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Flux-Profile Relationship in the Atmospheric Surface Layer
Abstract
Wind and temperature profiles for a wide range of stability conditions
have been analyzed in the context of Monin-Obukhov similarity theory.
Direct measurements of heat and momentum fluxes enabled determination of
the Obukhov length L, a key independent variable in the steady-state,
horizontally homogeneous, atmospheric surface layer. The free constants
in several interpolation formulas can be adjusted to give excellent fits
to the wind and temperature gradient data. The behavior of the gradients
under neutral conditions is unusual, however, and indicates that von
Kármán's constant is 0.35, rather than 0.40 as usually
assumed, and that the ratio of eddy diffusivities for heat and momentum
at neutrality is 1.35, compared to the often-suggested value of 1.0. The
gradient Richardson number, computed from the profiles, and the Obukhov
stability parameter z/L, computed from the measured fluxes, are found to
be related approximately linearly under unstable conditions. For stable
conditions the Richard on number approaches a limit of 0.21 as stability
increases. A comparison between profile-derived and measured fluxes
shows good agreement over the entire stability range of the
observations.
... This height is illustrated by circular markers in Fig. 9. The widely used empirical similarity relations of the form α m/h + β m/h (z/L O ) from Businger et al. (1971) are indicated by the black dashed lines. It is clear that close to the surface (for z < 0.1h θ ), the linear similarity relations hold reasonably well. ...
... For the dimensionless temperature gradient above 0.1h θ , a departure from the linear profile depending on Buoyancy and subsidence numbers is observed. Remarkably, it seems that the simulations with stronger buoyancy and subsidence Businger et al. (1971). ...
... Only data in the range 0.03 < z/h θ < 0.3 is included. The meaning of the colors corresponds to Fig. 5, and the linear black dashed lines correspond to empirical relations from (a,b) Businger et al. (1971) and (c,d) Heisel and Chamecki (2023) Z match rather well, while the cases with strong subsidence from set S (dark blue lines) have a larger offset. A last point to underline here is that Nieuwstadt (1984) introduced a 'local scaling' framework in order to extend MOST to the entire SBL. ...
The stable boundary layer (SBL) subjected to large-scale subsidence is studied through large-eddy simulations (LESs) with fixed surface temperature and a linear subsidence velocity profile. These boundary layers reach a truly steady state, where thermal equilibrium is established by a balance between surface cooling and subsidence-induced heating. We identify three governing dimensionless groups by scaling the governing equations with the geostrophic wind and Coriolis frequency, and systematically investigate the impact of these external parameters on global flow properties and mean profiles in the steady state. The SBL depth, low-level jet, and the magnitude of the turbulent momentum flux are reduced when the subsidence rate or Buoyancy number increases, while surface heat flux is enhanced. The shape of normalized mean profiles of temperature and heat flux is mainly determined by the subsidence rate, while they collapse for varying buoyancy and surface Rossby numbers. We develop empirical correlations for the stability parameter $h_{\theta}/L_O$ and a thermal shape factor, and propose a new unidirectional geostrophic drag law, to form a closed set of equations that estimates relevant flow properties from external parameters. The estimation errors compared to the LES data are less than 5% for friction velocity and surface heat flux, and at most 10% for the SBL depth $h_{\theta}$. Within the surface layer, dimensionless velocity and temperature gradients in the steady SBL with subsidence show acceptable agreement to Monin-Obukhov similarity theory, while the collapse is improved when a recently proposed mixed scaling parameter, that includes $h_{\theta}/L_O$, is used.
... In the literature, researchers have developed various formulations for these similarity functions based on the datasets from different field experiments conducted at different locations (Webb 1970;Businger et al. 1971;Carl et al. 1973;Dyer 1974;Hicks 1976;Holtslag and De Bruin 1988;Brutsaert 1992;Bruin 1999;Wilson 2001;Cheng and Brutsaert 2005;Grachev et al. 2007). These formulations ranging from linear to non-linear forms differ in terms of their functional forms, the coefficients appearing in each form, and the extent to which they can be applied under moderately to strongly stable conditions. ...
... Various studies reported in the literature imply that the applicability of these linear and non-linear functional forms is constrained by the values of the bulk Richardson number (Ri B ) and ζ. For example, linear functional forms (Webb 1970;Businger et al. 1971;Dyer 1974) are only relevant under nearneutral to moderately stable conditions, and their applicability is restricted to Ri B values less than 0.2 (Sharan et al. 2003). Moreover, Sharan and Kumar (2011) have estimated the upper bounds for the applicability of linear (Webb 1970;Brutsaert 1992) as well as nonlinear (Clarke 1970;Hicks 1976;Holtslag and De Bruin 1988;Beljaars and Holtslag 1991;Cheng and Brutsaert 2005;Grachev et al. 2007) functional forms in terms of ζ and Ri B for the computation of surface fluxes. ...
... Recently, Srivastava and Sharan (2019) carried out a systematic mathematical analysis to analyze the behavior of sensible heat flux (SHF) as a function of ζ, using linear (Businger et al. 1971) and non-linear (Holtslag and De Bruin 1988;Cheng and Brutsaert 2005;Grachev et al. 2007) similarity functions in the MOST framework. The study suggests that the variation of computed SHF with ζ is consistent with the observed behaviour for linear functional form; however, for non-linear functions (specifically Holtslag and De Bruin 1988;Cheng and Brutsaert 2005), more than two values of ζ having the same magnitude of SHF may occur, implying the existence of multiple critical points, which contradicts the observed behavior of SHF with ζ. ...
In this study, a systematic mathematical analysis has been presented for the extent of applicability of various non-linear similarity functions for momentum (φm)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({{\upvarphi }}_{{\text{m}}})$$\end{document} and heat (φh)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({{\upvarphi }}_{{\text{h}}})$$\end{document} under stable conditions to compute surface turbulent fluxes in numerical models. The investigation is carried out for equal and unequal momentum (z0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({{\text{z}}}_{0})$$\end{document} and heat (zh)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({{\text{z}}}_{{\text{h}}})$$\end{document} roughness lengths. The study reveals that φm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\upvarphi }}_{{\text{m}}}$$\end{document} and φh\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\upvarphi }}_{{\text{h}}}$$\end{document} utilized in the National Centre for Atmospheric Research Community Atmosphere Model version 5 (NCAR-CAM5) (Holtslag et al. in Mon Weather Rev 118:1561–1575, 1990) have several restrictions on their applicability in moderately to strongly stable cases. If the ratios of z0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\text{z}}}_{0}$$\end{document} and zh\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\text{z}}}_{{\text{h}}}$$\end{document} to the height (z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\text{z}})$$\end{document} from the surface (i.e., z0z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{{\text{z}}}_{0}}{{\text{z}}}$$\end{document} and zhz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{{\text{z}}}_{{\text{h}}}}{{\text{z}}}$$\end{document}) lie in the range (0.2,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(0.2, 1)$$\end{document}, the functions are valid for a limited range of ζ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upzeta $$\end{document} (stability parameter) in strong stable conditions ζ>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left(\upzeta >1\right)$$\end{document}; however, when z0z≤0.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{{\text{z}}}_{0}}{{\text{z}}}\le 0.2$$\end{document} and zhz≤0.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{{\text{z}}}_{{\text{h}}}}{{\text{z}}}\le 0.2$$\end{document}, the validity of functions is unrestricted. In terms of bulk Richardson number RiB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left({{\text{Ri}}}_{{\text{B}}}\right)$$\end{document}, the functions are valid for a limited range of moderately to strongly stable conditions. These theoretically derived upper limits have also been validated using observations from the UK Meteorological Office’s Cardington and Cooperative Atmosphere-Surface Exchange Study-99 datasets. On the other hand, similarity functions based on Cheng and Brutsaert (Boundary-Layer Meteorol 114:519–538, 2005), Grachev et al. (Boundary-Layer Meteorol 124:315–333, 2007), Srivastava et al. (Meteorol Appl 27, 2020), and Gryanik et al. (J Atmos Sci 77:2687–2716, 2020) are found to be theoretically valid for all values of ζ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upzeta $$\end{document} and RiB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\text{Ri}}}_{{\text{B}}}$$\end{document}. The efforts have also been made to implement these functions in the Weather Research and Forecasting as well as global scale models.
