Probability Distribution Function Research Articles

Distributionally Robust Optimization for integrated energy system accounting for refinement utilization of hydrogen and ladder-type carbon trading mechanism

This study presents a hydrogen-IES with hydrogen refinement utilization under the framework of ladder-type carbon trading mechanism (LCTM). To navigate the uncertainties associated with RE in the proposed hydrogen-IES, we introduce a data-driven Distributionally Robust Optimization (DRO) method based on an innovative ambiguity set construction approach. This method leverages nonparametric Kernel Density Estimation (KDE) to fit the error probability distribution function and determine the predicted interval for wind turbine (WT) and photovoltaic (PV) output under a given confidence level. Subsequently, Latin hypercube sampling (LHS) and a reduction method based on probability distance are employed to generate original and typical scenarios, respectively. Ultimately, the construction of ambiguity sets imposes constraints on typical scenarios and probabilities using 1-norm and ∞-norm. Case study is conducted to validate the effectiveness of the proposed innovations. The results underscore the significant advantages of hydrogen refinement utilization within the proposed framework. Specifically, it demonstrates notable economic benefits, with costs lower by 11.98%, 2.46%, and 1.53% compared to scenarios omitting gas synthesis, hydrogen blending combustion in CHP and GB, and hydrogen storage, respectively. Moreover, hydrogen refinement exhibits superior performance in accommodating WT and PV, with ratios 25.29%, 0.43%, and 1.91% higher than alternative methods, with lower carbon emissions of 42.23%, 11.91%, and 6.13%. The LCTM can reduce more carbon emissions by 7.60% and 0.145% compared to scenarios without carbon trading mechanisms and with fixed-price trading mechanisms. The probability distribution derived from nonparametric KDE aligns closely with the true distribution, fostering a more objective analysis and mitigating the conservatism of the ambiguity set and optimization scheduling. Finally, sensitivity analyses are conducted in detail, including hydrogen blending ratio, basic price and growth ratio of LCTM.

Effect of nonlinearity of discrete Langevin model on behavior of extremes in generated time series

In this work we analyze the influence of nonlinearity on the behavior of extremal values of time series generated by two discrete Langevin models: fixing the diffusion function in the first (M1), the probability distribution function in the second (M2). The extremes were generated by applying the run theory. A mathematical relationship was found between nonlinearity of models and means and distributions of run lengths and inter-extreme times as well as with the clustering of extremes. Furthermore, the Allan factor curves of the extremes suggest that the sequences of extremes are fractal for timescales up to the mean inter-extreme time. Our main findings are that the variation of the nonlinearity parameter in model M1 (leading to the increase of the distribution tail length) can cause a significant variation of the extreme characteristics and an increase of the clustering while the variation of the nonlinearity parameter in model M2 (with fixed distribution) has a little effect on extremes.

A sensitivity study on the PDFs treating uncertainties in severe accidents for pressurized heavy water reactors

This research article introduces a study regarding the uncertainties treatment during severe accidents for Pressurized Heavy Water Reactors (PHWRs). The present study is focused upon the unmitigated Station BlackOut (SBO) accident analysis for a CANada Deuterium Uranium (CANDU) type reactor emphasizing the impact of the uncertainties treatment on the relevant key timings of the SBO accident progression through different approaches for the uncertainty parameters’ Probabilistic Distribution Functions (PDFs). A comparison between the sensitivity analysis results is provided in the present research study.The uncertainty analysis is performed with the RELAP/SCDAPSIM code with the Integrated Uncertainty Analysis (IUA) package from the code.Results from the research would support the advancements on the best-practices for uncertainty analyses with respect to the parameter's uncertainties distribution functions. Data dispersion is a key element for the realistic quantification of uncertainties in nuclear power plant safety analyses, including severe accidents.

