The second generation of the EUMETSAT Polar System (EPS-SG) will include the
Ice Cloud Imager (ICI), the first operational sensor covering sub-millimetre
wavelengths. Three copies of ICI will be launched that together will give a
measurement time series exceeding 20 years. Due to the novelty of ICI, preparing
the data processing is especially important and challenging. This paper
focuses on activities related to the operational product planned, but also
presents basic technical characteristics of the instrument. A retrieval
algorithm based on Bayesian Monte Carlo integration has been developed. The
main retrieval quantities are ice water path (IWP), mean mass height (Zm)
and mean mass diameter (Dm). A novel part of the algorithm is that it fully
presents the inversion as a description of the posterior probability
distribution. This is preferred for ICI as its retrieval errors do not always
follow Gaussian statistics. A state-of-the-art retrieval database is used to
test the algorithm and to give an updated estimate of the retrieval
performance. The degrees of freedom in measured radiances, and consequently
the retrieval precision, vary with cloud situation. According to present
simulations, IWP, Zm and Dm can be determined with 90 % confidence at
best inside 50 %, 700 m and 50 µm, respectively. The
retrieval requires that the data from the 13 channels of ICI are
remapped to a common footprint. First estimates of the errors introduced by
this remapping are also presented.
Introduction
Satellite data are today an indispensable part of numerical weather prediction
(NWP); see for example . The first observations from space
directed towards weather prediction were made during the early 1960s by the
TIROS (Television InfraRed Observation Satellite) program, using optical and
infrared sensors . According to
, the first satellite-based microwave observations of
Earth's atmosphere were made by Cosmos 243 and 384, launched by the Soviet Union
in 1968 and 1970, respectively. Atmospheric humidity and liquid cloud water were
measured using channels at 22.235 and 37 GHz. These first, brief
measurements (two weeks and two days, respectively) were followed by NEMS
(Nimbus E Microwave Spectrometer), which was functional 2.4 years after its
launch 1972 with Nimbus-5. The channels of NEMS were placed at 22.235, 31.4,
53.65, 54.9 and 58.86 GHz. The additional channels around
55 GHz gave information on the atmospheric temperature profile
. Another microwave sensor on board Nimbus-5 was ESMR
(Electrically Scanning Microwave Radiometer), which had a single channel at
19.35 GHz and showed that rainfall can be detected from space
.
More regular microwave soundings started around 1979 with the MSU (Microwave
Sounding Unit) and SSM/T (Special Sensor Microwave – Temperature) sensor
series. Both of these instruments only had channels between 50 and 60 GHzsee for example. The SSM/I (Special Sensor
Microwave – Imager), introduced in 1987, had humidity, cloud liquid water and
precipitation as the main atmospheric targets, with channels at 19.4, 22.2, 37.0
and 85.5 GHzsee for example, and thus
extended the coverage of the microwave region to higher frequencies. The next
main step was taken during the 1990s with the SSM/T-2 (Special Sensor
Microwave – Humidity) and AMSU-B (Advanced Microwave Sounding Unit – B)
instruments that both included three channels around 183.3 GHzsee for example. One of the main
motivations for extending the coverage up to 183 GHz was to obtain
vertical information on humidity, and not only column values. Today a
relatively high number of microwave sensors are operational, mainly in
sun-synchronous orbits but also in other orbits, such as SAPHIR (Sondeur
Atmospherique du Profil d'Humidite Intertropicale par Radiometrie) and GMI
(Global precipitation mission Microwave Imager). Across-track and conically
scanning microwave radiometers are by tradition denoted as sounders or imagers,
respectively. The origin to this classification is that conically scanning
instruments have tended to be optimised for deriving surface properties, while
vertical sounding of the atmosphere has mainly been implemented through across-track
instruments.
In NWP the capability of providing information on temperature and humidity with
no or a small impact of clouds has traditionally been seen as the main
justification for launching microwave sounders. It has been recognised that
passive microwave data also contain valuable information on clouds and
precipitation and these features have been used in various stand-alone
retrievals
e.g.,
but this fraction of the data has been rejected inside NWP as assimilation
systems have been incapable of using these observations. This situation
has started to change, and there are already indications of a strong increase
in the relative impact of microwave data inside NWP .
The present growing impact of microwave data is mainly due to improved
assimilation software in combination with increased computing power, but
new versions of the instruments having a higher number of channels has also been
beneficial. But one limitation has remained for two decades:
that operational microwave observations are so far limited to frequencies below
195 GHz. This situation will change in 2023 with the launch of ICI (Ice
Cloud Imager), which will extend the coverage up to 670 GHz. ICI is one
of the instruments planned for the next generation of Metop satellites; see Sect. for further details. The frequencies 195 and 670 GHz correspond
to wavelengths of 1.5 and 0.45 mm, respectively, and ICI will thus open
up the sub-millimetre region for NWP.
The main objective of ICI is to provide data on humidity and ice hydrometeors,
particularly the bulk ice mass. The advantage of using sub-millimetre
observations for deriving such information was first pointed out by Frank Evans
and coworkers in a series of articles . The initial idea was to have a sub-millimetre
instrument on board CloudSat to complement its cloud radar, but this part was
later descoped.
The idea of a sub-millimetre cloud ice sounder was picked up again in
a mission called CIWSIR, which was proposed to the European Space
Agency ESA as an “Earth Explorer”
in 2002 and again in 2005 . CIWSIR was not
selected, but ESA funded preparatory studies that lead to a
consolidated mission proposal called CloudIce for Earth Explorer 8 in
2010 . It featured channels near 183.31,
243.20, 325.15, 448.00 and 664.00 GHz. Shortly thereafter, a
similar sensor was also proposed for the international space station
(ISS-ICE), with a reduced set of channels.
While CloudIce was not selected for Earth Explorer 8, it was taken as blueprint
for the ICI instrument part of EUMETSAT Polar System – Second Generation
(EPS-SG). Its channel configuration, given explicitly in Table ,
is identical to CloudIce, except that the number of channels near
183 GHz was reduced from 6 to 3.
ICI will be the first operational sub-millimetre mission, but measurements by other instruments of
our atmosphere at such wavelengths already exist, mainly
by limb sounding instruments. The main objective of these instruments is to
monitor gases in the strato- and mesosphere, but at their lowest tangent
altitudes they perform observations that have similarities with ICI. Retrievals
of ice cloud mass have also been developed for all three sub-millimetre limb
sounders launched so far: Aura MLS , Odin/SMR
and SMILES . Observations at 887 GHz were recently
demonstrated by a “cubesat” mission (IceCube, ). The
observation approach behind ICI has also been used by some airborne
instruments. The pioneering instruments were MIR (Millimeter-wave Imaging
Radiometer) and CoSSIR (Compact Scanning Submillimeter Imaging Radiometer)
. More recently, ISMAR (International
SubMillimetre Airborne Radiometer) has been developed largely to support the
preparations for ICI . These instruments and the associated
data analysis, besides their intrinsic scientific value, provided justification
for ICI in the selection process and provide useful input when designing
processing algorithms for ICI.
