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A review of the relationships describing the signal of a Large Aperture Scintillometer
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... Saturation occurs when turbulence becomes stronger that the weakscattering assumption no longer applies and the basic scintillometer equation no longer holds (Kleissl et al., 2010). For LAS with equal aperture diameters of the receiver and the transmitter, several practical criteria for the onset of saturation have been proposed (Kleissl et al., 2010;Kohsiek et al., 2006;Moene et al., 2004). In this study, values of C n1n1 were checked by an empirical threshold of C n1n1 < 0.1805 L − 8/3 λ 1/3 D 5/3 that is much close to the saturation correction recommended by Ochs and Wilson (1993). ...
Observations of kilometer-scale turbulent fluxes of sensible (H) and latent heat (LE) are required for the validation of flux estimate algorithms from satellite remote-sensing data and the development of parameterization schemes in the hydro-meteorological models. Since 2019, two sets of Optical and Microwave scintillometer (OMS) systems have been operated in the Heihe River Basin of northwestern China, one on an alpine grassland of upper reaches, another on an oasis cropland of middle reaches, to measure both the areal H and LE. Combined with the observations of eddy-covariance (EC) and meteorological tower systems in both sites, an improved procedure for OMS data processing is proposed. The newly proposed procedure especially improves the preprocessing of raw scintillation data, properly uses the current probably better Lüdi et al. (2005) method in deriving meteorological structure parameters, and chooses the coefficients of similarity functions by Kooijmans and Hartogensis (2016) in calculating fluxes. Evaluated with the results of rather homogeneous grassland, the area-averaged H and LE over the heterogeneous oasis are then determined. Estimates of H and LE agree reasonably well with those obtained from EC in most cases. However, the most interesting is that LE over the oasis during the early crop growing stages is clearly larger than that of EC; while both agree well during the longer crop grown periods. Footprint analysis shows that, compared with EC, the OMS has clearly larger source area that contains a slight area of orchard and shelterbelts distributed near the light path, leading to larger LE during the early stages of crop growth. The area-averaged evapotranspiration (ET) over the oasis is then analyzed more acceptably, which varies from 3 to 5 mm day−1 depending on meteorological conditions during the 39 days of the crop growing period. These results are used to validate the Penman-Monteith-Leuning Version 2 (PML-V2) scheme.
... Monin-Obukhov similarity theory (MOST) is an important theoretical method that describes near-surface turbulence characteristics [7] by establishing universal function relationships between the surface-layer scaling parameters and the stability parameter ξ = z/L [8] (z is the measuring height and L is the Monin-Obukhov length). Since the 1970s, scholars have conducted numerous experiments, explored the universal functions of the scaling parameters and stability, and applied the findings to flux measurement [9][10][11][12], near-surface turbulence parameters [13], and atmospheric structure constants [14,15] under different underlying surface conditions. As early as 1971, Businger et al. [16] demonstrated that MOST can be applied to homogeneous atmospheric boundary layers. ...
The refractive index structure constant Cn2 near the ocean surface is an important parameter for studying atmospheric optical turbulence over the ocean. The measured refractive index structure constant and meteorological parameters, such as temperature and three-dimensional wind speed, near the sea surface on the South China Sea during the period from January to November 2020 were analyzed. On the basis of Monin–Obukhov similarity theory, the dimensionless temperature structure parameter function fT near the sea surface was established, and a new parameterized model of the near-sea surface was proposed. The new model improved the error of the widely used model proposed by Wyngaard in 1973 (W73) and better reproduced the daily variation in the measured Cn2. Further analysis of the seasonal applicability of the new model indicated that the correlation coefficients between the estimated and measured Cn2 in the spring, summer, autumn, and winter were 0.94, 0.94, 0.95, and 0.89, respectively, and the root mean square errors were 0.32, 0.41, 0.46, and 0.40 m−2/3, respectively. Compared with the Cn2 estimated by the W73 model, the correlation coefficient of Cn2 estimated by the new model and measured by the micro-thermometer increased by 0.05–0.27 and the root mean square error decreased by 0.04–0.56. The improved fT demonstrated higher accuracy than the existing models, which can lay a foundation for estimating turbulence parameters in different sea areas.