The influence patterns of carbon flux in different climatic zones in China —Based on the complex network approach

Research on ecosystem carbon flux can provide important methodological and strategic support for climate change mitigation. The existing studies focus on the calculation of carbon flux, ignoring the intertwined effects between regions. The quantification and analysis of the interaction patterns of carbon flux is crucial for understanding the global carbon cycle process, forecasting and coping with climate change. In this study, carbon flux network model sequences are established based on complex network theory using carbon flux data spanning from December 1, 2005, to November 30, 2020. The time delay effect is introduced to accurately quantify the influence patterns of carbon flux within climate zones across China. The findings indicate that the probability distribution function of the link weights during the various seasons of each year exhibits a bimodal distribution with distinct positive and negative components. The delay probability distribution function reveals the significant impact of delay effects, which are especially pronounced and mostly significant long-term lag effects in nodes with negative weights. Further, the results of the interactions of carbon flux among climate zones demonstrate that changes in carbon flux in the plateau and southern temperate regions have either positive or negative impacts on other climate zones. Therefore, controlling carbon flux changes in these climatic zones can effectively optimize the distribution of carbon flux. The modeling framework and results presented in this paper provide useful insights for the regulation and distribution optimization of carbon flux in China.

Inertial active harmonic particle with memory induced spreading by viscoelastic suspension.

We investigate the self-propulsion of an inertial active particle confined in a two-dimensional harmonic trap. The particle is suspended in a non-Newtonian or viscoelastic suspension with a friction kernel that decays exponentially with a time constant characterizing the memory timescale or transient elasticity of the medium. By solving the associated non-Markovian dynamics, we identify two regimes in parameter space distinguishing the oscillatory and non-oscillatory behavior of the particle motion. By simulating the particle trajectories and exactly calculating the steady-state probability distribution functions and mean square displacement; interestingly, we observe that with an increase in the memory time scale, the effective temperature of the environment increases. As a consequence, the particle becomes energetic and spread away from the center, covering larger space inside the confinement. On the other hand, with an increase in the duration of the activity, the particle becomes trapped by the harmonic confinement.

Probabilistic estimation of the source component of seismic hazard in North-Eastern Brazil

Stable continental regions pose unique challenges for conducting Probabilistic Seismic Hazard Analysis because the earthquake activity driving mechanisms are poorly understood. For instance, the lower seismicity (hence the paucity of data) and the absence of well-defined active fault systems complicate accurately determining seismic source parameters. Northeastern Brazil is a stable continental region exhibiting moderate-size events recorded with significant seismic intensities and provoking the collapse of poorly constructed buildings in the last century. Thus, assessing the seismic hazard is critical for seismic risk mitigation. The seismic hazard depends on three components: source, path, and site, and here, we present the probabilistic seismic hazard analysis of the source component for NE Brazil. Spatial aggregation of earthquake sources outlined four areal seismic zones. A goodness-of-fit test rejected the Gutenberg-Richter model of magnitude frequency distribution in one of the studied seismic zones. For this reason, we estimated the magnitude probability distribution function in that zone using a nonparametric adaptive kernel estimator. In other zones the Gutenberg-Richter magnitude frequency model was applied. In either way of the magnitude probability distribution modelling we considered the upper bound for magnitude equal to 6.6 mR, based on the upper bound of a 95 % confidence interval for the standard normal distribution of palaeoearthquake sizes. Our findings suggests that potentially damaging events are likely to occur, and we cannot neglect chances for the occurrence of earthquakes exceeding 5.2 mR. The calculated mean return periods indicate significantly shorter intervals between consecutive large events than palaeoseismic records.

Caterpillar movement mediates spatially local interactions and determines the relationship between population density and contact.

