evaluation of laser heterodyne radiometry for numerical...

Received 6 September 2017 Revised 29 May 2018 Accepted 1 June 2018

DOI 101002qj3365

R E S E A R C H A R T I C L E

Evaluation of laser heterodyne radiometry for numerical weatherprediction applications

Fiona Smith1 Stephan Havemann1 Alex Hoffmann2 William Bell1dagger

Damien Weidmann2 Stuart Newman1

1Met Office Exeter UK2Space Science and Technology Department STFCRutherford Appleton Laboratory Oxfordshire UK

CorrespondenceDamien Weidmann Space Science amp TechnologyDepartment STFC Rutherford AppletonLaboratory Harwell Campus Didcot OX11 0QXUKEmail damienweidmannstfcacuk

Fiona Smith Met Office FitzRoy Road ExeterDevon EX1 3PB UKEmail fionasmithmetofficegovukdaggerPresent address European Centre forMedium-Range Weather Forecasts Shinfield ParkReading RG2 9AX UK

Funding informationScience and Technology Facilities CouncilSTM0071541

This article reports the results of a preliminary mission study to assess the poten-tial of space-borne laser heterodyne radiometry (LHR) for the remote sensing oftemperature for assimilation in a numerical weather prediction (NWP) model TheLHR instruments are low cost and small in size lending themselves to a wide vari-ety of satellite platforms The impact of different configurations of an idealizedLHR instrument is assessed against the Infrared Atmospheric Sounding Interfer-ometer (IASI) via single-column linear information content analysis using inputsconsistent with the background errors of the Met Office 4D-Var assimilation sys-tem Multiplexed configurations give promising results in particular for soundingof upper-atmospheric temperatures

KEYWORDS

DFS IASI information content laser heterodyne radiometer numerical weatherprediction temperature sounding upper atmosphere

1 INTRODUCTION

Steady progress has been made over the last two decades inimproving the skill of global numerical weather prediction(NWP) models which now provide the basis for forecast guid-ance 7 days ahead Much of the gain in skill is attributableto the improved use of satellite data through improved dataassimilation systems as well as through the growth of acomprehensive and diverse satellite observing system (egCollard et al 2011 and references therein)

Operational NWP centres typically assess the contribu-tion to forecast skill from each existing component of theobserving system using both observing system experiments(OSEs) in which specific types of data are denied fromthe forecast system and adjoint techniques such as forecastsensitivity to observation impact (FSOI eg Lorenc andMarriott 2014) These paint a broadly consistent pictureshowing that the radiometric measurements from hyper-spectral infrared sounding instruments together with themicrowave instruments provide most benefit for NWP

One of the hyperspectral sounders used in NWP isthe Infrared Atmospheric Sounding Interferometer (IASISimeacuteoni et al 1997) The instrument measures a spectralrange that spans the thermal infrared (IR) (645ndash2760 cmminus1)at a moderately high spectral resolution of 05 cmminus1 andwith relatively good radiometric sensitivity (noise equiv-alent delta temperature NEdT of 015ndash02 K across thelong-wave temperature sounding channels) IASIrsquos goodradiometric performance is coupled with excellent reliabilityand data availability and the instrument represents currentstate-of-the-art in hyperspectral IR sounding IASIrsquos majorcontribution to the observing network comes at the cost ofsize weight and power (14 m3 210 kg and 200 W) whichmeans it must be deployed on dedicated and costly satelliteplatforms

For meteorological sounding applications targeting temper-ature and humidity most useful information is confined torelatively small sub-regions of the thermal infrared specifi-cally the regions around the CO2 1205842 band centred at 667 cmminus1

for temperature sounding and the H2O 1205842 band centred at

This is an open access article under the terms of the Creative Commons Attribution License which permits use distribution and reproduction in any medium provided the originalwork is properly citedcopy 2018 The Authors Quarterly Journal of the Royal Meteorological Society published by John Wiley amp Sons Ltd on behalf of the Royal Meteorological Society

Q J R Meteorol Soc 20181ndash20 wileyonlinelibrarycomjournalqj 1

2 SMITH ET AL

FIGURE 1 Schematic diagram of a laser heterodyne radiometer [Colour figure can be viewed at wileyonlinelibrarycom]

1595 cmminus1 for humidity sounding This raises the generalquestion as to whether more compact spectro-radiometerscould be developed covering only these key spectral regionsto provide equivalent or better performance for meteorolog-ical applications at lower cost

Infrared heterodyne spectro-radiometers (LHRs) based oncarbon dioxide lasers and tuneable lead-salt diode lasershave been used in atmospheric research for decades (Allarioet al 1983) However their features (size the requirementfor cryogenic operation and power requirements) precludethem for deployment on small satellites The development ofquantum cascade lasers (QCLs) during the 1990s heraldedthe advent of solid state compact robust and continuouslytuneable mid-IR laser sources well suited to providing ther-mal infrared local oscillators Since then the technology hasmatured considerably such that QCLs can be considered foroperational deployment in space (Myers et al 2015)

QCL-based LHR technology has advanced rapidly in thelast decade initially for trace-gas detection in Earth obser-vation and planetary applications (Weidmann et al 2007a)Atmospheric science applications have included ozone pro-filing (Weidmann et al 2007b) multi-constituent profiling(Weidmann et al 2011a Tsai et al 2012) and most recentlyatmospheric CO2 measurements (Hoffmann et al 2016)Developments are currently underway to miniaturize theLHRs using optical integration technologies (Weidmannet al 2011b) and make them suitable for small satelliteapplications (Weidmann et al 2017) As well as the compactsize QCL LHRs offer the combined advantages of ultra-highspectral resolution (sim0001 cmminus1) over narrow spectralmicrowindows (01ndash1 cmminus1) high horizontal resolution dueto the inherently narrow field-of-view (a few hundred metresor less from low Earth orbit) and ideally a radiometric sen-sitivity determined by the shot-noise induced by the randomarrival of photons onto the detectors

The next generation of European operational meteoro-logical satellites are due to launch in the next few yearsand will serve weather and climate applications until 2040There is therefore a window of opportunity to evaluate anddemonstrate new technologies in time to be considered ascomponents of future operational missions The purpose of

this preliminary study was to establish the potential for anadir-viewing LHR to meet future NWP requirements pri-marily by assessing the expected performance of an LHR inprofiling temperature from low Earth orbit (LEO) and geosta-tionary orbit (GEO) platforms using an information contentmethod IASI has been used as a benchmark so that the poten-tial of an LHR can be placed in the context of a well-knownhigh quality operational spectrometer

The principles of laser heterodyne radiometry are brieflyintroduced in section 2 Section 3 describes the main orbitconfigurations considered in this study and the attendantconstraints on integration and sampling times In section4 the framework for the assessment of the idealised LHRperformance is described including the Degrees of Freedomfor Signal (DFS) metric Section 5 details the inputs to theDFS calculations including background and instrument errormodels input profiles and the radiative transfer modellingdetails The main results of the study are given in sections6ndash8 Some future directions are outlined in section 9 andconclusions are drawn in section 10

2 A BRIEF INTRODUCTION TO LASERHETERODYNE RADIOMETRY

Laser heterodyne radiometers (LHRs) bear some similaritiesto radio receivers but transposed into the optical domainThey are passive sounders that use a laser source in this casea QCL as a local oscillator (LO) Figure 1 shows a simpli-fied schematic of an LHR illustrating its operating principlesThe thermal IR radiation to be analysed is collected by theprimary mirror (not shown) It is then superimposed withthe coherent optical field of the LO The requirement tomatch the wave-fronts of the two fields determines the max-imum tolerable angular misalignment of the LO and sourcebeams which in turn determines the field-of-view of theinstrument The two superimposed fields are imaged ontoa high-speed photodiode serving as a photomixer whichdown-converts the spectral information of the incoming radi-ation centred at the LO frequency and within the elec-trical bandwidth of the photomixer to the radio-frequency

SMITH ET AL 3

(RF) domain This signal is usually called the intermediatefrequency (IF)

21 Modes of operation

The LHR makes measurements at very high spectral resolu-tion across a small region of the spectrum referred to here asa microwindow The instrument can be operated in one of twomodes depending on whether the LO frequency is fixed orcontinuously tuned

In Multiplexing Mode the LO frequency is fixed and thespectral coverage of the instrument is defined by the photo-diode electrical bandwidth RF spectral analysis is requiredto reconstruct a spectrum for example using a bank of IF fil-ters (Mumma et al 1982) an acousto-optical spectrometer(Schieder et al 1989) or correlation spectrometers This tech-nology sets the spectral resolution It is currently feasible andconservative to assume up to 20 channels each as narrow as0005 cmminus1 covering a microwindow of 01 cmminus1 Currentlyavailable resonant optical cavity mercury cadmium telluridephotodiodes achieve 01 cmminus1 (3 GHz) bandwidth In the nearfuture quantum-well-based structures are very promisingas 35 cmminus1 (gt100 GHz) bandwidth has been demonstrated(Grant et al 2006) An Advanced Multiplexing Mode isdefined as relying on such devices which would allow a1 cmminus1 bandwidth Multiplexing Mode is efficient in terms ofintegration time but adds to the instrument complexity

On the other hand in Scanning Mode the spectral resolu-tion is set by the bandwidth of a fixed RF filter but the spectralcoverage is obtained by continuously tuning the LO over agiven frequency range usually limited by the laser sourceThis is easier to implement technically but the sequentialacquisition has the drawback that the total time needed tomeasure across the microwindow is much longer than forMultiplexing Mode For the purposes of this study a 01 cmminus1

microwindow is considered at a maximum spectral resolutionof 0001 cmminus1

22 Instrument trade-offs

Since the throughput (also known as etendue or AΩ product)is constant in an LHR relying on a single detector (Siegman1966) only the spectral resolution and the integration time120591 (ie the time to acquire a single spectral channel) deter-mine the instrument noise governed by relationships that willbe described in section 531 The total acquisition time trepresents the time required to acquire a full spectrum for asingle field of view (FOV) Thus in an ideal situation theacquisition time in Scanning mode is simply t= 120591 times n wheren is the number of channels in a microwindow In Multi-plexing mode where channels are measured simultaneouslywe assume t= 120591 Here a single detector instrument (onesingle FOV) is assumed but cross-track scanning could beimplemented using scanning mirrors to control the FOV ifthe acquisition time was sufficient

TABLE 1 LHR modes of operation considered in this study SSM MMand AMM stand for Spectral Scanning mode Multiplexing mode andAdvanced Multiplexing mode respectively

Mode

Spectralresolution(cmminus1)

Microwindowwidth (cmminus1)

Sub-samplingresolution (cmminus1)

Numberofchannels

SSM 0001 01 - 100

SSM 0001 01 0002 50

SSM 0001 01 0004 25

SSM 0001 01 0006 17

SSM 0001 01 0008 13

SSM 0002 01 - 50

SSM 0002 01 0004 25

SSM 0002 01 0006 17

SSM 0002 01 0008 13

MM 0005 01 - 20

MM 001 01 - 10

AMM 0005 10 - 200

AMM 001 10 - 100

AMM 002 10 - 50

There is thus a trade-off to be made between the spectralresolution and the microwindow size for a given acquisitiontime a wider microwindow and higher spectral resolutionwill both result in more channels reducing integration timein Scanning mode Higher spectral resolution comes at theexpense of a lower signal-to-noise ratio (SNR) but may allowhigher vertical resolution in the sounding whereas a widermicrowindow gives an increase in the number of spectral linesavailable for sounding

The integration time is probably the most important con-straint on the feasibility of a space-borne LHR instrumentfor NWP as the acquisition time will be highly constrainedby the satellite orbit parameters for low earth (LEO) andrevisit time for geostationary orbit (GEO) It can thereforebe anticipated that spectral multiplexing will give better SNRperformance

The LHR spectral acquisition modes that were consideredin this study have been summarized in Table 1 Within eachmode various sub-modes are possible such as

bull acquiring non-contiguous samples such that spectral res-olution is higher than sampling resolution This will onlybe of potential benefit in Spectral Scanning mode as themain effect would be to allow an increase in integrationtime within the same acquisition time

bull trading off the spectral resolution and SNR (see section531) For example in Multiplexing mode rather thanusing 20 channels of 0005 cmminus1 resolution 10 channels of001 cmminus1 could be considered

One further possibility is to put two or more differentLHR instrument modules (or laser sub-systems) together onthe same platform to extend spectral coverage and diversityThe number of permutations to optimize information retrievalfor multiple LHRs is very large and will not be considered

4 SMITH ET AL

further in this study However it could be an attractive optionfor a combined temperature and water vapour (or ozone)sounding mission