It is expected that ICI data will be used in two main ways. In NWP the data
will mainly be ingested as basic radiances; for a review of challenges,
expected benefits and approaches of “all-sky” assimilation, see
. The data of ICI can also be “inverted” in stand-alone
algorithms to produce a number of geophysical quantities; see
. The produced retrieval datasets can be concerning for
short-term weather forecasting, but will likely mainly be used for different
climate applications, such as the verification of global models made by the
similar ice cloud products derived from limb sounders
e.g.. This
article describes activities performed under the auspices of EUMETSAT in
preparation of a “day-one” retrieval product (i.e. the product released
directly after commissioning), as well as to provide general support for using
ICI data.
The ICI instrument and its main characteristics are introduced in
Sect. , while the following Sect. outlines the
retrieval algorithm in focus. The expected performance is investigated in
Sect. using simulated data. The two final sections provide an
outlook and conclusions.
The Ice Cloud ImagerOverview of EPS-SG
The ICI mission is part of the EUMETSAT Polar System second-generation system
(EPS-SG). The space segment will consist of two satellites,
referred to as Metop-SG satellite A and B. There will be three satellite pairs,
where each satellite will have a nominal lifetime of 7.5 years to span a total
operational lifetime over 21 years. These satellites will fly, like the present
Metop, in a sun-synchronous mid-morning orbit at 09:30 local time of descending
node. The altitude profile over the Earth geoid varies between 848 and
823 km (832 km mean altitude). The orbit repeat cycle will be
29 d (412 orbits per repeat cycle). The main ground station will be
Svalbard, but also McMurdo will be used to improve the timeliness of
data. The ground segment also includes regional ground stations for receiving a Direct Data Broadcast. See https://www.eumetsat.int/website/home/Satellites/FutureSatellites/EUMETSATPolarSystemSecondGeneration/index.html (last access: 15 December 2019) for further details.
ICI will be on board the B satellites, also carrying MWI (Micro-Wave Imager),
SCA (Scatterometer), RO (Radio Occultation sounder) and ARGOS-4 (Advanced Data
Collection System). In particular, MWI is a conically scanning radiometer which
observes 18 frequencies ranging from 18 to 183 GHz. All channels up to
89 GHz will observe in dual polarisation, while only vertical
polarisation will be provided for higher frequencies. MWI has the same
requirements for incidence angle and fore-view observation as ICI. Combined,
the MWI and ICI radiometers will provide an unprecedented set of microwave
passive measurements, from 18.7 GHz up to 664 GHz.
It is noteworthy that MWI will cover the 118.75 GHz oxygen and the
183.15 GHz water vapour molecular transitions with four and five
channels, respectively. This gives MWI sounding capabilities, and this instrument
narrows down the traditional separation between “imagers” and “sounders”.
The receiver package
The ICI radiometer consists of seven double sideband
front ends, operating with local oscillator (LO) frequencies of 183.31, 243.20,
325.15, 448.00 and 664.00 GHz. The frequencies 183.31, 325.15 and
448.00 correspond to three water vapour transitions, while 243.20 and
664.00 GHz are “window” channels
seeFig. 10. There is a receiver at each of these LO
frequencies providing data matching vertical (V) polarisation inside the
atmosphere. At both the two window frequencies there is also a second receiver
covering horizontal (H) polarisation. A spectrometer of filter-bank type is
attached to each front end. The receiver package will be kept in thermal
balance by passive cooling. Presently, the receiver noise temperature is
expected to be about 600, 900, 1700, 1500 and 2600 K at the five LO
frequencies, respectively. See for example
for an introduction to the concept of receiver noise temperature.
Specifications of the ICI receiver. ICI has double sideband
receivers, indicated by ± in the third column, and the bandwidth
refers to the width of single passbands, i.e. the intermediate frequency
bandwidth. “NEΔT” and “Max bias” are reported as the requirements, and
final performance should be better. Further comments are found in the text
(the last two columns are discussed in Sect. ).
For the window frequency receivers the filter-bank consists of a single
channel, while the other filter-banks have three channels each. Position and
width of all the channels are reported in Table and are
visualised in Fig. .
Frequency coverage of the sidebands for each ICI channel. The
simulated spectrum (blue line) is based on a mid-latitude winter scenario.
The dotted lines are simulations ignoring ozone.
Antenna system, scanning and calibration
The receiver package is integrated with a conically scanning antenna system.
The diameter of the main reflector is 0.26 m (slightly elliptical), and
the system is rotating at 1.333 Hz (i.e. 45 r.p.m.). Atmospheric
observations are made over about 120∘, around the platform's (forward)
flight direction. This gives a swath width of roughly 1500 km. The
platform will perform yaw manoeuvres to keep the swath centred around the
sub-nadir orbit track. During the remaining part of each rotation, calibration
data will be obtained by observing “cold sky” and an internal calibration
target that will have a temperature of around 300 K. The overall requirement
on random (NEΔT) and systematic (bias) uncertainties of calibrated antenna
temperatures are found in Table .
The horn antennas are designed to keep the angular resolution the same between
channels (about 0.5∘), but the footprints of the receivers still
differ, as the antenna of each front end is placed at a different position
in the focal plane. The angular offsets are found in
Table . The reference angle for the elevation offsets is
44.767∘, measured from the nadir direction. This gives a configuration
of instantaneous footprints at surface level as depicted in Fig. ,
with surface incidence angles varying between 51.5∘ and 53.8∘.
The instantaneous footprint sizes at surface level are about 17 (20 km)
along the track and 7.3 (8.5 km) across-track for the
footprints having a positive (negative) elevation offset (at -3dB, and
slightly varying with latitude). The angular movement
inside the integration time increases the effective across-track size.
Instantaneous ICI footprints. The inner and outer contours
represent the -3 and -6dB level of normalised antenna
patterns. The assumed sensor position is 6.9∘ S,
175.3∘ E at an altitude of 824.5 km.
Although the combination of conical scanning and the platform's movement in
total gives a continuous coverage over the swath, there will not be any perfect
matches in horizontal coverage between the channels. Accordingly, some
post-processing is required to obtain data suitable for an inversion using
channels from more than one front end. To support footprint “remapping” a
high across-track sampling will be applied, and data will be recorded every
0.661 ms. This corresponds to an across-track movement of the
bore sights between samples of about 2.7 km, giving 785 samples per scan.
The distance along the track between subsequent scans will be about 9 km.
This gives substantial overlap of sample footprints, both in along- and
across-track dimensions, giving some freedom in setting the target resolution in
the remapping of footprints. The requirement on final footprint size is
16 km (as the average between along- and across-track resolution), and the
requirement of NEΔT, for example, is defined for this horizontal resolution. The
noise in individual samples will be higher. It is expected that averaging over
four subsequent across-track samples will meet the requirements, and
about 200 footprints per scan will effectively be provided. L1b data will only
contain the original samples; the optimal remapping will differ depending on
application.
