Monin-Obukhov Similarity Theory Research Articles

Terrestrial Ecosystem Model in R (TEMIR) version 1.0: simulating ecophysiological responses of vegetation to atmospheric chemical and meteorological changes

Abstract. The newly developed offline land ecosystem model Terrestrial Ecosystem Model in R (TEMIR) version 1.0 is described here. This version of the model simulates plant ecophysiological (e.g., photosynthetic and stomatal) responses to varying meteorological conditions and concentrations of CO2 and ground-level ozone (O3) based on prescribed meteorological and atmospheric chemical inputs from various sources. Driven by the same meteorological data used in the GEOS-Chem chemical transport model, this allows asynchronously coupled experiments with GEOS-Chem simulations with unique coherency for investigating biosphere–atmosphere chemical interactions. TEMIR agrees well with FLUXNET site-level gross primary productivity (GPP) in terms of both the diurnal and monthly cycles (correlation coefficients R2>0.85 and R2>0.8, respectively) for most plant functional types (PFTs). Grass and shrub PFTs have larger biases due to generic model representations. The model performs best when driven by local site-level meteorology rather than reanalyzed gridded meteorology. Simulation using gridded meteorology agrees well for annual GPP in seasonality and spatial distribution with a global average of 134 Pg C yr−1. Application of Monin–Obukhov similarity theory to infer canopy conditions from gridded meteorology does not improve model performance, predicting an increase of +7 % in global GPP. Present-day O3 concentrations simulated by GEOS-Chem and an O3 damage scheme at high sensitivity show a 2 % reduction in global GPP with prominent reductions of up to 15 % in eastern China and the eastern USA. Regional correlations are generally unchanged when O3 is present and biases are reduced, especially for regions with high O3 damage. An increase in atmospheric CO2 concentration of 20 ppmv from the level in 2000 to the level in 2010 modestly decreases O3 damage due to reduced stomatal uptake, consistent with ecophysiological understanding. Our work showcases the utility of this version of TEMIR for evaluating biogeophysical responses of vegetation to changes in atmospheric composition and meteorological conditions.

Using the Sensible Heat Flux Eddy Covariance-Based Exchange Coefficient to Calculate Latent Heat Flux from Moisture Mean Gradients Over Snow

In absence of the high-frequency measurements of wind components, sonic temperature and water vapour required by the eddy covariance (EC) method, Monin–Obukhov similarity theory (MOST) is often used to calculate heat fluxes. However, MOST requires assumptions of stability corrections and roughness lengths. In most environments and weather situations, roughness length and stability corrections have high uncertainty. Here, we revisit the modified Bowen-ratio method, which we call C-method, to calculate the latent heat flux over snow. In the absence of high-frequency water vapour measurements, we use sonic anemometer data, which have become much more standard. This method uses the exchange coefficient for sensible heat flux to estimate latent-heat flux. Theory predicts the two exchange coefficients to be equal and the method avoids assuming roughness lengths and stability corrections. We apply this method to two datasets from high mountain (Alps) and polar (Antarctica) environments and compare it with MOST and the three-layer model (3LM). We show that roughness length has a great impact on heat fluxes calculated using MOST and that different calculation methods over snow lead to very different results. Instead, the 3LM leads to good results, in part due to the fact that it avoids roughness length assumptions to calculate heat fluxes. The C-method presented performs overall better or comparable to established MOST with different stability corrections and provides results comparable to the direct EC method. An application of this method is provided for a new station installed in the Pamir mountains.