3 SATELLITE PLATFORM AND VIEWINGMODE

This study focuses on the application of a nadir-viewingsatellite-mounted LHR for temperature sounding ineither LEO or GEO The LHR is also appropriate fora limb-sounding mission in passive or solar occultationmode on LEO satellites for example as a stratospherictemperature-sounding mission but investigating this viewingmode is beyond the scope of this study

31 LEO satellite

A typical satellite in sun-synchronous LEO at an altitude of700ndash800 km has a tangential speed of sim75 kms An obser-vationrsquos acquisition time is therefore strongly limited if onewishes to maintain spatial resolution and homogeneity of thescene observed A comparison with existing high-resolutionthermal infrared instruments gives some indication of thepotential acquisition times to be considered For instance

bull IASI a cross-track scanner with 30 fields of regard (FOR)plus calibration targets within a 15 s scan cycle has aninterferogram acquisition time of 015 s per FOR (fourFOVs within each FOR are acquired simultaneously)

bull TES (Tropospheric Emission Spectrometer) has severalmodes of operation including limb sounding and nadirviewing For the ldquoStepampStarerdquo nadir-viewing mode theacquisition time is 4 s giving one footprint approximatelyevery 45 km along the satellite track In this time thesatellite itself moves 39 km

Motion compensation can be achieved at instrument levelusing a scan mirror IASI uses a two-axis scan mirror toachieve motion compensation while cross-track scanningWithout cross-track scanning (requiring only a one-axis scanmirror) a maximum acquisition time of 1ndash2 s would allowrelatively dense sampling along track whilst keeping sceneheterogeneity low

At the longest acquisition times even though motion com-pensation can maintain the ground point the observation willencompass a wide swath of upper atmosphere (given thesmall ground footprint of the LHR the sampled footprint willbe a very narrow wedge) This will introduce some hetero-geneity into the measured scene For a mode like the TESldquoStepampStarerdquo mode with 4 s acquisition time the sampledregion expands from the nominal nadir footprint tosim05 km at10 km altitude and sim28 km at 50 km altitude However het-erogeneity in the upper levels is unlikely to pose too much of aproblem as the length-scales on which temperature varies aregreater in the upper atmosphere Water vapour content which

is spatially highly variable in the troposphere is extremelylow in the stratosphere

32 GEO satellite

With GEO platforms the satellite orbits at a velocity thatmaintains a fixed position relative to the Earth which meansthat the acquisition time can be longer per dwell The con-straints are the changing of the measurement scene during theacquisition (for example features such as clouds drifting inand out of the field of view) and the requirement to coverthe desired portions of the Earth disc at reasonable repeattimes Five seconds was chosen as an acceptable maximumacquisition time from a GEO platform

33 Choice of acquisition time

As a result of the previous considerations three acquisitiontimes have been considered in this study

bull t= 015 s representing a cross-track scanning mode andequivalent to the acquisition time for IASI

bull t= 1 s representing a push-broom measurement mode foran LEO instrument

bull t= 5 s representing measurement time for a GEO instru-ment or an LEO instrument in point-and-stare mode

The impact of these different acquisition times on the per-formance of the LHR is taken into account via the instrumentnoise model described in section 531 Note that because ofthe small size of the LHR even without implementing a scanmirror several instruments could be mounted on the satelliteplatform with different viewing angles so that in push-broomor point-and-stare modes a swath could be measured

4 METHOD FOR ASSESSING THESUITABILITY OF LHR FOR NWP

The potential of the LHR was assessed via information con-tent calculations for a profile retrieval of temperature withinput assumptions appropriate for NWP applications Thechosen measure of information content used in this studyis degrees of freedom for signal (DFS) derived from linearoptimal estimation (OE eg Rodgers 2000) DFS is chosenbecause it is a widely used and well-understood measure thatimparts information on how much the error in a retrieval hasbeen reduced overall from that of the prior state by the incor-poration of information from an observation The approachtaken in this study is therefore consistent with OE informa-tion content studies for atmospheric chemistry (eg Tsai et al2012 for the LHR)

Most NWP models assimilate data via variational analy-sis (usually three-dimensional (3D-) or 4D-Var eg Rawlinset al 2007) The 1D OE system used here is a huge simplifi-cation of the actual NWP 4D-Var analysis system However

SMITH ET AL 5

TABLE 2 Summary of instrument parameters for a compact and ruggedized infrared LHR compared with those of IASI

Parameter IASI LHR Comment

Size Weight Power 1452 m3

210 kg 200 W0016 m3 39 kg 25 W SSP or piggybacking LHRs offer the possibility of (a) cost reduc-

tions compared to larger instruments and (b) multiple instru-ments (on a constellation) giving improved spatial and temporalcoverage within a single large satellite instrument budget

Spectral resolution 035ndash05 cmminus1 sim0001 cmminus1 The LHRrsquos spectral resolution enables (a) derivation of alti-tude information from measured line shapes and (b) improvedspectral selectivity

Radiometric sensitivity 025 K 005ndash50 K Radiometric sensitivity is a key parameter in determining theimpact of a radiance observation in an NWP system For theLHR this will be strongly dependent on integration time andresolution The trade-off is part of this study

Nadir footprint 12 km sim50ndash70 m (from LEO) The LHRrsquos inherently small FOV could allow (a) increasedobservation frequency by making better use of clear sky betweenclouds and (b) intelligent targeting of ldquointerestingrdquo weather athigh spatial resolution (particularly from GEO)

Spectral coverage 645ndash2762 cmminus1

(155ndash362120583m)Up to a maximumof 15 cmminus1 (herelt1 cmminus1)

For NWP well-defined and narrow measurement channelsshould provide sufficient information These are accessible withconventional QCL devices targeted at specific wavelengths

a 1D analogue is a useful tool to establish preliminary per-formance data especially for an inherently vertical problemsuch as satellite sounding By comparing the results for a newinstrument with an instrument already in operational use (inthis case the LHR and IASI respectively) we can use theDFS measure to give an indication of whether the new instru-ment will provide benefit in a 4D-Var assimilation systemThe theory is covered in section 41 and the use of IASI as abenchmark in section 42 The inputs to the DFS calculationsare detailed in section 5

41 Theoretical background to the informationcontent study

DFS is calculated according to the equation

119863119865119878 = Tr(I minus ABminus1) (1)

where A is the analysis (or retrieval) error covariance matrixand B is the background (or a priori) error covariance matrixAccording to optimal estimation theory A can be calculatedas

A = (Bminus1 + HTRminus1H)minus1 (2)where R is the combined instrument and representation errorcovariance matrix (including forward model error as definedin Janjic et al 2017) and H is the Jacobian matrix The Jaco-bian matrix represents the change in radiance of each channelresulting from a unit change in each element of the input atmo-spheric state vector A radiative transfer model is requiredto simulate H the Havemann Taylor Fast Radiative TransferModel (HT-FRTC Havemann 2006 Havemann et al 2016)was chosen for this study

DFS is a scalar measure it is effectively an average of theimpact of the observation over the whole of the state vec-tor relative to the information contained in the backgroundprofile It is usually interpreted to show the number of inde-pendent pieces of information imparted by the observation to

the retrieval but gives no indication of where this new infor-mation is located in profile space In order to examine whichparts of the atmospheric column the LHR instrument impactsit is necessary to examine the averaging kernels KH whereK is the optimal estimation weight matrix also known asthe Kalman Gain matrix Averaging kernels are the functionsthat spread the information from the observation onto theretrievalanalysis grid They are calculated using the equation

KH = (Bminus1 + HTRminus1H)minus1HTRminus1H (3)

42 Comparing the LHR with IASI

The performance of the LHR was assessed by compari-son with IASI Table 2 summarises the characteristics ofa QCL-based LHR in comparison with IASI IASI as across-track scanner has a wide swath of 2200 km and a rel-atively large footprint size of 125 km and as such deliversgood spatial coverage A LEO LHR on the other hand willhave poor noise performance as a cross-track scanner becauseof the short integration time (see sections 74 and 75) Asingle-view instrument would have limited impact on NWPwhere the main advantage of satellite data is in the wide globalcoverage that sounders typically provide However a swathcan be created by mounting instruments side-by-side but weenvisage a narrower andor more widely spaced swath thanfor IASI

On the other hand the FOV for the LHR will be very smalltypically of the order of 01 mrad yielding ground footprintsof approximately 70 m from LEO or 3ndash4 km from GEO Thisoffers an advantage in terms of improved scene homogeneityprovided the acquisition time is suitably short It is worth not-ing that an IR instrument with a small FOV is of interest to theNWP community The proposal to reduce the field-of-viewsize of the NOAA-series hyperspectral sounder (Wang et al2016) has support from operational NWP centres despite the

6 SMITH ET AL

implication that the instrument noise would increase becausethe radiative transfer modelling of cloudy scenes is generallybetter from more homogeneous fields of view

The assessment of differences in viewing geometrybetween the LHR and IASI is difficult and is not consideredin quantitative detail here However if an LHR could poten-tially deliver benefits comparable to IASI for a given FOVbut at relatively low cost it would be worth further studyAn advantage of the small size and low cost is that it is anideal candidate for mounting on a constellation of satellitesincreasing the options for improving spatial and temporalcoverage

5 INPUTS TO THE INFORMATIONCONTENT CALCULATIONS

This section describes the inputs used to calculate the DFSand averaging kernels according to the equations in section41

51 Radiative transfer model

As described above the RT model used in this study isthe HT-FRTC run in ldquoline-by-linerdquo mode The LHR instru-ment line-shape function (ILS) was approximated by a top-hatfunction whose width was set to the instrument spectral res-olution (consistent with the use of a low-pass RF filter)Radiative transfer simulations were run at 00001 cmminus1 res-olution and subsequently integrated over the ILS For IASIthe standard Gaussian-apodised Level 1c channel definitionswere used

52 Background error covariance matrix

The DFS and the form of the averaging kernels are stronglydependent on the background error covariance matrix B Thesame instrument will have a higher information content in dif-ferent retrieval systems especially where a climatological B isused (Hilton et al 2009a) For standalone retrieval schemesB is usually estimated from climatological variability and it isnot uncommon to design the form of B such that the retrievalwould have certain desired properties (see for example Deeteret al (2010) where a justification for changes in the a prioricovariance matrix in a retrieval system is made) The maindifference in approach between an NWP-based informationcontent study and a traditional OE retrieval for chemistry andair-quality applications is that NWP benefits from a moreaccurate background (or prior) state estimate obtained byprojecting a previous analysis forward in time (by 6ndash12 h)using a forecast model The background error covariancematrix is an inherent part of the system being derived fromthe model itself The results in this study would vary if a dif-ferent NWP model were assumed nevertheless the results

FIGURE 2 LHR noise equivalent delta temperature at the ideal shot-noiselimit as a function of receiver (filter) double-side bandwidth (here given inequivalent spectral resolution) and integration time The instrument ismeasuring around 750 cmminus1 with a heterodyne efficiency of 05 has anoptical efficiency of 1 and looks at a blackbody of 280 K referencetemperature [Colour figure can be viewed at wileyonlinelibrarycom]

obtained here are broadly representative of the expected effectof LHR data on current NWP models

The B matrix used in this study was a 1D representation ofthe temperature-based component of the 4D-Var error covari-ance in operational use at the Met Office in March 2012It was constructed using a randomisation method (Wlasak2013 similar to the technique used by Andersson et al 2000)In 4D-Var the errors in the control vector are assumed to fol-low a Gaussian distribution of zero mean and unit varianceVarious transform functions are used to map the elements ofthe control vector to physical variables (Wlasak and Cullen2014) The randomisation method makes a large number ofvertical samples of the control vector error using locationsacross the globe These error vectors are mapped back intomodel variables (such as temperature) through the 4D-Varparameter transforms The average of the outer products ofthese individual error vectors gives the 1D B matrix Thematrix employed here was described in detail and used exten-sively in Smith (2015) and in Eyre and Hilton (2013) forinformation content studies The standard deviation of theerrors in profile space can be seen in the black lines of Figure 5(see figure 33c of Smith (2015) for the covariance structure)

53 Observation error covariance matrix

531 LHR noise modelThe LHR instrument noise model is based on an ideal receiversignificantly dominated by shot noise (Figure 2) In this casethe noise equivalent power (NEP) of the LHR is expressedfollowing Weidmann et al (2007a) as

119873119864119875 = 120588ℎ119907

120578

radicB120591 (4)

SMITH ET AL 7

FIGURE 3 IASI noise equivalent delta temperature at a referencetemperature of 280 K and noise equivalent spectral radiance as used inthis study to calculate DFS [Colour figure can be viewed atwileyonlinelibrarycom]

where h is the Planck constant 120584 is the optical frequency120578 is the detector heterodyne efficiency B the receiver band-width (or spectral resolution) and 120591 the integration time Theoptional unitless degradation factor 120588 can be used as a multi-plier to account for noise larger than the ideal shot-noise limitin ground-based solar occultation experimental studies thishas been found to be of the order of 2ndash5 (Hoffmann et al2016) This noise model is used to define the diagonal ele-ments of the R matrix Measurements on the ground-basedLHR demonstrator have shown that the measurement noisecovariance matrix is diagonal