AlgorithmAim and constraints
The planned output of the EPS-SG Overall Ground Segment at EUMETSAT
Headquarters includes the MWI-ICI-L2 product, which will contain retrievals
based on MWI and ICI and be delivered in near real time. The objective of the
IWP product of MWI-ICI-L2 is to provide a day-one robust retrieval that
reflects the main information content of ICI radiances. For some centrally
generated level 2 products, the EUMETSAT Satellite Application Facilities
(SAFs) provide support by specifying the level 2 processing algorithms and
share responsibility for the products. The SAF supporting nowcasting (NWC-SAF)
retains the scientific ownership of the IWP product and delivered the IWP
algorithm theoretical basis definition . To allow for
the procurement and implementation in the ground segment, the IWP algorithm
definition had to be finished during 2018, with further changes in the
algorithm specifications so that the basic architecture and design would not be impacted. The
efforts so far have focused on the core algorithm and the retrieval database
discussed below has been produced as an initial working basis. Future studies
will be required to elaborate the final database. Additional products from ICI
will be generated directly by the SAFs located at weather services in EUMETSAT
member and co-operating states.
Overview
A first, crucial decision was the selection of retrieval approach.
“Optimal estimation” (a.k.a. 1DVAR) was not selected as it would demand a forward
model handling multiple scattering of polarised radiation and capable of providing
the Jacobian with respect to the retrieval quantities. Such a model was simply
not at hand. With respect to sub-millimetre cloud observations, optimal
estimation has so far only been used for theoretically inclined studies
.
Further, the retrieval problem at hand is non-linear and involves
non-Gaussian statistics, and a more general solution of the Bayes theorem
should be preferable. For practical reasons this leads to approaches based on a
retrieval database . The most straightforward
implementation can be denoted as BMCI (Bayesian Monte Carlo integration), and
has been the method of choice for Evans and coworkers
e.g..
There are close connections between BMCI and the standard use of
neural nets NNs. Such NNs, a
form of machine learning, have been applied on both simulated ICI data
and ISMAR field data
. Both approaches (BMCI and NNs) were considered
initially, but NNs were eventually rejected as it was found that a very
high number of nets would be required and there was no established
way to estimate retrieval uncertainties.
Following the selection of BMCI, a complete retrieval algorithm was designed
(Fig. ). The algorithm consists of two main parts: a series
of pre-processing steps and the actual inversion by BMCI. Only the most
critical aspects are discussed in the following sections; for details we refer
to . The generation of the final retrieval database is a
task for the future, but a possible manner to generate the database is still
outlined in Sect. .
The overall data flow of the algorithm.
Input and output
The main input to the retrieval algorithm are geo-located and
calibrated antenna temperatures, i.e. L1b data. Data from a number of
footprints will be involved in each inversion, being remapped to the
target footprint specified (Sect. ). The target
footprint also governs the extraction of geophysical variables
(Sect. ). All important retrieval parameters are set by
a configuration data structure.
The main output variables (L2) are ice water path (IWP), mean mass
height (Zm) and mean mass diameter (Dm). These three variables are all
reported as percentiles of the estimated posterior distribution (Sect. ) and are defined as antenna weighted means. For example,
the reported IWP is an estimation of
IWP=∫z0∞∫Ωr(Ω)IWC(x(Ω),y(Ω),z)dΩdz∫Ωr(Ω)dΩ,
where r is the antenna (or radiation) pattern (in sr-1, with the
satellite as reference point); Ω is antenna pattern solid angle, x, y and
z are Cartesian coordinates (with arbitrary origin); and IWC is ice
water content:
IWC=∫0∞n(dveq)m(dveq)ddveq,
where n is particle size distribution, m is particle mass and
dveq is equivalent volume diameter (ρ is the density of ice):
dveq=6m/πρ3.
That is, dveq is the diameter of an “ice sphere” with the same
mass. The start of the altitude integration in Eq. (), z0, is
presently set to be the surface altitude, but it can be changed.
Mean mass height is defined as
Zm=∫z0∞z∫Ωr(Ω)IWC(x(Ω),y(Ω),z)dΩdzIWP,
and mean mass size as cf. for exampleEq. 3Dm=∫0∞dveq4∫z0∞∫Ωr(Ω)n(dveq)dΩdzddveq∫0∞dveq3∫z0∞∫Ωr(Ω)n(dveq)dΩdzddveq.
These equations are applied to calculate the IWP etc. of the database cases,
and thus will represent the “true” values. As these equations take
inhomogeneities into account, both vertically and horizontally, the impact of
“beam filling” will automatically be included in the
estimated retrieval uncertainty.
The L2 data will contain further data, such as retrieved water vapour column,
but the exact L2 format is not finalised and only the three main retrieval
quantities are discussed below.
Pre-processing partTarget footprint and remapping of data
The exact geo-location of samples differs between channels
(Sect. ), but the time integration of individual samples is
shorter than the time period necessary to sweep out a single projected field of
view. This allows for a footprint-matching procedure by remapping of the
original data. A toolbox for performing such remappings has been developed in a
dedicated study issued by EUMETSAT . The toolbox is
based on the Backus–Gilbert methodology
, which was previously
successfully applied for footprint-matching between various satellite data
e.g..
In short, the Backus–Gilbert methodology can be used to obtain a set of optimal
weighting coefficients for neighbouring samples, both within the scan and from
adjacent scans, to create a remapped representation of the data matching a
specified target footprint. A remapped value is a linearly weighted combination
of data of the channel of concern. The weights are found, after a trade-off
analysis, by minimisation of a penalty function that considers both the
effective noise of the remapped data and the fit to the target footprint.
The centre position of a retrieval is set by selecting one of the sample
footprints of ICI-1V. The exact shape of the target footprint around this
position will be determined later, but it is expected to be
≈16km and close to circular. The effective noise of remapped samples
should be equal or below the “NEΔT” reported in Table .
Example results are found below, in Sect. .
Bias correction
The algorithm allows for a simple “bias correction” of the data:
Ta,jc=aj+bjTa,j,
where Ta,jc is the corrected antenna temperature for channel j, Ta,j is
the value as given by the remapping toolbox and aj, and bj are channel
specific coefficients.
The purpose of the bias correction is to remove systematic differences between
remapped L1b data and the simulations behind the retrieval database. A bias can
originate from calibration issues, the remapping and incorrect
spectroscopic data in the simulations, for example. This module will only be applied as a
rough temporary solution if any bias is detected, until the source to the bias has
been understood and corrected.
