the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
A Differentiable Framework for Global Circulation Model Precipitation Bias Correction
Abstract. Systematic biases in General Circulation Model (GCM) outputs limit their direct applicability in regional planning, making bias correction a technically demanding but necessary step for both short-term and long-term impact assessment. Correcting precipitation is particularly challenging due to its non-Gaussian distribution, intermittent nature, and heavy-tailed extremes. However, traditional statistical bias-correction methods have limited ability to learn systematic patterns from large datasets or generalize to new locations. While machine learning (ML) provides greater flexibility, it can produce unpredictable and difficult-to-interpret results, limiting generalization across GCMs and locations. In this study, we propose a differentiable bias-adjustment framework called δCLIMBA, or dCLIMBA, that learns a spatiotemporally adaptive parametric bias-adjustment procedure, rather than corrected precipitation directly, between historical CMIP6 model outputs and a gridded observation-based dataset, Livneh. Results demonstrate that the proposed method corrects the magnitude and distribution of extreme precipitation with particularly strong performance in the upper tail. The quantile distribution of precipitation was well reproduced across diverse U.S. cities, and spatial patterns were comparable to those from the widely used LOCA2 statistical downscaling product. In addition, the framework showed partial future trend preservation and promising attenuation of marginal biases in unseen regions. This work presents a modular and efficient bias-correction approach. The differentiable approach provides an easy-to-use option for connecting atmospheric-model outputs to on-the-ground impacts.
Status: final response (author comments only)
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CEC1: 'Comment on egusphere-2026-2546 - No compliance with the policy of the journal', Juan Antonio Añel, 21 Jun 2026
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CC1: 'Reply on CEC1', Kamlesh Sawadekar, 27 Jun 2026
Hello Dr. Añel,
I am posting here the doi of the zenodo deposit containing the code and processed data required to reproduce the results in the paper.
https://doi.org/10.5281/zenodo.20839571
We appreciate your patience on this matter. Let us know if you need anything else.
Thank you,
Kamlesh Sawadekar
Citation: https://doi.org/10.5194/egusphere-2026-2546-CC1
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CC1: 'Reply on CEC1', Kamlesh Sawadekar, 27 Jun 2026
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RC1: 'Comment on egusphere-2026-2546', Anonymous Referee #1, 23 Aug 2026
I found this manuscript to be technically promising and generally useful. I also think it is potentially valuable as it attempts to offer "an easy-to-use option for connecting atmospheric-model outputs to on-the-ground impacts." I broadly support publication but I first invite the authors to entertain the critiques below.
My general concern is about the role and importance of differentiability in this work.
The neural architecture in this manuscript is differentiable in that it allows gradients to propagate back and forth. The manuscript though appears to suggest that the underlying model is a physics model that was made differentiable. The neural architecture here isn't coupled to a process-based physics model or constrained by a physics scheme, right?
I do mean this as diminishing the potential value of the method. The authors should clarify what scientific or practical capability is enabled specifically by differentiability. In addition, the authors should address how this approach would differ from adapting an established bias-correction method into a differentiable parameterized form and optimizing it with comparable losses? Does gradient-based, end-to-end optimization provide demonstrated benefits in performance, efficiency, interpretability, transferability, or coupling to downstream models Relatedly, ablation studies are needed to identify which design choices drive the reported gains. Without standard ablation studies, it is hard to take some of the claims made in the manuscript at face value.
Citation: https://doi.org/10.5194/egusphere-2026-2546-RC1 -
CC2: 'Reply on RC1', Kamlesh Sawadekar, 07 Sep 2026
We thank the reviewer for their positive assessment of the manuscript and for raising this important question about the role of differentiability. We agree that the original did not distinguish clearly enough between (i) a fully coupled differentiable physics-machine-learning model and (ii) the differentiable, parameterized bias adjustment framework introduced here. We will revise the manuscript to make this distinction explicit.
