We use the third version of the Canadian Local Climate Model as a diagnostic tool to study the climatology of observed CG lightning activity at Maniwaki (latitude: 46,23°N; Longitude: 75,58°W). We examine the dependence between the hourly lightning activity and the related atmospheric variables during the warm season of sixteen years (between 1984 and 2004). The goal of this research is: a) to evaluate the atmospheric static state evolution and its moisture contents for conditions having generated lightning occurrence, b) to develop a CG lightning parameterization, and c) to verify this CG lightning parameterization on other Canadian areas. The freezing level altitude and the precipitable water content are used to estimate the static air instability and its moisture content respectively. These two parameters are served to develop the CG lightning parameterization. A comparison between the observations and simulations CG lightning occurrence and frequency at Maniwaki showed a mean absolute error rate of 27% and 55% respectively. We apply this parameterization at four Canadian regions, distributed from west to east. The simulated CG lightning results are comparable to observed CG lightning at Maniwaki and tested regions. The application of the CG lightning parameterization to the daily data enabled us to find the monthly results. This application represents a preliminary stage for validation this parameterization in regional numerical models in Canada during the historic period.

A 3-month (June-August) regime of the year 2002 summer rainfall (JJA2002) was simulated with 30 physics combinations using the Weather Research and Forecasting (WRF) model at 12-km horizontal grid resolution. The objective is to examine summer rainfall sensitivity to parameterization of microphysical, convective, and boundary layer processes and identify the best possible combination of parameterization options that perform relatively better in simulating the spatial and temporal distribution of summer rains over Ethiopia. The WRF simulated rainfall was evaluated against station data and satellite rainfall products (CHIRPS and ENACTS) using mean absolute error, Pearson and Pattern correlation coefficients (PCC), pattern correlation, and error in a number of rainy days as evaluation metrics. Summer rainfall is found to be most sensitive to the choice of cumulus parameterization and least sensitive to cloud microphysics. All simulations captured the spatial distribution of mean seasonal precipitation with PCC ranging from 0.89-0.94. However, all simulations overestimated precipitation amount and number of rainy days. Out of the 30, the simulations that use a combination of Grell-3D cumulus scheme, ACM2 boundary layer, Lin Microphysics, Dudhai shortwave radiation, and RRTM longwave radiation scheme ranked the top and provided the most realistic simulation in terms of amount and spatio-temporal distribution of summer rainfall.

Cumulus parameterization schemes model the subgrid-scale effects of moist convection, affecting the prognostic of cloud formation, rainfall, energy levels reaching the surface, and air quality. Working with a spatial resolution of 1 km, we studied the influence of cumulus parameterization schemes coded in the Weather Research & Forecasting with Chemistry Version 3.2 (WRF-Chem 3.2) for atmospheric modeling in Cuenca, an Andean city of Southern Ecuador (2500 masl), during September 2014. For assessing the performance, we used meteorological records from the urban area and stations located mainly over the Cordillera, with heights above 3000 masl, and air quality records from the urban area. Firstly, we did not use any cumulus parameterization (0 No Cumulus). Then we considered four schemes: 1 Kain-Fritsch, 2 Betts-Miller-Janjic, 3 Grell-Devenyi, and 4 Grell-3 Ensemble. On average, the 0 No Cumulus option was better for modeling meteorological variables over the urban area, capturing 66.5% of records and being the best for precipitation (77.8%). However, 1 Kaint-Fritsch was better for temperature (78.7%) and 3 Grell-Devenyi for wind speed (77.0%) and wind direction (37.9%). All the options provided acceptable and comparable performances for modeling short-term and long-term air quality variables. The results suggested that using no cumulus scheme could be beneficial for holistically modeling meteorological and air quality variables in the urban area. However, all the options, including deactivating the cumulus scheme, overestimated the total amount of precipitation over the Cordillera, implying that its modeling needs to be improved, particularly for studies on water supply and hydrological management. New WRF-Chem versions and microphysics parameterization, the other component directly related to cloud and rainfall processes, must be assessed.

