This study focuses on the reliable parametrization of the full Soil Water Retention Curve (SWRC) from saturation to oven-dryness using high resolution but limited range measured water retention data by the Hydraulic Property Analyzer (HYPROP) system. We studied the performance of five unimodal water retention models including the Brooks and Corey model (BC model), the Fredlund and Xing model (FX model), the Kosugi model (K model), the van Genuchten constrained model with four free parameters (VG model), and the van Genuchten unconstrained model with five free parameters (VGm model). In addition, eleven alternative expressions including Peters–Durner–Iden (PDI), bimodal, and bimodal-PDI variants of the original models were evaluated. We used a data set consisting of 94 soil samples from Turkey and the United States with high-resolution measured data (a total of 9264 measured water retention data pairs) mainly via the HYPROP system and supplemented for some samples with measured dry-end data using the WP4C instrument. Among unimodal expressions, the FX and the K models with the Mean Absolute Error (MAE) values equal to 0.005 cm3 cm−3 and 0.015 cm3 cm−3 have the highest and the lowest accuracy, respectively. Overall, the alternative variants provided a better fit than the unimodal expressions. The unimodal models, except for the FX model, fail to provide reliable dry-end estimations using HYPROP data (average MAE: 0.041 cm3 cm−3, average r: 0.52). Our results suggested that only models that account for the zero water content at the oven dryness and properly shift from the middle range to dry-end (i.e., the FX model and PDI variants) can adequately represent the full SWRC using typical data obtained via the HYPROP system.

In this paper, for the first time, to model the discharge coefficient of labyrinth weirs, the evolutionary firefly algorithm (FFA) is used for optimizing the membership functions of the adaptive neuro-fuzzy inference system (ANFIS). Also, to enhance the performance of the ANFIS and ANFIS-FFA models, the Monte Carlo simulations (MCs) are employed. Additionally, the k-fold cross-validation is utilized for training and testing the methods. Next, some input dimensionless parameters including the Froude number (Fr), the ratio of the head above the weir to the weir height (H T /P), cycle sidewall angle (α), the ratio of length of the weir crest to the channel width (L c /W), the ratio of length of apex geometry to the width of a single cycle (A/w) and the ratio of the width of a single cycle to the weir height (w/P) are determined. After that, seven different models are developed for ANFIS and ANFIS-FFA. Then, by conducting a sensitivity analysis, the superior models (ANFIS-FFA 5 and ANFIS 5) and the most effective input parameter (Froude number) are identified. Moreover, the error distribution results exhibit that about 70% of the superior model results have errors less than 5%. Subsequently, the discharge coefficient is simulated by means of a computational fluid dynamics (CFD) model. Furthermore, a comparison of the CFD model with the ANFIS and ANFIS-FFA models reveals that the ANFIS-FFA model is significantly more accurate. Also, an uncertainty analysis is performed for the CFD, ANFIS and ANFIS-FFA models. Finally, a very simple code calculating the discharge coefficient of labyrinth wires is presented. This code can be easily employed without any knowledge on ANFIS, FFA and prior information about MATLAB.

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