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

Abstract

<p lang="en-GB" align="justify">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 (<span lang="en-US">ET) processes. Understanding ET process is the key to optimize cooling effect. ET estimation can be achieved either directly</span><em> </em><em><span lang="en-US">(</span></em><span lang="en-US">weighing lysimeters) or indirectly (e</span><span lang="en-US">.</span><span lang="en-US">g., </span>Penman-Monteith equation). Micro-meteorological approaches have<span lang="en-US"> been developed in recent years. Among which scintillometer can evaluate ET by its measurement parameter C<sub>n</sub><sup>2</sup></span> (<span lang="en-US">which corresponds to the fluctuations of air refractive index n </span>) in combination with surface energy balance (SEB) and Monin-Obukhov similarity theory (MOST) <span lang="en-US">.</span> Hence, <span lang="en-US">C<sub>n</sub><sup>2</sup></span><span lang="en-US"> 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, </span><span lang="en-US">the research area lies on the top of the </span>Carnot and Bienvenüe buildings<span lang="en-US"> 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 </span>December 2019 and January 2020 on BGW is used in this study<span lang="en-US">. Three estimates of C<sub>n</sub><sup>2</sup></span><span lang="en-US">(Cn2_UCn2, Cn2_PUCn2 and Cn2_Var) </span>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 C<sub>1</sub>≥0<sub> </sub>and 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<span lang="en-US"> scale invariance, which could be used for upscaling and downscaling. </span><span lang="en-US">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<sub>n</sub><sup>2</sup></span><span lang="en-US">.</span> <span lang="en-US">This research provides a complete grasp of the properties of C<sub>n</sub><sup>2 </sup></span><span lang="en-US">and sets the stage for its future application in precise ET estimates.</span></p> <p lang="en-GB" align="justify"><span lang="en-US"> </span></p>