... However, the exact 26 functional forms for these functions have not been provided by MOST, rather it suggests some asymptotic predictions under 27 near neutral to very stable and unstable conditions which are tuned with field data. Over the years, researchers have developed 28 many functional forms for these functions based on the different experiments, conducted over different locations and have 29 separate expressions for stable and unstable stratifications (Webb, 1970;Businger, 1971;Carl et al., 1973;Dyer, 1974; Hicks, the observed CD shows non-monotonic behaviour with − , unlike the behaviour of predicted CD from MOST based 48 parameterization using commonly used φ m and φ h (Businger et al., 1971;Carl et al., 1973;Fairall et al., 1996). Later, a 49 theoretical study by Srivastava and Sharan (2021) revealed that the three-sublayer model based on Kader and Yaglom (1990) 50 is able to predict CD consistent with its observed non-monotonic behaviour. ...
... However, the exact 26 functional forms for these functions have not been provided by MOST, rather it suggests some asymptotic predictions under 27 near neutral to very stable and unstable conditions which are tuned with field data. Over the years, researchers have developed 28 many functional forms for these functions based on the different experiments, conducted over different locations and have 29 separate expressions for stable and unstable stratifications (Webb, 1970;Businger, 1971;Carl et al., 1973;Dyer, 1974; Hicks, the observed CD shows non-monotonic behaviour with − , unlike the behaviour of predicted CD from MOST based 48 parameterization using commonly used φ m and φ h (Businger et al., 1971;Carl et al., 1973;Fairall et al., 1996). Later, a 49 theoretical study by Srivastava and Sharan (2021) revealed that the three-sublayer model based on Kader and Yaglom (1990) 50 is able to predict CD consistent with its observed non-monotonic behaviour. ...
... The study by Srivastava and Sharan (2021) also analyzed the possible uncertainties associated with the use of different 55 functional forms of φ m and φ h under convective conditions. To quantify the impacts of different functional forms, they 56 classified available φ m and φ h in four classes based on the exponents appearing in the expressions of φ m and φ h as (1) 57 functional forms having the exponents of φ m and φ h as −1/4 and −1/2, respectively (Businger et al. 1971;Hogstrom 1996). 58 ...
Accurate parameterization of atmospheric surface layer processes is crucial for weather forecasts using numerical weather prediction models. Here, an attempt has been made to improve the surface layer parameterization in the Weather Research and Forecasting Model (WRFv4.2.2) by implementing similarity functions proposed by Kader and Yaglom (1990) to make it consistent in producing the transfer coefficient for momentum observed over tropical region (Srivastava and Sharan 2015). The surface layer module in WRFv4.2.2 is modified in such a way that it contains all commonly used φm and φh under convective conditions instead of the existing single functional form. The updated module has various alternatives of φm and φh, which can be controlled by a flag introduced in the input file. The impacts of utilizing different functional forms have been evaluated using the bulk flux algorithm as well as real-case simulations with the WRFv4.2.2 model. The model-simulated variables have been evaluated with observational data from a flux tower at Ranchi (23.412N, 85.440E; India) and the ERA5-Land reanalysis dataset. The transfer coefficient for momentum simulated using the implemented scheme is found to agree well with its observed non-monotonic behaviour in convective conditions (Srivastava and Sharan 2022). The study suggests that the updated surface layer scheme performs well in simulating the surface transfer coefficients and could be potentially utilized for parameterization of surface fluxes in the numerical weather prediction model.
... In addition, the stably stratified velocity log law is found when z L > 3 (in ReD2700, L + = 160) using the MOST stability parameter. However, the MOST stability correction functions proposed by both Businger et al. [68] and Gryanik et al. [70] suggest that velocity profiles will significantly deviate from a log law in such stably stratified conditions [ Fig. 2(d)]. In fact, the stability correction functions of MOST proposed by Businger et al. [68] are only defined in the range 0 < z L < 1 in stably stratified conditions due to its poor behavior in more stratified conditions [71]. ...
... However, the MOST stability correction functions proposed by both Businger et al. [68] and Gryanik et al. [70] suggest that velocity profiles will significantly deviate from a log law in such stably stratified conditions [ Fig. 2(d)]. In fact, the stability correction functions of MOST proposed by Businger et al. [68] are only defined in the range 0 < z L < 1 in stably stratified conditions due to its poor behavior in more stratified conditions [71]. Therefore, the proposed velocity log law is fundamentally different from MOST and might be applied to a wider range of buoyant conditions. ...
... The coefficient of determination for U −U h1 u τ and ln(z + ) falls in the range R 2 > 0.88 in all 40 selected periods (see Supplemental Material [69] for more atmospheric observations), indicating the linear relation between U −U h1 u τ and ln(z + ) and thus the presence of a velocity log law. We also compare the velocity profile based on MOST [68,70,72,73] with field observations. There are substantial deviations in the MOST function proposed by Businger et al. [68] across stably stratified conditions in the range 0.22 z/L 15.68 (Fig. 3), where z = 10 m (at one vertical level of tower observations). ...
The universal velocity log law proposed by von Kármán in wall-bounded turbulent flows is one of the cornerstones of turbulence theory. When buoyancy effects are important, the universal velocity log law is typically believed to break down according to Monin-Obukhov similarity theory (MOST), which has been used in almost all global weather and climate models to describe the dependence of the mean velocity profiles on buoyancy near the earth's surface and to characterize the surface-atmosphere exchange of momentum, heat, water vapor, and carbon dioxide. In contrast to MOST, we propose logarithmic profiles of near-wall mean velocity in the stably stratified atmospheric boundary layers based on direct numerical simulations and field observations across a wide range of buoyancy effects. We find that buoyancy does not seem to change the logarithmic nature of velocity profiles but instead modifies the slope of the log law in stably stratified conditions. This paper provides a perspective on wall turbulence and can be applied to numerical simulations of turbulence, weather, and climate.
... The dimensionless wind shear takes different functional forms depending on the atmospheric stability conditions. It is usually described by the experimentbased Businger-Dyer functions (Businger et al., 1971;Dyer, 1974): ...
... Nevertheless, the reliability of the optimisation method proposed by Lo (1979) can be considered questionable because of different mathematical issues reported by Zhang (1981). Of the remaining three methods, the recent one by Basu (2019) -the socalled Hybrid-Wind (HW) method-is an enhanced version of the Swinbank (1964), in which the surface-layer wind profile follows an exponential profile instead of MOST (Businger et al., 1971;Dyer, 1974;Peña et al., 2009;Holtslag et al., 2015;. HW estimates the Obukhov length from three levels of wind speed measurements. ...
Monitoring the atmospheric boundary layer (ABL) is a matter of interest for many applications, such as weather forecasting, pollutantdispersion models and wind energy. The ABL is the most turbulent part of the troposphere, and it is directly affected by the earth’s surface characteristics. Thus, monitoring the ABL is a complex task that requires continuous improvement of the remote sensing techniques.
This PhD thesis tackles remote sensing as the key technology to assess different ABL parameters in both over-land and over-sea dimensions. The over-land dimension is oriented to the study of the ABL height (ABLH), whereas the over-sea dimension is focused in assessment of surface-layer atmospheric stability from solely wind profiles in the context of wind energy.
In the over-land dimension, a synergistic ABLH estimation method via a combination of microwave-radiometer and lidar-ceilometer-based estimates is presented. The synergistic method uses these two instruments in a cooperative way with the aim of providing an enhanced high-resolution ABLH estimation. Data gathered by multiple remotesensing instruments during the HOPE campaign at Julich, Germany, are used to outline the robustness of the synergistic method in relation to estimates which rely on a single instrument.
