Induced surface fluxes: a new framework for attributing Arctic sea ice volume balance biases to specific model errors

West, Alex; Collins, Mat; Blockley, Ed; Ridley, Jeff; Bodas-Salcedo, Alejandro

doi:https://doi.org/10.5194/tc-13-2001-2019

Articles | Volume 13, issue 7

https://doi.org/10.5194/tc-13-2001-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/tc-13-2001-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 13, issue 7

Research article

|

19 Jul 2019

Research article |

| 19 Jul 2019

Induced surface fluxes: a new framework for attributing Arctic sea ice volume balance biases to specific model errors

Alex West, Mat Collins, Ed Blockley, Jeff Ridley, and Alejandro Bodas-Salcedo

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Final revised paper (published on 19 Jul 2019)
Supplement to the final revised paper
Preprint (discussion started on 06 Apr 2018)
Supplement to the preprint

Interactive discussion

Status: closed

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

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RC1: 'Review of "Attribution of sea ice model biases to specific model errors enabled by new induced surface flux framework"', Anonymous Referee #1, 16 May 2018
SC1: 'Review', Francois Massonnet, 08 Jun 2018
- RC2: 'Review', François Massonnet, 13 Jun 2018
AC1: 'Author response to reviewer comments', Alex West, 06 Jul 2018

Peer-review completion

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

AR by Alex West on behalf of the Authors (26 Oct 2018)

ED: Referee Nomination & Report Request started (01 Nov 2018) by Dirk Notz

RR by Francois Massonnet (19 Nov 2018)

Suggestions for revision or reasons for rejection

Second review of Best et al., "Attribution of sea ice model biases to specific model errors enabled by new induced surface flux framework"

by F. Massonnet

The authors have to be commended for the hard work in reshaping and revising the manuscript. I appreciate the work done to expand their framework to include subgrid ice thickness distribution information, to estimate the role of oceanic heat convergence in setting the biases, and the discussion on the validity of the approach (especially the new Fig. 5, Fig. 7, Fig. A1; these figures are very important for explaining the methodology and were clearly missing from the first ersion). It is fair to say that the manuscript has gained much in scientific quality. The structure of the text is still a bit dense, with sections 4 and 5 being hard to digest in one reading, with a lot of equations and formulas within the text. Also, adding subsections could help for orienting oneself in the manuscript. Finally, I would move the feedback discussion, currently in the "Discussion" section, as a sub section of Section 5.

An interesting finding, which I did not fully appreciate during my first review, is that observational inaccuracy is so large that it participates greatly in the estimated model bias (e.g., page 12, lines 34-36). This statement should be better emphasized, for example in the abstract, because it is of high importance for future evaluation studies. Most researchers think that the "model minus obs" quantity reflects a genuine model bias, while it can be caused by many other factors including observational inaccuracies.

I still have a couple of minor comments, which when addressed will give the green lights for publication. My comments are referenced with "p/l" where p is the page number and l the line number.

1/9 "allows the local dependence": I have the impression a verb is missing --> "allows emphasizing the local dependence" or "allows singling out the local dependence"

1/13 after "variable", there is a ". ' ." --> remove

1/35 "Massonnet" takes two n's.

2/6 "Ice volume is, to first order, proportional to the heat required to melt the ice" is somewhat imprecise. "heat required to melt the ice" might be interpreted as "heat needed to trigger melt onset", while what the authors mean is "heat required to melt the ice out" or "heat required to entirely melt the ice".

2/19 Calling HadGEM2-ES a "member" of CMIP5 is troubling because "member" is usually a term reserved to mean "individual realizations" within the same model.

2/19 "ensemblewhich"

3/33 Does the definition of "Arctic Ocean" come from somewhere, or did you make it up yourselves? How was the region defined? Can you elaborate in Fig. 1 caption?

4/5-8 The second part of the sentence "The approach..." seems to be missing something: "... and to use as reference datasets [WHAT?]"

4/9 Consider "concentration" instead of "fraction" to be consistent.