The throughput (G) of a heterodyne receiver corresponds tothat of a diffraction-limited laser beam and can thus be writtenas the square of the operating wavelength (120582) G= 1205822 follow-ing Siegman (1966) The noise equivalent spectral radiance(NESR in W mminus2 srminus1 Hzminus1) is then simply

NESR = 119873119864119875

G sdot B(5)

(in this study it is expressed in mW mminus2 srminus1 (cmminus1)minus1)The fixed value for the LHR throughput constrains the

SNR no improvement in SNR can be achieved by increasingthe size of the FOV beyond the coherent limit Converselythe spatial footprint can be reduced without loss of SNR byincreasing the collection optics aperture

NWP systems typically assimilate data in units of bright-ness temperature and are therefore used to express instrumentnoise as a noise equivalent delta temperature (NEdT in K)following multiplication of the NESR by the inverse of thepartial derivative of Planckrsquos spectral radiance with respectto T

dL120584T

119889119879= 2 sdot h2 sdot 1205844 sdot e

h120584119896119879

k sdot c2 sdot T2 sdot(

eh120584119896119879 minus 1

)2(6)

where T is a blackbody reference temperature (280 K is oftenused for satellite interferometers) L is spectral radiance andk is the Boltzmann constant Figure 2 shows the LHR NEdTas a function of integration time varying between 1 ms and

10 s and of spectral resolution varying between 30 MHz(0001 cmminus1) and 3 GHz (01 cmminus1) at the shot-noise limit(120588= 1) around 750 cmminus1 and for T = 280 K

Within the context of the information analysis followinghereafter the NESR is used for all calculations and the noisemodel requires specification of the integration time per chan-nel 120591 the spectral resolution (bandwidth) and the centralwave number of the channel The detectorrsquos heterodyne effi-ciency 120578 is stipulated to be 05 and the degradation factor 120588set to a constant 10 which is based on an assumed ideal shotnoise-limited LHR

Suitable values of integration time are affected by twomajor factors the design of the LHR itself (scanning or mul-tiplexing) and satellite viewing geometry as discussed insections 2 and 3

532 IASI noise covariance matrixThe performance of IASI is assessed using a diagonal instru-ment error covariance matrix of which the diagonal is shownin Figure 3 provided by the European Organisation for theExploitation of Meteorological Satellites (EUMETSAT) viathe eigenvector files used in their Level 1 principal componentscore data processing (these are described in EUMETSATDocument EUMOPS-EPSSPE080195) The performanceof IASI is in fact optimistic using the diagonal noise represen-tation calculations performed using a tri-diagonal instrumentnoise matrix that takes account of the inter-channel correla-tions introduced by apodisation (provided by Centre NationaldrsquoEacutetudes Spatiales (CNES) Eric Pequignot personal com-munication) produce lower information content by between 4and 25 depending on the channel selection The results pre-sented here are for the diagonal case as it presents a higherbenchmark for the LHR

533 Radiative transfer model error and errorsof representationMuch of the error associated with the radiative transfer cal-culation such as uncertainties in spectroscopic parameters ordifferences between fast model and line-by-line model mapsinto a systematic error or bias rather than a random termAnother possibly more important source of error that shouldbe incorporated into the observation error term during assimi-lation is the error of representation in other words horizontalor vertical scale mismatch between the observation and theNWP model grid

For this study RT model error and errors of representa-tion are ignored in other words we assume a perfect RTcalculation and a perfect mapping between model grid andobservation spatial resolution For the LHR when combinedwith the perfect instrument assumption the results presentedhere are therefore optimistic in terms of the impact on theNWP model However to compare possible LHR instrumentconfigurations against each other the assessment of RT and

8 SMITH ET AL

scale mismatch errors is a secondary consideration for reasonsoutlined below

It is justifiable to ignore RT errors because variability in theradiative transfer error within such a small portion of the spec-trum as covered by an LHR is expected to be small especiallywhere absorbing gases are intentionally avoided Secondlyfor NWP applications there would normally be some addi-tional contribution from the use of a fast RT model whereparametrization often adds error over a line-by-line modelHowever the errors of HT-FRTC relative to the well-knownline-by-line model LBLRTM122 (Clough et al 2005) arevery small for the 15120583m CO2 band (Havemann 2015)

Representation or scale mismatch errors will indeed varyconsiderably depending on the precise application ndash in par-ticular they will depend on the grid size of the assimilat-ing model For an LEO LHR mismatch will be high for aglobal model with a grid size of 10 km but reasonably lowfor a convective-scale model with a sub-km grid Howeverbetween LHR configurations on the same platform they willbe constant and are therefore not critical in deciding whichLHR configuration is best There would be some variationbetween LEO and GEO platforms because of the differencein footprint size but for this preliminary study the detailrequired to estimate representation error is not justified NWPcentres that assimilate data with correlated errors tend to usea diagnostic method to estimate the whole error covariancestructure empirically (Desroziers et al 2005 Weston et al2014) It is not easy to apply these methods to simulated data

When comparing the LHR against IASI it is important thatwe do not penalise IASI by incorporating more sources oferror than were used for the LHR Although it would be possi-ble to use the operational error covariance matrix for IASI forthe operational channels (derived using the Desroziers diag-nostics) to ensure a consistent comparison only the instru-ment error is used Furthermore a Desroziers diagnosis is notpossible for channels that are not currently assimilated

A drawback of this comparison is that errors of represen-tation are likely to be different for the two instruments Theresults of this study are optimistic because it is clear thatthese other error terms are important contributions to themeasured departures between observation and model fore-casts (along with background errors) However it is also clearthat real IASI observations have a strong positive impactwhen assimilated in current NWP systems (Hilton et al2012) so matching the information content from IASI ina controlled simulation is a sound indication that the LHRwould also deliver benefits in the assimilation system on aper-observation basis

54 Profiles used to calculate Jacobians

Jacobians were calculated with HT-FRTC as described insection 51 The DFS was calculated as an average over eightatmospheric profiles on the 70 Met Office Unified Model(UM) levels spanning a range of latitudes and atmospheric

FIGURE 4 Plot of profiles used in the study Each profile is plotted in adifferent colour The US Standard Atmosphere is marked with blue circles[Colour figure can be viewed at wileyonlinelibrarycom]

TABLE 3 Average DFS for various IASI channel selections fromBands 1 and 2 The spectral range 645ndash720 cmminus1 is the long-waveCO2 band where most of the temperature sounding channels arelocated

IASI Channel selectionAverage DFSfull profile

Average DFSabove 68 km

The currently operationalchannel selection (listed inHilton et al 2009b) from 645to 1900 cmminus1 (127 channels)

607 334

All channels from 645 to1900 cmminus1 (5116 channels)

1100 801


572 480

Operational Channel selection645ndash720 cmminus1 (52 channels)

212 178

conditions These profiles are plotted in Figure 4 Seven ofthe profiles are taken directly from the UM the eighth is theUS Standard Atmosphere The same profiles were used foran IASI channel selection in Smith (2015) Where averag-ing kernels are shown below they are for the US StandardAtmosphere

6 PERFORMANCE BENCHMARKINGAGAINST IASI

For comparison with the LHR the average DFS across theeight atmospheric profiles was calculated for a tempera-ture retrieval using IASI Jacobians for a range of channelselections (Table 3) Since one of the proposed applicationsfor the LHR is upper atmospheric sounding (investigated insection 76) the DFS for just the highest 40 levels of the UM(68ndash80 km roughly 420 to 001 hPa) was also calculatedThese results are also included in Table 3

SMITH ET AL 9

(a) (b) (c) (d)

FIGURE 5 (a and b) Averaging kernels (a) and retrievalbackground error comparison (b) for IASI for 127 operational channels (c and d) Full spectrum to1900 cmminus1 Every 10th model level is plotted as a horizontal line in the same colour as the kernel for that level to aid interpretation [Colour figure can beviewed at wileyonlinelibrarycom]

The associated averaging kernels for the full profileretrieval for IASI for the two channel selections from thespectral range 645ndash1900 cmminus1 are shown in Figure 5 (Notethat the averaging kernels for the topmost layer appear tocontain an artefact from the radiative transfer model thatincorrectly boosts the information content at these levels)The operational channel selection strongly targets the tropo-sphere Inclusion of the full spectrum does add informationabove 35 km with some channels providing information ona broad layer average temperature for the region 35ndash70 kmbut the information remains primarily focused in the loweratmosphere

7 PERFORMANCE OF THE LHR FORTEMPERATURE SOUNDING

71 Initial spectral survey for microwindows

The aim of this study was to identify spectral windows thatcould be targeted by an LHR instrument for temperaturesounding via CO2 absorption lines To be suitable for thistask there should be no contamination from water vapour(as the signal could alias between the two species) or fromtrace gases including ozone Many NWP centres includingthe Met Office do not currently have a sophisticated approachto simulating the effects of a varying ozone profile on theobserved radiances

For CO2 the spectral region around 13120583m has beentargeted which is a small stretch from the readily avail-able QCLs and photodiodes (sim125 120583m) but achievablethrough dedicated development The full CO2 band cov-ers approximately 550ndash800 cmminus1 The search for temper-ature sounding microwindows is kept to the short-waveside of 645 cmminus1 in line with operational IR sounders

Below 645 cmminus1 H2O lines absorb significantly and thecontribution from the water vapour continuum can be 05 Kor more

The first step was to manually survey low-resolution sim-ulations of an infrared spectrum between 645 cmminus1 up toaround 1200 cmminus1 (the short-wave end of the main watervapour absorption band) to find regions with strong CO2

absorption lines but few absorption lines for contaminatingspecies and weak absorption by contaminants This processidentified the most promising spectral region for tempera-ture sounding to be 685ndash721 cmminus1 The information contentof an idealised LHR instrument with a spectral resolutionof 0001 cmminus1 and an integration time of 25 s was assessedacross this region The DFS was calculated for 1 cmminus1

(Advanced Multiplexing) and 01 cmminus1 (Scanning and Mul-tiplexing) microwindows across the spectral range to findthose with the most promising spectral features for sound-ing The integration time was intentionally high in order toensure a very low contribution of instrument noise to the DFSsuch that the differences in performance between microwin-dows could be isolated more easily At this stage thereforethe magnitude of the DFS is not representative of what theinstrument can achieve

The best microwindows will have maximum DFS butminimum contamination by interfering chemical speciesA detailed survey of contaminants was undertaken usingthe US Standard Atmospheric profile calculating absorp-tion to the top of the atmosphere using LBLRTM122 andassessing a standard contribution of all the gases referencedin the High-resolution Transmission molecular absorption(HITRAN) 2012 spectroscopic database (Rothman et al2013) by removing them completely from the RT calculationperforming calculations at 0001 cmminus1 spectral resolutionFigure 6 shows the absorption lines of the only gases to have

10 SMITH ET AL

FIGURE 6 Gas absorption for the region 685ndash721 cmminus1 (the range of the x-axis) The plotted quantity is the effect on the simulated brightness temperatureof completely removing the gas from the simulation Note that the y-axis range is variable The only gases to have an effect bigger than 1 K at any frequencyare H2O CO2 O3 and N2 [Colour figure can be viewed at wileyonlinelibrarycom]

significant absorption in this spectral region Other than H2OCO2 and O3 these are

bull O2 and N2 which make up the bulk of the atmosphere suchthat removing them will not give a realistic RT simulationGiven that they are well-mixed gases they will in any casenot cause problems for this application

bull HCN for which absorption is limited to a spectral regionbetween 710 and 715 cmminus1

bull N2O NO2 CH3Cl C2H2 and H2O2 which have verysmall contributions below the 005 K level and can beignored for the purposes of microwindow selection at thisstage

Figure 7 shows the DFS for Advanced Multiplexing10 cmminus1 microwindows at 0001 cmminus1 spectral resolution for685ndash715 cmminus1 together with the maximum effect on bright-ness temperature from ozone water vapour and other gasabsorption that occurs in any part of each microwindowThe DFS is plotted at the start frequency of the microwin-dow The spectrum from 715 to 720 cmminus1 is more heavilycontaminated by HCN and N2 absorption lines so was not

examined in detail but 7200ndash7206 cmminus1 was assessed (notshown) It appears that no microwindow is completely clearof ozone absorption Two or three small regions where theozone contribution is less than 5 K are visible between 700and 705 cmminus1 but in all of these cases either the water vapourcontamination is too high or the DFS is too low comparedto other microwindows Accepting significant ozone contam-ination which tends to occur in isolated lines (see section75) plenty of microwindows with minimal contamination bywater vapour lines are available

