the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
The suitability of differentiable, learnable hydrologic models for ungauged regions and climate change impact assessment
Dapeng Feng
Hylke Beck
Kathryn Lawson
Abstract. Differentiable, learnable process-based hydrologic models (abbreviated as δ or delta models) with regionalized parameterization pipelines were recently shown to provide daily streamflow prediction performance that closely approach state-of-the-art long short-term memory (LSTM) deep networks. Meanwhile, δ models provide a full suite of diagnostic physical variables and guaranteed mass conservation. Due to their physical constraints, we hypothesize that they are suitable for making extrapolated predictions. Here, we ran experiments to test (1) their ability to extrapolate to regions far from streamflow gauges; and (2) their ability to make credible projections of long-term (decadal-scale) change trends. We evaluate the models based on daily hydrograph metrics (Nash-Sutcliffe model efficiency coefficient, etc.), as well as projected decadal streamflow trends. The results show that, for spatial interpolation (test in randomly sampled ungauged basins, or PUB), δ models have mixed comparisons with LSTM, presenting better trends for annual mean flow and high flow but slightly worse for low flow. For spatial extrapolation (test in regionally held out basins, or PUR, representing a highly data-scarce scenario), δ models’ advantages in mean and high flows are more prominent. In addition, an untrained variable, evapotranspiration, retained good seasonality even for extrapolated cases. δ models’ parameterization pipeline produces parameter fields that maintain remarkably stable spatial patterns even in highly data-scarce scenarios, which explains their robustness. Combined with their interpretability and ability to assimilate multi-source observations, δ models are strong candidates for regional and global scale hydrologic simulations for climate change impact assessment.
Dapeng Feng et al.
Status: closed
-
CC1: 'Comment on hess-2022-245', John Ding, 12 Aug 2022
An autoregressive process of the streamflow as a candidate model
The paper presents results from a model comparison of an LSTM vs. HBV and its two surface-runoff-storage variants called the delta models and having one or two time-dependent "dynamic parameters." Their Figure 3 for PUB (B for basins in Prediction for Ungauged Basins) and, especially, Figure 6 for PUR (R for regions) call into question a prevailing claim about the superiority of the LSTM in hydrology, Mai et al. (2022) being a latest.
To cover the spectrum/range of hydrologic models, the authors may want to include one from time series models, such as autogressive processes of (only) the streamflow.
I suggest the authors consider a simplest AR(2) model, a second-order autoregressive process of the form, e.g., Mizukami et al. (2021, SC1 by Ding therein):
Qsim[t+1]=2.0*Qobs[t]-Qobs[t-1].
This has been put forward as an alternate reference or baseline model to the observed mean flow one in the popular though rudimentary NSE (Nash-Sutcliffe efficiency) criterion. Azmi et al. (2021, SC1 by Ding & AC1 therein) showed this a good performance model.
I look forward to seeing an expansion of Figures 3 and 6 in a future study covering the AR(2).
References
Azmi, E., Ehret, U., Weijs, S. V., Ruddell, B. L., and Perdigão, R. A. P.: Technical note: “Bit by bit”: a practical and general approach for evaluating model computational complexity vs. model performance, Hydrol. Earth Syst. Sci., 25, 1103–1115, https://doi.org/10.5194/hess-25-1103-2021, 2021.
Mai, J., Shen, H., Tolson, B. A., Gaborit, É., Arsenault, R., Craig, J. R., Fortin, V., Fry, L. M., Gauch, M., Klotz, D., Kratzert, F., O'Brien, N., Princz, D. G., Rasiya Koya, S., Roy, T., Seglenieks, F., Shrestha, N. K., Temgoua, A. G. T., Vionnet, V., and Waddell, J. W.: The Great Lakes Runoff Intercomparison Project Phase 4: the Great Lakes (GRIP-GL), Hydrol. Earth Syst. Sci., 26, 3537–3572, https://doi.org/10.5194/hess-26-3537-2022, 2022.
Mizukami, N., Rakovec, O., Newman, A. J., Clark, M. P., Wood, A. W., Gupta, H. V., and Kumar, R.: On the choice of calibration metrics for “high-flow” estimation using hydrologic models, Hydrol. Earth Syst. Sci., 23, 2601–2614, https://doi.org/10.5194/hess-23-2601-2019, 2019.
