the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
GNSS radio occultation excess phase processing for climate applications including uncertainty estimation
Josef Innerkofler
Gottfried Kirchengast
Marc Schwärz
Christian Marquardt
Yago Andres
Abstract. Earth observation from space provides a highly valuable basis for atmospheric and climate science, in particular also through climate benchmark data from suitable remote sensing techniques. Measurements by Global Navigation Satellite System (GNSS) radio occultation (RO) qualify to produce such benchmark data records as they globally provide accurate and long-term stable datasets for essential climate variables (ECVs) such as temperature. This requires a rigorous processing from the raw RO measurements to ECVs, with narrow uncertainties. In order to fully exploit this potential, Wegener Center’s Reference Occultation Processing System (rOPS) Level 1a (L1a) processing subsystem includes uncertainty estimation in both precise orbit determination (POD) and excess phase profile derivation.
Here we introduce the new rOPS L1a excess phase processing, the first step in the RO profiles retrieval down to atmospheric profiles, which extracts the atmospheric excess phase from raw SI-traceable RO measurements. This excess phase processing, for itself algorithmically concise, includes integrated quality control and uncertainty estimation, which requires a complex framework of various subsystems that we first introduce before describing the implementation of the core algorithms. The quality control and uncertainty estimation, computed per RO event, are supported by reliable forward-modeled excess phase profiles based on the POD orbit arcs and collocated short-range forecast profiles of the European Reanalysis ERA5. The quality control removes or alternatively flags excess phase profiles of insufficient or degraded quality. The uncertainty estimation accounts both for relevant random and systematic uncertainty components and the resulting (total) uncertainty profiles serve as starting point for the subsequent uncertainty propagation through the retrieval processing chain down to the atmospheric ECV profiles.
We also evaluated the quality and reliability of the resulting excess phase profiles based on Metop-A/B/C RO datasets for three 3-month periods in 2008, 2013, and 2020 by way of a sensitivity analysis for three representative atmospheric layers (tropo-, strato-, mesosphere), investigating consistency with ERA5-derived profiles, influences of different orbit and clock inputs and consistency across the different Metop satellites. These consistencies range from centimeter to submillimeter levels, indicating that the new processing can provide highly accurate and robust excess phase profiles. Furthermore, cross-validation and inter-comparison with excess phase data from the established data providers EUMETSAT and UCAR revealed subtle discrepancies but overall very close agreement, with larger differences against UCAR in the boundary layer. The new rOPS L1a processing can hence be considered capable to produce reliable long-term data records including uncertainty estimation for the benefit of climate applications.
- Preprint
(6089 KB) - Metadata XML
- BibTeX
- EndNote
Josef Innerkofler et al.
Status: closed
-
RC1: 'Comment on amt-2023-28', Anonymous Referee #1, 05 Jun 2023
Summary
The authors present a detailed and valuable summary of the rOBS L1a excess phase processing system that includes excess phase uncertainty estimation. The detailed processing description is well done. The uncertainty estimate portion of the paper should be updated to address the questions/comments below. One aspect that the paper does not include and should, that would improve it, would be to include a discussion in the intro of how the uncertainty estimates described here would be used to improve the quality of the final ECVs. Are these uncertainties being used now to better derive BA, N, ..? Or will they only be propagated to higher level to provide uncertainty estimates of the ECVs? What about vertically correlated phase errors, or phase rates, due to LEO orbits, GNSS clocks or ionosphere residuals? Are they taken into account? These correlations will lead to larger errors for ECVs when integrated downward with the Abel inversion. Another concern is the 3 data periods used in the study – they do not cover the most challenging regimes that RO has to track in. Analyzing a more challenging period may shed more light on RO error sources and uncertainty and better inform the community.
I believe this paper is a valuable contribution to RO and climate research and should be published with minor revisions.
Details Questions/Comments
L121: 3 3-month time periods:
- 2008 (Jul-Sep), solar min
- 2013 (Jul-Sep), solar max, but not in Equatorial plasma bubble scintillation season
- 2019-20 (Dec-Feb), solar min
These 3 periods do not present the strongest challenge for RO data processing, quality control, and uncertainty evaluation. Solar max periods during Sept-March present the greatest challenge for RO especially in the equatorial region. This paper would provide a better understanding of RO uncertainty and issues if it included the most challenging conditions for RO during solar max and Fall-spring periods. If the authors can’t include analysis of these data, then they should at least discuss any issues seen in these more challenging data.