The current implementation of δCLIMBA is not coupled to a process-based physical model, nor does it modify or feed information back into the parent GCM. Rather, dCLIMBA is a bias adjustment model in which the neural network predicts parameters for the prescribed transformation that maps raw GCM precipitation to bias-adjusted precipitation. Differentiability in this work refers specifically to the fact that the full computational chain, i.e., from the GCM precipitation and static attributes, through the temporal and spatial encoders, to the parameters of the monotonic transformation and the composite loss is differentiable with respect to the trainable neural-network parameters. This permits gradients of the quantile, wet-day, and spatial-correlation losses to be propagated through the transformation and used to optimize the parameter-generating network end to end.
To clarify the practical role of differentiability, it is useful to distinguish the contributions of the mapping, neural encoders, and optimization framework. The prescribed monotonic softplus-based mapping provides the structural constraint: it enforces non-negativity and monotonicity and makes the adjustment mechanism more transparent than direct black-box prediction of corrected precipitation. The temporal and spatial encoders provide context-dependent parameterization of this mapping using GCM behavior, neighboring-grid information, and static attributes, which can support adaptation across heterogeneous locations. Differentiability then enables these components to be trained jointly: gradients from the quantile, wet-day, and spatial-correlation losses propagate through the mapping to optimize the encoder-generated parameters end to end. Thus, differentiability is the optimization mechanism, rather than the source of the mapping’s transparency or constraints. We will revise the manuscript to make this distinction explicit.
The reviewer is also correct that established bias-correction approaches could, in principle, be reformulated as differentiable parameterized operators and optimized using comparable objectives. However, traditional empirical quantile-mapping methods often contain nondifferentiable operations such as sorting, lookup, interpolation, or hard thresholds, so differentiable reformulations would generally require smooth approximations or alternative parameterizations.. Adapting such methods would therefore require smooth or differentiable approximations, and the resulting method would no longer be exactly identical to its conventional implementation. We will clarify that δCLIMBA should be viewed as one differentiable parameterization within a broader class of potentially differentiable bias-adjustment methods, rather than as a claim that conventional methods cannot be adapted in this way.
The framework also provides a pathway (not a demonstrated capability in the present manuscript) for future coupling with differentiable downstream models or physical schemes. For example, a differentiable hydrological model could be appended downstream of the bias-adjustment module, allowing an impact-relevant loss, such as streamflow error or water-balance error, to inform the bias-adjustment parameters through backpropagation. We will revise the discussion to clearly identify these as future opportunities and not as features evaluated in the current work.
In response to the request for ablation studies, we agree that these are needed to identify the contributions of the principal architectural choices. We will add ablation experiments in the Supplementary Material that evaluate:
- dCLIMBA without static spatial attributes
- dCLIMBA using only the temporal encoder
- a direct-output neural baseline using the same or comparable encoders and losses but predicting corrected precipitation directly rather than parameters of the prescribed transformation
Citation: https://doi.org/10.5194/egusphere-2026-2546-CC2 -
AC1: 'Reply on RC1', Chaopeng Shen, 09 Sep 2026
Dear Reviewer,
Thank you for your comment. The CC2 posted by Kamlesh Sawadekar is indeed our author's reply to you. I would just add that a single NN can be trained over many data points in space, creating the potential for widespread spatial application in the future, although this is not the focus of this paper.
