Limiters in Third-Generation Wind Wave Models

Third-generation ocean wave models include a so-called limiter in the integration of the source terms to guarantee numerical stability at economical numerical time steps. The original limiter has previously been associated with the sensitivity of model results to the numerical time step. More recent limiters appear to remove this sensitivity by eliminating the numerical convergence from the resulting integration scheme. This is contrary to rudimentary numerical principles as well as the underlying philosophy of third-generation wave models. The present study investigates the effects of limiters and large model time steps using time-limited wave growth test. It is shown that the conventional limiter results in stable model results even if the numerical time step violates the time scales of wave growth. Contrary to common belief, its impact is not necessarily limited to the equilibrium range of the spectrum, and the limiter systematically enhances growth rates in the intermediate stages of wave growth. Particularly initial growth errors increase significantly with increasing maximum discrete spectral frequency f max . Relaxation of the limiter is shown to reduce initial growth errors, but does so at the expense of notable errors in the spectral shape. In the present paper the limiter was relaxed by introducing a new asymmetric limiter that retains full convergence. Initial results obtained with this limiter are similar to those of the advocated nonconvergent limiters. Although this limiter still needs rigorous testing and further development, its initial results suggest that there is no justification for using nonconvergent limiters.     

Modelling Boundary-Layer Clouds With a Statistical Cloud Scheme and a Second-Order Turbulence Closure

We present a second-order turbulence model for the cloudy planetary boundary layer (PBL), which includes a statistical scheme of the sub-grid scale condensation. The model contains prognostic equations for the turbulent kinetic energy, total water, and liquid water temperature, the latter two being assumed to be conservative variables. Using these conservative thermodynamic variables the condensation process is formulated as a function of the departure of the total water from saturation and its variance. The computation of the variance requires second moment correlations which are modelled through the parameterization of the third-order moments using a convective mass-flux formulation. The inclusion of these third moments and new assumptions on heat flux transport lead to a nonlocal turbulence scheme with counter-gradient effects. The final form for the heat flux turns out to be a linearized version of a previously established result. For the statistical cloud formulation, a linear combination of a Gaussian and a positively skewed distribution function is used with a modified liquid water flux expression to account fornon-Gaussian behaviour.The effect of the turbulence scheme on the boundary-layer cloud structure is discussed and the performance of the model is tested by comparing it against the large eddy simulation (LES) of the undisturbed period of the Atlantic Stratocumulus Transition Experiment (ASTEX). The model is able to produce both mean and turbulent quantities that are in reasonable agreement with the LES output of ASTEX.     

Parameterization of sea surface drag under varying sea state and its dependence on wave age

Momentum and energy exchange at air–sea interface through wind stress is very important for air–sea interaction studies, ocean modeling, and climate studies. The accurate representation of wind stress, in terms of drag coefficient, is a key factor in estimating the momentum transfer at the interface. The drag coefficient, in general, estimated using bulk formulae does not take into account the influence of wave age. This study examines the dependence of wave age on computed surface drag coefficient obtained by combining the Toba 3/2-power law with Froude number scaling, resulting in a new drag formulation (hereafter referred as RP formulation). We demonstrate that our proposed formulation is in good conjunction with established theories for both young and mature waves. Our investigation shows the theoretical formulation advocated earlier by Guan and Xie (hereafter referred as GX) overestimated the surface drag for mature waves as wind speed tends to increase. In addition, the formulation by GX was not verified by observational data. In the present work, for validation purpose, we use time series measurement of meteorological and oceanographic data from a deep water location in the Indian Ocean which was tested with both RP and GX formulations. We find that the proposed RP formulation, which embeds the 3/2 power of wave-age, shows a better match for both young and mature waves with the results of Janssen compared to the hypothesis of conventional wave age used by GX.     

气候模式中积雪覆盖率参数化方案的对比研究

利用基于NCEP再分析的近地面气候资料驱动陆面过程模型NCAR CLM3,检验了6种积雪覆盖率参数化方案(CLM3、Douville1995、Roesch2001、Wu2004、Yang1997、Niu2007)模拟的积雪覆盖率的季节变化,并与NOAA AVHRR得到的观测结果进行了对比分析.结果表明,在NCARCLM3的物理过程框架之下,CLM3、Douville1995、Roesch2001三种方案低估了广大地区的积雪覆盖率,模拟的雪线位置偏北,尤其是在秋季积雪初期;Wu2004方案低估了秋季欧亚大陆的积雪覆盖率;Yang1997方案模拟的积雪覆盖率有些偏高,尤其是在积雪覆盖区的南部边缘;考虑积雪密度变化的Niu2007方案一定程度上克服了Yang1997方案的正偏差.春季末期,6种方案模拟的雪线位置都偏北.在地形比较平缓的地区,Niu2007方案的整体效果最好.观测和模拟的积雪覆盖率的出现频数大部分集中在低(小于0.2)和高(大于0.8)覆盖率等级,中等覆盖率所占比例很少.     