While interactions in nature are inherently local, ecological models often assume homogeneity across space, allowing for generalization across systems and greater mathematical tractability. Density-dependent disease models are a prominent example of models that assume homogeneous interactions, leading to the prediction that disease transmission will scale linearly with population density. In this study, we examined how the scale of larval butterfly movement interacts with the resource landscape to influence the relationship between larval contact and population density in the Baltimore checkerspot (Euphydryas phaeton). Our study was inspired by the recent discovery of a viral pathogen that is transmitted horizontally among Baltimore checkerspot larvae. We used multi-year larvae location data across six Baltimore checkerspot populations in the eastern U.S. to test whether larval nests are spatially clustered. We then integrated these spatial data with larval movement data in different resource contexts to investigate whether heterogeneity in spatially local interactions alters the assumed linear relationship between larval nest density and contact. We used Correlated Random Walk (CRW) models and field observations of larval movement behavior to construct Probability Distribution Functions (PDFs) of larval dispersal, and calculated the overlap in these PDFs to estimate conspecific contact within each population. We found that all populations exhibited significant spatial clustering in their habitat use. Subsequent larval movement rates were influenced by encounters with host plants and larval age, and under many movement scenarios, the scale of predicted larval movement was not sufficient to allow for the "homogeneous mixing" assumed in density dependent disease models. Therefore, relationships between population density and larval contact were typically non-linear. We also found that observed use of available habitat patches led to significantly greater contact than would occur if habitat use were spatially random. These findings strongly suggest that incorporating larval movement and spatial variation in larval interactions is critical to modeling disease outcomes in E. phaeton. Epidemiological models that assume a linear relationship between population density and larval contact have the potential to underestimate transmission rates, especially in small populations that are already vulnerable to extinction.

On the Bivariate Extension of the Extended Standard U-quadratic Distribution

This paper derives the bivariate version of the extended standard U-quadratic (eSU) distribution using the method of compounding or pseudo family of distributions. The joint probability and cumulative distribution functions of the derived distribution are obtained and it is observed that the said distribution can generate bivariate shape with the following properties: $(i)$ $X$ and $Y$ have bathtub shapes; $(ii)$ $X$ has constant and $Y$ has bathtub shapes; and $(iii)$ $X$ has inverted bathtub and $Y$ has bathtub shapes. Moreover, some properties of the derived distribution such as the marginal distribution, conditional distributions, conditional moments, product and ratio moments are derived. Further, the maximum likelihood estimation is performed to estimate the parameters of the derived distribution. Also, a simulation study is carried out to evaluate the behavior of the estimates of the parameters. Moreover, we derive a new bivariate Kumaraswamy distribution and use it to simulate bivariate data with $X$ and $Y$ having bathtub shapes. Furthermore, A new bivariate version of the Cubic Transmuted Uniform (CTU) distribution is also derived. Finally, the proposed Bivariate eSU distribution is applied to simulated data and compared with the said Bivarite Cubic Transmuted Uniform distribution. The result shows that the proposed Bivariate eSU distribution provides a better fit for the said simulated dataset as compared with the Bivariate CTU distribution.

A Deformation Analysis Method for Sluice Structure Based on Panel Data

Deformation, as the most intuitive index, can reflect the operation status of hydraulic structures comprehensively, and reasonable analysis of deformation behavior has important guiding significance for structural long-term service. Currently, the health evaluation of dam deformation behavior has attracted widespread attention and extensive research from scholars due to its great importance. However, given that the sluice is a low-head hydraulic structure, the consequences of its failure are easily overlooked without sufficient attention. While the influencing factors of the sluice’s deformation are almost identical to those of a concrete dam, nonuniform deformation is the key issue in the sluice’s case because of the uneven property of the external load and soil foundation, and referencing the traditional deformation statistical model of a concrete dam cannot directly represent the nonuniform deformation behavior of a sluice. In this paper, we assume that the deformation at various positions of the sluice consist of both overall and individual effects, where overall effect values describe the deformation response trend of the sluice structure under external loads, and individual effect values represent the degree to which the deformation of a single point deviates from the overall deformation. Then, the random coefficient model of panel data is introduced into the analysis of sluice deformation to handle the unobservable overall and individual effects. Furthermore, the maximum entropy principle is applied, both to approximate the probability distribution function of individual effect extreme values and to determine the early warning indicators, completing the assessment and analysis of the nonuniform deformation state. Finally, taking a project as an example, we show that the method proposed can effectively identify the overall deformation trend of the sluice and the deviation degree of each measuring point from the overall deformation, which provides a novel approach for sluice deformation behavior research.

