Estimating the transient storage parameters for pollution modeling in small streams: a comparison of newly developed hybrid optimization algorithms.

The transient storage model (TSM) is a common approach to assess solute transport and pollution modeling in rivers. Several formulas have been developed to estimate TSM parameters. This study develops a new hybrid optimization algorithm consisting of the dragonfly algorithm and simulated annealing (DA-SA) algorithms. This robust method provides accurate formulas for estimating TSM parameters (e.g., kf, T, $$\varepsilon$$ ). A dataset gathered by previous scholars from several rivers in the USA was used to assess the proposed formulas based on several error metrics ( $$\mathrm{e}.\mathrm{g}.,RMSE,MAE,$$ and $$NSE$$ ) and visual indicators. According to the results, DA-SA-based formulas adequately estimated the $${k}_{f}$$ ( $$RMSE:15.5$$ , $$NSE:0.94$$ ), $$T$$ ( $$RMSE:138.8,$$ $$NSE:0.99$$ ), and $$\varepsilon$$ ( $$RMSE:0.001,$$ $$NSE:0.99$$ ) parameters. Moreover, the DA-SA-1 showed higher accuracy by improving the RMSE and MAE by 98% compared to the DA and DA-SA-1 as alternatives. The formulas developed in this study significantly outperformed the results of previously proposed models by enhancing the NSE up to 70%. The hybrid DA-SA algorithm method proved highly reliable models to estimate the TSM parameters in the water pollution routing problem, which is vital for reactive solute uptake in advective and transient storage zones of stream ecosystems.