Surface heat fluxes at coarse blocky Murtèl rock glacier (Engadine, eastern Swiss Alps)

Abstract. We estimate the surface energy balance (SEB) of the Murtèl rock glacier, a seasonally snow-covered permafrost landform with a ventilated coarse blocky active layer (AL) located in the eastern Swiss Alps. We focus on the parameterisation of the turbulent heat fluxes. Seasonally contrasting atmospheric conditions occur in the Murtèl cirque, with downslope katabatic jets in winter and a strongly unstable atmosphere over the heated blocky surface in summer. We use a novel comprehensive sensor array both above the ground surface and in the coarse blocky AL to track the rapid coupling by convective heat and moisture fluxes between the atmosphere, the snow cover, and the AL for the time period September 2020–September 2022. The in situ sensor array includes a sonic anemometer for eddy-covariance flux above-ground and sub-surface long-wave radiation measurements in a natural cavity between the AL blocks. During the thaw seasons, the measurements suggest an efficient (∼ 90 %) export of the available net radiation by sensible and latent turbulent fluxes, thereby strongly limiting the heat available for melting ground ice. Turbulent export of heat and moisture drawn from the permeable AL contributes to the well-known insulating effect of the coarse blocky AL and partly explains the climate resiliency of rock glaciers. This self-cooling capacity is counteracted by an early snow melt-out date, exposing the low-albedo blocky surface to the intense June–July insolation and causing reduced evaporative cooling due to exacerbated moisture scarcity in the near-surface AL during dry spells. With climate change, earlier snowmelt and increased frequency, duration, and intensity of heat waves and droughts are projected. Regarding the parameterisation of the turbulent fluxes, we estimated the year-round turbulent fluxes using a modified Louis (1979) scheme. The monthly SEB is closed within 20 W m−2 except during the snowmelt months and under katabatic drainage winds in winter. Detected sensible turbulent fluxes from nocturnal ventilation processes, although a potentially important ground cooling mechanism, are within our 20 W m−2 uncertainty because nighttime wind speeds are low. Wintertime katabatic wind speeds needed to be scaled to close the SEB, which hints at the limits of parameterisations based on the Monin–Obukhov similarity theory in complex mountain terrain and katabatic drainage winds. The present work contributes to the process understanding of the SEB and climate sensitivity of coarse blocky landforms.

Extending the wind profile beyond the surface layer by combining physical and machine learning approaches

Abstract. Accurate estimation of the wind profile, especially in the lowest few hundred meters of the atmosphere, is of great significance for the weather, climate, and renewable energy sector. Nevertheless, the Monin–Obukhov similarity theory fails above the surface layer over a heterogeneous underlying surface, causing an unreliable wind profile to be obtained from conventional extrapolation methods. To solve this problem, we propose a novel method called the PLM-RF method that combines the power-law method (PLM) with the random forest (RF) algorithm to extend wind profiles beyond the surface layer. The underlying principle is to treat the wind profile as a power-law distribution in the vertical direction, with the power-law exponent (α) determined by the PLM-RF model. First, the PLM-RF model is constructed based on the atmospheric sounding data from 119 radiosonde (RS) stations across China and in conjunction with other data such as surface wind speed, land cover type, surface roughness, friction velocity, geographical location, and meteorological parameters from June 2020 to May 2021. Afterwards, the performance of the PLM-RF, PLM, and RF methods over China is evaluated by comparing them with RS observations. Overall, the wind speed at 100 m from the PLM-RF model exhibits high consistency with RS measurements, with a determination coefficient (R2) of 0.87 and a root mean squared error (RMSE) of 0.92 m s−1. By contrast, the R2 and RMSE of wind speed results from the PLM (RF) method are 0.75 (0.83) and 1.37 (1.04) m s−1, respectively. This indicates that the estimates from the PLM-RF method are much closer to observations than those from the PLM and RF methods. Moreover, the RMSE of the wind profiles estimated by the PLM-RF model is relatively large for highlands, while it is small for plains. This result indicates that the performance of the PLM-RF model is affected by the terrain factor. Finally, the PLM-RF model is applied to three atmospheric radiation measurement sites for independent validation, and the wind profiles estimated by the PLM-RF model are found to be consistent with Doppler wind lidar observations. This confirms that the PLM-RF model has good applicability. These findings have great implications for the weather, climate, and renewable energy sector.

Applicability of the generalized wind profile model over mountainous forests.

