This paper proposes a complex new way to do bias correction as a function of time scale.   They claim that this technique is useful for impact analysis and improves on older simpler methods.  But the paper does not provide any examples of this.  It would greatly benefit from a couple examples where the new technique provides significantly improved understanding of the effects of climate change on a particular impact.

Why does the paper use such old simulations to demonstrate the technique?

The paper seems to ignore the diurnal cycle.  If you are going to bias correct based on time scales, this needs to be included.  The daily maximum and minimum temperatures are very important for many impacts.  Just using daily means is not sufficient for temperature.  And why is bi-weekly the shortest timescale?  Many impacts depend on daily or subdaily timescales.  Some extremes, which are very important, occur on these short time scales, including heatwaves and floods.

Without addressing the above items, it is difficult to determine whether this paper is useful or not.

Figure 1 has several problems.  It is colored, but there is no information about what the colors mean.  The caption that a colorbar is not needed is absolutely wrong.  What is the variable and how was it calculated?  Also, there are no x- and y-axes.  And the edges of the boxes are not discernible.  There needs to be a table with each region and its location with the lat and lon of each edge.

The paper has very many acronyms, and learning all of them makes the paper hard to read.  And some of them are not defined at all.  If the terms are not used multiple times, don’t use acronyms and just write them out.  And it would help to include an appendix with a list of the acronyms and their definitions.

What about spatial scale?  Usually bias correction is paired with downscaling.  Are they independent?  Does it matter in what order they are done?

Figure 2 has too many panels with tiny font that is illegible.  I can’t read the subpanels in the first row.  The text in the last row is too tiny.  And what is this time series?  Please explain where the data for the observations and model came from.  

Line 203 says, “At longer timescales (seasonal or annual), biases often manifest in more systematic patterns that persist across multiple years.” but the authors provide no evidence for this.  Why do you think the climate system would behave this way?  Please provide references.

The paper uses “validation” in many places where it should be “evaluation.”  Please correct these.  Validation means that you already know the results are valid.

Figures 3 and 4 are missing units.  And what is Wasserstein?

The first three panels in Fig. 5 just show lots of colored lines, and it is impossible to compare them.  The last row only has 4 lines, but the colors are similar and again it is hard to figure out which line is which.  And what is MSE and what are its units?  Why are the last three panels centered on 0?  Are these anomalies?  With respect to what?

For the example in Fig. 5, the largest differences in the annual temperature are just for three years.  Why, and how does this skew the average scores?

Why are some plots semi-annual and others annual?

In Fig. 6 in the last row, I can’t tell any differences in the distributions.  Are the differences really significant?

Figs. 7-9:  There is not enough information to understand what is plotted?  What are the exact time periods?  What are the sources of the data?

Also, any response has to address the 30 comments in the attached annotated manuscript.

The authors have combined various existing bias correcting methods of the literature to account for timescale-aware bias corrections. They compared a model to a set of observations on a historical period and propagated the bias correction to mid- and long-term predictions. For some timescales, this bias correction method improves upon existing methods, on one specific region studied here and for an atmospheric model. The paper reads well and has many figures illustrating the results.

However, the text and the figures should be improved to clarify the method, the results and their performance. Thank you.

Here are some general comments:

• Please clarify the novelty of the method: combining several methods (name them) into one framework?
• To improve the performance study it would be helpful to broaden the evaluation: why is a regional dataset enough (USA)? what about using a larger spatial extent (global instead of USA)? Can the method be compared to other methods (mentioned in the Introduction) to illustrate its performance? If only one model is used in the end, add name of the model in the title.
• When explaining the methods, one or several schematics would help -> with method is used for which time scale, how is the data used for the evaluation, etc…
• The figures should be more understandable, some graphs are not readable, all plots should be commented. Please add a letter to each sub-figure and refer to the letter in the text.

Here are some specific comments:

L5: “Meteorological signal”-> “Atmospheric variables” ? Which variables / components of the earth system model? which time scales? Which area (USA)?

L7: “Experimental validations demonstrate that this finer-grained method substantially improves upon existing bias-correction techniques such as quantile mapping“: it was not demonstrated. “illustrates”? And add on which timescale it improves.

L8-10: add the limitations of the method (see conclusion).

Introduction

L 21. “Unlike statistical downscaling”: first define statistical downscaling.

L 25. “Region-level modeling”: North America Mearns et al. 2012, North American component of the Coordinated regional downscaling experiment NA-CORDEY, Mearns et al, 2017 -> add other examples on other regions and other authors?

L 29-31: “Despite these improvements… from forcing data and inherent systematic errors such as those ….”-> add references for the source of the RCMs biases

L47. QM method: transfer function based on the quantile distribution, daily values -> not necessarily daily?

