The sensitivity of numerical simulation to vertical mixing parameterization schemes: a case study for the Yellow Sea Cold Water Mass

The vertical mixing parameterization scheme,by providing the eff ects of some explicitly missed physical processes and more importantly closing the energy budgets,is a critical model component and therefore imposes signifi cant impacts on model performance.The Yellow Sea Cold Water Mass(YSCWM),as the most striking and unique phenomenon in the Yellow Sea during summer,is dramatically aff ected by vertical mixing process during its each stage and therefore seriously sensitive to the proper choice of parameterization scheme.In this paper,a hindcast of YSCWM in winter of 2006 was implemented by using the Regional Ocean Modeling System(ROMS).Three popular parameterization schemes,including the level 2.5 Mellor-Yamada closure(M-Y 2.5),Generic Length Scale closure(GLS)and K-Profi le Parameterization(KPP),were tested and compared with each other by conducting a series of sensitivity model experiments.The infl uence of diff erent parameterization schemes on modeling the YSCWM was then carefully examined and assessed based on these model experiments.Although reasonable thermal structure and its seasonal variation were well reproduced by all schemes,considerable diff erences could still be found among all experiments.A warmer and spatially smaller simulation of YSCWM,with very strong thermocline,appeared in M-Y 2.5 experiment,while a spatially larger YSCWM with shallow mixed layer was found in GLS and KPP schemes.Among all the experiments,the discrepancy,indicated by core temperature,appeared since spring,and grew gradually by the end of November.Additional experiments also confi rmed that the increase of background diff usivity could eff ectively weaken the YSCWM,in either strength or coverage.Surface wave,another contributor in upper layer,was found responsible for the shrinkage of YSCWM coverage.The treatment of wave eff ect as an additional turbulence production term in prognostic equation was shown to be more superior to the strategy of directly increasing diff usivity for a coastal region.

Analysis of soluble chemical transfer from soil to surface runoff and incomplete mixing parameter identification

A two-layer mathematical model proposed by Tong et al. （2010） was used to predict soluble chemical transfer from soil into surface runoff with ponded water on the soil surface. Infiltration-related incomplete mixing parameter γ and runoff-related incomplete mixing parameter a in the analytical solution of the Tong et al. （2010） model were assumed to be constant. In this study, different laboratory experimental data of soluble chemical concentration in surface runoff from initially unsaturated and saturated soils were used to identify the variables γ and a based on the analytical solution of the model. The values of γ and a without occurrence of surface runoff were constant and equal to their values at the moment when the surface runoff started. It was determined from the results that γ decreases with the increase of the ponded water depth, and when the initial volumetric water content is closer to the saturated water content, there is less variation of parameter γ after the occurrence of surface runoff. As infiltration increases, the soluble chemical concentration in surface runoff decreases. The values of parameter a range from 0 to 1 for the fine loam and sand under the controlled infiltration conditions, while it can increase to a very large value, greater than 1, for the sand under the restrained infiltration conditions, and the analytical solution of the model is not valid for experimental soil without any infiltration if a is expected to be less than or equal to 1. The soluble chemical concentrations predicted from the model with variable incomplete mixing parameters γ and α are more accurate than those from the model with constant γ and α values.

Parameterization of ocean wave-induced mixing processes for finite water depth

Three dimensional wave-induced mixing plays an important role in shallow water area. A quite direct approach through the Reynolds average upon characteristic length scale is proposed to parameterize the horizontal and vertical shallow water mixing. Comparison of finite depth case with infinite depth results indicates that the difference of the wave-induced mixing strength is evident. In the shallow water condition, the infinite water depth approximation overestimates the mixing strength in the lower layers. The nonzero horizontal wave-induced mixing presents anisotropic property near the shore. The Prandtl＇s mixing length theory underestimated the wave-induced mixing in the previous studies.

A simulation study on the measurement of D^0-■ mixing parameter y at BESⅢ

We established a method on measuring the D^0-D^0 mixing parameter y for BESIII experiment atthe BEPC II e^＋e^- collider. In this method, the doubly tagged 4（3770） D^0-D^0 events, with one D decaysto CP-eigenstates and the other D decays semileptonically, are used to reconstruct the signals. Since this analysis requires good e/π separation, a likelihood approach, which combines the dE/dx, time of flight and the electromagnetic shower detectors information, is used for particle identification. We estimate the sensitivity of the measurement of y to be 0.007 based on a 20 fb^-1 fully simulated MC sample.