Geophysical data and RTTOV
The retrieval performance can be improved by incorporating various geophysical
data. These data will be taken from the ECMWF forecast system. Data of dynamic
character that will be used include temperature, ozone and surface wind speed,
while static data are various parameters to characterise surface altitude and
type. The water vapour profile is also imported from ECMWF, but it is modified
below the tropopause to have a constant relative humidity (a configuration
setting). The logic behind this approach is to incorporate information on atmospheric temperatures and ozone from ECMWF (ICI has no temperature
channels), for example, while letting humidity be constrained by the ICI data. The last
column in Table gives the mean impact of ozone based on a set of
simulations. The maximum impact found was 2.1 K, for ICI-11 and a
mid-latitude winter scenario.
Using the ECMWF data as input, radiative transfer calculations will be performed by
applying the RTTOV software , to obtain the first
estimate of the atmospheric optical thickness and
a reference antenna temperature (Tar). These calculations assume
“clear-sky” conditions (i.e. no impact of hydrometeors), are run for all ICI
channels and are discussed further below.
Channel mean transmission between altitudes in the atmosphere and ICI,
according to a mid-latitude winter scenario. The dotted line corresponds to an
optical thickness of 1.
Channel selection
Modelling of surface effects will, at least initially, be one of the main obstacles for
these retrievals. Simulating these effects for land surfaces is already a challenge
at low microwave frequencies. The situation for water bodies is better,
particularly as the TESSEM sea-surface emissivity parameterisation has been
updated to cover the full frequency range of ICI . Some
validation of TESSEM has been made (using ISMAR), but presently relatively
large model uncertainties are expected even for water surfaces.
The impact of surface effects on measured radiances depends mainly on the
atmospheric transmission. The transmission varies strongly between the ICI
channels, as exemplified in Fig. . It also varies with the
atmospheric situation. Estimates of the altitude at which the transmission to ICI
equals e-1, for clear-sky conditions, are found in the column “τ=1”
of Table . The lowest altitudes are associated with the driest
atmospheric scenario considered, and vice versa. The table shows that surface
effects are in general of no concern for ICI 7V, 10V, 11V and 11H, for example, while
for some channels the surface must always be considered.
As a consequence, an adaptive selection of data is required. A channel mask is
formed by evaluating
τcs,j+chmτhm,j≥τts,
where τcs,j is the clear-sky optical thickness of channel j
obtained by RTTOV, chm is a configuration setting,
τhm,j is estimated additional optical thickness due to
hydrometeors and τts is a threshold value for surface type s. Data
from channels fulfilling this criterion are included in the calculations. In
the pre-processing part τhm is set to zero. The channel mask
is re-evaluated as part of the BMCI module. At this stage, hydrometeor attenuation is considered. Both chm and τts are configurable
variables, and the latter is specified for five different surface types. The
selection of τts should consider the extent to which surface emissivity
variability is represented in the final retrieval database, as well as the
extent to which the error model in Sect. covers remaining modelling
uncertainty.
Detection of clear-sky data
The algorithm includes an optional module for identifying observations that
with a high probability match clear-sky conditions, which thus can be set to
give IWP=0 without doing an actual inversion. This procedure results
in the L2 structure not being fully filled, e.g. the water vapour column
will not be retrieved, and this module will only be activated if it will be
necessary to decrease the overall calculation burden of the processing. As the
module likely will not be applied, we refer to for
details.
Inversion partTheory and retrieval representation
The retrieval is performed by the BMCI method (Sect. ). For a
description of BMCI and its relationship to Bayesian estimation, see for example
or . In short, BMCI
is based on a “retrieval database” consisting of n pairs of atmospheric state,
xi, and corresponding observation, yi, with the constraint that
xi is approximately distributed according to reality, i.e. represents the prior
distribution of x. The essence of BMCI is, for a given measurement y,
to attribute a posterior probability, pi(xi|y), to each
database state as
pi(xi|y)=wiai/∑i=1nwiai,
where wi is a measure on the agreement between y and yi, and
wi=exp(-(y-yi)TSo-1(y-yi)/2),
with So being the covariance matrix describing measurement and forward
model uncertainties . The factors ai can be
seen as a priori weights. They can be used to optimise the retrievals for a
given database size. For example, it could be justified to accept cases with
IWP=0 only with some probability r<1 during database generation
(Sect. ). If this thinning is performed, remaining database
cases with IWP=0 will obtain ai=1/r (instead of 1).
As Eq. () involves So, this has the consequence that all
uncertainties covered by this covariance matrix must approximately follow
Gaussian statistics (as for 1DVAR). On the other hand, BMCI allows any prior
distribution of variables (unlike 1DVAR), and “outliers”, for example, can be
included in the generation of the retrieval database.
The actual solution of BMCI is the estimated posterior distribution (as for all
Bayesian methods), but it is unpractical to report sets of p. Some more
compact description is needed. If the posterior distribution follows a Gaussian
distribution it suffices to report the expectation value and the width of the
distribution. ICI retrievals do not fall into this category and it was decided
to instead use a more general description based on the cumulative distribution
function, in the continuous case defined as
Fx|y(x)=∫-∞xp(x′|y)dx′,
where p denotes a probability density function, and in the framework of BMCI
is obtained by summing the probability of all cases with xi<x:
Fxi|y(x)=∑xi<xpi(xi|y).
Using Eq. (), Fx|y is calculated on a wide grid of
x values. These data are then used to obtain the inverse distribution
function, F-1, numerically by interpolation to a set of fixed
percentiles. A more descriptive name of F-1 is the quantile function. For
example, F-1(0.5) is the median and the 90th percentile is F-1(0.9).
Figure exemplifies prior and posterior quantile functions.
Example quantile functions. The blue line represents the retrieval
database applied in Sect. , acting as prior for a test
retrieval (red line). For example, the prior and posterior median values are
0 and 117 gm-2, respectively. The black line matches a
hypothetical retrieval with a Gaussian posterior of
100±32gm-2. The symbol * identifies the 5th, 16th, 50th, 84th
and 95th percentiles of each distribution.
It is presently planned to report the 5th, 16th, 50th, 84th and 95th
percentiles in the L2 data. If the retrieval must be condensed to a single
value, the first candidate to “best estimate” should be the 50th
percentile. The other percentiles can be used in different ways. For example,
if the 5th percentile for IWP is >0 then a correct detection of
ice hydrometeors is highly probable. The 16th–84th percentile range matches
±1σ for a Gaussian distribution. The true value is between the 5th and
95th percentiles with a probability of 90 %, etc.
Database extraction and iterations
Not all database cases are included in the BMCI summation, a filtering
is done based on surface type, pressure, wind speed and temperature,
as well as ΔTa (as defined below in Eq. ). Wind
speed is applicable only over water. The database extraction is done
in an iterative manner, where the filter limits are adjusted with an
iteration counter, in order to fetch both the most relevant and a
sufficient number of matches. The filtering does not involve latitude
or season. This results in, for example, a tropical database case being able to influence the inversion of a mid-latitude summer measurement, if there
is a match in surface temperature etc.
