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Keywords:

  • atmospheric remote sensing;
  • climate change monitoring;
  • greenhouse gases;
  • infrared-laser occultation;
  • microwave occultation;
  • thermodynamics and wind

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Method
  5. 3. Feasibility and Performance
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[1] Accurate, long-term, consistent data are fundamental to climate science and satellite observations are the key to obtain such data globally in the Earth's atmosphere. Current methods are unable to jointly and consistently observe essential climate variables including thermodynamic ones (temperature, pressure, humidity), wind, and greenhouse gases. Here we introduce a method that profiles these variables over the upper troposphere and lower stratosphere and beyond as consistent benchmark dataset (e.g., monthly-mean temperature accurate to 0.1 K, wind to 0.5 m s−1, carbon dioxide concentration to within 1 ppm). It combines microwave and infrared-laser occultation between satellites in low Earth orbit for thermodynamic state, greenhouse gas and line-of-sight wind profiling. With adequate scaling it can also be applied beyond Earth's atmosphere such as in planetary atmospheres. The method may become an authoritative reference standard for global monitoring of greenhouse gases and climate change in Earth's free atmosphere over the 21st century.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Method
  5. 3. Feasibility and Performance
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[2] Expanding the observational foundation for climate change studies by accurate, long-term, consistent benchmark data [Goody et al., 1998; Leroy et al., 2006] is a fundamental need of climate science [Intergovernmental Panel on Climate Change (IPCC), 2007; World Meteorological Organization (WMO), 2004] and Earth observation from space is the key means to obtain such data globally [WMO, 2006; Committee on Earth Observation Satellites (CEOS), 2006]. Current methods of satellite remote sensing of Earth's free atmosphere (from ∼2 km height upwards) collectively enable the global observation of essential climate variables [WMO, 2004, 2006], including on the thermodynamic state (temperature, pressure, humidity), dynamical state (wind), and composition (ozone, carbon dioxide, methane, other greenhouse gases), but are unable to provide them as a consistent climate benchmark dataset [Leroy et al., 2006]. The latter requires joint sensitivity to all essential variables, measurement stability over decades and longer, high accuracy traceable to international metrological standards and un-biased spatiotemporal sampling. Despite the need [IPCC, 2007; WMO, 2004; Goody et al., 2002; Trenberth et al., 2006], and a valuable starting point using refractivity from radio occultation [Kursinski et al., 1997; Leroy et al., 2006; Ho et al., 2009], such a method did not exist so far.

[3] Aiming to fulfill this need we started with the “grand question”: Is it possible to simultaneously observe, with global coverage, high accuracy, long-term stability, and negligible sensitivity to a priori information, a complete and consistent set of atmospheric variables that covers thermodynamics (temperature, pressure, humidity), dynamics (wind), and climate/chemistry (greenhouse gases and isotopes), perhaps complemented with simultaneously measured aerosol, cloud, and turbulence information? With the new atmospheric sounding method between Low Earth Orbit (LEO) satellites we introduce here, termed LMIO hereafter (LEO-LEO microwave and infrared-laser occultation), we affirmatively answer this question with focus on the upper troposphere and lower stratosphere, a domain sensitively tracing natural and anthropogenic climate and composition changes [IPCC, 2007; Li et al., 2008; Steiner et al., 2009].

[4] LMIO is founded on the occultation principle [Phinney and Anderson, 1968; Kirchengast, 2004] that enables the profiling of all variables noted above over the upper troposphere and lower stratosphere (∼5 to 35 km) and beyond with ∼1 km height resolution as a consistent benchmark dataset. It combines microwave occultation signals for thermodynamic state profiling [Kursinski et al., 2002, 2009; Herman et al., 2004; Kirchengast and Hoeg, 2004; Schweitzer et al., 2011a] with infrared-laser occultation signals within 2 to 2.5 μm for greenhouse gas and line-of-sight wind profiling. Such occultation measurements that exploit the refraction and absorption of coherent signals along inter-satellite links can provide self-calibrated Doppler shift and transmission data which are traceable to international time and frequency standards (fundamentally the SI second) [Kirchengast, 2004; Leroy et al., 2006]. This leads to a unique combination of high accuracy and long-term stability that enables the method to rigorously monitor how greenhouse gas and climatic changes evolve over monthly to decadal scales and longer. We introduce the method in Section 2, discuss its feasibility and performance in Section 3, and provide conclusions in Section 4; auxiliary material contains complementary information (including Figures S1–S9 and Tables S1–S3).

