A new model is proposed for the so-called scalar footprint and flux footprint in the atmospheric boundary layer. The underlying semi-analytical model allows computing the scalar concentration and flux fields related to turbulent diffusion of heat, water-vapor or to the dispersion of any scalar (e.g. passive pollutant) in the framework of K-theory. It offers improved capabilities regarding the representation of the gradual stratification in the boundary layer. In this model, the boundary layer is split in a series of sublayers in which the aerodynamic inertivity (a compound parameter aggregating wind-speed and eddy-diffusivity) is approximated by a sum of two power-law functions of a new vertical scale corresponding to the height-dependent downwind extension of the plume. This multilayer approach allows fitting with vanishing error any boundary-layer stratification, in particular those described by the Monin–Obukhov similarity theory (MOST) in the surface layer, while keeping the computation time of the footprint to low values. As a complement, a fully analytical surrogate model is presented for practical applications. For MOST profiles, the flux (resp. concentration) footprint is, to a RMS difference less than 1% (resp. 1.2%), equal (resp. equal to a constant multiplicative factor) to the inverse Gamma distribution. The optimal parameters of this distribution were evaluated for a broad range of atmospheric conditions and height. Regression formulas were also provided to compute the crosswind-integrated flux footprint distribution easily and with less than 1.6% RMS residual error. A comparison with the well-known footprint approximate model by Kormann and Meixner and the one by Hsieh, Katul and Chi has allowed quantifying their performances and limitations.

针对大气边界层中所谓的标量足迹和通量足迹提出了一个新模型。底层的半解析模型允许在 K 理论的框架内计算与热、水蒸气的湍流扩散或任何标量（例如被动污染物）的扩散相关的标量浓度和通量场。它提供了有关边界层中逐渐分层表示的改进功能。在这个模型中，边界层被分成一系列子层，其中空气动力学惯性（聚合风速和涡流扩散系数的复合参数）由新垂直尺度的两个幂律函数之和近似，该新垂直尺度对应于羽流的高度相关的顺风延伸。这种多层方法允许用消失误差拟合任何边界层分层，特别是表面层中 Monin-Obukhov 相似性理论 (MOST) 所描述的那些，同时将足迹的计算时间保持在较低的值。作为补充，为实际应用提出了一个完全分析的替代模型。对于 MOST 配置文件，通量（分别为浓度）足迹，RMS 差异小于 1%（分别为 1.2%），等于（分别为常数乘法因子）逆伽马分布。该分布的最佳参数针对广泛的大气条件和高度进行了评估。还提供了回归公式来轻松计算侧风积分通量足迹分布，且 RMS 残差小于 1.6%。与 Kormann 和 Meixner 以及 Hsieh、Katul 和 Chi 的著名足迹近似模型进行比较，可以量化它们的性能和局限性。