An additional iteration scheme has been added around the core BMCI
calculations. One of the first reasons is to better make use of the observations in
situations with significant hydrometeor contents. The optical thickness
associated with hydrometeors is estimated alongside of the L2 data in each
iteration. Based on this updated estimate of the total optical thickness,
Eq. () is reevaluated for all channels. If this results in more channels being able to be included, BMCI is reiterated with the new channel mask.
This iteration is important as the channels that are sensitive to the surface in a
clear-sky situation, and thus ignored in the initial iteration, are the most
important ones to obtain good estimates at high IWP.
The second reason is to handle the fact that the retrieval database only
provides a discrete coverage of the distribution of y. If one
yi happens to agree closely with y, one wi can be orders of
magnitude bigger than all other w and the summation in Eq. ()
will be dominated by one database case. While the median value found can be
realistic, this results in an underestimation of the retrieval uncertainty. It
could also be the case that no yi gives a significant match with
y. Both of these situations are primarily handled by increasing the
variances in So, effectively making the “search radius” larger. If
this does not suffice, channels will be rejected until an acceptable number of
significant weights are obtained.
For further details of the filtering and iteration schemes, see
. All critical parameters are part of the configuration
data.
Measurement vector and uncertainties
The measurement vector (y) incorporates data from channels fulfilling
the optical thickness criterion of Eq. () as a difference:
ΔTa,j=Ta,jc-Ta,jr,
where Ta,jc is defined by Eq. () and Ta,jr is a
simulated antenna temperature (by RTTOV, Sect. ). To match this,
the retrieval database contains the difference between a full (all-sky)
simulation and one (clear-sky) matching Ta,jr.
The matrix So (Eq. ) represents both instrument and
simulation uncertainties. It is kept diagonal due to a lack of relevant information
on uncertainty correlations between channels. The knowledge regarding such
correlations is especially poor for surface emissivity. The variances
σ2 are set as
σj2=NEΔTj2+(ΔϵTskine-τcs,j)2+(cΔTa,j)2,
where NEΔT is uncertainty due to thermal noise
and calibration. The second term aims to represent the impact of
unknown surface emissivity, where Δϵ is emissivity uncertainty,
Tskin is the ECMWF surface skin temperature, and it is assumed
that the emissivity is relatively high. The antenna
temperature is then approximately Ta=ϵTskine-τcs,j+Te(1-e-τcs,j),
where Te is an effective temperature of the atmosphere, and thus
dTa/dϵ≈Tskine-τcs,j.
The last term covers uncertainty in modelling of hydrometeor scattering. To our
best knowledge, no investigation of such modelling errors has been made. The
uncertainty is zero for clear-sky conditions, and it should in general increase
with the strength of scattering. Based on these two simple observations, we
decided to simply model the error as proportional to the deviation from
the clear-sky reference simulation. NEΔT for each
channel (j), Δϵ for water and land, and c are constants, part
of the configuration data.
Performance testsRemapping of data
Samples from all ICI channels will be convolved into the field of view of
ICI-1V. This section summarises the main findings obtained by applying the
Backus–Gilbert toolbox developed (Sect. ).
Simulate test data
To test the toolbox four full orbits were simulated. The orbit parameters were
taken from Metop-A (orbits 4655, 4656, 6985 and 9744). Geophysical data for the
time of the four orbits were taken from ERA5
(https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5, last access: 15 December 2019). ERA5 lacks data on precipitation
of a convective nature. To compensate for this, precipitation was added from a
separate database (provided by Alan Geer at ECMWF), based on similarities of
large-scale precipitation profiles and some other variables. Using these
data, radiances were simulated for all MWI and ICI channels, covering an area
broader than the instrument's swath and representing a set of incidence angles.
These simulations were done by running the ARTS software in its three-dimensional
mode . Absorption due to gases and liquid water
content was calculated following and
, and surface emissivities following
and . The size distribution of rain
drops and ice hydrometeors were set following and
, respectively. Particle properties were taken from
, applying ID 25 for rain and IDs 15 and 20 for ice
hydrometeors (the name of these habits are found in Table ).
Using the set of pre-calculated pencil-beam radiances as a “look-up” table,
antenna weighted brightness temperatures could be generated with a relatively low
calculation burden, taking full account of MWI's and ICI's scanning and
footprints characteristics, for different assumptions of the exact syncing
between the instruments. In all parts, the WGS-84 reference ellipsoid was
applied.
Main findings
The assumption here is that the goal of the remapping is to obtain data as
would be observed with a synthetic instrument with a common footprint for all
channels (implying the same surface incidence angle for all channels). As will
be shown, this cannot be achieved perfectly. However, these “errors” can at
least partly be considered in the retrieval process and the final impact can be
relatively low. Most importantly, the basic impact of different incidence
angles can be included in both 1DVAR and BMCI retrievals.
A bias-free convolution was demonstrated as long as the remapping does not
involve a change in incidence angle. However, this is strictly true only for
ICI-2V and ICI-3V. These two channels share bore sight with ICI-1V, but the
antenna patterns differ somewhat and a remapping is still required.
Figure exemplifies the issues that appear for the other
channels, with an incidence angle that differs from the one of ICI-1V (Table ). Considerable remapping errors are found for ICI-11V. The
elevation offset of this channel deviates to ICI-1V with 1.53∘, which
scales to a ∼2∘ lower incidence angle at surface level. This angular
difference results in a remapping error even in the absence of hydrometeors, as
exemplified by the upper-left portion of the simulated area. The remapping
generates data that are 0.4–0.6 K too warm,
as the toolbox cannot compensate for the original difference in incidence
angle. The “clear-sky” brightness temperature is higher at a lower incidence
angle.
Remapping of ICI-5V and ICI-11V brightness temperatures (K) for an
example scene. Panels (a) and (b) show simulations representing the expected
result after remapping (figures showing the data before remapping look
identical plotted in this manner). Panels (c) and (d) display the error found
when remapping simulated, noise-free observations.
The same effect can be noted for areas with relative homogeneous cloud
distributions, but brightness temperatures vary more strongly with incidence
angle in cloudy conditions and the error for ICI-11V is here instead about
0.5–2 K (see for example the area directly south of 0∘ N, 10∘ E). Further, at the edges of areas with hydrometeors even higher errors can be
noted, as well as errors of opposite sign. These errors originate in horizontal
inhomogeneities. The target footprint is defined at the altitude of the
reference ellipsoid and the remapping is optimal for this altitude.
However, the effective footprint for some altitude inside the atmosphere is the
one at zero altitude projected upwards, following the incidence angle of each
channel. That is, the footprints will not overlap perfectly, with a horizontal
displacement that increases with altitude. As example, for ICI-11V it is about
700 m at 12 km.
Hence, the noted errors match the change in brightness
temperature for horizontal shifts of that order. However, the atmospheric data
used in the simulations do not have this high horizontal resolution and the
magnitude of these errors are just indicative.
The errors found for ICI-5V (Fig. ) show a similar spatial
pattern, but have the reversed sign and are of lower magnitude. This is
expected as the zenith offset of ICI-5V is only 0.04∘ smaller than the one
of ICI-1V, in contrast to the larger, positive shift for ICI-11V.
