Data assimilation for volcanic ash plumes using a satellite observational operator: a case study on the 2010 Eyjafjallajökull volcanic eruption

Fu, Guangliang; Prata, Fred; Lin, Hai Xiang; Heemink, Arnold; Segers, Arjo; Lu, Sha

doi:https://doi.org/10.5194/acp-17-1187-2017

Articles | Volume 17, issue 2

https://doi.org/10.5194/acp-17-1187-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/acp-17-1187-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 17, issue 2

Research article

|

25 Jan 2017

Research article |

| 25 Jan 2017

Data assimilation for volcanic ash plumes using a satellite observational operator: a case study on the 2010 Eyjafjallajökull volcanic eruption

Guangliang Fu, Fred Prata, Hai Xiang Lin, Arnold Heemink, Arjo Segers, and Sha Lu

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Final revised paper (published on 25 Jan 2017)
Supplement to the final revised paper
Preprint (discussion started on 14 Jul 2016)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC2: 'Review acp-2016-436', Anonymous Referee #2, 12 Aug 2016
- AC1: 'Reply to Anonymous Reviewer #2', Guangliang Fu, 20 Sep 2016
  - AC2: 'One extended answer to reviewer's one comment', Guangliang Fu, 26 Sep 2016
RC3: 'Review', Anonymous Referee #1, 18 Aug 2016
- EC1: 'Review replaced', Thomas von Clarmann, 19 Aug 2016
AC3: 'Responses to other comments', Guangliang Fu, 05 Oct 2016

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Guangliang Fu on behalf of the Authors (05 Oct 2016) Author's response Manuscript

ED: Referee Nomination & Report Request started (07 Oct 2016) by Thomas von Clarmann (deceased)

RR by Anonymous Referee #1 (15 Oct 2016)

RR by Anonymous Referee #3 (18 Oct 2016)

RR by Anonymous Referee #4 (31 Oct 2016)

Suggestions for revision or reasons for rejection

This manuscript describes an effort to combine satellite observations and model simulations of volcanic ash to derive a best estimate of the ash concentration evolution as a function of 3D space and time. The Eyjafjallajökull eruption of 2010 is used as a test case. The ash transport model LOTOS-EUROS is used, along with ash loading estimates from the SEVERI satellite instrument. An ensemble data assimilation (DA) framework is used, with ensemble members branched with different plume heights, representing the uncertainty in this parameter. The results of the DA appear to produce much better results than the ensemble mean of the pure model simulations.

DA is a powerful tool for forecasting, and it is increasingly being explored as a method to be used in forecasting the evolution of volcanic ash plumes. The subject matter is of relevance to ACP.

However, the manuscript does not adequately describe a significant advance in the development of volcanic ash DA. DA has already been shown to improve the forecasting of volcanic ash transport (e.g., Fu et al., 2015, 2016). The main contribution of the paper appears to be the introduction of a satellite observational operator (SOO), which is not convincingly needed or effective. The authors also claim to quantify the duration of forecast improvement brought about by DA, but the single case study explored here, especially in the manner presented, is not suited to any general conclusions about the timescale of volcanic ash forecast skill.

Major comments:

1.
The authors state that the satellite observations “are often two-dimensional (2D), and cannot easily be combined with a three-dimensional (3D) volcanic ash model”, which motivates their development of a satellite observational operator (SOO). In fact, this issue is common to many DA applications using satellite measurements. Satellite instruments using nadir viewing geometry measure 2D fields. The standard technique in DA is to apply an observational operator (H) to the model output, to be able to compare model and satellite data in measurement space. Satellite observational operators (SOO) are sometimes used to transform observations closer to model space before assimilation. Using an SOO simplifies some aspects of the DA, but does so at the cost of including some set of assumptions in the SOO. In the present case, I find the motivation for the use of a SOO to be lacking (a mismatch between 2D and 3D fields is not sufficient).

Furthermore, the assumptions that are included into this SOO appear to be questionable. The authors argue that volcanic ash clouds have thicknesses between 0.5 and 3.0 km, although they quote studies having measured even smaller thicknesses. Given the relative large range, it is not clear why even smaller thicknesses are not included in the range. Then they calculate a range of possible concentrations by dividing the satellite retrieved ash loading (in g/km^2) by thicknesses between 0.5 and 3.0 km. They take the mean and SD of these concentrations as their best guess (and uncertainty in) ash concentration. This seems like a complicated way of assuming a mean thickness of 1.75 km. Then the authors focus on the ash concentration at cloud top, which appears to be the quantity which is compared to the model output within the DA (although this is not sufficiently explained). There is no real justification for why the focus is restricted to the concentration at cloud top, and this process seems like it discards a significant amount of useful information (e.g., the total mass loading).

Most of these assumptions and complications would be avoided if measurements and model results were compared in measurement space rather than model space, as is the standard in DA. This would simply require the observation operator H to take the vertical integral of the modeled ash profile.

