A study on the simulation of carbon and water fluxes of Dangxiong alpine meadow and its response to climate change

The alpine meadow ecosystem accounts for 27%of the total area of the Tibetan Plateau and is also one of the most important vegetation types.The Dangxiong alpine meadow ecosystem,located in the south-central part of the Tibetan Plateau,is a typical example.To understand the carbon and water fluxes,water use efficiency(WUE),and their responses to future climate change for the alpine meadow ecosystem in the Dangxiong area,two parameter estimation methods,the Model-independent Parameter Estimation(PEST)and the Dynamic Dimensions Search(DDS),were used to optimize the Biome-BGC model.Then,the gross primary productivity(GPP)and evapotranspiration(ET)were simulated.The results show that the DDS parameter calibration method has a better performance.The annual GPP and ET show an increasing trend,while the WUE shows a decreasing trend.Meanwhile,ET and GPP reach their peaks in July and August,respectively,and WUE shows a“dual-peak”pattern,reaching peaks in May and November.Furthermore,according to the simulation results for the next nearly 100 years,the ensemble average GPP and ET exhibit a significant increasing trend,and the growth rate under the SSP5–8.5 scenario is greater than that under the SSP2–4.5 scenario.WUE shows an increasing trend under the SSP2–4.5 scenario and a significant increasing trend under the SSP5–8.5 scenario.This study has important scientific significance for carbon and water cycle prediction and vegetation ecological protection on the Tibetan Plateau.

Comparison of ERA5 turbulent fluxes at the air-sea interface with measurements from a wave-following platform

Turbulent fluxes at the air-sea interface were estimated with data collected in 2011-2020 with a low-profile platform named OCARINA during eight experiments in five regions:2011,2015,and 2016 in the Iroise Sea;2012 in the tropical Atlantic;2014 in the Chilie-Peru upwelling;2017 and 2018 in the Mediterranean Sea,and 2018 and 2020 in Barbados.The observations were carried out with moderate winds(2-10 m s^(-1))and average wave heights of 1.5 m.In this study,the authors used the fluxes calculated by the bulk method using OCARINA-sampled data as the input.These data can validate the fluxes estimated from ERAS reanalysis data.The OCARINA and ERA5 data were taken concomitantly.To do this,the authors established an algorithm to extract the OCARINA data as closely as possible to the reanalysis data in time and position.The measurements of the OCARINA platform can conclude on the relevance of the widely used reanalysis data.

Seasonal response of nitrogen exchange fluxes to crab disturbance at sediment-water interface in coastal tidal wetlands

Coastal wetlands are hotspots for nitrogen(N)cycling,and crab burrowing is known to transform N in intertidal marsh soils.However,the underlying mechanisms remain unclear.This study conducted field experiments and used indoor control test devices to investigate the seasonal response of nitrogen to crab disturbance at the sediment-water interface in coastal tidal flat wetlands.The results showed that crab disturbance exhibited significant seasonality with large seasonal differences in cave density and depth.Due to crab disturbance,nitrogen fuxes at the sediment-water interface were much greater in the box with crabs than in the box without crabs.In summer,NH-N showed a positive flux from the sediment to the overlying water,but NO2-N and NOg-N showed positive fluxes from the sediment to the overlying water only in early stages.In winter,NH-N showed a positive flux from the sediment to the overlying water,but NO-N and NO,-N both exhibited positive and negative fluxes.These results indicated that the presence of crab burrows can cause the aerobic layer to move downward by approximately 8-15 cm in summer and directly promote nitrification at the sediment surface.

Impact of Initial Soil Conditions on Soil Hydrothermal and Surface Energy Fluxes in the Permafrost Region of the Tibetan Plateau

Accurate initial soil conditions play a crucial role in simulating soil hydrothermal and surface energy fluxes in land surface process modeling.This study emphasized the influence of the initial soil temperature(ST)and soil moisture(SM)conditions on a land surface energy and water simulation in the permafrost region in the Tibetan Plateau(TP)using the Community Land Model version 5.0(CLM5.0).The results indicate that the default initial schemes for ST and SM in CLM5.0 were simplistic,and inaccurately represented the soil characteristics of permafrost in the TP which led to underestimating ST during the freezing period while overestimating ST and underestimating SLW during the thawing period at the XDT site.Applying the long-term spin-up method to obtain initial soil conditions has only led to limited improvement in simulating soil hydrothermal and surface energy fluxes.The modified initial soil schemes proposed in this study comprehensively incorporate the characteristics of permafrost,which coexists with soil liquid water(SLW),and soil ice(SI)when the ST is below freezing temperature,effectively enhancing the accuracy of the simulated soil hydrothermal and surface energy fluxes.Consequently,the modified initial soil schemes greatly improved upon the results achieved through the long-term spin-up method.Three modified initial soil schemes experiments resulted in a 64%,88%,and 77%reduction in the average mean bias error(MBE)of ST,and a 13%,21%,and 19%reduction in the average root-mean-square error(RMSE)of SLW compared to the default simulation results.Also,the average MBE of net radiation was reduced by 7%,22%,and 21%.

