Implication of community-level ecophysiological parameterization to modelling ecosystem productivity:a case study across nine contrasting forest sites in eastern China

Parameterization is a critical step in modelling ecosystem dynamics.However,assigning parameter values can be a technical challenge for structurally complex natural plant communities;uncertainties in model simulations often arise from inappropriate model parameterization.Here we compared five methods for defining community-level specific leaf area(SLA)and leaf C:N across nine contrasting forest sites along the North-South Transect of Eastern China,including biomass-weighted average for the entire plant community(AP_BW)and four simplified selective sampling(biomass-weighted average over five dominant tree species[5DT_BW],basal area weighted average over five dominant tree species[5DT_AW],biomass-weighted average over all tree species[AT_BW]and basal area weighted average over all tree species[AT_AW]).We found that the default values for SLA and leaf C:N embedded in the Biome-BGC v4.2 were higher than the five computational methods produced across the nine sites,with deviations ranging from 28.0 to 73.3%.In addition,there were only slight deviations(<10%)between the whole plant community sampling(AP_BW)predicted NPP and the four simplified selective sampling methods,and no significant difference between the predictions of AT_BW and AP_BW except the Shennongjia site.The findings in this study highlights the critical importance of computational strategies for community-level parameterization in ecosystem process modelling,and will support the choice of parameterization methods.

Parameterization, sensitivity, and uncertainty of 1-D thermodynamic thin-ice thickness retrieval

Retrieval of Thin-Ice Thickness(TIT)using thermodynamic modeling is sensitive to the parameterization of the independent variables(coded in the model)and the uncertainty of the measured input variables.This article examines the deviation of the classical model’s TIT output when using different parameterization schemes and the sensitivity of the output to the ice thickness.Moreover,it estimates the uncertainty of the output in response to the uncertainties of the input variables.The parameterized independent variables include atmospheric longwave emissivity,air density,specific heat of air,latent heat of ice,conductivity of ice,snow depth,and snow conductivity.Measured input parameters include air temperature,ice surface temperature,and wind speed.Among the independent variables,the results show that the highest deviation is caused by adjusting the parameterization of snow conductivity and depth,followed ice conductivity.The sensitivity of the output TIT to ice thickness is highest when using parameterization of ice conductivity,atmospheric emissivity,and snow conductivity and depth.The retrieved TIT obtained using each parameterization scheme is validated using in situ measurements and satellite-retrieved data.From in situ measurements,the uncertainties of the measured air temperature and surface temperature are found to be high.The resulting uncertainties of TIT are evaluated using perturbations of the input data selected based on the probability distribution of the measurement error.The results show that the overall uncertainty of TIT to air temperature,surface temperature,and wind speed uncertainty is around 0.09 m,0.049 m,and−0.005 m,respectively.

A New Result on Regular Designs under Baseline Parameterization

The study on designs for the baseline parameterization has aroused attention in recent years. This paper focuses on two-level regular designs for the baseline parameterization. A general result on the relationship between K-aberration and word length pattern is developed.

Performance of physical-informed neural network (PINN) for the key parameter inference in Langmuir turbulence parameterization scheme

The Stokes production coefficient(E_(6))constitutes a critical parameter within the Mellor-Yamada type(MY-type)Langmuir turbulence(LT)parameterization schemes,significantly affecting the simulation of turbulent kinetic energy,turbulent length scale,and vertical diffusivity coefficient for turbulent kinetic energy in the upper ocean.However,the accurate determination of its value remains a pressing scientific challenge.This study adopted an innovative approach by leveraging deep learning technology to address this challenge of inferring the E_(6).Through the integration of the information of the turbulent length scale equation into a physical-informed neural network(PINN),we achieved an accurate and physically meaningful inference of E_(6).Multiple cases were examined to assess the feasibility of PINN in this task,revealing that under optimal settings,the average mean squared error of the E_(6) inference was only 0.01,attesting to the effectiveness of PINN.The optimal hyperparameter combination was identified using the Tanh activation function,along with a spatiotemporal sampling interval of 1 s and 0.1 m.This resulted in a substantial reduction in the average bias of the E_(6) inference,ranging from O(10^(1))to O(10^(2))times compared with other combinations.This study underscores the potential application of PINN in intricate marine environments,offering a novel and efficient method for optimizing MY-type LT parameterization schemes.