4/11 If I'm not mistaken, PIOMAS also assimilates sea surface salinity. Check it out.

5/5 "From 1980-1999" --> "From 1980 to 1999"

5/21-26 I find your discussion on Fig. 3 interesting but it deserves more physical explanations. (This is somehow briefly discussed later at page 13, lines 11-22). Essentially, your results suggest (Fig. 3) that the October to April change in thickness is overestimated with respect to reference products, and you find that there is a "clear association between areas where modelled annual mean ice thickness is biased low, and areas where the modelled seasonal cycle is overamplified". The physical reason is - I think - that the negative ice-growth ice thickness feedback is much stronger for thin ice. When ice is biased thin, much more ice is grown in winter than if there was no bias. We have somehow shown this in our recent paper (Massonnet et al., 2018, https://www.nature.com/articles/s41558-018-0204-z) with the introduction of the "Ice Formation Efficiency" (IFE). The IFE is the regression between ice volume produced during winter on summer sea ice volume. It is negative in all CMIP5 models: a summer sea ice volume negative anomaly results in a higher-than-normal ice production; and it is strongly mean-state dependent, being more intense at low thickness (see Fig. 2a of our paper). It might be good to comment the results of Fig. 3 in light of this paper.

6/26 See my comment 2/6

7/4 By "surface flux", do you mean "net surface flux"? Be more specific.

7/9 When giving the analytical formula for estimating the induced surface flux bias, it might be worth already mentioning here that the partial derivative needs to be evaluated at a reference state (otherwise the equation at line 9 gives a functional dependence but is not of practical use).

7/16 Use "ice concentration" instead of "ice area"

7/23 The equation (1) features a term $\gamma^{cat}_{ice-REF}$ but in the text that term is referred to as $\gamma^{cat}_{REF}$

8/26 "... variables which have the required property to affect the surface flux on timescales shorter than on which they affect each other". (Also at page 7 line 5). Can you be a bit less vague here? I understand the general idea, but can you give rough time scales of how surface fluxes respond to these state variables and rough time scales of how these variables affect each other?

9/23 Add white space between 0 and "m".

9/24 Expanding the induced surface flux bias framwork to account for the ice thickness distribution is a good idea, but it readily opens new problems, e.g. as how to estimate biases at the subgrid scale. I somehow follow the authors reasoning here, and think there is just no best solution given that the problem is underconstrained (too much information to create). I think it would be useful for the general audience to sketch what is the geometric idea behind your redistribution of thickness biases among categories. I'm asking because the formula that you give at line 26 does not give a good idea of what is going on physically.

11/3 "anomalous" --> biased?

11/4 "anomalous" --> biased?

14/19 There are two consecutive dots.

14/24 A white space is missing between SW and bias.

14/24 A white space is missing between bias and "is"

15/3 A dot is missing between two sentences.

17/22 There is a white space before the "In"

17/32-35 I am not sure to understand the meaning of this paragraph: do you mean that the approach can also be used to understand the sensitivity of model results to the inclusion of new processes?

Figure 2 Readers might be puzzled that for panels b, c, d, the model (black) lines are different from panel to panel. I understand that the average thickness is computed for the corresponding observational region of coverage each time (this is acknowledged in the figure caption). However, does the time period for averaging change as well from panel to panel? It looks it does not (1980-1999 according to the caption). However, the ERS product runs from 1993 to 2000. Does that mean that averages are not done on consistent periods? Also, it would be good to use similar y-axis limits in panels b-d and to set the lower bound at zero.

Figure 3 Font size appears to change from sentence to sentence in the caption.

Figure 4 Change "anomaly" in your difference plots to "bias".

Figure 4 The units of y-axes are W/m-2, they should be W/m2

Figure 5 In panel C, the units W/m2 are missing.

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RR by Anonymous Referee #1 (14 Dec 2018)

Suggestions for revision or reasons for rejection

Dear Authors,

Dear Editor,

I have now completed my reading of the revised version of « Attribution of sea ice model biases to specific model errors enabled by new induced surface flux framework ».

