Accurate estimation of drought events is vital for the mitigation of their adverse consequences on water resources, agriculture and ecosystems. Machine learning algorithms are promising methods for drought prediction as they require less time, minimal inputs, and are relatively less complex than dynamic or physical models. In this study, a combination of machine learning with the Standardized Precipitation Evapotranspiration Index (SPEI) is proposed for analysis of drought within a representative case study in the Tibetan Plateau, China, for the period of 1980-2019. Two timescales of 3 months (SPEI-3) and 6 months (SPEI-6) aggregation were considered. Four machine learning models of Random Forest (RF), the Extreme Gradient Boost (XGB), the Convolutional neural network (CNN) and the Long-term short memory (LSTM) were developed for the estimation of the SPEIs. Seven scenarios of various combinations of climate variables as input were adopted to build the models. The best models were XGB with scenario 5 (precipitation, average temperature, minimum temperature, maximum temperature, wind speed and relative humidity) and RF with scenario 6 (precipitation, average temperature, minimum temperature, maximum temperature, wind speed, relative humidity and sunshine) for estimating SPEI-3. LSTM with scenario 4 (precipitation, average temperature, minimum temperature, maximum temperature, wind speed) was relatively better for SPEI-6 estimation. The best model for SPEI-6 was XGB with scenario 5 and RF with scenario 7 (all input climate variables, i.e., scenario 6 + solar radiation). Based on the NSE index, the performances of XGB and RF models are classified as good fits for scenarios 4 to 7 for both timescales. The developed models produced satisfactory results and they could be used as a rapid tool for decision making by water-managers.

A theoretical method was used to derive an equation for the discharge coefficient of sluice gates in rectangular channels under orifice-flow (both free and submerged) conditions. The proposed equation allows for the effects of energy dissipation between the upstream section of the gate and the vena contracta. The hydraulic energy loss in the upstream pool is attributable to the induced turbulence by the recirculating region and to the growth of bottom boundary layer. For the submerged-flow condition, turbulent shear-layer entrainment is also responsible for the energy loss. This energy loss is introduced into the equations through a coefficient k that has been conventionally assumed to be negligible. Experimental data from the literature were used to validate the equation, which showed good agreement with the measured values. It is also shown that the magnitude of the energy-loss factor is a function of the geometry of the gate and can modify the discharge coefficient. An equation for the distinguishing c...

Friction factor determination is important for modeling fluid flows in pipes. The Colebrook equation has been widely used for estimating the pipe friction factor in fully developed turbulent regime. Because of the implicit nature of Colebrook equation, various regression-based approximations, Lambert W-function-based solutions, series-based solutions, and analytical approximations are developed for explicitly determining the friction factor. This study focuses on approximate analytical solutions for the Colebrook equation with a minimum number of natural logarithms and noninteger powers (lower computational cost). For this, a new mathematically equivalent representation of the Colebrook equation is presented. This form consists of two nonlinear equations which are very well suited for developing the analytical solutions for the friction factor. The simple analytical solutions developed in this study with the maximum relative errors less than 0.85, 0.25, 0.054, and 0.0028% (solutions with different degrees of accuracy) are among the most accurate analytical approximations to the Colebrook equation. Simple form and superior efficiency of the proposed solutions make them preferable to currently available approximate solutions to the Colebrook equation.