L146: ERA5 analysis used for validation of RO profiles. This validation is tricky, since ERA5 analysis already assimilates the RO profiles.
L152: use suit, not suite
L164: What if you don’t have the GNSS navigation bits from the ground network? Do you process it anyway?
L175: use builds, not builts
L181: use pseudo-range, not pseudocode
L185: Can you provide some information in the text about the magnitudes of the computed systematic and random orbit uncertainties?
L200: Table 2, should the units of GNSS clock bias be seconds (not m)?
L242: Does the linear combination of L1 and l2 phase at the same time result in over estimation of uncertainty. I assume it does since the L1 and L2 ray paths are different.
L270: Q: how good is your model excess phase profile? Why not raytrace through ERA5 to get the model excess phase profile? I guess this won’t work in the lower troposphere, but I doubt the excess phase data in the LT are very useful. You could at least validate your model excess phase above the LT where signal is small with the raytracing excess phase.
L304: use, occultations that may miss ….
L310-315: One disadvantage of the GRAS OL approach that should be mentioned here is that since it must track the CA code, it loses lock when the CA signal gets too noisy in the LT which results in some data gaps. Data gaps are bad for RO and can break SI-traceability of the observations. What do you do about data gaps?
L359: remove ‘most’. I don’t think most RO missions use USO’s like Metop, i.e., C-1, Spire, Champ, Kompsat-5, ..
L461: A problem with this is that if you apply a conservative QC before uncertainty estimation, your uncertainty estimates will be under-estimated. Can you add some discussion on how you came up with the proper QC to obtain reliable uncertainty estimates?
L465-470: Figure 7, is the BB, just the LC – FMO?
Also, Fig7 right panel, shouldn’t the HPBB have the high frequency variations, and the LPBB have the low frequency variations?
L477: use, shorter weak signal
L517: If an outlier is detected, do you remove it so there is a gap in the data, or do you replace it with an interpolated value? Also, what if your model profile is far from truth, how can you be sure you are not removing accurate data? If you remove outliers and create gaps, how can you be sure that you maintain SI-traceability throughout the profile?
L525: What happens with the outlier detection when there is a cycle slip? L1 or L2? A cycle slip will look like a step in the BB excess phase. Also, it is assumed that occultations with large small-scale ionosphere residuals are captured with your QC algorithm. Which QC check best catches these ionospherically disturbed profiles? You showed combined QC %’s for all 3 data periods. Did you notice any differences in the QC %’s for the 3 different data periods? I would expect there to be a higher percentage of QC’d profiles for the solar max period.
L563: use, sampling rate along the vertical profile.
L573: I don’t see S/C attitude uncertainty included in the uncertainty equation. Every SC has attitude jitter. What is performance of Metop SC? Effect is smaller for larger sc, but it should be mentioned.
L612: I don’t understand this, ‘carrier wave cycles in order of several cm.’ Cycle slips can occur at ½ to N cycles, and therefore can be much larger than several cm.
L617: I don’t understand c = 0.001 m/min? So does this mean you apply an uncertainty due to cycle slips of 2 mm over a 2-min occultation event? This would be too small. Please explain.
L619: use, Local spacecraft multipath.
This description of local sc mp is not very well substantiated. First of all, the period of local sc mp on orbit will be closer to the orbital period of 100 min. Also, the amplitude of the effect is related to the geometry of the antenna on the LEO sc and to surface property of the reflecting surface. We found with rough calculation that this effect can result in a phase error rate of close to 0.1 mm/s for a strong reflector. Since the geometry on the sc is fixed, these error may manifest as a basic systematic phase rate error that may not cancel in a climate study using an ensemble of occultations. This ‘basic systematic phase rate error’ aspect of local sc mp should be mentioned in the text.
L622: Has this statement, ‘can be reduced by modelling’, been demonstrated experimentally for phase multipath on LEOs? ‘The possible phase shifts of up to a few centimeters, introduced by local multipath, can be reduced by modeling the effect and the use of directional antennas’
L627: The amplitude of 0.5mm used here seems incredibly small, and the period is much too small. The authors should provide a better justification for numbers or provide references.
