Review of

Correction of temperature and relative humidity biases in ERA5 by bivariate quantile mapping: Implications for contrail classification

by K. Wolf et al. (egusphere-2023-2356)

The paper evaluates the ability of ERA5 to correctly represent temperature and relative humidity in the upper troposphere using data from IAGOS as reference. Biases in both fields are detected and characterised and a correction method is applied that corrects both T and then RHi using the so-called quantile mapping method. It is found that this method indeed is able to reduce the biases. Unfortunately it turns out that in spite of this improvement the prediction of contrail formation or contrail persistence is not improved. But at least, for other quantities that are relevant for the assessment of aviation climate impacts, e.g. the optical thickness of contrails, improved estimation seems possible (not individually, but in a statistical sense).

While the method leads certainly to a significant improvement of the RHi-statistics of ERA5, the investigations and analyses in the paper are somtimes a bit lengthy and, at least to my view, not always necessary. The differences between the original ERA5, and after the application of the QM method of the correction of Teoh et al are often minor and it is not sure whether they are always real or simply caused by statistical noise. But even if they are real in certain cases, it is not always clear to me why the reader needs to know the potential causes of these differences. I have the feeling that the reader can easily get lost in these details and that the straight way from the analysis to the results and conclusions becomes unclear. So, I think, there is potential to make the paper more concise and to clearly convey a message.

This paper needs at some places more elaborateness in its formulations. For instance, the sentence (Page 1) "IAGOS flight trajectories are used to extract co-located meteorological conditions - temperature, relative humidity, and wind speed - and are compared with the IAGOS measurements" is obviously a faulty. In short, it says that IAGOS trajectories are compared with IAGOS measurements, which is evidently nonsense.

Also "representation of contrail occurrence in ERA5" (P 1) is misleading, since contrails are not represented in the ECMWF model and reanalysis.

Therefore I recommend a major revision of this paper to make its messages stronger and clearer.

Major issues:

Reading the abstract it seems that the evaluation merely uses bulk statistics, which I deem insufficient. An good indication of this is figure 5, where, apart from MD, all other measures are very insensitive to the applied corrections. The r² hardly change (and these tiny changes may be insignificant on a p=0.05 level). The r², like the other insensitive statistics, are bulk measures, that say nothing to a point-by-point comparison. The authors acknowledge this in the first sentence of section 3.4. 

Section 3.4: The selection of the score values is an unlucky choice to my view, since the TN cases dominate in this data set. Thus, if one would ignore everything and always predict "no ISS", one would already get an impressive accuracy and FA rate. The statement "which indicates that the overall performance of ERA5, even in the uncorrected form, is at least similar or even has improved" is thus misleading. It may be that the author made their choice to compare with Tompkins et al. (2007). If the goal of the paper is to provide better data on the occurrence of ISS, this might be ok, although I still think, that scores that downweight the default TN would be better. If the ultimate goal is, however, forecast of contrail persistence, I think, that the authors should better compare with Gierens et al. (2020) and also use the ETS score described there.

Minor issues:

Lines 34-38: I suggest that you state that RF is a global (or at least regional) quantity, averaged over a long time period. On first reading, it was not so clear to me whether you refer to single contrails or contrails in general. Furthermore, aren't the quoted values ERF values (in Lee et al.) rather than RF values? 

L 48 and following: This text mixes up different things which is not good. In order to avoid contrails, one needs a precise PREDICTION of where they WILL occur. Knowledge of their occurrence is insufficient, it can only result in a kind of climatology. Schumann's use of the roof-camera is a bad example for predictive purposes, as it shows contrails that already exist and perhaps exist already quite some time. The same comment can be made for satellite or other observations of already present contrails. Then, contrail simulations in a climate model are not intended for contrail avoidance or prediction. CoCiP is the only example here where contrail prediction is the intention, but of course only, if it is fed with actual weather forecasts, not with ERA5. 

L 75: It is a bit surprising that a "fourth approach" is now mentioned. I believe that the mixed-up list from above (L 48 ff) is now continued, but that is not sufficiently clear. Again, this is not an approach to prediction and should thus not be mentioned as something that has to do with contrail avoidance. I find also, that this section interrupts the logic of the argumentation. It would be better if the paragraph that introduces various correction attempts would directly by followed with tha paragraph explaining the goal of the present paper.

Fig. 2 and corresponding text: it seems that either the information in the figure is useless or something is wrong. For instance, why are there so many 175hPa data for EU, where I would expect a lot of landing and departures (i.e. low altitudes)? How do I have to read the figures? It seems, the interpratation is: on 300 hPa most flights are over EU etc..... and on 175 hPa again most flights are over EU. Is this, because most flights are over EU anyway? Then the information is useless. Should't it rather be the following: In EU most flights are on lower altitudes because of a lower fraction of cruise, similar in US but perhaps not as strong, and over the NA all flights are in cruise, therefore a predominance of high altitudes (or low pressures). It seems, the data should be organised the other way, i.e three panels "EU", "NA", "US" and then showing the fraction of pressure levels in the threee panels.

