The Precision Solar Spectroradiometer (PSR) is a new spectroradiometer
developed at Physikalisch-Meteorologisches Observatorium Davos – World
Radiation Center (PMOD–WRC), Davos, measuring direct solar irradiance at the
surface, in the 300–1020 nm spectral range and at high temporal resolution. The
purpose of this work is to investigate the instrument's potential to
retrieve integrated water vapour (IWV) using its spectral measurements. Two
different approaches were developed in order to retrieve IWV: the first one
uses single-channel and wavelength measurements, following a theoretical water
vapour high absorption wavelength, and the second one uses direct sun
irradiance integrated at a certain spectral region. IWV results have been
validated using a 2-year data set, consisting of an AERONET sun-photometer
Cimel CE318, a Global Positioning System (GPS), a microwave radiometer profiler (MWP) and radiosonde retrievals recorded at Meteorological
Observatorium Lindenberg, Germany. For the monochromatic approach, better
agreement with retrievals from other methods and instruments was achieved using
the 946 nm channel, while for the spectral approach the 934–948 nm
window was used. Compared to other instruments' retrievals, the monochromatic approach
leads to mean relative differences up to 3.3 % with the coefficient of
determination (R2) being in the region of 0.87–0.95, while for the
spectral approach mean relative differences up to 0.7 % were recorded
with R2 in the region of 0.96–0.98. Uncertainties related to IWV
retrieval methods were investigated and found to be less than 0.28 cm for
both methods. Absolute IWV deviations of differences between PSR and other
instruments were determined the range of 0.08–0.30 cm and only in extreme
cases would reach up to 15 %.
Introduction
Water vapour is a very important component of the thermodynamic state of the
atmosphere (Hartman et al., 2013), being a greenhouse gas with relatively
high concentrations. The quantity of water in the vapour state depends on
temperature. So, from a climate change perspective, it is considered to be a
feedback agent (Soden and Held, 2006). Also, it is an important component of
the hydrological cycle and estimations of it are used in meteorological
forecast models (e.g. Hong et al., 2015; Bock et al., 2016). Finally, a
robust estimation is needed to study microphysical processes that lead to the
formation of clouds and determine their composition (water droplets or ice
crystals) as well as the statistical shape and size of these components
(Reichard et al., 1996; Yu et al., 2014).
IWV in the vertical atmospheric column is a very common variable in
meteorological and climatological studies. It is defined as the height that
water would stand at if completely condensed and collected in a vessel of the
same unit cross section (American Meteorological Society, 2015). Water vapour
in the atmosphere has been monitored through radiosondes and
provided through measurements of vertical profiles of humidity. These
measurements are limited to relatively infrequent (radiosonde) launches;
thus, during the last decades methods have been developed to retrieve
IWV from other devices:
Continuous monitoring of IWV is established through Global Positioning
System (GPS) satellite observations (Bevis et al., 1992), which can be
used to retrieve IWV anywhere in the globe at relatively high temporal
frequencies. The theoretical basis for these measurement is that delays in
the signals emitted by GPS satellites are caused by the amount of water in
the atmosphere, and through proper calibration, such delays could be
expressed as a function of the IWV. Thus, as long as there are ground-based
GPS receivers, after the appropriate post-processing of the received
signals, IWV can be retrieved.
Microwave radiometer profilers (MWPs) measure the emitted microwave radiation
of the atmosphere and retrieve water vapour vertical profiles and then IWV,
providing continuous data at very high frequencies under all weather
conditions (e.g. Güldner and Spänkuch, 2001; Güldner, 2013).
These instruments provide very high accuracy but are not very common.
Measurements from sun photometers (e.g. CIMEL, PREDE-POM, MFR) have also been
used to calculate water vapour transmittance and thus estimate IWV. Filter
radiometer recordings in the spectral region around water vapour absorption
bands in the near-infrared region are used to calculate this quantity
(Halthore et al., 1997; Campanelli et al., 2018; Nyeki et al., 2005). The
World Meteorological Organization (WMO) recommends the use of spectral
windows centred around 719, 817 and 946 nm, though the most frequently used
is the 946 nm bandpass, which Ingold et al. (2000) showed provides the
most robust results.
Global networks of deployed sun-photometric devices are capable of providing
IWV time series. The AErosol RObotic NETwork (AERONET) retrieves IWV at more
than 500 stations around the globe since the 1990s (Holben et al.,
1998, https://aeronet.gsfc.nasa.gov/) using the Cimel instrument. Other
sun photometers such as precision filter radiometers (PFRs) (Nyeki et al.,
2005) have also been used by the Global Atmosphere Watch (GAW) WMO programme to
monitor IWV. Furthermore, the SKYNET radiometer network (details at
http://atmos2.cr.chiba-u.jp/skynet/) also retrieves IWV using Prede-POM
sun photometers at many stations (Campanelli et al., 2012, 2014). Finally,
national networks of sun photometers that are installed and operating in some
countries also provide integrated water vapour (IWV) retrievals; e.g. China
Aerosol Remote Sensing NETwork (CARSNET) uses the 936 nm channel to
provide IWV (Che et al., 2016).
