the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
DAR-type model based on "long memory-threshold" structure: a competitor for daily streamflow prediction under changing environment
Abstract. The non-stationarity, non-linearity, and time-varying fluctuations of streamflow have increased with changes in the environment, challenging accurate streamflow prediction. Furthermore, the overlook of long-term memory features could lead to biases in model parameter estimation and testing of time series properties. The classical linear Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (AR-GARCH) model has a narrow parameter range, and the moment conditional requirements for parameter estimation are relatively strict, limiting its applicability and prediction accuracy in modelling and predicting daily streamflow. Under the premise of long-term memory, a dual-threshold double autoregressive (DTDAR) model is proposed to capture the non-linear patterns in streamflow series. Using 15 hydrological stations in the Yellow River basin in China as an example, DAR models are compared with AR-GARCH models to assess their applicability and predictive ability. The results indicate that the DAR-type models have a stronger predictive ability for daily streamflow than the AR-GARCH-type models. The threshold models (DTDAR, TAR-GARCH) convert non-linear transformations into several linear problems, improving the prediction accuracy of single linear structural models (DAR and FDAR, AR-GARCH and FAR-HARCH), among which the R2 value is improved by 29.15 % and 15.06 %, 25.53 % and 15.53 %, and the NSE value is increased by 0.29 and 0.16, 0.24 and 0.15. Compared to the normal distribution, the student's t distribution for residuals is a better choice for predicting daily streamflow time series in the study area. This study enriches the stochastic hydrological models and improves the accuracy of streamflow prediction.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-1305', Anonymous Referee #1, 09 Jun 2025
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AC1: 'Reply on RC1', Gengxi Zhang, 15 Jul 2025
Dear reviewer,
We express our great appreciation for your constructive comments on improving the manuscript. We have fully addressed all of the comments in the revised manuscript. Please see the response details in the attached file.
Sincerely, Gengxi Zhang
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AC1: 'Reply on RC1', Gengxi Zhang, 15 Jul 2025
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RC2: 'Comment on egusphere-2025-1305', Anonymous Referee #2, 26 Jun 2025
Summary:
This manuscript proposes an innovative modelling approach - the dual-threshold double autoregressive (DTDAR) model - designed to improve the prediction of daily streamflow under non-stationarity, long memory, and non-linearity in the field in the field of hydrology. By integrating fractional differencing with a threshold-based structure in both the first- and second-order moments, the authors develop a long memory-threshold framework (FDTDAR) that is shown to outperform conventional models (AR-GARCH, TAR-GARCH) at multiple stations across the Yellow River Basin.
General remarks:
1. The manuscript is well structured, comprehensive in analysis, and the methodology is methodically laid out. The proposed approach makes a meaningful contribution to the field of stochastic hydrological modelling and represents a promising alternative to existing linear and GARCH-based models. However, several aspects require clarification or revision before the manuscript can be recommended for publication.
2. While the DTDAR/FDTDAR model is a novel approach, it is structurally complex, with numerous parameters and thresholds. The paper would benefit from a clearer explanation of how parameter identifiability, estimation convergence, and computational burden are handled. Practitioners will benefit from a discussion on model tractability and software implementation.
3. The manuscript focuses primarily on comparisons with AR-GARCH and TAR-GARCH models. While these are relevant, the absence of modern nonlinear or machine learning models (e.g., LSTM, hybrid deep learning models) in the comparison set limits the extent to which the results can be considered broadly applicable. Even if not implemented, a discussion acknowledging this limitation and the rationale for focusing on DAR-type models would be appropriate.
4. While the use of average interval width (AIW) and containing ratio (CR) are appropriate to assess the prediction uncertainty, the manuscript lacks detail on how prediction intervals were constructed. Clarification on whether these are based on analytical variance, bootstrapping, or Monte Carlo simulations is necessary.
5. The analysis clearly shows that the Student’s t-distribution improves predictive performance over the Gaussian assumption. The authors are encouraged to provide more discussion on how degrees of freedom were selected, and whether any skewed or generalized t-distributions were considered or could be more appropriate for heavy-tailed hydrological data.
Apart from these general comments, the authors should also take into consideration a few minor points.
Minor remarks:
1. Terms such as FDTDAR-n and FDTDAR-t should be introduced earlier and used consistently.
2. Several grammatical and syntactic issues are present throughout the manuscript. A round of professional language editing is recommended.
3. Recent advances in time series forecasting using deep learning could be briefly referenced to contextualize the DTDAR approach.
Citation: https://doi.org/10.5194/egusphere-2025-1305-RC2 -
AC2: 'Reply on RC2', Gengxi Zhang, 16 Jul 2025
Dear reviewer,
We express our great appreciation for your constructive comments on improving the manuscript. We have fully addressed all of the comments in the revised manuscript. Please see the response details in the attached file.
Sincerely, Gengxi Zhang
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AC2: 'Reply on RC2', Gengxi Zhang, 16 Jul 2025
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I have read the paper, “DAR-type model based on "long memory-threshold" structure: a competitor for daily streamflow prediction under changing environment”. Overall, the paper aims to develop and test a stochastic model for simulating daily streamflow, taking care of the nonlinearity, nonstationarity, and most importantly, the long-term memory of the streamflow. This is one of the few papers in the field of stochastic hydrology that has devoted greater attention to reproducing the long-term memory component of streamflow, which is really appreciated.
My major observation is that the paper is not sufficiently motivated, and the flow of the arguments in the paper is not smooth. For example, there are many times in the paper when an arbitrary number of statistical tests are being performed without any prior reasoning. The structure of section 2.3 does not clearly give enough reason why the current modeling paradigm is failing to reproduce the nonlinear, non-stationary models that fail to reproduce the long-term memory properties of the streamflow. Further, this section does not provide enough evidence to go with the FDTDAR model. There are many figures in the paper which is more suitable in the supplementary file rather than the main manuscript.
The following comments need to be addressed to improve the structure of the paper and the overall motivation behind this work.
Major comment:
Other comments: