# Stochastic Modeling of Forces on Jacket-Type Offshore Structures Colonized by Marine Growth

*Reviewer 1:*Anonymous

*Reviewer 2:*Anonymous

**Round 1**

*Reviewer 1 Report*

Overall, the manuscript is well written and structured. I only have some minor comments listed here:

(1) Figure 4, it seems no relationship between DS and temperature. Why?

(2) What is R^2 value of equation (3) obtained from Figure 6 through curve fitting.

(3) Figure 7: It is difficult to see what the authors want to present?

(4) Figure 8: What did the solid lines represent?

(5) I would suggest to add some description in Appendix, also the heading of the appendix. Alternatively, you can just include these figures in the main text.

(6) a few table and figures cross the page, I would suggest to put the whole table or figure in one page.

*Author Response*

Overall, the manuscript is well written and structured. I only have some minor

comments listed here.

Correction are reported in blue in the revised version. We thanks the reviewer for this positive comment.

(1) Figure 4, it seems no relationship between DS and temperature. Why?

This is true. Growth is very much governed by chlorophyll. On line 302, we’ve added that more clearly: « That means that temperature is not a key driver of shell growth ».

(2) What is R^2 value of equation (3) obtained from Figure 6 through curve fitting.

It was 0.74 and it is added in the document.

(3) Figure 7: It is difficult to see what the authors want to present?

We want to show that the gamma model is able to capture the uncertainty (including extreme values) given by the DEB simulation. we added a precision in the sentence.

(4) Figure 8: What did the solid lines represent?

They represent the mean value: that has been adde in the Figure caption.

(5) I would suggest to add some description in Appendix, also the heading of the appendix. Alternatively, you can just include these figures in the main text.

We have completed the appendix:

Appendix A: additional information about the growth of blue mussels.

This appendix describes mode in detail the intrinsic characteristics of shell growth of blue mussels (Figure A1), the comparison between calibrated DEB model and the database in terms of shell growth and weight increase (Figure A2). Figures A3 illustrates the fair strait correlation between inception date and chlorophyll a.

(6) a few table and figures cross the page, I would suggest to put the whole table or figure in one page.

Thank you, we changed that.

Author Response File: Author Response.pdf

*Reviewer 2 Report*

Please see pdf

Comments for author File: Comments.pdf

*Author Response*

The paper presents an interdisciplinary model to analyze the biological marine growth process together with

the hydrodynamic engineering effects of it. For the marine growth process, an initiation phase with random

starting points (depending on temperature) is modelling and is complemented by a stochastic (gamma) model

with the growth propagation being mainly driven by chlorophyll concentration. On the hydrodynamic side, an

(uncertainty) model for the drag coefficient in the Morison equation is developed that depends on the thickness

and the roughness of the marine growth.

The interdisciplinary approach of modelling the effects of marine growth on offshore structures using a

stochastic model is a very interesting topic. On the structural side - being the expertise of the reviewer - so far,

marine growth is modelled fairly simplified. Hence, this work can help to make this modelling more realistic.

Therefore, the overall review is a quite positive one. Nevertheless, there are some major points that have to be

addressed before it can be published. Moreover, several minor points could improve the quality of this work,

but do not have to be addressed.

**We thank the reviewer for this overall positive comments. We addressed the comments below.**

Major points:

The introduction is quite lengthy and somehow unstructured. I know that for interdisciplinary work,

it is quite complicated to make it understandable for everyone. Still, some parts are repeated. For

example, l.45-61 are more or less repeated later on again. You might rewrite/shorten the introduction.**This is true and Introduction was reviewed carefully for increasing its impact and clarity. **

L 225: How do you get 10-days periods from bimonthly data. Please explain.**It comes from a linearization. That has been added and completed in the paper:The average value of all temperatures and chl. a values measured during each decade has been assigned as the decade temperature and Chl. a values. It should be noted that the water temperature cannot change abruptly in each decade. On the other hand, Chl. a will not interfere directly in the model but rather will form the growth potential parameter which is explained in next section. That is why if there were no available measurements available for some decades, a linear interpolation from adjacent measurements was carried out.**

Eq. 1: t>0 not t>=0, as t=1 are the first 10 days of January?