Section 2.1: Please indicate whether all data are used along a flight (it seems so) or a subset to avoid autocorrelation which might spoil the statistics. If autocorrelation has not been avoided, a check should be made whether this affects the results or at least good arguments for this should be given.

L 153/154: I suggest to delete this statement since the procedure is better explained below from L 173 on. Anyway, I think the argument is weak (I don't remember Schumann's reasons for this) and refers rather to interpolation of specific humidity than relative humidity. 

L 210/211: The statement "The CDFs describe the probability that a certain quantity, for example temperature or relative humidity, exists in the underlying data set" is wrong. I think, we know which quatities are in the data sets, therefore the probability is either zero or one. Please consult a textbook on probability and correct the sentence or leave it out.  

L 239/240: You should delete the second part of the sentence. Contrail formation takes place a few tenths of a second after exhaust. It has nothing at all to do with the vortex phase which starts at, perhaps 20 seconds. I also dislike the next sentence. The SAC has been tested on many flights long ago, and it works excellently. There is a figure in the 1999 IPCC report that shows this (I think, the figure has been taken from a paper by Kärcher).

Section 2.4: I miss information on your choice of an overall propulsion efficiency.

L 272: is there really a general decrease of r_ice with p? Why then occurs ISS mostly directly below the tropopause?

L 297/298: it is not clear to me why the T22 correction cannot modify the shape of the pdf. Please explain.

L 370 ff: To my view the discussion of the differences between the QM and T22 is not convincing. For instance, the quoted  thresholds from CoCiP are very very low, so they are not really a constraint. To me, the first question is, whether these differences are statistically robust. If a subset of four out of the five years is used, how large is the change of the quoted values? If it is much smaller than the difference between QM and T22, then a real difference seems more plausible. Second, it might be that you compare apples with oranges, i.e. for instance contrail distance with relative frequency of occurrence. 

L 408 ff: It is not clear to me how you interpret the SAc. Why does an r_crit occur? As far as I understand it, the SAc gives a threshold temperature which is the maximum T where a contrail could in principle form (at 100% RH). Is r_crit the RHi values along the tangential mixing line between the T threshold (r_crit=100% RH) and the lower temperature below which contrails are always formed (r_crit=0%). This is not completely clear to me. 

Figure 7 and corresponding text: This text contains a lot of details and numbers that I find not necessary. What is the take-away message that the reader learns from these details? Again, how robust are these values, if you leave one your out, then another one, etc.?

L 482: "Applying ... more correctly DETECTED...", please reformulate. The QM method does not change any detection.

L 493-506: This is an interesting consideration. But it comes too late. Perhaps a lot of not-so-important numbers could be saved if this consideration would be presented earlier.

Section 3.5 and Figure 9: please state whether you use for the analysis original or QM corrected ERA5 data. 

L 536-539: If that happens only on 225 hPa, is it then really likely that small scale variations cause these differences? Don't such variations occur on the neighbouring pressure levels as well? In which sense are T and r_ice "more homogeneous" on 200 hPa? What does that mean and from where do you derive such a conclusion? 

L 539/540: Isn't this a trivial statement? Did you expect something else? Perhaps there are more interesting results in this section that could be more elaborated. For instance, which error usually dominates, is it the error in T or the error in r_ice. It would also be interesting to see how the differences in absolute humidity contribute to the misclassifications. What is here the conclusion? What needs to be fixed in the ECMWF model more urgently, is it T or the water vapour field? What is the effect of the QM correction in this analysis? I suggest you add a second set of points (squares or empty points), perhaps with arrows, to show how the QM correction shrinks the errors. Please think also on getting rid of the "default" class in the figure. It seems as if a couple of dots are hidden behind the big black dot in the middle.

L 575: "So from a statistical perspective, that the original ERA5 model output is able to adequately represent contrail formation." First, the sentence is gramatically incorrect. Second, please explain what means that contrail formation is adequately represented FROM A STATISTICAL PERSPECTIVE? Assume, the model would only predict ISS and PC over Antarctica and nowhere else, but with the correct frequency of occurrence averaged globally, then one could also state that the formation is represented adequately from a statistical perspective. So my question is, whether your statement makes sense.

L 590/591: Isn't it the other way, that is, the special bias combination leads to the corresponding entry in the contingency table?

Section 4: should not be entitled "Summary and discussion", since it does not contain any discussion. 

Miscellaneous

Line 3: upper tropospheric

L 19: underlying

L 30: delete "bonds"

L 31: What is WC?

