ALMOST ANALYTIC SOLUTIONS AND THEIR TESTS OF THE HORIZONTAL DIFFUSION EQUATION FOR THE MOVEMENT OF WATER IN UNSATURATED SOIL

This paper discusses the analytic solutions of the diffusion equation for the movement of water in unsaturated soil. Firstly, according to the experience relation between the diffusivity 'D(theta)' and water content in soil 'theta', and through variable substitution, the original diffusion equation is converted into the form easy to solve. Then, the variables separation method together with the Boltzmann transform method is used to find out the solution of the new partial differential equation. so the analytic function of 0(x, t) is obtained, which is verified by the experiment of water flow through unsaturated soil.

Energetics of lateral eddy diffusion/advection: Part III. Energetics of horizontal and isopycnal diffusion/ advection

Gravitational Potential Energy （GPE） change due to horizontal/isopycnal eddy diffusion and advection is examined. Horizontal/isopycnal eddy diffusion is conceptually separated into two steps： stirring and sub scale diffusion. GPE changes associated with these two steps are analyzed. In addition, GPE changes due to stirring and subscale diffusion associated with horizontal/isopycnal advection in the Eulerian coordinates are analyzed. These formulae are applied to the SODA data for the world oceans. Our analysis indicates that horizontal/isopycnal advection in Eulerian coordinates can introduce large artificial diffusion in the model. It is shown that GPE source/sink in isopycnal coordinates is closely linked to physical property distribution, such as temperature, salinity and velocity. In comparison with z-coordinates, GPE source/sink due to stir ring/cabbeling associated with isopycnal diffusion/advection is much smaller. Although isopycnal coordi nates may be a better choice in terms of handling lateral diffusion, advection terms in the traditional Eule rian coordinates can produce artificial source of GPE due to cabbeling associated with advection. Reducing such numerical errors remains a grand challenge.

Improving Numerical Weather Prediction in Low Latitudes by Optimizing Diffusion Coefficients

The horizontal diffusion coefficients of the operational model (T42L9) in numerical weather prediction are optimized by the steepest descent search of multi-dimensional optimization. In order to improve prediction accuracy in low latitudes, the optimum horizontal diffusion coefficients are chosen, with changing variation of the basic diffusion coefficient with the passage of time, and later forecasts are also made better. In view of the averages of forecast verifications of 9 cases, the forecasts with optimum diffusion coefficients are an improvement on operational forecasts. It means that the forecasts are got much better with optimum values of some important parameters by optimization in numerical weather prediction.

Energetics of lateral eddy diffusion/advection: Part IV. Energetics of diffusion/advection in sigma coordinates and other coordinates

Gravitational potential energy （GPE） source and sink due to stirring and cabbeling associated with sigma dif fusion/ advection is analyzed. It is shown that GPE source and sink is too big, and they are not closely linked to physical property distribution, such as temperature, salinity and velocity. Although the most frequently quoted advantage of sigma coordinate models are their capability of dealing with topography; the exces sive amount of GPE source and sink due to stirring and cabbeling associated with sigma diffusion/advec tion diagnosed from our analysis raises a very serious question whether the way lateral diffusion/advection simulated in the sigma coordinates model is physically acceptable. GPE source and sink in three coordinates is dramatically different in their magnitude and patterns. Overall, in terms of simulating lateral eddy diffu sion and advection isopycnal coordinates is the best choice and sigma coordinates is the worst. The physical reason of the excessive GPE source and sink in sigma coordinates is further explored in details. However, even in the isopycnal coordinates, simulation based on the Eulerian coordinates can be contaminated by the numerical errors associated with the advection terms.

^(226)Ra and ^(228)Ra tracer study on nutrient transport in east coastal waters of Hainan Island,China

Material fluxes （e.g., nutrients） from coastal waters to offshore areas play an important role in controlling the water quality of the adjacent sea areas not only by increasing nutrient concentration hut also by changing nutrient structures. In this study, naturally occurring isotopes, ^226Ra and ^228Ra, were measured with the alpha spectrometry in the Wenjiao-Wenchang and Wanquan estuaries and adjacent sea areas along the east coast of Hainan Island. The excess ^226Ra and ^228Ra activities were observed by comparison with the values derived from the conservative mixing of freshwater and seawater end-members in both estuaries. Using a one-dimensional diffusion model, the horizontal eddy diffusion coefficient of 3.1 6 × 10^5 cm^2/s, for nutrients diffusing from their sources, was derived from 228Ra activities. Consequently, the corresponding nutrient fluxes flowing into the coastal waters were assessed. The results can provide useful information for the study of the mixing and exchange processes of coastal waters as well as dissoluble pollutant transport in this sea area.