Citation: https://doi.org/10.5194/hess-2022-245-CC1 -
AC7: 'Reply on CC1', Chaopeng Shen, 04 Dec 2022
Thanks a lot for the comments regarding autoregressive models. Since the main topic discussed in this paper is the prediction in ungauged regions which assume there are no observations in the target regions, we don’t think autoregressive models with observations at previous time steps as inputs are appropriate for the topic. Moreover, we have already compared the deep learning LSTM models with AR models for streamflow forecasting in our previous studies (please see Table 3 in Feng et al., 2020, and also Fang et al., 2017), which has shown deep learning models can largely outperform AR models for integrating historical observations.
Feng et al., 2020. https://doi.org/10.1029/2019WR026793
Fang et al., 2017. http://onlinelibrary.wiley.com/doi/10.1002/2017GL075619/full
Citation: https://doi.org/10.5194/hess-2022-245-AC7
-
AC7: 'Reply on CC1', Chaopeng Shen, 04 Dec 2022
-
AC1: 'Comment on hess-2022-245', Chaopeng Shen, 07 Oct 2022
Dear reviewers and readers
We have released our code, which has a script for this example in this paper here. Page 4 of the documentation describes how you can run the example for this paper.https://zenodo.org/record/7147450Please let us know if there are more questions.Citation: https://doi.org/10.5194/hess-2022-245-AC1 -
AC3: 'Reply on AC1', Chaopeng Shen, 24 Oct 2022
We have found a small bug for fresh downloads. We have fixed it. The URL to the new link is the following:
https://doi.org/10.5281/zenodo.7091334
This link is for the whole zenodo repo and is always up to date. btw, when looking at zenodo links, please check if there are updates.
Citation: https://doi.org/10.5194/hess-2022-245-AC3
-
AC3: 'Reply on AC1', Chaopeng Shen, 24 Oct 2022
-
RC1: 'Comment on hess-2022-245', Anonymous Referee #1, 24 Oct 2022
The paper proposes a novel hydrologic modeling approach taking advantage of the recent deep-learning techniques. It appears this approach is quite useful for ungaged basins. It is well written. The source code, however, is not very well structured and the example provided is not easy to follow. I have asked my ph.D. student who has multi-year's experience in Python to run the source code and repeat the example (https://zenodo.org/record/7147450), but he did not succeed. The error message he got is below. I'd suggest that the authors perform careful check themselves, and also ask a third-party to independently verify their code and example. I will ask my student to give it another try later on.
===========================================
Traceback (most recent call last):
File "dPLHBVrelease/hydroDL-dev/example/dPLHBV/traindPLHBV.py", line 96, in
camels.initcamels(
File "dPLHBVrelease/hydroDL-dev/example/dPLHBV/../../hydroDL/data/camels.py", line 549, in initcamels
calStatAll()
File "dPLHBVrelease/hydroDL-dev/example/dPLHBV/../../hydroDL/data/camels.py", line 388, in calStatAll
x = readForcing(idLst, forcingLst)
TypeError: readForcing() missing 2 required positional arguments: 'fordata' and 'nt'
Citation: https://doi.org/10.5194/hess-2022-245-RC1 -
AC2: 'Reply on RC1', Chaopeng Shen, 24 Oct 2022
Sorry about this. It just came to our attention that there was a bug for a fresh download. We updated the code release and at the Zedono release you should see the following information about this bug fix. Could you please give it a try again?
==================================
This release contains the codes and related data to train models with differentiable parameter learning (dPL) applied to HBV backbone as shown in these papers below. Please read the instruction file and this BUG FIX FILE (https://bit.ly/3TOKmqK) for running the released codes.
=== if you go to this file, you will see the following information
Here we summarize the small bugs you should fix before running the released codes. We will also update a new version soon with several bugs solved together. Feel free to contact duf328@psu.edu or cshen@engr.psu.edu for any question.
- Please comment out or delete line 499 to 503 in this file ‘dPLHBVrelease/hydroDL-dev/hydroDL/data/camels.py’ as below:
# statFile = os.path.join(dirDB, 'Statistics_basinnorm.json')
# if not os.path.isfile(statFile):
# calStatAll()
# with open(statFile, 'r') as fp:
# statDict = json.load(fp)
Otherwise, you may have a TypeError: readForcing() missing 2 required positional arguments: 'fordata' and 'nt'
Citation: https://doi.org/10.5194/hess-2022-245-AC2 -
AC4: 'Reply on RC1', Chaopeng Shen, 24 Oct 2022
Oh. When looking at zenodo, please check for updates on the side. Actually, the link below always points to the latest code. Please use this link:
https://doi.org/10.5281/zenodo.7091334
Citation: https://doi.org/10.5194/hess-2022-245-AC4 -
RC2: 'Reply on AC4', Anonymous Referee #1, 24 Oct 2022
My student gave it another try, and it worked this time.