For 01 cmminus1 microwindows (Scanning and Multiplexingmodes) the DFS is much more variable but selectivity isenhanced as expected from a narrower microwindow As aresult regions with little interference from ozone are iden-tifiable Figure 8 is the same as Figure 7 but for 01 cmminus1

microwindows Only those microwindows with a DFS greaterthan 5 and contamination less than 1 K are shown Manymicrowindows across the analysed spectral range appearsuitable Three promising regions dense with appropriatemicrowindows were selected for closer investigation formicrowindows starting between

SMITH ET AL 11

FIGURE 7 Average DFS (in black) for 10 cmminus1 microwindows that start at a given wave number and a hypothetical 25 s integration time Below is themaximum effect of ozone absorption (green) water vapour absorption (red) and other gas absorption (blue) across the microwindow The spectral rangecovered in this plot is 685ndash715 cmminus1 The spectrum from 715 to 720 cmminus1 is contaminated by HCN and N2 absorption lines so was not examined in detailThe range 7200ndash7206 cmminus1 was examined but is not shown [Colour figure can be viewed at wileyonlinelibrarycom]

bull 69611 and 69731 cmminus1



72 Microwindow selection

The three regions selected above were scrutinized to locatethe optimum microwindows for each proposed LHR config-uration using an integration time of 25 s per channel (noteagain that this integration time serves the purpose of selec-tion only) Figure 9a shows as an example DFS and max-imum contamination across the 7055ndash7075 cmminus1 spectralregion for 01 cmminus1 microwindows (Spectral Scanning modeor Multiplexing mode) at 0005 cmminus1 spectral resolutionIt is possible to identify 01 cmminus1 microwindows that min-imize both ozone and water vapour contamination whilstmaximizing DFS

Figure 9b shows the same information for 10 cmminus1

microwindows (Advanced Multiplexing mode) with0005 cmminus1 spectral resolution The information content ishigher for the 10 cmminus1 microwindows and less sensitive tothe precise spectral location because the spacing of the CO2

absorption lines is such that it is generally possible to findat least one in a 1 cmminus1 microwindow For all spectral reso-lutions considered the general pattern of regions of higherand lower DFS is the same even though the location of themicrowindow with the maximum DFS does vary

For each of the three measurement modes a microwindowwith very high DFS and low contamination was selected ineach of the promising spectral regions to conduct an analysisinto the trade-offs between spectral resolution microwin-dow width and integration time For ease of comparisonthe microwindow was not changed when the influence ofspectral resolution was studied (eventually a microwindowre-optimization will be needed if the best window is to beselected for future studies) For Multiplexing and AdvancedMultiplexing modes DFS calculations were performed forthe three listed acquisition times 015 10 and 50 s In everymeasurement mode and for a given spectral resolution DFS ishighest with the longest acquisition time as this improves thenoise performance considerably In Spectral Scanning modedifferent sampling resolutions were considered for an acqui-sition time of 50 s Table 4 summarizes these DFS results

73 Performance in Spectral Scanning mode

Recall that in Spectral Scanning mode each channel is mea-sured successively meaning that the integration time is afraction of the total acquisition time that depends on the sam-pling resolution of the instrument In general the integrationtime is extremely short which has a large detrimental impacton the NEdT

The integration time can obviously be increased withlonger acquisition times but also by reducing the measure-mentrsquos spectral resolution from the highest achievable or by

12 SMITH ET AL

FIGURE 8 Same as Figure 7 but for 01 cmminus1 microwindows (note change of y-axis scale) Only microwindows where the average DFS gt50 and themaximum contamination from any gas lt10 K are shown [Colour figure can be viewed at wileyonlinelibrarycom]

(a) (b)

FIGURE 9 Average DFS for 01 and 10 cmminus1 microwindows with maximum absorption from other species (a) ScanningMultiplexing 0005 (b)Advanced Multiplexing 0005 [Colour figure can be viewed at wileyonlinelibrarycom]

reducing the sampling resolution (spectral under-sampling)Individual channels need not be contiguous For examplewith a spectral resolution of 0001 cmminus1 using a step-functionfor the laser current successive samples could instead bespaced by eg 0002 cmminus1 0004 cmminus1 etc These optionsto improve the instrumentrsquos noise performance were inves-tigated Although they made quite a difference the bestperforming instrument still has an NEdT at 280 K of around07 K (NESR 08 mW mminus2 srminus 1 (cmminus1)minus1) For compari-son at these wave numbers IASIrsquos NEdT is around 018 KFurthermore even though reducing the sampling resolutionimproves the noise this does not necessarily translate intoa higher DFS because important spectral features can bemissed by the coarser sampling

The poor noise performance at these short integration timesassociated with the very high spectral resolution coupledwith the limited width of the microwindow means that theDFS is very small The best performing instrument (sampling0002 cmminus1-wide channels every 0008 cmminus1 ie 13 channelsfor the microwindow at 720434 cmminus1) gives a DFS of only085 ie less than one piece of information and not evenenough to estimate a column average In summary SpectralScanning mode is unsuitable for NWP

74 Performance in Multiplexing mode

In Multiplexing mode acquisition time is equal to integra-tion time This means that for a 5 s integration time a

SMITH ET AL 13

TABLE 4 Information content for idealized LHR instruments

ModeInstrument lowerbound (cmminus1)

Measurementresolution (cmminus1)

Samplingresolution(cmminus1)

Number ofchannels

Integration time120649 (s)

NESR(mW mminus2 srminus 1 (cmminus1)minus1)

Average DFS(full profile)

SSM 696117 0002 0002 50 010 1641 043

SSM 706568 0002 0008 13 038 0875 061

SSM 720434 0002 0008 13 038 0927 085

MM 706570 0005 20 015 0886 07

MM 706570 0005 20 1 0343 23

MM 706570 0005 20 5 0153 44

MM 720500 0005 20 015 0939 08

MM 720500 0005 20 1 0364 23

MM 720500 0005 20 5 0163 37

AMM 696260 0002 500 015 1341 31

AMM 696260 0002 500 1 0519 66

AMM 696260 0002 500 5 0232 91

AMM 705760 0002 500 015 1396 26

AMM 705760 0002 500 1 0541 60

AMM 705760 0002 500 5 0242 89

AMM 720220 0002 500 015 1484 33

AMM 720220 0002 500 1 0575 65

AMM 720220 0002 500 5 0257 91

AMM 696260 002 50 015 0424 23

AMM 696260 002 50 1 0164 482

AMM 696260 002 50 5 0073 683

AMM 705760 002 50 015 0441 177

AMM 705760 002 50 1 0171 416

AMM 705760 002 50 5 0076 641

AMM 720220 002 50 015 0469 188

AMM 720220 002 50 1 0182 418

AMM 720220 002 50 5 0081 641

Note In Spectral Scanning mode (SSM) all instruments have an acquisition time of 5 s and a microwindow of 01 cmminus1 In Multiplexing mode (MM) instru-ments have 01 cmminus1 microwindows and the same acquisition time as 120591 Advanced Multiplexing mode instruments (AMM) have 10 cmminus1 microwindowsand the same acquisition time as 120591 Values that match IASI DFS are shown in italics

good NESR of around 015 mW mminus2 srminus-1 (cmminus1)minus1 can beachieved equivalent to 01 K NEdT at 280 K This is in linewith state-of-the-art performance in operational IR hyper-spectral sounders Two spectral resolutions were considered(0005 and 001 cmminus1) The DFS was similar for the two spec-tral resolutions but the higher spectral resolution instrumentshad a marginally higher DFS in each microwindow

Referring to Table 4 performance at 015 s integration timeis too poor to make an LHR of that type useful for NWPEven at 1 s there are only around 1ndash2 pieces of informationavailable for the full 70-level temperature profile With 5 savailable to make the measurements this number increases tomore than 3 pieces of information for two of the microwin-dows still not enough to provide any kind of a profile Ifhowever the instrument could be optimised such that the 3pieces of information were to be located in the very high-est levels of the atmosphere it might be worth consideringas there are few other observations of the uppermost atmo-sphere Section 76 explores microwindows for a dedicatedupper-atmosphere mission

75 Performance in Advanced Multiplexing mode

Advanced Multiplexing mode differs from Multiplexingmode only in that it has a wider microwindow of 10 cmminus1In this case however as we considered future technol-ogy an extended range of spectral resolutions was exploredTable 4 shows the performance of the Advanced Mul-tiplexing modes for spectral resolutions of 0002 and002 cmminus1 which were the highest and lowest valuesexamined

The average DFS is much higher for Advanced Multiplex-ing mode than for Multiplexing mode because of the widermicrowindow The higher spectral resolutions give a higherDFS but even at 002 cmminus1 instruments with a DFS com-petitive with IASI are possible At resolutions higher than0005 cmminus1 mounting on an LEO platform in push-broomconfiguration also becomes viable with over 6 pieces ofinformation per profile at a 1 s integration time Performanceon a cross-track scanner (015 s) is still marginal with around3 pieces of information at the highest spectral resolutionThese results are promising suggesting that as multiplexing

14 SMITH ET AL

FIGURE 10 Absorption lines for CO2 (purple) H2O (red) and O3 (green)plotted across an optimised Advanced Multiplexing 10 cmminus1 microwindowstarting at 720220 cmminus1 The DFS increase for each additional channel ofthe microwindow calculated with a 5 s integration time is plotted with athick black line [Colour figure can be viewed at wileyonlinelibrarycom]

options improve the LHR could be a viable instrument forapplication in NWP

Figure 10 shows the increase in DFS across one of thechosen microwindows (72022 cmminus1) for the Advanced Mul-tiplexing 0002 cm-1 instrument with a 5 s integration timeas each additional channel is added overlain by the spectralabsorption features in the microwindow There is an increasein information content as channels that sample the centreof a new CO2 absorption line are added Not all absorptionlines appear to add new information for example the line at7210 cmminus1 The reason for this is not currently known butcould relate to the coincident ozone lines

Although it is not possible to avoid ozone contaminationacross the whole microwindow the absorption features arevery sharp At 0002 cmminus1 spectral resolution there will be500 channels in a microwindow The channels sensitive toozone could easily be dropped for assimilation via a standardchannel selection mechanism probably without a significantchange in the information content since in most cases thesechannels do not coincide with a portion of the microwindowwhere the DFS is increasing sharply

Figure 11 shows the averaging kernels for the samemicrowindow along with the error in the retrieved tempera-ture profile Comparison with the result for IASI (Figure 5)shows that the LHR is providing complementary informationabove 20 km

76 Performance for upper-atmospheric temperaturesounding

Given that the IASI averaging kernels are so heavily weightedtowards sounding the lower atmosphere the most promis-ing application for the LHR instrument would be to soundthe uppermost levels of the atmosphere where there are

presently few observations In the stratosphere the horizontallength-scales of temperature variation are long enough that anobservation offering relatively sparse spatial sampling andorwith a relatively large footprint along-track could prove tobe beneficial Thus retaining a short integration time on aLEO-mounted instrument is less critical opening possibili-ties for point-and-stare viewing mode This section explorestargeting microwindow selection for the upper atmosphere

In order to find the best microwindow for upper-atmospheresounding the selection process was altered to choose thebest frequencies for sounding in the top 40 levels of the UMspanning 68ndash80 km (roughly 420ndash001 hPa) Table 5 showsthe DFS for the best-performing Multiplexing and AdvancedMultiplexing modes evaluated in terms of the DFS over theselevels

Figure 12 shows the increasing DFS across a10 cmminus1 Advanced Multiplexing 0002 cm-1 upperatmosphere-optimised microwindow The DFS increasesmost rapidly as the wing of the extremely strong absorptionline the signal from lower layers of the atmosphere the sharpincrease in DFS is the result of a channel near the centreof the line enabling a previously unsampled very high layerof atmosphere to be measured The high spectral resolutionallows the contribution from the very narrow region close tothe centre of the line to be resolved

Both Multiplexing and Advanced Multiplexing modes givehigh information content for the upper atmospheric layersand consequently the associated vertical resolution is highas can be seen in the averaging kernels (Figure 13) For theAdvanced Multiplexing mode instrument the sounding isrestricted to levels above 6 km and for the 01 cmminus1 Mul-tiplexing Mode instrument there is no contamination frombelow 17 km In these plots the averaging kernels are plot-ted for the full profile retrieval although the microwindowswere chosen for information content using DFS over the top40 levels only it turns out that these microwindows are inany case free from contamination from the lower atmosphereEven with 1 s integration time the DFS of a MultiplexingMode instrument is reasonable Therefore the LHR holdsgreat promise in this area seeming to provide novel mea-surements that are complementary to those from soundersfocusing on the lower atmosphere