Citation: https://doi.org/10.5194/egusphere-2026-2546-AC1
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CC2: 'Reply on RC1', Kamlesh Sawadekar, 07 Sep 2026
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RC2: 'Comment on egusphere-2026-2546', Anonymous Referee #2, 31 Aug 2026
The manuscript by Sawadekar et al. describes a machine-learning-based
bias-correction method for GCM-based precipitation. While classical
quantile mapping tries to correct the statistical distribution of the
quantity of interest, precipitation, on a point-by-point basis,
disregarding spatial correlations. Several newer methods, cited here,
go one step beyond that by explicitly taking spatial correlations and
physically relevant covariates (for precipitation eg the structure of
the underlying topgraphy) into account. But being based on machine
learning they are difficult to interpret and can violate physical
constraints, e.g. water mass balance. The method presented here does
one additional step, by using the mashine learning not to learn
precipitation bias correction directly, but to learn PARAMETERS for a
mapping between GCM-produced and bias-corrected precipitation fields
with a pre-defined mathematical structure. While the first step,
learning the parameters using machine learning, is still to some
extent a black box, teh second step is transparent, and can be made in
such a way that physical constraints, like mass conservation, are
taken into account explicitly.Overall I find this a promising method and support publication. I only
have some little criticism on the way it is presented.Firstly, I agree with the first reviewer, that the authors should make
it clear to the reader what they mean exactly by differentiability
(i.e. explain differentiable to which variables). Although this can be
inferred from equations (2) an explicit statement would be
helpful. Second I also agree that the authors should explain what the
practical advantage is of have a differentiable bias correction,
rather than one that does not have this property.Secondly, there are a number of typos in the mathematical equatons and
their explanations in the text. Here are the ones that I saw:In equation (2), on the right-hand side, the small 'x' should be
capital 'X' I believe. Also the upper bound on the summation should be
capital 'Z', not 'z'.Three lines below eq. (2), the italicized 'It' should be 'I with subscript t'
First line below eq. (6): The sentence 'is the sigmoid function'
should read 'sigma is the sigmoid function'. The next sentence as well
should start with 'alpha'. Both, of course as greek symbols. The same
again in the second line below eq. (8): The greek 'epsilon' has
vanished.Minor comments
--------------Page 1, fourth line of the introduction: The manuscript uses output
from CMIP6, so would it not be better to cite a more recent IPCC
report than IPCC AR4?Page 2, end of second paragraph (PS: line numbers would have been
great): 'adjusting bias .. can distort the simulation': This can
happen only if the bias corection is used directly within the coupled
climate model, so that there is a feedback of the bias-corrected
fields to the GCM. Is this the purpose in the end? This was not clear
to me. In all other parts, the aim is stated 'flexible data-driven
bias correction of GCM outputs' and this wahat is done in the
manuscript.Page 5, second paragraph: While the term 'loss function' is probably
standard in the ML literature, it would be good to clarify that it is
the function that the learning process is set to minimize. In the data
assimilation literature this would be called a 'cost function'
instead.Citation: https://doi.org/10.5194/egusphere-2026-2546-RC2 -
CC3: 'Reply on RC2', Kamlesh Sawadekar, 07 Sep 2026
We thank the reviewer for the encouraging assessment of our framework and for the careful, constructive recommendations. We appreciate the reviewer’s clear articulation of the central idea of our approach: neural networks generate parameters for a prescribed bias-adjustment mapping, rather than directly predicting bias-corrected precipitation. As the reviewer notes, this separation retains a structured and transparent adjustment step while allowing the parameterization to depend on spatiotemporal context and relevant static attributes.
We will revise the manuscript to clarify the meaning and practical role of differentiability in the framework, including which components are differentiable with respect to the trainable parameters. We will also clarify the distinct roles of the prescribed mapping, neural encoders, and end-to-end gradient-based optimization.
We thank the reviewer for identifying the typographical and notation issues in the equations and accompanying text. We will carefully correct these issues, including the notation in Eqs. (2), (6), and (8). We will also incorporate the requested revisions regarding the IPCC citation, the wording on possible distortion of GCM simulations, and a clearer definition of the loss function as the objective minimized during training.
Citation: https://doi.org/10.5194/egusphere-2026-2546-CC3 -
AC2: 'Reply on RC2', Chaopeng Shen, 09 Sep 2026
Dear Reviewer #2,
The CC3 posted by Kamlesh Sawadekar to you is indeed the author's response to you. Thank you for your comment.
Citation: https://doi.org/10.5194/egusphere-2026-2546-AC2
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CC3: 'Reply on RC2', Kamlesh Sawadekar, 07 Sep 2026
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Geosci. Model Dev. Executive Editor