In the over-sea dimension, the 2D parametric-solver algorithm is presented as an alternative method to assess surface-layer parameters from solely floating Doppler wind lidar measurements. Comparative results with reference retrievals from the IJmuiden meteorological mast show that the 2D accurately estimates the friction velocity, and it correctly determines atmospheric stability via its Obukhov length estimation. Accordingly, the 2D algorithm corroborates to stand the floating Doppler wind lidar as the wind-energy-industry preferred solution to replace the off-shore metmast.
... Following the introduction of MOST, evaluations of field measurements from meteorological towers have largely corroborated the surface layer theory and universality of φ m (ζ ) and φ h (ζ ). For a convective ABL (CBL) with L < 0 typical of daytime conditions, several experimental campaigns and reevaluations proposed power-law relations for φ m and φ h with some variability in the fitted parameters but a consistent general form for the functions (see, e.g., Dyer and Hicks 1970;Businger et al. 1971;Carl et al. 1973;Yaglom 1977;Högström 1988;Wilson 2001;Katul et al. 2011). The most common of these empirical relations are the Businger-Dyer profiles for convective conditions (Businger et al. 1971;Dyer 1974): ...
... For a convective ABL (CBL) with L < 0 typical of daytime conditions, several experimental campaigns and reevaluations proposed power-law relations for φ m and φ h with some variability in the fitted parameters but a consistent general form for the functions (see, e.g., Dyer and Hicks 1970;Businger et al. 1971;Carl et al. 1973;Yaglom 1977;Högström 1988;Wilson 2001;Katul et al. 2011). The most common of these empirical relations are the Businger-Dyer profiles for convective conditions (Businger et al. 1971;Dyer 1974): ...
Large-eddy simulations are used to evaluate mean profile similarity in the convective boundary layer (CBL). Particular care is taken regarding the grid sensitivity of the profiles and the mitigation of inertial oscillations in the simulation spin-up. The nondimensional gradients \(\phi \) for wind speed and air temperature generally align with Monin–Obukhov similarity across cases but have a steeper slope than predicted within each profile. The same trend has been noted in several other recent studies. The Businger-Dyer relations are modified here with an exponential cutoff term to account for the decay in \(\phi \) to first-order approximation, yielding improved similarity from approximately 0.05\(z_i\) to above 0.3\(z_i\), where \(z_i\) is the CBL depth. The necessity for the exponential correction is attributed to an extended transition from surface scaling to zero gradient in the mixed layer, where the departure from Monin–Obukhov similarity may be negligible at the surface but becomes substantial well below the conventional surface layer height of 0.1\(z_i\).
... The Monin-Obukhov Similarity Theory (MOST) also allows us to express the correction functions in stably or unstably stratified conditions in the ASL as functions of the stability parameter (e.g., Businger et al. 1971;Dyer 1974, etc.). Therefore, we can obtain Pr t as a function of the stability parameter (thermal stratification) using the Businger relation as follows (Businger et al. 1971;Li 2019): ...
... The Monin-Obukhov Similarity Theory (MOST) also allows us to express the correction functions in stably or unstably stratified conditions in the ASL as functions of the stability parameter (e.g., Businger et al. 1971;Dyer 1974, etc.). Therefore, we can obtain Pr t as a function of the stability parameter (thermal stratification) using the Businger relation as follows (Businger et al. 1971;Li 2019): ...
Wildland fire–atmosphere interaction generates complex turbulence patterns, organized across multiple scales, which inform fire-spread behaviour, firebrand transport, and smoke dispersion. Here, we utilize wavelet-based techniques to explore the characteristic temporal scales associated with coherent patterns in the measured temperature and the turbulent fluxes during a prescribed wind-driven (heading) surface fire beneath a forest canopy. We use temperature and velocity measurements from tower-mounted sonic anemometers at multiple heights. Patterns in the wavelet-based energy density of the measured temperature plotted on a time–frequency plane indicate the presence of fire-modulated ramp–cliff structures in the low-to-mid-frequency band (0.01–0.33 Hz), with mean ramp durations approximately 20% shorter and ramp slopes that are an order of magnitude higher compared to no-fire conditions. We then investigate heat- and momentum-flux events near the canopy top through a cross-wavelet coherence analysis. Briefly before the fire-front arrives at the tower base, momentum-flux events are relatively suppressed and turbulent fluxes are chiefly thermally-driven near the canopy top, owing to the tilting of the flame in the direction of the wind. Fire-induced heat-flux events comprising warm updrafts and cool downdrafts are coherent down to periods of a second, whereas ambient heat-flux events operate mainly at higher periods (above 17 s). Later, when the strongest temperature fluctuations are recorded near the surface, fire-induced heat-flux events occur intermittently at shorter scales and cool sweeps start being seen for periods ranging from 8 to 35 s near the canopy top, suggesting a diminishing influence of the flame and increasing background atmospheric variability thereat. The improved understanding of the characteristic time scales associated with fire-induced turbulence features, as the fire-front evolves, will help develop more reliable fire behaviour and scalar transport models.
... Because of the nature of Businger et al. (1971) function for stable stratification (φ m = 1 + βz/L), the functional form of the length scale remains the same, with a different effective maximum length scale ( max,eff ): ...
... where β = 4.7 is the coefficient derived by Businger et al. (1971) from the Kansas experiment. From a practical perspective, Eq. 11 implies that for stable stratification we can use the original B62 length scale formulation with a reduced value of the length scale in the outer layer ( max,eff < max ) that depends on the inverse Obukhov length. ...
Recent studies have highlighted the importance of accurate meteorological conditions for urban transport and dispersion calculations. In this work, we present a novel scheme to compute the meteorological input in the Quick Urban & Industrial Complex (QUIC) diagnostic urban wind solver to improve the characterization of upstream wind veer and shear in the Atmospheric Boundary Layer (ABL). The new formulation is based on a coupled set of Ordinary Differential Equations (ODEs) derived from the Reynolds Averaged Navier–Stokes (RANS) equations, and is fast to compute. Building upon recent progress in modeling the idealized ABL, we include effects from surface roughness, turbulent stress, Coriolis force, buoyancy and baroclinicity. We verify the performance of the new scheme with canonical Large Eddy Simulation (LES) tests with the GPU-accelerated FastEddy solver in neutral, stable, unstable and baroclinic conditions with different surface roughness. Furthermore, we evaluate QUIC calculations with and without the new inflow scheme with real data from the Urban Threat Dispersion (UTD) field experiment, which includes Lidar-based wind measurements as well as concentration observations from multiple outdoor releases of a non-reactive tracer in downtown New York City. Compared to previous inflow capabilities that were limited to a constant wind direction with height, we show that the new scheme can model wind veer in the ABL and enhance the prediction of the surface cross-isobaric angle, improving evaluation statistics of simulated concentrations paired in time and space with UTD measurements.
... If the model resolution is coarser than 100 m and more than one land-use class is present within a model grid cell, GRAMM-SCI uses the median land-use parameters (e.g., albedo and roughness length) instead of the mean over all represented land-use classes. Radiation is calculated following Somieski (1988) and the surface fluxes depend on stability and roughness-length following the flux relations proposed by Businger et al. (1971). No microphysics scheme is implemented in GRAMM-SCI. ...
... where z 1 is the height of the lowest model level above ground, z 0 the roughness length, θ g and θ z 1 the potential temperature at the surface and the first model level, respectively, L the Obukhov length, and Ψ h the similarity function for heat according to Businger et al. (1971). For all measurements higher than the first grid point, a linear interpolation between the model levels is used to derive the quantities at the sensor heights. ...