Impact of Revised Trigger and Closure of the Double-Plume Convective Parameterization on Precipitation Simulations over East Asia

A double-plume convective parameterization scheme is revised to improve the precipitation simulation of a global model(Global-to-Regional Integrated Forecast System;GRIST).The improvement is achieved by considering the effects of large-scale dynamic processes on the trigger of deep convection.The closure,based on dynamic CAPE,is improved accordingly to allow other processes to consume CAPE under the more restricted convective trigger condition.The revised convective parameterization is evaluated with a variable-resolution model setup(110–35 km,refined over East Asia).The Atmospheric Model Intercomparison Project(AMIP)simulations demonstrate that the revised convective parameterization substantially delays the daytime precipitation peaks over most land areas,leading to an improved simulated diurnal cycle,evidenced by delayed and less frequent afternoon precipitation.Meanwhile,changes to the threshold of the trigger function yield a small impact on the diurnal amplitude of precipitation because of the consistent setting of dCAPE-based trigger and closure.The simulated mean precipitation remains reasonable,with some improvements evident along the southern slopes of the Tibetan Plateau.The revised scheme increases convective precipitation at the lower levels of the windward slope and reduces the large-scale precipitation over the upper slope,ultimately shifting the rainfall peak southward,which is in better agreement with the observations.

Impact of seepage flow on sediment resuspension by internal solitary waves:parameterization and mechanism

Sediment incipient motion is the first step in sediment resuspension.Previous studies ignored the effect of seepage flow on the mobility of sediment particles and simplified the seabed surface as a rigid boundary.A flume experiment was designed to innovatively divide the seabed into two parts to control the dynamic response of the seabed and control the seepage conditions.In the experiment,the seabed sediments and the amplitude of internal solitary waves(ISWs)were changed to compare and analyze the impact of seepage flow on the sediment resuspension by shoaling ISWs.Moreover,parametric research and verification were carried out.Results indicate that seepage flow can greatly influence fine sand,promote sediment resuspension,and increase the amount of suspension by two times on average.However,seepage flow had a little effect on the suspension of clayey silt and sandy silt.Besides,seepage force was added to the traditional gravity,drag force,and uplift force,and the parameterization of threshold starting shear stress of coarse-grained sediments was developed.The results of this parameterization were verified,and seepage force was critical to parameterization.The threshold starting shear stress was reduced by 54.6%after increasing the seepage force.The physical mechanism of this process corresponded to the vertical reciprocating transient seepage in and out the seabed interface caused by the wave-induced transient excess pore water pressure.This quantitative study on seepage flow for shear stress of coarse-grained sediments induced by ISWs is critical to geohazard assessment.

Parameterization Transfer for a Planar Computational Domain in Isogeometric Analysis

In this paper,we propose a parameterization transfer algorithm for planar domains bounded by B-spline curves,where the shapes of the planar domains are similar.The domain geometries are considered to be similar if their simplified skeletons have the same structures.One domain we call source domain,and it is parameterized using multi-patch B-spline surfaces.The resulting parameterization is C1 continuous in the regular region and G1 continuous around singular points regardless of whether the parameterization of the source domain is C1/G1 continuous or not.In this algorithm,boundary control points of the source domain are extracted from its parameterization as sequential points,and we establish a correspondence between sequential boundary control points of the source domain and the target boundary through discrete sampling and fitting.Transfer of the parametrization satisfies C1/G1 continuity under discrete harmonic mapping with continuous constraints.The new algorithm has a lower calculation cost than a decomposition-based parameterization with a high-quality parameterization result.We demonstrate that the result of the parameterization transfer in this paper can be applied in isogeometric analysis.Moreover,because of the consistency of the parameterization for the two models,this method can be applied in many other geometry processing algorithms,such as morphing and deformation.

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).

