Volume, Side-Area, and Force Direction of Berkovich and Cubecorner Indenters, Novel Important Insights

The iteration-free physical description of pyramidal indentations with closed mathematical equations is comprehensively described and extended for creating new insights in this important field of research and applications. All calculations are easily repeatable and should be programmed by instrument builders for even easier general use. Formulas for the volumes and side-areas of Berkovich and cubecorner as a function of depth are deduced and provided, as are the resulting forces and force directions. All of these allow for the detailed comparison of the different indenters on the mathematical reality. The pyramidal values differ remarkably from the ones of so-called “equivalent cones”. The worldwide use of such pseudo-cones is in severe error. The earlier claimed and used 3 times higher displaced volume with cube corner than with Berkovich is disproved. Both displace the same amount at the same applied force. The unprecedented mathematical results are experimentally confirmed for the physical indentation hardness and for the sharp-onset phase-transi- tions with calculated transition energy. The comparison of both indenters provides novel basic insights. Isotropic materials exhibit the same phase transition onset force, but the transition energy is larger with the cube corner, due to higher force and flatter force direction. This qualifies the cube corner for fracture toughness studies. Pile-up is not from the claimed “friction with the indenter”. Anisotropic materials with cleavage planes and channels undergo sliding along these under pressure, both to the surface and internally. Their volumes add to the depression volume. These volumes are essential for the exemplified pile-up management. Phase-transitions produce polymorph interfaces that are nucleation sites for cracks. Technical materials must be developed with onset forces higher than the highest thinkable stresses (at airliners, bridges, etc.). This requires urgent revision of ISO 14577-ASTM standards.

A Study on Sulfate Optical Properties and Direct Radiative Forcing Using LASG-IAP General Circulation Model

The direct radiative forcing （DRF） of sulfate aerosols depends highly on the atmospheric sulfate loading and the meteorology, both of which undergo strong regional and seasonal variations. Because the optical properties of sulfate aerosols are also sensitive to atmospheric relative humidity, in this study we first examine the scheme for optical properties that considers hydroscopic growth. Next, we investigate the seasonal and regional distributions of sulfate DRF using the sulfate loading simulated from NCAR CAM-Chem together with the meteorology modeled from a spectral atmospheric general circulation model （AGCM） developed by LASG-IAP. The global annual-mean sulfate loading of 3.44 mg m-2 is calculated to yield the DRF of -1.03 and -0.57 W m-2 for clear-sky and all-sky conditions, respectively. However, much larger values occur on regional bases. For example, the maximum all-sky sulfate DRF over Europe, East Asia, and North America can be up to -4.0 W m-2. The strongest all-sky sulfate DRF occurs in the Northern Hemispheric July, with a hemispheric average of -1.26 W m-2. The study results also indicate that the regional DRF are strongly affected by cloud and relative humidity, which vary considerably among the regions during different seasons. This certainly raises the issue that the biases in model-sinmlated regional meteorology can introduce biases into the sulfate DRF. Hence, the model processes associated with atmospheric humidity and cloud physics should be modified in great depth to improve the simulations of the LASG-IAP AGCM and to reduce the uncertainty of sulfate direct effects on global and regional climate in these simulations.

Anthropogenic Direct Radiative Forcing of Tropospheric Ozone and Aerosols in 1850 and 2000 Estimated with IPCC AR5 Emissions Inventories

This study estimates direct radiative forcing by tropospheric ozone and all aerosols between the years 1850 and 2000, using the new IPCC AR5 （the Intergovernmental Panel on Climate Change Fifth Assessment Report） emissions inventories and a fully coupled chemistry-aerosol general circulation model. As compared to the previous Global Emissions Inventory Activity （GEIA） data, that have been commonly used for forcing estimates since 1990, the IPCC AR5 emissions inventories report lower anthropogenic emissions of organic carbon and black carbon aerosols and higher sulfur and NOx emissions. The simulated global and annual mean burdens of sulfate, nitrate, black carbon （BC）, primary organic aerosol （POA）, secondary organic aerosol （SOA）, and ozone were 0.79, 0.35, 0.05, 0.49, 0.34, and 269 Tg, respectively, in the year 1850, and 1.90, 0.90, 0.11, 0.71, 0.32, and 377 Tg, respectively, in the year 2000. The estimated annual mean top of the atmosphere （TOA） direct radiative forcing of all anthropogenic aerosols based on the AR5 emissions inventories is -0.60 W m^-2 on a global mean basis from 1850 to 2000. However, this is -2.40 W m-2 when forcing values are averaged over eastern China （18-45°N and 95-125°E）. The value for tropospheric ozone is 0.17 W m^-1 on a global mean basis and 0.24 W m^-2 over eastern China. Forcing values indicate that the climatic effect of aerosols over eastern China is much more significant than the globally averaged effect.