Congratulation to the authors on the excellent work!
Citation: https://doi.org/10.5194/hess-2022-245-RC2 -
AC5: 'Reply on RC2', Chaopeng Shen, 25 Oct 2022
Thank you (and your student) for spending effort on it!
I am not sure if the editor would count your review as complete (unless the editor reads our whole conversation), so any additional comments you might have would be appreciated!
Citation: https://doi.org/10.5194/hess-2022-245-AC5
-
AC5: 'Reply on RC2', Chaopeng Shen, 25 Oct 2022
-
RC2: 'Reply on AC4', Anonymous Referee #1, 24 Oct 2022
-
AC2: 'Reply on RC1', Chaopeng Shen, 24 Oct 2022
-
RC3: 'Comment on hess-2022-245', Anonymous Referee #2, 11 Nov 2022
This study analyzes the ability of deep learning, and physics-informed learning models to make predictions in regions that are outside of the training set. This is an interesting problem, particularly in testing the limits of learning-based models to make predictions in conditions that are outside of the training set. This paper is a valuable contribution to the hydrological modeling literature, and would like to see it published. While there are some wording issues (listed below), and some issues (also listed below) that I would like to see addressed. In particular, there are a couple of points on the training procedure for the LSTM, which limit its performance, ensembling randomly initialized models and including multiple precipitation products are known to boost the LSTM performance in other experiments, it would be good to check if that would have the same result for ungauged regions. In terms of presenting results, since this paper is about region specific (as in regions held out of the training set) models, I would hope to see region specific results, which are mentioned in the text (in terms of model parameters), but results are not quantified nor plotted.
Line 18: Is “PUR” an acronym for “Prediction in Ungauged Region”, or is it a general term for “regionally held out basins”?
Lines 148-149: Can you please clarify the training periods for all the models. You mention that “Each training instance had two years’ worth of meteorological forcings, but the first year was used as a warmup period so the loss was only calculated on the subsequent one year of simulation”, this reads to me that your models were trained on just on year of data. This isn’t the case, is it? I imaging that, in the training process you cycle through many more years, you just train the model with batches of these individual year? Oh. I read on line 245 that “we used only 10 years of training period”. Okay, can you maybe re-word this?
Line 169: Why was Maurer selected? Especially since many studies suggest Daymet is the more informative forcing, including Feng et al., 2022? It is also the case that using a combination of the three forcing products from CAMELS results in improved model performance (Kratzert et al., 2021), can you expand on your decision in the context of using multiple precipitation sources?
There should be a direct link to the analysis done for this paper. I browsed around the HydroDL github repository, and it was not clear to me where I should look for the code that was used for these particular experiments. NEVERMIND ABOUT THIS. I NOW SEE THE AUTHOR'S RESONSE TO ANOTHER REVIEWER.
The issue of ungauged regions is not particularly relevant to the United States (U.S.), but I do see the value of using the U.S. gauged basins for this experiment. Other groups (Le et al., 2022) have done ungauged region experiments outside the U.S., and this could be a bit more compelling. Perhaps this is worth some discussion in the paper?
Line 245: You mention that there was no ensembling of models trained from random initialization. But then go on to say that you used the same settings as Kratzert et al., 2019, but they used ensembles of 10 models trained with random initializations. From their paper:
“Because of this, the LSTM-type models give better predictions when used as an ensemble. It is not necessarily the case that if one particular LSTM model performs poorly in one catch-ment that a different LSTM trained one exactly the same data will also perform poorly.” This is generally an accepted practice when using deep learning models. Can you explain further why you decided not to use model ensembles?Line 308: Breaking down Figure 6 by region would add a lot more value to the results. This would be super valuable for understanding some of the regional trends in model performance in general, particularly in Regions 4 and 5.
REFERENCES:
Le, M.-H., Kim, H., Adam, S., Do, H. X., Beling, P., and Lakshmi, V.: Streamflow Estimation in Ungauged Regions using Machine Learning: Quantifying Uncertainties in Geographic Extrapolation, Hydrol. Earth Syst. Sci. Discuss. [preprint], https://doi.org/10.5194/hess-2022-320, in review, 2022.