Generation of retrieval database
Retrieval databases for ICI must so far be generated by radiative transfer
simulations. The input to the simulations can be obtained from atmospheric
models, providing a sufficiently detailed description of hydrometeors
. This approach relies on the
model mimicking reality with sufficient accuracy, as it represents the estimated posterior distribution for the BMCI retrieval. Another option is to base the simulations directly on
observations as far as possible. As the spatial resolution of ICI is limited,
the most important input is information on vertical and horizontal structures
in hydrometeor fields. Today such data are available through cloud radars, even
on global scale by CloudSat .
The cloud radar data can be used in various ways. Some options are explored by
, while the results reported below
are based on the methodology developed in
. The basic idea is to produce
simulated passive observations that are consistent with the basic information
provided by the radar, i.e. measured reflectivities. This is done for some
assumptions of particle size and shape distributions. That is, external
retrievals of IWC, for example, are not involved; the mapping from radar
reflectivities to particle optical properties at the frequencies of the passive
data is done by an internal, implicit retrieval. The retrieval database should
contain simulations for a set of different particle assumptions, to reflect the
variability and our limited knowledge of particle shapes and sizes. Remaining
atmospheric data can be taken from some analysis (such as ECMWF's ERA5), but
this still represents a drawback of the approach as consistency is not
guaranteed. Most importantly, corrections are likely required to avoid
improbable relative humidities where hydrometeors are present.
ICI retrieval performanceTest retrieval database
At this stage, the simulations are based on stretches of CloudSat
reflectivities, selected randomly and with no preference regarding longitudes,
land–ocean etc. That is, the simulations have two dimensions, vertical and
along the track. The ICI slant geometry and antenna pattern are represented fully
inside this 2-D geometry. So far the extension of the antenna pattern in the
across-track dimension is neglected, but can be included by mapping the
CloudSat data to three dimensions . Consideration of
the antenna pattern is required to avoid systematic modelling biases due to
“beam filling” .
The procedure applied to map radar reflectivities to microwave radiances is
described in detail by . The radiative transfer
calculations were performed with the ARTS software ,
using its interface to the RT4 scattering solver.
RT4 is applied following the “independent beam approximation” (see further
Sect. ), inside the two-dimensional atmosphere formed based on
the CloudSat data. Absorption due to gases and liquid water was treated as
in Sect. .
The microphysical models applied are described in Table . For
middle and high latitudes simulations with a modified gamma distribution (for
two habits) were also produced, but the resulting Dm was found to be
unrealistically high (a significant fraction above even 2 mm) and
this part of the database is here rejected. Oriented and melting particles are
so far ignored.
Observations over both water and land were simulated. Ocean surface emissivity
was modelled according to . Due to a lack of any model for
ICI's frequency range, land emissivity was simply set to vary randomly around
0.9 (with a log-normal distribution). The data used below contain in total
6.2×106 cases, based on 1373 CloudSat orbits between September 2015 and January 2016.
Combinations of particle size distribution and habit model included
in the test retrieval database. is
shortened to MH97. defined a tropical and a
mid-latitude version of their size distribution, and both are used. Each
habit model consists of single scattering data selected from
, where both name and ID number are specified.
Hydro-SizeHabitIDLatitudemeteordistributionnameregionIceSector snowflake3TropicsIceEvans snow aggregate1TropicsIceMH97Thick plate + large plate aggregate15+20TropicsIceEvans snow aggregate1Middle and highRainLiquid sphere25Global
Statistical comparison of simulated and real ATMS channel 21
(183.31±1.8GHz) measurements, for zenith angles of
180∘ (nadir) and 135∘ (roughly the one of ICI). Based on data
collected between 15∘ S to 15∘ N August 2015 (all longitudes
included, all ATMS day-time data included, 170 randomly selected CloudSat
orbits used). The simulations are shown as monochromatic brightness temperatures.
Besides the retrieval database, a smaller dataset was also simulated for
channels 16–21 of the Advanced Technology Microwave Sounder (ATMS) and a statistical
comparison to actual observations was made. The simulated data were generated
exactly as done for the retrieval database, except that the footprint averaging
followed the specifications of ATMS. Example results are displayed in
Fig. . The peak in the distribution around 255 K
corresponds to “clear-sky” situations (low-level cloud can still be present),
while most cases below ∼230 K should contain influences of ice
hydrometeors. The agreement between simulations and observations is high down
to about 200 K. For lower brightness temperatures the simulations show
higher occurrence rates than the observations. This deviation is at least
partly a consequence of the full antenna pattern and particle orientation
not yet being considered in the simulations. The better agreement for nadir
simulations, where ATMS has a smaller footprint, indicates the impact of the
first of these two effects. By assuming totally random particle orientation,
radar back-scattering is under-estimated and our procedure will generate clouds
with a high bias in IWC. There is a compensating effect when simulating the
passive data, by a similar under-estimation of extinction, but it is smaller, at
least for angles away from nadir where particle orientation has a smaller
impact on the projected cross section .
The approach behind the database generation reproduces GMI
data in a similar manner, even when focusing on the
tropical Pacific where deep convective systems control the impact of ice
hydrometeors on ICI and the radiative transfer simulations are especially
challenging .
A similar comparison is found in Fig. 13 of . They
obtained a poorer agreement with observations, with an underestimation starting
at about 225 K. Similar particle models were used and the better
agreement found here is likely a consequence of the simulations being based
on CloudSat, and not model data. The agreement is similar for the other ATMS
channels considered; see . A graphical manner for
exploring whether the retrieval database covers the multi-dimensional space spanned
by the observations to be inverted is found in
Fig. 2.
Degrees of freedom
As an introduction to the information provided by ICI, Fig.
displays an estimate of the measurements' degrees of freedom (DoF) for tropical
conditions. The DoF can be seen as a measure of the effective number of
channels.
Each DoF value is calculated by finding the (left) eigenvectors (E) of
the simulated set of measurement vectors in consideration (without noise
added). These eigenvectors and the covariance matrix (Sy) of
the data are related as follows:
Sy=EΛET,
where Λ is a diagonal matrix, holding the eigenvalues. See for example for further details. The uncertainty due to thermal
noise, in the eigenvalue space, is
SΛ=ESϵET,
where Sϵ has NEΔT2 as its diagonal
elements and is zero elsewhere (see Eq. ). As
Sϵ is diagonal, SΛ will also be diagonal
due to properties of the eigenvectors (orthonormality). The number of diagonal
elements in Sy that are larger than the corresponding value in
SΛ can be taken as the DoF. This calculation of DoF is
essentially the same as the analysis described in Sect. 2.4.1 of
, but is somewhat more general as it is based on
Sy and does not involve the Jacobian matrix, so it
can be easily computed even in cases where Jacobians are not available.