A method for solving the turbulence equations embedded in the sigma ocean general ocean circulation model is proposed. Like the general circulation model, the turbulence equations are solved using the splitting method by physical processes. The turbulence equations are split into two main stages describing transport-diffusion and generation-dissipation processes. Parameterization of turbulence in the framework of equations allows, at the generation-dissipation stage, to use both numerical and analytical solutions and to ensure high efficiency of the algorithm. The results of large-scale ocean dynamics simulation taking into account the parameterization of vertical turbulent exchange are considered. Numerical experiments were carried out using k-omega turbulence model embedded to the Institute of Numerical Mathematics Ocean general circulation Model (INMOM). Both the circulation and turbulence models are solved using the splitting method with respect to physical processes. The coupled model is used to simulate the hydrophysical fields of the North Atlantic and Arctic Oceans for 1948--2009. The model has a horizontal resolution of 0.25 degree and 40 sigma-levels along the vertical. The sensitivity of the solution to the changes in mixing parameterization is studied. Experiments demonstrate that taking into account the climatic annual mean buoyancy frequency improves the reproduction of large-scale ocean characteristics. There is a positive effect of Prandtl number variations for reproducing the upper mixed layer depth. The experiments also demonstrate the computational effectiveness of the proposed approach in solving the turbulence equations.

We consider a classial case of irrational integrals containing a square root of a quadratic polynomial. It is well known that they can be expressed in terms of elementary functions by one of three Euler’s substitutions. It is less known that the Euler substittutions have a beautiful geometric interpretation. In the framework of this interpretation one can see that the number 3 is not the most suitable. We show that it is natural to introduce the fourth Euler substitution. By the way, it is not clear who was the first to attribute these three substitutions to Euler. In his original treatise Leonhard Euler uses two substitutions which are sufficient to cover all cases.

This paper studies the optimization method of pump hydraulic performance based on the response surface method. A parametric model of impeller and diffuser is established. Three-dimensional optimization is carried out on the basis of the initial model obtained by one-dimensional design method. We select the pump hydraulic efficiency and the head as objective function and constraint function. Response surface models are constructed to analyze the relationship between the objectives and the design variables, and the global optimization of hydraulic performance is realized. According to the internal flow characteristics of pump, this paper proposes the strategy of two steps optimization, which aims at meridional plane and blade shape, respectively, to solve the problem of large numbers of design parameters and computational cost. The optimization results show that the hydraulic efficiency of pump increased by 3.7%, and the head is nearly the same.

Mangroves offer vital ecological advantages including air and water filtration, coastal and estuarine habitat provision, sediment stabilization, and wave energy absorption. Their intricate root systems play a key role in safeguarding shorelines from tsunamis and erosive storms by dissipating wave energy. Moreover, mangroves shield against boat wakes and wind-waves, bolstering shoreline defense. Wave dissipation is a function of forest width, tree diameter, and forest density. Restoration efforts of juvenile mangroves in Florida’s Indian River Lagoon (IRL) aim to reduce wave energy in areas vulnerable to erosion. Physical model testing of wave dissipation through mangroves is limited due to the complexity in representing the mangrove structure, where prop roots are non-uniform in both diameter and location. Previous studies have quantified wave dissipating effects through use of scaled and parameterized mangrove structures. This study measures the dissipation effects of live mangroves in a wave flume, forced by conditions representative of the IRL. These measurements are used to validate a parameterized dowel model. Error between wave attenuation factors for the live mangrove and dowel system was on average 2.5%. Validation of the modularized dowel system allowed for further parameterized testing to understand forest structure effects, such as sediment stabilization and wave attenuation.

An integrated approach to active flow control is proposed by finding both the drooping leading edge and the morphing trailing edge for flow management. This strategy aims to manage flow separation control by utilizing the synergistic effects of both control mechanisms, which we call the Combined Morphing Leading Edge and Trailing Edge (CoMpLETE) technique. This design is inspired by a bionic porpoise nose and the flap movements of the cetacean species. The motion of this mechanism achieves a continuous, wave-like, variable airfoil camber. The dynamic motion of the airfoil's upper and lower surface coordinates in response to unsteady conditions is achieved by combining the thickness-to-chord (t/c) distribution with the time-dependent camber line equation. A parameterization model was constructed to mimic the motion around the morphing airfoil at various deflection amplitudes at stall angle of attack and morphing actuation start times. The mean properties and qualitative trends of the flow phenomena are captured by the transition-SST (Shear Stress Transport) model. The effectiveness of the dynamically morphing airfoil as a flow control approach is evaluated by obtaining the flow field data, such as velocity streamlines, vorticity contours, and aerodynamic forces. Different cases are investigated for the CoMpLETE morphing airfoil, which evaluates the airfoil’s parameters, such as its morphing location, deflection amplitude, and morphing starting time. The morphing airfoil’s performance is analyzed to provide further insights into the dynamic lift and drag force variations at pre-defined deflection frequencies of 0.5 Hz, 1 Hz, and 2 Hz. The findings demonstrate that adjusting the airfoil camber reduces streamwise adverse pressure gradients, thus preventing significant flow separation. Although the trailing edge deflection and its location along the chord influence the generation and separation of the Leading-Edge Vortex (LEV), these results show that the combined effect of the morphing leading edge and trailing edge has the potential to mitigate flow separation. The morphing airfoil successfully contributes to the flow reattachment and significantly increases the maximum lift coefficient (c_(l,max))). This work also broadens its focus to investigate the aerodynamic effects of a dynamically morphing leading and trailing edge, which seamlessly transitions along the side edges. The aerodynamic performance analysis is investigated across varying morphing frequencies, amplitudes, and actuation times.

