Summary

This article sets out to demonstrate a three-part bias correction method for hydrology model outputs. At river gauge stations with runoff measurements, the method splits the observed and modelled runoff timeseries data into three percentile-based bins (0-20%, 20-80%, and 80-100%), and calculates & applies a constant correction factor for each bin. A smoothing factor is added to patch up discontinuities at the percentile boundaries. These correction factors are calculated at the river gauging stations, transferred unmodified to the river mouths (except for a weighted averaging when multiple gauges transfer to one river mouth), and interpolated to nearby (<200km away) river mouths that do not have gauge data.

The authors describe a pair of datasets that were used to force a HydroPy+HD model setup that simulates the land-surface water balances and routes the discharge to river mouths. This hydrology model setup is not the focus of the article; it is used to produce a pair of modelled discharge datasets for which to test the bias correction.

The bias correction is applied and scoring presented in comparison with the uncorrected data and with a simple bias correction. The scenario of transferring correction factors computed with one period to a different period is also briefly explored. Lastly ocean simulations are conducted to check whether forcing with the bias corrected runoff is reflected in improved near-surface ocean salinity.

General comments

The article is logically structured, writing quality is clear (although a bit heavy on acronyms), and figures appropriate.

The article is submitted to Ocean Science, but the focus is on a hydrology model bias correction method. Freshwater runoff is an important forcing of coastal ocean simulations, and the article includes ocean simulations as a diagnostic. The journal-fit is not bad, but the readers of Ocean Science may be somewhat unfamiliar with hydrology models and water routing. More attention on summarizing the pertinent information for a oceanographer audience would be worthwhile, particularly sections 2.2 and 2.3.

The primary deficiency in this article is the absence of comparisons with other bias correction methods. Including such comparisons would put the proposed method into perspective in a landscape of methods. This would enable an exploration into it’s relative strengths/weaknesses, and reveal scenarios where it should and should not be applied. E.g. does it generally outperform others, or overcome a common deficiency in others, or have better transferability, or work in scenarios where others do not, etc.

A lesser shortcoming is the limited use of the ocean simulations and observational datasets as a check on the bias correction method through nearshore ocean salinity. Improved agreement on an 8-year mean sea surface salinity comparison does not showcase the strengths of this 3-band bias correction method – simple bias correction, or the climatology runoff datasets, should be able to achieve that result. While a reduced RMSE is shown with respect to salinity station data, it is unclear if that is RMSE or CRMSE; the former may be dominated by the bias improvement, while the latter would indicate improved salinity variability. The salinity observations and ocean model data should be examined more closely to look for improvements in the salinity at shorter time scales.

Summarizing, the article has potential but needs to showcase the 3-band method in the context of established bias correcting methods. The ocean simulations and salinity observations are underutilized for the purpose of showing improved nearshore salinity following the bias correction; a focus on improved salinity variability would put them to better use and strengthen the findings.

Specific comments

Lines 53-66: the authors note that quantile mapping is an established bias correction method, providing a couple references where it was used successfully and a couple where it did not perform well. (a) is quantile mapping expected to succeed or fail for the present case of European runoff? Meanwhile, there is no mention of other bias correction methods except for a hint that they may be found in Kim et al 2021. (b) are these methods all inadequate as well? The background section should put more effort into discussing the inventory of existing bias correction methods, and include some indication of why they are not up to the task of correcting hydrology output here.

Line 71-73: (a) What is “a high degree of consistency”? Is it related to correlation?  Is there a definition for this? (b) The proposed method applies correction factors to the simulated runoff data based on the percentile band the data lands in (discharges that get correction factor 1 notwithstanding); this is a fairly intrusive change that modifies the data significantly, as per Table 3, and requires discontinuity patching. What is the key aspect about the 3-band method that enables it to maintain a ‘high degree of consistency’, where other methods are deficient and would presumably degrade this consistency?

Line 107-119, sec 2.1: on the atmospheric products description, this is exceedingly brief! There should be more explanation about how the datasets differ, temporal resolution and relative strengths/weaknesses of each, and why they were ultimately chosen.

Line 115-117: this reads as if the present authors employed the WFD method to derive this WFDE5 dataset. Suggest to restructure this section to be clear that these were not generated as part of this present work, and include the rationale for selecting them.

Line 120-143, sec 2.2 & 2.3: on the hydrology model setup, scant details are included here. It is well established that hydrology models require calibration and/or data assimilation to produce good results. Is the HydroPy+HD setup calibrated or uncalibrated – either in the present work, or prior work? I gather there is no data assimilation, but it would help to be explicit about this.

