Model Of Temperature Distribution Research Articles

Imaging performance prediction of a hypersonic target in a geosynchronous orbit based on multi-dimensional information correlation of radiation, multi-spectral, and polarization

Hypersonic target detection based on infrared intensity characteristics is easily disturbed by sea surface and cloud flares when detected by space-based optical systems, which results in a low detection rate, high false alarm, and difficulty in stable detection. This paper explores a method to improve target detection performance based on the correlation of infrared radiation, multi-spectral and polarization. Firstly, the comprehensive factors that influence complex ambient illumination, atmospheric transmission, and clutter background on spectral-polarization characteristics of hypersonic targets are analyzed. Based on the global radiation scattering theory, the temperature distribution model of the hypersonic target is established by using FLUENT. The polarization emission and pBRDF model of the target is established, and the radiation polarization transfer model is generated. Secondly, the sea surface temperature distribution is obtained by inversion of Landsat8 remote sensing data. The radiation polarization transfer model of the sea surface is established based on the Cox-Munk model combined with pBRDF and the polarization emission model. Thirdly, the polarization scattering effect of atmospheric particles on the upward radiation of the interaction of the target with the sunlight is considered comprehensively, and the 6SV radiative transfer model is used to calculate the polarization effect of atmospheric particles on the upward radiation transmission of the target and the background. Then, combined with the point diffusion of the optical system and the photoelectric conversion of the detector, the multi-dimensional full-chain imaging prediction model of the hypersonic target-sea background-ambient atmosphere-optical system-detector is established. The imaging characteristics and detection performance of the target in different imaging dimensions are simulated and analyzed with the signal-to-clutter ratio (SCR). The research shows that in the direction of reflected sunlight from the sea surface, the sea surface glare is suppressed and the target is highlighted through a target detection method of multi-dimensional information. This method has better detection results than the infrared multi-spectral detection method.

Modeling of temperature distribution and clad geometry of the molten pool during laser cladding of CoCrCuFeNi alloys

Modeling of temperature distribution and clad geometry of the molten pool during laser cladding of CoCrCuFeNi alloys

A two-dimensional semi-analytic thermal model for global temperature distribution predicting and hot spot monitoring in interior permanent magnet synchronous motor

A two-dimensional semi-analytical thermal model (SATM) is presented, aiming to quickly and accurately achieve global temperature distribution predicting and hot spot monitoring for interior permanent magnet synchronous motor (IPMSM). Thereby, it provides a reliable analysis tool for thermal behavior evaluation and prevents undesired consequences induced by excessive temperature rise, which is of great worth and significance in promoting the flourishing of IPMSM. SATM combines the analytical method, lumped parameter thermal network, and finite element analysis to obtain an analytical solution for thermal behavior through mathematical derivation by considering the complicated configuration, heat source distribution, heat dissipation condition, and material thermal dependence. Through SATM, it is possible to observe the global temperature distribution as well as the location and size of hot spots in each element. The temperature distribution gradient on the static is more pronounced than that on the dynamic; secondly, the area with the most severe heating is mainly found on the winding; furthermore, the hot spot on the winding is mainly located a little bit inside the center. Moreover, the thermal behavior of IPMSM at rated load is investigated by numerical analysis and experiments. A comprehensive comparison with SATM is done. The computational deviations between SATM and numerical analysis regarding the hot spot, minimum, and average temperatures on each element are all within 4.06%. However, SATM consumes only 20.92% of the time and 68.29% of the storage of the numerical analysis. The measured data also fully prove the reliability and validity of the comparison. It is certain that SATM can well break through the limitation of the existing non-numerical technique to quickly and accurately achieve global temperature distribution predicting and hot spot monitoring of IPMSM. It provides researchers and engineers engaged in thermal behavior evaluation with good analysis means, design guidance, and optimization direction.

A mathematical model of temperature distribution along the length of the oil production well

The paper gives a systems analysis in the field of heat transfer and temperature distribution (TD) along the length of oil production wells (OPW). The analysis shows that the existing mathematical models are suitable only for determining TD along the length of casing string (CS) and are not suitable for determining TD along the length of the tubing run, since the existence of the interfacial (between the CS and the tubing) annulus of the fluid and gas layers with heat capacity and thermal conductivity that differ significantly from the heat capacity and thermal conductivity of rocks surrounding the CS. Given the above, mathematical models taking into account the impact of the fluid and gas layers in the annulus on the heat transfer from the upward fluid flow to the tubing wall and from the wall to the interfacial annulus are developed. To ensure the technological effectiveness of the obtained model, formulas for quantitative estimation of the heat transfer of the fluid flow into the surrounding environment are given.

