Minimization Of Cost Function Research Articles

ADAPTIVE CONTROL OF A SUBMARINE FOR VARIOUS DIVING DEPTHS USING AN EXPONENTIAL

Due to the progress of deep submergence capabilities, a submarine is extensively employed on many sides of marine science. For that reason, it has become necessary to design an effective submarine position controller while achieving a fast and stable mission. An adaptive analytical scheme for the underwater submarine was developed. The main purpose of the adaptive analytical scheme is to provide a powerful analytical controller that can successfully steer the submarine from the current state under the water to the surface of water in a short time. To achieve that, a seventh-term exponential function was proposed to reshape the reference diving depth while maintaining the control variable limitation and satisfying initial and final boundary conditions. The direct search method with two cascade loops was employed to achieve a minimum cost function by determining an appropriate constant of the function and minimum final time. However, using the direct search method can be time-consuming since a number of algebraic operations are executed inside these two loops. Therefore, the curve fitting method was used to fit the set of direct search method data using power functions. Then, at a certain diving depth, the function coefficients were computed based on the final settling time and function constant using the Gaussian elimination method. A nominal numerical simulation of the submarine’s model was implemented using both adaptive analytical and linear controllers.

Modified Memoryless Spectral-Scaling Broyden Family on Riemannian Manifolds

AbstractThis paper presents modified memoryless quasi-Newton methods based on the spectral-scaling Broyden family on Riemannian manifolds. The method involves adding one parameter to the search direction of the memoryless self-scaling Broyden family on the manifold. Moreover, it uses a general map instead of vector transport. This idea has already been proposed within a general framework of Riemannian conjugate gradient methods where one can use vector transport, scaled vector transport, or an inverse retraction. We show that the search direction satisfies the sufficient descent condition under some assumptions on the parameters. In addition, we show global convergence of the proposed method under the Wolfe conditions. We numerically compare it with existing methods, including Riemannian conjugate gradient methods and the memoryless spectral-scaling Broyden family. The numerical results indicate that the proposed method with the BFGS formula is suitable for solving an off-diagonal cost function minimization problem on an oblique manifold.

Securing Internet-of-Medical-Things networks using cancellable ECG recognition

Reinforcement of the Internet of Medical Things (IoMT) network security has become extremely significant as these networks enable both patients and healthcare providers to communicate with each other by exchanging medical signals, data, and vital reports in a safe way. To ensure the safe transmission of sensitive information, robust and secure access mechanisms are paramount. Vulnerabilities in these networks, particularly at the access points, could expose patients to significant risks. Among the possible security measures, biometric authentication is becoming a more feasible choice, with a focus on leveraging regularly-monitored biomedical signals like Electrocardiogram (ECG) signals due to their unique characteristics. A notable challenge within all biometric authentication systems is the risk of losing original biometric traits, if hackers successfully compromise the biometric template storage space. Current research endorses replacement of the original biometrics used in access control with cancellable templates. These are produced using encryption or non-invertible transformation, which improves security by enabling the biometric templates to be changed in case an unwanted access is detected. This study presents a comprehensive framework for ECG-based recognition with cancellable templates. This framework may be used for accessing IoMT networks. An innovative methodology is introduced through non-invertible modification of ECG signals using blind signal separation and lightweight encryption. The basic idea here depends on the assumption that if the ECG signal and an auxiliary audio signal for the same person are subjected to a separation algorithm, the algorithm will yield two uncorrelated components through the minimization of a correlation cost function. Hence, the obtained outputs from the separation algorithm will be distorted versions of the ECG as well as the audio signals. The distorted versions of the ECG signals can be treated with a lightweight encryption stage and used as cancellable templates. Security enhancement is achieved through the utilization of the lightweight encryption stage based on a user-specific pattern and XOR operation, thereby reducing the processing burden associated with conventional encryption methods. The proposed framework efficacy is demonstrated through its application on the ECG-ID and MIT-BIH datasets, yielding promising results. The experimental evaluation reveals an Equal Error Rate (EER) of 0.134 on the ECG-ID dataset and 0.4 on the MIT-BIH dataset, alongside an exceptionally large Area under the Receiver Operating Characteristic curve (AROC) of 99.96% for both datasets. These results underscore the framework potential in securing IoMT networks through cancellable biometrics, offering a hybrid security model that combines the strengths of non-invertible transformations and lightweight encryption.