L 51. QM improve model accuracy for both mean and extreme events “(Wood, 2002; Wood et al., 2004; Boé et al., 2007; Piani et al., 2009, 2010; Ashfaq et al., 2010; Teutschbein and Seibert, 2012; Gudmundsson, 2012)” : split the references between the type of application

L61: “generally parallels that of quantile-based techniques and does not address the core challenge of biases that occur across multiple distinct timescales” -> “generally” suggests it is well known in the literature -> add other references. What does Dhawan et al 2024 show?

L62. Biases different at daily monthly seasonal annual scales -> different in what sense? not multi annual? Or decadal?

L67 “Empirical mode decomposition-based bias correction (EMDBC)”: leveraging the adaptive nature of Empirical Mode Decomposition EMD and its ensemble variant EEMD: explain on which timescale it is used and on which timescale QDM is used

L 73: section 3: demonstrates EMDBC effectiveness-> “demonstrates” is too strong here

Methods:

L 80: why is this dataset used?

L 78. observed and modeled temperature -> detail what is used for what?

L 80: WRF-CCSM: explain acronym. Only atmosphere or coupled ?

L 81 “moodeled“

L 85. “RCP 8.5 scenario is used“: explain acronym + add reference

L 90: “3x10s^1” -> why s^1?

L 93: why is this dataset used?

L 97 “leverage observation data“-> in which way?

L 98: typo: “is used to THE learn“

L99: daily mean temp data calculated from the 3h outputs of WRF CCSM to match the temporal resolution of the observed Livneh data -> upscaling

L 102: Statistical framework is then applied to identify and learn the systematic biases in the simulation data. -> what statistical framework? which simulation data, WRF-CCSM or Livneh?

L 104 “the model generates bias-corrected future predictions that scale more closely with observational data“-> which observations are available for future predictions ? or maybe the authors refer to the next paragraph ? this paragraph should probably be merged with the next paragraph for clarity. Not clear how Livneh data is used: the data is spilt into 2 parts?

L 116: QM and QDM: add a Graphic illustrating the concepts of BQM and QDM (many examples in the literature, e.g. HESS - Peer review - Precipitation ensembles conforming to natural variations derived from a regional climate model using a new bias correction scheme + https://doi.org/10.1007/s40641-016-0050-x -> maybe also add these two references)

L 120: F(T) and CDF: give the formula

L 122: which model outputs?

L123 and 131: Eq 1 and Eq2: “p” refers to what?

L 135: “Nonparametric empirical CDFs are commonly used for flexibility, although parametric and semiparametric distributions can also be employed” -> which formula for parameter (Semi-) distributions? which adjustable parameters?

L 143: “meteorological time series“ is it meteorological modelling or climate modelling ? is it “meteorological variables” in a “climate model”

L 146: “future projections“ -> is it fitted only to climate projections or also to short term weather forecasts?

L 153: “Can suffer mode mixing” -> explain more how this occurs

L 155. Add other references using EEMD in Climate sciences: e.g.

Investigating monthly precipitation variability using a multiscale approach based on ensemble empirical mode decomposition | Paddy and Water Environment

 Identification of relationships between climate indices and long-term precipitation in South Korea using ensemble empirical mode decomposition - ScienceDirect,

The multi-timescale temporal patterns and dynamics of land surface temperature using Ensemble Empirical Mode Decomposition - ScienceDirect,

A time series processing tool to extract climate-driven interannual vegetation dynamics using Ensemble Empirical Mode Decomposition (EEMD) - ScienceDirect

L160 Explain why the noise helps

L161. All the operation can be done with the Python package PyEMD?

L 171. “Total number of extracted IMFs m^s” -> why “^s”?

L 174. “To address this, we implement an additional hyperparameter-tuning step that reinforces distinct frequency separation and minimizes overlap among IMFs“-> give type of procedure used in a few words ?

Eq 6: write the formula showing how it aggregates: To=…

Eq 6: what is “tau 1 m T0“? “tau 2 m T0“?

L 177 and L 181: give the values of the thresholds tau_1 and tau_2. How are they estimated?

L 181: “selecting τ1 and τ2 such that the IMFs most closely matching each frequency range are grouped together.“ -> give the formula to select the values

L 179: maybe change the order in the sentence: “In this study, we use the butter function available in scipy (Virtanen et al., 2020) to perform bandpass filtering of the original signal, isolating the frequencies associated with each timescale” -> “In this study, we perform bandpass filtering of the original signal, isolating the frequencies associated with each timescale using the butter function available in scipy (Virtanen et al., 2020).”

[ Appendix A

L 345: What is the relative change in frequency between consecutive IMFs?: there is a gab or no gap between IMFs?

L 355: Show the case of 2 IMFs: values of f0, f1, f2

L 355: Tuned through cross-validation? with which data?