Time-dependent model of temperature distribution in continuous flow pulsed electric field treatment chambers

A key component of a continuous flow pulsed electric field (PEF) system is the treatment chamber, where the product is exposed to electric pulses. Determination of the temperature distribution in the chamber during PEF treatment is important since high local increases in temperatures can affect the quality of the product. Coupled simulations of electric field, fluid flow, and heating in the existing literature do not model each individual electric pulse, but rather employ a “duty cycle” approach, which does not account for transient variations in treatment intensity and temperature changes in the medium. We present a time-dependent approach to modelling PEF treatment in continuous flow treatment chambers, which can model each pulse separately, and thus enables a more accurate study of temporal and spatial distributions of electric field and temperature. The model has been validated on laboratory scale treatment chambers of parallel plate or colinear design and using realistic protocols. Industrial relevance textThe paper is relevant to all pulsed electric field (PEF) applications either on laboratory or industrial scale that implement a continuous flow treatment chamber. It presents an improved modelling approach which allows for an analysis of the electrical current, electric field, and temperature distribution in the chamber during, at the end, and in between application of electrical pulses. The model can be used to predict the peak temperature at the end of each pulse in the hot spots, which if large enough could potentially lead to thermal damage of the product or in extreme cases even potential local boiling of the medium, resulting not only in degradation of the treated product, but also in accelerated electrode fouling, oxidation, and dissolution (etching), as well as arcing. This would not only affect the quality of the treated product but would also affect the wear and lifetime of electrodes/chambers, and of the pulse generator. The model can also be used to avoid expensive trial-and-error optimization of the PEF protocols and chamber geometries in situ.

Quantification of geometrical errors and thermal effects during wire EDM of thin wall structures—A numerical study

Machining thin-walled structures with a high aspect ratio using Wire EDM can lead to geometrical errors, primarily of two types; overcut error due to kerf formation and thermal deformation of the entire wall section. To understand the driving mechanisms behind these errors three distinct numerical models were developed. Initially, a model based on a moving heat source was created, employing the apparent heat capacity approach to predict kerf width and the associated overcut error. These insights were then utilized to formulate a transient temperature distribution model with a redesigned geometry, considering time-dependent evolution of the kerf and corresponding changes in the material properties of the sub-domains. Finally, a thermo-mechanical coupled model was developed to predict geometrical errors caused by the deflection of the wall, considering the varying stiffness of the part. A series of experiments were conducted to gain insight into the effect of the designed wall thickness on wall deflection. For the selected design profile and machine parameters, the model predicts a 62.4% reduction in thickness and a corresponding over-cut error of 188μm. Similarly, the model predicts wall deformation in the range of 6μm to 312μm for various wall thickness levels and these findings were validated with experimental observations.

Gas turbine circumferential temperature distribution model for the combustion system fault detection

The gas turbine combustion system operates under harsh conditions, and any faults such as nozzle clogging, cracks, etc. can endanger the downstream components and cause catastrophic accidents. Thus, monitoring the combustion system status and detecting its performance degradation timely are crucial for gas turbine safety. The current predominant method for monitoring involves analyzing exhaust gas temperature (EGT) dispersion, utilizing thermocouples placed at the turbine outlet to indirectly assess combustion system performance. However, the EGT is affected not only by faults but also by various non-fault disturbances, such as operational conditions, atmospheric variations, compressor performance degradation, and uneven hot gas mixing and rotating. To improve the sensitivity of fault detection, it is necessary to investigate how various factors affect the EGT dispersion and differentiate between EGT changes due to interference and those due to combustion system faults. However, using actual operational data from gas turbines to analyze and reveal these impact mechanisms is challenging. Therefore, this paper develops a gas turbine model for combustion system fault detection that accurately reflects the uneven circumferential distribution of EGT. The model incorporates a multi-combustor burner, a multi-channel turbine, and a module for simulating the mixing and rotating of the hot gas. Using this model, simulations are conducted to study the effects of non-fault interference factors, such as variations in ambient temperature, fuel flow changes, and compressor performance degradation, on EGT distribution. Additionally, simulations are conducted to analyze the effects of faults, including combustor cracks, uneven fuel distribution, and the coupling of interferences with faults, on EGT distribution. By comparing the normal and abnormal modes, the study reveals the different EGT responses due to non-fault interferences and combustion system faults. Based on these findings, a fault detection method for coupled conditions is proposed. The research results provide a basis for the fault detection of combustion system, enabling practitioners to reduce interference in fault detection and to increase the detection sensitivity.

