Multi-model integrated error correction for streamflow simulation based on Bayesian model averaging and dynamic system response curve

Review of Recent Developments in Hydrologic Forecast Merging Techniques

“…The simple arithmetic averaging distributes equal weights among hydrological models, mirroring the theoretical approach of EWA. EWA: Equal-weighted average of individual forecast [39] Mean: Merging without assigning any specific weight [39] Trimmed Mean: Trim outlier before averaging [4] Weighted Granger and Newbold Methods: Weight estimation with (type 1) or without (type 2) correlations consideration [41] WAM-OLS: Weight estimation through multiple linear regression [42] RTMOCM: Linear Transfer Function Model integration [43] RSWM: Runoff-scale weighting with flow stages [44] WAM-MOGWO: Multi-objective grey wolf optimization for weighting [41] Granger and Ramanathan Methods GRA: Ordinary least squares (OLS)-based weighting Easy and quick implementation; Hedging against the use of bad model; Only GRC has bias correction steps GRA cannot construct density forecasts; GRC sometimes produces unrealistic results [41] GRB: Weights are constrained unity [41] GRC: Weighting with a bias correction [7] Regression Methods PLSR: Regression coefficient estimation using partial OLS [31] CCR: Bias correction with a constant term [39] PCR: Transfer predictor variable to orthogonal variables [45] SWR: Lagged forecast error and unbiased forecast [46] NGR: Gaussian mean as regression coefficient [47] CBP-MLR: Conditional bias incorporation for error reduction [47] Com-MLR: Weighted average of MLR and CBP-MLR [2] Bayesian QR-BMA: Quantile regression-based BMA [48] BMA-LR: BMA in linear regression model [48] BMA-GLM: BMA in the generalized linear model [49] SBMC: Sequential addition of new information [50] BMA-WVC: BMA-based ensemble multi-wavelet Volterra coupled approach [51] CBMA: Copula function integrated BMA [52] HBMA: Hierarchical BMA for uncertainty segregation [53] CBP-BMA: Copula Bayesian Processor with BMA for PDF relaxation [54] (e-Bay) BMA: Ensemble-based dynamic Bayesian averaging [55] BMA-DSRC: BMA integrated with the dynamic system response curve [56] VB-LSTM: Regression-based Variational Bayesian Long Short-Term Memory…”

“…Several complex BMA-based merging methods have also been developed and applied, such as integrating BMA and data assimilation for uncertainty reduction [95], BMA-based ensemble multi-wavelet Volterra approach (BMA-WVC) for uncertainty reduction [50], Copula Bayesian Processors with BMA (CBP-BMA) for uncertainty analysis [53], Ensemble-based dynamic Bayesian averaging approach (e-Bay) for uncertainty quantification [54], Quantile regression-based BMA (QR-BMA) for bias correction and enhanced forecasting [9], Regression based Variational Bayesian Long Short-Term Memory network (VB-LSTM) to address the impact of ensemble members [56]. BMA is integrated with a dynamic system response curve (BMA-DSRC) [55]. These methods aim to further enhance the performance and capabilities of multi-model combinations using BMA.…”

“…BMA and DREAM optimization, employing bias-corrected satellite precipitation products, significantly enhanced streamflow accuracy [75,107]. Furthermore, DSRC, in conjunction with BMA, improved the effectiveness and robustness of the multimodel streamflow simulation [55]. Regionalization studies (e.g., [102]) found the pooling method effective for ungauged catchments [106].…”

“…In merging quantile forecasts and predictive distributions of streamflow, BLP yielded slightly better results than BMA and NGR in terms of continuous rank probability score (CRPS), albeit being more time-consuming in parameter estimation, potentially resulting in suboptimal solutions that could limit its effectiveness [55]. Awol et al [131] highlighted the superiority of forecast merging methods with nonnegative weights, such as CLS and BMA, over those without constraints, like InvR and BGA.…”

Application of the Improved K-Nearest Neighbor-Based Multi-Model Ensemble Method for Runoff Prediction

“…The estimation of these weights can be based on a variety of methodologies, including multivariate linear regression [21], least squares methods [16], machine-learning techniques [20,22], or Bayesian model averaging [23][24][25]. Wang et al [26] constructed two multi-model ensemble models based on the dynamic system response curve (DSRC) and Bayesian model averaging (BMA). The integrated forecast results for three process-driven hydrological models (XAJ, HBV, and VHY models) were significantly superior to the baseline model.…”