The analytical equation based on Monin-Obukhov (M-O) similarity theory (i.e., wind profile equation) has been adopted since 1970s for using in the prediction of wind vertical profile over flat terrains, which is mature and accurate. However, its applicability over complex terrains remains unknown. This applicability signifies the accuracy of the estimations of aerodynamic parameters for the boundary layer of non-flat terrain, such as zero-displacement height (d) and aerodynamic roughness length (z0), which will determine the accuracy of frequency correction and source area analysis in calculating carbon, water, and trace gas fluxes based on vorticity covariance method. Therefore, the validation of wind profile model in non-flat terrain is the first step to test whether the flux model needs improvement. We measured three-dimensional wind speed data by using the Ker Towers (three towers in a watershed) at Qingyuan Forest CERN in the Mountainous Region of east Liaoning Province, and compared them with data from Panjin Agricultural Station in the Liaohe Plain, to evaluate the applicability of a generalized wind profile model based on the Monin-Obukhov similarity theory on non-flat terrain. The results showed that the generalized wind profile model could not predict wind speeds accurately of three flux towers separately located in different sites, indicating that wind profile model was not suitable for predicting wind speeds in complex terrains. In the leaf-off and leaf-on periods, the coefficient of determination (R2) between observed and predicted wind speeds ranged from 0.12 to 0.30. Compared to measured values, the standard error of the predicted wind speeds was high up to 2 m·s-1. The predicted wind speeds were high as twice as field-measured wind speed, indicating substantial overestimation. Nevertheless, this model correctly predicted wind speeds in flat agricultural landscape in Panjin Agricultural Station. The R2 between observed wind speeds and predicted wind speed ranged from 0.90 to 0.93. The standard error between observed and predicted values was only 0.5 m·s-1. Results of the F-test showed that the root-mean-square error of the observed and predicted wind speeds in each secondary forest complex terrain was much greater than that in flat agricultural landscape. Terrain was the primary factor affecting the applicability of wind profile model, followed by seasonality (leaf or leafless canopy). The wind profile model was not applicable to the boundary-layer flows over forest canopies in complex terrains, because the d was underestimated or both the d and z0 were underestimated, resulting in inaccurate estimation of aerodynamic height.

Research on optimization method of evaporation duct prediction model based on particle swarm algorithm

The sea surface roughness parameterization and universal stability functions, as key components of the evaporation duct prediction models rooted in the Monin-Obukhov similarity theory, dictate the model performance which further impacts the efficiency and accuracy of offshore electromagnetic applications. In this paper, layered meteorological and hydrological observations are collected during two cruises and processed to obtain the reference modified refractivity profiles close to the sea surface, and then particle swarm algorithm is utilized to optimize the parameters of the sea surface roughness parameterization and universal stability functions. The results show that compared with the pre-optimization model, the prediction accuracy of the optimized model is improved by 5.09% and 8.12% under stable conditions, and by 9.97% and 31.51% under unstable conditions for observation dataset from each cruise, which proves the feasibility of the proposed method for evaporation duct prediction model optimization.

Surface energy fluxes and energy balance closure using large aperture scintillometer-based ET station on heterogeneous agricultural landscape in north India

This study was carried out to understand the pattern of surface energy fluxes over a periodical scale and energy balance closure using Large Aperture Scintillometer and Micrometeorological tower. The standalone technique as ‘Scintillometry’ which observes the structure parameter of refractive index based on Monin-Obukhov Similarity theory, has the potential to measure the sensible heat flux precisely. This paper discusses the surface energy balance components and energy balance closure over a period of August 2017 to June 2018. The maximum mean energy fluxes Rn, G, H and LE were observed in September (98.6 Wm-2), May (13.9 Wm-2), June (53.3 Wm-2) and August (82.1 Wm-2), respectively. The overall mean ET was observed at the rate of 1.36 mm day-1 during the study period. This scintillometry technique may further use in evapotranspiration modelling from polar orbiting satellite to geostationary satellite over a heterogeneous and undulated landscape.

