Hybrid Gaussian-cubic radial basis functions for scattered data interpolation

Scattered data interpolation schemes using kriging and radial basis functions (RBFs) have the advantage of being meshless and dimensional independent; however, for the datasets having insufficient observations, RBFs have the advantage over geostatistical methods as the latter requires variogram study and statistical expertise. Moreover, RBFs can be used for scattered data interpolation with very good convergence, which makes them desirable for shape function interpolation in meshless methods for numerical solution of partial differential equations. For interpolation of large datasets, however, RBFs in their usual form, lead to solving an ill-conditioned system of equations, for which, a small error in the data can cause a significantly large error in the interpolated solution. In order to reduce this limitation, we propose a hybrid kernel by using the conventional Gaussian and a shape parameter independent cubic kernel. Global particle swarm optimization method has been used to analyze the optimal values of the shape parameter as well as the weight coefficients controlling the Gaussian and the cubic part in the hybridization. Through a series of numerical tests, we demonstrate that such hybridization stabilizes the interpolation scheme by yielding a far superior implementation compared to those obtained by using only the Gaussian or cubic kernels. The proposed kernel maintains the accuracy and stability at small shape parameter as well as relatively large degrees of freedom, which exhibit its potential for scattered data interpolation and intrigues its application in global as well as local meshless methods for numerical solution of PDEs.     

Hydroclimatological Perspective of the Kerala Flood of 2018

Flood is among the deadliest disasters in India, and the frequency of floods and extreme precipitation events is projected to increase under the warming climate. The frequency of floods in India varies geographically as some regions are more prone to floods than the others. The Kerala flood of 2018 caused enormous economic damage, affected millions of people, and resulted in the death of more than 400 people. Here we provide a hydroclimatological perspective on the Kerala flood of 2018. Using the observations and model simulations from the Variable Infiltration Capacity (VIC) model, we show that the 2018 extreme precipitation and runoff conditions that caused flooding were unprecedented in the record of the past 66 years (1951–2017). Our results show that mean monsoon precipitation has significantly declined while air temperature has significantly increased during 1951–2017 in Kerala. The drying and warming trends during the monsoon season resulted in a declined total runoff in large part of the state in the last 66 years. Apart from the mean hydroclimatic conditions, extreme precipitation, and extreme total runoff have also declined from 1951 to 2017. However, 1 and 2-day extreme precipitation and extreme runoff conditions in August 2018 exceeded substantially from the long-term 95^th percentiles recorded during 1951–2017. Since there is no increase in mean and extreme precipitation in Kerala over the last six decades, the extreme event during August 2018 is likely to be driven by anomalous atmospheric conditions due to climate variability rather anthropogenic climate warming. The severity of the Kerala flood of 2018 and the damage caused might be affected by several factors including land use/land cover change, antecedent hydrologic conditions, reservoir storage and operations, encroachment of flood plains, and other natural factors. The impacts of key drivers (anthropogenic and natural) on flood severity need to be established to improve our understanding of floods and associated damage.     

Determination of Suitable Pillar Size for Protecting Gas Well Drilled Through a Longwall Mining Abutment Pillar Using Numerical Modelling Approach: A Case Study

Gas well drilled through longwall mining abutment pillar could potentially face instability issue due to the strata deformation following longwall panel extraction. Therefore, it is imperative to adequately design the pillar size of a longwall mining in order to ensure the stability of the gas well penetrated longwall mining abutment pillar. In this paper, the determination of suitable pillar size for protecting gas well subjected to longwall mining operation was investigated. Two scenarios of longwall gateroad system including the three and four entry system with varying pillar sizes were assessed using numerical modelling approach. The results of this study indicate that the pillar geometry plays an important role on the vertical gas well stability. In addressing the suitable pillar size for the given case study considering three entry system, the suitable chain pillar and abutment pillar size were found to be 80 ft (24.4 m) wide by 120 ft (36.6 m) length and 104 ft (31.7 m) wide by 120 ft (36.6 m) length rib to rib, respectively. Whereas, if four entry system is used, the suitable chain pillar size is 48 ft (14.6) wide by 120 ft (36.6 m) length and the abutment pillar size is 104 ft (31.7 m) wide by 120 ft (36.6 m) length rib to rib. The proposed numerical modelling procedure presented in this paper can be a viable alternative and applied to other similar projects in order to determine an optimal pillar size for protecting gas well in longwall mining area.

     

Upper ocean high resolution regional modeling of the Arabian Sea and Bay of Bengal