8 INSTRUMENT TRADE-OFFS

The previous section established a first picture of the potentialof the LHR for NWP and identified the most promising appli-cations In this section trade-offs between different aspects ofthe instrument design are discussed in more detail

81 Microwindow width

The choice of a 10 cmminus1 microwindow in AdvancedMultiplexing mode is somewhat arbitrary A smaller

SMITH ET AL 15

(a) (b)

FIGURE 11 (a) Averaging kernels and (b) retrievalbackground error comparison for the Advanced Multiplexing 0002 retrieval at 72022 cmminus1 with0002 cmminus1 resolution and a 5 s integration time Every 10th model level is plotted as a horizontal line in the same colour as the kernel for that level to aidinterpretation [Colour figure can be viewed at wileyonlinelibrarycom]

TABLE 5 Upper-atmosphere information content for Multiplexing and Advanced Multiplexing (01 and 1 cmminus1) microwindows optimised forupper-air sounding (same acquisition time as 120591)

Instrument lower bound (cmminus1)

Measurementresolution(cmminus1)

Number ofchannels

Integrationtime 120649 (s)

NESR(mW mminus2 srminus1 (cmminus1)minus1)

AverageDFS

Multiplexing mode693580 0005 20 5 0145 52

693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31

Advanced multiplexing mode692820 0002 500 5 0229 94

692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73

Note Values that exceed IASI upper atmosphere DFS are shown in italic

microwindow (08 cmminus1 for example) would be cheaper and

could suffice depending on the application Examining the

increase in DFS across a 10 cmminus1 microwindow as shown

in Figures 10 and 12 we see that the DFS increases more

sharply across certain parts of the microwindow depend-

ing on the locations of the main absorption features On the

other hand each additional channel does bring an incremen-

tal amount of information to the retrieval which does not

necessarily plateau (for example the DFS is still increasing

steadily at the end of the microwindow in Figure 10)

Because of the strong dependence on specific absorptionfeatures it is difficult to establish a generic optimal microwin-dow width Associated trade-offs should be analysed onceappropriate photomixers are more mature the technologyhas been demonstrated and the target application is bet-ter specified On the other hand there are certain benefitsto restricting the instrument to a narrow microwindow forexample for an upper-atmosphere mission where a widemicrowindow appears not to be strictly necessary a narrowwindow provides the benefit of avoiding sensitivity to thelower atmosphere

16 SMITH ET AL

FIGURE 12 Same as Figure 10 (with 5 s integration time) but for amicrowindow starting at 69282 cmminus1 optimised for upper-atmospheresounding [Colour figure can be viewed at wileyonlinelibrarycom]

82 Spectral resolution

In general increasing the spectral resolution improves theinformation content despite the increasing noise (comparenumbers at 0002 cmminus1 resolution with those at 002 cmminus1

resolution for Advanced Multiplexing mode in Table 4)Figure 14 shows the averaging kernels at four differentspectral resolutions (0002 0005 001 and 002 cmminus1)in Advanced Multiplexing mode for a microwindow at70576 cmminus1 and 5 s integration time These plots show thatthe main impact of reducing the spectral resolution is toreduce the vertical resolution of the retrieval in the upperatmosphere as spectral features associated with the nar-rowest line width emission (ie lowest pressures) are nolonger resolved Where possible the highest spectral res-olution feasible should thus be chosen particularly for anupper-atmospheric sounding instrument

83 Integration time

The results in section 7 show that the effects of integrationtime on instrument noise and consequently on informationcontent are very high For temperature sounding in the 13120583mregion of the CO2 band an LEO cross-track scanning LHR isnot feasible nor is an instrument in Spectral Scanning modebecause the acquisition time is too short to allow for sufficientintegration time for reducing the noise

Figure 15 shows the impact of decreasing the integrationtime from 5 to 1 to 015 s in Advanced Multiplexing 0002cm-1 mode at 70576 cmminus1 Whilst the overall informationcontent drops dramatically (from 89 to 60 to 26) as theintegration time is reduced the shape of the averaging ker-nels also changes significantly In particular the informa-tion content below 30 km drops to near zero by 015 s butthere remains some information content aloft albeit withpoor vertical resolution This is almost certainly because the

upper-atmospheric levels are more poorly modelled by theUM relative to the mid- to lower troposphere so the back-ground errors are larger and noisy observations still havesome value This suggests that if integration time is restrictedit is certainly worth focusing on an upper-atmosphericsounder to provide novel measurements for NWP

84 Trade-off conclusions

Unsurprisingly the ideal instrument that offers the bestflexibility in sounding applications would have the widestmicrowindow with the highest spectral resolution possibleand the longest integration time However these parametersare not independent and must realistically be traded off in linewith space-borne LHR mission objectives

Some of the scenarios analysed rely on prospective technol-ogy advances particularly in terms of spectral multiplexingOptimal combinations of microwindow width and spectralresolution should be revisited as the technology developsNevertheless there are already indications as to which typeof instrument would contribute most to NWP The resultspresented in section 76 indicate that for a dedicated strato-spheric sounding mission a recommendation of high spectralresolution over a wide microwindow could be made A Mul-tiplexing mode instrument (with a 01 cmminus1 microwindow)operating at high spectral resolution (0001 cmminus1) would bea good candidate for an in-orbit demonstration of a strato-spheric sounding mission from a small satellite platform

Conversely as stated in section 75 a wide microwindowcan provide useful information on broad layers of the upperatmosphere even at lower spectral resolution It seems reason-able to recommend for a full-atmosphere sounding missionthat a wide microwindow should be prioritised over highspectral resolution

With an integration time of 5 s the noise performance ofthe LHR is acceptable in either Multiplexing or AdvancedMultiplexing mode Such an instrument could target eithera GEO platform or an LEO satellite with a point-and-stareinstrument For GEO platforms further work is needed tooptimise a viewing configuration although targeted soundinghas been mooted in the context of examining severe weatherfeatures such as hurricanes it is not clear how useful this typeof configuration would be for an upper-atmosphere sounderA sparse full-disk scanning mode might be preferable

A LEO point-and-stare configuration seems plausible foran upper-atmosphere sounder given that the atmosphere issmoother in structure in the stratosphere and that the generallack of existing observations means that sparse measurementscan still add information to the NWP model For troposphericsounding where spatial information is more critical a lack ofcross-track measurements would certainly limit the impact ofan LHR given a global observing system already saturatedwith hyperspectral IR sounding missions with wide spatialcoverage from both LEO and GEO platforms

SMITH ET AL 17

(a) (b) (c) (d)

FIGURE 13 Same as Figure 11 (with 5 s integration time) but optimised for upper-atmosphere sounding (a b) in Advanced Multiplexing mode with0002 cmminus1 resolution and (c d) in Multiplexing mode with 0005 cmminus1 resolution [Colour figure can be viewed at wileyonlinelibrarycom]

(a) (b) (c) (d)

FIGURE 14 Averaging kernels for a 10 cmminus1 microwindow at 70576 cmminus1 with 5 s integration time for four different spectral resolutions (andashd 00020005 001 and 002 cmminus1) Every 10th model level is plotted as a horizontal line in the same colour as the kernel for that level to aid interpretation [Colourfigure can be viewed at wileyonlinelibrarycom]

9 FUTURE DIRECTIONS

A secondary aim of this study was to identify other areaswhere the LHR may contribute and thus further study is mer-ited Two areas were considered water vapour sounding andmesospheric temperature sounding

91 Water vapour sounding

In the 6 120583m water vapour band which is traditionally used forwater vapour sounding by infrared satellite instruments thenoise performance of the LHR would be very poor at all real-istic acquisition times for a nadir-viewing instrument (NESRof 12 mW mminus2 srminus 1 (cmminus1)minus1 at 5 s integration time givingan NEdT of 29 K compared with around 02 K for IASI)

This leads to extremely low DFS and optimal instrumentconfigurations were not pursued

Given the relatively unpromising results in the main watervapour band an initial survey of the prospects of water vapoursounding below 600 cmminus1 was undertaken At long wave-lengths between 500 and 600 cmminus1 (167 to 20 120583m) thenoise performance of the LHR is excellent (NESR of 006mW mminus2 srminus 1 (cmminus1)minus1 or NEdT of around 01 K for an inte-gration time of 1 s at 0005 cmminus1 resolution) and there isstrong water vapour absorption but little contamination fromtrace gases Initial calculations with the existing B matrix gaveextremely high DFS of 35ndash45 for Advanced Multiplexing and10ndash20 for Multiplexing mode instruments

The averaging kernels for these instruments show thatthe information is highly concentrated above 45 km which

18 SMITH ET AL

(a) (b) (c)

FIGURE 15 Averaging kernels for a 10 cmminus1 microwindow at 70576 cmminus1 with 0002 cmminus1 spectral resolution for decreasing integration time (andashc 5 1and 015 s) The associated DFS are 89 60 and 26 respectively [Colour figure can be viewed at wileyonlinelibrarycom]

immediately raises concerns about the validity of the Bmatrix The 4D-Var error covariance statistics are derivedthrough analysis of an ensemble of model fields Since thewater vapour content of the stratosphere is extremely low andthere are no observations to constrain the model the relativeerrors in the fields will be very large Although using the log-arithm of the mixing ratio protects to a certain extent againstthis it is extremely unlikely that the 4D-Var covariance statis-tics will be at all reliable in this region In consequence the1D B matrix is not well-enough constrained to deliver rea-sonable DFS results However what can be said from theseinitial results is that there is clearly information on the upperatmospheric water vapour profile at these wavelengths andthis application certainly merits further investigation

One other thing to note is that in Multiplexing mode theDFS for water vapour sounding was very insensitive to inte-gration time Thus if the high information content predictedby this study can be confirmed with more realistic backgrounderrors the LHR could target an LEO platform as a cross-trackscanner

From a technology standpoint whilst the results look verypromising a significant level of technological developmentis required to produce suitable single-mode continuous waveQCLs operating in the far IR along with the associatedphotomixers

92 Mesosphere temperature sounding

One other possible application is mesospheric temperaturesounding Studying the information content in this part of theatmosphere is not easy the Met Officersquos UM currently hasonly six levels between 50 and 80 km and the background

error covariance model is not optimised for the topmost lev-els Although a test configuration exists with a higher verticalresolution there are currently no plans to extend the model topbeyond 80 km though space weather models typically start at100 km Nevertheless it would be interesting to target theseuppermost levels of the atmosphere as there is a definite gapin observations that can anchor the temperature there Themission could also link Earth and space weather as a primeobjective

Another future mission study could be limb soundingfor upper atmospheric temperature Many upper-atmosphericinstruments on LEO platforms are limb-sounders which pro-vide high vertical-resolution information of the upper levelsalbeit with low horizontal resolution (as previously men-tioned low horizontal resolutions are less important at thelonger horizontal length-scales in the upper atmosphere)Although NWP models typically do not yet assimilate datafrom IR limb sounders RT models exist (such as RFM Dud-hia 2016) that have the relevant forward modelling capabilityand there have been studies into the use of 2D operators forinstruments such as GNSS-RO (Global Navigation SatelliteSystem Radio Occultation)

10 CONCLUSIONS AND OUTLOOK FORTHE LHR IN NWP

The main aim of this study was to assess whether a laser het-erodyne radiometer measuring in narrow spectral microwin-dows (01ndash10 cmminus1) at very high spectral resolutions(0001ndash001 cmminus1) could provide useful additional informa-tion on atmospheric temperature for NWP applications The

SMITH ET AL 19

baseline performance targeted is that achieved by currentinterferometric radiometers (IASI) operating at moderatelyhigh resolution (025 cmminus1) and spanning the whole of themid-infrared region of the spectrum (645ndash2760 cmminus1)

The study ruled out the following configurations of theLHR as feasible candidate missions

bull For the necessarily short acquisition times appropriate fora cross-track scanning nadir sounder from low Earth orbit(015 s for IASI) the noise levels achievable by the LHRare insufficiently low for the LHR to be a candidate

bull For an LHR in Spectral Scanning mode where eachchannel is measured sequentially with narrow 01 cmminus1

microwindows and a 5 s total acquisition time NEdT val-ues are around 07 K (in contrast to IASI which has anNEdT of 018 K for a 015 s acquisition time) resultingin low DFS The study therefore concluded that the LHRcould not be used in Spectral Scanning mode