L 41-42: The word "defined" is too strong. In fact, this was never defined. There is only a vague understanding that contrails that survive the vortex phase are somehow persistent. 

L 67: "due to the high temporal and spatial distribution of WV" ???

L 73: What is "contrail estimation"?

L 126: Replave "multiple" by "many". I believe "multiple years" is nonsense.

L 199: The expression "minimizing the C... test" is confusing. How can a test be minimized. I think this sentence can be dropped since it does not provide essential information.

L 241: criterion (singular).

L 244: slow

L 335: r_ice IS

L 433: remove one instance of correction

Table 6: the caption says "TO07" while the table headline says "T07"

L 513: delete comma after ERA5

L 658: require

L 671: showS and remainS

Table A1: eta should be labelled "overall propulsion efficiency". It is not necessary (and not good) to introduce new notions.

Figure A1(e): The y-label contains [*2e6]. Please check.

The authors compare ERA5 temperature and relative humidity at pressure levels of 175hPa to 300hPa with collocated IAGOS observations. A slight cold bias and a dry bias are found that peak at 200hPa and 250hPa, respectively. A bias correction method is applied that reduces the cold and dry bias. Finally, the impact of the correction on the probability of contrail formation is analyzed and compared with simpler corrections used in the literature. The probability of non-persistent and persistent contrail formation in uncorrected ERA5 data are found to agree quite well with the respective estimates from IAGOS data. This agreement improves very slightly for persistent contrail formation (correction reduces the probability of contrail formation) and deteriorates for non-persistent contrail formation after the correction of ERA5 data.

My main objection to the paper is that I am not convinced of the UT dry bias in ERA5 (see my point 1 below). I appreciate that the authors are careful to compare ERA5 and IAGOS data on a similar scale but I worry that the resulting (close to in-cloud) RH PDF (their figure 6) is unphysical. Nevertheless, as the authors point out, many studies in the literature have used a ‘correction’, often multiplying ERA5 RH with a constant factor. The factor is often determined by comparing ERA5 RH interpolated onto the aircraft track to IAGOS. The present study is designed to call into question such approaches and additionally shows that if the comparison between ERA5 and IAGOS is performed on a similar scale, the correction that can be inferred has close to no impact on contrail formation.

Major comments:

• The ERA5 dry bias in extratropical UT RH:
  • The authors cite Dyroff et al. (2015) and Bland et al. (2021) as showing the LS moist and cold bias and Kunz et al., 2014; Gierens et al., 2020; Schumann et al., 2021 as presenting the UT underestimation of water vapor concentrations and ice supersaturation in ERA-interim and ERA5. 
  • Kunz et al. (2014) analyzed ERA-interim and operational IFS data from the years 2001 to 2011 and finds a LS moist and UT dry bias. They note that the agreement with measurement data was improving within the analyzed time period due to model updates. Bland et al. (2021) evaluate the ERA5 UT humidity fields using radiosonde data and find a slight moist bias or no bias depending on the type of radiosonde. Krüger et al. (2022) report a slight moist bias in the ERA5 UT when comparing to the active Differential Absorption Lidar (DIAL) WAter vapour and Lidar Experiment in Space (WALES; Wirth et al., 2009). This slight moist bias in water vapor mixing ratio coupled with the cold bias should lead to an UT moist bias in relative humidity (RH). Gierens et al., 2020 and Schumann et al., 2021 both compare ERA5 to MOZAIC / IAGOS RH data partly at relatively low resolution and interpolate ERA5 data to the flight track which leads to comparing observed and simulated RH at different resolutions.
  • Based on the above literature I am not convinced that there is an UT dry bias in ERA5.

1. When comparing IAGOS and ERA5 data you filter the IAGOS data because of their higher resolution. In order to determine the resolution of the comparison you estimate the resolution of the ERA5 data from the grid point distance of the Gaussian grid at the latitude of interest. In a spectral model, such as IFS, this is not the model resolution. The model resolution (grid length at the equator) of ERA5 is 31km. Even then the ERA5 grid box value is of course representative of the 3D volume and the IAGOS observation of a small subset of this volume so that ERA5 should be expected to display a lower variability.
2. The only reason given for the dry bias in ERA5 RH is saturation adjustment within clouds (section 2.2.1 and in lines 278-279). If this is your hypothesis then I would suggest using the IAGOS particle number concentration N_ice and splitting up the data set into cloudy and cloud free measurements and doing the same for ERA5 (using cloud cover) and then comparing the RH CDF for cloudy and cloud-free instances separately. The comparison could also be extended to include the data of Krämer et al (2009, 2020) that show an increased probability at RH = 100% (unlike IAGOS data). Corrections could and should be done for cloudy cases only.
   • You do something similar in section 3.2 but sort both ERA5 and IAGOS data dependent on ERA5 cloudiness into in-cloud and cloud-free data. Since you do not check in figure 6 whether IAGOS measurements are representative of cloudy or cloud-free conditions (see also my comment 4) the differences between ERA5 and IAGOS PDFs worsen with increasing ERA5 cloud cover. Since you have calculated already a ‘IAGOS cloud cover’ it is not clear to me why you use it only in order to correlate the IAGOS and ERA cloud cover and don’t do the IAGOS in-cloud with ERA in-cloud comparison.
   • Nevertheless, it is also not clear to me why a correction of in-cloud RH is needed since contrail formation studies are mainly interested in contrail formation within cloud free air.