Dissolved inorganic carbon and CO_(2) fluxes across Jiaozhou Bay air-water interface

On the basis of data collected in the Jiaozhou Bay in June and July 2003, the DIC distribution in seawater is studied, and an average air-sea flux of CO2 is estimated. The results show that the content of DIC inside the bay is markedly higher than outside the bay in June, but the content of DIC outside the bay is markedly higher than inside the bay in July. The trend of DIC distribution inside the bay is similar, viz. the content is the maximum in the northeast, then decreases gradually toward the west, and the content is the minimum in the west. The total trend of vertical distribution is to increase gradually from surface to bottom. This characteristic of DIC distribution is determined by Jiaozhou Bay hydrology and there is a close relation between DIC and particulate N,P. Average CO2flux across the air-sea interface is 0.55 mol/(m2-a) in June and 0.72 mol/(m2-a) in July. Jiaozhou Bay is considered as a net annual source for atmospheric CO2 in June and July, and the total CO2 flux from seawater into atmosphere is about 740t in June and 969 t in July.

Carbon dioxide partial pressure and carbon fluxes of air-water interface in Taihu Lake, China

To obtain carbon dioxide （CO2） flux between water-air interface of Taihu lake, monthly water samplers at 14 sites and the local meteorological data of the lake were collected and analyzed in 1998. Carbon dioxide partial pressures （pCO2） at air-water interface in the lake were calculated using alkalinity, pH, ionic strength, active coefficient, and water temperature. The carbon fluxes at different sublakes and areas were estimated by concentration gradient between water and air in consideration of Schmidt numbers of 600 and daily mean windspeed at 10 m above water surface. The results indicated that the mean values of pCO2 in Wuli Lake,Meiliang Bay, hydrophyte area, west littoral zone, riverine mouths, and the open lake areas were 1 807.8±1 071.4（mean±standard deviation）μatm （latm=1.013 25×10^5pa）, 416.3±217.0μatm, 576.5±758.8μatm, 304.2±9.43.5μatm, 1 933.6±1 144.7 μatm, and 448.5±202.6μatm, respectively. Maximum and minimum pCO2 values were found in the hypertrophic （4 053.7μatm） and the eutrophic （3.2 μatm） areas. The riverine mouth areas have the maximum fluxes （82.0±62.8 mmol/m^2a）. But there was no significant difference between eutrophic and mesotrophic areas in pCO2 and the flux of CO2. The hydrophyte area, however, has the minimum （--0.58±12.9mmol/m^2a）. In respect to CO2 equilibrium, input of the rivers will obviously influence inorganic carbon distribution in the riverine estuary. For example, the annual mean CO2 flux in Zhihugang River estuary was 19 times of that in Meiliang Bay, although the former is only a part of the latter. The sites in the body of the lake show a clear seasonal cycle with pCO2 higher than atmospheric equilibrium in winter, and much lower than atmospheric in summer due to CO2 consumption by photosynthesis. The CO2 amount of the net annual evasion that enters the atmosphere is 28.42×10^4 t/a, of which those from the west littoral zone and the open lake account for 53.8% and 36.7%, respectively.

A data assimilation-based forecast model of outer radiation belt electron fluxes

Because radiation belt electrons can pose a potential threat to the safety of satellites orbiting in space,it is of great importance to develop a reliable model that can predict the highly dynamic variations in outer radiation belt electron fluxes.In the present study,we develop a forecast model of radiation belt electron fluxes based on the data assimilation method,in terms of Van Allen Probe measurements combined with three-dimensional radiation belt numerical simulations.Our forecast model can cover the entire outer radiation belt with a high temporal resolution(1 hour)and a spatial resolution of 0.25 L over a wide range of both electron energy(0.1-5.0 MeV)and pitch angle(5°-90°).On the basis of this model,we forecast hourly electron fluxes for the next 1,2,and 3 days during an intense geomagnetic storm and evaluate the corresponding prediction performance.Our model can reasonably predict the stormtime evolution of radiation belt electrons with high prediction efficiency(up to~0.8-1).The best prediction performance is found for~0.3-3 MeV electrons at L=~3.25-4.5,which extends to higher L and lower energies with increasing pitch angle.Our results demonstrate that the forecast model developed can be a powerful tool to predict the spatiotemporal changes in outer radiation belt electron fluxes,and the model has both scientific significance and practical implications.