L 356: yielded satisfactory results: which criteria is used?

In Algo 1: Recompute f(j)max -> how are the frequencies updated?

A schematic of the algorithm would help.]

Fig 1: how are regions selected? Add color bar or remove colors.

Fig 2: Difficult to understand which are the important information on the plots

Fig. 2: Why not compared directly the observation VS the corrected on the same plots? and the input VS corrected output on the same plots? and the Timescales VS Corrected Timescales on the same plot.

Fig 2: A schematic of the method would help understand the successive plots

L 186 “the nature of the biases can vary greatly depending on whether we are dealing with short-term fluctuations (e.g., biweekly scales) or longer-term patterns (e.g., seasonal or annual). “ -> indicate how it changes

1. 191” At the biweekly scale, signals often exhibit substantial variability and frequent extremes, yet show little in the way of stable temporal patterns that persist across years“ : reference ?

L 192- 193“Because a more complex regression approach is unlikely to provide significant benefits at this resolution, we use the QDM to correct these components“: reference?

L 202: Were other methods tested to confirm the hypothesis that QDM is the best here?

L 203 “At longer timescales (seasonal or annual), biases often manifest in more systematic patterns that persist across multiple years.” -> reference?

L 237: Here a schematic showing the successive steps would be very helpful

L 237: Was the QDM tested also on these timescale to confirm the hypothesis that the used method is better than the QDM on these timescales?

L 237: When is EEMD applied?

2.5 Visualization:

L 239: Give the numbers of the figures here -> is a sub section (2.5) needed just for 1 sentence?

Results

- Fig3: in the caption: explain what values are represented in the box VS lines VS dotes

- L 242: “we apply a spatial smoothing procedure to the bias corrected daily temperature fields” can you justify why?

- L 253: “Section 2.1.Figure 3“ need a space before “Figure”

- L 257: give the definition (and/or a reference) for the WD

- L.258: Fig 3 top: comment on why larger bias for some regions (S, N, MidWest) and larger uncertainties for SW, NW?

- Fig 3 bottom: why similar WD for all region although biases are bigger for some regions (top)? I would expect a larger WD for the regions with higher biases?

- Fig 4 and L273: with Northern and Midwest regions have larger biases for the GDM corrected datasets than for the not corrected datasets? -> should not be used then here?

- Figure 5: add letters for sub plots (also in other figures):

- Figure 5: difficult to see something. In particular in the top 2 plots: we cannot see the curves. “While QDM achieves performance comparable to EMDBC at the daily (training) scale,” -> how is this observed?

- Figure 5: in the legend add the “Reference datasets” to the “Livneh” legend. Change the Livneh curve to a dotted line.

- Figure 5: the biweekly plot is not commented in the caption

- Figure 6: explain what is plotted in the box plots (box, line, dotes) and in the violin plots (tail cutted? what is the black box and the white line?)

- Figure 6: not color-blind compatible?

- L. 275 “These results demonstrate that EMDBC successfully preserves bias-corrected signals over a broad range of temporal frequencies” -> but it is a specific dataset, is it representative of other regions and other periods?

- 3.2 “Over full domain” which domain here? temporal spatial? which domain was used previously?

- Figure 7: what should “Mid-century” violin plots be compared too? it is misleading to have them on the same plot at the historical data -> it should not be compared to it? Maybe bring the violins that should be compared closer to one another. E.g. 3 block: 1 historical bloc (Livneh + historical models) -> then a gap -> 1 block with 3 mid-century violins-> gap -> 1 bog with 3 Late-century violins

- L 285 “In each sub-region, the top panel compares the absolute temperature bias between the model projected and the observed series before and after correction with EMDBC and QDM, whereas the right panel shows the distribution of the average temperature” -> “the top panel”… “whereas the right panel” ? is it here “whereas the bottom panel”?

- Fig 8: CONUS is not defined?

- L 295: Fig 9 and Fig8 -> Fig 8 and Fig 9

- Fig 8 and Fig9. give letters to the subplots

- L 295: please comment each of the subplots or remove if not used in the text.

- Fig 8 and 9: why northern America has large biases (left column)?

Conclusion:

L303-304: add the spatial extent of the output on which it is applied, and the resolution.

L304: add “temporal” to “Temporal downscaled”

L305: add the years to the periods: “historical 19..-19.., mid-century 20..-20.. and late-century 20..-20..”

L312: “meteorological variables“ -> „atmospheric“  ?

Code and reproducibility: The zenodo repository contains only 1 script for 1 figure that is not one of the figures of the paper. It would be nice to have the scripts to compute plots of the paper. Could the repository be added to a public github page ? The link given is not public:  https://git.cels.anl.gov/jfeinstein/emdbc-paper (Feinstein, 2025). Thank you.