Performance Evaluation of Three Parameterizations on Internal Tidal Mixing in the Northern Pacific

The accurate assessment of the energy dissipation of internal tides(ITs)is of great importance because ITs contribute significantly to abyssal mixing.Thus,in this study,the IT-driven dissipation and diapycnal diffusion in the northern Pacific are esti-mated using parameterizations proposed by St.Laurent et al.(2002),Koch-Larrouy et al.(2007),and de Lavergne et al.(2020)(hereaf-ter referred to as LSJ02,KL07,and dL20,respectively).The performances of the three parameterizations are evaluated by comparing the calculated results with fine structure observations.In particular,the dissipation estimated by LSJ02 parameterization shows a bottom-intensified characteristic,with the patterns showing good agreement with the observations near seamounts.Moreover,43%of the results calculated using the LSJ02 parameterization have errors lower than one order of magnitude in the generation sites of ITs.Meanwhile,the strongest dissipation estimated by the KL07 parameterization shifts to the thermocline,with the results showing the highest level of consistency with observations in the generation sites.The proportion of results with errors lower than one order of magnitude is 80.7%.Furthermore,the results calculated by dL20 parameterization agree well with the observations in the upper and middle layers,with the parameterization showing an accurate estimation of the remote dissipation.The percentages of the errors lower than one order of magnitude between the dL20 parameterization and observations account for 77.1%and 88.7%in the genera-tion sites and far-field regions,respectively.

The Importance of the Shape Parameter in a Bulk Parameterization Scheme to the Evolution of the Cloud Droplet Spectrum during Condensation

The shape parameter of the Gamma size distribution plays a key role in the evolution of the cloud droplet spectrum in the bulk parameterization schemes. However, due to the inaccurate specification of the shape parameter in the commonly used bulk double-moment schemes, the cloud droplet spectra cannot reasonably be described during the condensation process. Therefore, a newly-developed triple-parameter condensation scheme with the shape parameter diagnosed through the number concentration, cloud water content, and reflectivity factor of cloud droplets can be applied to improve the evolution of the cloud droplet spectrum. The simulation with the new parameterization scheme was compared to those with a high-resolution Lagrangian bin scheme, the double-moment schemes in a parcel model, and the observation in a 1.5D Eulerian model that consists of two cylinders. The new scheme with the shape parameter varying with time and space can accurately simulate the evolution of the cloud droplet spectrum. Furthermore, the volume-mean radius and cloud water content simulated with the new scheme match the Lagrangian analytical solutions well, and the errors are steady, within approximately 0.2%.

Parameterization Method of Wind Drift Factor Based on Deep Learning in the Oil Spill Model

Oil spill prediction is critical for reducing the detrimental impact of oil spills on marine ecosystems,and the wind strong-ly influences the performance of oil spill models.However,the wind drift factor is assumed to be constant or parameterized by linear regression and other methods in existing studies,which may limit the accuracy of the oil spill simulation.A parameterization method for wind drift factor(PMOWDF)based on deep learning,which can effectively extract the time-varying characteristics on a regional scale,is proposed in this paper.The method was adopted to forecast the oil spill in the East China Sea.The discrepancies between predicted positions and actual measurement locations of the drifters are obtained using seasonal statistical analysis.Results reveal that PMOWDF can improve the accuracy of oil spill simulation compared with the traditional method.Furthermore,the parameteriza-tion method is validated with satellite observations of the Sanchi oil spill in 2018.

Skeleton-Based Volumetric Parameterizations for Lattice Structures

Lattice structures with excellent physical properties have attracted great research interest.In this paper,a novel volume parametric modeling method based on the skeleton model is proposed for the construction of threedimensional lattice structures.The skeleton model is divided into three types of nodes.And the corresponding algorithms are utilized to construct diverse types of volume parametric nodes.The unit-cell is assembled with distinct nodes according to the geometric features.The final lattice structure is created by the periodic arrangement of unit-cells.Several different types of volume parametric lattice structures are constructed to prove the stability and applicability of the proposed method.The quality is assessed in terms of the value of the Jacobian matrix.Moreover,the volume parametric lattice structures are tested with the isogeometric analysis to verify the feasibility of integration of modeling and simulation.