Robust predictive control strategy of SCIG-based drive system

This article presents a robust finite control set predictive scheme for a stand-alone squirrel cage induction generator (SCIG) drive. This technique is considered an alternative to the drive system due to the inclusion of system nonlinearities and fast dynamic response. The control objective in the distributed generation environment is to fix the output voltage to follow the stand-alone requirement. The strategy establishes optimized switching instants for cost function minimization for both source and load converter control and diminished cross-coupling amid active and reactive power during transient scenarios. The scheme is designed to achieve the minimal effect caused by the parameter uncertainties. During source and load changes, this work will also address the maintenance of dc-link voltage, machine, and load variables at the set value, supported by machine and load-end converter control to achieve stand-alone load objectives. In addition, the presented scheme is also tested with random variation of speed to check the efficacy of the control configuration. The drive performance is evaluated by simulation using MATLAB/Simulink environment. Comprehensive real-time findings obtained from a scaled laboratory test bench using dSPACE-1104 are provided to verify the feasibility of the predictive solution.

High-resolution US methane emissions inferred from an inversion of 2019 TROPOMI satellite data: contributions from individual states, urban areas, and landfills

Abstract. We quantify 2019 annual mean methane emissions in the contiguous US (CONUS) at 0.25° × 0.3125° resolution by inverse analysis of atmospheric methane columns measured by the Tropospheric Monitoring Instrument (TROPOMI). A gridded version of the US Environmental Protection Agency (EPA) Greenhouse Gas Emissions Inventory (GHGI) serves as the basis for the prior estimate for the inversion. We optimize emissions and quantify observing system information content for an eight-member inversion ensemble through analytical minimization of a Bayesian cost function. We achieve high resolution with a reduced-rank characterization of the observing system that optimally preserves information content. Our optimal (posterior) estimate of anthropogenic emissions in CONUS is 30.9 (30.0–31.8) Tg a−1, where the values in parentheses give the spread of the ensemble. This is a 13 % increase from the 2023 GHGI estimate for CONUS in 2019. We find emissions for livestock of 10.4 (10.0–10.7) Tg a−1, for oil and gas of 10.4 (10.1–10.7) Tg a−1, for coal of 1.5 (1.2–1.9) Tg a−1, for landfills of 6.9 (6.4–7.5) Tg a−1, for wastewater of 0.6 (0.5–0.7), and for other anthropogenic sources of 1.1 (1.0–1.2) Tg a−1. The largest increase relative to the GHGI occurs for landfills (51 %), with smaller increases for oil and gas (12 %) and livestock (11 %). These three sectors are responsible for 89 % of posterior anthropogenic emissions in CONUS. The largest decrease (28 %) is for coal. We exploit the high resolution of our inversion to quantify emissions from 70 individual landfills, where we find emissions are on median 77 % larger than the values reported to the EPA's Greenhouse Gas Reporting Program (GHGRP), a key data source for the GHGI. We attribute this underestimate to overestimated recovery efficiencies at landfill gas facilities and to under-accounting of site-specific operational changes and leaks. We also quantify emissions for the 48 individual states in CONUS, which we compare to the GHGI's new state-level inventories and to independent state-produced inventories. Our posterior emissions are on average 27 % larger than the GHGI in the largest 10 methane-producing states, with the biggest upward adjustments in states with large oil and gas emissions, including Texas, New Mexico, Louisiana, and Oklahoma. We also calculate emissions for 95 geographically diverse urban areas in CONUS. Emissions for these urban areas total 6.0 (5.4–6.7) Tg a−1 and are on average 39 (27–52) % larger than a gridded version of the 2023 GHGI, which we attribute to underestimated landfill and gas distribution emissions.