High-Resolution Reconstruction Model for Spatial Temperature Distribution in Grain Storage Based on 3DSRCNN_Resnet

High-Resolution Reconstruction Model for Spatial Temperature Distribution in Grain Storage Based on 3DSRCNN_Resnet

3D Electrothermal Model for Internal Temperature Distribution in Lithium-Ion Battery Cell and Module

In recent years, lithium-ion batteries (LIBs) have been massively developed in many applications as they provide high energy and power densities, high efficiency and long lifespan compared to other battery technologies. Despite remarkable improvements, Li-ion batteries still face thermal issues, which cause performance drop, limited calendar life, safety concerns and temperature-caused degradation. Therefore, proper thermal management for a LIB is necessary to control its temperature and to extend its lifetime. Internal temperature measurement remains very challenging for LIB. So, electrothermal LIB models, developed to forecast both electrical performances and temperature distributions, seems to be a powerful and complementary tool to experiments, in particular to obtain battery temperatures in use. Most of models, assume simplified approach considering that heat sources are either located in the center of the cell or uniformly distributed in the volume of the cell and so do not consider the real internal geometry of the cells.In this work, a 3D electrothermal model of a large commercial prismatic NMC-type lithium-ion cell (25 Ah) is developed based on the internal geometry reconstructed from tomography. The electrothermal model, developed with the COMSOL Multiphysics® software with the real internal geometry as well as the anisotropy of the thermal properties, accounts for irreversible and reversible heat sources. The entropy variation profiles were estimated by Entroview™ using their patented method. The validation of the model is performed thank to temperature measurement during charge and discharge at several currents in a climatic chamber at 25°C. Simulation results highlight exothermal and endothermal behaviors related to the entropy change along with the charge and discharge stages. Moreover, the internal temperature distribution is thoroughly impacted by the internal geometry of the cell and the anisotropy of the thermal properties.Finally, the 3D electrothermal model is extended to a module of 12 cells in series (12S) to evaluate the heterogeneities of internal temperatures considering the real geometry of each cell. Once validated, simulation (as shown of figure 1) underline the heterogeneous temperature distribution at the module scale and the importance of having an efficient battery thermal management system to limit an excessive increase of the temperatures which can cause performance drops until irreversible degradations. Figure 1

Numerical modeling of non-uniform indoor temperature distribution for coordinated air flow control

The indoor thermal environment is usually non-uniformly distributed in parameters such as temperature and velocity. For precise control of indoor environment, it is necessary to figure out the indoor non-uniform temperature distribution (INUTD) that empowers independently zone control according to the different requirements of occupants. Computational Fluid Dynamics (CFD) tool is usually used to obtain the INUTD, but it consumes huge computational resources and time, which may not be suitable for coupling with control system. To address this research question, this study proposes a numerical modeling method for predicting the INUTD and air flowrate response of multiple diffusers for coordinated air flow control. Firstly, we establish a dataset with 5000 cases, along with the results of INUTD for each case. Then two models, namely room thermal response model (RTRModel) and air flowrate prediction model (AFPModel), are developed by machine learning algorithms to predict indoor temperature and supply air flowrate, respectively. The results show that proposed models are both fast in prediction, less than 1 s for each case. The standard deviation of error in RTRModel developed with support vector machine algorithm is 0.0041 while that in AFPModel developed with Convolutional Neural Network algorithm is 0.0198. Further, a comparative analysis has been conducted between the AFPModel with and without optimization algorithm. The results reveal that using optimization algorithm is more accurate, but it takes more time. While numerical modeling can instantaneous response with qualified accuracy. The proposed method can contribute to independently zonal environment control and occupant-centered micro-environment control.