Using WRF as a benchmark, GRAMM-SCI simulations are performed for a case study of thermally driven valley-and slope winds in the Inn Valley, Austria. A clear-sky, synoptically undisturbed day was selected when large spatial heterogeneities occur in the components of the surface-energy budget driven by local terrain and land-use characteristics. The models are evaluated mainly against observations from four eddy-covariance stations in the valley. While both models are able to capture the main characteristics of the surface-energy budget and the locally driven wind field, a few overall deficiencies are identified: (i) Since the surface-energy budget is closed in the models, whereas large residuals are observed, the models generally tend to overestimate the daytime sensible and latent heat fluxes. (ii) The partitioning of the available energy into sensible and latent heat fluxes remains relatively constant in the simulations, whereas the observed Bowen ratio decreases continuously throughout the day because of a temporal shift between the maxima in sensible and latent heat fluxes, which is not captured by the models. (iii) The comparison between model results and observations is hampered by differences between the real land use and the vegetation type in the model. Recent modifications of the land-surface scheme in GRAMM-SCI improve the representation of nighttime katabatic winds over forested areas, reducing the modeled wind speeds to more realistic values.
... In non-neutral conditions, the shape of the M and H functions requires empirical determination and was thus developed initially through extensive experimental measurements. For example, the pioneering Kansas 1968 experiment, performed over ideally spatially homogeneous wheat fields, is the basis for the development of the so-called Businger-Dyer flux-gradient relations (Businger et al., 1971). These relations were modified (Högström, 1988), and ultimately formalized (Högström, 1996, hereon referred to as HÖ96) to the following form: ...
Monin–Obukhov similarity theory (MOST) is used in virtually all Earth System Models to parametrize the near‐surface turbulent exchanges and mean variable profiles. Despite its widespread use, there is high uncertainty in the literature about the appropriate parametrizations to use. In addition, MOST has limitations in very stable and unstable regimes, over heterogeneous terrain and complex orography, and has been found to represent the surface fluxes incorrectly. A new approach including turbulence anisotropy as a non‐dimensional scaling parameter has recently been developed and has been shown to overcome these limitations and generalize the flux‐variance relations to complex terrain. In this article, we analyze the flux‐gradient relations for five well‐known datasets, ranging from flat and homogeneous to slightly complex terrain. The scaling relations show substantial scatter and highlight the uncertainty in the choice of parametrization even over canonical conditions. We show that, by including information on turbulence anisotropy as an additional scaling parameter, the original scatter becomes well bounded and new formulations can be developed that drastically improve the accuracy of the flux‐gradient relations for wind shear () in unstable conditions and for temperature gradient () in both unstable and stable regimes. This analysis shows that both and are strongly dependent on turbulence anisotropy and allows us finally to settle the extensively discussed free convection regime for , which clearly exhibits a power law when anisotropy is accounted for. Furthermore, we show that the eddy diffusivities for momentum and heat and the turbulent Prandtl number are strongly dependent on anisotropy and that the latter goes to zero in the free convection limit. These results highlight the necessity to include anisotropy in the study of near‐surface atmospheric turbulence and lead the way for theoretically more robust simulations of the boundary layer over complex terrain.
... where S = dū/dz is the mean wind shear, and N 2 = db/dz is the square of the Brunt-Väisälä frequency. Businger et al. (1971) further elaborated the formulas, and proposed φ m = 1+4.7ξ and φ h = 0.74 + 4.7ξ . ...
The present paper shows that local similarity theories, proposed for the strongly-stratified boundary layers, can be derived as invariant solutions defined under the Lie-group theory. A system truncated to the mean momentum and buoyancy equations is considered for this purpose. The study further suggests how similarity functions for the mean profiles are determined from the vertical fluxes, with a potential dependence on a measure of the anisotropy of the system. A time scale that is likely to characterize the transiency of a system is also identified as a non-dimensionalization factor.
... in Fig. 2. VCWG combines multiple models into a fully coupled scheme. The VCWG utilizes the Monin-Obukhov similarity theory (MOST), which considers the effects of thermal stability and roughness length to generate vertical profiles of potential temperature, specific humidity, and friction velocity at rural weather station (Businger et al., 1971;Dyer, 1974;Paulson, 1970). This model allows the creation of a vertical profile of weather variables from measurements at 10 m above ground level, which is widely available. ...
Modeling tools are often used to obtain a better understanding of the characteristics of urban microclimates. Among the different approaches to physics-based modeling, urban canopy models tend to be computationally faster than computational fluid dynamics (CFD) simulations. However , the evaluation of current urban canopy models for different urban characteristics is still limited, especially for wind speed. This study aims to evaluate the potential usability of the existing urban canopy model for microclimate variable prediction in different urban contexts, specifically the vertical city weather generator (VCWG) v1.4.5, which can predict microclimate variables at different vertical heights. The measurement data used in model evaluation were obtained from 248 weather stations in Seoul, Republic of Korea. The results showed that among the input parameters, a few variables had significant impact on the wind speed prediction results, namely, the turbulent coefficient during unstable conditions, the pressure gradient coefficient, and the aerodynamic roughness length. The discrepancy in wind-speed prediction tended to be lower during the summer season, with lower wind speeds at the rural weather station. Further investigations also addressed the significant parameters of wind speed prediction related to the calculation of the turbulent diffusion coefficient and pressure gradient.
... The surface fluxes can be either diagnosed from the similarity theory or specified as forcing. In this study, the surface fluxes are diagnosed with the particles in the lowest model layer with the Businger-Dyer similarity functions (Businger et al. 1971;Dyer 1974). ...
A single-column turbulence model for stratified atmospheric boundary layer (ABL), which solves the transport equations of turbulence probability density function (PDF) using a Lagrangian stochastic modeling (LSM) approach, is proposed in this study. This study adopts previously developed stochastic differential equations (SDEs) for particle velocity and temperature and extends the LSM to simulate inhomogeneous turbulence. The proposed LSM is tested for its ability to fully simulate statistics of inhomogeneous stratified turbulence. In the model, particles evolve by SDEs, and turbulence statistics are calculated by averaging the properties of particles. The model provides a full representation of turbulence PDF and simulates turbulent transport without any modeling assumption. The model performance is evaluated against large-eddy simulation (LES) results in the simulations of convective and stable ABL cases. For the convective ABL, LSM realistically simulates the entrainment process with the temperature and heat flux profiles that closely match with LES. The joint PDF simulated by LSM reproduces a curved and highly skewed shape, and some distinct features, like the asymmetric distribution of vertical velocity and the separation of the PDF in the entrainment zone, are simulated. LSM also reproduces the entrainment enhancement by wind shear in the simulation of sheared convective ABL. The LSM simulation of stable ABL predicts realistic turbulence intensity and mean field profiles, where Gaussian-like PDFs are simulated both in LSM and LES.
... K is also used to predict variance in optical turbulence 36 and to parameterize the flux-gradient relationship within the atmosphere. 8,37,38 Here, we test if the relationship between m qq and m ww varies with thermal stratification across the air-sea interface. For the three lowest measurement levels, a linear trend showed less than 1% change in m qq /m ww per degree K [Figs. ...
The −5/3 power law over the inertial subrange of the turbulence kinetic energy spectrum is one of the most well-known concepts in fluid physics. Obukhov and Corrsin extended the original hypothesis to a passive tracer, leading to the concept of an inertial-convective subrange. These postulates have been empirically validated in the atmospheric turbulence over land but have not been comprehensively studied in the marine air flow. During a recent oceanic campaign, the platform FLIP was deployed with an array of sensors to measure the perturbation wind velocity, temperature, and water vapor. Using these data, a previous study found that Kolmogorov's hypothesized −5/3 was not universally valid over the ocean. Here, we continue that work to analyze the spectrum of temperature and water vapor to empirically evaluate the theoretical extension by Obukhov-Corrsin. For temperature, the observed spectra were too noisy for thorough analysis; our conjecture for the source of noise and its implications for near-surface observations of atmospheric turbulence are discussed. For water vapor, we found strong agreement with the previous analysis of the kinetic energy spectrum. These findings corroborate (1) the theoretical notion of the scalar energy dissipation subrange driven by the inertial motions in the marine boundary layer and (2) evidence for non-Kolmogorov turbulence in the high Reynolds flow immediately above ocean waves. Our analysis shows a strong relationship with distance from the wavy surface; using linear extrapolation, we find that divergence from −5/3 persists in the lowest 25 m of the atmosphere.