2. The Method

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Method
  5. 3. Feasibility and Performance
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[5] The LMIO method (Figure 1), where we employ LEO-LEO infrared-laser occultation (LIO) in synergy with LEO-LEO microwave occultation (LMO), can be considered a next generation of the successful GPS-LEO radio occultation (GRO) method [Kursinski et al., 1997; Steiner et al., 2009; Ho et al., 2009]. GRO exploits decimeter-wave signals at two frequencies of the Global Positioning System GPS, and of other navigation satellites in future, for benchmark-quality profiling of refractivity [Ho et al., 2009] and derived parameters, like temperature above ∼8 km height [Steiner et al., 2009].

image

Figure 1. LMIO observation concept. Carefully chosen (Table 1 and Figure 2) and simultaneously transmitted microwave signals (orange) and infrared-laser signals (red) used in limb sounding geometry between LEO transmitter (Tx) and receiver (Rx) satellites join in the LMIO method to rigorously collect fundamental atmospheric state information from refraction and absorption along closely aligned signal propagation paths. During each near-vertical scan through the atmosphere from the motion of the counter-rotating Tx and Rx satellites (black LEO velocity vectors), called an occultation event taking ∼32 to 40 s within 3 to 80 km height, this yields consistent and accurate profiles of greenhouse gases (symbolized by the green profile), temperature (red profile) and pressure, humidity (blue profile), and line-of-sight wind (light-blue-vectors profile) in the upper troposphere/lower stratosphere and beyond (for a full list of variables and height ranges see Table S1). The profiles are attributed to the (mean) tangent point location, the geographic location where the points of closest approach of the signal ray paths to the Earth's surface, termed tangent points, occur (black vertical axis). The observation information is effectively collected within ∼300 km (±150 km) about tangent points, i.e., this is the horizontal resolution of the data [Kursinski et al., 1997].

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[6] For LMIO we use a set of purpose-made centimeter- and millimeter-wave signals for LMO and micrometer-wave signals for LIO (Table 1). We chose the frequency channels for the signals to match desired absorption lines of trace species of interest and to include suitable reference channels, enabling effective use of differential transmission between channels (Table 1 and Figure 2). For the LMO part, developed to good maturity previously [Kursinski et al., 2002, 2009; Herman et al., 2004; Kirchengast and Hoeg, 2004; Schweitzer et al., 2011a], we focus on channels at the wings of the 22 and 183 GHz water vapor absorption lines (Figures 2a and 2b). These enable accurate thermodynamic state retrieval by exploiting refraction plus differential transmission data [Kursinski et al., 2002; Schweitzer et al., 2011a]. The LIO channel choices, introduced in this study, are discussed separately below.

image

Figure 2. Spectral bands and distribution of the LMIO channels. LMIO frequency channels of Table 1 (vertical lines) marked on LEO-LEO transmission spectra (from absorption loss), which were computed at representative tangent point heights (“HeightTP”) by EGOPS modeling (LMO) and RFM/HITRAN modeling (LIO) using a FASCODE/U.S. standard atmosphere (see auxiliary material). LMO channels including (a) centimeter-wave signals in X/K band (core channels K1–K3), exploiting the 22 GHz water vapor absorption line, and (b) millimeter-wave signals in M band (primary channels M1–M2), exploiting the 183 GHz water vapor line and the 195 GHz ozone line. All LMO channels are compliant with international frequency regulations (which, in particular, reserve the 182–185 GHz sub-band exclusively for passive remote sensing). LIO channels including shortwave-infrared (SWIR) laser signals (c) in the 2.3 to 2.5 μm SWIR-B band, exploiting absorption lines of stratospheric ozone and water vapor, water isotopes, carbon monoxide and methane, and (d) in the ∼2.1 μm SWIR-A band, exploiting lines of nitrous oxide, carbon dioxide and isotopes, and water vapor. (e) Zoom into a narrow sub-range of the SWIR-A band, highlighting a special “demonstration” band of only ∼4 nm (10 cm−1) width, suitable to probe the key variables CO2 and isotopes, H2O, and l.o.s. wind within the mode-hop free tuning range of single SWIR diode lasers. (f and g) Further refined zoom in SWIR-A, highlighting the “wind line” band of only ∼40 pm (0.1 cm−1) width. The selected two wind measurement channels sit at the inflection points of the highly symmetric and stable C18OO line (Figure 2f) and the spectral derivative of the transmission (Figure 2g) confirms that the wind channels sit at maximum gradient providing highest sensitivity to wind-induced Doppler shift of the line.