Improved Surface Temperature Identification Method for Remote Observations of Sample Return Capsules

A new method for the identification of the peak temperature of the heat shield based on remote spectral irradiance measurements is proposed and tested through the analysis of results from the Hayabusa sample return capsule. To identify the peak temperature of the heat shield, a parameterized empirical model for the surface temperature distribution on the geometry is developed, and it is then used to simulate spectra for optimized fitting with a measured spectral radiance. This new peak temperature identification method is shown to be insensitive to the wavelengths resolved, the view of the geometry, and measurement noise. The peak temperature of the Hayabusa capsule geometry at the representative condition considered (3330 K) was resolved to within 20 K for the three instruments investigated, while the effective temperature varied by around 600 K depending on which instrument was used. The error in the peak temperature model is also shown to be an order of magnitude less sensitive to measurement noise than the effective temperature approach. The new peak temperature method facilitates the direct comparison of results from instruments with different bandwidths and/or different view angles of the capsule, which was previously not possible.

Stratified thermal energy storage model with constant layer volume for predictive control — Formulation, comparison, and empirical validation

Recent developments in heating systems have witnessed a significant increase of heat pumps with a highly temperature-dependent efficiency. Optimal real-time operation of these heating systems with predictive control requires a thorough understanding and modeling of the internal temperature distribution of the associated thermal energy storage. At the same time, the thermal energy storage models need to be sufficiently simple to ensure computational tractability in real-time predictive control. Therefore, this article presents a stratified thermal energy storage model with constant layer volume and variable temperature suitable for real-time predictive control. The model employs a novel formulation with quadratic or simpler constraints which enable high accuracy at low computation burden. The proposed model is validated experimentally and compared with other models available in literature. The results show that the proposed stratified thermal energy storage model represents the real-world behavior of a thermal energy storage with great accuracy, while reducing the required computational burden as compared to other models for real-time operation and control. A case study further demonstrates that the increased accuracy of the proposed new model leads to cost and energy savings for the operator.

Modeling and solving of temperature field of screw–nut pair based on geometric error distribution probability

Random geometric errors are inevitable during the machining process of the screw raceway, ball and nut raceway, which makes the contact state between the ball and raceway diverse, further leading to the generation of nonequal strength heat sources inside the screw–nut pair. In the past, when studying the temperature field of the screw–nut pair, it was assumed that all the balls were evenly loaded. To achieve more accurate temperature field modeling, the modeling of temperature field of the screw–nut pair based on geometric error distribution probability was studied. First, a quantitative relationship between geometric error and contact angle are established. Second, the axial force generated by ball and raceway with different joint geometric errors is determined when subjected to axial loads. Then, on the basis of geometric error statistics, the relationship between the error probability distribution and the heat source intensity distribution is connected, and the corresponding temperature field is solved by the finite difference method. Finally, the probabilistic temperature distribution theory is verified indirectly by a multi-axis thermal deformation experiment. The probabilistic temperature distribution model shows the dynamic change process of the temperature field with the probability of geometric error distribution and has guiding significance for the temperature field modeling of the screw–nut pairs with different precision. When the joint error presents a rectangular distribution, the maximum intensity heat source will be generated, and the ultimate temperature field will be induced.

Water spray effects on fire smoke temperature distribution beneath a symmetrical V-shaped tunnel ceiling

The coupling effects of the double-slope stack effect, the thermal buoyancy induced by the V-shaped tunnel fire and the drag force generated by the water spray system alter fire smoke flow regulation compared to fire smoke flow in a horizontal tunnel. By numerical simulation, this work investigates the effect of water spray flow rate (0 L/min – 600 L/min), atomization angle (0–150°) and the length within fire source and the grade change point (0–120 m) on smoke temperature distribution beneath a symmetrical V-shaped ceiling. The findings indicate that the cooling effect on smoke temperature can be significantly improved by increasing the rate of water spray flow, while water spray increasing angle and tunnel slope have little contribution to the cooling smoke temperature. Thus an improved ceiling smoke temperature distribution model is proposed by importing the flow rate, angle coefficients and tunnel slope. As the fire source distance from the grade change point increases, stack effect on fire smoke flow could be categorized into three zones, which are the double-slope control zone, the transition zone and the single-slope control zone, which causes that downstream smoke temperature become higher gradually than the upstream one, while the smoke temperature difference tends to stabilize at the single-slope control stage. Finally, a global ceiling smoke temperature distribution in the symmetrical V-shaped tunnel installed a water spray system is established by introducing fire source distance coefficients.