... For example, Monin-Obukhov similarity theory reduced the problem of parameterizing turbulence in a thin (∼100 m) layer near the surface to finding universal functions that characterize the vertical structure of turbulent fluxes (Foken, 2006). Later, these functions were empirically derived based on measurements over a field of wheat stubble during the summer of 1968 in Kansas (Businger et al., 1971); they have since been widely incorporated into climate models. This represents a success story for the process-based approach. ...
Accelerating progress in climate modeling is urgent for proactive and effective climate change adaptation. The central challenge lies in accurately representing processes that are small in scale yet are climatically important, such as turbulence and cloud formation. These processes are not explicitly resolvable, necessitating the use of parameterizations. We propose a balanced approach that leverages the strengths of traditional process-based parameterizations and contemporary AI-based data-driven methods to model subgrid-scale processes. This strategy focuses on employing AI to derive data-driven closure functions from both observational and simulated data, integrated within parameterizations that encode system knowledge and conservation laws. Increasing resolution to resolve a larger fraction of small-scale processes can aid progress toward improved and interpretable climate predictions outside the observed climate distributions, but it must still allow the generation of large ensembles for model calibration and the broad exploration of possible climate outcomes – currently O(10 km) horizontal resolutions are feasible. By synergizing decades of scientific development with advanced AI techniques, this approach aims to significantly boost the accuracy, interpretability, and trustworthiness of climate predictions.
... Therefore, before analyzing the characteristics of the fluctuating wind field, it is generally necessary to judge the thermally neutral stability of air flows. The Obukhov length (Businger et al. 1971) and Richardson number (Golder 1972) are two commonly used judgment methods. In the wind engineering field, based on the statistical analysis of a large number of field observations, researchers have found that the atmosphere usually contains significant non-stationary components when the wind speed is low. ...
A downburst is a strong downdraft that causes radiating, catastrophic winds at or near the ground. Relevant research conducted in the past decades shows that downbursts not only bring damage to the built environment but also have surprisingly destructive effects on aircraft and other flying objects. However, due to the complexity of atmospheric phenomena and limited measurement datasets, many uncertainties remain to be clarified in the understanding and modelling of the downburst wind field. To further explore the evolution characteristics of thunderstorms, this study uses data recorded during thunderstorms by a Doppler profiler of the Hong Kong Observatory and a near-ground anemometer installed at the Hong Kong International Airport to conduct a detailed feature analysis of the vertical profile and turbulence characteristics of downbursts within the atmospheric boundary layer. Based on long-term field measurements during thunderstorm events, the occurrence of a thunderstorm should be determined by a combination of simultaneous variations in multiple meteorological factors, including wind speed and direction, vertical wind speed, and signal-to-noise ratio (SNR). During thunderstorms, extreme wind speeds occurred in the lower atmosphere and the height of the local peaks seems to be stable in the thunderstorm wind profiles. In addition, both methods, which consider a constant mean component (stationary) and a slowly varying mean component (non-stationary), are used to decompose the measured wind speed and are then compared to investigate the turbulence characteristics of downbursts. Although the gust factor and turbulence intensity show some deviation due to the influence of atmospheric stratification instability, this effect does not appear to be reflected in the turbulence integral scale.
... For temperature, the heat balance equation is used at the upper boundary (z = 0), and the continuity of temperature and heat flux is at z = H (H is the maximum depth of the reservoir). The heat balance on the surface is calculated under a given time series of shortwave and longwave radiation fluxes and basic meteorological parameters; the turbulent fluxes of sensible, latent heat and momentum are calculated using the Monin-Obukhov similarity theory [46,47]. ...
The mechanistic model LAKE2.3 was tested for its capability to predict of methane (CH4) emissions from reservoirs. Estimates of CH4 emissions from the Mozhaysk reservoir (Moscow region) provided by the model showed good agreement with instrumental in situ observations for several parameters of the water ecosystem. The average CH4 flux calculated by the model is 37.7 mgC-CH4 m−2 day−1, while according to observations, it is 34.4 mgC-CH4 m−2 day−1. Ebullition makes the largest contribution to the emissions from reservoirs (up to 95%) due to low methane solubility in water and the high oxidation rate of diffusive methane flux. During the heating period, an increase in methane emission is observed both in the model and empirical data, with a maximum before the onset of the autumn overturn. An effective parameter for calibrating the diffusive methane flux in the model is the potential rate of methane oxidation. For ebullition flux, it is the parameter q10 (an empirical parameter determining the relationship between methane generation and temperature) because methane production in bottom sediments is the most important. The results of this research can be used to develop mechanistic models and provide a necessary step toward regional and global simulations of lacustrine methane emission using LAKE2.3.
... Three prominent similarity-theory-based models are generally used in atmospheric studies -the Businger-Dyer (BD;Businger et al., 1971;Dyer, 1974), Beljaars and Holtslag (BH;Beljaars and Holtslag, 1991), and Vickers and Mahrt (VM;Vickers and Mahrt, 1999) models. For reference, their stability functions are given here. ...
Two buoys equipped with Doppler lidars owned by the US Department of Energy (DOE) were deployed off the coast of California in autumn of 2020 by Pacific Northwest National Laboratory. The buoys collected data for an entire annual cycle at two offshore locations proposed for offshore wind development by the Bureau of Ocean Energy Management. One of the buoys was deployed approximately 50 km off the coast near Morro Bay in central California in 1100 m of water. The second buoy was deployed approximately 40 km off Humboldt County in northern California in 625 m of water. The buoys provided the first-ever continuous measurements of the air–sea transition zone off the coast of California. The atmospheric and oceanographic characteristics of the area and estimates of annual energy production at both the Morro Bay and Humboldt wind energy areas show that both locations have a high wind energy yield and are prime locations for future floating offshore wind turbines. This article provides a description and comprehensive analysis of the data collected by the buoys, and a final post-processed dataset is uploaded to a data archive maintained by the DOE. Additional analysis was conducted to show the value of the data collected by the DOE buoys. All post-processed data from this study are available on the Wind Data Hub website: https://a2e.energy.gov/data# (last access: 14 September 2023). Near-surface, wave, current, and cloud datasets for Humboldt and Morro Bay are provided at https://doi.org/10.21947/1783807 (Krishnamurthy and Sheridan, 2023b) and https://doi.org/10.21947/1959715 (Krishnamurthy and Sheridan, 2023a), respectively. Lidar datasets for Humboldt and Morro Bay are provided at https://doi.org/10.21947/1783809 (Krishnamurthy and Sheridan, 2023d) and https://doi.org/10.21947/1959721 (Krishnamurthy and Sheridan, 2023c), respectively.
... In METRIC, sensible heat flux (H) is estimated using an iterative process by simultaneously solving equations for H, aerodynamic resistance (r ah ) from a roughness length for heat transfer plus displacement height (z 0h + d 0 ) to the reference height (z) , and frictional velocity (u * ) (Eqs. 4-6) and stability functions (Allen et al. 2007) using Monin-Obukhov similarity theory (Businger et al. 1971, Brutsaert 1999) from hot and cold pixels: ...