Kratzert, F., Klotz, D., Herrnegger, M., Sampson, A. K., Hochreiter, S., & Nearing, G. S. (2019). Toward improved predictions 540 in ungauged basins: Exploiting the power of machine learning. Water Resources Research, 55(12), 11344–11354. https://doi.org/10/gg4ck8
Kratzert et al., 2021. A note on leveraging synergy in multiple meteorological data sets with deep learning for rainfall–runoff modeling. https://doi.org/10.5194/hess-25-2685-2021
Citation: https://doi.org/10.5194/hess-2022-245-RC3 - AC6: 'Reply on RC3', Chaopeng Shen, 04 Dec 2022
Status: closed
-
CC1: 'Comment on hess-2022-245', John Ding, 12 Aug 2022
An autoregressive process of the streamflow as a candidate model
The paper presents results from a model comparison of an LSTM vs. HBV and its two surface-runoff-storage variants called the delta models and having one or two time-dependent "dynamic parameters." Their Figure 3 for PUB (B for basins in Prediction for Ungauged Basins) and, especially, Figure 6 for PUR (R for regions) call into question a prevailing claim about the superiority of the LSTM in hydrology, Mai et al. (2022) being a latest.
To cover the spectrum/range of hydrologic models, the authors may want to include one from time series models, such as autogressive processes of (only) the streamflow.
I suggest the authors consider a simplest AR(2) model, a second-order autoregressive process of the form, e.g., Mizukami et al. (2021, SC1 by Ding therein):
Qsim[t+1]=2.0*Qobs[t]-Qobs[t-1].
This has been put forward as an alternate reference or baseline model to the observed mean flow one in the popular though rudimentary NSE (Nash-Sutcliffe efficiency) criterion. Azmi et al. (2021, SC1 by Ding & AC1 therein) showed this a good performance model.
I look forward to seeing an expansion of Figures 3 and 6 in a future study covering the AR(2).
References
Azmi, E., Ehret, U., Weijs, S. V., Ruddell, B. L., and Perdigão, R. A. P.: Technical note: “Bit by bit”: a practical and general approach for evaluating model computational complexity vs. model performance, Hydrol. Earth Syst. Sci., 25, 1103–1115, https://doi.org/10.5194/hess-25-1103-2021, 2021.
Mai, J., Shen, H., Tolson, B. A., Gaborit, É., Arsenault, R., Craig, J. R., Fortin, V., Fry, L. M., Gauch, M., Klotz, D., Kratzert, F., O'Brien, N., Princz, D. G., Rasiya Koya, S., Roy, T., Seglenieks, F., Shrestha, N. K., Temgoua, A. G. T., Vionnet, V., and Waddell, J. W.: The Great Lakes Runoff Intercomparison Project Phase 4: the Great Lakes (GRIP-GL), Hydrol. Earth Syst. Sci., 26, 3537–3572, https://doi.org/10.5194/hess-26-3537-2022, 2022.
Mizukami, N., Rakovec, O., Newman, A. J., Clark, M. P., Wood, A. W., Gupta, H. V., and Kumar, R.: On the choice of calibration metrics for “high-flow” estimation using hydrologic models, Hydrol. Earth Syst. Sci., 23, 2601–2614, https://doi.org/10.5194/hess-23-2601-2019, 2019.
Citation: https://doi.org/10.5194/hess-2022-245-CC1 -
AC7: 'Reply on CC1', Chaopeng Shen, 04 Dec 2022
Thanks a lot for the comments regarding autoregressive models. Since the main topic discussed in this paper is the prediction in ungauged regions which assume there are no observations in the target regions, we don’t think autoregressive models with observations at previous time steps as inputs are appropriate for the topic. Moreover, we have already compared the deep learning LSTM models with AR models for streamflow forecasting in our previous studies (please see Table 3 in Feng et al., 2020, and also Fang et al., 2017), which has shown deep learning models can largely outperform AR models for integrating historical observations.