Mesoscale eddies and their dispersive environmental impacts in the Persian Gulf

As the mesoscale eddies in oceans and semi-enclosed seas are significant in horizontal dispersion of pollutants,we investigate the seasonal variations of these eddies in the Persian Gulf(PG)that are usually generated due to seasonal winds and baroclinic instability.The sea surface height(SSH)data from 2010 to 2014 of AVISO are used to identify and track eddies,using the SSH-based method.Then seasonal horizontal dispersion coefficients are estimated for the PG,using the properties of eddies.The results show an annual mean of 78 eddies with a minimum lifetime of one week.Most of the eddies are predominantly cyclonic(59.1%)and have longer lifetimes and higher diffusion coefficients than the anti-cyclonic eddies.The eddy activity is higher in warm seasons,compared to that of cold seasons.As locations with high eddy diffusion coefficients are high-risk areas by using maps of horizontal eddy diffusion coefficients,perilous times and locations of the release of pollutants are specified to be within the longitude from 51.38°E to 55.28°E.The mentioned areas are located from the Strait of Hormuz towards the northeast of the PG,closer to Iranian coast.Moreover,July can be considered as the most dangerous time of pollution release.

Sensitivity of Typhoon Lingling(2019)simulations to horizontal mixing length and planetary boundary layer parameterizations

Forecasting the intensity of typhoons is a difficult problem in numerical weather prediction.It is subject to many factors,among which the selection of physical parameterization schemes for the model is a hot topic of research.In this study,the effects of horizontal mixing length(represented by h_diff)and planetary boundary layer(PBL)schemes were investigated.Six idealized and four operational sensitivity experiments were designed based on simulation of the typhoon Lingling,which occurred over the western Pacific in 2019,using the Hurricane Weather Research and Forecasting model.The results of the idealized experiments showed that,as h_diff was increased,the slope of the typhoon eye area also increased,and its intensity became stronger.On the other hand,the results of the sensitivity experiments indicated that the intensity of the simulated typhoon was sensitive to the choice of PBL scheme,with the forecast bias of the QNSE(Quasi-Normal Scale Elimination)scheme being smaller than that of the GFDL(Geophysical Fluid Dynamics Laboratory)scheme.Angular momentum budget analyses indicated that,when increasing the h_diff,the convergence of angular momentum was larger in the boundary layer,which led to a faster spin-up of the vortex,further increasing the intensity of the typhoon.From the calculated horizontal and vertical vortex spread it was found that,when the h_diff was increased,the corresponding horizontal and vertical diffusion eddies also showed an increasing trend,which was also the reason for the strengthening of the typhoon.Meanwhile,the forecast bias decreased significantly with increasing horizontal mixing length when using the same PBL scheme.

THE MODELING IMPROVEMENT OF HURRICANE ANDREW BY THE TECHNIQUE OF IRREVERSIBLE THERMODYNAMIC OPERATORS

Although incorporating the horizontal diffusion into the atmospheric governing equations is a part of the dynamics of a model,it is based on the computational consideration originally,which is to overcome the nonlinear aliasing or computational instability and smooth the physical fields at the same time.The generally used forms of the fourth-order diffusion,either linear or nonlinear, however,can not properly describe the real physical diffusion processes and thus affect the accuracy of forecasting and modeling.In this paper,based on the nature of the physical diffusion. the scheme of horizontal diffusion of the MM5 Version 3 is improved according to the second law of thermodynamics which controls the irreversable evolutionary direction of a many-body system and the potential ability of the improvement of the new scheme in modeling accuracy is revealed by introducing the technique suggested in this paper,via a theoretical case and the computational case of the hurricane Andrew that landed on Florida in 1992.