A Novel Similarity Approach for Describing the Bulk Shear in the Atmospheric Surface Layer

The Monin–Obukhov Similarity Theory (MOST) is a cornerstone of boundary layer meteorology and the basis of most parameterizations of the atmospheric surface layer. Due to its significance for observations and modelling, we generalize the dimensional analysis of MOST by considering the bulk gradient directly, enabling the study of any sublayer of the atmospheric surface layer. This results in a family of similarity relations describing all gradients from the local gradient to the full-layer bulk gradient. By applying the profiles derived from the law-of-the-wall and MOST, we are able to derive analytic expressions for this family of similarity relations. Under stable conditions, we discover that the log-linear profile of Businger–Dyer generalizes from the local to the bulk shear where the slope is dependent on the choice of the layer. The simplicity of the general log-linear relation allows for estimating the influence of stability on the non-dimensional gradients. It is shown that bulk gradients are less sensitive to stability than the local gradient. By correctly filtering cases where the full-layer bulk gradient is influenced by stability, we demonstrate that MOST is compatible with the Hockey-Stick Transition. For unstable conditions, the Kader and Yaglom (J Fluid Mech 212(151):637-662, 1990) model represents the local gradient well but was not successful in representing the bulk gradient, demonstrating the need for further analysis of scaling relations for the unstable atmospheric surface layer.

An Investigation of LES Wall Modeling for Rayleigh–Bénard Convection via Interpretable and Physics-Aware Feedforward Neural Networks with DNS

Abstract The traditional approach of using the Monin–Obukhov similarity theory (MOST) to model near-surface processes in large-eddy simulations (LESs) can lead to significant errors in natural convection. In this study, we propose an alternative approach based on feedforward neural networks (FNNs) trained on output from direct numerical simulation (DNS). To evaluate the performance, we conduct both a priori and a posteriori tests. In the a priori (offline) tests, we compare the statistics of the surface shear stress and heat flux, computed from filtered DNS input variables, to the stress and flux obtained from the filtered DNS. Additionally, we investigate the importance of various input features using the Shapley additive explanations value and the conditional average of the filter grid cells. In the a posteriori (online) tests, we implement the trained models in the System for Atmospheric Modeling (SAM) LES and compare the LES-generated surface shear stress and heat flux with those in the DNS. Our findings reveal that vertical velocity, a traditionally overlooked flow quantity, is one of the most important input features for determining the wall fluxes. Increasing the number of input features improves the a priori test results but does not always improve the model performance in the a posteriori tests because of the differences in input variables between the LES and DNS. Last, we show that physics-aware FNN models trained with logarithmic and scaled parameters can well extrapolate to more intense convection scenarios than in the training dataset, whereas those trained with primitive flow quantities cannot. Significance Statement The traditional near-surface turbulence model, based on a shear-dominated boundary layer flow, does not represent near-surface turbulence in natural convection. Using a feedforward neural network (FNN), we can construct a more accurate model that better represents the near-surface turbulence in various flows and reveals previously overlooked controlling factors and process interactions. Our study shows that the FNN-generated models outperform the traditional model and highlight the importance of the near-surface vertical velocity. Furthermore, the physics-aware FNN models exhibit the potential to extrapolate to convective flows of various intensities beyond the range of the training dataset, suggesting their broader applicability for more accurate modeling of near-surface turbulence.

Large-eddy-model closure and simulation of turbulent flux patterns over oasis surface

Abstract. Large-eddy simulations (LESs) have been increasingly used for studying atmosphere and land surface interactions over heterogeneous areas. However, parameterizations based on Monin–Obukhov Similarity Theory (MOST) often violate the basic assumptions of the very theory, generate inconsistencies with the LES turbulence closures, and produce surface flux estimates depending on LES model resolutions. Here, we propose a novel scheme for turbulent flux estimates in LES models. It computes the fluxes locally using the LES subgrid closure, which is then constrained on the macroscopic scale using MOST. Compared with several other schemes, the new scheme performs better for the various types of land surfaces tested. We validate our scheme by comparing surface flux estimates with field measurements obtained over an oasis surface at various height levels. Additionally, we scrutinize other quantities related to the surface energy balance, including net radiation, ground heat flux, and surface skin temperature, all of which align well with observational data. Our sensitivity experiments, focusing on model horizontal resolution, underscore the robustness of our scheme, as it maintains its corrective efficacy despite changes in horizontal grid spacing. We find that the macroscopic constraint imposed by MOST on LES-estimated fluxes strengthens as the horizontal grid spacing decreases, with a more pronounced influence on sensible than latent heat fluxes. These findings collectively highlight the promise and adaptability of our scheme for improved surface flux estimates in LES models.