Ensemble variational Bayesian approximation for the inversion and uncertainty quantification of Darcy flows in heterogeneous porous media with random parameters

The inversion and uncertainty quantification of physical parameters are important for many science and engineering problems. For nonlinear parameter inversion problems of flows in hydrocarbon reservoirs, estimating the true posterior probability distribution function for the random parameter is difficult when the dimension of the parameter is relatively high. Inversion methods such as gradient-based or heuristic optimization methods searching for the maximum a posterior are generally point-estimate, while uncertainty quantification using MCMC is computationally expensive. In the current study, a new ensemble variational Bayesian approximation method is developed to estimate the posterior probability density using an ensemble of realizations regarded as a trial sample distribution. The objective is to optimize the trial sample distribution such that the evidence lower bound is maximized indicating that the distance between the trial and true posterior distribution is minimized. A subspace is built using principle component analysis based on finite samples to obtain a diagonal positive-definite covariance matrix, and ensemble-based data assimilation is used to optimize the trial distribution efficiently. Heterogeneous 2D and 3D test cases of transient single- and two-phase Darcy flows are presented for validation.

Evaluation of multiple machine learning models for ASR expansion of concrete

Machine learning algorithms (MLA) show promise in predicting alkali-silica reaction (ASR) expansion. Nevertheless, the predictive performance of different machine learning algorithms (MLAs) varies across various engineering scenarios and datasets. Given that, this study was devoted to constructing an appropriate predictive model for ASR expansion of concrete. Multiple MLAs including evolutionary-based, support vector-based, assembly-based, and neural network-based algorithms, were employed to establish predictive models. An optimization technique, the particle swarm optimization algorithm, was also utilized and integrated with the aforementioned MLA models to effectively search for optimal hyperparameters and topological structures. The predictive performance was evaluated using statistical methods, which showed that the extreme gradient boosting (XGBoost) model had the best fitting goodness among the standard algorithms, with an R2 value of 0.9695. Moreover, the Particle Swarm Optimization (PSO) model significantly improved the predictive performance of all Machine Learning Algorithm (MLA) models. The error distribution analysis was then performed. There are fewer large errors in the predicted values of the PSO-XGBoost model. Monte Carlo simulation and probability distribution functions were used to thoroughly analyze the stability of each model after multiple independent runs. The results show that all models have excellent stability. The PSO-XGBoost model performed the best and was subsequently employed to conduct feature analysis to determine the significance of each input parameter and capture the underlying evidence of ASR expansion.

Beyond radial profiles: using log-normal distributions to model the multiphase circumgalactic medium

ABSTRACT Recent observations and simulations reveal that the circumgalactic medium (CGM) surrounding galaxies is multiphase, with the gas temperatures spanning a wide range at most radii, ∼104 K to the virial temperature (∼106 K for Milky Way). Traditional CGM models using simple density profiles are inadequate at reproducing observations that indicate a broad temperature range. Alternatively, a model based on probability distribution functions (PDFs) with parameters motivated by simulations can better match multiwavelength observations. In this work, we use log-normal distributions, commonly seen in the simulations of the multiphase interstellar and circumgalactic media, to model the multiphase CGM. We generalize the isothermal background model by Faerman et al. to include more general CGM profiles. We extend the existing probabilistic models from 1D-PDFs in temperature to 2D-PDFs in density–temperature phase space and constrain its parameters using a Milky Way-like Illustris TNG50-1 halo. We generate various synthetic observables such as column densities of different ions, UV/X-ray spectra, and dispersion and emission measures. X-ray and radio (Fast Radio Burst) observations mainly constrain the hot gas properties. However, interpreting cold/warm phase diagnostics is not straightforward since these phases are patchy, with inherent variability in intercepting these clouds along arbitrary lines of sight. We provide a tabulated comparison of model predictions with observations and plan to expand this into a comprehensive compilation of models and data. Our modelling provides a simple analytical framework that is useful for describing important aspects of the multiphase CGM.