A 3D attention U-Net network and its application in geological model parameterization

To solve the problems of convolutional neural network–principal component analysis(CNN-PCA)in fine description and generalization of complex reservoir geological features,a 3D attention U-Net network was proposed not using a trained C3D video motion analysis model to extract the style of a 3D model,and applied to complement the details of geologic model lost in the dimension reduction of PCA method in this study.The 3D attention U-Net network was applied to a complex river channel sandstone reservoir to test its effects.The results show that compared with CNN-PCA method,the 3D attention U-Net network could better complement the details of geological model lost in the PCA dimension reduction,better reflect the fluid flow features in the original geologic model,and improve history matching results.

Parameterization and Explicit Modeling of Cloud Microphysics:Approaches, Challenges, and Future Directions

Cloud microphysical processes occur at the smallest end of scales among cloud-related processes and thus must be parameterized not only in large-scale global circulation models(GCMs)but also in various higher-resolution limited-area models such as cloud-resolving models(CRMs)and large-eddy simulation(LES)models.Instead of giving a comprehensive review of existing microphysical parameterizations that have been developed over the years,this study concentrates purposely on several topics that we believe are understudied but hold great potential for further advancing bulk microphysics parameterizations:multi-moment bulk microphysics parameterizations and the role of the spectral shape of hydrometeor size distributions;discrete vs“continuous”representation of hydrometeor types;turbulence-microphysics interactions including turbulent entrainment-mixing processes and stochastic condensation;theoretical foundations for the mathematical expressions used to describe hydrometeor size distributions and hydrometeor morphology;and approaches for developing bulk microphysics parameterizations.Also presented are the spectral bin scheme and particle-based scheme(especially,super-droplet method)for representing explicit microphysics.Their advantages and disadvantages are elucidated for constructing cloud models with detailed microphysics that are essential to developing processes understanding and bulk microphysics parameterizations.Particle-resolved direct numerical simulation(DNS)models are described as an emerging technique to investigate turbulence-microphysics interactions at the most fundamental level by tracking individual particles and resolving the smallest turbulent eddies in turbulent clouds.Outstanding challenges and future research directions are explored as well.

Effect of Different Microphysical Parameterizations on the Simulations of a South China Heavy Rainfall

A heavy rainfall event in south China was simulated by the Weather Research and Forecasting(WRF) model with three microphysics schemes, including the Morrison scheme, Thompson scheme, and Milbrandt and Yau scheme(MY), which aim to evaluate the capability to reproduce the precipitation and radar echo reflectivity features, and to evaluate evaluate their differences in microphysics and the associated thermodynamical and dynamical feedback. Results show that all simulations reproduce the main features crucial for rainfall formation. Compared with the observation, the MY scheme performed better than the other two schemes in terms of intensity and spatial distribution of rainfall. Due to abundant water vapor, the accretion of cloud droplets by raindrops was the dominant process in the growth of raindrops while the contribution of melting was a secondary effect. Riming processes, in which frozen hydrometeors collect cloud droplets mainly, contributed more to the growth of frozen hydrometeors than the Bergeron process. Extremely abundant snow and ice were produced in the Thompson and MY schemes respectively by a deposition process. The MY scheme has the highest condensation and evaporation, but the lowest deposition. As a result, in the MY scheme, the enhanced vertical gradient of condensation heating and evaporation cooling at low levels produces strong positive and weak negative potential vorticity in Guangdong, and may favor the formation of the enhanced rainfall center over there.

Application of the two different salinity parameterization schemes in the sea ice model

In this study, we mainly introduce two salinity parameterization schemes used in Sea Ice Simulator （SIS）, that is, isosaline scheme and salinity profile scheme. Comparing the equation of isosaline scheme with that of salinity profile scheme, we found that there was one different term between the two schemes named the salinity different term. The thermodynamic effect of the salinity difference term on sea ice thickness and sea ice concentration showed that： in the freezing processes from November to next May, the sea ice temperature could rise on the influence of the salinity difference term and restrain sea ice freezing; at the first melting phase from June to August, the upper ice melting rate was faster than the lower ice melting rate. Then sea ice temperature could rise and accelerate the sea ice melting; at the second melting phase from September to October, the upper ice melting rate was slower than the lower ice melting rate, then sea ice temperature could decrease and restrain sea ice melting. However, the effect of the salinity difference term on the sea ice thickness and sea ice concentration was weak. To analyze the impacts of the salinity different term on Arctic sea ice thickness and sea ice concentration, we also designed several experiments by introducing the two salinity parameterizations to the ice-ocean coupled model, Modular Ocean Model （MOM4）, respectively. The simulated results confirmed the previous results of formula derivation.