... The random variable at any position ( ) of a four-dimensional space (time or space), can be described with the statistical additive moments … (Moene et al., 2004). The -th order moments were defined by Monin & Yaglom (1971), as the mean values of products of values of the field: ...
Rapid urbanisation rate and the modification of surface properties have altered energy balance and wind dynamics within the cities. This has modified locate climate, enhancing the Urban Heat Island (UHI). This phenomenon creates elevated temperatures are experienced in dense areas, mainly at night. Likewise, climate change could induce intensity and frequency of extreme events (such as heatwaves) are higher, becoming the UHI a challenge and threat of urban resilience. Nature-Based Solution (NBS), such as green roof, have appeared as a strategy for mitigation of elevated temperatures, because of the effect of evapotranspiration (ET) from vegetation. Nevertheless, the performance of NBS to cooling the air and its variability across different temporal and spatial scales are still unclear. As well, conditions that can influence their implementation in complex urban environments are unstudied.In this context, this thesis focuses on the evaluation of elements than could influence their installation across scales. First, campaigns of measure of the ET process were carried out in the Blue Green Wave (BGW), a green roof located in Bienvenüe building in front of the Ecole des Ponts ParisTech, in the Cité Descartes (eastern of Paris). The thermal and physical performance of the BGW was characterised through three different methods: the surface energy balance (SEB), the evapotranspiration chamber and the water balance during dry conditions. Differences in the three methods of measure were observed and the errors causing these were discussed. A sensitivity analysis served to determine principal variables affecting SEB estimations and make recommendations for further campaigns of measure.Second, the fractal geometry was used to analyse the complexity and heterogeneity of the spatial distribution in the case study of Est-Ensemble (eastern of Paris), and to develop a multiscale scenario of NBS deployment. More specifically, fractal dimension helped to analyse the hierarchical organisation of the built-up structure and NBS across different scales. These properties served in the multiscale scenario to reconcile the built-up structure with the NBS, by installing NBS of different sizes in the spaces not occupied by the buildings (lacunas) but over the fractal structure of buildings too.Finally, in order to improve the understanding of thermal flux variability measured in the BGW, statistical multiscale data analysis was used. The preliminary results demonstrated than air temperature and structure parameter of refraction index of air (Cn2), impacting ET, exhibit a scaling behaviour affecting by intermittency, a commonly observed feature of turbulent flows. In addition, results suggested the need to investigate the additional meteorological parameters affecting turbulent activity in the BGW, such as wind speed.
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https://www.theses.fr/2022ENPC0013
https://pastel.archives-ouvertes.fr/tel-03764898
... The C n 2 parameter can be further related to the sensible heat flux (H, Wm -2 ) with input of additional variables including the Bowen Ratio, and by employing the Monin-Obukhov Similarity Theory for a thermally stratified surface layer. For a comprehensive discussion on the theory and equations supporting the use of the LAS, the reader is referred to Moene et al. (2005). Since the primary output of the LAS is H, further measurement of R n and G variables are necessary to compute ET by energy balance. ...
... The receiver measures intensity fluctuations in the radiation emitted by the transmitter caused by refractive scattering of turbulent eddies in the scintillometer path. Scintillometers exist since the 1970's (Wang et al., 1978), and mostly use large aperture devices (Moene et al., 2004) to measure the refractive index structure parameter C 2 n with the variance of intensity fluctuation measurements. ...