Third-Order Moment Closure Through A Mass-Flux Approach

The parameterization of the third moments, the flux of the heat flux and the flux of the potential temperature variance, is considered. It is shown that present parameterizations of these moments using the mass-flux approach with a `top-hat' profile assumption lead to a significant underestimation, resulting in an inaccurate representation of second moments in the convective boundary layer. It is also shown that the underestimation is a result of the `top-hat' profileassumption in which the sub-plume contributions to the total fluxes are ignored. By including these contributions a new parameterization is proposed, whichsatisfies the physical requirements of symmetry andrealizability, and gives results that are in fair agreement with thelarge-eddy simulation data.     

基本气流和边界层顶高度对低纬大气数值模拟的影响

本文研究了一个包含波动CISK(Convective Instability of the Second Kind)机制的扰动方程数值模式中,基本气流对低频振荡数值模拟的影响。结果显示,当基本气流为纬向均匀风场U时,振荡周期随U的增加而减小:当U取2 m s-1时,周期从50～60 d减小到30 d;当U减小到-1 m s-1时,振荡周期增加为70～80 d。这是由于低频振荡是从西向东传播,西风基本气流能加快扰动东传,反之东风基本气流会抑制扰动东传,使振荡周期增加。同时,模式中的边界层顶出现误差时,模拟结果会有敏感的响应。若边界层顶取值比标准值高,对流加热反馈作用过大,出现扰动增长过快的现象,传播到80°～90°E附近时,扰动不再继续传播,而是无限增长;而边界层顶取值比标准值低时,对流加热反馈过小,扰动增长小且衰减加快,扰动传播不远便耗散到零,扰动循环周期表现为热源的周期。     

非均匀下垫面边界层的观测和数值模拟研究(II):逆湿现象的数值模拟研究

研究了逆湿现象,针对陆面过程模式的缺陷,利用文献[1]给出的逆湿现象形成的物理模型,设计了新的陆面过程参数化方案.该新方案成功地模拟出了发生在绿洲附近的沙漠上的逆湿现象,模拟结果与实际观测的结果相互吻合,这表明所建立的新的陆面过程参数化方案是可行的.这些结论将为今后非均匀陆面过程研究提供有益的启示.     

MJO随机强迫对CNOP型初始误差演变的影响

用Zebiak-Cane模式和季节内振荡(Madden-Julian Oscillation,MJO)的参数化表述以及条件非线性最优扰动(Conditional Nonlinear Optimal Perturbation,CNOP)方法,分析了以ENSO事件为基态的CNOP型初始误差的空间结构增长规律。结果表明,参数化的MJO对CNOP型初始误差的发展影响较小,其影响主要是使中东太平洋的海表面温度异常增大。CNOP型初始误差比由MJO不确定性产生的模式误差的影响大,前者可能是造成ENSO事件预报不确定性的主要误差来源。由于CNOP型初始误差的局地性,本结论可用来指导ENSO的目标观测和适应性资料同化。     

不同云滴数浓度参数化方案对硝酸盐气溶胶 第一间接效应影响的比较研究

在区域气候化学模式系统（RegCCMS）中,分别采用Hegg、Hansen、Ghan、Jones等4种云滴数浓度参数化方案,模拟研究了2003年10月硝酸盐气溶胶的浓度分布和第一间接气候效应,并对不同方案进行比较。结果表明,不同方案模拟的硝酸盐气溶胶分布大体上一致,主要集中在河南、山东、河北、四川等地,地面浓度最大值达18 μg/m3。Hegg、Hansen、Ghan、Jones等 4种云滴数浓度参数化方案计算得到的由硝酸盐气溶胶所造成的第一间接辐射强迫全国平均值分别为-148、-205、-161和-140 W/m2。4种方案模拟的硝酸盐气溶胶间接效应都表现为近地面气温下降,降水减少,其中Hansen方案的间接效应最强,Ghan、Hegg方案次之,Jones方案最弱。     

敦煌荒漠戈壁地区裸土地表反照率参数化研究

利用敦煌站观测资料,选取其中观测资料完整且连续性好的7个年份每年5～10月的地表净辐射四分量和土壤湿度资料,分析研究了敦煌荒漠戈壁地区裸土地表反照率与太阳高度角和表层土壤含水量之间的关系,结果表明:地表反照率与太阳高度角呈e指数关系,随太阳高度角的增大而减小,当太阳高度角大于40°时,地表反照率趋于稳定。表层土壤含水量的增大可导致地表反照率的减小,地表反照率与5 cm深土壤湿度呈线性关系。另外,建立了敦煌荒漠戈壁地区裸土地表反照率与太阳高度角和表层土壤含水量之间的双因子参数化公式,提出了一种更加适合该地区的地表反照率参数方案,并且选取2002年6～9月的实测资料对拟合的参数化公式进行模拟验证。本文所提出的地表反照率参数化方案能够很好地再现该地区裸土地表反照率的“U”型日变化特征,可准确地模拟出地表反照率的动态变化趋势。基于此参数化方案计算得到的地表反射辐射与实测值基本一致。