Acoustic 2-D Full-Waveform Inversion with Non-Balanced Finite differences and Adaptive Weight Decay Methods

Full waveform inversion (FWI) is a powerful seismic imaging technique that aims to achieve high-resolution subsurface models by iteratively comparing recorded seismic waveforms with modeled waveforms. The success of FWI relies on the precision of forward modeling algorithms and the effectiveness of optimization strategies. In this study, we propose a FWI methodology that leverages non-balanced staggered-grid finite differences schemes (NBFD) in the forward modeling process. By employing operators with spatial differencing of varying lengths, these schemes enhance the efficiency of forward modeling.For the optimization process, we employ adaptive gradient-based optimization with weight decay, a widely-used approach in machine learning and deep learning algorithms for model training. These methods demonstrate efficient optimization processing for large data volumes with high precision. The objective of adaptive gradient-based optimization is to dynamically adjust the update rate model parameters during the iterative process. This facilitates improved convergence speed, enhances stability, and overcomes challenges associated with traditional fixed-rate adjustment methods.To ensure accurate inversion results and avoid local minima in the cost function minimization, we implement a Multiscaling inversion strategy within the workflow. The obtained results are compared with those achieved through conventional FWI using standard staggered finite differences and various optimization methods. Our findings demonstrate that employing non-balanced staggered-grid finite differences scheme leads to significant improvements compared to the previously reported results in the literature.

Output feedback distributed optimization algorithms of higher‐order uncertain nonlinear multi‐agent systems

AbstractOutput feedback distributed optimization problem is studied for higher‐order multi‐agent systems with uncertain nonlinearities, which are assumed to satisfy linear growth conditions. The agents dynamics are permitted to be heterogenous with different nonlinearities. The problem is solved by embedded control approach based output feedback distributed optimization algorithms. First, a first‐order optimal signal generator is designed, of which outputs reach the minimizer of the global cost function. Second, embedding the generator into the feedback loop and taking the outputs of the generator as the reference outputs of the agents, output feedback tracking controllers are designed for the higher‐order multi‐agent systems on the basis of nonseparation principle and feedback domination technique. Under the proposed control algorithms, all the agents outputs asymptotically approach a bounded neighbor region of the global minimizer. Simulations demonstrate the effectiveness of the proposed output feedback distributed optimization algorithms.

Predictive controllers for synchronous reluctance motor drive systems

This paper proposes the design and implementation of predictive controllers for synchronous reluctance motor drive systems to enhance their dynamic responses. The predictive speed and current controllers in this paper are designed in systematic procedures. The predictive speed controller is implemented by using Laguerre function procedure. The Laguerre function is used to simplify the algorithm and to minimize the execution time of the digital signal processor. For predictive current controller, a finite control set method improves the current tracking ability. The measured currents are used to predict the future phase-current based on the motor model. The optimal control inputs of both predictive controllers are determined by using a cost function minimization method. Experimental results show the proposed drive system provides a wide adjustable speed range, from 2 r/min to 1800 r/min. It has better performance than a proportional-integral (PI) controller including fast rise time, which is 0.9 second, small steady state error, which is 0.32 r/min, and small current ripples. A 32-bit floating-point digital signal processor, TMS-320-F-28335 DSP, is employed to implement the control algorithms.

A minimum objective function trim procedure for VTOLs noise reduction

The present paper proposes a novel approach for multi-rotor acoustic nuisance mitigation based on the identification of optimal control settings. This strategy is possible thanks to the peculiarity of multi-rotor systems (like, for instance, those involved in urban air mobility applications) to have redundant controls. The idea is to take full advantage of the control redundancy by defining the control settings that guarantee the desired steady-state flight conditions while, at the same time, optimizing selected target functions such as performance or noise emissions. To this aim, the trim problem is recast into a constrained cost function minimization problem. Since the objective is to reduce as much as possible the noise disturbance of trimmed VTOL, an aeroacoustic tool based on the chordwise-compact form of the Farassat 1A formulation for the evaluation of noise radiation is suitably coupled with a trim solver. The numerical investigations consider quadcopter and hexacopter configurations in level flight at several advancing speeds. Comparisons of the proposed minimum-noise trim strategy with two other trim strategies based on the minimization of rotor torque and control effort prove its capability to provide an overall reduction of noise throughout the entire velocity range examined.