Feng et al., 2020. https://doi.org/10.1029/2019WR026793
Fang et al., 2017. http://onlinelibrary.wiley.com/doi/10.1002/2017GL075619/full
Citation: https://doi.org/10.5194/hess-2022-245-AC7
-
AC7: 'Reply on CC1', Chaopeng Shen, 04 Dec 2022
-
AC1: 'Comment on hess-2022-245', Chaopeng Shen, 07 Oct 2022
Dear reviewers and readers
We have released our code, which has a script for this example in this paper here. Page 4 of the documentation describes how you can run the example for this paper.https://zenodo.org/record/7147450Please let us know if there are more questions.Citation: https://doi.org/10.5194/hess-2022-245-AC1 -
AC3: 'Reply on AC1', Chaopeng Shen, 24 Oct 2022
We have found a small bug for fresh downloads. We have fixed it. The URL to the new link is the following:
https://doi.org/10.5281/zenodo.7091334
This link is for the whole zenodo repo and is always up to date. btw, when looking at zenodo links, please check if there are updates.
Citation: https://doi.org/10.5194/hess-2022-245-AC3
-
AC3: 'Reply on AC1', Chaopeng Shen, 24 Oct 2022
-
RC1: 'Comment on hess-2022-245', Anonymous Referee #1, 24 Oct 2022
The paper proposes a novel hydrologic modeling approach taking advantage of the recent deep-learning techniques. It appears this approach is quite useful for ungaged basins. It is well written. The source code, however, is not very well structured and the example provided is not easy to follow. I have asked my ph.D. student who has multi-year's experience in Python to run the source code and repeat the example (https://zenodo.org/record/7147450), but he did not succeed. The error message he got is below. I'd suggest that the authors perform careful check themselves, and also ask a third-party to independently verify their code and example. I will ask my student to give it another try later on.
===========================================
Traceback (most recent call last):
File "dPLHBVrelease/hydroDL-dev/example/dPLHBV/traindPLHBV.py", line 96, in
camels.initcamels(
File "dPLHBVrelease/hydroDL-dev/example/dPLHBV/../../hydroDL/data/camels.py", line 549, in initcamels
calStatAll()
File "dPLHBVrelease/hydroDL-dev/example/dPLHBV/../../hydroDL/data/camels.py", line 388, in calStatAll
x = readForcing(idLst, forcingLst)
TypeError: readForcing() missing 2 required positional arguments: 'fordata' and 'nt'
Citation: https://doi.org/10.5194/hess-2022-245-RC1 -
AC2: 'Reply on RC1', Chaopeng Shen, 24 Oct 2022
Sorry about this. It just came to our attention that there was a bug for a fresh download. We updated the code release and at the Zedono release you should see the following information about this bug fix. Could you please give it a try again?
==================================
This release contains the codes and related data to train models with differentiable parameter learning (dPL) applied to HBV backbone as shown in these papers below. Please read the instruction file and this BUG FIX FILE (https://bit.ly/3TOKmqK) for running the released codes.
=== if you go to this file, you will see the following information
Here we summarize the small bugs you should fix before running the released codes. We will also update a new version soon with several bugs solved together. Feel free to contact duf328@psu.edu or cshen@engr.psu.edu for any question.
- Please comment out or delete line 499 to 503 in this file ‘dPLHBVrelease/hydroDL-dev/hydroDL/data/camels.py’ as below:
# statFile = os.path.join(dirDB, 'Statistics_basinnorm.json')
# if not os.path.isfile(statFile):
# calStatAll()
# with open(statFile, 'r') as fp:
# statDict = json.load(fp)
Otherwise, you may have a TypeError: readForcing() missing 2 required positional arguments: 'fordata' and 'nt'
Citation: https://doi.org/10.5194/hess-2022-245-AC2 -
AC4: 'Reply on RC1', Chaopeng Shen, 24 Oct 2022
Oh. When looking at zenodo, please check for updates on the side. Actually, the link below always points to the latest code. Please use this link:
https://doi.org/10.5281/zenodo.7091334
Citation: https://doi.org/10.5194/hess-2022-245-AC4 -
RC2: 'Reply on AC4', Anonymous Referee #1, 24 Oct 2022
My student gave it another try, and it worked this time.
Congratulation to the authors on the excellent work!
Citation: https://doi.org/10.5194/hess-2022-245-RC2 -
AC5: 'Reply on RC2', Chaopeng Shen, 25 Oct 2022
Thank you (and your student) for spending effort on it!
I am not sure if the editor would count your review as complete (unless the editor reads our whole conversation), so any additional comments you might have would be appreciated!