Research on Optimization Method of Evaporation Duct Prediction Model

The sea surface roughness parameterization and the universal stability function are key components of the evaporation duct prediction model based on the Monin–Obukhov similarity theory. They determine the model’s performance, which in turn affects the efficiency and accuracy of electromagnetic applications at sea. In this study, we collected layered meteorological and hydrological observation data and preprocessed them to obtain near-surface reference modified refractivity profiles. We then optimized the sea surface roughness parameterization and the universal stability function using particle swarm optimization and simulated annealing algorithms. The results show that the particle swarm optimization algorithm outperforms the simulated annealing algorithm. Compared to the original model, the particle swarm optimization algorithm improved the prediction accuracy of the model by 5.09% under stable conditions and by 9.97% under unstable conditions, demonstrating the feasibility of the proposed method for optimizing the evaporation duct prediction model. Subsequently, we compared the electromagnetic wave propagation path losses under two different evaporation duct heights and modified refractivity profile states, confirming that the modified refractivity profile is more suitable as the accuracy criterion for the evaporation duct prediction model.

Evaluation of methods to determine the surface mixing layer height of the atmospheric boundary layer in the central Arctic during polar night and transition to polar day in cloudless and cloudy conditions

Abstract. This study evaluates methods to derive the surface mixing layer (SML) height of the Arctic atmospheric boundary layer (ABL) using in situ measurements inside the Arctic ABL during winter and the transition period to spring. An instrumental payload carried by a tethered balloon was used for the measurements between December 2019 and May 2020 during the year-long Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition. Vertically highly resolved (centimeter scale) in situ profile measurements of mean and turbulent parameters were obtained, reaching from the sea ice to several hundred meters above ground. Two typical conditions of the Arctic ABL over sea ice were identified: cloudless situations with a shallow surface-based inversion and cloudy conditions with an elevated inversion. Both conditions are associated with significantly different SML heights whose determination as accurately as possible is of great importance for many applications. We used the measured turbulence profile data to define a reference of the SML height. With this reference, a more precise critical bulk Richardson number of 0.12 was derived, which allows an extension of the SML height determination to regular radiosoundings. Furthermore, we have tested the applicability of the Monin–Obukhov similarity theory to derive SML heights based on measured turbulent surface fluxes. The application of the different approaches and their advantages and disadvantages are discussed.

An update to WRF surface layer parameterization over an Indian region

Surface layer parameterization schemes in numerical weather prediction models are based on the Monin-Obukhov similarity theory (MOST), which utilizes empirical functions to incorporate the effects of near-surface atmospheric stability. In the present study, an effort has been made to implement and evaluate the performance of recently developed similarity functions under stable stratification in the surface layer parameterization of Weather Research and Forecasting Model version 4.2.2 (WRFv4.2.2). For this purpose, the commonly used revised version of MM5 surface layer module in WRF model is updated using the similarity functions suggested by Srivastava et al. (2020). The model is configured with three nested domains around the flux tower installed at Ranchi (23.412° N, 85.440°E), India. The simulations are carried out for a complete year, and the model simulated near-surface atmospheric variables are compared with the observations. The study reveals that updated similarity functions lead to a noticeable improvement in WRF model performance. In particular, the modified scheme reduced the mean absolute error and root mean square error for 10-m wind speed (2-m temperature) by about 22 % (10 %) and 23 % (8 %), respectively, with improved correlation coefficients during January. The analysis suggests that the new similarity functions could potentially be used in weather forecast model over the Indian region.