Technical note: Bimodal parameterizations of in situ ice cloud particle size distributions

Abstract. The cloud particle size distribution (PSD) is a key parameter for the retrieval of microphysical and optical properties from remote-sensing instruments, which in turn are necessary for determining the radiative effect of clouds. Current representations of PSDs for ice clouds rely on parameterizations that were largely based on aircraft in situ measurements where the distribution of small ice crystals were uncertain. This makes current parameterizations deficient to simulate remote-sensing observations sensitive to small ice, such as from lidar and thermal infrared instruments. In this study we fit the in situ PSDs of ice crystals from the JULIA (JÜLich In situ Aircraft data set) database, which consists of 11 campaigns covering the tropics, midlatitudes and the Arctic, consistently processed and considered more robust in their measurements of small ice. For the fitting, we implement an established approach to PSD parameterizations, which consists of finding an adequate set of parameters for a modified gamma function after normalization of both PSD axes. These parameters are constrained to match in situ measurements when predicting microphysical properties from the PSDs, via a cost function minimization method. We selected the ice water content and the ice crystal number concentration, which are currently key parameters for modern satellite retrievals and model microphysics schemes. We found that a bimodal parameterization yields better results than a monomodal one. The bimodal parameterization has a lower spread for almost all ice crystal sizes over the entire range of analyzed temperatures and fits better the observations, especially for particles between 20 and about 110 µm at temperatures between −60 and −20 ∘C. For this temperature range, the root mean square error for the retrieved Nice is reduced from 0.36 to 0.20. This demonstrates a clear advantage to considering the bimodality of PSDs, e.g., for satellite retrievals.

Solving traffic data occlusion problems in computer vision algorithms using DeepSORT and quantum computing

Inaccuracies of traffic sensors during traffic counting and vehicle classification have persisted as transportation agencies have been prompted to calibrate sensors periodically. Detection of multiple objects, heavy occlusions, and similar appearances in congested places are some causes of computer vision model inaccuracies. This paper used the YOLOv5 model for detection and the DeepSORT model for tracking objects. Due to the nature of the reported problem caused by many misses and mismatches, the power of quantum computing with the alternating direction method of multipliers (ADMM) optimizer was leveraged. A basic Kalman filter and the Hungarian algorithm features were used in combination with a quantum optimizer to present robust multiple object tracking (MOT) algorithms. This hybrid combination of the classical and quantum model has fastened learning the occludes during frame matching of tracks and detections by generating minimum quantum cost function value. Comparisons with the existing models indicated a significant increase in the primary MOT metric multiple object tracking accuracy (MOTA) by 16% more than the regular YOLOv5-DeepSORT model when using a quantum optimizer. Also, a 6% multiple object tracking precision (MOTP) increases and a 6% identification metrics (F1) score increase were observed using the quantum optimizer with identity switching reduced from 6 to 4. This model is expected to assist transportation officials in improving the accuracy of traffic counts and vehicle classification and reduce the need for regular computer vision software calibration.

A game approach to multi-dimensional opinion dynamics in social networks with stubborn strategist agents

In a social network, individuals express their opinions on several interdependent topics, and therefore the evolution of their opinions on these topics is also mutually dependent. In this work, we propose a differential game model for the multi-dimensional opinion formation of a social network whose population of agents interacts according to a communication graph. Each individual’s opinion evolves according to an aggregation of disagreements between the agent’s opinions and its graph neighbors on multiple interdependent topics exposed to an unknown extraneous disturbance. For a social network with strategist agents, the opinions evolve over time with respect to the minimization of a quadratic cost function that solely represents each individual’s motives against the disturbance. We find the unique Nash/worst-case equilibrium solution for the proposed differential game model of coupled multi-dimensional opinions under an open-loop information structure. Moreover, we propose a distributed implementation of the Nash/worst-case equilibrium solution. We examine the non-distributed and proposed distributed open-loop Nash/worst-case strategies on a small social network with strategist agents in a two-dimensional opinion space. Then we compare the evolved opinions based on the Nash/worst-case strategy with the opinions corresponding to social optimality actions for non-strategist agents.

A Low-Complexity Double Vector Model Predictive Current Control for Permanent Magnet Synchronous Motors

Compared to the conventional finite control set model predictive control (FCS-MPC), the double vector model predictive current control (DVMPCC) for permanent magnet synchronous motors (PMSMs) has a better steady-state performance without significantly increasing the switching frequency. However, determining optimal vectors with their dwell times requires a high computational burden. A low-complexity DVMPCC in the steady state was proposed in this study to address this problem. Firstly, the operating state of the motor was judged according to the speed error. During steady-state operation, the first optimal active vector was selected from three candidate vectors adjacent or identical to the active vector applied in the previous control period, reducing the number of comparisons by half. Next, the second optimal vector was selected from the other two active vectors, and the zero vector, the second optimal vector with the duty cycle, was determined according to the deadbeat condition of the q-axis current and cost function minimization. Finally, simulation and experimental results proved that the proposed low-complexity DVMPCC for surface-mounted permanent magnet synchronous motors is practical and feasible.