Thermodynamic properties and mixing thermodynamic parameters of binary homogeneous metallic melts

After the investigation on the thermodynamic properties and mixingthermodynamic parameters of binary homogeneous metallic melts involving compound, peritectic as wellas solid solution, it was found that the equations of mixing free energy DELTA G^m and excess freeenergy DELTA G^(XS) of them can he expressed by the following equations: DELTA G^m = SIGMA x [SIGMAN_i DELTA G_I^(THETA) + RT(SIGMA N_j ln N_j + SIGMA N_i ln N_i )] and DELTA G^(XS) = DELTA G^m -RT(a ln a + b ln b), respectively.

Thermodynamic Properties and Mixing Thermodynamic Parameter of Binary Metallic Melt Involving Compound Formation

Based on the coexistence theory of metallic melts involving compound formation, the theoretical calculation equations of mixing thermodynamic parameters are established by giving up some empirical parameters in the associated solution model. For Fe-Al, Mn-Al and Ni-Al, the calculated results agree well with the experimental values, testifying that these equations can exactly embody mixing thermodynamic characteristics of these melts.

Thermodynamic properties and mixing thermodynamic parameters of two-phase metallic melts

Based on the calculating model of metallic melts involving eutectic, the calculating equations of mixing thermodynamic parameters for two phase metallic melts have been formulated in the light of those equations of homogeneous solutions. Irrespective as to whether the activity deviation relative to Raoultian behavior is positive or negative, or the deviation is symmetrical or unsym-metrical, the evaluated results not only agree well with experimental values, but also strictly obey the mass action law. This testifies that these equations can authentically reflect the structural reality and mixing thermodynamic characteristics of two-phase metallic melts. The calculating equations of mixing thermodynamic parameters for the model of two phase metallic melts offer two practical criteria (activity and mixing thermodynamic parameters) and one theoretical criterion (the mass action law).

Covalent bonding and J–J mixing effects on the EPR parameters of Er^(3+) ions in GaN crystal

The EPR parameters of trivalent Er（3＋） ions doped in hexagonal Ga N crystal have been studied by diagonalizing the 364×364 complete energy matrices. The results indicate that the resonance ground states may be derived from the Kramers doublet Γ6. The EPR g-factors may be ascribed to the stronger covalent bonding and nephelauxetic effects compared with other rare-earth doped complexes, as a result of the mismatch of ionic radii of the impurity Er（3＋）ion and the replaced Ga（3＋） ion apart from the intrinsic covalency of host Ga N. Furthermore, the J–J mixing effects on the EPR parameters from the high-lying manifolds have been evaluated. It is found that the dominant J–J mixing contribution is from the manifold 2K（15/2）, which accounts for about 2.5%. The next important J–J contribution arises from the crystal–field mixture between the ground state 4I（15/2） and the first excited state4I（13/2）, and is usually less than 0.2%. The contributions from the rest states may be ignored.

Parameterized thermal model of a mixed mantle convection

Simple parameterized models, either whole mantle convection or layered mantleconvection, cannot explain the tectonic characteristics of the Earth's evolution history, therefore a mixed mantle convection model has been carried out in this paper. We introduce a time-dependent parameter F, which denotes the ratio betWeen the mantle material involved in whole mantle convection and the material of the entire mantle, and introduce a local Rayleigh number Raloc as well as two critical numbers Ra1 and Ra2. These parameters are used to describe the stability of the phase boundary between the upper and lower mantle. The result shows that the mixed mantle convection model is able to simulate the episodic tectonic evolution of the Earth.

A climatic dataset of ocean vertical turbulent mixing coefficient based on real energy sources

Using data on wind stress, significant height of combined wind waves and swell, potential temperature, salinity and seawater velocity, as well as objectively-analyzed in situ temperature and salinity, we established a global ocean dataset of calculated wind- and tide-induced vertical turbulent mixing coefficients. We then examined energy conservation of ocean vertical mixing from the point of view of ocean wind energy inputs, gravitational potential energy change due to mixing(with and without artificially limiting themixing coefficient), and K-theory vertical turbulent parameterization schemes regardless of energy inputs. Our research showed that calculating the mixing coefficient with average data and artificial limiting the mixing coefficient can cause a remarkable lack of energy conservation, with energy losses of up to 90% and changes in the energy oscillation period. The data also show that wind can introduce a huge amount of energy into the upper layers of the Southern Ocean, and that tidesdo so in regions around underwater mountains. We argue that it is necessary to take wind and tidal energy inputs into account forlong-term ocean climate numerical simulations. We believe that using this ocean vertical turbulent mixing coefficient climatic dataset is a fast and efficient method to maintain the ocean energy balance in ocean modeling research.