Parametric description of intermittent probability distribution functions in solar wind and magnetohydrodynamic turbulence

ABSTRACT In this work, we find empirical evidence that the scale-dependent statistical properties of solar wind and magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-yr-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a $2048^3$ mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behaviour.

Improving and extending non-Poissonian distributions for satellite galaxies sampling in HOD: applications to eBOSS ELGs

ABSTRACT Halo occupation distribution (HOD) models help us to connect observations and theory, by assigning galaxies to dark matter haloes. In this work, we study one of the components of HOD models: the probability distribution function (PDF), which is used to assign a discrete number of galaxies to a halo, given a mean number of galaxies. For satellite galaxies, the most commonly used PDF is a Poisson Distribution. PDFs with super-Poisson variances have also been studied, allowing for continuous values of variances. This has not been the case for sub-Poisson variances, for which only the nearest integer distribution, with a single variance, has been used in the past. In this work, we propose a distribution based on the binomial one, which provides continuous sub-Poisson variances. We have generated mock galaxy catalogues from two dark-matter only simulations, unit and outerrim, with HOD models assuming different PDFs. We show that the variance of the PDF for satellite galaxies affects the one-halo term of the projected correlation function, and the count-in-cells (CIC) one point statistics. We fit the clustering of eBOSS emission line galaxies, finding results consistent with the literature, when we only vary the parameter controlling the PDF variance and the fraction of satellites. Using a mock catalogue as a reference, we have also included both the clustering and CIC to constrain the parameters of the HOD model. CIC can provide strong constraints to the PDF variance of satellite galaxies.

Structural properties of different sphere packings with arbitrary porosities for planetary-science applications

Granular solids in planetary science are found in the regolith that covers planetary surfaces as well as in the bulk of rubble-pile asteroids, comets and planetesimals. To help understand the physics of these planetary bodies, we aim at deriving the structural properties of granular packings over a large range of porosities. Relevant to fluid flow and gas diffusion are the void spaces inside the granular packings so that we analyze the mean free path of point-like particles, their diffusion constant and their total traveled path lengths. For mechanical and heat-transport properties, the coordination number and the absolute chain length of the inter-connected particles are important. Generally, we also derive the homogeneity and isotropy of the granular solids. We compare granular packings generated by four algorithms for porosities in the range between 85 and 42%, which are the upper and lower limits for natural packings of equal-sized spheres. All produced sphere packings arrive at very similar quantities for the mean free path, the free path probability distribution function, the diffusion constant and the total traveled path length for the entire range of porosities. Hence, transport processes governed by the void-space properties are independent of the specific generation algorithm for the granular packing. In contrast, heat conduction or mechanical stresses almost exclusively depend on the existence and properties of particle contacts and particle chains in the network of spheres. In this case, the four algorithms deliver very different results.Graphic abstract

Connecting flow duration curve and precipitation duration curve based on the relationship deduced from machine learning in the watersheds of northern China