Figure 8: caption says thick orange line, but it is blue in the figure.
Fig8: Can you also include daily mean values (different color) in addition to daily median values? This will give some additional information on the impact of outliers.
L654: use, ‘on average’
L655: why do the Metop counts get smaller for the later missions?
L675-679 and Fig 10: It appears that the solar max period of 2013 has larger differences for all altitude regimes, as expected due to larger iono residuals. Is this statistically significant? This deserves some discussion from the authors in the text since ionospheric residuals are one of the largest challenges for RO especially at higher altitudes.
L686: Table 5, why do the orbit differences increase for the later 2020 period? Also, how do you go from the results in Table 5 to specifying the orbit velocity uncertainty above on L604, 0.02 mm/s? 0.02 mm/s seems too small for specifying the orbit velocity uncertainty.
L692: Figure 11. How are the excess phase differences computed that are used to generate the stats in the figure? Are they the rms over the altitude region of interest? The maximum difference? Please state in text.
L763: How do the inter-center excess phase differences compare to your previously estimated excess phase errors? It looks like the inter-center differences are much larger than the earlier estimated uncertainties? Are these just due to mismatching (time/space) atmospheric differences? The estimates should be close to the inter-center differences. The authors should include more detailed discussion of the comparison between your estimated uncertainties and the inter-center differences.
L775: use, as a synthesis result.
L782: Fig 16, Why is there no kink in the curve between SLTPA of -20 and -40 for the 2008 period, and there is a kink for the later periods? The authors should discuss this clear difference in the text.
Citation: https://doi.org/10.5194/amt-2023-28-RC1 - AC1: 'Reply on RC1', Josef Innerkofler, 10 Aug 2023
-
RC2: 'Comment on amt-2023-28', Anonymous Referee #2, 06 Jun 2023
- AC2: 'Reply on RC2', Josef Innerkofler, 10 Aug 2023
-
RC3: 'Comment on amt-2023-28', Anonymous Referee #3, 22 Jun 2023
This manuscript provides an overview of Level 1a (L1a) processing of radio occultation (RO), a thorough description of the authors’ newly-developed processing system, and demonstration of the quality of said processing system. L1a processing transforms the raw measurements between GNSS satellites and low-earth orbiting RO receivers into measurements of excess phase – the phase “added” by propagation through the atmosphere. Precise estimation of this excess phase is critical to the processing chain of occultation events from GNSS signals to, e.g., temperature – a so-called essential climate variable (ECV). Thorough documentation, quality control, and uncertainty estimation is important for the community to understand what was done and why, and how the choices in processing affect the resultant ECVs.
I acknowledge and applaud the authors for this manuscript. The advancement of RO science at their center is evident in their completeness of the document. I certainly learned a great deal about the steps that go into excess phase retrieval, and I believe that is an important contribution to our subfield and, more broadly, atmospheric science. I think the quality of the retrieval is showcased nicely in their analysis in section 4. And, should they be coming, I look forward to the next publication(s) on later steps in the RO processing chain.
My primary, minor comment for the authors to address relates to the use of ERA5 analysis for their sensitivity analysis. Typically, one thinks that comparing an observation to an analysis that assimilates that observation would lead to artificially small difference statistics. I don’t suspect that the use of, say, ERA5 forecasts instead will lead to significant changes in the calculated O-B values. But, I do think it warrants consideration and some discussion.
Line-by-line comments
Line 35: suggest “By observing Essential…”
Line 56: suggest “Evaluation of basic…”
Line 78: suggest “subdivided into sensitivity…analyses”
Line 152: suggest “…data suit the…”
Line 154: suggest removing “in order”
Line 175: “that builds on”
Line 205: suggest “surface at the point…line connects between”
Line 207: apologies if I missed it, but is the mean tangent point identified in Fig. 3? It’s not needed to add it to the figure if it is not already there.
Line 222: “In principle”
Line 278: recommend removing “also”
Line 279: recommend removing “level”
Line 304: “occultations that may”
Line 320: closed parentheses that is unmatched
Line 357: the sentence ends with a fragment. Consider rewording.
Line 442: given that Eq. (9) has a factor 2k*pi, should this be “are always within 2pi”?