In this paper, effort is made to demonstrate the quality of high-resolution regional ocean circulation model in realistically simulating the circulation and variability properties of the northern Indian Ocean(10°S–25°N,45°–100°E) covering the Arabian Sea(AS) and Bay of Bengal(BoB). The model run using the open boundary conditions is carried out at 10 km horizontal resolution and highest vertical resolution of 2 m in the upper ocean.The surface and sub-surface structure of hydrographic variables(temperature and salinity) and currents is compared against the observations during 1998–2014(17 years). In particular, the seasonal variability of the sea surface temperature, sea surface salinity, and surface currents over the model domain is studied. The highresolution model's ability in correct estimation of the spatio-temporal mixed layer depth(MLD) variability of the AS and BoB is also shown. The lowest MLD values are observed during spring(March-April-May) and highest during winter(December-January-February) seasons. The maximum MLD in the AS(BoB) during December to February reaches 150 m (67 m). On the other hand, the minimum MLD in these regions during March-April-May becomes as low as 11–12 m. The influence of wind stress, net heat flux and freshwater flux on the seasonal variability of the MLD is discussed. The physical processes controlling the seasonal cycle of sea surface temperature are investigated by carrying out mixed layer heat budget analysis. It is found that air-sea fluxes play a dominant role in the seasonal evolution of sea surface temperature of the northern Indian Ocean and the contribution of horizontal advection, vertical entrainment and diffusion processes is small. The upper ocean zonal and meridional volume transport across different sections in the AS and BoB is also computed. The seasonal variability of the transports is studied in the context of monsoonal currents.     

Nonlinear model to study filamentation instability of circularly polarized dispersive Alfvén waves in solar wind plasmas

This paper examines the small-scale solar wind turbulence driven in view of the Alfvén waves subjected to ponderomotive nonlinearity. Filamentation instability is known to take place for the case of dispersive Alfvén wave (DAW) propagating parallel to the ambient magnetic field. The ponderomotive force associated with DAW is responsible for wave localization and these webs of filaments become more intense and irregular as one proceeds along the spatial domain. The ponderomotive force associated with pump changes with pump parameters giving rise to different evolution patterns. This paper studies in detail the nonlinear evolution of filamentation instability introduced by dispersive Alfven waves (DAWs) which becomes dispersive on account of the finite frequency of DAW i.e., pump frequency is comparable to the ion cyclotron frequency. We have explicitly obtained the perturbation dynamics and then examined the impact of pump magnitude on the driven magnetic turbulence using numerical simulation. The results show steepening at small scales with increasing pump amplitude. The compressibility associated with acoustic fluctuations may explain the variation in spectral scaling of solar wind turbulence as observed by Alexandrova et al. (Astrophys. J. 674:1157, 2008).     

Behaviour of physical parameters in extended gravity with hyperbolic function

In this paper, we have constructed the cosmological model of the universe in f(R, T) theory of gravity in a Bianchi type \(\mathrm{VI}_h\) universe for the functional f(R, T) in the form \(f(R,T)=\mu R+\mu T\), where R and T are respectively Ricci scalar and trace of energy momentum tensor and \(\mu \) is a constant. We have made use of the hyperbolic scale factor to find the physical parameters and metric potentials defined in the space-time. The physical parameters are constrained from different representative values to build up a realistic cosmological model aligned with the observational behaviour. The state finder diagnostic pair is found to be in the acceptable range. The energy conditions of the model are also studied.     

Upper Ocean Four-Dimensional Variational Data Assimilation in the Arabian Sea and Bay of Bengal

A regional ocean circulation model with four-dimensional variational data assimilation scheme is configured to study the ocean state of the Indian Ocean region (65°E–95°E; 5°N–20°N) covering the Arabian Sea (AS) and Bay of Bengal (BoB). The state estimation setup uses 10 km horizontal resolution and 5 m vertical resolution in the upper ocean. The in-situ temperature and salinity, satellite-derived observations of sea surface height, and blended (in-situ and satellite-derived) observations of sea surface temperature alongwith their associated uncertainties are used for data assimilation with the regionally configured ocean model. The ocean state estimation is carried out for 61 days (1 June to 31 July 2013). The assimilated fields are closer to observations compared to other global state estimates. The mixed layer depth (MLD) of the region shows deepening during the period of assimilation with AS showing higher MLD compared to the BoB. An empirical forecast equation is derived for the prediction of MLD using the air–sea forcing variables as predictors. The surface and sub-surface (50 m) heat and salt budget tendencies of the region are also investigated. It is found that at the sub-surface, only the advection and diffusion temperature and salt tendencies are important.     

Global spectra of energy and enstrophy and their fluxes during July 1979

Transient and stationary spectra of kinetic energy (KE), available potential energy (APE) and enstrophy (EN), and their spectral fluxes as a function of the two-dimensional wavenumbern were computed for July 1979. Triangular truncation at zonal wavenumber 42 was used for computation. The slopes of various spectra in the wavenumber range 14≤n≤25 were obtained by fitting a straight line in log-log scale by the least square method. The transientKE, APE andEN spectra in the lower (upper) troposphere had slopes −2·21 (−2·30), −2·65 (−2·64) and −0·36 (−0·46), respectively. The effect of stationary and divergent motion on the slope values was investigated. The possible correlation between the slope and percentage of transient component in the combined energy and enstrophy was examined to identify the transient motion of the atmosphere with the two-dimensional homogeneous isotropic turbulence. The vertically averaged slope of kinetic energy and enstrophy in the lower (upper) troposphere was close to the value at 700 (200) hPa level. The spectral fluxes of kinetic energy and enstrophy in the wavenumber range 14≤n≤25 satisfied, to a very rough approximation, the criteria of inertial subrange. The stationary fluxes were small. The estimated stationary-transient component of flux was larger, comparable and less than the corresponding transient flux of APE, KE and EN. Representative levels for computation of energy and enstrophy spectra and their fluxes in the lower and upper troposphere were identified.