Atmospheric turbulence, generated by a differential temperature between the Earth's surface and the atmosphere, causes effects on optical waves that have been of great interest to scientists for many years. Wave front distortions in the optical wave induced by atmospheric turbulence result in a spreading of the beam beyond that due to pure diffraction, random variations of the position of the beam centroid, and a random redistribution of the beam energy within a cross section of the beam leading to irradiance fluctuations. Those effects have far-reaching consequences on astronomical imaging, free space optics (FSO) communications, remote sensing, laser satellite communication, astronomical imaging, adaptive optics, target designation, hyperspectral LiDAR, and other applications that require the transmission of optical waves through the atmosphere. Throughout this thesis, we introduce a globally concept of turbulence, focusing in atmospheric turbulence.Diverse experiments have been carried out, for instance, the propagation of two parallel thin beams under geometrical optics condition for studying the parameters of optical turbulence, and besides, the same optical configuration was used to investigate the best sampling rate for optical turbulence. Furthermore, we have measured evapotranspiration by remote sensing, in which we have heeded the fluctuations of the refractive index through the intensities of the turbulence. Finally, experiments which involve a new beam are also developed, such as phase-flipped Gaussian beam. This beam shows an experimental reduction on its irradiance fluctuations induced by the turbulence, which means that it has a high performance in optical communications. The experimental reduction aforementioned is proved through the comparison with the theory developed.
... In this context, a suitable technique to measure turbulent fluxes is scintillometry, which can give measurements of sensible heat flux (H) at larger scale, providing averages over heterogeneous surfaces. Sensible heat flux is derived from the measurement of turbulent intensity of the air refraction index, in the theoretical framework of Monin-Obukhov similarity theory [1]. Average ET over the source area can then be estimated as residual of the surface energy balance [2]. ...
The assessment of evapotranspiration (ET) is of primary interest, especially for agricultural and environmental issues. Traditional micrometeorological techniques require homogenous surface and are characterized by limited footprint. Thus, they cannot be applied to assess ET over inhomogeneous and extensive surfaces, typical conditions at the catchment scale and of extensive farming systems. In this context, a suitable technique to measure turbulent fluxes is scintillometry, which can give measurements of sensible heat flux at larger scale, providing averages over heterogeneous surfaces. ET can then be estimated as residual of the energy budget. In this study, we present results from a one-week campaign held during summer 2016 in Southern Italy. We deployed a Large Aperture Scintillometer (LAS) in an extensive vineyard of 140 ha on a path length of 760 m. The site was characterized by gently slope terrain with uniform crop. In order to have reference measurements of local sensible heat flux, we deployed three sonic anemometers along the scintillometer path. The aim of the study was to test the ability of scintillometry to provide a spatially averaged flux, representative of the possibly diverse conditions in an extended footprint upwind to the measurement path. The relationship between sensible heat flux measured by EC and LAS showed to be very good for the EC station in the middle of the path, whereas off-centre areas were less represented.
... Well-designed and managed weighing lysimeters are considered the most accurate method for measurement of ET (Allen et al., 2011). However, the expense and management overhead of large weighing facilities have led to the proliferation of indirect measurement methods of ET, including Bowen Ratio systems (Fritschen, 1965;Malek and Bingham, 1993), eddy covariance (Burba, 2013), and scintillometry (Moene et al., 2004). Bowen Ratio systems calculate ET based on the ratio of temperature and vapor pressure measurements separated by a vertical distance. ...
Evapotranspiration (ET) or crop water use is the major consumptive use of irrigation and precipitation, commonly accounting for the largest component of the water balance. As water resources become scarce, agricultural research aims to increase water use efficiency by maintaining profitable crop yields while reducing ET. Advanced understanding of ET in the soil-plant-atmosphere continuum requires quantification of evaporation (E) and transpiration (T) components. However, the partitioning of E and T can be challenging even when using high quality ET data. Microlysimeters can be used to measure E from the soil surface and estimate T by subtraction using quality ET data. However, an understanding of the limitations of small, hydraulically isolated microlysimeters is required for meaningful interpretation of results. Proper design, fabrication, and operation of microlysimeters can yield reliable estimates of E from bare soil. Multiple microlysimeters and strategic placement may be required for accurate estimates of E in row crops, particularly during incomplete plant canopy conditions. Periodic weighing of lysimeter cores allows for time-averaged measurements of E but precludes E rate data at finer time scales. Design and testing of continuous weighing platforms to improve temporal density of microlysimeter measurements is needed. We present design and fabrication details of a compact, inexpensive, microlysimeter for field estimates of E in agricultural soils. Installation and operation techniques are also provided with discussion of example field data. Keywords: Evapotranspiration, Lysimetry, Microlysimeter, Soil evaporation.