Grid-cell Aerosol Direct Shortwave Radiative Forcing Calculated Using the SBDART Model with MODIS and AERONET Observations：An Application in Winter and Summer in Eastern China

Taking winter and summer in eastern China as an example application, a grid-cell method of aerosol direct radiative forcing（ADRF） calculation is examined using the Santa Barbara DISORT Atmospheric Radiative Transfer（SBDART） model with inputs from MODIS and AERONET observations and reanalysis data. Results show that there are significant seasonal and regional differences in climatological mean aerosol optical parameters and ADRF. Higher aerosol optical depth（AOD）occurs in summer and two prominent high aerosol loading centers are observed. Higher single scattering albedo（SSA） in summer is likely associated with the weak absorbing secondary aerosols. SSA is higher in North China during summer but higher in South China during winter. Aerosols induce negative forcing at the top of the atmosphere（TOA） and surface during both winter and summer, which may be responsible for the decrease in temperature and the increase in relative humidity.Values of ADRF at the surface are four times stronger than those at the TOA. Both AOD and ADRF present strong interannual variations; however, their amplitudes are larger in summer. Moreover, patterns and trends of ADRF do not always correspond well to those of AOD. Differences in the spatial distributions of ADRF between strong and weak monsoon years are captured effectively. Generally, the present results justify that to calculate grid-cell ADRF at a large scale using the SBDART model with observational aerosol optical properties and reanalysis data is an effective approach.

Direct Radiative Forcing and Climatic Effects of Aerosols over East Asia by RegCM3

The authors used a high-resolution regional climate model （RegCM3） coupled with a chemistry/ aerosol module to simulate East Asian climate in 2006 and to test the climatic impacts of aerosols on regional- scale climate. The direct radiative forcing and climatic effects of aerosols （dust, sulfate, black carbon, and organic carbon） were discussed. The results indicated that aerosols generally produced negative radiative forcing at the top-of-the-atmosphere （TOA） over most areas of East Asia. The radiative forcing induced by aerosols exhibited significant seasonal and regional variations, with the strongest forcing occurring in summer. The aerosol feed- backs on surface air temperature and precipitation were clear. Surface cooling dominated features over the East Asian continental areas, which varied in the approximate range of-0.5 to -2℃ with the maximum up to -3℃ in summer over the deserts of West China. The aerosols induced complicated variations of precipitation. Except in summer, the rainfall generally varied in the range of-1 to 1 mm d^-1 over most areas of China.

Effect of Particle Shape on Dust Shortwave Direct Radiative Forcing Calculations Based on MODIS Observations for a Case Study

Assuming spheroidal and spherical particle shapes for mineral dust aerosols,the effect of particle shape on dust aerosol optical depth retrievals,and subsequently on instantaneous shortwave direct radiative forcing（SWDRF） at the top of the atmosphere（TOA）,is assessed based on Moderate Resolution Imaging Spectroradiometer（MODIS） data for a case study.Specifically,a simplified aerosol retrieval algorithm based on the principle of the Deep Blue aerosol retrieval method is employed to retrieve dust aerosol optical depths,and the Fu–Liou radiative transfer model is used to derive the instantaneous SWDRF of dust at the TOA for cloud-free conditions.Without considering the effect of particle shape on dust aerosol optical depth retrievals,the effect of particle shape on the scattering properties of dust aerosols（e.g.,extinction efficiency,single scattering albedo and asymmetry factor） is negligible,which can lead to a relative difference of at most 5% for the SWDRF at the TOA.However,the effect of particle shape on the SWDRF cannot be neglected provided that the effect of particle shape on dust aerosol optical depth retrievals is also taken into account for SWDRF calculations.The corresponding results in an instantaneous case study show that the relative differences of the SWDRF at the TOA between spheroids and spheres depend critically on the scattering angles at which dust aerosol optical depths are retrieved,and can be up to 40% for low dust-loading conditions.