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Table 1. LMIO Frequency Channels and Characteristicsa
Ch.IDFrequency (GHz)Wavelength (cm)Channel Utility LMO X/K band 8–30 GHzΔλar/λr (%)
  • a

    Channel ID (“Ch.ID”) uniquely identifies the selected channels (used in Figure 2). Channel Utility indicates the target variables (p…pressure, T…temperature, usual chemical symbols for the trace gases, l.o.s. wind…line-of-sight wind) to which the channels are sensitive, for the strongly varying H2O also height ranges of main sensitivity, and the function as absorption (Abs) or reference (Ref) channel or both (in the latter case noting primary/secondary function, e.g., Abs/Ref). LMO channels comprise those found most suitable in previous studies, where Ch.ID in parentheses denotes optional channels while K1–K3 are indispensable core and M1–M2 primary complement [Schweitzer et al., 2011a]. LIO absorption channels nominally sit within <3 × 10−8 relative frequency error at absorption line centers; the frequencies listed are of sufficient accuracy to identify the single lines in IR spectral databases. Δλar/λr is the wavelength separation of any absorption channel from its reference.

(X1)9.703.0906p, T, Ref[H2O] ∼2–7 km(Ref)
(X2)13.502.2207p, T, Abs/Ref[H2O] ∼2–7 km−28.15
K117.251.7379p, T, Ref/Abs[H2O] ∼5–12 km(Ref)
K220.201.4841p, T, Abs/Ref[H2O] ∼5–12 km−14.60
K322.601.3265Abs/Ref[H2O] ∼5–12 km−10.62
Ch.IDFrequency (GHz)Wavelength (mm)Channel Utility LMO M band 175–200 GHzΔλar/λr (%)
M1179.001.6748Ref/Abs[H2O] ∼10–18 km(Ref)
M2181.951.6477Abs[H2O] ∼10–18 km−1.618
(M3)191.851.5626Ref[O3](Ref)
(M4)195.351.5346Abs[O3]−1.792
Ch.IDWavenumber (cm−1)Wavelength (μm)Channel Utility LIO SWIR-B band 2.3–2.5 μmΔλar/λr (%)
I014029.1102.481938Abs[O3]+0.2006
I024037.212.47696Ref[O3]Ref1
I034090.8722.444467Abs[H218O]+0.1876
I044098.562.43988Ref[H218O]Ref2
I054204.8402.378212Abs[H2O-1] ∼13–48 km+0.5259
I064227.072.36571Ref[H2O, HDO, CO]Ref3
I074237.0162.360151Abs[HDO]−0.2353
I084248.3182.353873Abs[CO]−0.5027
I094322.932.31325Ref[CH4]Ref4
I104344.1642.301939Abs[CH4]−0.4912
Ch.IDWavenumber (cm−1)Wavelength (μm)Channel Utility LIO SWIR-A band ∼2.1 μmΔλar/λr (%)
I114710.3412.122989Abs[N2O]+0.4373
I124723.4152.117112Abs[13CO2]+0.1610
I134731.032.11371Ref[N2O, 13CO2, H2O]Ref5
I144733.0452.112805Abs[H2O-4] ∼4–8 km−0.0426
I154747.0552.106569Abs[H2O-3] ∼5–10 km−0.3387
I164767.0372.097739Abs[C18OO-w1], l.o.s. wind+0.0653
I174767.0412.097737Abs[C18OO]+0.0652
I184767.0452.097735Abs[C18OO-w2], l.o.s. wind+0.0651
I194770.152.09637Ref[12CO2, C18OO, H2O, wind]Ref6
I204771.6212.095724Abs[12CO2]−0.0308
I214775.8032.093889Abs[H2O-2] ∼8–25 km−0.1185