2.
Fig 1a shows ash mass loadings from SEVERI, with values between 0 and 5 g/m^2 (although values could be higher). Taking 3 g/m^2 as a typical value, and under the assumption that cloud thicknesses are between 0.5 and 3 km thick (and that concentrations are uniform within the cloud), one would expect typical concentrations between 1-6 mg/m^3. The SOO extracted measurements in Fig 3a are around an order of magnitude less than this, with most values falling between 0.1-0.6 mg/m^3. The rough concentrations estimated here (1-6 mg/m^3) are also more in line with the model results shown in Fig 4. Given the apparent simplicity of the SOO, it should be possible for the reader to gain a quantitative feel for the magnitudes of the concentrations involved. At present, this is not possible. If the SOO is more complicated than I have understood it, then the description needs fair amount more detail.

3.
There is only a small amount of evidence shown to support the conclusion that “satellite data assimilation can force the volcanic ash state to match the satellite observations, and that it improves the forecast of the ash state.” Fig 5 shows a snapshot of ash loadings at a single time, comparing the SEVERI measurements with results from the model with and without assimilation. While the assimilation does seem to correct a rather large bias in the pure model output, it’s not clear that the DA result is better in all locations: while the values over the Netherlands may be more realistic, it appears that the DA results over the west coast of Norway may be underestimated by the DA system. Whether the authors have chosen this single comparison randomly, or if this is a best- or worse-case is not stated. One would expect some overall measure of skill with respect to time and space for such a comparison, in order to gauge the impact of DA.

4.
Apparently, DA has already been shown to improve the forecasting of volcanic ash transport (Fu et al., 2015, 2016). The present study claims to quantify the duration of such improvement. Fig 6 shows a comparison of DA forecast results with in situ airplane measurements. Again, the DA initiation helps to correct for a major over estimation by the model without DA. The authors conclude from this comparison that with initial conditions taken from DA, the “effective duration of the improved regional volcanic ash forecasts is about a half day”, although this is a “conservative” estimate, which is based only on this single case, and is in fact limited by the 15 h duration of the airplane measurements. It’s not clear why the continuous satellite measurements were not used to quantify the duration of the improved forecast. The duration of the skill improvement also likely has much to do with the assumptions regarding the noise added to the plume height estimates. A convincing assessment of the skill duration would require a much more thorough and detailed analysis.

Specific comments

Abstract

P1, L1: “Data assimilation” is very general, the focus on ash forecasting should be clearer.

P1, L5: It doesn’t appear that cloud thickness *data* is being included in the DA. Data-based assumptions, maybe.

P2, l4: A number of eruption source parameters are mentioned here, but only plume height is included in the DA ensemble generation. Some discussion would be nice at the end of the paper on the potential impact of uncertainties in the other ESPs.

P2, l10: Actually, you would hope that the VATDM was fairly accurate, and the DA was used because of unknowns in the ESPs.

P2, l11: DA does more than provide the initial conditions.

P2, l17: It’s not clear if these measurements are specific to Eyjafjallajökull, or more general.

P2, l25: should mention that the satellite is geostationary here.

P2, l26: Earth’s

P3, l6: Following from general comment, sparseness of data is not a real impediment to its use in DA, in fact, one could argue that sparse data is exactly what DA is useful for!

P3, l9: This discussion seems to assume that ash clouds have very well defined edges, but could there not be cases where the ash concentration decays smoothly over some vertical range? How is the thickness defined in such cases?

P3,l10: “hundreds of meters”

P3, l16: “Kasatochi”?

P3, l16: Personal communication should probably list from whom the information is from.

P3, l21: Whether thin ash clouds are less of a concern to aviation or not does not necessarily make them less of a concern for a data assimilation system.

P4, l12: “As a parameter…” The meaning of this sentence is hard to understand.

P4, l15: Also unclear, in the previous paragraph a number of data are described as SEVIRI products.

P5, l25: “ML_blue” is not an intuitive terminology, something physically motivated would be much better.

P6, Eq. 7: Where does this formula come from? Usually, uncorrelated errors add in quadrature. On line 13, a “conditional probability relation” is mentioned, but this does not make Eq. 7 easier to understand.

P7, l12: This description of the plume height needs much more detail to be understandable.

P8, l6: “… which is mainly due to lack of sedimentation processes” scared me quite a bit, but Fu et al. (2016) only state that the model contains sedimentation processes, but not coagulation, evaporation and resuspension. I guess assumptions about the size distribution are also important here.

P8, l7: Using DA to correct for model overestimation is a rather unphysical “solution”. It would be more satisfying to improve the physics of the model if in fact this is the source of the over-estimation.

P8, l26: This is not a very convincing validation of the SOO.

P8, l27: Is there a reason why SEVIRI mass loading retrieval error and the standard deviation of the mass loadings should be similar? The reason is not apparent.