An extended iterative direct-forcing immersed boundary method in thermo-fluid problems with Dirichlet or Neumann boundary conditions

An iterative direct-forcing immersed boundary method is extended and used to solve convection heat transfer problems.The pressure,momentum source,and heat source at immersed boundary points are calculated simultaneously to achieve the best coupling.Solutions of convection heat transfer problems with both Dirichlet and Neumann boundary conditions are presented.Two approaches for the implementation of Neumann boundary condition,i.e.direct and indirect methods,are introduced and compared in terms of accuracy and computational efficiency.Validation test cases include forced convection on a heated cylinder in an unbounded flow field and mixed convection around a circular body in a lid-driven cavity.Furthermore,the proposed method is applied to study the mixed convection around a heated rotating cylinder in a square enclosure with both iso-heat flux and iso-thermal boundary conditions.Computational results show that the order of accuracy of the indirect method is less than the direct method.However,the indirect method takes less computational time both in terms of the implementation of the boundary condition and the post processing time required to compute the heat transfer variables such as the Nusselt number.It is concluded that the iterative direct-forcing immersed boundary method is a powerful technique for the solution of convection heat transfer problems with stationary/moving boundaries and various boundary conditions.

Development of RAMS-CMAQ to Simulate Aerosol Optical Depth and Aerosol Direct Radiative Forcing and Its Application to East Asia

The air quality modeling system RAMS (Regional Atmospheric Modeling System)-CMAQ (Models-3 Community Multi-scale Air Quality) is developed to simulate the aerosol optical depth (AOD) and aerosol direct forcing (DF). The aerosol-specific extinction, single scattering albedo, and asymmetry factor are parameterized based on Mie theory taking into account the aerosol size distribution, composition, refractive index, and water uptake of solution particles. A two-stream solar radiative model considers all gaseous molecular absorption, Rayleigh scattering, and aerosols and clouds. RAMSCMAQ is applied to simulate all major aerosol concentrations (e.g., sulfate, nitrate, ammonium, organic carbon, black carbon, fine soil, and sea salt) and AOD and DF over East Asia in 2005. To evaluate its performance, the simulated AOD values were compared with ground-based in situ measurements. The comparison shows that RAMSCMAQ performed well in most of the model domain and generally captured the observed variations. High AOD values (0.2 1.0) mainly appear in the Sichuan Basin as well as in central and southeastern China. The geographic distribution of DF generally follows the AOD distribution patterns, and the DF at the top-of-the-atmosphere is less than 25 and 20 W m 2 in clear-sky and all-sky over the Sichuan Basin. Both AOD and DF exhibit seasonal variations with lower values in July and higher ones in January The DF could obviously be impacted by high cloud fractions.

Aerosol Direct Radiative Forcing over Shandong Peninsula in East Asia from 2004 to 2011

Recent vigorous industrialization and urbanization in Shandong Peninsula,China,have resulted in the emission of heavy anthropogenic aerosols over the region.The annual means of aerosol optical depth(AOD),Angstrom exponent(α),single-scattering albedo(SSA),aerosol direct radiative forcing(ARF),surface radiative forcing(SRF),and top-of-the atmospheric radiative forcing(TOA) recorded during 2004–2011 were respectively 0.67±0.19,1.25±0.24,0.93±0.03,47±9 W m-2,-61±9 W m-2,and-14±8 W m-2.The aerosol optical properties and ARF characteristics showed remarkable seasonal variations due to cycle changes in the aerosol components and dominance type.The atmosphere-surface system was cooled by ARF in all years of the study due to anthropogenic sulfate and nitrate emission and sea salt aerosols.The magnitude of TOA cooling was larger in summer(-15±17 W m-2) and autumn(-12±7 W m-2) than that in spring(-8±4 W m-2) and winter(-9±10 W m-2).

