only-RL. Green: only MWR. In blue: the MWR+RL. The dashed horizontal lines enclose the region where the lidar data are used.

Cumulative degrees of freedom per profile for the different
instrument combinations: in red, only-RL; in green, only-MWR and in blue,
MWR+RL. The dotted-dashed lines represent the degrees of freedom for the case
where the RL uncertainty has been multiplied by 4. The average number of DOF
in every region are summarized on Table

Another parameter to assess the retrieval performance is the DOF (see Sect.

Degrees of freedom for signal comparison for absolute humidity. Average over 636 profiles. The atmosphere is separated into three regions according to lidar availability. The DOF are presented for three cases: only RL, only MWR and the combination of both instruments. In the upper part, no increment on the RL uncertainty has been considered. In the bottom part, the RL uncertainty has been multiplied by a factor of 4.

As argued in Sect.

Figure

In Sect.

The magnitude of the increase in RL measurement uncertainty is chosen based
on the discrepancy between the theoretical error (0.1 g m

The results of this test are plotted in Fig.

In addition, when an increment in the RL uncertainty is considered, the amount of
useful information provided by this instrument is smaller, and thus the DOF
are reduced. This reduction can been seen in all regions where the RL is
involved (Fig.

Mean theoretical error over 636 clear sky cases during the complete
HOPE period. Red: only RL has been introduced in the algorithm. Green:
only-MWR. In blue, the combination of RL and MWR. The dashed horizontal black
lines define the region where lidar data have been considered available. The
dashed red and blue lines represent the result when the lidar uncertainty has
been incremented by a factor of 4. The dotted-dashed red and blue lines
correspond to the case where lidar data have been suppressed from ground until
500 m. Solid lines show the errors without increments, as shown in Fig.

The results presented so far confirm that the RL+MWR water vapor synergy is meaningful and advantageous. In addition, they suggest that a careful specification of the instrument uncertainties, especially for the RL, is required.

Atmospheric humidity is an essential variable for the description of any meteorological process. Highly resolved, accurate and continuous measurements of this parameter are required for a deeper understanding of many atmospheric phenomena. However, nowadays there is no single instrument that can provide all of the following requirements simultaneously: complete vertical coverage, high vertical and temporal resolution of the atmospheric humidity profiles and satisfactory performance under all weather conditions. This is why the synergy of different sensors has come more and more into focus in the last years.

In this paper, we present a new and robust method to combine water vapor mixing ratio Raman lidar profiles and multifrequency brightness temperatures from a microwave radiometer. The joint algorithm that combines the two sensors is based on an optimal estimation method, and can be also applied to measurements from one instrument alone. Results for 53 h of clear sky measurements during the HOPE period are presented for absolute humidity profile retrievals.

The improvements of merging both instrument systems have been consistently
analyzed in terms of both the reduction of the theoretical error and the
increase of DOF. Significant advantages of instrument synergy are clearly
shown above the highest valid lidar signal. For example, when applying the
combined retrieval to the complete HOPE period, the absolute humidity
theoretical error above

With the expansion of the ground-based network of atmospheric profiling
stations, the application of the OEM at several sites under different climate
conditions will become possible. In this respect, the definition of an
appropriate background uncertainty covariance needs to be carefully
addressed. Further studies will extend the algorithm to cloudy cases and to
temperature and relative humidity profiling. In addition, the method will be
applied, not only to ground-based measurements, but also to airborne data

The data used in this study are available
at the HD(CP)

Acknowledgements: This research has been financed by ITARS (