Comprehensive evaluation of typical planetary boundary layer (PBL) parameterization schemes in China – Part 1: Understanding expressiveness of schemes for different regions from the mechanism perspective

Abstract. The optimal choice of the planetary boundary layer (PBL) parameterization scheme is of particular interest and urgency to a wide range of scholars, especially for many works involving models. At present, there have been many works to evaluate the PBL schemes. However, little research has been conducted into a more comprehensive and systematic assessment of the performance capability of schemes in key regions of China, especially when it comes to the differences in the mechanisms of the schemes themselves, primarily because there is scarcely sufficient observational data, computer resources, and storage support to complete the work. In this companion paper (i.e., Part 1), four typical schemes (i.e., YSU, ACM2, BL, and MYJ) are selected to systematically analyze and evaluate near-surface meteorological parameters, PBL vertical structure, PBL height (PBLH), and turbulent diffusion coefficient (TDC) in five key regions of China (i.e., North China Plain, NCP; Yangtze River Delta, YRD; Sichuan Basin, SB; Pearl River Delta, PRD and Northwest Semi-arid region, NS) in different seasons (i.e., January, April, July, and October). The differences in the simulated 2 m temperatures between the nonlocal closure schemes are mainly affected by the downward shortwave radiation, but to compare the nonlocal closure schemes with the local closure schemes, the effect of sensible heat flux needs to be further considered. The 10 m wind speed is under the influence of factors like the momentum transfer coefficient and the integrated similarity functions at night. The wind speeds are more significantly overestimated in the plains and basin, while less overestimated or even underestimated in the mountains, as a result of the effect on topographic smoothing in the model. Moreover, the overestimation of small wind speeds at night is attributable to the inapplicability of the Monin–Obukhov similarity theory (MOST) at night. The model captures the vertical structure of temperature well, while the wind speed is outstandingly overestimated below 1000 m, largely because of the TDC. The difference between the MOST and the mixing length theory, PBLH, and Prandtl number is cited as the reason for the difference between the TDC of the YSU and ACM2 schemes. The TDCs of the BL and MYJ schemes are affected by the mixing length scale, which of BL is calculated on the basis of the effect of buoyancy, while MYJ calculates it with the consideration of the effect of the total turbulent kinetic energy. The PBLH of the BL scheme is better than the other schemes because of the better simulation results of temperature. In general, to select the optimal scheme, it is necessary to offer different options for different regions with different focuses (heat or momentum). The first focus is on the temperature field. The BL scheme is recommended for January in the NCP region, especially for Beijing, and the MYJ scheme is better for the other 3 months. The ACM2 scheme would be a good match for the YRD region, where the simulation differences between the four schemes are small. The topography of the SB region is more complex, but for most of the areas in the basin, the MYJ scheme is proposed, and if more stations outside the basin are involved, the BL scheme is recommended. The MYJ scheme is applied to the PRD region in January and April, and the BL scheme in July and October. The MYJ scheme is counseled for the NS region. The second focus is the wind field. The YSU scheme is recommended if the main concern is the near-surface layer, and the BL scheme is suggested if focusing on the variation in the vertical direction. The final evaluation of the parameterization scheme and uncertainties will lay the foundation for the improvement of the modules and forecasting of the GRAPES_CUACE regional model developed independently in China.

On the Efficacy of Monin–Obukhov and Bulk Richardson Surface-Layer Parameterizations over Drylands