Sea spray induced air-sea heat and salt fluxes based on the wavesteepnessdependent sea spray model

Sea spray,which comprises amounts of small ocean droplets,plays a significant role in the air-sea coupling,atmospheric and oceanic dynamics,and climate.However,it remains arduous to arrive at estimates for the efficiency and accuracy of the sea spray induced air-sea heat and salt fluxes.This is because the microphysical process of sea spray evolution in the air is of extreme complexity.In this study,we iteratively calculated the sea spray induced air-sea heat and salt fluxes at various weather condition.To do so,we implemented one novel wave-steepness-dependent sea spray model into a bulk air-sea fluxes algorithm and utilized other sea spray models as comparisons.Based on the improved wave-dependent bulk turbulent algorithm,we observed that despite the negative contribution of sea spray to the sensible heat fluxes,the sea spray positively contributes to the air-sea latent heat fluxes,leading to an overall increase in the total air-sea heat fluxes.The additional heat fluxes caused by sea spray may be the missing critical process that can clarify the discrepancies observed between measured and modelled Tropical Cyclone’s development and intensification.In addition to heat fluxes,we observed that sea spray has significant impacts on the air-sea salt fluxes.As the sea salt particles are one of the main sources of the atmosphere aerosol,our results imply that sea spray could impact global and regional climate.Thus,given the significance of sea spray on the air-sea boundary layer,sea spray effects need to be considered in studies of air-sea interaction,dynamics of atmosphere and ocean.

Diffusion and reaction mechanism of limestone and quartz in fluxed iron ore pellet roasting process

The increase to the proportion of fluxed pellets in the blast furnace burden is a useful way to reduce the carbon emissions in the ironmaking process.In this study,the interaction between calcium carbonate and iron ore powder and the mineralization mechanism of fluxed iron ore pellet in the roasting process were investigated through diffusion couple experiments.Scanning electron microscopy with energy dispersive spectroscopy was used to study the elements’diffusion and phase transformation during the roasting process.The results indicated that limestone decomposed into calcium oxide,and magnetite was oxidized to hematite at the early stage of preheating.With the increase in roasting temperature,the diffusion rate of Fe and Ca was obviously accelerated,while the diffusion rate of Si was relatively slow.The order of magnitude of interdiffusion coefficient of Fe_(2)O_(3)-CaO diffusion couple was 10^(−10) m^(2)·s^(−1) at a roasting temperature of 1200℃for 9 h.Ca_(2)Fe_(2)O_(5) was the initial product in the Fe_(2)O_(3)-CaO-SiO_(2) diffusion interface,and then Ca_(2)Fe_(2)O_(5) continued to react with Fe_(2)O_(3) to form CaFe_(2)O_(4).With the expansion of the diffusion region,the sillico-ferrite of calcium liquid phase was produced due to the melting of SiO_(2) into CaFe_(2)O_(4),which can strengthen the consolidation of fluxed pellets.Furthermore,andradite would be formed around a small part of quartz particles,which is also conducive to the consolidation of fluxed pellets.In addition,the principle diagram of limestone and quartz diffusion reaction in the process of fluxed pellet roasting was discussed.

FPGA-based position reconstruction method for neutron beam flux spatial distribution measurement in BNCT

A new measurement method for the spatial distribution of neutron beam flux in boron neutron capture therapy(BNCT)is being developed based on the two-dimensional Micromegas detector.To address the issue of long processing times in traditional offline position reconstruction methods,this paper proposes a field programmable gate array based online position reconstruction method utilizing the micro-time projection chamber principle.This method encapsulates key technical aspects:a self-adaptive serial link technique built upon the dynamical adjustment of the delay chain length,fast sorting,a coordinate-matching technique based on the mapping between signal timestamps and random access memory(RAM)addresses,and a precise start point-merging technique utilizing a circular combined RAM.The performance test of the selfadaptive serial link shows that the bit error rate of the link is better than 10-12 at a confidence level of 99%,ensuring reliable data transmission.The experiment utilizing the readout electronics and Micromegas detector shows a spatial resolution of approximately 1.4 mm,surpassing the current method’s resolution level of 5 mm.The beam experiment confirms that the readout electronics system can obtain the flux spatial distribution of neutron beams online,thus validating the feasibility of the position reconstruction method.The online position reconstruction method avoids traditional methods,such as bubble sorting and traversal searching,simplifies the design of the logic firmware,and reduces the time complexity from O(n2)to O(n).This study contributes to the advancement in measuring neutron beam flux for BNCT.