Schneider et al. (2010) provided a very detailed comparison of different
instrument retrievals over a 4-year data set recorded at Izaña
Atmospheric Observatory, Tenerife, Spain. They found that MWP is the most
precise technique and is independent of weather conditions,
while sun-photometric retrievals were limited by clouds and biased by
dry/humid atmospheres, and GPS-retrieved IWV showed deviations at lower IWV
values. Deviations were also recorded when compared to radiosondes, which was
explained by the difference in air masses and timescales among radiosondes
and other IWV retrievals.
Technological advances in recent years have made feasible the
manufacturing of operational spectral sun photometers for environmental
monitoring. The Precision Solar Spectroradiometer (PSR), designed and
manufactured at PMOD–WRC, Davos, Switzerland, is one of the most accurate
instruments of this class (Gröbner et al., 2012). In this study we
developed tools to retrieve IWV using PSR recordings, adopting two different
approaches, one using single wavelength channels and another retrieving from
a wider spectral region, the latter being impossible with filter radiometers.
Retrievals in different channels and spectral windows in the water vapour
absorbing region of the near-infrared spectrum were evaluated and selected. Both
methods were applied to a 2-year-long PSR data set at the German
Meteorological Service (Deutscher Wetterdienst, DWD) site in Lindenberg,
Germany and results have been compared with sun-photometric (CIMEL), GPS,
radiosonde and MWP IWV data sets from the same station. This study presents
the technical details of all instrumentation used, describes all the details
of the development of these two methodological approaches, estimates the
uncertainties linked to them, and finally all the comparisons for the 2-year
data set are reported.
Instrumentation
Methodologies for retrieving IWV were applied to PSR measurements at
Meteorologisches Observatorium Lindenberg – Richard Assmann Observatorium
(MOL–RAO) from the German Meteorological Service
(DWD) in Lindenberg (Tauche), in the north-east of Germany (52∘12′ N,
14∘7′ E), where a 2-year-long PSR data set is available (May
2014–April 2016). MOL–RAO is a supersite for measurements of aerology and
radiation; thus it provides a variety of collocated measurements that could
be used for validation. MOL–RAO is exclusively devoted to instrumental
measurements of the atmosphere and a sizeable technical staff guarantees
daily maintenance of the instruments. All instruments and corresponding
techniques are described below. Sunshine at the area ranges from
55 h month-1 in December to 256 h month-1 during summer months
on average; also, rain is recorded almost for a third of days over all
12 months (Beyrich and Adam, 2005). Minimum solar zenith angle (SZA) reaches
30∘ during summer months while during winter it is over 70∘.
Aerosol optical depth (AOD) is generally very low in the area, with maximum mean monthly values of
0.25 and 0.27 during June and July.
PSR
A new generation of solar spectroradiometer, the Precision Solar
Spectroradiometer (PSR) (Fig. 1), is being developed at PMOD–WRC in order to
eventually replace current filter sun photometers. It is based on a grating
monochromator of stabilised temperature with a 1024 pixel Hamamatsu
diode-array detector, operating in a hermetically sealed nitrogen-flushed
enclosure. The spectroradiometer is designed to measure the solar spectrum
within the 300–1020 nm wavelength range with an average step of
∼ 0.7 nm and spectral resolution from 1.5 to 6 nm (full width at half
maximum, depending on the measured wavelength) (Kouremeti and Gröbner,
2012). The design benefits from the experience gained from successive
generations of the successful precision filter radiometers (PFRs), including
an in-built solar pointing sensor, an ambient pressure sensor and temperature
sensors to provide routine quality control information, which allows
autonomous operation at remote sites with state-of-the-art data exchange via
Ethernet interfaces. The PSR used in this study is the PSR#006, which is
installed on the MOL–RAO site. This instrument has been calibrated at
PMOD–WRC using a 1000 W transfer standard lamp source, in May 2014 and
October 2015. A comparison between the two calibrations showed relative
differences less than 1 % for most spectral channels and more than
2 % only in the region above 980 nm (Kouremeti et al., 2015). Moreover,
stray light corrections have been applied and absolute direct and global
(horizontal) irradiance time series are available for all 1024 available
channels (Gröbner et al., 2014). The cycle of routine measurements during
this period was in a set of five direct solar irradiance and five dark current
measurements, and average values for each pixel were saved at 1 min
resolution. An evaluation of AOD retrievals from PSR has been performed
during the 4th Filter Radiometer Comparison (WMO, 2016; Kazadzis et al.,
2017).
PSR#004 and PSR#006 installed on a sun-tracking device at
MOL–RAO.
CIMEL sun photometer
The CIMEL sun photometer is a filter radiometer developed by Cimel
Electronique (Paris, France), which performs direct sun and sky radiance
measurements. These measurements are processed centrally and are widely
available through the AErosol RObotic NEtwork (AERONET) (Holben et al., 1998).