However the study found promising results for the LHR inNWP under the following conditions

bull In Multiplexing mode with currently achievable interme-diate frequencies (IFs) in the range 0ndash3 GHz the LHRoffers marginally viable full-profile sounding for opti-mised microwindows of 01 cmminus1 width at resolutions of0005ndash001 cmminus1 and for integration times of 5 s plausi-ble for geostationary satellites or for a point-and-stare LEOmission

bull The Advanced Multiplexing mode requiring intermediatefrequencies in the range 0ndash30 GHz enabled useful infor-mation on temperature to be obtained for microwindowsof 1 cmminus1 width and integration times of 1 s consistentwith LEO deployment in a push-broom configuration DFSvalues were acceptable for all spectral resolutions consid-ered For integration times of 5 s (GEO or point-and-staredeployment) very competitive DFS values of 91 wereobtained for a spectral resolution of 0002 cmminus1 This ishigher than that obtained with the operational IASI channelselection

bull The LHR offers very competitive performance for tem-perature sounding throughout the stratosphere and lowermesosphere Microwindows of 10 cmminus1 width optimisedfor upper atmospheric temperature sounding with an inte-gration time of 5 s gave DFS values of 73ndash94 for thetop 40 levels of the Met Officersquos Unified Model (span-ning 68ndash80 km roughly 420ndash001 hPa) These comparefavourably with 33 for the operational IASI channel selec-tion and 8 for the full spectrum from 645 to 1900 cmminus1On the other hand narrow 01 cmminus1 microwindows yieldDFS values of 45ndash52 while also enabling sensitivity tothe midndashlower troposphere to be minimised providingcomplementary information to IASI

Whilst these results for the LHR are promising muchof the impact of IASI results from the excellent globalcoverage the instrument provides due to its wide swath

The actual impact of an LHR in NWP would rely on somemethod of establishing global coverage possibly with apush-broom multi-instrument configuration or a constella-tion The study also identified that there was a high probabilityof information on water vapour content very high in theatmosphere using the region of the spectrum between 500and 600 cmminus1 This promising avenue should be pursued ifthe reliability of background covariance information can beimproved

This study concludes that a multiplexing LHR is worthyof consideration as an instrument for NWP on both LEOand GEO platforms It is of particular interest for filling inthe upper-atmosphere gap in the operational satellite observ-ing system Further research should be undertaken to developmultiplexing technology that would yield an instrument thatcould be used for mid-to-upper atmospheric sounding

ACKNOWLEDGEMENTS

This work was carried out with financial support from TheScience and Technology Facilities Council Global ChallengeConcepts Scheme award number STM0071541

ORCID

Fiona Smith httporcidorg0000-0002-8068-913XStephan Havemann httporcidorg0000-0002-3259-091XAlex Hoffmann httpsorcidorg0000-0003-1247-8135

Damien Weidmann httpsorcidorg0000-0002-0178-7904

REFERENCESAllario F Katzberg SJ and Hoell JM (1983) Tunable laser heterodyne

spectrometer measurements of atmospheric species In Killinger DK andMooradian A (Eds) Optical and Laser Remote Sensing Berlin HeidelbergSpringer pp 50ndash70 httpsdoiorg101007978-3-540-39552-2_8

Andersson E Fisher M Munro R and McNally A (2000) Diagnosis of back-ground errors for radiances and other observable quantities in a variationaldata assimilation scheme and the explanation of a case of poor convergenceQuarterly Journal of the Royal Meteorological Society 126 1455ndash1472

Clough S Shephard MW Mlawer E Delamere JS Iacono MCady-Pereira K Boukabara S and Brown PD (2005) Atmospheric radia-tive transfer modeling a summary of the AER codes Journal of QuantitativeSpectroscopy and Radiative Transfer 91 233ndash244 httpsdoiorg1010169jjqsrt200405058

Collard A Hilton F Forsythe M and Candy B (2011) From observationsto forecasts ndash Part 8 The use of satellite observations in numerical weatherprediction Weather 66 31ndash36 httpsdoiorg101002wea736

Deeter MN Edwards DP Gille JC Emmons LK Francis G Ho S-PMao D Masters D Worden H Drummond JR and Novelli PC (2010)The MOPITT version 4 CO product algorithm enhancements validation andlong-term stability Journal of Geophysical Research 115 D07306 httpsdoiorg1010292009JD013005

Desroziers G Berre L Chapnik B and Poli P (2005) Diagnosis of observa-tion background and analysis error statistics in observation space QuarterlyJournal of the Royal Meteorological Society 131 3385ndash3396

Dudhia A (2016) The reference forward model (RFM) Journal of QuantitativeSpectroscopy and Radiative Transfer 186 243ndash253 httpsdoiorg101016jjqsrt201606018

20 SMITH ET AL

Eyre JR and Hilton FI (2013) Sensitivity of analysis error to themis-specification of background error covariance Quarterly Journal of theRoyal Meteorological Society 139 524ndash533 httpsdoiorg101002qj1979

Grant D Dudek R Buchanan M and Liu HC (2006) Room-temperature het-erodyne detection up to 110 GHz with a quantum-well infrared photodetectorIEEE Photonics Technology Letters 18(21) 2218ndash2220 httpsdoiorg101109LPT2006884267

Havemann S (2006) The development of a fast radiative transfer model based onan empirical orthogonal functions (EOF) technique SPIE Proceedings 64054050ndash4058 httpsdoiorg10111712693995

Havemann S (2015) Report on global comparisons of HT-FRTC with traditionalRTTOV calculations Met Office Internal Report

Havemann S Thelen J-C Taylor JP and Harlow RC (2016) TheHavemannndashTaylor fast radiative transfer code (HT-FRTC) a multipurposecode based on principal components Journal of Quantitative Spectroscopyand Radiative Transfer httpsdoi101016jqsrt201809008

Hilton FI Antonelli P Calbet X Hultberg T Lavanant L Liu XMasiello G Newman S Taylor J Serio C and Zhou D (2009a) Aninvestigation into the performance of retrievals of temperature and humidityfrom IASI Proc 2009 Eumetsat Meteorological Satellite Conference 21ndash25September 2009 Bath UK Available at httpwwweumetsatintwebsitewcmidcidcplgIdcService=GET_FILEampdDocName=PDF_CONF_P55_S7_37_HILTON_PampRevisionSelectionMethod=LatestReleasedampRendition=Web [Accessed 29 August 2018]

Hilton FI Atkinson N English S and Eyre JR (2009b) Assimilation of IASIat the Met Office and assessment of its impact through observing system exper-iments Quarterly Journal of the Royal Meteorological Society 135(639)495ndash505 httpsdoiorg101002qj379

Hilton FI Armante R August T Barnet C Bouchard A Camy-Peyret CCapelle V Clarisse L Clerbaux C Coheur P Collard A Crevoisier CDufour G Edwards D Faijan F Fourrieacute N Gambacorta A GoldbergM Guidard V Hurtmans D Illingworth S Jacquinet-Husson N Kerzen-macher T Klaes D Lavanant L Masiello G Matricardi M McNallyA Newman S Pavelin E Payan S Peacutequignot E Peyridieu S PhulpinT Remedios J Schluumlssel P Serio C Strow L Stubenrauch C TaylorJ Tobin D Wolf W and Zhou D (2012) Hyperspectral Earth observa-tion from IASI five years of accomplishments Bulletin of the AmericanMeteorological Society 93 347ndash370 httpsdoiorg101175BAMS-D-11-000271

Hoffmann A Macleod NA Huebner M and Weidmann D (2016) Thermalinfrared laser heterodyne spectroradiometry for solar occultation atmosphericCO2 measurements Atmospheric Measurement Techniques 9 5975ndash5996httpsdoiorg105194amt-9-5975-2016

Janjic T Bormann N Bocquet M Carton JA Cohn SE Dance SLLosa SN Nichols NK Potthast R Waller JA and Weston P (2017) Onthe representation error in data assimilation Quarterly Journal of the RoyalMeteorological Society httpsdoiorg101002qj3130

Lorenc AC and Marriott RT (2014) Forecast sensitivity to observations in theMet Office Global numerical weather prediction system Quarterly Journalof the Royal Meteorological Society 140 209ndash224 httpsdoiorg101002qj2122

Mumma MJ Kostiuk T Duhl D Chin G and Zipoy D (1982) Infrared het-erodyne spectroscopy Optical Engineering 21(2) 212ndash313 httpsdoiorg101117127972901

Myers TL Cannon BD Brauer CS Hansen SM and Crowther BG (2015)Proton and gamma irradiation of FabryndashPerot quantum cascade lasers for spacequalification Applied Optics 54 527ndash534

Rawlins F Ballard SP Bovis KJ Clayton AM Li D Inverarity GWLorenc AC and Payne TJ (2007) The Met Office global four-dimensionalvariational data assimilation scheme Quarterly Journal of the Royal Meteo-rological Society 133 347ndash362 httpsdoiorg101002qj32

Rodgers CD (2000) Inverse Methods for Atmospheric Sounding Theory andPractice Singapore World Scientific

Rothman LS Gordon IE Babikov Y Barbe A Benner DC Bernath PFBirk M Bizzocchi L Boudon V Brown LR and Campargue A (2013)The HITRAN2012 molecular spectroscopic database Journal of Quantita-tive Spectroscopy and Radiative Transfer 130 4ndash50 httpsdoiorg101016jjqsrt201307002

Schieder R Tolls V and Winnewisser G (1989) The Cologne acousto-opticalspectrometers Experimental Astronomy 1 101ndash121

Siegman AE (1966) The antenna properties of optical heterodyne receiversProceedings of the IEEE 54(10) 1350ndash1356 httpsdoiorg101109PROC19665122

Simeacuteoni D Singer C and Chalon G (1997) Infrared atmospheric soundinginterferometer Acta Astronautica 40 113ndash118

Smith FI (2015) Improving the information content of IASI assimilation fornumerical weather prediction PhD thesis Leicester UK University ofLeicester Available at httpslraleacukhandle238132040 [Accessed 28August 2018]

Tsai TR Rose RA Weidmann D and Wysocki G (2012) Atmospheric verti-cal profiles of O3 N2O CH4 CCl2F2 and H2O retrieved from external-cavityquantum-cascade laser heterodyne radiometer measurements Applied Optics51 8779ndash8792 httpsdoiorg101364AO51008779

Wang L Chen Y and Han Y (2016) Impacts of field of view configuration ofcrosstrack infrared sounder on clear sky observations Applied Optics 55(25)7113ndash7119

Weidmann D Reburn WJ and Smith KM (2007a) Ground-based prototypequantum cascade laser heterodyne radiometer for atmospheric studies Reviewof Scientific Instruments 78(7) 073107 httpsdoiorg10106312753141

Weidmann D Reburn WJ and Smith KM (2007b) Retrieval of atmosphericozone profiles from an infrared quantum cascade laser heterodyne radiometerresults and analysis Applied Optics 46 7162ndash7171 httpsdoiorg101364AO46007162

Weidmann D Tsai T Macleod NA and Wysocki G (2011a) Atmosphericobservations of multiple molecular species using ultra-high-resolution exter-nal cavity quantum cascade laser heterodyne radiometry Optics Letters 361951ndash1953 httpsdoiorg101364OL36001951

Weidmann D Perrett BJ Macleod NA and Jenkins RM (2011b)Hollow waveguide photomixing for quantum cascade laser heterodynespectro-radiometry Optics Express 19 9074ndash9085 httpsdoiorg101364OE19009074

Weidmann D Hoffmann A Macleod N Middleton K Kurtz J Barra-clough S and Griffin D(2017) (2017) The Methane Isotopologues by SolarOccultation (MISO) nanosatellite mission spectral channel optimization andearly performance analysis Remote Sensing 9 1073 httpsdoiorg103390rs9101073

Weston PP Bell W and Eyre JR (2014) Accounting for correlated error inthe assimilation of high resolution sounders Quarterly Journal of the RoyalMeteorological Society 140 2420ndash2429 httpsdoiorg101002qj2306

Wlasak MA (2013) VAR technical documentation paper 46_1 randomisationmethod for background covariance estimates Internal Met Office Documen-tation Paper VTDP 46_1

Wlasak MA and Cullen MJP (2014) Modelling static 3-D spatial backgrounderror covariances ndash the effect of vertical and horizontal transform orderAdvances in Science and Research 11 63ndash67 httpsdoiorg105194asr-11-63-2014

How to cite this article Smith F Havemann S Hoff-mann A Bell W Weidmann D Newman S Evalua-tion of laser heterodyne radiometry for numericalweather prediction applications Q J R Meteorol Soc20181ndash20 httpsdoiorg101002qj3365

2 SMITH ET AL

FIGURE 1 Schematic diagram of a laser heterodyne radiometer [Colour figure can be viewed at wileyonlinelibrarycom]

1595 cmminus1 for humidity sounding This raises the generalquestion as to whether more compact spectro-radiometerscould be developed covering only these key spectral regionsto provide equivalent or better performance for meteorolog-ical applications at lower cost