Obtaining reliable hydrological data for ungauged watersheds has always been a significant challenge in the water resources management. The flow duration curve (FDC) and precipitation duration curve (PDC) are classical methods to address this challenge. However, traditional FDC and PDC methods mostly rely on pre-assumed probability distribution function form, which may result in sub-optimal model parameters and consequently sub-optimal simulation results of hydrological data, and the common function forms are not applicable to deal with the data including zero-values, which often occurs in the discharge data of arid region and daily rainfall data. To address the issues in FDC and PDC , this study firstly determines the most suitable function form to describe FDC and PDC from various distribution functions, i.e., Log Normal, Generalized Pareto Distribution and H2018 function, from 1960 to 2010 in 7 watersheds in the north of China. The multiple methods including Random Forest, polynomial, Multilayer Perceptron and K-Nearest Neighbor are employed to simulate the parameters of the functions, aiming to deduce the optimal parameters of FDC functions. The results show that, H2018 function form has the best performance in simulating the PDC and FDC and in general, parameter a and b of H2018 function indicate an opposite trend, and parameter k declines in mostly condition at the annual scale from 1960 to 2010. The results of different methods indicate that the Random Forest method is the most efficient and accurate approach to deduce FDC parameters from measured precipitation and climate factors, compared with polynomial, Multilayer Perceptron and K-Nearest Neighbor. Based on the relationship between PDC parameters and FDC parameters, the FDC of ungauged basins can be deduced from the observed precipitation data. The research findings provide a new method to estimate FDC for the water resources management in the ungauged basins.

Hydrological drought assessment using the standardized groundwater index and the standardized precipitation index in the Berg River Catchment, South Africa

Study regionBerg River Catchment (BRC), South Africa (SA). Study focusHydrological droughts threaten water security and climate Change and groundwater abstractions may exacerbate their impact. Thus, early detection and prediction of droughts is essential. The integration of the Standardised Groundwater Index (SGI) with the Standardised Precipitation Index (SPI), has been applied worldwide, it but not explored in South Africa (SA). The aim of this study was to evaluate the integration of the SGI and SPI for hydrological drought assessment within the BRC, SA. New hydrological insights for the regionThe sensitivity of the SGI to selected Probability Distribution Functions (PDFs) was examined, resulting in the Gamma and Log-Normal PDFs being preferred in the BRC. SGI-Gamma and SPI-Gamma comparisons validated the SGI method and shed light on the key factors influencing groundwater-related droughts in the BRC. The following was revealed: Hydrological droughts in the BRC are influenced by climate factors, surface and groundwater interactions, and groundwater abstractions. When conducting hydrological drought assessments using the SGI and the SPI, the initial focus should be on catchment-scale assessments before expanding to national-scale evaluations. Groundwater in the BRC exhibit significant resilience to droughts induced by climate factors, and thus useful to mitigate the risk of future droughts. Finally, The SGI performed satisfactorily in the BRC with limited groundwater level data.

Probability-Distribution-Configurable True Random Number Generators Based on Spin-Orbit Torque Magnetic Tunnel Junctions.

The incorporation of randomness into stochastic computing can provide ample opportunities for applications such as simulated annealing, non-polynomial hard problem solving, and Bayesian neuron networks. In these cases, a considerable number of random numbers with an accurate and configurable probability distribution function (PDF) are indispensable. Preferably, these random numbers are provided at the hardware level to improve speed, efficiency, and parallelism. In this paper, how spin-orbit torque magnetic tunnel junctions (SOT-MTJs) with high barriers are suitable candidates for the desired true random number generators is demonstrated. Not only do these SOT-MTJs perform excellently in speed and endurance, but their randomness can also be conveniently and precisely controlled by a writing voltage, which makes them a well-performed Bernoulli bit. By utilizing these SOT-MTJ-based Bernoulli bits, any PDF, including Gaussian, uniform, exponential, Chi-square, and even arbitrarily defined distributions can be realized. These PDF-configurable true random number generators can then promise to advance the development of stochastic computing and broaden the applications of the SOT-MTJs.