P9, l3: I don’t see why satellite measurements wouldn’t be better to test the duration of improvements to forecasts from DA. That satellite measurements have “big uncertainties” seems a strange argument, given that the preceding portions of the paper have used satellite measurements for the DA. While I don’t mean to play down the importance of in situ measurements, in this case, the airplane flight track sampled only the very edges of the old ash plume, with concentrations orders of magnitude less than the peak values and much lower than the threshold for airplane safety. Therefore, the accuracy of the forecasts at the times and places of the in situ data used here seem to be of little importance to the question of how good the model is at predicting ash concentrations dangerous to airplanes.

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ED: Reconsider after major revisions (04 Nov 2016) by Thomas von Clarmann (deceased)

AR by Guangliang Fu on behalf of the Authors (30 Nov 2016) Author's response Manuscript

ED: Referee Nomination & Report Request started (02 Dec 2016) by Thomas von Clarmann (deceased)

RR by Anonymous Referee #4 (13 Dec 2016)

Suggestions for revision or reasons for rejection

I thank the authors for their consideration of my comments on the previous version. They have definitely done a lot of work to address those comments and improve the study. Here I highlight a few issues in need of further attention.

1. While the description of the SOO in Sec 3 is improved, I still don’t follow completely. In equations 2 and 3, you assume that a range of concentrations are possible, given the observed mass loading (M_v) and a set of possible thicknesses. So far, so good. Then, in equation 4, you calculate an average concentration (C) from the assumed distribution of possible concentrations (C_i). Is this the only concentration that is used in the DA? If so, why not just calculate C as M_v/T_m, where T_m is an assumed thickness? It works out to be the same thing. In your method, using a range of T from 0.2-3 km, with step sizes of 0.05 km, works out to a T_m of 1.0 km (where T_m=1/N * sum(1/T_i). This value seems consistent with the values shown in Figure 1d and Figure 3 (although with different color-scales it’s hard to be sure). But then, pg 6, l22-23, you say C is used as the concentration between the altitudes H_{top}-T_{high} and H_{top}. The thickness of this layer is T_{high}, i.e., 3 km. If the concentration C is calculated implicitly assuming a thickness of 1 km, and then a vertical profile is constructed with a concentration extending over 3 km, won’t the vertical integral of your constructed profile have a mass loading 3 times larger than the actual measurement?

Maybe I’m missing something here. The construction of an ensemble of concentrations (C_i) hints at a more innovative methodology: is this ensemble of concentrations used in the assimilation? It’s not clear that it is, and the introduction of the mean concentration C makes me think that only a single value is used. I would suggest that if this is the case, that a simpler description be used here—if in effect you are assuming a constant, static plume thickness, it is important that that be known by the reader. And of course, it is very important that the vertical profile of ash concentration used in the DA be consistent with the satellite mass loading!

2. Equations 5 and 6 are unnecessarily complicated. C=M_v/T_m (with T_m a constant defined above), so sigma_C=sigma_M/T_m.

3. The way that ensemble members are created is still not quite clear. I guess that different ensemble members have different assumed plume heights of the ash injection, which is based on observed plume heights and uncertainties. The discussion about the relationship between plume heights and mass injection should probably be brought up to the method description.

4. It is great that the authors have repeated their DA without the SOO to illustrate the impact of the SOO. But, I have to admit I just don’t understand how any DA, which ingests observations which have values less than half that of the ensemble mean forecast can produce an analysis which barely differs in magnitude from the forecast (Fig 6, b vs. d). I therefore worry that the apparent different between “with SOO” and “without SOO” might be due to other considerations, e.g., perhaps differences in the weighting of the observations in each case based on their estimated uncertainties. For example, if in the SOO case, the estimated concentration above the retrieved cloud height is zero, and has a small estimated uncertainty, this could be a very strong constraint in the DA which the “without SOO” analysis wouldn’t have. I get the impression that the “without SOO” analysis only includes the mass loadings, not the cloud height, so if this is true, the comparison is not quite fair. At least some discussion of these issues should be included.

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ED: Reconsider after major revisions (13 Dec 2016) by Thomas von Clarmann (deceased)

AR by Guangliang Fu on behalf of the Authors (19 Dec 2016) Author's response Manuscript

ED: Referee Nomination & Report Request started (20 Dec 2016) by Thomas von Clarmann (deceased)

RR by Matthew Toohey (04 Jan 2017)

ED: Reconsider after minor revisions (Editor review) (05 Jan 2017) by Thomas von Clarmann (deceased)

AR by Guangliang Fu on behalf of the Authors (05 Jan 2017) Author's response Manuscript

ED: Publish as is (09 Jan 2017) by Thomas von Clarmann (deceased)

AR by Guangliang Fu on behalf of the Authors (10 Jan 2017)

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Short summary

A Satellite Observational Operator (SOO) is proposed to translates satellite-retrieved 2-D volcanic ash mass loadings to 3-D concentrations. The SOO makes the analysis step of assimilation comparable in the 3-D model space, and thus it avoids the artificial vertical correlations by not involving the integral operator in directly assimilating 2-D data. The results show that satellite data assimilation with SOO can efficiently improve the estimate of volcanic ash state and the forecast.