Infrared heterodyne spectro-radiometers (LHRs) based oncarbon dioxide lasers and tuneable lead-salt diode lasershave been used in atmospheric research for decades (Allarioet al 1983) However their features (size the requirementfor cryogenic operation and power requirements) precludethem for deployment on small satellites The development ofquantum cascade lasers (QCLs) during the 1990s heraldedthe advent of solid state compact robust and continuouslytuneable mid-IR laser sources well suited to providing ther-mal infrared local oscillators Since then the technology hasmatured considerably such that QCLs can be considered foroperational deployment in space (Myers et al 2015)

QCL-based LHR technology has advanced rapidly in thelast decade initially for trace-gas detection in Earth obser-vation and planetary applications (Weidmann et al 2007a)Atmospheric science applications have included ozone pro-filing (Weidmann et al 2007b) multi-constituent profiling(Weidmann et al 2011a Tsai et al 2012) and most recentlyatmospheric CO2 measurements (Hoffmann et al 2016)Developments are currently underway to miniaturize theLHRs using optical integration technologies (Weidmannet al 2011b) and make them suitable for small satelliteapplications (Weidmann et al 2017) As well as the compactsize QCL LHRs offer the combined advantages of ultra-highspectral resolution (sim0001 cmminus1) over narrow spectralmicrowindows (01ndash1 cmminus1) high horizontal resolution dueto the inherently narrow field-of-view (a few hundred metresor less from low Earth orbit) and ideally a radiometric sen-sitivity determined by the shot-noise induced by the randomarrival of photons onto the detectors

The next generation of European operational meteoro-logical satellites are due to launch in the next few yearsand will serve weather and climate applications until 2040There is therefore a window of opportunity to evaluate anddemonstrate new technologies in time to be considered ascomponents of future operational missions The purpose of

this preliminary study was to establish the potential for anadir-viewing LHR to meet future NWP requirements pri-marily by assessing the expected performance of an LHR inprofiling temperature from low Earth orbit (LEO) and geosta-tionary orbit (GEO) platforms using an information contentmethod IASI has been used as a benchmark so that the poten-tial of an LHR can be placed in the context of a well-knownhigh quality operational spectrometer

The principles of laser heterodyne radiometry are brieflyintroduced in section 2 Section 3 describes the main orbitconfigurations considered in this study and the attendantconstraints on integration and sampling times In section4 the framework for the assessment of the idealised LHRperformance is described including the Degrees of Freedomfor Signal (DFS) metric Section 5 details the inputs to theDFS calculations including background and instrument errormodels input profiles and the radiative transfer modellingdetails The main results of the study are given in sections6ndash8 Some future directions are outlined in section 9 andconclusions are drawn in section 10

2 A BRIEF INTRODUCTION TO LASERHETERODYNE RADIOMETRY

Laser heterodyne radiometers (LHRs) bear some similaritiesto radio receivers but transposed into the optical domainThey are passive sounders that use a laser source in this casea QCL as a local oscillator (LO) Figure 1 shows a simpli-fied schematic of an LHR illustrating its operating principlesThe thermal IR radiation to be analysed is collected by theprimary mirror (not shown) It is then superimposed withthe coherent optical field of the LO The requirement tomatch the wave-fronts of the two fields determines the max-imum tolerable angular misalignment of the LO and sourcebeams which in turn determines the field-of-view of theinstrument The two superimposed fields are imaged ontoa high-speed photodiode serving as a photomixer whichdown-converts the spectral information of the incoming radi-ation centred at the LO frequency and within the elec-trical bandwidth of the photomixer to the radio-frequency

SMITH ET AL 3










Mode




Numberofchannels

SSM 0001 01 - 100

SSM 0001 01 0002 50

SSM 0001 01 0004 25

SSM 0001 01 0006 17

SSM 0001 01 0008 13

SSM 0002 01 - 50

SSM 0002 01 0004 25

SSM 0002 01 0006 17

SSM 0002 01 0008 13

MM 0005 01 - 20

MM 001 01 - 10

AMM 0005 10 - 200

AMM 001 10 - 100

AMM 002 10 - 50







4 SMITH ET AL




31 LEO satellite







32 GEO satellite











SMITH ET AL 5
























6 SMITH ET AL














119873119864119875 = 120588ℎ119907

120578

radicB120591 (4)

SMITH ET AL 7




NESR = 119873119864119875

G sdot B(5)




dL120584T

119889119879= 2 sdot h2 sdot 1205844 sdot e

h120584119896119879


eh120584119896119879 minus 1

)2(6)








8 SMITH ET AL













607 334


1100 801


572 480


212 178




SMITH ET AL 9

(a) (b) (c) (d)












10 SMITH ET AL










SMITH ET AL 11














12 SMITH ET AL


(a) (b)






SMITH ET AL 13





Number ofchannels




SSM 696117 0002 0002 50 010 1641 043

SSM 706568 0002 0008 13 038 0875 061

SSM 720434 0002 0008 13 038 0927 085

MM 706570 0005 20 015 0886 07

MM 706570 0005 20 1 0343 23

MM 706570 0005 20 5 0153 44

MM 720500 0005 20 015 0939 08

MM 720500 0005 20 1 0364 23

MM 720500 0005 20 5 0163 37

AMM 696260 0002 500 015 1341 31

AMM 696260 0002 500 1 0519 66

AMM 696260 0002 500 5 0232 91

AMM 705760 0002 500 015 1396 26

AMM 705760 0002 500 1 0541 60

AMM 705760 0002 500 5 0242 89

AMM 720220 0002 500 015 1484 33

AMM 720220 0002 500 1 0575 65

AMM 720220 0002 500 5 0257 91

AMM 696260 002 50 015 0424 23

AMM 696260 002 50 1 0164 482

AMM 696260 002 50 5 0073 683

AMM 705760 002 50 015 0441 177

AMM 705760 002 50 1 0171 416

AMM 705760 002 50 5 0076 641

AMM 720220 002 50 015 0469 188

AMM 720220 002 50 1 0182 418

AMM 720220 002 50 5 0081 641







14 SMITH ET AL
















SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































SMITH ET AL 3










Mode




Numberofchannels

SSM 0001 01 - 100

SSM 0001 01 0002 50

SSM 0001 01 0004 25

SSM 0001 01 0006 17

SSM 0001 01 0008 13

SSM 0002 01 - 50

SSM 0002 01 0004 25

SSM 0002 01 0006 17

SSM 0002 01 0008 13

MM 0005 01 - 20

MM 001 01 - 10

AMM 0005 10 - 200

AMM 001 10 - 100

AMM 002 10 - 50







4 SMITH ET AL




31 LEO satellite







32 GEO satellite











SMITH ET AL 5
























6 SMITH ET AL














119873119864119875 = 120588ℎ119907

120578

radicB120591 (4)

SMITH ET AL 7




NESR = 119873119864119875

G sdot B(5)




dL120584T

119889119879= 2 sdot h2 sdot 1205844 sdot e

h120584119896119879


eh120584119896119879 minus 1

)2(6)








8 SMITH ET AL













607 334


1100 801


572 480


212 178




SMITH ET AL 9

(a) (b) (c) (d)












10 SMITH ET AL










SMITH ET AL 11














12 SMITH ET AL


(a) (b)






SMITH ET AL 13





Number ofchannels




SSM 696117 0002 0002 50 010 1641 043

SSM 706568 0002 0008 13 038 0875 061

SSM 720434 0002 0008 13 038 0927 085

MM 706570 0005 20 015 0886 07

MM 706570 0005 20 1 0343 23

MM 706570 0005 20 5 0153 44

MM 720500 0005 20 015 0939 08

MM 720500 0005 20 1 0364 23

MM 720500 0005 20 5 0163 37

AMM 696260 0002 500 015 1341 31

AMM 696260 0002 500 1 0519 66

AMM 696260 0002 500 5 0232 91

AMM 705760 0002 500 015 1396 26

AMM 705760 0002 500 1 0541 60

AMM 705760 0002 500 5 0242 89

AMM 720220 0002 500 015 1484 33

AMM 720220 0002 500 1 0575 65

AMM 720220 0002 500 5 0257 91

AMM 696260 002 50 015 0424 23

AMM 696260 002 50 1 0164 482

AMM 696260 002 50 5 0073 683

AMM 705760 002 50 015 0441 177

AMM 705760 002 50 1 0171 416

AMM 705760 002 50 5 0076 641

AMM 720220 002 50 015 0469 188

AMM 720220 002 50 1 0182 418

AMM 720220 002 50 5 0081 641







14 SMITH ET AL
















SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































4 SMITH ET AL




31 LEO satellite







32 GEO satellite











SMITH ET AL 5
























6 SMITH ET AL














119873119864119875 = 120588ℎ119907

120578

radicB120591 (4)

SMITH ET AL 7




NESR = 119873119864119875

G sdot B(5)




dL120584T

119889119879= 2 sdot h2 sdot 1205844 sdot e

h120584119896119879


eh120584119896119879 minus 1

)2(6)








8 SMITH ET AL













607 334


1100 801


572 480


212 178




SMITH ET AL 9

(a) (b) (c) (d)












10 SMITH ET AL










SMITH ET AL 11














12 SMITH ET AL


(a) (b)






SMITH ET AL 13





Number ofchannels




SSM 696117 0002 0002 50 010 1641 043

SSM 706568 0002 0008 13 038 0875 061

SSM 720434 0002 0008 13 038 0927 085

MM 706570 0005 20 015 0886 07

MM 706570 0005 20 1 0343 23

MM 706570 0005 20 5 0153 44

MM 720500 0005 20 015 0939 08

MM 720500 0005 20 1 0364 23

MM 720500 0005 20 5 0163 37

AMM 696260 0002 500 015 1341 31

AMM 696260 0002 500 1 0519 66

AMM 696260 0002 500 5 0232 91

AMM 705760 0002 500 015 1396 26

AMM 705760 0002 500 1 0541 60

AMM 705760 0002 500 5 0242 89

AMM 720220 0002 500 015 1484 33

AMM 720220 0002 500 1 0575 65

AMM 720220 0002 500 5 0257 91

AMM 696260 002 50 015 0424 23

AMM 696260 002 50 1 0164 482

AMM 696260 002 50 5 0073 683

AMM 705760 002 50 015 0441 177

AMM 705760 002 50 1 0171 416

AMM 705760 002 50 5 0076 641

AMM 720220 002 50 015 0469 188

AMM 720220 002 50 1 0182 418

AMM 720220 002 50 5 0081 641







14 SMITH ET AL
















SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































SMITH ET AL 5
























6 SMITH ET AL














119873119864119875 = 120588ℎ119907

120578

radicB120591 (4)

SMITH ET AL 7




NESR = 119873119864119875

G sdot B(5)




dL120584T

119889119879= 2 sdot h2 sdot 1205844 sdot e

h120584119896119879


eh120584119896119879 minus 1

)2(6)








8 SMITH ET AL













607 334


1100 801


572 480


212 178




SMITH ET AL 9

(a) (b) (c) (d)












10 SMITH ET AL










SMITH ET AL 11














12 SMITH ET AL


(a) (b)






SMITH ET AL 13





Number ofchannels




SSM 696117 0002 0002 50 010 1641 043

SSM 706568 0002 0008 13 038 0875 061

SSM 720434 0002 0008 13 038 0927 085

MM 706570 0005 20 015 0886 07

MM 706570 0005 20 1 0343 23

MM 706570 0005 20 5 0153 44

MM 720500 0005 20 015 0939 08

MM 720500 0005 20 1 0364 23

MM 720500 0005 20 5 0163 37

AMM 696260 0002 500 015 1341 31

AMM 696260 0002 500 1 0519 66

AMM 696260 0002 500 5 0232 91

AMM 705760 0002 500 015 1396 26

AMM 705760 0002 500 1 0541 60

AMM 705760 0002 500 5 0242 89

AMM 720220 0002 500 015 1484 33

AMM 720220 0002 500 1 0575 65

AMM 720220 0002 500 5 0257 91

AMM 696260 002 50 015 0424 23

AMM 696260 002 50 1 0164 482

AMM 696260 002 50 5 0073 683

AMM 705760 002 50 015 0441 177

AMM 705760 002 50 1 0171 416

AMM 705760 002 50 5 0076 641

AMM 720220 002 50 015 0469 188

AMM 720220 002 50 1 0182 418

AMM 720220 002 50 5 0081 641







14 SMITH ET AL
















SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































6 SMITH ET AL














119873119864119875 = 120588ℎ119907

120578

radicB120591 (4)

SMITH ET AL 7




NESR = 119873119864119875

G sdot B(5)




dL120584T

119889119879= 2 sdot h2 sdot 1205844 sdot e

h120584119896119879


eh120584119896119879 minus 1

)2(6)