Citation: https://doi.org/10.5194/hess-2022-245-AC5
-
AC5: 'Reply on RC2', Chaopeng Shen, 25 Oct 2022
-
RC2: 'Reply on AC4', Anonymous Referee #1, 24 Oct 2022
-
AC2: 'Reply on RC1', Chaopeng Shen, 24 Oct 2022
-
RC3: 'Comment on hess-2022-245', Anonymous Referee #2, 11 Nov 2022
This study analyzes the ability of deep learning, and physics-informed learning models to make predictions in regions that are outside of the training set. This is an interesting problem, particularly in testing the limits of learning-based models to make predictions in conditions that are outside of the training set. This paper is a valuable contribution to the hydrological modeling literature, and would like to see it published. While there are some wording issues (listed below), and some issues (also listed below) that I would like to see addressed. In particular, there are a couple of points on the training procedure for the LSTM, which limit its performance, ensembling randomly initialized models and including multiple precipitation products are known to boost the LSTM performance in other experiments, it would be good to check if that would have the same result for ungauged regions. In terms of presenting results, since this paper is about region specific (as in regions held out of the training set) models, I would hope to see region specific results, which are mentioned in the text (in terms of model parameters), but results are not quantified nor plotted.
Line 18: Is “PUR” an acronym for “Prediction in Ungauged Region”, or is it a general term for “regionally held out basins”?
Lines 148-149: Can you please clarify the training periods for all the models. You mention that “Each training instance had two years’ worth of meteorological forcings, but the first year was used as a warmup period so the loss was only calculated on the subsequent one year of simulation”, this reads to me that your models were trained on just on year of data. This isn’t the case, is it? I imaging that, in the training process you cycle through many more years, you just train the model with batches of these individual year? Oh. I read on line 245 that “we used only 10 years of training period”. Okay, can you maybe re-word this?
Line 169: Why was Maurer selected? Especially since many studies suggest Daymet is the more informative forcing, including Feng et al., 2022? It is also the case that using a combination of the three forcing products from CAMELS results in improved model performance (Kratzert et al., 2021), can you expand on your decision in the context of using multiple precipitation sources?
There should be a direct link to the analysis done for this paper. I browsed around the HydroDL github repository, and it was not clear to me where I should look for the code that was used for these particular experiments. NEVERMIND ABOUT THIS. I NOW SEE THE AUTHOR'S RESONSE TO ANOTHER REVIEWER.
The issue of ungauged regions is not particularly relevant to the United States (U.S.), but I do see the value of using the U.S. gauged basins for this experiment. Other groups (Le et al., 2022) have done ungauged region experiments outside the U.S., and this could be a bit more compelling. Perhaps this is worth some discussion in the paper?
Line 245: You mention that there was no ensembling of models trained from random initialization. But then go on to say that you used the same settings as Kratzert et al., 2019, but they used ensembles of 10 models trained with random initializations. From their paper:
“Because of this, the LSTM-type models give better predictions when used as an ensemble. It is not necessarily the case that if one particular LSTM model performs poorly in one catch-ment that a different LSTM trained one exactly the same data will also perform poorly.” This is generally an accepted practice when using deep learning models. Can you explain further why you decided not to use model ensembles?Line 308: Breaking down Figure 6 by region would add a lot more value to the results. This would be super valuable for understanding some of the regional trends in model performance in general, particularly in Regions 4 and 5.
REFERENCES:
Le, M.-H., Kim, H., Adam, S., Do, H. X., Beling, P., and Lakshmi, V.: Streamflow Estimation in Ungauged Regions using Machine Learning: Quantifying Uncertainties in Geographic Extrapolation, Hydrol. Earth Syst. Sci. Discuss. [preprint], https://doi.org/10.5194/hess-2022-320, in review, 2022.
Kratzert, F., Klotz, D., Herrnegger, M., Sampson, A. K., Hochreiter, S., & Nearing, G. S. (2019). Toward improved predictions 540 in ungauged basins: Exploiting the power of machine learning. Water Resources Research, 55(12), 11344–11354. https://doi.org/10/gg4ck8
Kratzert et al., 2021. A note on leveraging synergy in multiple meteorological data sets with deep learning for rainfall–runoff modeling. https://doi.org/10.5194/hess-25-2685-2021
Citation: https://doi.org/10.5194/hess-2022-245-RC3 - AC6: 'Reply on RC3', Chaopeng Shen, 04 Dec 2022
Dapeng Feng et al.
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