... The main issue with the EC method is the lack of accuracy, as reported throughout the literature. Although scintillometers are being used in atmospheric research [17], applications in irrigation management research are relatively new and few in number. A thorough evaluation of scintillometers is needed to determine if they are suitable to measure ET for the purposes of irrigation scheduling and developing crop coefficients. ...
Accurate estimates of actual crop evapotranspiration (ET) are important for optimal irrigation water management, especially in arid and semi-arid regions. Common ET sensing methods include Bowen Ratio, Eddy Covariance (EC), and scintillometers. Large weighing lysimeters are considered the ultimate standard for measurement of ET, however, they are expensive to install and maintain. Although EC and scintillometers are less costly and relatively portable, EC has known energy balance closure discrepancies. Previous scintillometer studies used EC for ground-truthing, but no studies considered weighing lysimeters. In this study, a Surface Layer Scintillometer (SLS) was evaluated for accuracy in determining ET as well as sensible and latent heat fluxes, as compared to a large weighing lysimeter in Bushland, TX. The SLS was installed over irrigated grain sorghum (Sorghum bicolor (L.) Moench) for the period 29 July-17 August 2015 and over grain corn (Zea mays L.) for the period 23 June-2 October 2016. Results showed poor correlation for sensible heat flux, but much better correlation with ET, with r 2 values of 0.83 and 0.87 for hourly and daily ET, respectively. The accuracy of the SLS was comparable to other ET sensing instruments with an RMSE of 0.13 mm·h −1 (31%) for hourly ET; however, summing hourly values to a daily time step reduced the ET error to 14% (0.75 mm·d −1). This level of accuracy indicates that potential exists for the SLS to be used in some water management applications. As few studies have been conducted to evaluate the SLS for ET estimation, or in combination with lysimetric data, further evaluations would be beneficial to investigate the applicability of the SLS in water resources management.
... The receiver measures intensity fluctuations in the radiation emitted by the transmitter caused by refractive scattering of turbulent eddies in the scintillometer path. Scintillometers exist since the 1970's [1], and mostly use large aperture devices [2] to measure the refractive index structure parameter C n 2 with the variance of intensity fluctuation measurements. Other techniques used to obtain C n 2 consist in the acquisition of the angle of arrival (AoA) or the beam wandering. ...
We compare in this study two simple optical setups to measure the atmospheric turbulence characterized by the refractive index structure parameter . The corresponding heat flux values sensed by the laser beam propagation are calculated leading to the plant evapotranspiration. The results are discussed and compared to measurements obtained with a well-known and calibrated eddy-covariant instrument. A fine analysis gives a good insight of the accuracy of the optical devices proposed here to measure the crop evapotranspiration. Additional evapotranspiration values calculated with meteorological sensor data and the use of different models are also compared in parallel.
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In my note (Kolmogorov 1941 a ) I defined the notion of local isotropy and introduced the quantities B d d ( r ) = [ u d ( M ′ ) − u d ( M ) ] 2 , ¯ [ u n ( M ′ ) − u n ( M ) ¯ ] 2 , where r denotes the distance between the points M and M' , u d (M) and u d (M') are the velocity components in the direction MM' ¯¯ at the points M and M' , and u n (M) and u n (M') are the velocity components at the points M and M' in some direction, perpendicular to MM' .