Fig. 7: the middle and right panels cut off quite a bit of interesting information due to the bounds at +- 15 cm. Is it possible to expand/shift these bounds while retaining resolution of some of the fine-scale features from 10+ km?
Line 493: “Schwarz et al.” ends up in parentheses when it should be outside of them.
Table 4: if it is sensible to do, please include the total rejection fraction in the table caption.
Line 540: suggest “profile is done by checking”
Line 567: “despite averaging”
Line 656: suggest “worthwhile to take into account”
Line 664: references are given in Bibtex format
Line 665: suggest removing “core-strength” or rewording
Line 682: references inside parentheses have parentheses
Section 4.1.3: what are the counts of the co-located Metop profiles used in this section? The robustness of the results is not clear without that information. If it was provided elsewhere, please reference to it.
Lines 717-718: “with the help of which the RO events” is not clear. Consider rewording.
Fig. 11 and text: is this given as WEGC minus EUMETSAT? Please make this clear.
Line 779: is there an example percent or range of representative percents that could be given?
Citation: https://doi.org/10.5194/amt-2023-28-RC3 - AC3: 'Reply on RC3', Josef Innerkofler, 10 Aug 2023
Status: closed
-
RC1: 'Comment on amt-2023-28', Anonymous Referee #1, 05 Jun 2023
Summary
The authors present a detailed and valuable summary of the rOBS L1a excess phase processing system that includes excess phase uncertainty estimation. The detailed processing description is well done. The uncertainty estimate portion of the paper should be updated to address the questions/comments below. One aspect that the paper does not include and should, that would improve it, would be to include a discussion in the intro of how the uncertainty estimates described here would be used to improve the quality of the final ECVs. Are these uncertainties being used now to better derive BA, N, ..? Or will they only be propagated to higher level to provide uncertainty estimates of the ECVs? What about vertically correlated phase errors, or phase rates, due to LEO orbits, GNSS clocks or ionosphere residuals? Are they taken into account? These correlations will lead to larger errors for ECVs when integrated downward with the Abel inversion. Another concern is the 3 data periods used in the study – they do not cover the most challenging regimes that RO has to track in. Analyzing a more challenging period may shed more light on RO error sources and uncertainty and better inform the community.
I believe this paper is a valuable contribution to RO and climate research and should be published with minor revisions.
Details Questions/Comments
L121: 3 3-month time periods:
- 2008 (Jul-Sep), solar min
- 2013 (Jul-Sep), solar max, but not in Equatorial plasma bubble scintillation season
- 2019-20 (Dec-Feb), solar min
These 3 periods do not present the strongest challenge for RO data processing, quality control, and uncertainty evaluation. Solar max periods during Sept-March present the greatest challenge for RO especially in the equatorial region. This paper would provide a better understanding of RO uncertainty and issues if it included the most challenging conditions for RO during solar max and Fall-spring periods. If the authors can’t include analysis of these data, then they should at least discuss any issues seen in these more challenging data.
L146: ERA5 analysis used for validation of RO profiles. This validation is tricky, since ERA5 analysis already assimilates the RO profiles.
L152: use suit, not suite
L164: What if you don’t have the GNSS navigation bits from the ground network? Do you process it anyway?
L175: use builds, not builts
L181: use pseudo-range, not pseudocode
L185: Can you provide some information in the text about the magnitudes of the computed systematic and random orbit uncertainties?
L200: Table 2, should the units of GNSS clock bias be seconds (not m)?
L242: Does the linear combination of L1 and l2 phase at the same time result in over estimation of uncertainty. I assume it does since the L1 and L2 ray paths are different.
L270: Q: how good is your model excess phase profile? Why not raytrace through ERA5 to get the model excess phase profile? I guess this won’t work in the lower troposphere, but I doubt the excess phase data in the LT are very useful. You could at least validate your model excess phase above the LT where signal is small with the raytracing excess phase.
L304: use, occultations that may miss ….
L310-315: One disadvantage of the GRAS OL approach that should be mentioned here is that since it must track the CA code, it loses lock when the CA signal gets too noisy in the LT which results in some data gaps. Data gaps are bad for RO and can break SI-traceability of the observations. What do you do about data gaps?