Measurements are performed at nine bandpass filters between 340 and 1640 nm
(eight of them are dedicated to AOD retrieving and one used for IWV). Direct
measurements are performed usually every 10–15 min. Direct sun measurements
at 940 nm are used to retrieve IWV. At this channel the full width at half
maximum is 10 nm (Schmid et al., 2001), which means that the solar signal
recorded represents a relatively wide spectral region. The method used to
retrieve IWV is described in detail in Smirnov et al. (2004). The principle
of this method is to calculate the fit of two constant using radiative transfer
model calculations in order to retrieve IWV from the transmittance recorded at
940 nm. The precision of this retrieval was investigated by Alexandrov et
al. (2009), who showed an error in the region of 0.05–0.18 cm depending on
the amount of IWV.
The CIMEL level 2 AOD data for MOL–RAO has been directly downloaded from
AERONET website (https://aeronet.gsfc.nasa.gov/). During the 2 years of
this study, the station has been equipped with three different instruments:
Cimel CE318N, #787;
Cimel CE318N, #873 supplying #787 during its AERONET calibration;
Cimel CE318T (Triple) since October 2015, instrument of higher temporal
resolution (∼ 1 min).
Global Positioning System
GPS is a space-based system that uses the signal transmitted from specific
satellite instrumentation in order to define the geolocation of ground-based
receivers. The signal delays could be separated into dry (dependent on dry
air gases) and wet (water vapour) components. The biggest fraction of
the delay is caused by the dry component, estimated by hydrostatic
equations using the surface pressure and subtracted from the total
delay. This is considered a very accurate retrieval of the wet component, to
which IWV is directly proportional (Bevis et al., 1992). Wang et al. (2007)
showed that the random error of GPS IWV retrievals is of the order of
0.7 mm. GPS IWV retrievals are very valuable, since this method could be
applied to any receiver and a very reliable and dense data set of
frequent observations could be obtained both for daytime and night-time, without being
affected by cloud conditions. Differences among GPS and sun-photometric
retrievals are expected, as different optical paths are used in each case and
different air masses are detected: the GPS path is a quasi-random path depending
on the position of the satellites while the sun-photometer path is defined by
the sun-instrument's relative positions.
Microwave radiometer profiler
At MOL–RAO, a 22-channel MWP, MP-3000A Radiometrics (Ware et al., 2003)
provides vertical temperature and humidity profiles. In principle,
observations from these instruments are based on recording the downwelling
thermal emission of the atmosphere in the region between 22 and 30 GHz,
using a zenith-sky sensor. A full description of the water vapour
retrieval methodology of MWP can be found at Westwater et al. (2005).
Cadeddu et al. (2013) have estimated the uncertainty of this technique to the
order of 5 % for IWV less than 10 mm.
Meteorological radiosonde
Meteorological radiosondes (RS) are launched in many places around the world,
recording vertical profiles of various meteorological variables (temperature,
wind speed, humidity, etc). Water vapour profiles provided by the soundings can
be used to calculate IWV. This is the most objective approach for validating
ground-based remote sensing techniques, since water vapour is measured in situ
during the ascending procedure. Uncertainty for IWV retrieval in this
approach is introduced by the nature of the method, as the total ascendant of
a radiosonde to the stratosphere takes approximately an hour and the path of
the radiosonde in the atmosphere is determined by winds; thus, it is not
directly comparable to sun-photometric estimations, which retrieve water
vapour on the sun-point of the observation optical path. High uncertainties – up
to 20 % – for relative humidity, caused by warming due to sunlight and
thermal lag, have been reported (Pratt, 1985). Also, studies have reported
differences due to the use of different sensors (e.g. Soden and Lanzante,
1996). Vaisalla RS92 radiosondes are used in this study with a reported
uncertainty of the order of 5 % for the RH (relative humidity)
measurements during daytime in the troposphere
(Miloshevich et al., 2009). Radiosondes from MOL–RAO are launched 4 times per
day (00:00, 06:00, 12:00, 18:00 h UTC). So, for this study 1–3 daytime
soundings per day can be used, depending on the season. Corrections, as
suggested by Vömel et al. (2007) for the dependence of the humidity
sensor on temperature and radiation, were applied.
Methodology
In the near-infrared measuring spectral region of PSR the most important
water absorption has been found in the 700–1000 nm wavelength region.
Figure 2 shows the transmittance from Rayleigh scattering, aerosols and IWV,
as calculated by the MODerate resolution atmospheric TRANsmisson radiative
transfer model (MODTRAN RTM) (Berk et al., 1987, 1999). Aerosols direct
effect on irradiance is measured through AOD, which is
the integrated extinction coefficient on vertical column due to aerosols.
Spectral variation of AOD at different wavelengths is measured through
Ångström exponent. For the example in Fig. 2, Ångström
exponent equal to 1.5 was considered and aerosol of AOD 0.1 and 0.2.
Inclination of aerosol transmittance lines is proportional to
Ångström exponent and higher AOD will lead to lower absolute values.
WMO (2005) recommends 719, 817 and 946 nm central wavelengths to retrieve
IWV, which appears as significant drops in the solar transmittance spectra in
Fig. 2. Ingold et al. (2000) investigated the quality of the retrievals at
these wavelengths and found that the one at 946 nm is the most robust, which
could be translated as the wavelength range with the strongest absorption of
IWV. Considering that absorption of water vapour is higher in the 910–950 nm
region, all calculations were performed for PSR channels in the spectral
range.