High-chromium vanadium-titanium magnetite all-pellet integrated burden optimization and softening-melting behavior based on flux pellets

High-chromium vanadium-titanium magnetite(HVTM)is a crucial polymetallic-associated resource to be developed.The allpellet operation is a blast furnace trend that aims to reduce carbon dioxide emissions in the future.By referencing the production data of vanadium-titanium magnetite blast furnaces,this study explored the softening-melting behavior of high-chromium vanadium-titanium magnetite and obtained the optimal integrated burden based on flux pellets.The results show that the burden with a composition of 70wt%flux pellets and 30wt%acid pellets exhibits the best softening-melting properties.In comparison to that of the single burden,the softening-melting characteristic temperature of this burden composition was higher.The melting interval first increased from 307 to 362℃and then decreased to 282℃.The maximum pressure drop(ΔPmax)decreased from 26.76 to 19.01 kPa.The permeability index(S)dropped from 4643.5 to 2446.8 kPa·℃.The softening-melting properties of the integrated burden were apparently improved.The acid pellets played a role in withstanding load during the softening process.The flux pellets in the integrated burden exhibited a higher slag melting point,which increased the melting temperature during the melting process.The slag homogeneity and the TiC produced by over-reduction led to the gas permeability deterioration of the single burden.The segregation of the flux and acid pellets in the HVTM proportion and basicity mainly led to the better softening-melting properties of the integrated burden.

Variation in the surface heat flux on the north and south slopes of Mount Qomolangma

The distinctive conditions present on the north and south slopes of Mount Qomolangma,along with the intricate variations in the underlying surfaces,result in notable variations in the surface energy flux patterns of the two slopes.In this paper,data from TESEBS(Topographical Enhanced Surface Energy Balance System),remote sensing data from eight cloud-free scenarios,and observational data from nine stations are utilized to examine the fluctuations in the surface heat flux on both slopes.The inclusion of MCD43A3 satellite data enhances the surface albedo,contributing to more accurate simulation outcomes.The model results are validated using observational data.The RMSEs of the net radiation,ground heat,sensible heat,and latent heat flux are 40.73,17.09,33.26,and 30.91 W m^(−2),respectively.The net radiation flux is greater on the south slope and exhibits a rapid decline from summer to autumn.Due to the influence of the monsoon,on the north slope,the maximum sensible heat flux occurs in the pre-monsoon period in summer and the maximum latent heat flux occurs during the monsoon.The south slope experiences the highest latent heat flux in summer.The dominant flux on the north slope is sensible heat,while it is latent heat on the south slope.The seasonal variations in the ground heat flux are more pronounced on the south slope than on the north slope.Except in summer,the ground heat flux on the north slope surpasses that on the south slope.

Evaluating Parameterizations for Turbulent Fluxes over the Landfast Sea-Ice Surface in Prydz Bay, Antarctica

It is crucial to appropriately determine turbulent fluxes in numerical models.Using data collected in East Antarctica from 8 April to 26 November 2016,this study evaluates parameterization schemes for turbulent fluxes over the landfast seaice surface in five numerical models.The Community Noah Land Surface Model with Multi-Parameterizations Options(Noah_mp)best replicates the turbulent momentum flux,while the Beijing Climate System Model(BCC_CSM)produces the optimum sensible and latent heat fluxes.In particular,two critical issues of parameterization schemes,stability functions and roughness lengths,are investigated.Sensitivity tests indicate that roughness lengths play a decisive role in model performance.Based on the observed turbulent fluxes,roughness lengths over the landfast sea-ice surface are calculated.The results,which can provide a basis for setting up model parameters,reveal that the dynamic roughness length(z0m)increases with the increase of frictional velocity(u*)when u*≤0.4 m s^(−1) and fluctuates around 10^(−3 )m when u*>0.4 m s^(−1);thermal roughness length(z0t)is linearly related to the temperature gradient between air and sea-ice surface(ΔT)with a relation of lg(z0t)=−0.29ΔT−3.86;and the mean water vapor roughness length(z0q)in the specific humidity gradient(Δq)range ofΔq≤−0.6 g kg^(−1) is 10^(−6) m,3.5 times smaller than that in the range ofΔq˃−0.6 g kg^(−1).