**This is true and it was corrected (idem in eq; (5)).**

Table 2: Line 4, the occurrence should be 3?

**This is true and it was corrected.**

Table 2: The last line is missing?

**This is true and it was corrected.**

Section 2.5.2: You say that no growth database was available close to your site. What about other databases, especially, since your calibration is done for “Mont Saint-Michel Bax” not for “Le Croisic”. So for the calibration, you also do not use specific site data. Please comment on this.

**The objective is to find a biological growth model for blue mussel in similar water. Mont Saint-Michel Bay respects this requirement. That has been clarified in the text:**

« This biological model was calibrated a site with similar environmental characteristics and for the same species of mussels ».

« This biological model was calibrated a site with similar environmental characteristics and for the same species of mussels ».

Section 2.8.3: You validate your model with the same data you have used for the learning phase (if I am right). So, you might considering using e.g. 12 years for learning and 5 years for validation or crossvalidation. At least, you have to discuss it.

**In fact we compare two models: the reference model (DEB) and the calibrated ones (Gama Process). There is no need for cross validation because only hyper-parameters of the game process are calibrated. After, the stochastic content of the game process gives the ransom shape. For calibration we need the full time period. That is why there are more curves for the Gama Process than for the DEB. More over, the most important is to represent the asymptotic behavior and that is the case.**

It has been highlighted in the revised version:

« Moreover, the stabilization is reached (asymptotic behavior) after the 30th time periods when the growth is stabilized at a mature age ».

It has been highlighted in the revised version:

« Moreover, the stabilization is reached (asymptotic behavior) after the 30th time periods when the growth is stabilized at a mature age ».

Fig. 10: Please revise this figure (e.g. alea?, is C_D still a function of C_{DS}, if C_{DS} is a function of K/De?, definition of De, Z:cste?). Moreover, it would help, if you directly refer the points (l.538-553) to the figure e.g. add (1), (2), …

**This figure has been revised.**

Eq. 12 is wrong. Remove D_c in the definition of theta_{mg}

**That is true and it was corrected.**

L561: Does your mussels’ model fit for the “Gulf of Guinea”? I could imagine that it is quite different, much warmer there, so that you have a completely different marine growth there. Please comment on this.

**Gulf of Guinea is only used here for introducing non linearities in the computation of CD. The structure of the spectrum of is similar as the one in french atlantic coast. it has been added:**

«Moreover, it gathers wave and wind-sea and the spectrum is very similar to the one in French Atlantic offshore sites. Using meteocean data from this region allowed us to cover a large range of KCmg to better illustrate the non-linear effects of marine growth on the drag coefficient evolution and hence on the load probabilistic distribution. This covers almost all configurations of Atlantic French offshore sites. »

«Moreover, it gathers wave and wind-sea and the spectrum is very similar to the one in French Atlantic offshore sites. Using meteocean data from this region allowed us to cover a large range of KCmg to better illustrate the non-linear effects of marine growth on the drag coefficient evolution and hence on the load probabilistic distribution. This covers almost all configurations of Atlantic French offshore sites. »

Add some limitations of your work in the conclusion. You have mentioned quite a few earlier in the text.

**That has been added:**

« Some limitations discussed in the paper highlight that further research is requested:

- A single species was studied where we can find barnacles even algae. For the latter, relationships for the computation of drag coefficients are less developed and research is required;

- There is uncertainty in the definition of the roughness and its use by engineers. That is the reason why an uncertainty of modeling is added in the paper. Recent works [60] proposed some improvements but that is still an open area. Quantification from on site inspections is possible [54] and that opens a new area for more representative tests in laboratory;

- Probability of occurrence of storms depends on seasons and it could be introduced in view to reduce the conservatism;

- In the same manner, inertia forces and current could be added to get a more global influence of marine growth."