Assessment of Individual Direct Radiative Effects of Major Aerosol Species in East Asia

To assess individual direct radiative effects of diverse aerosol species on a regional scale, the air quality modeling system RAMS-CMAQ （Regional Atmospheric Modeling System and Community Multiscale Air Quality） coupled with an aerosol optical properties/radiative transfer module was used to simulate the temporal and spatial distributions of their optical and radiative properties over East Asia throughout 2005. Annual and seasonal averaged aerosol direct radiative forcing （ADRF） of all important aerosols and individual components, such as sulfate, nitrate, ammonium, black carbon （BC）, organic carbon （OC）, and dust at top-of-atmosphere （TOA） in clear sky are analyzed. Analysis of the model results shows that the annual average ADRF of all important aerosols was in the range of 0 to -18 W m-z, with the maximum values mainly distributed over the Sichuan Basin. The direct radiative effects of sulfate, nitrate, and ammonium make up most of the total ADRF in East Asia, being concentrated mainly over North and Southeast China. The model domain is also divided into seven regions based on different administrative regions or countries to investigate detailed information about regional ADRF variations over East Asia. The model results show that the ADRFs of sulfate, ammonium, BC, and OC were stronger in summer and weaker in winter over most regions of East Asia, except over Southeast Asia. The seasonal variation in the ADRF of nitrate exhibited the opposite trend. A strong ADRF of dust mainly appeared in spring over Northwest China and Mongolia.

Model Analysis of Influences of Aerosol Mixing State upon Its Optical Properties in East Asia

The air quality model system RAMS （Regional Atmospheric Modeling System）-CMAQ （Models-3 Com- munity Multi-scale Air Quality） coupled with an aerosol optical/radiative module was applied to investigate the impact of different aerosol mixing states （i.e., externally mixed, half externally and half internally mixed, and internally mixed） oil radiative forcing in East Asia. The simulation results show that the aerosol optical depth （AOD） generally increased when the aerosol mixing state changed from externally mixed to internally mixed, while the single scattering albedo （SSA） decreased. Therefore, the scattering and absorption proper- ties of aerosols can be significantly affected by the change of aerosol mixing states. Comparison of simulated and observed SSAs at five AERONET （Aerosol Robotic Network） sites suggests that SSA could be better estimated by considering aerosol particles to be internally mixed. Model analysis indicates that the impact of aerosol mixing state upon aerosol direct radiative forcing （DRF） is complex. Generally, the cooling effect of aerosols over East Asia are enhanced in the northern part of East Asia （Northern China, Korean peninsula, and the surrounding area of Japan） and are reduced in the southern part of East. Asia （Sichuan Basin and Southeast China） by internal mixing process, and the variation range can reach ＋5 W m 2. The analysis shows that the internal mixing between inorganic salt and dust is likely the main reason that the cooling effect strengthens. Conversely, the internal nfixture of anthropogenic aerosols, including sulfate, nitrate, ammonium, black carbon, and organic carbon, could obviously weaken the cooling effect.

Aerosol optical properties and its direct radiative forcing over Tibetan Plateau from 2006 to 2017

Studies on optical properties of aerosols can reduce the uncertainty for modelling direct radiative forcing(DRF)and improve the accuracy for discussing aerosols effects on the Tibetan Plateau(TP)climate.This study investigated the spatiotemporal variation of aerosol optical and microphysical properties over TP based on OMI and MERRA2,and assessed the influence of aerosol optical properties on DRF at NamCo station(30°46.44′N,90°59.31′E,4730 m)in the central TP from 2006 to 2017 based on a long measurement of AERONET and the modelling of SBDART model.The results show that aerosol optical depth(AOD)exhibits obvious seasonal variation over TP,with higher AOD500nm(>0.75)during spring and summer,and lower value(<0.25)in autumn and winter.The aerosol concentrations show a fluctuated rising from 1980 to 2000,significant increasing from 2000 to 2010 and slight declining trend after 2013.Based on sensitivity experiments,it is found that AOD and single scattering albedo(SSA)have more important impact on the DRF compared withαvalues and ASY.When AOD440nm increases by 60%,DRF at the TOA and ATM is increased by 57.2%and 60.2%,respectively.When SSA440nm increases by 20%,DRF at the TOA and ATM decreases by 121%and 96.7%,respectively.

