Multifractal analysis of Cn2 scitillometer data and consequences for evapotranspiration estimates in urban areas

The cooling impact of green roofs is highlighted in the context of urbanisation and urban heat island (UHI) effect. And it is usually described and quantified by evapotranspiration (ET) processes. Understanding ET process is the key to optimize cooling effect. ET estimation can be achieved either directly (weighing lysimeters) or indirectly (e.g., Penman-Monteith equation). Micro-meteorological approaches have been developed in recent years. Among which scintillometer can evaluate ET by its measurement parameter C_n² (which corresponds to the fluctuations of air refractive index n ) in combination with surface energy balance (SEB) and Monin-Obukhov similarity theory (MOST) . Hence, C_n² improvement in Cn2 data would result in better ET estimation. But it is often overlooked and very little research has focused on it. In this project, the research area lies on the top of the Carnot and Bienvenüe buildings in Ecole des Ponts Paristech. Covering an area of ​​1 ha, it is a wavy and vegetated large green roof, known as the Blue Green Wave (BGW). Data from a large aperture scintillometer (LAS) with 10-minute time step during December 2019 and January 2020 on BGW is used in this study. Three estimates of C_n²(Cn2_UCn2, Cn2_PUCn2 and Cn2_Var) were analysed with structure function and universal multifractal model (UM). Such framework has been widely use to characterize geophysical fields extremely variable across wide range of space-time scales. There are two relevant parameters in an UM model, the mean codimension of intermittency C₁≥0and multifractality index 0≤α≤2. α=0, indicates monofractal; α=2, indicates log-normal model. Data in UM framework is analysed by Trace Moment (TM) method and Double Trace Moment (DTM) method. All of estimates demonstrated scale invariance, which could be used for upscaling and downscaling. Cn2_Var performed well even during measurement malfunction, but UM analysis showed it was contradictory to the hypothesis of lognormality. It implies the way it calculates Cn2_Var need some revisions and an assessment of the scintillometer could be achieved by analysing C_n². This research provides a complete grasp of the properties of C_n² and sets the stage for its future application in precise ET estimates.