Transmittance of water vapour, aerosols and Rayleigh scattering in
the spectral region 700–1000 nm, calculated using MODTRAN set at 0.1 nm
resolution, at SZA = 0∘ IWV = 1 cm, IWV = 2 cm and
AOD = 0.1 and AOD = 0.2 at 700 nm using an Ångström exponent
of 1.5. Black vertical dotted lines represent WMO recommendations for IWV
retrieval.
Monochromatic approach
The methodology in use is described in detail by Ingold et al. (2000) and it
is the most common procedure to calculate IWV for sun-photometric devices
using individual wavelength (filter) measurements. It is labelled as
monochromatic in contrast to the second approach presented in Sect. 3.2,
although it is calculated for a spectral region defined by the instrument's
slit function or the limits of its bandpass filter.
The first step of the procedure is to calculate the water vapour transmittance
Tw in the spectral window of use and afterwards to develop
empirical formulas using RTM calculations to determine the IWV from the
calculated transmittance.
For specific spectral regions in the near infrared, where absorption of
dominant trace gases can be considered negligible, we can express the
transmittance of the Atmosphere (Tatmo) as follows:
Tatmo=IλI0,λ,
where Iλ is the recorded spectral irradiance at wavelength
λ (in W m-2 nm-1) and I0,λ is the value of
the solar irradiance at the top of the atmosphere at the same wavelength.
We can express the Beer–Lambert law (Swinehart, 1962) ith respect to water
vapour transmittance as follows:
Tatmo=e(-mrayτray,λ-maτa,λ)×TwTw=Iλe(mrayτray,λ+maτa,λ)I0,λ,
where Tw is the transmittance of water vapour, τray
is the Rayleigh scattering optical depth, τa is the aerosol
optical depth (AOD), and m is the relative optical air mass of aerosol and
Rayleigh scattering accordingly. For the Rayleigh scattering cross section we
used the formula found in Bodhaine et al. (1999).
Also, for I0λ we used extraterrestrial values calculated for
each of the PSR wavelengths measured as presented by Gröbner et
al. (2017a, b). Spectral AODs were calculated using the Beer–Lambert law and
the above extraterrestrial solar spectrum (Kouremeti and Gröbner, 2012).
To calculate AOD at the wavelengths in the 920–950 nm region, where
direct sun measurements are affected by water vapour, we applied a least
square quadratic spectral extrapolation, using ln(AOD) as a function of
ln(wavelength) and the PSR AODs at 500–865 nm following Eck et
al. (1999) suggestion for AERONET
retrievals.
In order to convert Tw into IWV we used the three-parameter
expression found in Ingold et al. (2000):
Tw=ce-aχb,
where
χ=umwu0,
with u0=10 kg m-2, u representing IWV, mw as the
H2O air mass and a, b, c the three-wavelength-dependent
coefficients. At this step the coefficients of Eq. (4) can be estimated. For
that purpose, we used MODTRAN multiple runs for solar zenith angle (SZA)
in the region of 0 to 85∘ with steps of 2.5∘. We used
the midlatitude built-in model atmosphere in the spectral region 0.7 to
1.0 µm and IWV from 0 to 40 mm with steps of 2 mm for site
elevation set at 110 m (MOL–RAO). The modelled spectra were convolved by the
spectrally dependent instrument slit function in order to derive comparable
(model-PSR) results. Then Tw retrieved from the output spectra was
calculated as a function of slant water vapour path (mw∗u), and a fit
of these values is used to estimate the coefficients (a,b,c) of Eq. (4).
This procedure was repeated for all PSR channels in the whole spectral region
of 900–950 nm. In Fig. 3, we present these fits for wavelengths 935.5 and
946 nm. Fits for wavelengths lower than 926 nm were unsatisfactory (R2<0.7), suggesting that a different parameterisation should be used in this
area instead of Eq. (4).
After determining the coefficients a, b, c, equations could be solved
in order to calculate the IWV:
IWV=1mwlnTw/c-a1/b.
Thus, IWV now depends only on Tw and air mass, although the
coefficients depend on the altitude of the measurement site; so, different
RTM runs are needed for each installation.
Transmittance of IWV versus slant water vapour path
(mw∗u) calculated by MODTRAN and three-parameter expression
fit for 935 and 946 nm bandpasses.
In order to test the above methodology, we retrieved IWV on
30 September 2015 for each PSR channel in the 920–950 nm region
separately, after calculating wavelength-dependent a, b, and c
coefficients. Also, aerosol and Rayleigh transmissions were calculated
separately for each wavelength. The standard deviation of the residuals
retrieved from different wavelengths is 0.11. The IWV retrievals at 946 and
935.5 nm have the smallest deviations compared to the GPS and CIMEL
retrievals, because at these wavelengths the absorption due to water vapour
absorption is higher. At these two wavelengths, the agreement with CIMEL
measurements is very good, with correlations (expressed as the R2
coefficient) of 0.94 and 0.93. The lowest R2 is found for
wavelengths shorter than 928 nm which is of the order of 0.6. At Fig. 4 the
mean IWV from all wavelengths for 1 day (30 September 2015) is presented as
an example, alongside with the standard deviation of all monochromatic
retrievals and retrievals at 946 nm are presented as reference. The standard
deviation of the residuals retrieved from different wavelengths is 0.11.