I well appreciated the energetic and thorough effort to address both (sometimes contradictory) reviewer’s comments.

However, the main comment from my first review has not been successfully addressed, I'm afraid: science looks a priori fine, but awkward writing and logics makes proper understanding of the paper hard.

The methods section is at the centre of this: too much time is spent on the details and to little is made to explain the very main points of the reasoning, the assumptions and the validity of the method.

The ultimate strengths and weaknesses of the methods, which are essential points, are hidden into the limbs of the paper.

I'm afraid this more or less applies to the whole paper. I'm still encouraging, though. I'm pretty sure all elements are there to turn the paper properly.

---

These are my major points.

1. Make sure the paper is fully understandable.

2. Correctly qualify the confidence in your methods. There have been progresses, but the situation is still blurred. To be clearer on how your method is reliable, you could show 3 things on the same seasonal cycle plot: the mean ISF; estimated minus directly retrieved surface flux with HadGEM; sum of all ISF contributors minus ISF.

3. The explanation on the early melt onset problem is not entirely convincing (page 11, lines 3-12). You claim ice melts too early in HadGEM (end of May). Based on the used datasets, melt onset is supposed to happen in mid-late June. However, in my experience, surface melt onset in the Arctic falls quite regularly near June 1st. It was true at SHEBA (29 May, Persson et al JGR 2002), it is true at Barrow I believe. It also seems generally true from passive microwave datasets (Markus et al., GRL2009, Fig. 3). Hence your claim that melt onset is too early sounds invalid, and the melt pond explanation as well. I would tend to think that melt onset looks fine. What could be wrong is that the initial drop in sea ice albedo, that could be happening too fast.

4. There are important observational references on surface energy fluxes (Lindsay 98, Personn et al 2002) that could be of help to select which products are more plausible than others.
(Page 6, line 9-12). These two papers analyse the energy budget in the Arctic as derived from in situ measurements in the ~50 Russian polar drift stations, and from SHEBA. Regarding downwelling longwave fluxes these references suggest between 150 and 160 W/m2, and nothing above 170 W/m2. I guess this places your model at the low range and places ISCCP out of the game.

A few minor items:

- Make sure your figures are absolutely clear. Fig. 2, 3, 4 could be better labelled to warrant immediate understanding.

- Explain how consistent time periods are between reference and model products in the construction of Fig. 2 and 3.

- Don't use "observation" to refer to PIOMAS. Use "reference data set" throughout.

- Color scales and axes scales are to be carefully chosen. In particular, on Fig. A1 there are no means to know the order of magnitude of the differences. Use line contours ?

- Page 6, line 25. In the SM0L framework, "latent heat storage" and ice volume are equivalent not because sensible heat is small, but by construction

- I still find the use of « latent heat flux » for internal energy storage in sea ice confusing.

- There are many small typos or poorly constructed sentences.

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ED: Reconsider after major revisions (18 Dec 2018) by Dirk Notz

AR by Alex West on behalf of the Authors (05 Mar 2019) Author's response Manuscript

ED: Referee Nomination & Report Request started (22 Mar 2019) by Dirk Notz

RR by Francois Massonnet (12 Apr 2019)

Suggestions for revision or reasons for rejection

Third review of "Induced surface fluxes: A new framework for attributing Arctic sea ice mass balance biases to specific model errors"

by F. Massonnet.

Once again, I want to underline the great effort made by the authors to take my comments into account. As far as my comments are concerned, the paper is good to go for publication. I have noted the re-writing of Section 4, with a step-by-step illustration of the method with two processes. This will be of much help for those interested to apply the framework in the future, for the authors' own benefit.

I have made a couple of minor comments while reading the new version of the manuscript. Note that the page/line numbers below refer to the track-change version of the manuscript that was appended after the response to reviews.