L359: remove ‘most’. I don’t think most RO missions use USO’s like Metop, i.e., C-1, Spire, Champ, Kompsat-5, ..
L461: A problem with this is that if you apply a conservative QC before uncertainty estimation, your uncertainty estimates will be under-estimated. Can you add some discussion on how you came up with the proper QC to obtain reliable uncertainty estimates?
L465-470: Figure 7, is the BB, just the LC – FMO?
Also, Fig7 right panel, shouldn’t the HPBB have the high frequency variations, and the LPBB have the low frequency variations?
L477: use, shorter weak signal
L517: If an outlier is detected, do you remove it so there is a gap in the data, or do you replace it with an interpolated value? Also, what if your model profile is far from truth, how can you be sure you are not removing accurate data? If you remove outliers and create gaps, how can you be sure that you maintain SI-traceability throughout the profile?
L525: What happens with the outlier detection when there is a cycle slip? L1 or L2? A cycle slip will look like a step in the BB excess phase. Also, it is assumed that occultations with large small-scale ionosphere residuals are captured with your QC algorithm. Which QC check best catches these ionospherically disturbed profiles? You showed combined QC %’s for all 3 data periods. Did you notice any differences in the QC %’s for the 3 different data periods? I would expect there to be a higher percentage of QC’d profiles for the solar max period.
L563: use, sampling rate along the vertical profile.
L573: I don’t see S/C attitude uncertainty included in the uncertainty equation. Every SC has attitude jitter. What is performance of Metop SC? Effect is smaller for larger sc, but it should be mentioned.
L612: I don’t understand this, ‘carrier wave cycles in order of several cm.’ Cycle slips can occur at ½ to N cycles, and therefore can be much larger than several cm.
L617: I don’t understand c = 0.001 m/min? So does this mean you apply an uncertainty due to cycle slips of 2 mm over a 2-min occultation event? This would be too small. Please explain.
L619: use, Local spacecraft multipath.
This description of local sc mp is not very well substantiated. First of all, the period of local sc mp on orbit will be closer to the orbital period of 100 min. Also, the amplitude of the effect is related to the geometry of the antenna on the LEO sc and to surface property of the reflecting surface. We found with rough calculation that this effect can result in a phase error rate of close to 0.1 mm/s for a strong reflector. Since the geometry on the sc is fixed, these error may manifest as a basic systematic phase rate error that may not cancel in a climate study using an ensemble of occultations. This ‘basic systematic phase rate error’ aspect of local sc mp should be mentioned in the text.
L622: Has this statement, ‘can be reduced by modelling’, been demonstrated experimentally for phase multipath on LEOs? ‘The possible phase shifts of up to a few centimeters, introduced by local multipath, can be reduced by modeling the effect and the use of directional antennas’
L627: The amplitude of 0.5mm used here seems incredibly small, and the period is much too small. The authors should provide a better justification for numbers or provide references.
Figure 8: caption says thick orange line, but it is blue in the figure.
Fig8: Can you also include daily mean values (different color) in addition to daily median values? This will give some additional information on the impact of outliers.
L654: use, ‘on average’
L655: why do the Metop counts get smaller for the later missions?
L675-679 and Fig 10: It appears that the solar max period of 2013 has larger differences for all altitude regimes, as expected due to larger iono residuals. Is this statistically significant? This deserves some discussion from the authors in the text since ionospheric residuals are one of the largest challenges for RO especially at higher altitudes.
L686: Table 5, why do the orbit differences increase for the later 2020 period? Also, how do you go from the results in Table 5 to specifying the orbit velocity uncertainty above on L604, 0.02 mm/s? 0.02 mm/s seems too small for specifying the orbit velocity uncertainty.
L692: Figure 11. How are the excess phase differences computed that are used to generate the stats in the figure? Are they the rms over the altitude region of interest? The maximum difference? Please state in text.
L763: How do the inter-center excess phase differences compare to your previously estimated excess phase errors? It looks like the inter-center differences are much larger than the earlier estimated uncertainties? Are these just due to mismatching (time/space) atmospheric differences? The estimates should be close to the inter-center differences. The authors should include more detailed discussion of the comparison between your estimated uncertainties and the inter-center differences.
L775: use, as a synthesis result.