For very low IWP and most wet atmospheres, the DoF is only 2. For these
conditions, ICI is primarily sensitive to humidity in the middle and upper
troposphere. The DoF increases with decreasing IWV, as humidity at lower
altitudes then gets a growing impact. The DoF is here about 3, consistent
with the fact that ICI has three channels around each water vapour transition
covered (1V–3V, 5V–7V and 9V–11V, respectively), and that there is a high
redundancy in information between these groups of channels (which together give
an improved precision for water vapour retrievals). Figure
shows that the two innermost 448 GHz channels cover higher altitudes
than the other channels, but it appears that these two channels add little
information in single-footprint retrievals due to relatively high noise
(Table ). A further analysis of ICI's overall performance for clear-sky
conditions is left for a future study. For most dry atmospheres, there is also
a surface contribution to the DoF, mainly by channels 4V and 4H, from the various
variables affecting surface emission and reflectivity.
Estimated degrees of freedom (DoFs) of ICI observations, as a function
of integrated water vapour (IWV) and IWP. Based on the tropical part of the
retrieval database (Sect. ).
The DoF is considerably higher at high IWP. The maximum DoF in
Fig. is 8, but the true number is likely
higher. The figure is based on simulations only including totally
random particle orientation and thus the full information given by the
dual polarisation channels is not reflected. The simulations also lack
melting particles and still use a relatively low number of
particle models, and the full variability of hydrometeors is probably
not yet reflected.
There is an intermediate range, extending between about 10 and
500 gm-2, where DoF is increasing with IWP. This analysis shows that
ICI acts mainly as a coarse humidity sounder for IWP below
∼10gm-2, but, as designed, provides more rich data with
increasing ice hydrometeor content. This indicates that ICI is suitable for
measuring IWP, but the DoF gives no information on retrieval precision or if
other quantities also can be constrained.
Overall performance
The retrieval performance was estimated by repeatedly dividing the data
generated between a retrieval database and test data (Fig. ). The
algorithm described in Sect. was followed, except that no
footprint remapping or run of RTTOV was performed. Since particle orientation
is not yet included, these retrievals did not include the extra 243 and
664 GHz channels that measure H polarisation. Noise was added following the
NEΔT of Table , but present tests indicate that lower noise
will actually be achieved. Both these aspects should lead to a conservative
estimate of the performance at low IWP, or compensate for error sources not
yet considered. The results in Fig. are averages of retrievals
over both water and land.
The best performance is found for tropical conditions where IWP above about
50 gm-2 can be retrieved without a clear bias. ICI also provides information
for lower IWP, down to about 10 gm-2, but then with an increasing
influence of prior information causing a low bias. This bias occurs
because the prior data are dominated by cases with IWP = 0. Accordingly, the bias could be
decreased strongly by an independent method of cloud detection, effectively
removing all, or most, IWP = 0 from the prior distribution.
The retrieval precision in Fig. is reported as the range between
the 5th and 95th percentile. This range corresponds to a 50 % uncertainty above
about 200 gm-2. The precision is poorer for lower IWP, particularly on
the 5th percentile side. This percentile reaches IWP = 0 when the true value
is ∼15gm-2. Mean altitude, Zm, is well estimated over its
full range (for the type of ice clouds of concern for ICI), i.e. between about
4 and 12 km, with a median precision in the order of 700 m. The
retrieval of Dm is best between 175 and 400 µm, where the median
precision is about 50 µm, but the retrievals should be competitive
between about 100 and 800 µm.
As a contrast, results for mid-latitude late-autumn–winter conditions are also
found in Fig. . There are likely higher uncertainties in these
simulations (e.g. they involve only a single particle habit) and these results
should be approached with more care. Compared to tropical conditions, the
performance is poorer, especially for IWP below 100 gm-2. This is the
case because the ice hydrometeors here are found at lower altitudes, often
below the sounding range of the high-frequency channels. Low IWP is best
estimated by the 664 GHz channels, but they have sensitivity only down
to about 5 km (Fig. ). Low-altitude clouds also make the
choice of τts (Eq. ) critical. For these test retrievals,
it was set to 1 for oceans and 3 for all other surface types. Zm is
retrieved without any significant bias between 2 and 10 km, but the
posterior distribution is highly skewed below 3 km. That is, the 50th
percentile is in general a good estimate, but the retrieval cannot fully rule
out considerably higher Zm. The accuracy is good for Dm between 150 and
600 µm, while there is a quickly growing low bias above
650 µm.
These results do not deviate significantly from earlier similar
studies. The most similar one is ,
particularly as it also used IWP, Zm and Dm as retrieval
quantities. They found a better retrieval performance for low IWP,
which likely is due to a smaller retrieval database and fewer
considered error sources. Our results should be more realistic, albeit
somewhat conservative, as explained at the start of this
section. made a study focusing on
relatively severe weather over Europe and obtained similar IWP
accuracy to that reported here. They did not consider Zm and Dm, but
retrieval of separate hydrometeor classes as well as joint inversion
of data from MWI and ICI. When comparing results between studies, the
error range definition considered must be noted. We use a wider range
(matching ±2σ) compared to most others.
Estimated retrieval performance for IWP (a), Zm
(Eq. , b) and Dm (Eq. , c).
Tropical refers to data at latitudes between 30∘ S and 30∘ N,
while mid-latitude includes data for November to January between
35 and 65∘ N. The blue and yellow solid lines show the median
of retrieved median value, while the corresponding dashed lines show the
median of retrieved 5th and 95th percentile. The performance for Zm and
Dm is shown for states with an IWP above 25 and 50 gm-2 for
tropical and middle latitudes, respectively.
Outlook
The basic algorithm will not be modified until some time after the launch of
ICI and the main concern for the coming years is to refine the retrieval
database generation. A required extension is to include particle orientation,
as shown by and . The first
data on scattering properties at sub-millimetre wavelengths of oriented
particles have just been presented . Varying orientation
distributions should be used in the database generation. Scattering solvers
handling oriented particles include RT4 and DOIT
.
In the database used in this work, a strict separation between liquid and ice
hydrometers was assumed. This is a simplification in several ways. Super-cooled
liquid cloud droplets are common in the atmosphere
e.g., frequently as part of “mixed-phase” clouds.
Results in indicate that ICI has some sensitivity to such
super-cooled liquid water and it should thus be considered in future work. Also
the super-cooled liquid water in updraft regions of convective cells should be
taken into account, especially as the drops here can be of millimetre size and the
liquid water content can reach several grams per cubic metre
. This should lead to a significant impact on
both CloudSat and ICI data. Finally, the impact of melting ice hydrometeors
should be assessed and included if found relevant. However, data on single
scattering properties of such particles are still lacking for the frequency
range of ICI.
A broader range of particle size distributions and particle shapes should be
used, compared to the simulations used in this work. The simulations should of
course make use of most recent studies of these particle properties, preferably
applying data tailored for each cloud type of concern. ISMAR should be an
essential tool for validating microphysical assumptions. The first study of this
type has already been performed .