Optimal parameterization of conic curves

Optimal parameterization of specified segment on the algebraic curves is a hot issue in CAGD and CG. Take the optimal approximation of arc-length parameterization as the criterion of optimal parameterization, and the optimal or close to optimal rational parameterization formula of any specified segment on the conic curves is obtained. The new method proposed in this paper has ad- vantage in quantity of calculation and has strong self-adaptability. Finally, a experimental comparison of the results obtained by this method and by the traditional parametric algorithm is conducted.

Optimal Rational Parameterization of Quadratic Curves Based on the Geographic Information of Both Ends

In this paper, we rewrote the equation of algebraic curve segmentswith the geometric informationonboth ends. The optimal or nearly optimal rationalparametric equation is determinedbythe principle that parametricspeedsat both endsareequal. Comparing withotherliteratures, the methodofthis paper has advantage in efficiency andiseasy to realize. The equation of optimal rational parameterization can be obtained directly by the information of both ends. Large numbers ofexperimental data show that our method hasbeen given withmore self-adaptability and accuracy than that ofotherliteratures, and if the parametricspeedat any end reaches its maximum or minimum value, the parameterization is optimal; otherwise itis close tooptimal rational parameterization.

Improving the CoLM in Taklimakan Desert Hinterland with Accurate Key Parameters and an Appropriate Parameterization Scheme

Improving and validating land surface models based on integrated observations in deserts is one of the challenges in land modeling. Particularly, key parameters and parameterization schemes in desert regions need to be evaluated in-situ to improve the models. In this study, we calibrated the land-surface key parameters and evaluated several formulations or schemes for thermal roughness length （z 0h ） in the common land model （CoLM）. Our parameter calibration and scheme evaluation were based on the observed data during a torrid summer （29 July to 11 September 2009） over the Taklimakan Desert hinterland. First, the importance of the key parameters in the experiment was evaluated based on their physics principles and the significance of these key parameters were further validated using sensitivity test. Second, difference schemes （or physics-based formulas） of z 0h were adopted to simulate the variations of energy-related variables （e.g., sensible heat flux and surface skin temperature） and the simulated variations were then compared with the observed data. Third, the z 0h scheme that performed best （i.e., Y07） was then selected to replace the defaulted one （i.e., Z98）; the revised scheme and the superiority of Y07 over Z98 was further demonstrated by comparing the simulated results with the observed data. Admittedly, the revised model did a relatively poor job of simulating the diurnal variations of surface soil heat flux, and nighttime soil temperature was also underestimated, calling for further improvement of the model for desert regions.

The Influences of Boundary Layer Parameterization Schemes on Mesoscale Heavy Rain System

The mesoscale numerical weather prediction model (MM4) in which the computations of the turbulent exchange coefficient in the boundary layer and surface fluxes are improved, is used to study the influences of boundary layer parameterization schemes on the predictive results of the mesoscale model. Seven different experiment schemes (including the original MM4 model) designed in this paper are tested by the observational data of several heavy rain cases so as to find an improved boundary layer parameterization scheme in the mesoscale meteorological model. The results show that all the seven different boundary layer parameterization schemes have some influences on the forecasts of precipitation intensity, distribution of rain area, vertical velocity, vorticity and divergence fields, and the improved schemes in this paper can improve the precipitation forecast. Key words Boundary layer parameterization - Mesoscale numerical weather prediction (MNWP) - Turbulent exchange coefficient - Surface fluxes - Heavy rain This paper was supported by the National Natural Science Foundation of China (Grant No. 49875005 and No. 49735180).