Optimizing the NACA0015 airfoil which is widely applied in small-scale vertical axis wind turbine to make it has a better aerodynamic performance. In the optimization process, using CST parameterization method to perturb the airfoil geometry, the thickness and camber of the airfoil are selected as the constraint, and the value of the maximum tangential force coefficient is chosen as the objective function, the genetic algorithm based on non-dominated sorting (NSGA-II)is selected as an optimization method, calculates the aerodynamic performance of the airfoil by applying the approach of combining XFOIL program and Viterna-Corrigan post-stall mode ,and establishes the optimizing process by the optimization software modefrontier for NACA0015 airfoil’s muti-point optimization, validate the airfoil’s performance with CFD finally. The result illustrates that, by comparing with the NACA0015 airfoil, the optimized airfoil’s lift to drag ratio is improved over a wide range of attack angles, the stall performance is more gentle. The maximum lift coefficient, the maximum lift-drag ratio and the maximum tangential force coefficient are increased by 7.5%,9 and 8.87%, respectively. The optimized airfoil has a wide variable condition performance, more suitable for the operating conditions of a vertical axis wind turbine. Finally, predict the rotor efficiency with optimized airfoil and NACA0015 airfoil for different tip speed ratios and different solidities with multiple streamtube model, the result shows the rotor with optimized airfoil has a higher efficiency.

Location-and-scale transformation of a random variable underpins normal distribution, but it is however fundamentally incorrect for scale estimation such as relative dispersion. In this paper, a parametrized alternative to a normal distribution, called scaloc-normal distribution, is proposed that efficiently works and is fundamentally correct with absolute and relative dispersion estimators. The Monte Carlos simulation experiment was used to generate a total of 600,000 artificial datasets in 600 different simulation scenarios from loc-normal (normal) and scaloc-normal distributions. The absolute and relative dispersion were estimated and compared from the two distributions. The results show that scaloc-normal distribution is a good parametrized alternative to loc-normal distribution, fundamentally correct and efficient with both standard deviation and coefficient of variation. The key statistical advancement from loc-normal to scaloc-normal distribution is its fundamental correctness (i.e., scale-invariant property) with an efficient relative estimator of dispersion (i.e., coefficient of variation). Parametrically, the loc-normal and scaloc-normal distributions are very different, but both have linear transformations.

Two coupled climate models which participated the CMIP6 project (Coupled Model Intercomparison Project Phase 6), the Earth System Model of Chinese Academy of Sciences version 2 (CAS-ESM2-0) and the Nanjing University of Information Science and Technology Earth System Model version 3 (NESM3), were assessed in terms of the impact of four new sea ice parameterization schemes. These four new schemes are related to air-sea heat flux, radiation penetration and absorption, melt ponds, ice-ocean flux, respectively. To evaluate the effectiveness of these schemes, key sea ice variables with and without these new schemes, such as sea ice concentration (SIC) and sea ice thickness (SIT), were compared against observation and reanalysis product from 1980 to 2014. The simulations followed the design of historical experiments within the CMIP6 framework. The results revealed that both models demonstrated improvements in simulating Arctic SIC and SIT when the new parameterization schemes were implemented. The model bias of SIC in some marginal sea ice zones of Arctic was reduced, especially during March. The SIT was increased and the transpolar gradient of SIT was reproduced. The changes of spatial pattern of SIC and SIT after adding new schemes bear similarities between the two coupled models. This suggests that the new schemes have potential for broad application in climate models, especially for those with underestimated SIT.