Deep kinematic inference affords efficient and scalable control of bodily movements.

Performing goal-directed movements requires mapping goals from extrinsic (workspace-relative) to intrinsic (body-relative) coordinates and then to motor signals. Mainstream approaches based on optimal control realize the mappings by minimizing cost functions, which is computationally demanding. Instead, active inference uses generative models to produce sensory predictions, which allows a cheaper inversion to the motor signals. However, devising generative models to control complex kinematic chains like the human body is challenging. We introduce an active inference architecture that affords a simple but effective mapping from extrinsic to intrinsic coordinates via inference and easily scales up to drive complex kinematic chains. Rich goals can be specified in both intrinsic and extrinsic coordinates using attractive or repulsive forces. The proposed model reproduces sophisticated bodily movements and paves the way for computationally efficient and biologically plausible control of actuated systems.

Reconstruction coefficient analysis of honeybee collapse due to pesticide contamination

In this paper we consider the inverse problems of identifying space-dependent coefficients of the mortality rate of the bees and the rate of contamination of the forager bees by pesticides. The model is described by a weakly coupled system of two reaction-diffusion equations for the spatial distribution of uncontaminated and contaminated foraging bees. Final time t = T observations of the density of uncontaminant and contaminant forager bees are used. We propose two approaches for studying the problems. The first one uses the overspecified information to transform the problems into non-linear parabolic equations involving the solution values at the final time. This allows us to prove, using fixed-point arguments, existence of solution to the inverse problems. The second study employs the concept of the quasi-solution to establish existence of solution to the inverse problems as minimizers of least-square cost functionals.

Enhancing speaker verification accuracy with deep ensemble learning and inclusion of multifaceted demographic factors

<span lang="EN-US">Effective speaker identification is essential for achieving robust speaker recognition in real-world applications such as mobile devices, security, and entertainment while ensuring high accuracy. However, deep learning models trained on large datasets with diverse demographic and environmental factors may lead to increased misclassification and longer processing times. This study proposes incorporating ethnicity and gender information as critical parameters in a deep learning model to enhance accuracy. Two convolutional neural network (CNN) models classify gender and ethnicity, followed by a Siamese deep learning model trained with critical parameters and additional features for speaker verification. The proposed model was tested using the VoxCeleb 2 database, which includes over one million utterances from 6,112 celebrities. In an evaluation after 500 epochs, equal error rate (EER) and minimum decision cost function (minDCF) showed notable results, scoring 1.68 and 0.10, respectively. The proposed model outperforms existing deep learning models, demonstrating improved performance in terms of reduced misclassification errors and faster processing times.</span>

Application of cell mapping to control optimization for an antenna servo system on a disturbed carrier

Abstract. The cell-mapping method, due to its global optimality, has been applied to solve multi-objective optimization problems (MOPs) and optimal control problems. However, the curse of dimensionality limits its application in high-dimensional systems. In this paper, the multi-parameter sensitivity analysis is investigated to reduce the parameter space dimension, which broadens the application of cell mapping to MOPs in high-dimensional parameter space. A post-processing algorithm for MOPs is introduced to help choose proper control parameters from the Pareto set. The proposed scheme is applied successfully in the control parameter optimization of an adaptive nonsingular terminal sliding-mode control for an antenna servo system on a disturbed carrier. Moreover, as the existing global optimal tracking control with an adjoining cell-mapping method may generate tracking-phase differences, an optimal-sliding-mode combined-control strategy is proposed. By using the combined-control strategy, the azimuth and pitch angles of the antenna system are controlled to catch up to a target trajectory with the minimum cost function and to keep high-precision tracking after that.