[7] LMIO needs quasi-monochromatic (coherent) signals with 1) highly stable frequencies tied to frequency and time standards (oscillators/lasers linked to atomic transition lines used as frequency reference and to GPS reference time), 2) highly stable amplitude/intensity over an occultation event (variations <0.1% r.m.s.), and 3) adequate power to supply high signal-to-noise ratio at the receiver (>500 at a 50 Hz sampling rate). For LMO, signals derived from ultra-stable oscillators, similar to the ones of GRO but with superior amplitude stability, fulfill this need as shown previously [Kirchengast and Hoeg, 2004; European Space Agency (ESA), 2004]. For LIO, signals derived from Distributed Feedback laser diodes [Kraft et al., 2005], the optical analogues of voltage-controlled oscillators at microwave frequencies, fulfill the need; these diodes are used broadly in telecommunications [Kraft et al., 2005] but also in trace species measurements by laser techniques like cavity ring-down spectroscopy [Crosson, 2008].

[8] Regarding the orbital constellation we use purpose-designed satellite orbits (500 km to 600 km altitude, near-polar inclination) for optimized global coverage and local time coverage within every season or at fixed local time (Figure S1). About 240 / 960 occultation events per day (7200 / 28800 per month) occur for 2 / 4 transmitter and receiver satellites. This provides reliable large-scale monitoring at <1800 km / 900 km horizontal resolution on a monthly basis, consistent with scientific needs for global benchmark data (Table S2).

[9] Utilizing the channels of Table 1 we vastly expand with LMIO the “refractivity bound” profiling capacity of GRO to a “full atmospheric state” profiling capacity. This comprises the greenhouse gases H2O (plus HDO, H218O below ∼12 km), CO2 (plus 13CO2, C18OO), CH4, N2O, O3, CO, and the line-of-sight wind speed from LIO, and pressure, temperature and humidity from LMO. Profiles of cloud layering, aerosol extinction, and turbulence strength are obtained as a complement (Table S1). We exploit the geodetic leveling capability of LMO, based on precise satellite orbits and atmospheric excess phase data as for GRO [ESA, 2004], and on the link of LIO to LMO signal paths addressed below, to obtain the LMIO profiles with accurate altitude knowledge (all levels known to <10 to 20 m uncertainty [Schweitzer et al., 2011a; Kursinski et al., 1997]). Likewise, tangent point locations are accurately known horizontally (<1 km uncertainty). This accurate geolocation intrinsic to LMIO is the geometric key to its benchmarking capability.

[10] We selected the LIO channels within 2 to 2.5 μm because we realized, and quantitatively confirmed point by point with focus on 5 to 35 km height, that infrared-laser signals in this range provide a unique opportunity to enhance LMO to LMIO by building on the following fundamental characteristics:

[11] 1. The infrared refractivity [Boensch and Potulski, 1998] within 2 to 2.5 μm is nearly non-dispersive and nearly identical to the microwave refractivity [Thayer, 1974] (<0.1% difference), implying closely similar propagation paths of LIO and LMO signals. This holds except for the term due to orientation polarization of H2O in microwave refractivity [Thayer, 1974], relevant in moist air below about 8 to 12 km height [Kursinski et al., 1997]. The latter difference can be accurately accounted for by employing LMO-derived altitude and thermodynamic profiles to construct infrared refractivity, refraction angles, and related LIO altitude levels.

[12] 2. Within 2 to 2.5 μm there is a “hole” between the shortwave-solar and longwave-terrestrial Planck spectra [Liou, 2002], implying that the solar radiation scattered into the receiver telescope is minimal to negligible (comparable to or below receiver noise level; Table S3) and that the received atmospheric thermal radiation is negligible. This ensures high signal-to-noise ratio of LIO measurements also in bright daylight and provides independence from atmospheric emission characteristics.