Following WMO guidelines, we decided to use retrievals at 946 nm for this
study and the monochromatic approach.
Retrievals of monochromatic approach on 30 September 2015 at various
wavelengths. Average IWV retrieved using the monochromatic approach at
different wavelengths represented by blue line; the shaded area represents
the standard deviation (1σ) of retrievals at different wavelengths,
the green line represent retrievals at suggested 946 nm and the red curve
represents the IWV retrieved from GPS.
IWV retrieval using integrated spectral windows
In order to benefit from the high resolution spectral measurements available
from the PSR we developed a method that uses direct sun integrated
irradiances for a spectral window in contrast to individual/single
wavelengths as previously described. This methodology is expected to improve
the IWV retrieval, since the large variability found in the IWV retrievals at
different wavelengths suggests that an approach that combines different
wavelengths could possibly be more accurate. Figure 5 shows two theoretical
spectra in the region of 700–1000 nm (calculated using MODTRAN), at
SZA = 0∘ with no aerosol load and with 0 and 2 cm of IWV
respectively. In this approach we used the transmittance of the whole
spectral window, and then Eq. (3) can be written as follows:
Tw,Δλ=∫λ1λ2I(λ)exp(mrayτray(λ)+maτa(λ))I0(λ)dλΔλ,
where λ1 and λ2 are the area wavelength limits, and
Δλ=λ2-λ1.
Spectra of direct solar irradiance at
SZA = 0∘ with AOD = 0 and IWV = 0 cm (black) and 2 cm
(red), as calculated from MODTRAN 5.2.1 RTM.
A similar methodology for converting transmittance to IWV, as in the
monochromatic approach described above is applied again in order to calculate
a third-order polynomial function, valid for the wide spectral region. The
same MODTRAN outputs were used as in the monochromatic approach but
integrated over each spectral window, and the coefficients for Eq. (4) were
calculated accordingly. Calculations have been performed for spectral windows
with variable wavelength limits. An investigation on the selection of
spectral window has been performed because, as monochromatic retrievals
suggested (Fig. 4), the IWV calculation depends on the wavelength region in
use. This investigation was made by changing the window, keeping the upper
limit fixed at 948 nm and having the lower one varying between 930 to
946 nm with a step of 1 nm. This selection was made based on the water
vapour absorption features as shown in Fig. 5, so that the spectral window
always includes the high absorption region of 943–947 nm. Longer than
947 nm wavelengths were avoided as there were higher uncertainties in the
PSR calibration (Kouremeti et al., 2015; Gröbner et al.,
2017a). As demonstrated in Fig. 6 (for
the 934–948 nm window), fitting of the 3-parameter equation had results of
similar statistics with the monochromatic approach in that region. Residuals
from fitting at this window are at average at 0.007 but there are also some
up to 0.04. So, for each spectral window a new 3-parameter function is
calculated.
Integrated transmittance of IWV in the 934–948 nm window versus
the slant water vapour path (mw∗u) calculated by MODTRAN with a third-order polynomial fit (upper plot) and the residuals of this fit (lower plot).
In Fig. 7 results from different spectral windows have been compared to other
instruments' retrievals for the whole MOL–RAO data set. The coefficient of
determination R2 has been used to evaluate the performance of the
spectral approach at different spectral windows, and was calculated as below:
R2=1-∑i(yi-fi)2∑i(yi-<y>)2,
where yi are the IWV values from the other instruments (CIMEL, MW, GPS,
RS), <y> is the average of those values and fi are the IWV values from
PSR.
Horizontal axis of Fig. 7 represents the lower limit of the spectral window,
the higher always being fixed at 948 nm. The aim of this step is to find out
which spectral window produces the more robust IWV retrieval results. These
comparisons suggest that selection of different spectral windows leads to
different coefficients of determination for IWV retrieval compared with
different instruments. However, results converge to define a lower
wavelength limit between 932 and 936 nm that will provide the best
agreement for all the comparisons. The window 934–948 nm was selected to be
used for further analysis, as a median of the above-mentioned area.
IWV retrievals from PSR using a spectral approach with different
spectral windows, a fixed upper boundary at 946 nm and a moving lower
boundary on the x axis, compared to synchronous ones of CIMEL, GPS, MWP and
radiosonde for the full 2-year measuring period.
It is interesting to observe different R2 of the PSR IWV retrievals
compared to using different instruments. Especially the fact that by minimising
the spectral window the R2 decrease, showing a minimum window of
939–946 nm. For this particular range all R2 are below 0.85 with the
one for CIMEL-PSR showing a minimum. The differences observed when comparing
the PSR using different instruments can be partly explained based on the
results of Sect. 5.
Uncertainty budget of IWV retrievals
Uncertainty estimation of the IWV retrieval is crucial for evaluating
our comparison results. Beginning from Eqs. (3) and (7) and the calculations
of Tw, errors introduced from each variable are estimated and
their propagation to the total uncertainty of IWV retrieval is calculated.