Sharp interface direct forcing immersed boundary methods： A summary of some algorithms and applications

Body-fitted mesh generation has long been the bottleneck of simulating fluid flows involving complex geometries. Immersed boundary methods are non-boundary-conforming methods that have gained great popularity in the last two decades for their simplicity and flexibility, as well as their non-compromised accuracy. This paper presents a summary of some numerical algori- thms along the line of sharp interface direct forcing approaches and their applications in some practical problems. The algorithms include basic Navier-Stokes solvers, immersed boundary setup procedures, treatments of stationary and moving immersed bounda- ries, and fluid-structure coupling schemes. Applications of these algorithms in particulate flows, flow-induced vibrations, biofluid dynamics, and free-surface hydrodynamics are demonstrated. Some concluding remarks are made, including several future research directions that can further expand the application regime of immersed boundary methods.

б-sharpen immersed boundary method(б-SIBM)—New method for solving the horizontal pressure-gradient force(PGF) problem of б-coordinate

Although G-coordinate is one of the most popular methods used in marine and estuarine modeling, it has long suffered from the so-called ＂steep boundary problem＂, namely, the PGF problem. In this paper, a new method called the ＂σ-sharpen immersed boundary method＂ （σ-SIBM） is put forward. In this method, the virtual flat bottom boundary is creatively introduced in regions with the steep boundary and is taken as the boundary of numerical domain. By this, OH/Ox of numerical domain changes to be a controllable value and the steep bottom problem is then transformed to the non-conforming boundary problem, which is, in turn, solved by the SIBM. The accuracy and efficiency of the σ-sharpen immersed boundary method （σ-SIBM） has been showed by both comparative theoretical analysis and classical numerical tests. First, it is shown that the σ-SIBM is more effective than the z-level method, in that σ-SIBM needs special treatment only in the steep section, but the z-level method needs the special treatment in each grid note. Second, it is superior to the p-method in that it is not restricted by the density distribution. This paper revisits the classical seamount numerical test used in numerous studies to prove the sigma errors of the pressure gradient force （PGFE） and their long-term effects on circulation. It can be seen that, as for the maximum erroneous velocity and kinetic energy, the value of σ-SIBM is much less than that of the z-level method and the traditional σ-method.

Observation Study of Aerosol Radiative Properities over China

With a simplified radiation balance model, study is performed of aerosol direct radiation forcing in relation to its optical properties and surface reflectance, indicating that with the thickened aerosol layer the earth-atmosphere system may increase or weaken the solar radiation albedo, depending upon different combinations of aerosol single scattering albedo （SSA, ω^-o）, asymmetry factor （g）, and surface albedo （ag） rather than relying directly on the aerosol optical depth （δ）, which has its value just in proportion to the changed range of albedo alone. As indicated by the model results, systematic observations of aerosol radiative properties are required to make quantitative study of aerosol direct radiative forcing. Observational research of the properties has been undertaken based on ground and space measurements over China, including ground-based sunphotometeraerosol optical depth （AOD）, nephelometer-aerosol scattering coefficients, aethalometer-aerosol absorption coefficients, and MODIS products-retrieved AOD. The satellite retrieved AOD is validated against in situ sun photometer measured AOD, indicating that for eastern China remote sensing given AODs are acceptable owing mainly to lower surface reflectance there whereas for poor vegetation in the north of China the surface reflectance may be underestimated in AOD retrieval. However, appropriate modification of the scheme of aerosol remote sensing is likely to improve the retrieval accuracy. The aerosol single scattering albedo in dry condition is around 0.80 from surface-measured scattering and absorption coefficients. It requires further studies based on more observations to improve our understanding of the issue.