1. I believe there could be another reason for differences in the PDF of RH between IAGOS and ERA5 which is connected with sampling. Petzold et al. (2020) discuss sampling issues in their figure 5 when comparing MOZAIC measurements with measurements from research flights (Krämer et al. 2009). They say that the reason why the research flights show a much higher probability of RH around 100% than IAGOS is because campaign measurements often target clouds in which RH is often around 100%. In the same way, it is likely that IAGOS pilots tend to avoid clouds and rather fly through cloud free air or very thin clouds while ERA5 data represent cloudy, partly cloudy and cloud free situations purely based on their probability of occurrence.
2. Figure 6 shows that the ERA QM data display a maximum probability of RH of ~105% for close to full cloud cover and of ~115% for cloud cover of between 0.6 and 0.8. Uncorrected ERA data show that RH = 100% has the highest probability in cloudy situations in line with Krämer et al. 2009 and 2020 and in line with theory that predicts significantly large in-cloud supersaturation only if supersaturation forcing is very large or if ice crystal number concentrations are very small. Both conditions are not the most probable inside clouds. To be fair, the other methods that you mention within your paper, e.g. scaling up RH with a constant factor, will have exactly the same (or possibly a worse) impact on in-cloud RH.
3. I am surprised that the averaging of IAGOS data does not change the RH PDF. Averaging should always decrease the variability of data and I would expect the probability of very high ice supersaturation to be reduced. Since this result is used as an argument to claim that mixing ratios are too low I think the figure should be included. Note also that the result that averaging of IAGOS does not improve the comparability to IAGOS data is in contradiction to Reutter et al. (2020) who finds that the IAGOS data show a very high percentage of small-scale ice supersaturated areas which ERA-interim cannot resolve but that ERA-interim and IAGOS fit well once the IAGOS resolution is reduced to the resolution of ERA-interim.
4. Despite the fact that I am not convinced of the need to ‘correct’ ERA RH data, I still think that your work points out an important point in relation to the earlier attempts to study contrail formation using ERA5 data. You show that if you take care to compare ERA5 and IAGOS data on a similar scale that correction has hardly any impact on the contrail formation probability. This means that the ERA5 RH scaling of earlier studies that is calculated by interpolating ERA5 data to the aircraft track and comparing to IAGOS data, lead to an increase in contrail formation probability that is not supported by IAGOS data.

Minor:

The text is generally difficult to read because it is often not clear which figure is being discussed. E.g. at the beginning of section 3.1 you mention fig. 2 and fig. 5e in the first 10 lines but actually you are discussing probably figure 3 which you fail to say. This problem is repeated in other places.

line5 (abstract): You extract wind speed but I can’t find the place where you use this variable.

Line 31: You did not define ‘WC’.

Line 59: Bickel et al. (2020) discusses the difference between radiative forcing and effective radiative forcing. The model that is used in Bickel et al. is described in Bock and Burkhardt (2016).

Line 67: Instead of the word ‘distribution’ you mean probably ‘variability’.

Line 68 ff: Please include Krüger et al (2021) and improve the description of findings of the papers (see above).

Line 75 ff: You may want to include Krämer et al. (2009, 2020)

Line 196: The multiplication of ERA5 RH with a factor is only common to the studies that you cite afterwards and not generally common.

Line 276-277: I am not sure what you are talking about. I don’t see any rectangular shapes.

Line 340-341: ‘r_ice close to 100% are likely associated with cloud formation’ – no this is not the case. Cirrus formation happens at high relative humidity relative to ice.

Line 366-367: ‘All data points that do not belong to any of the categories are flagged for no contrail formation (NoC).’ Isn’t you R category also no contrail formation?

Line 395-396: please reformulate the sentence ‘but the saturation is insufficient to reach supersaturation to …’

Line 671-672: ‘The mode in Fm,h is primarily caused by the saturation adjustment in ERA5 (see Sec. 2.2.1)’. As said above, Krämer et al shows that the mode around 100% RH is a naturally occurring mode and not a modelling feature.

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