Lines 147-163: The article would benefit greatly from an explanation/justification about how this method differs from existing quantile mapping (QM) methods (e.g. empirical QM, delta QM, …). If I’ve understood correctly, the proposed method is similar to QM: considering quintiles, the low and high bands correspond to the first and last quintile, while the middle corresponds to a merged 2^nd, 3^rd and 4^th quintile. Thus, the method is not that far from a quintile-based QM method without interpolation, where the middle three quintiles are merged and a workaround added to mitigate the two discontinuities. Pondering the connection: (a) if the middle three quintiles were un-merged, would it degrade the performance? (b) if linear interpolation were added, that would replace the discontinuity workaround; any reason not to do it? (c) if a and b are ok, then we’ve basically arrived at (a coarse) empirical quantile mapping. (d) reversing this thought process: can the present method be better described as a special case of quantile mapping? E.g. tail-focused quantile mapping, or nonuniform quantile mapping, or 1:3:1 quantile mapping?

Line 174-180: The method of interpolating bias correction factors from gauged river mouths to not-gauged river mouths, up to a maximum distance, seems reasonable. Is this an established approach, or is it part of the present method? Are there any references to what other hydrologists have done for transferring bias corrections to ungauged rivers?

Line 267-269: What was used for the initial conditions -- presumably ORAS5?

Line 325-327: on ‘selected rivers’, there is no rationale given for the river selection. There must be a reason those ones were chosen

Line 487-488: The simulation starts in 2010, and the evaluation also starts in 2010. There should be a “spin up” time scale here where you allow the model to adjust to the new forcing and evaluate after a number of those time scales have elapsed (eg, 2-3).  What is the residence time for surface waters in the German Bight area? This time scale may be fast (days? weeks? months?) but should be included for context. Meanwhile, same question for the deeper waters – is the residence time here large or small? This is for putting “not much happened below 30m” into context.

Line 495-496: Evaluating mean sea-surface salinity (SSS) over eight years will wipe out the variability. I would expect the 8-year mean SSS bias to be impacted by biases in the mean freshwater input, and less so by the variability in the freshwater input. As in the general comments section, this particular evaluation does not showcase well the 3-band bias correction method’s strengths. If you run the ocean simulation with simple bias correction (e.g. Table 3 middle part), or with the climatology freshwater datasets, you should get the 8-year mean SSS comparable to that from the 3-band method. If I’ve got this wrong, then showing the climatology or simple bias correction cases alongside would strengthen the case for the 3-band method. Meanwhile, as I understand it the strength of the 3-band method is the better capturing of the variability -- and indeed Figures 7,8,10 support this -- so one should look for better salinity /variability/ in the ocean model simulations: (a) are there runoff events or interannual variability in discharge (e.g. Fig7 top panel) that appear, perhaps with some lag, as salinity drops in the DB and EMS station data, and are these signals better represented with the bias-corrected ocean model run? (b) similar question but for the satellite-based surface salinity product; are runoff events / interannual variability better represented when looking at shorter time scales than 8 yr mean – daily, weekly, seasonally, interannually?

Line 507-508: If this is actually RMSE then it is unclear if the reduction in RMSE is due to reduced error in variability or due to reduced bias: RMSE^2 = CRMSE^2 + bias^2. Additionally reporting CRMSE here (and/or another mean-removing metric such as correlation, or gamma^2), would better capture improvement in variability.

Lines 518-530: This reads like the 3.6km model is too coarse to get good nearshore salinity and is not up to the task. Are there any higher-resolution NEMO models available for the German Bight that could be used as a higher-resolution downscale? That is, to capture some of the estuaries and better resolve the coastline

Lines 587-590: This should be reworded to be more precise about what aspects of the sea-surface salinity were improved (e.g., the 8 yr mean, and pending resolution of comments for line 507-508, variability at stations)

Lines 593-603: the 3-band method is similar to quantile mapping (as per comments above for lines 147-163), and quantile mapping has been flagged as potentially not suitable for climate simulations as it has been shown to degrade trends (i.e. references in Cannon 2015), where Cannon 2015 proposed a delta QM that preserves trends (by extracting them, applying the quantile mapping, and reinserting them). The 3-band method proposed here does not take any special care about preserving trends. Adding some rationale for why this method is applicable to climate simulations, particularly when contrasted with other bias correction methods that are not applicable, would strengthen this conclusion.

Technical corrections

Line 26: include ocean keywords such as nearshore or sea-surface salinity, or ocean model?