Abstract Surface-layer parameterizations for heat, mass, momentum, and turbulence exchange are a critical component of the land surface models (LSMs) used in weather prediction and climate models. Although formulations derived from Monin–Obukhov similarity theory (MOST) have long been used, bulk Richardson (Rib) parameterizations have recently been suggested as a MOST alternative but have been evaluated over a limited number of land-cover and climate types. Examining the parameterizations’ applicability over other regions, particularly drylands that cover approximately 41% of terrestrial land surfaces, is a critical step toward implementing the parameterizations into LSMs. One year (1 January–31 December 2018) of eddy covariance measurements from a 10-m tower in southeastern Arizona and a 200-m tower in western Texas were used to determine how well the Rib parameterizations for friction velocity (), sensible heat flux (H), and turbulent kinetic energy (TKE) compare against MOST-derived parameterizations of these quantities. Independent of stability, wind speed regime, and season, the Rib and TKE parameterizations performed better than the MOST parameterizations, whereas MOST better represented H. Observations from the 200-m tower indicated that the parameterizations’ performance degraded as a function of height above ground. Overall, the Rib parameterizations revealed promising results, confirming better performance than traditional MOST relationships for kinematic (i.e., ) and turbulence (i.e., TKE) quantities, although caution is needed when applying the Rib H parameterizations to drylands. These findings represent an important milestone for the applicability of Rib parameterizations, given the large fraction of Earth’s surface covered by drylands. Significance Statement Weather forecasting models rely upon complex mathematical relationships to predict temperature, wind, and moisture. Monin–Obukhov similarity theory (MOST) has long been used to forecast these quantities near the land surface, even though MOST’s limitations are well known in the scientific community. Researchers have suggested an alternative to MOST called the bulk Richardson (Rib) approach. To allow for the Rib approach to be used in weather forecasting models, the approach needs to be tested over different land-cover and climate types. In this study, we applied the Rib approach to dry areas of the United States and found that the approach better represented turbulence variables than MOST relationships. These findings are an important step toward using Rib relationships in weather forecasting models.

Research on a Multimodel Fusion Diagnosis Method for Evaporation Ducts in the East China Sea

Evaporation ducts are abnormal states of the atmosphere in the air–sea boundary layer that directly affect the propagation trajectory of electromagnetic (EM) waves. Therefore, an accurate diagnosis of the evaporation duct height (EDH) is important for studying the propagation trajectory of EM waves in evaporation ducts. Most evaporation duct models (EDMs) based on the Monin–Obukhov similarity theory are empirical methods. Different EDMs have different levels of environmental adaptability. Evaporation duct diagnosis methods based on machine learning methods only consider the mathematical relationship between data and do not explore the physical mechanism of evaporation ducts. To solve the above problems, this study observed the meteorological and hydrological parameters of the five layers of the low-altitude atmosphere in the East China Sea on board the research vessel Xiangyanghong 18 in April 2021 and obtained the atmospheric refractivity profile. An evaporation duct multimodel fusion diagnosis method (MMF) based on a library for support vector machines (LIBSVM) is proposed. First, based on the observed meteorological and hydrological data, the differences between the EDH diagnosis results of different EDMs and MMF were analyzed. When ASTD ≥ 0, the average errors of the diagnostic results of BYC, NPS, NWA, NRL, LKB, and MMF are 2.57 m, 2.92 m, 2.67 m, 3.27 m, 2.57 m, and 0.24 m, respectively. When ASTD < 0, the average errors are 2.95 m, 2.94 m, 2.98 m, 2.99 m, 2.97 m, and 0.41 m, respectively. Then, the EM wave path loss accuracy analysis was performed on the EDH diagnosis results of the NPS model and the MMF. When ASTD ≥ 0, the average path loss errors of the NPS model and MMF are 5.44 dB and 2.74 dB, respectively. When ASTD < 0, the average errors are 5.21 dB and 3.46 dB, respectively. The results show that the MMF is suitable for EDH diagnosis, and the diagnosis accuracy is higher than other models.

High spatial resolution long-term temperature profiling to inform near-shore atmospheric sound propagation

Atmospheric sound propagation depends on factors such as surface characteristics and meteorological parameters. Effective numerical modeling of atmospheric sound propagation requires reliable and realistic input parameters. One of the most influential factors is the air temperature profile. This work examines the application of experimentally determined air temperature profiles in acoustic modeling of littoral environments. Long term measurements of near-surface air temperature profiles over water and marsh grass are presented. Data have been recorded using temperature loggers affixed to two permanent 7 m masts. The loggers were positioned with a 1 m vertical spacing. A common approach to characterize the near-surface boundary layer uses Monin–Obukhov Similarity Theory (MOST). This work compares high spatial resolution air temperature measurements with measurement-informed profiles based on MOST. The development of a more experimentally grounded set of assumptions will ultimately contribute to the improvement of atmospheric acoustic transmission loss models in near shore environments.