Cross-satellite calibration of high-energy electron fluxes measured by FengYun-4A based on Arase observations

We use the High-energy Electron Experiments(HEP)instrument onboard Arase(ERG)to conduct an energy-dependent cross-satellite calibration of electron fluxes measured by the High Energy Particle Detector(HEPD)onboard FengYun-4A(FY-4A)spanning from April 1,2017,to September 30,2019.By tracing the two-dimensional magnetic positions(L,magnetic local time[MLT])of FY-4A at each time,we compare the datasets of the conjugate electron fluxes over the range of 245–894 keV in 6 energy channels for the satellite pair within different sets of L×MLT.The variations in the electron fluxes observed by FY-4A generally agree with the Arase measurements,and the percentages of the ratios of electron flux conjunctions within a factor of 2 are larger than 50%.Compared with Arase,FY-4A systematically overestimates electron fluxes at all 6 energy channels,with the corresponding calibration factors ranging from 0.67 to 0.81.After the cross-satellite calibration,the electron flux conjunctions between FY-4A and Arase show better agreement,with much smaller normalized root mean square errors.Our results provide a valuable reference for the application of FY-4A high-energy electron datasets to in-depth investigations of the Earth’s radiation belt electron dynamics.

Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws

This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws.The basic idea is that the“meaningful objects”are the fluxes,evaluated across domain boundaries over time intervals.The fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional setting.It implies that a weak solution indeed satisfies the balance law.In fact,it is shown that the flux is Lipschitz continuous with respect to suitable perturbations of the boundary.It should be emphasized that the weak solutions considered here need not be entropy solutions.Furthermore,the assumption imposed on the flux f(u)is quite minimal-just that it is locally bounded.

Optimum Profiles of Endwall Contouring for Enhanced Net Heat Flux Reduction and Aerodynamic Performance

Successfully utilized non-axisymmetric endwalls to enhance turbine efficiencies(aerodynamic and turbine inlet temperatures)by controlling the characteristics of the secondary flow in a blade passage.This is accomplished by steady-state numerical hydrodynamics and deep knowledge of the field of flow.Because of the interaction between mainstream and purge flow contributing supplementary losses in the stage,non-axisymmetric endwalls are highly susceptible to the inception of purge flow exit compared to the flat and any advantage rapidly vanishes.The conclusions reveal that the supreme endwall pattern could yield a lowering of the gross pressure loss at the design stage and is related to the size of the top-loss location being productively lowered.This has led to diminished global thermal exchange lowered in the passage of the vane alone.The reverse flow adjacent to the suction side corner of the endwall is migrated farther from the vane surface,as the deviated pressure spread on the endwall accelerates the flow and progresses the reverse flow core still downstream.The depleted association between the tornado-like vortex and the corner vortex adjacent to the suction side corner of the endwall is the dominant mechanism of control in the contoured end wall.In this publication,we show that the non-axisymmetric endwall contouring by selective numerical shape change method at most prominent locations is advantageous in lowering the thermal load in turbines to augment the net heat flux reduction as well as the aerodynamic performance using multi-objective optimization.

Observing the air-sea turbulent heat flux on the trajectory of tropical storm Danas

Tropical cyclones constitute a major risk for coastal communities.To assess their damage potential,accurate predictions of their intensification are needed,which requires a detailed understanding of the evolution of turbulent heat flux(THF).By combining multiple buoy observations along the south north storm track,we investigated the THF anomalies associated with tropical storm Danas(2019)in the East China Sea(ECS)during its complete life cycle from the intensification stage to the mature stage and finally to its dissipation on land.The storm passage is characterized by strong winds of 10-20 m/s and a sea level pressure below 1000 hPa,resulting in a substantial enhancement of THF.Latent heat(LH)fluxes are most strongly affected by wind speed,with a gradually increasing contribution of humidity along the trajectory.The relative contributions of wind speed and temperature anomalies to sensible heat(SH)depend on the stability of the boundary layer.Under stable conditions,SH variations are driven by wind speed,while under near-neutral conditions,SH variations are driven by temperature.A comparison of the observed THF and associated variables with outputs from the ERA 5 and MERRA 2 reanalysis products reveals that the reanalysis products can reproduce the basic evolution and composition of the observed THF.However,under extreme weather conditions,temperature and humidity variations are poorly captured by ERA 5 and MERRA 2,leading to large LH and SH errors.The differences in the observed and reproduced LH and SH during the passage of Danas amount to 26.1 and 6.6 W/m^(2) for ERA 5,respectively,and to 39.4 and 12.5 W/m^(2) for MERRA 2,respectively.These results demonstrate the need to improve the representation of tropical cyclones in reanalysis products to better predict their intensification process and reduce their damage.