8 SMITH ET AL













607 334


1100 801


572 480


212 178




SMITH ET AL 9

(a) (b) (c) (d)












10 SMITH ET AL










SMITH ET AL 11














12 SMITH ET AL


(a) (b)






SMITH ET AL 13





Number ofchannels




SSM 696117 0002 0002 50 010 1641 043

SSM 706568 0002 0008 13 038 0875 061

SSM 720434 0002 0008 13 038 0927 085

MM 706570 0005 20 015 0886 07

MM 706570 0005 20 1 0343 23

MM 706570 0005 20 5 0153 44

MM 720500 0005 20 015 0939 08

MM 720500 0005 20 1 0364 23

MM 720500 0005 20 5 0163 37

AMM 696260 0002 500 015 1341 31

AMM 696260 0002 500 1 0519 66

AMM 696260 0002 500 5 0232 91

AMM 705760 0002 500 015 1396 26

AMM 705760 0002 500 1 0541 60

AMM 705760 0002 500 5 0242 89

AMM 720220 0002 500 015 1484 33

AMM 720220 0002 500 1 0575 65

AMM 720220 0002 500 5 0257 91

AMM 696260 002 50 015 0424 23

AMM 696260 002 50 1 0164 482

AMM 696260 002 50 5 0073 683

AMM 705760 002 50 015 0441 177

AMM 705760 002 50 1 0171 416

AMM 705760 002 50 5 0076 641

AMM 720220 002 50 015 0469 188

AMM 720220 002 50 1 0182 418

AMM 720220 002 50 5 0081 641







14 SMITH ET AL
















SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































SMITH ET AL 7




NESR = 119873119864119875

G sdot B(5)




dL120584T

119889119879= 2 sdot h2 sdot 1205844 sdot e

h120584119896119879


eh120584119896119879 minus 1

)2(6)








8 SMITH ET AL













607 334


1100 801


572 480


212 178




SMITH ET AL 9

(a) (b) (c) (d)












10 SMITH ET AL










SMITH ET AL 11














12 SMITH ET AL


(a) (b)






SMITH ET AL 13





Number ofchannels




SSM 696117 0002 0002 50 010 1641 043

SSM 706568 0002 0008 13 038 0875 061

SSM 720434 0002 0008 13 038 0927 085

MM 706570 0005 20 015 0886 07

MM 706570 0005 20 1 0343 23

MM 706570 0005 20 5 0153 44

MM 720500 0005 20 015 0939 08

MM 720500 0005 20 1 0364 23

MM 720500 0005 20 5 0163 37

AMM 696260 0002 500 015 1341 31

AMM 696260 0002 500 1 0519 66

AMM 696260 0002 500 5 0232 91

AMM 705760 0002 500 015 1396 26

AMM 705760 0002 500 1 0541 60

AMM 705760 0002 500 5 0242 89

AMM 720220 0002 500 015 1484 33

AMM 720220 0002 500 1 0575 65

AMM 720220 0002 500 5 0257 91

AMM 696260 002 50 015 0424 23

AMM 696260 002 50 1 0164 482

AMM 696260 002 50 5 0073 683

AMM 705760 002 50 015 0441 177

AMM 705760 002 50 1 0171 416

AMM 705760 002 50 5 0076 641

AMM 720220 002 50 015 0469 188

AMM 720220 002 50 1 0182 418

AMM 720220 002 50 5 0081 641







14 SMITH ET AL
















SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































8 SMITH ET AL













607 334


1100 801


572 480


212 178




SMITH ET AL 9

(a) (b) (c) (d)












10 SMITH ET AL










SMITH ET AL 11














12 SMITH ET AL


(a) (b)






SMITH ET AL 13





Number ofchannels




SSM 696117 0002 0002 50 010 1641 043

SSM 706568 0002 0008 13 038 0875 061

SSM 720434 0002 0008 13 038 0927 085

MM 706570 0005 20 015 0886 07

MM 706570 0005 20 1 0343 23

MM 706570 0005 20 5 0153 44

MM 720500 0005 20 015 0939 08

MM 720500 0005 20 1 0364 23

MM 720500 0005 20 5 0163 37

AMM 696260 0002 500 015 1341 31

AMM 696260 0002 500 1 0519 66

AMM 696260 0002 500 5 0232 91

AMM 705760 0002 500 015 1396 26

AMM 705760 0002 500 1 0541 60

AMM 705760 0002 500 5 0242 89

AMM 720220 0002 500 015 1484 33

AMM 720220 0002 500 1 0575 65

AMM 720220 0002 500 5 0257 91

AMM 696260 002 50 015 0424 23

AMM 696260 002 50 1 0164 482

AMM 696260 002 50 5 0073 683

AMM 705760 002 50 015 0441 177

AMM 705760 002 50 1 0171 416

AMM 705760 002 50 5 0076 641

AMM 720220 002 50 015 0469 188

AMM 720220 002 50 1 0182 418

AMM 720220 002 50 5 0081 641







14 SMITH ET AL
















SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































SMITH ET AL 9

(a) (b) (c) (d)












10 SMITH ET AL










SMITH ET AL 11














12 SMITH ET AL


(a) (b)






SMITH ET AL 13





Number ofchannels




SSM 696117 0002 0002 50 010 1641 043

SSM 706568 0002 0008 13 038 0875 061

SSM 720434 0002 0008 13 038 0927 085

MM 706570 0005 20 015 0886 07

MM 706570 0005 20 1 0343 23

MM 706570 0005 20 5 0153 44

MM 720500 0005 20 015 0939 08

MM 720500 0005 20 1 0364 23

MM 720500 0005 20 5 0163 37

AMM 696260 0002 500 015 1341 31

AMM 696260 0002 500 1 0519 66

AMM 696260 0002 500 5 0232 91

AMM 705760 0002 500 015 1396 26

AMM 705760 0002 500 1 0541 60

AMM 705760 0002 500 5 0242 89

AMM 720220 0002 500 015 1484 33

AMM 720220 0002 500 1 0575 65

AMM 720220 0002 500 5 0257 91

AMM 696260 002 50 015 0424 23

AMM 696260 002 50 1 0164 482

AMM 696260 002 50 5 0073 683

AMM 705760 002 50 015 0441 177

AMM 705760 002 50 1 0171 416

AMM 705760 002 50 5 0076 641

AMM 720220 002 50 015 0469 188

AMM 720220 002 50 1 0182 418

AMM 720220 002 50 5 0081 641







14 SMITH ET AL
















SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































10 SMITH ET AL










SMITH ET AL 11














12 SMITH ET AL


(a) (b)






SMITH ET AL 13





Number ofchannels




SSM 696117 0002 0002 50 010 1641 043

SSM 706568 0002 0008 13 038 0875 061

SSM 720434 0002 0008 13 038 0927 085

MM 706570 0005 20 015 0886 07

MM 706570 0005 20 1 0343 23

MM 706570 0005 20 5 0153 44

MM 720500 0005 20 015 0939 08

MM 720500 0005 20 1 0364 23

MM 720500 0005 20 5 0163 37

AMM 696260 0002 500 015 1341 31

AMM 696260 0002 500 1 0519 66

AMM 696260 0002 500 5 0232 91

AMM 705760 0002 500 015 1396 26

AMM 705760 0002 500 1 0541 60

AMM 705760 0002 500 5 0242 89

AMM 720220 0002 500 015 1484 33

AMM 720220 0002 500 1 0575 65

AMM 720220 0002 500 5 0257 91

AMM 696260 002 50 015 0424 23

AMM 696260 002 50 1 0164 482

AMM 696260 002 50 5 0073 683

AMM 705760 002 50 015 0441 177

AMM 705760 002 50 1 0171 416

AMM 705760 002 50 5 0076 641

AMM 720220 002 50 015 0469 188

AMM 720220 002 50 1 0182 418

AMM 720220 002 50 5 0081 641







14 SMITH ET AL
















SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































SMITH ET AL 11














12 SMITH ET AL


(a) (b)






SMITH ET AL 13





Number ofchannels




SSM 696117 0002 0002 50 010 1641 043

SSM 706568 0002 0008 13 038 0875 061

SSM 720434 0002 0008 13 038 0927 085

MM 706570 0005 20 015 0886 07

MM 706570 0005 20 1 0343 23

MM 706570 0005 20 5 0153 44

MM 720500 0005 20 015 0939 08

MM 720500 0005 20 1 0364 23

MM 720500 0005 20 5 0163 37

AMM 696260 0002 500 015 1341 31

AMM 696260 0002 500 1 0519 66

AMM 696260 0002 500 5 0232 91

AMM 705760 0002 500 015 1396 26

AMM 705760 0002 500 1 0541 60

AMM 705760 0002 500 5 0242 89

AMM 720220 0002 500 015 1484 33

AMM 720220 0002 500 1 0575 65

AMM 720220 0002 500 5 0257 91

AMM 696260 002 50 015 0424 23

AMM 696260 002 50 1 0164 482

AMM 696260 002 50 5 0073 683

AMM 705760 002 50 015 0441 177

AMM 705760 002 50 1 0171 416

AMM 705760 002 50 5 0076 641

AMM 720220 002 50 015 0469 188

AMM 720220 002 50 1 0182 418

AMM 720220 002 50 5 0081 641







14 SMITH ET AL
















SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































12 SMITH ET AL


(a) (b)






SMITH ET AL 13





Number ofchannels




SSM 696117 0002 0002 50 010 1641 043

SSM 706568 0002 0008 13 038 0875 061

SSM 720434 0002 0008 13 038 0927 085

MM 706570 0005 20 015 0886 07

MM 706570 0005 20 1 0343 23

MM 706570 0005 20 5 0153 44

MM 720500 0005 20 015 0939 08

MM 720500 0005 20 1 0364 23

MM 720500 0005 20 5 0163 37

AMM 696260 0002 500 015 1341 31

AMM 696260 0002 500 1 0519 66

AMM 696260 0002 500 5 0232 91

AMM 705760 0002 500 015 1396 26

AMM 705760 0002 500 1 0541 60

AMM 705760 0002 500 5 0242 89

AMM 720220 0002 500 015 1484 33

AMM 720220 0002 500 1 0575 65

AMM 720220 0002 500 5 0257 91

AMM 696260 002 50 015 0424 23

AMM 696260 002 50 1 0164 482

AMM 696260 002 50 5 0073 683

AMM 705760 002 50 015 0441 177

AMM 705760 002 50 1 0171 416

AMM 705760 002 50 5 0076 641

AMM 720220 002 50 015 0469 188

AMM 720220 002 50 1 0182 418

AMM 720220 002 50 5 0081 641







14 SMITH ET AL
















SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































SMITH ET AL 13





Number ofchannels




SSM 696117 0002 0002 50 010 1641 043

SSM 706568 0002 0008 13 038 0875 061

SSM 720434 0002 0008 13 038 0927 085

MM 706570 0005 20 015 0886 07

MM 706570 0005 20 1 0343 23

MM 706570 0005 20 5 0153 44

MM 720500 0005 20 015 0939 08

MM 720500 0005 20 1 0364 23

MM 720500 0005 20 5 0163 37

AMM 696260 0002 500 015 1341 31

AMM 696260 0002 500 1 0519 66

AMM 696260 0002 500 5 0232 91

AMM 705760 0002 500 015 1396 26

AMM 705760 0002 500 1 0541 60

AMM 705760 0002 500 5 0242 89

AMM 720220 0002 500 015 1484 33

AMM 720220 0002 500 1 0575 65

AMM 720220 0002 500 5 0257 91

AMM 696260 002 50 015 0424 23

AMM 696260 002 50 1 0164 482

AMM 696260 002 50 5 0073 683

AMM 705760 002 50 015 0441 177

AMM 705760 002 50 1 0171 416

AMM 705760 002 50 5 0076 641

AMM 720220 002 50 015 0469 188

AMM 720220 002 50 1 0182 418

AMM 720220 002 50 5 0081 641







14 SMITH ET AL
















SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































14 SMITH ET AL
















SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































SMITH ET AL 15

(a) (b)





Number ofchannels



AverageDFS


693580 0005 20 1 0325 35

691890 001 10 5 0102 45

691890 001 10 1 0288 31


692825 0005 200 5 0145 89

692830 001 100 5 0102 80

692840 002 50 5 0072 73













16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































16 SMITH ET AL





83 Integration time










SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































SMITH ET AL 17

(a) (b) (c) (d)


(a) (b) (c) (d)


9 FUTURE DIRECTIONS







18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































18 SMITH ET AL

(a) (b) (c)











SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































SMITH ET AL 19













ACKNOWLEDGEMENTS


ORCID











20 SMITH ET AL
































20 SMITH ET AL
































evaluation of laser heterodyne radiometry for numerical...

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