On the instrument side, a more detailed treatment of the full antenna pattern is
needed. This will increase the calculation burden, but to what extent is not yet
known. The present assumption is that an independent beam approximation (IBA)
can be applied, i.e. that the radiance at one location can be sufficiently well
estimated by a simulation of one-dimensional character. Test simulations have
revealed that this is not true for all situations, but full three-dimensional,
polarised simulations can so far only be performed by computationally costly
Monte Carlo methods, and therefore IBA would be preferable. The error by
applying IBA is being assessed as part of a EUMETSAT fellowship project.
As discussed in Sect. , the necessary spatial
remapping of channels causes some errors due to the differences in
incidence angle. These remapping errors must either be incorporated in the
generation of the database or be treated as an observation uncertainty. In the
latter case, an error model must be derived to set So
(Eq. ) accordingly. The information on temperature and ozone
obtained from ECMWF (Sect. ) has uncertainty and the resulting
impact on the retrievals has not yet been studied. The same is true for errors
in assumed spectroscopic parameters, used to calculate the absorption due to
gases. As ICI will operate in a relatively unexplored wavelength region,
considerably spectroscopic uncertainties cannot be ruled out at this point
.
ISMAR should also be a useful tool for validation here.
A number of retrieval configuration settings need to be determined. For
example, the optical thickness thresholds (τts, Eq. )
should be reevaluated at some point, preferably with improved knowledge,
obtained by ISMAR, of the variability of surface emissivity at the frequencies
of ICI. Another example is that a clear strategy for the database thinning
discussed in Sect. is lacking, and only rudimentary tests have
so far been made.
In a longer perspective, joint inversions of data from MWI and ICI shall be
considered. Such synergistic retrievals should be especially beneficial for
obtaining consistent data on liquid and ice hydrometeor properties
. The remapping toolbox is prepared to handle this
extension, but application of BMCI becomes more problematic as dealing with the
combined measurements drastically increases the required retrieval database
size. Machine learning could be an alternative. In
it is shown that quantiles of the posterior
distribution can be estimated by neural networks more efficiently than with
BMCI.
Conclusions
Ice hydrometeors presently constitute one of the components in Earth's
atmosphere that are least constrained by observation and modelling
systems. There is even a persistent large spread among zonal means of IWP
. ICI will provide
observations that could be used to decrease these uncertainties inside both
weather forecasting and stand-alone retrievals, as well as by model verification
through “satellite simulators”. ICI does not offer the spatial resolution of
cloud radars, such as the CloudSat one, but has the swath width needed for
obtaining semi-global coverage on a daily basis.
The focus of this article is the ICI retrieval algorithm
that will be applied operationally at EUMETSAT. At the
time of the algorithm selection, BMCI was judged a safer option than existing
machine learning alternatives. However, since machine learning is developing
rapidly, future scientific retrieval algorithms may well employ it.
The “day-one” algorithm described here aims to
extract the basic information of ICI on ice hydrometeors, which is the ice
water path, as well as cloud altitude and particle size. ICI also has the potential
to provide profiles of ice water content , but that
possibility has been so far left for research groups to investigate.
An innovative aspect of the new algorithm is that, to our best knowledge, it is
the first example where the retrieval result is presented fully as a
description of the posterior distribution (by reporting five percentiles), and
not as the expectation value and some uncertainty value. This more general
approach is preferable for ICI as the retrieval uncertainty can exhibit a highly
skewed distribution.
The core algorithm has successfully been tested using ISMAR and simulated ICI
data, but the final retrieval performance is mainly determined by the quality
of the retrieval database provided to the processing system. Such a database
has been produced for test purposes and to provide updated estimates of the
retrieval precision. The database reflects the state of the art, but the
retrieval error estimates should still be considered as tentative because some
tools needed to cover the full complexity of the observations are still
lacking.
It is hard to find stringent uncertainty estimates of other IWP retrievals, but
we note that the global mean of IWP given by the DARDAR inversions (mainly
based on CloudSat) changed by 26 % between the two most recent versions
. Based on present simulations, ICI will deliver a similar
accuracy at least above IWP = 200 gm-2. Above this IWP, there is no
intrinsic cause of bias in the retrievals, and the precision for single
retrievals is ±50 % (at quantiles matching ±2σ).
The use of ICI in numerical weather prediction (NWP) is not discussed here, but
several activities described are also relevant for this application. The most
notable example should be the development of ice hydrometeor single scattering
data , which is of direct relevance for “all-sky”
assimilation of ICI radiances. A problem common for NWP and stand-alone
retrievals is how to incorporate the effect of ice particle orientation without
making the radiative transfer calculations too costly. This extension is
required to make full use of ICI's double polarisation channels at 243 and
664 GHz.
In this paper we have tried to reflect the efforts already performed to prepare
for inversions using ICI, but also to indicate the work that remains to be
done. Combining the data of ICI and MWI is an especially interesting prospect
for future extensions. That combination can possibly provide a relatively full view
of water in all of its three phases (gas, liquid and ice).
As a last remark we would like to stress that ICI will provide the first
“operational” observations of our atmosphere in the sub-millimetre region and
its data will cover more than 20 years. This will give the weather forecasting
and climate communities a new important data source.
Code availability
The footprint remapping toolbox can be obtained by contacting
EUMETSAT. It will be distributed “as is” with no warranties and on the
condition of no redistribution, and this article and the EUMETSAT
study with contract EUM/C0/18/4600002075/CJA are cited where used. Other
numerical results in the article are based on various MATLAB and Python
scripts, kept in local SVN repositories, that can be obtained by contacting
the first two authors. Usage of these scripts requires assess to the ARTS and
Atmlab packages, available at http://www.radiativetransfer.org/ (last access: 15 December 2019).
Author contributions
PE and BR participated in most of the activities described
and lead the manuscript writing. VM and CA contributed to the work,
supervising and reviewing the algorithm development in its various phases, and
contributed to the paper writing. AT is in charge of the algorithm
development inside NWC-SAF and has revised the paper. UK is the main ICI
scientist at ESA/ESTEC and has provided the technical description. SAB has
contributed input and text, and revised the paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
The first version of the algorithm, based on neural nets, was outlined by
Gerrit Holl as project scientist at SMHI. Figure 8 was produced by Simon
Pfreundschuh (Chalmers). The science advisory group around MWI and ICI has
given feedback on the work described here. This project would not have been
possible without the many individuals that are contributing to the technical
development of ICI and the development of the ARTS infrastructure.
Financial support
This research has been supported by the Swedish National Space Agency (grant
no. 169/16) and the Deutsche Forschungsgemeinschaft (project no. 390683824).
The development of footprint remapping routines for ICI was performed under the
EUMETSAT study “Application of optimal interpolation procedures to EPS-SG MWI
and ICI”, contract EUM/C0/18/4600002075/CJA.
Review statement
This paper was edited by Alexander Kokhanovsky and reviewed by Ralph Ferraro and two anonymous referees.
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