Tw=Iλe(mrayτray,λ+maτa,λ)I0,λ
From Eq. (3), the term that introduces the higher uncertainty in the
retrieval of the IWV through the use of Beer–Lambert law is the AOD. A benefit
of the methodology applied in this case is that the same set of I0 are
used for calculating Tw and AOD, and so errors related to the
determination of I0 do not propagate in the calculations. PSR AOD
retrievals at 865 nm have been found in accordance with prototype PFR triad
when compared during FRC IV, 2015 (Filter Radiometer Comparison, WMO, 2016)
with average AOD differences at 865 nm less than 0.02. Also, a calibration
stability study of the PSR was performed (Kouremeti et al., 2015) and showed
that the instrument was stable in the 2-year data set of MOL–RAO,
demonstrating a mean difference of 0.3 % with a maximum of 4 % in some
channels. In addition, comparison with different CIMEL instruments for longer
periods in all cases showed differences smaller than 0.03 at AOD at visible
and near-infrared wavelengths (Kouremeti and Gröbner, 2014). So, the AOD-related uncertainty calculated in all studies for the PSR has a maximum
of 0.03.
Rayleigh optical depths in this spectral region are very low (∼ 0.01
for 1000 mb pressure) and the uncertainty is 1 % (Teillet, 1990) and,
thus, we may consider it negligible for the IWV retrieval. Air masses were
calculated using the formula found in Kasten (1965), which assumes a standard vertical profile of humidity in
the troposphere and introduces an error of 10 % at SZA higher than
85∘, due to variations in real atmospheric conditions but is
negligible for SZA lower than 75∘ (Tomasi et al., 1998).
Coefficients a, b, c derived from fitting MODTRAN outputs introduce
an uncertainty that is related to the goodness of the calculated fit. For the
monochromatic approach at 946 nm, root mean square error (RMSE) is 0.0021
and for the spectral approach at window 934–948 nm it is 0.0029. So, the
uncertainties introduced using the empirical equation to estimate IWV from
Tw is 0.2 and 0.3 % for each approach accordingly, due to the
fitting.
Uncertainty is also introduced by the extrapolation of AOD from the 865 nm
and lower wavelength region to water absorbing wavelengths in the range of
934–948 nm. A sensitivity analysis of the IWV retrieval with respect to
fluctuations in AOD caused by the uncertainty of AOD was performed. The
uncertainty of this extrapolation was calculated to be 0.03.
Figure 8 shows the total expected uncertainty of IWV retrieval with respect
to SZA, for the case of AOD = 0.3 at 865 nm and the case of IWV equal to
2 cm. The highest uncertainties are expected for higher than 75∘ SZA,
when IWV is very low or AOD very high. Very low IWV values can be found
only at very dry atmospheres and even then, those are rarely below 0.2 cm.
In the range of values found in the data set of MOL–RAO (0.3–4.5 cm), the
maximum uncertainty is 0.28 cm. For the 0.3–0.5 cm values in our data set,
absolute uncertainty is calculated as 0.08–0.12 cm. Thus, the maximum
expected uncertainty of the method using PSR instruments is found at the
range of 15 %, when the solar zenith angle is very high
(SZA > 75∘) and AOD is higher than 0.9.
Uncertainty (%) of IWV retrieved using the monochromatic approach at
946 nm for various solar zenith angles (∘) with respect
to AOD (when IWV = 2 cm) in the upper plot and IWV (when
AOD = 0.3) in the lower plot.
Results
In order to validate the results retrieved from both methodologies, we
used the various IWV data sets recorded at MOL–RAO. Calculations have been
performed for all PSR measurements, but we used only the ones
synchronous to CIMEL level data in order to avoid cloud contamination. So
indirectly the AERONET cloud-screening procedure (Smirnov et al., 2000) has
been used. For each CIMEL data point we calculated the synchronous PSR
value by averaging all values in a ±5 min interval. This approach
produced a data set of 3501 synchronous data points between PSR and CIMEL,
2507 between PSR and GPS and 2964 between PSR and MWP. For radiosondes, in
order to have a robust coincidence criterion, we followed the approach
of Schneider et al. (2010), averaging PSR measurements for ±20 min from
the time that the radiosonde reaches a 4 km height, in order to minimise
spatial and temporal PSR and radiosonde measurement differences.
For all the comparisons statistics are calculated for the differences
DX=IWVX-IWVPSR,
where x is the corresponding instrument/method, μX is the average
value for DX and
σ=∑1NDxi-μx2N-1,
where N is the number of available, quality controlled observations.
IWV retrievals from PSR using the monochromatic approach at 946 nm
compared to synchronous ones of CIMEL, GPS, MWP and radiosonde for the full
2-year measuring period.
For the monochromatic approach at 946 nm, the comparison is presented in
Fig. 9 and corresponding statistics are in Table 1. Better agreement was found
when PSR retrievals were compared to MWP retrievals, but at a similar level to the comparisons
with CIMEL and GPS retrievals. Mean absolute difference is slightly lower
when compared to GPS (0.01 cm), but the spread of the differences is almost
the same for CIMEL, GPS and MWP (standard deviation between 0.17 and
0.18 cm). Differences with the CIMEL retrieval are within the CIMEL uncertainty
range. It appears that PSR overestimates the IWV compared to CIMEL for IWV
larger than 3 cm, which causes a different slope in the graphs. This
feature is not shown in the comparison with GPS and MWP at these IWV values.