Title: Now the focus seems to be on sea ice mass balance biases, not on volume biases anymore. I understand the initial motivation behind this move: it is mass and not volume that is proportional to the heat required to melt the ice out. I'm a bit skeptical about this choice though, because there are no proper observational estimates of sea ice mass (that I know), so that it is implicitly assumed that modeled biases in sea ice density (or parameter values used) are not introducing further uncertainty in the estimated mass bias. In addition, throughout the text and figures, biases are still expressed in terms of thickness not mass. I do not understand why the focus has been changed and would stick to volume biases. Perhaps I'm missing something but then would appreciate a better justification. I understand that there is a big momentum with the sea ice mass budget intercomparisons within SIMIP that could justify this change, but it's not a good scientific reason I think.

1/17 "... along with the roles of model bias in variables external to the sea ice state...": Do you refer to atmospheric and ocean biases? If so, state it explicitly.

1/19 "There is mention of sea ice volume biases here in the abstract, but the title now states mass balance biases". It should be made clearer biases in which state variable are investigated (as written above I would suggest to stick to volume).

1/23 The sentence on observational uncertainty is much welcome and will be appealing to many readers I think.

3/1 Instead of "observed or reference" I would write: "Hence, using reference datasets (observational estimates or reanalyses)". A "reference" is anything that one can compare the model results to, regardless of its origin.

6/38 A "thin bias... in thickness" sounds a bit strange. How about "low bias in thickness"?

7/8 "a mass balance bias of 38 cm" is typically something that will confuse many readers, even though a few modellers might understand what is meant.

7/31 Units Wm-2: "-2" should come as an exponent

8/18 "we briefly digress" and the whole paragraph: this really sounds like a paragraph added because a reviewer wanted further information and you did not know where to add this information. Try being a bit less obvious :-)

- Regarding PIOMAS assimilation, the authors are right that no SSS data is assimilated.

Fig. 6 still has "anomaly" near the colorbars

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RR by Anonymous Referee #1 (10 May 2019)

ED: Publish subject to minor revisions (review by editor) (14 May 2019) by Dirk Notz

AR by Alex West on behalf of the Authors (28 May 2019) Author's response Manuscript

ED: Publish subject to technical corrections (29 May 2019) by Dirk Notz

Dear Alex, dear all,

I am now finally happy to accept your paper for publication in The Cryosphere.

I mark this as "acceptance subject to technical corrections" to allow you to still do the following changes if you agree that they can be useful. Note that I will not see those changes before publication, and I leave it to your judgement to decide in as how much you want to follow these recommendations:

1. Usage of the term "volume balance / volume budget": I agree with the second reviewer that the normal usage of the term "mass balance" to describe either measured or modelled changes in ice thickness is unfortunate. Hence, I am very happy that you now use the more suitable term "volume budget" throughout. However, I expect large parts of our community to have gotten used to the term "mass balance" to describe changes in ice thickness, so it might be helpful to briefly describe why you have moved away from this terminology. Note in particular that for example Untersteiner's 1961 study on sea-ice mass budget was indeed phrased in units of g/m2, while later studies really only looked at changes in sea-ice volume but still called it mass balance.

2. In agreement with reviewer 1, I also still find the paper somewhat hard to read in some places. It might be good if someone either from within or from outside the author team might go over the text to improve its clarity and readability wherever needed.

3. I was somewhat surprised that you do not acknowledge the, in my view, extremely helpful feedback by the reviewers, and the enormous amount of time they spent on their evaluation. You might want to re-consider this decision.

As indicated, these are both just recommendations. As they don't affect the scientific contents of this paper, but are only meant to support a broad readership of this study, you are, as indicated, free to address or ignore these comments - whatever you prefer.

Thanks again for your hard work on this study, which in my view has matured substantially during the review process.

All the best!

Dirk

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AR by Alex West on behalf of the Authors (18 Jun 2019) Author's response Manuscript

Short summary

This study presents a framework for examining the causes of model errors in Arctic sea ice volume, using HadGEM2-ES as a case study. Simple models are used to estimate how much of the error in energy arriving at the ice surface is due to error in key Arctic climate variables. The method quantifies how each variable affects sea ice volume balance and shows that for HadGEM2-ES an annual mean low bias in ice thickness is likely due to errors in surface melt onset.