基于FLUXNET站点数据的中纬度森林对地表通量的影响

利用最新FLUXNET数据集,采用森林站和非森林站(开阔地)的对比分析用以表征毁林的作用,探讨中纬度地区毁林对地表通量和波文比的季节和日内影响。结果表明,毁林使得地表通量和波文比降低,其中以感热通量的减少为主。通过对比不同森林类型毁林发现,在日尺度上,地表通量变化在正午达到最强值,混合林地表通量变化相比于常绿针叶林较强,而弱于落叶阔叶林。在季节尺度上,感热通量在常绿针叶林和混合林中减少,潜热通量则在常绿针叶林和落叶阔叶林中减少。通过对不同气候区下地表通量变化发现,毁林使得常湿冷温气候地表通量以潜热通量减少为主,而常湿温暖气候以感热通量减少为主。夏干温暖气候下冬季感热通量减少,潜热通量增加,夏季则感热通量增加,潜热通量减少。整体而言,不同森林类型毁林影响地表通量变化的符号存在差异,而背景气候也决定了地表通量变化是以感热还是潜热通量变化为主。研究揭示了中纬度毁林对地表通量的影响,可以为中纬度地区植被恢复/造林政策的制定和实施提供观测依据,也可以为模式检验提供一定参考价值。

基于Ameriflux通量观测数据的Hi-GLASS潜热通量产品验证

潜热通量产品的验证与分析对于研究气候变化及能量循环具有重要意义。全球陆表高分辨率蒸散产品(high resolution global lAnd surface evapotranspiration product,Hi-GLASS ET)融合了5种传统蒸散算法,能够生产出较高精度的陆表潜热通量产品,但目前没有针对此产品的验证研究。利用Ameriflux通量观测站点的潜热通量观测值与相应的Hi-GLASS陆表潜热通量产品估算值进行对比,获取多组有效验证数据。验证结果显示,所选站点实际观测值与产品估算值的决定系数(R 2)为0.6,均方根误差(RMSE)为34.4 W/m^(2),平均偏差(Bias)为-13.4 W/m^(2),克林-古普塔效率(Kling-Gupta efficiency,KGE)为0.49,Hi-GLASS潜热通量产品具有较高的精度,算法的拟合结果较好;此外,空间分布也表明Hi-GLASS陆表潜热通量产品符合正常的自然规律。由于数据获取的局限性,仅采用了美国地区18个站点数据对产品进行验证,在其他地区仍需进一步验证。

Study of the pressure transient behavior of directional wells considering the effect of non-uniform flux distribution

During the production,the fluid in the vicinity of the directional well enters the wellbore with different rates,leading to non-uniform flux distribution along the directional well.However,in all existing studies,it is oversimplified to a uniform flux distribution,which can result in inaccurate results for field applications.Therefore,this paper proposes a semi-analytical model of a directional well based on the assumption of non-uniform flux distribution.Specifically,the direction well is discretized into a carefully chosen series of linear sources,such that the complex well trajectory can be captured and the nonuniform flux distribution along the wellbore can be considered to model the three-dimensional flow behavior.By using the finite difference method,we can obtain the numerical solutions of the transient flow within the wellbore.With the aid of Green's function method,we can obtain the analytical solutions of the transient flow from the matrix to the wellbore.The complete flow behavior of a directional well is perfectly represented by coupling the above two types of transient flow.Subsequently,on the basis of the proposed model,we conduct a comprehensive analysis of the pressure transient behavior of a directional well.The computation results show that the flux variation along the direction well has a significant effect on pressure responses.In addition,the directional well in an infinite reservoir may exhibit the following flow regimes:wellbore afterflow,transition flow,inclined radial flow,elliptical flow,horizontal linear flow,and horizontal radial flow.The horizontal linear flow can be observed only if the formation thickness is much smaller than the well length.Furthermore,a dip region that appears on the pressure derivative curve indicates the three-dimensional flow behavior near the wellbore.