星载散射计测量的归一化后向散射截面是有关海面毛细重力波的大小和方向的函数:散射计的回波强度与海面毛细重力波的振幅成正比;风向对后向散射系数具有调制作用。因此,可以利用散射计的数据,根据地球物理模型反演出具有高精确度、无雨和中低风速条件下的海面风场矢量。然而高达10%的散射计测量数据会受到降雨影响(Nie, etal., 2008),尤其工作在Ku波段的散射计。降雨对海面散射幅度的影响主要包括:(1) 降雨对雷达波的衰减和散射;(2) 降雨改变海洋水面形态和海面粗糙度。本文建立了计及降雨衰减和散射影响后的海面散射正演模型,分析Ku波段不同入射角情况下降雨对海面后向散射系数的影响,进而通过雷达方程将降雨影响加入到扇形波束系统中进行分析。模型是基于降雨均匀分布在散射计视场范围内这一假设建立的。我们把整个降雨结构看作是雨滴填充在空气中的混合介质,并把降雨层按其高度分为12个子层,每一层用一特定值,即平均雨滴尺寸,来代表该子层的雨滴尺寸,而(每一个子层中雨滴尺寸随高度变化信息被忽略)。这样12个子层对应12个雨滴尺寸,从而描述了雨滴降落过程中尺寸的变化。本文忽略了雨滴下落过程中形状的变化,将雨滴均假设为球形,并用Mie散射理论计算出雨滴的双向散射相位矩阵。之后,按照耦合矩阵法计算出每一子层的相位矩阵。子层中降雨的水平分布用Gamma模型进行描述,从而计算不同降雨量时雨滴的体积含量。降雨与海面的下分界面和降雨与云的上分界面的面散射相位矩阵用面散射积分方程IEM(Integral Equation Method)进行计算。最后,再次应用矩阵耦合法(matrix doubling method),将12个降雨子层的相位矩阵和上下两个分界面的相位矩阵整合为降雨影响下海面风场的散射。模型的建立过程如下:(1) 首先将整个降雨层分成垂直分布的12个子层,假设每一个子层是统计均匀的,而且每一子层中雨滴尺寸不随垂直高度发生变化。采用Gamma模型描述子层中雨滴分布,根据Mie散射理论计算雨滴散射相位矩阵, P_i={S_i, T_i, S_i^*,T_i^*},i=1, …, N。(2) 将各个子层体散射相位矩阵整合为整个降雨结构的总体散射相位矩阵P_rain={S_rain, T_rain, S_rain^*, T_rain^*},计算方法如下: P_rain=P₁ P₂ ... P_N。(3) 利用IEM计算+Z和-Z入射时,反射及传输情况下降雨云与降雨分界面的有效面散射相位矩阵R_cr,Q_cr和R_cr^*,Q_cr^*,同理计算出降雨与海洋表面分界面反射情况下的有效面散射相位矩阵R_surface。(4) 利用以上已经计算出的体散射相位矩阵和面散射相位矩阵求出整个降雨层的总的散射矩阵,进一步得到受降雨影响的海洋表面的散射系数: 。(5) 对比模型结果与卫星测量数据,调整模型参数以优化模型,将优化后模型于卫星参数相结合,从而分析不同降雨情况下降雨对扇形波束散射计海面风场测量的影响。按照以上思路建立了降雨影响下海面的正演散射模型。其中用以模拟子层中雨滴分布的Gamma模型是利用位于赤道地区(新加坡)的Joss-Waldvogel Disdrometer (JWD)雨滴测量器计算得到,因此本文利用同样覆盖赤道地区的TRMMPR降雨雷达测量数据对模型进行了验证。验证结果显示,在3种降雨量情况下模型结果与TRMM测量数据都可以较好地吻合。利用验证后的模型,我们对降雨参数以及散射计系统参数对降雨影响下海面散射情况进行了分析,可以看到散射计工作频率、极化情况、雨滴大小以及雨滴含量都会产生较显著的影响,而且不同入射角时降雨对海面散射的影响不同。该模型满足了分析降雨在不同入射角情况下对散射计测量影响的需求,从而分析了扇形波束下降雨对海面散射的影响。

The effects of rainfall backscattering on space-borne rotating fan-beam scatterometer measurements at Ku-band were investigated in this study. A new scattering model based on Integral Equation Method (IEM) for sea surface with precipitation that accounts for the effects of rain column was presented. The relation between rain scattering and incidence was analyzed, and hence the rain effects on a rotating fan-beam scatterometer are obtained. The rain column is modeled as sublayers with different physical characteristics determined by the vertical profile of rainfall. Each sublayer is assumed to be statistically homogeneous, and the gamma distribution is used to model the drop size distribution within each sublayer. Sea surface is modeled as a rough surface, and its backscattering is calculated using the IEM model. Multiple scattering within and interactions between the rain layers and sea surface are accounted for in the matrix doubling formulation. The presented model is validated using published TRMM PR measurements. Results from model analyses show that rain effects are incident angle dependent, which can lead to non-uniform impacts within the footprint of a fan-beam scatterometer; these effects are strongly related to rain column vertical profile and rain rate, as different rain rate corresponds to different physical parameters.