Schneider et al. (2010) also observed different behaviour in CIMEL
retrievals compared to other methods, regarding dry or wet conditions in
the atmosphere and linked to filter characterisation errors. Radiosonde
retrievals had the largest deviations and more scattered differences, which is
expected because of the different temporal and spatial scales of the RS
retrieval. Percentiles 10–90 of the differences are also presented in
Table 1 and GPS, MWP and CIMEL retrievals have a spread of differences in the
range of the uncertainties described for these instruments. In general RS
retrievals demonstrate the most spread differences from the PSR retrievals,
though the average and median are in the uncertainty range of the
instruments. The high spread of the differences is explained by the random
error introduced by the temporal variability of IWV in the time range
averaged (±20 min) and by the different paths of the sounding.
Statistics of differences among retrievals from PSR using
monochromatic approach at 946 nm and retrievals from other instruments for
the whole data set.
NMeanStandardMedianPercentileMeanR2(cm)deviation (cm)(cm)10–90 (cm)relative (%)CIMEL3501-0.160.18-0.14-0.30 to -0.04-3.30.92GPS25070.010.170.01-0.11 to 0.140.40.94MWP2964-0.050.17-0.04-0.16 to 0.07-0.40.95RS414-0.411.03-0.10-1.42 to 0.22-2.70.79
A histogram of relative difference of this retrieval compared to the GPS is
demonstrated in Fig. 10. Also, relative differences of IWV retrievals are
shown against other parameters (AOD, SZA and IWV from GPS). A normal
distribution with a mean of 0.024 cm and standard deviation of 0.084 is fitted
to the differences and passed the one-sample Kolmogorov–Smirnov test
(Marsaglia et al., 2003). Thus 95 % of the absolute differences are lower
than 0.16 cm. IWV differences against AOD at 865 nm show that almost all
absolute relative differences higher than 0.2 cm (20 %) are linked to
AOD values higher than 0.5. This pattern could be connected to the larger
uncertainty of AOD calculated by extrapolation at 946 nm, when AOD values
are higher. Furthermore, it appears that most of the large differences appear
at high SZA, but there are also some individual points showing large
differences at lower SZA that could be linked to AOD uncertainty. Compared to
IWV retrieved from the GPS it appears that extreme differences are linked to
overestimations from PSR when the absolute value is above 2 cm, and to
underestimations when below, though GPS retrievals are not optimal at more
dry conditions (Schneider et al., 2010).
Histogram of relative difference among synchronous GPS and PSR
retrievals – using monochromatic approach at 946 nm – and plotted against
AOD (retrieved from PSR at 865 nm), solar zenith angle and IWV (retrieved
from GPS).
Comparison of the PSR spectral method with other instruments is presented in
Fig. 11 and corresponding statistics in Table 2. It is clear that the spread
of differences with all methods is significantly lower than for the
monochromatic approach. All comparisons are found with R2 between 0.96
and 0.98. CIMEL seems to underestimate, compared to this method, but also
compared with the other instruments at higher IWV values. Although the slope
caused by the overestimation is still presented in this approach, the spread
of the differences among CIMEL and PSR retrievals is significantly lower than
any other comparison, with σ=0.07 and 10–90 percentiles of
differences in a range of -0.23–0.02. Differences with GPS and MWP
retrievals have the same spread and statistical behaviour. Radiosonde data are
in significantly better agreement with the spectral approach retrieval than
with the monochromatic approach. Standard deviation of the differences is at
least halved compared to the monochromatic approach and all mean relative
differences when compared to any other instrument are lower than 0.7 %.
Comparison with RS data set still has a significantly larger standard deviation
than other comparisons but it is less than a quarter of the monochromatic
approaches. Extreme values observed with the monochromatic approach are
significantly reduced and the standard deviation is reduced to values of
0.07 for CIMEL to 0.18 for RS retrievals. A wider spread is observed at
higher SZA, which is explained by the increase of the instrument-related
uncertainty at these angles.
IWV retrievals from PSR using the spectral approach in the 934–948 nm
region, compared to synchronous ones of CIMEL, GPS, MWP and radiosonde, for
the full 2-year measuring period.
Statistics of differences among retrievals from PSR using the spectral
approach in a 934–948 nm window and retrievals from other instruments for
the whole data set.
NMeanStandardMedianPercentileMeanR2(cm)deviation (cm)(cm)10–90 (cm)relative (%)CIMEL3501-0.110.07-0.10-0.23 to -0.02-0.70.97GPS25070.050.100.04-0.06 to 0.180.40.97MWP2964-0.040.100.01-0.12 to 0.120.30.98RS4140.040.180.02-0.13 to 0.250.50.95
Figure 12 displays a histogram of relative differences of the spectral
approach for the spectral window 934–948 nm, the GPS data set and a relative
IWV comparison between AOD at 865 nm, SZA and GPS. A normal
distribution with a mean of 0.021 cm and σ at 0.042 is fitted to the
data, passes the one-sample Kolmogorov–Smirnov test (Marsaglia et al.,
2003),
and 95 % of differences are lower than 0.08 cm. The quality of spectral
retrieval shows no dependence on absolute IWV values, as the distribution of
differences in Fig. 12 is independent of IWV. When the IWV relative
difference is shown against AOD, higher relative differences than 0.1 are
more frequent for AOD lower than 0.2.