Effects of H2 enrichment on combustion characteristics in inverse swirl diffusion flames of H2-doped jet fuel using OH, CH2O, fuel and temperature imaging

Hydrogen (H2) and jet fuel co-firing is regarded as a promising transition strategy of decarbonization in aviation industry. Considering the simplicity and safety during highly hydrogen enrichment conditions, the inverse swirl diffusion (ISD) combustion holds research value. Given the current lack of understanding for the flame properties of H2-enriched pre-evaporative jet fuel ISD co-combustion, in this work, the simultaneous planar laser-induced fluorescence (PLIF) of hydroxyl (OH), formaldehyde (CH2O), and fuel, as well as the non-linear excitation regime two-line atomic fluorescence (NTLAF) thermography imaging, are used to study the effects of hydrogen enrichment on ISD flame intricate structure and temperature field. The results show the positive effects of H2 enrichment. The ISD flames display a blue hue and the increase in doping hydrogen helps the flames stabilize under global-lean conditions with almost no CO emission and low CO2 emission at the chamber exit. And the H2 enrichment contributes to inhibiting the CH2O formation upstream, reducing the generation of isolated reaction islands and promoting the strength of the flame wings, favoring the suppression of flame instability. In contrast, when at low H2 enrichment rate, the shift of the heat release zone and high-temperature zone, and the enlargement of the cold zone, are found in flame upstream. The analysis of the probability distribution functions (PDF) of temperatures confirms the effective effects of hydrogen on inhibiting the local flame fluctuations. Although the increase in the overall temperature level due to the hydrogen addition would lead to a promotion in NOx generation, the discussion on the structural analysis and flame propagation stability of ISD flames demonstrates the significance of H2 enrichment for the achievement of leaner low-NOx combustion of ultra-H2-enriched jet fuel in the future.

Characterization of the future northeast monsoon rainfall based on the clustered climate zone under CMIP6 in Peninsular Malaysia

The Northeast monsoon (NEM) exerts a significant influence on the climate system of Peninsular Malaysia (PM) and has profound implications for water resource management, flood control, and disaster preparedness in the region. This study employed CHIRPS rainfall data from 1981 to 2022 at a spatial resolution of 0.25° to generate climate zones. The performance of global climate models (GCMs) in replicating monthly rainfall was evaluated using multiple statistical metrics, with the top-ranked ones being used for the generation of future projection downscaled ensemble models. The NEM months (November, December, January, February, and March) were used as input parameters to form clustered homogeneous groups using the Ward hierarchical method. The optimal number of climate zones was determined using the elbow method, silhouette width values, and spatial evaluation. Ultimately, a 7-cluster solution was chosen due to its consistency and meaningful cluster formation. The zones were categorized into two regions: the West Coast and the East Coast, based on their geographical location and distinctive monthly NEM rainfall patterns. The analysis of the probability distribution function (PDF) showed that rainfall in the West Coast region had a more spread-out pattern with varying amounts, while rainfall in the East Coast region was more concentrated and consistent. The Northeast climate zone received the highest rainfall, attributed to its proximity to the South China Sea, mountainous areas, and the NEM convergence zone. In contrast, the Northwest and Lower Central-West climate zones received the lowest rainfall due to the rain shadow effect, limited moisture availability, and distance from major moisture sources. The CMCC-ESM2, CMCC-CM2-SR5, EC-Earth3, and CanESM5 consistently ranked among the highest performing models. After linear scaling bias correction, validated GCMs showed significant improvements, with improvements in MAE, NRMSE, PBIAS, RSR, NSE, MD, CP, R2, and KGE by 11–45%, 15–47%, 96–100%, 15–47%, 10–79%, 5–37%, 68–113%, 11–73%, and 9–51%, respectively. Analysis of NEM season rainfall patterns across climate zones indicated consistent mid-future increases for the Northwest and Lower Central-West zones (12.4–19.8%) and the Upper Central-West and Southwest zones (0.2–5.4%) across all scenarios. In the far-future, the Southeast zone saw an overall increase in rainfall (4.9–11.4%), while the Central-West zone exhibited mixed results (−4.0 to 5.6%). The results also highlighted spatial variability and the need to consider specific climate zones when assessing the impacts of climate change on the NEM, emphasizing the importance of incorporating these projections into long-term planning and decision-making processes.