[13] 3. Within 2 to 2.5 μm there exist spectral (vibration-rotation) absorption lines [Liou, 2002] (Figures S3 and 2c2e) for profiling all targeted greenhouse gases (H2O, CO2, CH4, N2O, O3, CO) plus isotopes (13CO2, C18OO, HDO, H218O), since the sensitivity of LEO-LEO limb sounding is two orders of magnitude higher than of nadir sounding. Furthermore, highly symmetric and stable lines exist, such as of C18OO, enabling reliable self-calibrated profiling of line-of-sight wind speed by dual laser signals (Figures 2f and 2g).

[14] 4. The spectral characteristics within 2 to 2.5 μm are suitable to allow pairs of absorption (λa) and reference (λr) channels for differential transmission profiles to feature at the same time high transmission contrast, for accurate species absorption measurements, and closely-spaced wavelength ratios ∣λaλr∣/λr within ∼0.5% (Table 1, rightmost column), effectively suppressing scintillations and all background effects (Figures S4, S5, and S7).

[15] 5. Infrared-laser signals are point sources, leading within 2 to 2.5 μm in LEO-LEO sounding to a Fresnel-zone diameter [Kursinski et al., 1997] of ∼3 m only and thus to very high native vertical resolution. This robustly enables profiling at targeted 1 to 2 km vertical resolution (Table S2) and also enables partial penetration of intermittent (cirrus) cloudiness (infrared signals directly interfered by a cloud are generally blocked). Furthermore, the signals allow single-pulse signal-to-noise ratios of >500 with pulse powers of max. 1 W (Table S3). Such high ratios are far out of range of natural point sources like stars [Kyrölä et al., 2004] and, on the other hand, spaceborne laser sounders using backscatter need about two orders of magnitude more pulse power [Wulfmeyer et al., 2005].

[16] 6. Within 2 to 2.5 μm highly stable diode lasers (Distributed Feedback lasers, see above) and highly sensitive infrared detectors (e.g., Extended InGaAs) are available, which fulfill technical LIO system needs (see auxiliary material).

[17] Utilizing these characteristics we chose the LIO channels (Table 1 and Figures 2c2g) by a sophisticated search process applying a range of sensible criteria (see auxiliary material). Any different or additional channels are, in principle, also possible and compatible with the LMIO method, including on different species and going beyond 2 to 2.5 μm. We found the selected ones listed in Table 1 best suited to the benchmark aims focused on here.

3. Feasibility and Performance

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Method
  5. 3. Feasibility and Performance
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[18] Having the LMIO foundation prepared in this way, we assessed, partly with scientific peer and industry support, details of scientific and technical feasibility and relevant processes and effects (see auxiliary material). With LMO established previously already as discussed above, this focused on LIO and included studies of atmospheric influences (aerosols, clouds, wind, turbulence, background losses), signal sequences design (such as received pulse signals paired with background signals for rigorous quality control of every single sample), and overall system design; detailed results will be published elsewhere (e.g., Schweitzer et al. [2011b] discuss atmospheric influences, including cloud limitations, and related design choices). The work established the feasibility of LIO as part of LMIO and confirmed that a signal-to-noise ratio of >500 at 50 Hz sampling rate is achievable. We can use this as a key system specification for estimating the performance of LMIO profiling.

[19] The performance estimation was carried out using retrieval error propagation analyses (Figure S6) and end-to-end simulations (Figure S8). The results are shown in Figure 3 (verification results for LIO from quasi-realistic modeling in Figure S9). They provide evidence that the greenhouse gas profiles from LIO can generally be retrieved within 5 to 35 km height with <1 to 4% r.m.s. error (outside clouds), l.o.s. wind with <2 m s−1 r.m.s. error (outside clouds), and temperature/ pressure/ humidity from LMO [Schweitzer et al., 2011a] with <0.5 K/ 0.2%/ 10% r.m.s. error (including in clouds), all at ∼1 km vertical resolution. Monthly-mean climatological profiles, assuming 30 to 40 profiles per “grid box” (Table S2) and reasonable systematic error bounds, are found accurate to <0.15 to 0.5% (greenhouse gases, e.g., CO2 <1 ppm), <0.1 to 0.2 K (temperature), and <0.5 to 1 m s−1 (l.o.s. wind).