Monitoring agricultural drought across a large area is challenging, especially in regions with limited data availability, like the Peshawar Valley, which holds great agricultural significance in Pakistan. Although remote sensing provides biophysical variables such as precipitation (P), land surface temperature (LST), normalized difference vegetation index (NDVI), and relative soil moisture (RSM) to assess drought conditions at various spatiotemporal scales, these variables have limited capacity to capture the complex nature of agricultural drought and associated crop responses. Here, we developed a composite drought index named “Temperature Vegetation ET Dryness Index” (TVEDI) by modifying the Temperature Vegetation Precipitation Dryness Index (TVPDI) and integrating NDVI, LST, and remotely sensed evapotranspiration (ET) using 3D space and Euclidean distance. Several statistical techniques were employed to examine TVPDI and TVEDI trends and relationships
with other commonly used drought indices such as the standardized precipitation index (SPI), standardized precipitation evapotranspiration index (SPEI), and standardized soil moisture index (SSI), as well as crop yield, to better understand how these indices captured the spatial and temporal distribution of agricultural drought in the Peshawar valley between 1986 and 2018.
... MOST fluxes could still capture the observed fluxes under weakly stable conditions where turbulence is continuously sustained and not intermittently suppressed. MOST fluxes here are computed using the Businger-Dyer relations (Businger et al., 1971) as those relations remain pervasively in use today. Such relations are expressed by non-dimensional gradient (diabatic) functions, Ψ s (ζ), relating the scalar concentration surface scale s * = w ′ s ′ /u * to the gradient following ...
Conventional and recently developed approaches for estimating turbulent scalar fluxes under stable conditions are evaluated. The focus is on methods that do not require fast scalar sensors such as the relaxed eddy accumulation (REA) approach, the disjunct eddy-covariance (DEC) approach, and a novel mixing length parametrization labelled as A22. Using high-frequency measurements collected from two contrasting sites (Utqiagvik, Alaska and Wendell, Idaho "during winter"), it is shown that the REA and A22 models outperform the conventional Monin-Obukhov Similarity Theory (MOST) utilized in Earth System Models. With slow trace gas sensors used in disjunct eddy-covariance (DEC) approaches and the more complex signal filtering associated with REA devices (here simulated using filtered signals from fast-response sensors), A22 outperforms REA and DEC in predicting the observed unfiltered (total) eddy-covariance (EC) fluxes. However, REA and DEC can still capture the observed filtered EC fluxes computed with the filtered scalar signal. This finding motivates the development of a correction, blending the REA and DEC methods, for the underestimated net averaged fluxes to incorporate the effect of sensor filtering. The only needed parameter for this correction is the mean velocity at the instrument height, a surrogate of the advective timescale.
Using two case studies, we analyze the effects of explicitly resolving polar lows in a global climate model (ICON‐Sapphire) with a high resolution of 2.5 km on the upper ocean and sea ice. We aim to understand the mechanism of how polar lows form in a global coupled model and how they interact with the upper ocean and sea ice. When polar lows form at the sea ice edge, they induce marine cold air outbreaks that lead to large heat loss from the ocean. This heat loss contributes to dense water formation in the Iceland and Greenland Seas, which replenishes the climatically important Denmark Strait Overflow Water (DSOW). The high wind speeds of polar lows open leads and polynyas in the sea ice cover, such as the Sirius Water Polynya in northeastern Greenland. Heat loss in polynyas is compensated for by the formation of new ice, and the rejected brine densifies the water on the Greenland shelf. In the Labrador Sea, polar lows intensify cold air outbreaks from the sea ice and rapidly deepen the ocean mixed layer. Resolving polar lows and kinematic features in the sea ice improves the realism of climate models, in particular the surface heat loss and the dense water formation in (sub)polar oceans.
Planetary boundary layer (PBL) modeling is a primary contributor to uncertainties in a numerical weather prediction (NWP) model due to difficulties in modeling the turbulent transport of surface fluxes. The Weather Research and Forecasting model (WRF) has provided many PBL schemes that may feature a non‐local transport component driven by large eddies or a one‐and‐half order turbulence closure model, but few of them possess the two features at once. In the present study, a turbulent kinetic energy (TKE)‐based eddy diffusivity/viscosity method is integrated into the non‐local Asymmetric Convective Model version 2 (ACM2) PBL scheme and implemented in WRF. The original first‐order eddy‐diffusivity term in ACM2 is discarded and an extra prognostic equation for TKE, which considers the tendency of TKE by buoyancy, wind shear, vertical transport, and dissipative processes, is supplied to calculate the diffusivity/viscosity. Non‐local transport is modeled the same as ACM2 using the transilient matrix method. Idealized tests using prescribed surface heat flux and roughness length are performed. TKE‐ACM2 displays advantages over the PBL scheme developed by Bougeault and Lacarrère (hereinafter referred to as Boulac) and ACM2 in the wind speeds (WS) profile because it better matches large‐eddy simulations results in the surface momentum flux. Real case simulations show that TKE‐ACM2 generally outperforms in the diurnal vertical profiles of WS under stable conditions. TKE‐ACM2 also produces a better alignment under moderately unstable conditions in the early nighttime at the urban LiDAR station. However, the model exhibits discrepancies more apparently under a more unstable condition during the winter daytime.
Accelerated progress in climate modeling is urgently needed for proactive and effective climate change adaptation. The central challenge lies in accurately representing processes that are small in scale yet climatically important, such as turbulence and cloud formation. These processes will not be explicitly resolvable for the foreseeable future, necessitating the use of parameterizations. We propose a balanced approach that leverages the strengths of traditional process-based parameterizations and contemporary artificial intelligence (AI)-based methods to model subgrid-scale processes. This strategy employs AI to derive data-driven closure functions from both observational and simulated data, integrated within parameterizations that encode system knowledge and conservation laws. In addition, increasing the resolution to resolve a larger fraction of small-scale processes can aid progress toward improved and interpretable climate predictions outside the observed climate distribution. However, currently feasible horizontal resolutions are limited to O(10 km) because higher resolutions would impede the creation of the ensembles that are needed for model calibration and uncertainty quantification, for sampling atmospheric and oceanic internal variability, and for broadly exploring and quantifying climate risks. By synergizing decades of scientific development with advanced AI techniques, our approach aims to significantly boost the accuracy, interpretability, and trustworthiness of climate predictions.
This study utilizes in situ measurements and numerical weather prediction forecasts curated during the Coupled Air–Sea Processes Electromagnetic Ducting Research (CASPER) east field campaign to assess how thermodynamic properties in the marine atmospheric surface layer influence evaporation duct shape independent of duct height. More specifically, we investigate evaporation duct shape through a duct shape parameter, a parameter known to affect the propagation of X-band radar signals and is directly related to the curvature of the duct. Relationships between this duct shape parameter and air sea temperature difference (ASTD) reveal that during unstable periods (ASTD < 0), the duct shape parameter is generally larger than in near-neutral or stable atmospheric conditions, indicating tighter curvature of the M-profile. Furthermore, for any specific duct height, a strong linear relationship between the near-surface-specific humidity gradient and the duct shape parameter is found, suggesting that it is primarily driven by near-surface humidity gradients. The results demonstrate that an a priori estimate of duct shape, for a given duct height, is possible if the near-surface humidity gradient is known.