Line 134, the reference is to a Zenodo link to the HD model code. This seems more appropriate for the data/code availability section, and the early part of sec 2.3 should explain the HD model

Line 119: “0.5 spatial resolution” requires units

Line 281: KGE defined here, no need to de-acronym it later (lines 308, 331, 381, 405)

Line 417: “Observed and simulated daily discharge of HD5-GSWP3” – surely this should be discharge of water

Line 510-512: if the NSB station is not used/usable in the eval, remove it entirely

Sec 2.3: Can the HD5-WFDE5 and HD5-GSWP3 acronyms be shortened? H5 and H3 perhaps?

Figure 7,8,10: use (a), (b), etc for the panels instead of first panel, second panel

Figures, general: in the copy of the manuscript received for review, the figures appear to be JPEGs. Suggest to switch to a vector format or PNG

Detailed river runoff data are needed for the coastal ocean models. Unfortunately, the observational data are often with too coarse resolution and/or of insufficient accuracy. Data coverage may be improved by hydrological modelling, but it creates specific errors. As a result of freshwater input bias, modelled ocean state may drift away from the real salinities and related variables, especially in climate-related long-term studies. Therefore, the approach of the present MS to elaborate and test bias correction for simulated river runoff is highly needed and scientifically interesting.

Obtained results are convincing. In particular, the model system gives too large peak discharges in the Elbe, Rhine, Weser and Odra rivers, while the modelled low discharges are close to the observed values. This range-dependent bias is effectively corrected by the applied method.

The MS has a good quality and should be published. When reading I found some problems, resolving of which in the revised MS would help the readers.

A) One problem lies within the title, that brings forward “three-part”. It is not clear what does it tell scientifically; what is the difference from “two-part” or “four-part” bias correction? I would prefer a scientific name for the developed bias corrected method. Is it the “quantile mapping bias correction”? Later it has been explained that the method has been specifically applied to “different correction factors for low, medium and high percentile ranges of river runoff over Europe”. Note that in the literature there are numerous uses of “three-step” bias correction that differ from the basic principles as well as from applications. Another possible interpretation of “three-part” is: (1) quantile mapping and correction at measurement sites, (2) transfer of bias correction to the river mouths, (3) interpolation of bias to the unsampled coastal sections. In short, the MS would benefit from having a well-defined title, not leaving space for ambiguity.

B) Quantile mapping is a well-known approach for bias correction in climate studies. The MS would benefit, if some basic statistical concepts and references are introduced in the introduction. Presently, the introductory paragraph in lines 53-66 is rather fragmentary and does not provide sufficient background information for the study. Specific to the river discharge, this paragraph is too much listing specific case studies and is lacking the references to the well-known studies, except for Madadgar et al (2014).

C) Introductory paragraph in lines 37-52 could be made more informative, backing the statements with appropriate references. In particular, the principle that “the river runoff is consistent with the atmospheric forcing” could be more elaborated and referenced. How bias correction changes this consistency? (Later this question is briefly discussed in lines 71-78).

D) The sub-section “2.4 Bias correction of river runoff” lacks references to the basic principles. It should have clear description of already known procedures (with references) and new/specific approaches. If the method is completely novel, this could be spelled out; then also more justification should be presented.

E) Lines 181-183 say that “bias correction can lead to spurious daily jumps in discharge when the percentile boundary is crossed and the bias correction factors differ between the percentile ranges”. This is suppressed by applied smoothing. It would be interesting to know if these jumps could be avoided (not suppressed) by some elaboration of the methods, for example by introducing continuous correction factors instead of stepwise correction.

Some technical remarks.

1. Principles and approaches of the HydroPy model and HD model (is it a unique name?) should be shortly outlined in the beginning of sections 2.2 and 2.3.

2. Smoothing formulae in lines 185-188 have different notations for q and Q than in lines 153-155.

3. Titles of Table 5 and Figure 12 contain “fractional area coverage” that is not defined.

4. Legends of Figures 5, 7-10 contain “HD5.2-HydroPy-WFDE5” that are not defined.

5. I counted 37 abbreviations; alphabetically from “20CR” to “WFDE5”. Some of the abbreviations are well-known like ECMWF, ESA, HELCOM, NASA, OSPAR and they do not complicate the reading. At the same time, there are abbreviations that occur only once (AHOI, GCOAST, RCSM, they appear only in the conclusions, BSH, RSME – they are not defined, GSM) or a few times (DB, EMS, GRDC, ISIMIP …). Reader would benefit from less abbreviations.