image

Figure 3. LMIO performance for profiling of greenhouse gases, wind, and thermodynamic variables. Retrieval performance estimated for (a) carbon dioxide and isotopes, (b) water vapor and isotopes, and (c) further greenhouse gases as well as for (d) line-of-sight wind and the thermodynamic variables (e) pressure, (f) temperature, and (g) specific humidity. The statistical errors shown have been estimated by ALPS modeling (greenhouse gases and wind from LIO, Figures 3a–3d; the “range bars” every 3 km on the mean error profiles show the spread from six representative atmospheres) and EGOPS modeling (thermodynamic variables from LMO, Figures 3e–3g), respectively (see auxiliary material). The upper axis of each panel quantifies the individual profile (IP) retrieval error, the lower axis the monthly mean (MM) error. The latter assumes 36 profiles averaged per climatologic grid box per month, consistent with the LMIO observational requirements (Table S2), which reduces the statistical IP error by a factor of 6. All “MM” quantities relate to the lower axis only, while all non-MM quantities also relate to the upper axis to see the IP error at this axis in addition to the MM error at lower axis. The colored vertical dashed lines mark monthly mean bias estimates (MM BE) in an expected upper bound sense (see auxiliary material). Figures 3a–3c for the trace gases show the MM BE in comparison with the statistical error estimates while Figures 3d–3g for wind and the thermodynamic variables show them together with the statistical error (standard deviation estimate, SDE) and the monthly mean r.m.s. error (MM RMSE), the latter combined from the MM BE and SDE. The vertical and horizontal dotted / dashed lines mark the target / threshold observational requirements for accuracy and height domain according to Table S2.

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4. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Method
  5. 3. Feasibility and Performance
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[20] We conclude from these encouraging results that the LMIO method has potential for ground-breaking contributions to scientific and societal goals such as benchmark monitoring of climate and climate model testing [Goody et al., 1998, 2002; Leroy et al., 2006; Trenberth et al., 2006], composition monitoring and analyses [Hollingsworth et al., 2008], anthropogenic change detection and attribution [Barnett et al., 2005], and provision of reference data for evaluating and calibrating data from other observing systems [WMO, 2006; CEOS, 2006]. Currently a ground-based LIO experiment targeting CO2, CH4, and H2O is being prepared for a 144 km link between high-altitude observatories at the Canary Islands, Spain, for a first demonstration under field conditions somewhat akin to a space link. We estimate that a real LMIO satellite mission could be operational as of about 2016 if implementation starts in 2012. With scaling of channels to other thermodynamic conditions, constituents and concentrations as well as scaling of system specifications to other geometrical sizes and space-time resolution, the LMIO methodology or LIO separately can also be applied beyond Earth's atmosphere such as in planetary atmospheres.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Method
  5. 3. Feasibility and Performance
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

[21] We thank V. Proschek, F. Ladstädter, J. Fritzer, C. Zwanziger, P. Bernath, J. Harrison, S. Syndergaard, V. Sofieva, C. Emde, A. Loescher, H. Krenn, A. Deninger, I. Bakalski and all ESA-ACTLIMB & -IRDAS project partners as well as all ACCURATE Science Team and Industry Support Team partners for their support in exploring the LMIO method. A. Dudhia, L. Rothman, and the ECMWF provided access to RFM&FASCODE, HITRAN, and atmospheric analyses&forecasts, respectively. The work was funded by FFG/ALR Austria and ESA/ESTEC Netherlands.

[22] The Editor thanks an anonymous reviewer for assistance in evaluating this paper.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Method
  5. 3. Feasibility and Performance
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Method
  5. 3. Feasibility and Performance
  6. 4. Conclusions
  7. Acknowledgments
  8. References
  9. Supporting Information

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