Calculating a collision avoidance maneuver for two unmanned ships by minimizing a cost function in MATLAB

An approach to the problem of collision avoidance of two unmanned vessels in certain area based on cost function minimization is presented in the paper. A script written in the MATLAB computational environment that calculates the optimal maneuver to prevent a collision is described. The cost function in this study is defined as the square of the difference between the safe distance and the Closest Point of Approach, and in order to find the optimal maneuver, it needs to be minimized, for which the fmincon (a MATLAB optimization function) is used in this code. The calculation of collision avoidance maneuvers is made “ from the perspective” of the VTS: it’s optimized for two vessels and allows the vessels to pass each other at a specified distance. The script, taking as input a matrix with data on pairs of approaching vessels (their x and y coordinates, speeds, and courses), by minimizing the cost function, calculates the optimal change in speeds and/or courses for two vessels, allowing them to pass each other at a safe distance. To verify the functionality of the script, a successful simulation is carried out in MATLAB. Several examples of its operation are given. These are situations where the closest point of approach (CPA) is grea-ter than safe one; situations where the CPA is less than safe distance, but the time to CPA is greater than safe time; and situations of dangerous convergence. The calculation results are illustrated with MATLAB graphs. The code of the script described in this paper can be further refined to work in conjunction with other algorithms, and it can also be used to create training datasets for training neural networks to predict safe maneuvers to prevent collisions of unmanned vessels at sea. In this study, the influence of wind and current is not considered, and the COLREGs‑72 is not also taken in consideration. Vessels can maneuver both to port and starboard, as well as reduce speed regardless of the type of approach situation.

Cost-effective energy management of an islanded microgrid

The interest in the integration of distributed energy resources in microgrids increased significantly in the last decade. The stochastic nature of some energy sources and the dynamic power demand has brought difficulties regarding the optimal control of microgrids. This current study addresses the energy management challenge in an islanded hybrid energy microgrid that includes three types of renewable energy resources (photovoltaic, geothermal and biomass) and a battery storage system, using intelligent management methods that optimize energy production costs. The proposed intelligent management methods are based on cost function minimization. These ensure optimal energy management operation under uncertain weather conditions, keeping to the minimum the price of the energy produced by the microgrid. Due to the erratic nature of solar irradiance and considering that solar energy is cheaper than its counterparts (geothermal and biomass in this case), forecasting the photovoltaic power production is an essential task for guaranteeing optimal microgrid operation. Day-ahead photovoltaic power forecasts are issued based on solar irradiance forecasts provided by the Global Forecasting System and further integrated into the day-ahead scheduling of the microgrid. This algorithm, together with the cost-optimization algorithms, gives intelligence to the management protocol generating the input parameters (power and operating time for each generating unit) for the microgrid Energy Management Controller. Different cost optimization methods are studied and compared, including mathematical models, such as Mixed Integer Linear Programming, or nature-inspired optimization algorithms, such as Genetic Algorithm, Harmony Search Algorithm, and Particle Swarm Optimization. It is shown that these algorithms provided suitable solutions for the energy balance and scheduling ensuring minimal operation costs for the microgrid. The study also highlights the differences and limitations of these algorithms and shows a method on how these energy management methods can be integrated into a real-world microgrid providing a step forward in the development of intelligent microgrids.

Three-Dimensional Variational Multi-Doppler Wind Retrieval over Complex Terrain

Abstract The interaction of airflow with complex terrain has the potential to significantly amplify extreme precipitation events and modify the structure and intensity of precipitating cloud systems. However, understanding and forecasting such events is challenging, in part due to the scarcity of direct in situ measurements. Doppler radar can provide the capability to monitor extreme rainfall events over land, but our understanding of airflow modulated by orographic interactions remains limited. The SAMURAI software is a three-dimensional variational data assimilation (3DVAR) technique that uses the finite element approach to retrieve kinematic and thermodynamic fields. The analysis has high fidelity to observations when retrieving flows over a flat surface, but the capability of imposing topography as a boundary constraint is not previously implemented. Here, we implement the immersed boundary method (IBM) as pseudo-observations at their native coordinates in SAMURAI to represent the topographic forcing and surface impermeability. In this technique, neither data interpolation onto a Cartesian grid nor explicit physical constraint integration during the cost function minimization is needed. Furthermore, the physical constraints are treated as pseudo-observations, offering the flexibility to adjust the strength of the boundary condition. A series of observing simulation sensitivity experiments (OSSEs) using a full-physics model and radar emulator simulating rainfall from Typhoon Chanthu (2021) over Taiwan are conducted to evaluate the retrieval accuracy and parameter settings. The OSSE results show that the strength of the IBM constraints can impact the overall wind retrievals. Analysis from real radar observations further demonstrates that the improved retrieval technique can advance scientific analyses for the underlying dynamics of orographic precipitation using radar observations.