This study evaluated the performance of remote sensing (RS) algorithms for the estimation of actual maize evapotranspiration (ETa) using different spaceborne, airborne, and proximal multispectral data in a semi-arid climate region to identify the optimal platform that provides the best ETa estimates to improve irrigation water management and help make irrigated agriculture sustainable. The RS platforms used in the study included Landsat-8 (30 m pixel spatial resolution), Sentinel-2 (10 m), Planet CubeSat (3 m), multispectral radiometer or MSR (1 m), and a small uncrewed aerial system or sUAS (0.03 m). Two-source surface energy balance (TSEB) models, implementing the series and parallel surface resistance approaches, were used in this study to estimate hourly maize ETa. The data used in this study were obtained from two maize research sites in Greeley and Fort Collins, CO, USA, in 2020 and 2021. Each research site had different irrigation systems. The Greeley site had a subsurface drip system, while the Fort Collins site had surface irrigation (furrow). Maize ETa predictions were compared to observed maize ETa data from an eddy covariance system installed at each research site. Results indicated that the MSR5 proximal platform (1 m) provided optimal RS data for the TSEB algorithms. The MSR5 “point-based” nadir-looking surface reflectance data and surface radiometric temperature combination resulted in the smallest error when predicting hourly (mm/h) maize ETa. The mean bias and root mean square errors (MBE and RMSE, respectively), when predicting maize hourly ETa using the MSR5 sensor data, were equal to −0.02 (−3%) ± 0.07 (11%) mm/h MBE ± RMSE and −0.02 (−3%) ± 0.09 (14%) mm/h for the TSEB parallel and series approaches, respectively. The poorest performance, when predicting hourly TSEB maize ETa, was from Landsat-8 (30 m) multispectral data combined with its original thermal data, since the errors were −0.03 (−5%) ± 0.16 (29%) mm/h and −0.07 (−13%) ± 0.15 (29%) mm/h for the TSEB parallel and series approaches, respectively. These results indicate the need to develop methods to improve the quality of the RS data from sub-optimal platforms/sensors/scales/calibration to further advance sustainable irrigation water management.
The Empty Quarter Desert, one of Earth's major dust sources, frequently experiences dust storms due to wind erosion. Despite its significance as a primary dust source on a global scale, in‐situ observations from this region had not been reported until very recently. In summer 2022, the WInd‐blown Sand Experiment (WISE) Phase‐1 was initiated in the Empty Quarter Desert of the United Arab Emirates, and continued until 7 February 2023. Utilizing a diverse array of instruments, we measured winds, temperature, humidity, radiation fluxes, saltation, and the physical and optical properties of dust aerosols, atmospheric electric fields, and soil characteristics. A total of 38 distinct sand‐saltation events were recorded from September 2022 to February 2023, with activity peaking between 13:00 and 14:00 local time. Key findings include the identification of dominant wind patterns, and the measurement of the average aerodynamic roughness length (z0) at 0.8 ± 0.6 mm, and the thermal roughness length (zh) at 0.3 ± 0.5 mm—the first estimation of zh for this area. In‐situ observations revealed that dust particle concentrations near the surface increased 1.7‐fold on days with saltation compared to days without it. Moreover, we determined a wind‐speed threshold for initiating saltation at 7.70 m s⁻¹. This comprehensive data set significantly advances our understanding of atmospheric‐soil interactions and sand movement dynamics, providing invaluable insights for ongoing research into desert environments and the global dust cycle.
In this study, the Noah land surface model used in conjunction with the Mellor–Yamada–Janjić surface layer scheme (hereafter, Noah-MYJ) and the Noah multiphysics scheme (Noah-MP) from the Weather Research and Forecasting (WRF) 4.5.1 mesoscale model are evaluated with regard to their performance in reproducing positive temperature gradients over forested areas in the Arctic winter. First, simplified versions of the WRF schemes, recoded in Python, are compared with conceptual models of the surface layer in order to gain insight into the dependence of the temperature gradient on the wind speed at the top of the surface layer. It is shown that the WRF schemes place strong limits on the turbulent collapse, leading to lower surface temperature gradient at low wind speeds than in the conceptual models. We implemented modifications to the WRF schemes to correct this effect. The original and modified versions of Noah-MYJ and Noah-MP are then evaluated compared to long-term measurements at the Ameriflux Poker Flat Research Range, a forest site in interior Alaska. Noah-MP is found to perform better than Noah-MYJ because the former is a two-layer model which explicitly takes into account the effect of the forest canopy. Indeed, a non-negligible temperature gradient is maintained below the canopy at high wind speeds, leading to overall larger gradients than in the absence of vegetation. Furthermore, the modified versions are found to perform better than the original versions of each scheme because they better reproduce strong temperature gradients at low wind speeds.
This introductory chapter provides the basics for this book, and terms such as micrometeorology, atmospheric boundary layer, and meteorological scales are defined and presented in relation to the subject matter of this book. Besides an historical outline, the energy and water balance equations at the Earth’s surface and the transport processes are discussed. Thus, the micrometeorological basics are described in order to be able to deepen theoretical and experimental questions in the following chapters.
Before starting the derivation of the equations for the turbulent fluxes of momentum, heat and trace gases (Sect. 2.3), we present a short introduction into the basic equations. These include the equations of mean and turbulent motions, describing the transport and for energy and matter (Sect. 2.1), and the conservation equation for the turbulence kinetic energy (Sect. 2.2). To illustrate the importance of micrometeorological equations and parameterizations for modelling on all scales, different closure techniques of the turbulent differential equations are described (Sect. 2.1.3). The more practical user of this book can proceed directly to Sect. 2.3.
The main approaches to mountain glacier simulation were reviewed, and Oerlemans minimal model was chosen as a parameterization core of mountain glaciation in the Earth System models. The proposed model is based on a one-dimensional equation of glacier mass balance. The mass balance components are calculated with the use of a specially developed model of orographic precipitation, an algorithm for correction of incoming solar radiation onto an inclined ice surface, and schemes of calculation of turbulent heat-moisture exchange based on the Monin–Obukhov theory. The model was implemented for the Djankuat glacier (the Central Caucasus), for which a long measurement series is available. The model gives a good reproduction of the dynamics of glacier length over the period 1985–2020 based on measured mass balance values: –13 m/year, which is in practically perfect agreement with the field data. This means that the Oerlemans model can be used in Earth system models. The results of simulation based on the calculated mass balance showed a significant positive trend in ablation at a slight change in accumulation, which is also in agreement with the reality. However, in this case, the values of the annual thawing depth and the glacier contraction are twice as large and those observed in reality. The further development of the model (the inclusion of a snow cover block, the incorporation of debris mantle and mountain–valley circulation) will eliminate these shortcomings.
The results of measurements of atmospheric turbulence characteristics were used to obtain parameterizations for calculating the dynamic roughness parameter and the roughness parameters for temperature and humidity for a shallow closed water body. At medium wind speeds, the results of calculations by Charnock formula are in agreement with observation data; in this case, the c parameter is three times as large as that in the case of an open ocean, and the passage from the viscous to wave mechanism occurs at high wind speeds, while the dynamic roughness parameter at the same wind speeds is greater. The roughness parameters for temperature and humidity at wind speed from 0.5 to 3 m/s are not equal. The empirical coefficients in the equations describing the ratio of the dynamic roughness to the roughness parameter for temperature (humidity) on Reynolds number are close to those obtained before for other closed water bodies, thus suggesting a common formation mechanism of transport processes in a viscous sublayer. The obtained parameterizations can be used in Earth system models and lake models for calculating turbulent flows over continental water bodies.
Description
A compendium of papers, divided into two parts:
Part 1 devoted to Air Quality Meteorology describes practical application of atmospheric measurements and interpretation of atmospheric data for solution of everyday, environmental problems
Part 2 devoted to Atmospheric Ozone describes techniques for studying life cycle of a pollutant in the atmosphere, the need for additional information, and the current state of knowledge of ozone.
In this study, the performance of a one‐source surface energy balance (OSEB) remote sensing (RS) of actual crop evapotranspiration (ET a ), incorporating data from different spaceborne, airborne and proximal multispectral data, was evaluated. The RS platforms in this study included Landsat‐8 (30 m pixel size), Sentinel‐2 (10 m), Planet CubeSat (3 m), a handheld (proximal) multispectral radiometer (MSR) (1 m) and an unmanned aerial system (UAS) (0.03 m). A 2‐year data set (2020 and 2021) from two maize research sites in Greeley and Fort Collins, Colorado, USA, provided ground‐based data for estimating and evaluating hourly ET a from the OSEB algorithm. The accuracy of OSEB hourly maize ET a estimates was evaluated using calculated hourly maize ET a using high‐frequency data collected with an eddy covariance energy balance system installed at each research site. The results indicated that the Planet CubeSat multispectral sensor (3 m), combined with on‐site surface temperature data, yielded the least errors when predicting maize ET a . The hourly ET a estimation errors for the Planet CubeSat were MBE ± RMSE of −0.02 (−3%) ± 0.07 (13%) mm h⁻ ¹ . These results suggest the urgent need for a specific approach to improve RS multispectral and thermal radiometric data (quality) to better support sustainable irrigation water management practices.