Relative difference among synchronous GPS and PSR retrievals –
using a spectral approach at 934–948 nm region – plotted against
(a) AOD (retrieved from PSR at 865 nm), (b) solar zenith
angle and (c) IWV (retrieved from GPS).
Conclusions
The aim of this study was to develop methodologies and tools in order to
retrieve IWV from PSR spectral measurements. The methods which were developed
can be applied to provide long-term time series of IWV using any direct sun
spectroradiometer able to measure in the 930–950 spectral range.
Two approaches to retrieve IWV from PSR spectral direct solar irradiance
measurements have been developed. The first one is the monochromatic approach
using an individual wavelength, and the second uses a spectral window. For
both methods the corresponding water vapour transmittance has been retrieved
from the PSR measurements, from which IWV can be calculated using a
three-parameter formula following the principles of Ingold et al. (2000).
The dependence of the retrievals on other parameters has been investigated
for both approaches and found to be affected in cases of low (< 0.2) AOD
coincidences. Larger deviations were observed at high solar zenith angles,
which are linked to higher uncertainties in those retrievals.
Comparisons to other instruments (CIMEL, MWP) and methods (GPS, radiosondes)
have been performed to select the optimum wavelength and spectral window for
the IWV retrieval of the PSR. All the channels in the infrared region of
900–950 nm were tested for a monochromatic approach and a 946 nm bandpass was
selected to give significantly better results than other channels. For the
spectral approach all possible spectral windows limits combinations were
tested and the spectral window of 934–948 nm was finally chosen.
Uncertainties of the methodologies have been investigated and in more
frequent atmospheric conditions have been found to be less than 5 %, but
might reach up to 15 % in cases of very high AOD, very low IWV and SZA
higher than 75∘ combined. In general, absolute uncertainty is found
to be in the range of 0.08–0.3 cm.
Retrievals from a 2-year-long time series at MOL–RAO in Lindenberg, Germany
showed that the monochromatic approach had differences of the order of
0.4 % compared to GPS and MWP, 2.7 % compared to RS
and 3.3 % compared to CIMEL; 95 % of differences with GPS retrievals
are less than 0.15 cm.
Spectral approach retrievals showed better agreement with other data sets,
having differences of 0.7 % compared to CIMEL, 0.4 % compared to GPS,
0.3 % compared to MWP and 0.5 % when compared to RS. Also, the
differences to other retrievals were always at least half spread compared to
the monochromatic approach. Differences with GPS retrievals were less than
0.08 cm in 95 % of the data set. Differences among the other instruments
found independent of other variables, suggesting robust appliance of the
method.
Overall, the accuracy of IWV retrieval is of the same order as the other
well-established methods and devices. The spectral approach, benefiting from
the characteristics of PSR, provided statistically better results. Also,
when the method was applied to a 2-year data set, it indicated a stable long-term
performance of the instrument, which shows that it can be used for IWV
calculations. The IWV method development and assessment presented in this
work provided an added value to the PSR instrument, being able to measure
simultaneously spectral solar irradiance components (direct and horizontal),
aerosol spectral optical properties (AOD, Ångström exponents) and IWV,
constituting the PSR as a unique sun-photometric instrument.
Data availability
All data sets used in the current study are freely available.
AERONET IWV data are downloadable from the AERONET webpage: https://aeronet.gsfc.nasa.gov. PSR data can be accessed through personal communication
with Lionel Doppler or Stelios Kazadzis. MWP and radiosonde data can be accessed though personal communication with Lionel Doppler.
Codes developed for spectral IWV retrievals can be used after consultation with corresponding author.
Abbreviations
AERONETAErosol RObotic NETworkAODAerosol optical depthCIMELSun photometer Cimel CE318 used in AERONET networkDWDDeutscher Wetterdienst (German Meteorological Service)GPSGlobal Positioning SystemIWVIntegrated water vapour (water vapour column)MODTRAN RTMMODerate resolution atmospheric TRANsmisson radiative transfer modelMOL–RAOMeteorologisches Observatorium Lindenberg – Richard Assmann ObservatoriumMWPMicrowave radiometer profilerPMOD–WRCPhysikalisch-Meteorologisches Observatorium Davos – World Radiation CenterPFRPrecision filter radiometerPSRPrecision Solar SpectroradiometerRHRelative humidityRSMeteorological radiosondesWMOWorld Meteorological Organisation
Competing interests
The authors declare that they have no conflict of
interest.
Special issue statement
This article is part of the special issue “SKYNET – the international
network for aerosol, clouds, and solar radiation studies and their applications”.
It is not associated with a conference.
Acknowledgements
This research was partly funded by theH2020 GEO-CRADLE project under grant agreement
no. 690133.
Edited by: Monica Campanelli
Reviewed by: three anonymous referees
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