Multifractal analysis of Cn2 scintillometer data

The cooling efficacy of green roofs in mitigating the urban heat island (UHI) effect within dense cities is largely attributed to evapotranspiration (ET) processes. Hence, accurate understanding and quantification of ET are pivotal for optimizing this 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   which corresponds to the fluctuations of air refractive index  ) in combination with surface energy balance and Monin-Obukhov similarity theory. Hence, improvement in  data as well as understanding of its variability across wide range of space-time scale would result in better ET estimation and ultimately optimization. Yet it is often overlooked, and little research has focused on it and notably its variability.

This study explores the ET estimation on a wavy and vegetated green roof covering an area of 1 ha, known as the Blue Green Wave, which is located in Ecole des Ponts Paristech campus. Data from a large aperture scintillometer with 10-minute timestep during December 2019 and January 2020 is adopted.   data variability across scales was analysed with the help of structure function and Universal Multifractal model (UM). The UM framework, widely employed for characterizing and simulating geophysical fields extremely variable across wide range of space-time scales, relies on two parameters with physical interpretation: the mean intermittency codimension  and multifractality index  (, indicates monofractal; , indicates log-normal model.) An additional one, which is needed for non-conservative fields such as ET is the non-conservativeness parameter H.

Both structure function and UM approaches reveal good scaling behaviour on scales ranging from 10 min to 2h, confirming the relevance of the framework and demonstrating the potential for upscaling and downscaling. UM analysis conducted through Trace Moment and Double Trace Moment methods, provided similar values for UM parameters around   H is approximately 0.44 in our case, which deviates from traditional scaling laws due to the intricate composition of the fluxes and requires further investigations. Indeed  is influenced by temperature, humidity, air pressure and wind speed. To interpret properly structure function analysis from UM analysis, it is necessary to introduce a parameter denoted a. It corresponds to the power to which the assumed conservative underlying field should be raised before fractional integration to account for non-conservativeness to retrieve the studied field.  Here, we observed that a is around 0.76 to ensure the highest consistency of the outcome from both the structure function and UM analyses. A better understanding of the underlying complexity and variability of Cn2 is achieved by our analysis. This, in turn, improves our understanding of the underlying physical processes generating variability and temporal-spatial dynamics in ET, which paves the way for future applications.