Dedicated to the 150th anniversary of the appearance of Gibbs' Fundamental Thermodynamic Relation. Abstract: Under typical marine conditions of about 80% relative humidity, evaporation of water from the ocean is an irreversible process accompanied by entropy production. In this article, equations are derived for the latent heat of irreversible evaporation and the related nonequilibrium entropy balance at the sea surface. To achieve this, linear irreversible thermodynamics is considered in a conceptual ocean evaporation model. The equilibrium thermodynamic standard TEOS-10, the International Thermodynamic Equation of Seawater-2010, is applied to irreversible evaporation under the assumption of local thermodynamic equilibrium. The relevance of local equilibrium conditions for irreversible thermodynamics is briefly explained. New equations are derived for the mass flux of evaporation and for the associated nonequilibrium enthalpies and entropies. The estimated entropy production rate of ocean evaporation amounts to 0.004 W m −2 K −1 as compared with the average terrestrial global entropy production of about 1 W m −2 K −1 .
Polar boundary layers are difficult to model due to the existence of intermittent turbulence within stable layers. Here we present a case study evaluation of coherent structures in a stable boundary layer observed during a series of flights with an uncrewed aircraft system (DataHawk2) on 19 October 2016 at Oliktok Point, Alaska as part of the ERASMUS (Evaluation of Routine Atmospheric Sounding Measurements using Unmanned Systems) field campaign. During a sequence of five flights over a nine-hour period, 57 profiles of atmospheric properties (0–400 m a.g.l) were collected. Turbulence was identified using derived Richardson Number, temperature structure function parameter, and turbulence kinetic energy dissipation. Throughout all flights on this strongly stable day, intermittent turbulence was observed. These turbulent layers showed well-mixed potential temperature profiles embedded within otherwise stable potential temperature profiles; often resulting in a characteristic staircase pattern. Turbulent layers ranged from 1 to 30 m deep, with most individual layers being 1–2 m deep. Vertical propagation velocities of layers in the lower atmosphere were on the order of a few cm s⁻¹, typical of non-convective environments. In different regions of the profile, turbulence was driven by a different balance of buoyancy and shear forces, with turbulence in the near surface environment driven by strong shear forces overcoming strong resistance to buoyancy, while turbulence in elevated layers characterized by weaker shear forces overcoming weaker resistance to buoyancy. We discuss the potential of such datasets for improving subgrid parameterizations of small-scale turbulence embedded within stable boundary layers.
O vento é uma importante variável de estudo. Isso porque é utilizado para muitas finalidades, além de, em casos extremos, provocar desastres naturais. Pelo ponto de vista energético, ele é um importante ente na geração de energia eólica e, portanto, sua correta estimativa torna-se essencial. Ainda sobre essa temática, a estimativa do perfil vertical de vento torna-se importante, já que os aerogeradores não se encontram em superfície, mas em níveis mais altos. Dessa forma, o objetivo deste trabalho foi estudar os perfis de vento offshore utilizando as metodologias de estimativas calculadas no trabalho de Carmo et al. (2021) e compará-las a uma nova metodologia desenvolvida em função da temperatura da superfície do mar (TSM) e temperatura do ar (T). Para tal, foram utilizados os dados da Reanálise ERA5, dados da plataforma P25 e dados da boia localizada na plataforma P18 no período entre 1° de agosto de 1999 e 31 de agosto de 1999. Os resultados mostraram que o método desenvolvido apresentou bons resultados para a região de estudo e que a atmosfera apresentou classe de estabilidade neutra, com valores de Skill Score (SS) e Nash–Sutcliffe Efficiency (NSE) relativamente mais representativos do que o dos outros métodos estudados. Comparativamente, a inserção da TSM e de T na estimativa dos perfis apresentou um ganho significativo na interpretação e precisão dos resultados. Palavras-chave: Perfil de Vento; Energia; Temperatura.
Radiosonde data recorded during the African Monsoon Multidisciplinary Analyses Special Observing Period 3 (AMMA SOP3) field campaign in West Africa (August 15–September 15, 2006) were used to examine air-coast/land coupling. Different turbulent radiosonde measurements were averaged over three levels (level 1: ~3 m, next level 2: ~10 m and lastly level 3: ~20 m) in the surface layer. These data enabled the comparison of turbulent fluxes with other variables, as well as the study of the scaling of surface layers for different areas in aerodynamically smooth/rough and relatively dry or wet conditions. Results showed stable and unstable stratifications at night-time. Drag coefficient over the coastal and inland footprints presents the same order of magnitude and could not be an indicator for the two different areas. However, the disparate night-time variation in sensible heat flux is substantially more pronounced over land than over the coast and can, therefore, be considered as an indicator of different surfaces. The underlying assumptions of Monin–Obukhov Similarity Theory (MOST) are consistently violated due to surface heterogeneities, but offsets from MOST are smaller for stable and unstable conditions, as well as for scaled standard deviations over the coast and overland. In addition, flux-profile relationships from MOST show a poor match with observations.
The symmetries of the governing equations of atmospheric flows constrain the solutions. The present study applies those symmetries identified from the governing equations to the atmospheric boundary layers under relatively weak stratifications (stable and unstable). More specifically, the invariant solutions are analyzed, which conserve their forms under possible symmetry transformations of a governing equation system. The key question is whether those invariant solutions can rederive the known vertical profiles of both vertical fluxes and the means for the horizontal wind and the potential temperature. The mean profiles for the wind and the potential temperature in the surface layer predicted from the Monin–Obukhov theory can be recovered as invariant solutions. However, the consistent vertical fluxes both for the momentum and heat no longer remain constant with height, as assumed in the Monin–Obukhov theory, but linearly and parabolically change with height over the dynamic sublayer and the above, respectively, in stable conditions. The present study suggests that a deviation from the constancy, though observationally known to be weak, is a crucial part of the surface-layer dynamics to maintain its symmetry consistency.
Significance Statement
The atmospheric flows are governed by a differential equation system, which is often difficult to solve in any satisfactory manner, either analytically or numerically. However, without solving them explicitly, many insights can be obtained by examining the “symmetries” of the governing equations. The study suggests that basic vertical profiles of the mean state of the atmospheric boundary layer is more strongly constrained by the symmetry consistency than suggested by standard similarity theories.
Monin-Obukhov similarity theory (MOST) is a widely used framework in atmospheric boundary layer (ASL) research. MOST predicts that the mean potential temperature profile deviates from the logarithmic law in buoyancy-dominated turbulence. However, recent studies show that the logarithmic profile remains intact in unstably stratified atmospheric boundary layers. Using data from the Qingtu Lake Observation Array(QLOA) with Reynolds number up to O(106), we investigate the similarity functions and mean temperature profile with different stability parameters and sand-bearing conditions. By assessing the accuracy of the logarithmic profile and the MOST-based empirical expressions obtained by Hogstrom and Wilson, we discover that the logarithmic law is a better fit than the MOST expressions. The Von Kármán constant of the potential temperature profile has a power function dependences on the stability parameter. In sand-laden ASLs, it is remarkable to find that the logarithmic law still holds, and the error of the MOST expressions amplifies. The von Kármán constant of potential temperature increases in sandiness conditions. Still, a quantitative theory that describes the sand effect on the mean temperature profile remains to be studied.
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