§1. We shall denote by u α ( P ) = u α ( x 1 , x 2 , x 3 , t ), α = 1, 2, 3, the components of velocity at the moment t at the point with rectangular cartesian coordinates x 1 , x 2 , x 3 . In considering the turbulence it is natural to assume the components of the velocity u α ( P ) at every point P = ( x 1 , x 2 , x 3 , t ) of the considered domain G of the four-dimensional space ( x 1 , x 2 , x 3 , t ) are random variables in the sense of the theory of probabilities (cf. for this approach to the problem Millionshtchikov (1939) Denoting by Ᾱ the mathematical expectation of the random variable A we suppose that ῡ ² α and (d u α /d x β ) ² ― are finite and bounded in every bounded subdomain of the domain G .
A new optical technique is described for measuring the path profiles of crosswind and of a refractive-index structure parameter C n 2 along a line-of-sight path. Different sizes of transmitters and receivers are used to control the path-weighting function so that it will peak at different path locations. Various linear combinations of these measurements yield the path profile of crosswind and C n 2. A prototype instrument has been built and tested. Experimental results show good agreement with the theoretical predictions.
An overview of atmospheric scattering is provided, taking into account
the role of scattering, the elements of radiometry and photometry, the
principal characteristics of scattering, scattering in the atmosphere,
visibility along an atmospheric path, and literature of atmospheric
optics. The structure and composition of the gas atmosphere are
examined, giving attention to factors from kinetic theory, the
atmospheric envelope, models of the atmosphere, measures of the overhead
atmosphere, and quantitative treatments of optical paths. Particles in
the atmosphere are considered along with Rayleigh scattering by
molecules, Mie scattering by monodispersions, and Mie scattering by
atmospheric polydispersions.
The refractive index structure function coefficient Cn2 is an atmospheric parameter needed to describe scintillation and small-scale phase fluctuations of electromagnetic radiation propagated in the atmospheric surface layer. Since systematic direct measurements of Cn for many climates and seasons are not available, an indirect method is developed in which Cn is calculated from the estimates of sensible and latent heat flux components of the surface energy budgets. This indirect method is primarily for heights less than 4 meters, because low intermittency and a near-unity value of the ratio of the eddy diffusivity of heat to that of momentum are assumed. Diurnal variations of Cn at several heights above land for six combinations of climates, seasons, and surface conditions are calculated from heat fluxes measured by different investigators at many locations for moderate to high wind velocities. These predictions of Cn agree well with some direct measurements of Cn when assumptions of nearly ideal weather and sites are met. The effect of water vapor on Cn is usually an increase of about 16/β%, where β is Bowen's ratio, and thus is usually negligible above dry land but can be significant above wet surfaces.
Recent theoretical and experimental advances have produced a model of the power spectrum of quantities mixed by turbulence. This model is applicable for arbitrary diffusivity and is thereby capable of predicting the high wavenumber shape of the spectra of refractivity, temperature, humidity, and the temperature-humidity cospectrum. Equations for the mean refractivity and the refractivity variance are formed from temperature, pressure, and humidity fluctuations; the accuracy of neglecting the higher-order terms in the fluctuations is determined. In order to apply the model power spectrum for temperature and humidity fluctuations in the atmosphere, it is first determined under what conditions temperature and humidity satisfy a simple continuity equation that balances temporal changes, advection, and diffusion. Experiments have shown that the temperature spectrum in air has a "bump" at high wave numbers. This feature is understood in terms of the theoretical model, and the bump is predicted to appear in the refractivity and humidity spectra and in the temperaturehumidity cospectrum as well as in the temperature spectrum. The bump in the humidity spectrum is smaller than that in the temperature-humidity cospectrum, which is in turn smaller than the bump in the temperature spectrum; this effect is caused by the fact that the diffusivity of water vapor in air is slightly greater than that of heat in air. The shape of the refractivity spectrum depends on the relative contributions of the temperature spectrum, humidity spectrum, and temperature-humidity cospectrum. The refractivity spectrum can have an enhanced bump if the contribution of the temperature-humidity cospectrum is negative and nearly cancels the contributions of the temperature and humidity spectra. The impact of these developments on radio wave propagation is discussed.