Fabrication of a Printed Heater Using a Composite of Silver Nanowires and Neutral PEDOT:PSS

In this work, a low resistance heater based on a composite of silver nanowires (Ag NWs) and neutral poly (3,4-ethylenedioxythiophene) poly(styrene sulphonate) (PEDOT:PSS) is fabricated. Pure Ag NWs have poor substrate adhesion, poor environmental and thermal stability, and high surface roughness. Local hotspots at wire junctions also leads to uneven joule heating. These disadvantages are overcome by blending the NWs with PEDOT:PSS. Specifically, neutral PEDOT:PSS is used in this work as it is less hygroscopic and possess greater environmental stability compared to the conventionally used acidic PEDOT:PSS. The composite is synthesized as a stable printable dispersion and deposited on a flexible polyethylene terephthalate (PET) substrate using an extrusion-based direct write system. Film thickness was optimized to achieve low sheet resistance and good adhesion and it is laminated with polydimethylsiloxane (PDMS) for environmental protection. The heater shows uniform temperature distribution with a short response time and low operating voltage. Temperature distribution modelling was carried out using COMSOL and correlated well with the experimental data. The heater also exhibits good repeatability and cyclic thermal stability. A prototype device with temperature cut-off and feedback was also implemented using an Arduino controller.

Modeling of Electron and Lattice Temperature Distribution Through Lifetime of Plasma Plume

When employing shorter (sub picosecond) laser pulses, in ablation kinetics the features appear which can no longer be described in the context of the conventional thermal model. Meanwhile, the ablation of materials with the aid of ultra-short (sub picosecond) laser pulses is applied for micromechanical processing. Physical mechanisms and theoretical models of laser ablation are discussed. Typical associated phenomena are qualitatively regarded and methods for studying them quantitatively are considered. Calculated results relevant to ablation kinetics for a number of substances are presented and compared with experimental data. Ultra-short laser ablation with two-temperature model was quantitatively investigated. A two-temperature model for the description of transition phenomena in a non-equilibrium electron gas and a lattice under picosecond laser irradiation is proposed. Some characteristics are hard to measure directly at all. That is why the analysis of physical mechanisms involved in the ablation process by ultra-short laser pulses has to be performed on the basis of a theoretical consideration of `indirect' experimental data. For Copper and Nickel metal targets, the two-temperature model calculations explain that the temperature of the electron subsystem increased suddenly and approached a peak value at the end of laser pulse. In addition, the temperature profile of lattice temperature subsystem evolution slowly, and still increasing after the end of laser pulse. A good agreement prevails when a comparison between the present results and published results.

A real time monitoring method for well-kick and lost circulation based on distributed fiber optic temperature measurement

In the process of oil drilling, if the formation pressure does not match the pressure in the borehole, it may cause well-kick or lost circulation. The existing methods of mud level monitoring and micro-flow monitoring have some shortcomings. In these methods, information feedback is untimely and inaccurate. Well-kick or lost circulation position cannot be located in time. In order to monitor the well-kick and lost circulation situation more accurately and find the location of well-kick or lost circulation in time, the borehole temperature distribution models under well-kick and lost circulation conditions were established and solved. The distribution law of wellbore temperature when well-kick and lost circulation occur during drilling was analyzed. Based on the above research results, this work proposes a method for real-time monitoring of well-kick and lost circulation based on distributed optical fiber temperature measurement. This method compares and analyzes the real-time measured temperature with the theoretically calculated temperature, promptly determines whether well-kick or lost circulation has occurred, identifies the location of well-kick or lost circulation, and issues an alarm. This method effectively solves the problems of low monitoring accuracy and information delay, shortens the time required to search for the locations of well-kick or lost circulation, and has broad application prospects.