L782: Fig 16, Why is there no kink in the curve between SLTPA of -20 and -40 for the 2008 period, and there is a kink for the later periods? The authors should discuss this clear difference in the text.
Citation: https://doi.org/10.5194/amt-2023-28-RC1 - AC1: 'Reply on RC1', Josef Innerkofler, 10 Aug 2023
-
RC2: 'Comment on amt-2023-28', Anonymous Referee #2, 06 Jun 2023
- AC2: 'Reply on RC2', Josef Innerkofler, 10 Aug 2023
-
RC3: 'Comment on amt-2023-28', Anonymous Referee #3, 22 Jun 2023
This manuscript provides an overview of Level 1a (L1a) processing of radio occultation (RO), a thorough description of the authors’ newly-developed processing system, and demonstration of the quality of said processing system. L1a processing transforms the raw measurements between GNSS satellites and low-earth orbiting RO receivers into measurements of excess phase – the phase “added” by propagation through the atmosphere. Precise estimation of this excess phase is critical to the processing chain of occultation events from GNSS signals to, e.g., temperature – a so-called essential climate variable (ECV). Thorough documentation, quality control, and uncertainty estimation is important for the community to understand what was done and why, and how the choices in processing affect the resultant ECVs.
I acknowledge and applaud the authors for this manuscript. The advancement of RO science at their center is evident in their completeness of the document. I certainly learned a great deal about the steps that go into excess phase retrieval, and I believe that is an important contribution to our subfield and, more broadly, atmospheric science. I think the quality of the retrieval is showcased nicely in their analysis in section 4. And, should they be coming, I look forward to the next publication(s) on later steps in the RO processing chain.
My primary, minor comment for the authors to address relates to the use of ERA5 analysis for their sensitivity analysis. Typically, one thinks that comparing an observation to an analysis that assimilates that observation would lead to artificially small difference statistics. I don’t suspect that the use of, say, ERA5 forecasts instead will lead to significant changes in the calculated O-B values. But, I do think it warrants consideration and some discussion.
Line-by-line comments
Line 35: suggest “By observing Essential…”
Line 56: suggest “Evaluation of basic…”
Line 78: suggest “subdivided into sensitivity…analyses”
Line 152: suggest “…data suit the…”
Line 154: suggest removing “in order”
Line 175: “that builds on”
Line 205: suggest “surface at the point…line connects between”
Line 207: apologies if I missed it, but is the mean tangent point identified in Fig. 3? It’s not needed to add it to the figure if it is not already there.
Line 222: “In principle”
Line 278: recommend removing “also”
Line 279: recommend removing “level”
Line 304: “occultations that may”
Line 320: closed parentheses that is unmatched
Line 357: the sentence ends with a fragment. Consider rewording.
Line 442: given that Eq. (9) has a factor 2k*pi, should this be “are always within 2pi”?
Fig. 7: the middle and right panels cut off quite a bit of interesting information due to the bounds at +- 15 cm. Is it possible to expand/shift these bounds while retaining resolution of some of the fine-scale features from 10+ km?
Line 493: “Schwarz et al.” ends up in parentheses when it should be outside of them.
Table 4: if it is sensible to do, please include the total rejection fraction in the table caption.
Line 540: suggest “profile is done by checking”
Line 567: “despite averaging”
Line 656: suggest “worthwhile to take into account”
Line 664: references are given in Bibtex format
Line 665: suggest removing “core-strength” or rewording
Line 682: references inside parentheses have parentheses
Section 4.1.3: what are the counts of the co-located Metop profiles used in this section? The robustness of the results is not clear without that information. If it was provided elsewhere, please reference to it.
Lines 717-718: “with the help of which the RO events” is not clear. Consider rewording.
Fig. 11 and text: is this given as WEGC minus EUMETSAT? Please make this clear.
Line 779: is there an example percent or range of representative percents that could be given?
Citation: https://doi.org/10.5194/amt-2023-28-RC3 - AC3: 'Reply on RC3', Josef Innerkofler, 10 Aug 2023
Josef Innerkofler et al.
Josef Innerkofler et al.
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 328 | 139 | 26 | 493 | 10 | 12 |
- HTML: 328
- PDF: 139
- XML: 26
- Total: 493
- BibTeX: 10
- EndNote: 12
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1