« Some limitations discussed in the paper highlight that further research is requested:

- A single species was studied where we can find barnacles even algae. For the latter, relationships for the computation of drag coefficients are less developed and research is required;

- There is uncertainty in the definition of the roughness and its use by engineers. That is the reason why an uncertainty of modeling is added in the paper. Recent works [60] proposed some improvements but that is still an open area. Quantification from on site inspections is possible [54] and that opens a new area for more representative tests in laboratory;

- Probability of occurrence of storms depends on seasons and it could be introduced in view to reduce the conservatism;

- In the same manner, inertia forces and current could be added to get a more global influence of marine growth."

Prove reading.

**That was made.**

**Minor points:**

they were all checked and corrected and we thank the reviewer for increasing the quality of the paper by these detailed comments.

Check corresponding author. Ameryoun or Schoefs?

OK.

Some citations in the first part of the introduction (l.27-44) might be helpful.

OK.

Section 2.3: A picture of the Mytilus edulis might be nice. I think, seeing it, everyone knows it, but nonbiologists do not know the name + Please be consistent in writing it in italics.

OK

L. 201: You state that there is no clear relationship between growths and temperature. Please refer to Fig. 4.

OK

Fig. 3 (or in general): For a non-biologist, it is not quite clear how the propagation process works with the three initial dates (and for more than one year, not modelled here). Is the propagation stopping before the next initiation/year (as shown in Fig. 1, but contradicting Fig. 3), or are the final lengths added up, if you do not clean your structure, or is this a more complicated process not considered here. This might be clear for biologists, but not for all readers of this interdisciplinary work. Some explanations might be really helpful.

Initiation cannot me measured and is not presented in Figure 3. A comment has been added.

L. 380: Before “N” was the number of years. Here, you state that it is the number of 10-day periods. What you probably mean is the number realizations of the same 10-day periods (e.g. first 10 days in January, etc.), which is actually the number of year. Your explanation is confusing in the present form.

It was corrected.

Section 2.8.3 wrong section title?

Yes, corrected.

Fig. 8 (and others): A legend would be nice, especially when printing in greyscale.

OK.

L456-461: Several inconsistencies with Eq. 7.

Yes, for Cm: corrected.

L.478: I am not sure whether you have introduced and explained “KC”.

It was not and has been added there.

L.554: Perhaps you shortly discuss that you do not consider breaking waves, although they might be quite relevant for 100-year waves.

Yes.

L. 570: Psi30’’ leg, what is this?

That is clarified now.

L. 570: Is the probability of a storm independent of the time? Normally, you have severe storm in winter (at least in the North Sea). I do not know how this is in France.

Yes but we don’t considered time variant storms. That is conservative.

L.575: This sentence seems to be a bit out of the context here.

No but the sentence has been completed.

L. 692: You do not compute structural reliability, but only wave loads.

Yes precision is given.

L. 706: Remove bullet point.

OK

L. 708: Multimodal is more common than not pluri modal

OK.

You might add “effects of the Cd variations on the dynamics” in the outlook, as you only talk about quasi-static extreme value loads, but normally fatigue is design driving for wind turbine jackets.

OK.

**Syntax, typos, etc.:**

Syntax in l.48: It reviews […]

L. 92: […] as consecutive stochastic jumps […]

L. 93: […] a state-dependent […] OR […] gamma processes […]

L. 205: ([30]-[32])

Fig. 2 and elsewhere: μgl-1

Eq. 2: C(t) is not used in this equation but C_{T_i:T_{i+n}}

L.326: […] a 10-day period […]

L.329: The best correlation […] has been […]

There are several more, I do not explicitly name, please prove read carefully, especially equations, indices, etc.!

Author Response File: Author Response.pdf