Data-constrained Solar Modeling with GX Simulator

To facilitate the study of solar flares and active regions, we have created a modeling framework, the freely distributed GX Simulator IDL package, that combines 3D magnetic and plasma structures with thermal and nonthermal models of the chromosphere, transition region, and corona. Its object-based modular architecture, which runs on Windows, Mac, and Unix/Linux platforms, offers the ability to either import 3D density and temperature distribution models, or to assign numerically defined coronal or chromospheric temperatures and densities, or their distributions, to each individual voxel. GX Simulator can apply parametric heating models involving average properties of the magnetic field lines crossing a given voxel, as well as compute and investigate the spatial and spectral properties of radio, (sub)millimeter, EUV, and X-ray emissions calculated from the model, and quantitatively compare them with observations. The package includes a fully automatic model production pipeline that, based on minimal users input, downloads the required SDO/HMI vector magnetic field data, performs potential or nonlinear force-free field extrapolations, populates the magnetic field skeleton with parameterized heated plasma coronal models that assume either steady-state or impulsive plasma heating, and generates non-LTE density and temperature distribution models of the chromosphere that are constrained by photospheric measurements. The standardized models produced by this pipeline may be further customized through specialized IDL scripts, or a set of interactive tools provided by the graphical user interface. Here, we describe the GX Simulator framework and its applications.

Numerical analytical model of metal temperature of steam boiler drum

The problem of developing and identifying a temperature distribution model in the wall of the boiler drum was solved. The numerical model is based on the analytical solution of the one-dimensional heat conduction equation with heat exchange at the boundaries at constant heat transfer coefficients. The model is implemented in a dynamic systems simulation package. Using the bounded series of eigenfunctions of the analytic solution, a representation of the plant in the state space was obtained. A universal algorithm for calculating the eigennumbers of the analytic solution was proposed. The eigenvalues dependences of the analytical solution on the values of heat transfer coefficients and thermal conductivity was investigated. Based on the results of the study, data tables were obtained to approximate the dependences of eigennumbers on heat transfer coefficients in a limited range of variation. The methodology for implementing a dynamic temperature distribution model, which takes into account changes in heat transfer coefficients during simulation, was tested. The time of change of coefficients is perceived as the beginning of a new transient from the current state of the model. Presented structural diagrams of the implementation of the model in dynamic systems simulation packages. The proposed structures allow the introduction of parametric disturbances at the time of their occurrence in the simulation. According to the experimental data of steam boiler firing, identification of the dependence of the heat transfer coefficient on the temperature of the metal wall of the boiler drum was carried out. The results showed that the heat transfer coefficients are influenced not only by the metal temperature, but also by additional parameters of the steam boiler operation. As a result of experiments, it was found that the accuracy of the model can be improved by taking into account the dependence of the heat transfer coefficient on the internal surface of the drum on the flow rate of feed water into the boiler drum. The results of the numerical experiment are presented.

Spatiotemporal Heterogeneity of Temperature and Precipitation in Complex Terrain along the Northeastern Margin of the Tibetan Plateau

The study of climate element distribution models under complex terrain conditions is a popular topic in the field of GIS application in climatology, especially in plateau areas with a complex topography and scarce meteorological station information. In this paper, the spatial and temporal heterogeneity of temperature and precipitation at the northeastern edge of the Tibetan Plateau was analyzed by taking the northeastern edge of the plateau as the study area and constructing a topographic spatial statistical model using 47 meteorological stations and digital elevation models from 1981 to 2010. The following conclusions were drawn from the study: (1) The ME of the temperature distribution model for each month is below 0.9 °C; the maximum ME of the precipitation distribution model for each month is −5.808 mm in July, and the precipitation distribution model has similar error characteristics with the temperature distribution model, which can reflect the horizontal zone distribution pattern of meteorological data and can clearly show the changes of temperature and precipitation as the altitude increases. (2) The spatial distribution pattern of temperature is as follows: the temperature in the study area gradually increases from the southwest to the northeast, with Zhouqu County in Linxia Prefecture and Gannan Prefecture as the main high-temperature areas; the spatial distribution of precipitation is as follows: the precipitation in the southwest of the study area is significantly higher than that in the north, and the precipitation in Linxia Prefecture is significantly lower than that in Gannan Prefecture. (3) The temporal distribution pattern of the temperature distribution model is as follows: the overall temperature in the study area is at its lowest level in January, and the maximum temperature is only 2.6 °C, until July, when the maximum temperature rises to 24.2 °C and then gradually starts to decline; the spatial distribution of precipitation is as follows: the precipitation in the study area gradually rises from January, and the maximum precipitation rises to July and then starts to decline, and in December the precipitation falls to the lowest level. The temporal distribution characteristics of the precipitation distribution model are similar to those of the air temperature model, with obvious hydrothermal synchronization characteristics.