The Impact of Surface Waves and Spray Injection Velocities on Air–Sea Momentum and Heat Fluxes

Surface waves and sea spray play a significant role in air–sea fluxes in high winds. The present study used a marine atmosphere surface layer (MASL), which couples the traditional Monin–Obukhov similarity theory, sea spray generation function, the balance of turbulent kinetic budget, and momentum/enthalpy conservation equations. Based on this model, the effects of wave states and spray injection velocities on air–sea momentum/enthalpy fluxes and near-surface wind/temperature profiles were theoretically investigated. Based on the assumption that the velocity of injected spray is the same as that of the ambient airflow, it was found that spray could increase the near-surface air turbulence intensity and inhibit air–sea fluxes at 10 m above the sea surface. Correspondingly, near-surface wind speeds and temperature increase in high winds. This phenomenon becomes prominent in cases of large wave ages or surface waves supporting a minority of air–sea fluxes. Based on the assumption that the velocity of the edges of breaking water bags is used to estimate that of spray injection, the opposite results were found: spray could weaken the near-surface air turbulence and increase total air–sea fluxes at 10 m above the sea surface. In this case, the near-surface wind speeds and temperature decreased. This reduction becomes remarkable when surface waves are full-developed or the majority of air–sea momentum fluxes are supported by waves.

Continuous daytime and nighttime forecast of atmospheric optical turbulence from numerical weather prediction models.

Future satellite-to-ground optical communication systems will benefit from accurate forecasts of atmospheric optical turbulence; namely for site selection, for the routing and the operation of optical links, and for the design of optical communication terminals. This work presents a numerical approach based on the Weather Research and Forecasting software that enables continuous forecast of the refractive index structure parameter, C n2, vertical profiles. Two different C n2 models are presented and compared. One is based on monitoring the turbulent kinetic energy, while the other is a hybrid model using the Tatarskii equation to depict the free atmosphere region, and the Monin-Obukhov similarity theory for describing the boundary layer. The validity of both models is assessed by using thermosonde measurements from the Terrain-induced Rotor Experiment campaign, and from day and night measurements of the coherence length collected during a six-day campaign at Paranal observatory by a Shack-Hartmann Image Motion Monitor. The novelty of this work is the ability of the presented approach to continuously predict optical turbulence both during daytime and nighttime, and its validation with measurements in day and night conditions.

Secondary flows induced by two-dimensional surface temperature heterogeneity in stably stratified channel flow

The structure and impact of thermally induced secondary motions in stably stratified channel flows with two-dimensional surface temperature inhomogeneities is studied using direct numerical simulation (DNS). Starting from a configuration with only spanwise varying surface temperature, where the streamwise direction is homogeneous (Bon & Meyers, J. Fluid Mech., 2022, pp. 1–38), we study cases where the periodic temperature strip length $l_x/h$ (with $h$ the half-channel height) assumes finite values. The patch width ( $l_y/h =\{{\rm \pi} /4, {\rm \pi}/8$ }) and length are varied at fixed stability and two different Reynolds numbers. Results indicate that for the investigated patch widths, the streamwise development of the secondary flows depends on the patch aspect ratio ( $a=l_x/l_y$ ), while they reach a fully developed state after approximately $25l_y$ . The strength of the secondary motions, and their impact on momentum and heat transfer through the dispersive fluxes, is strongly reduced as the length of the temperature strips decreases, and becomes negligible when $a\lesssim 1$ . We demonstrate that upward dispersive and turbulent heat transport in locally unstably stratified regions above the high-temperature patches lead to reduced overall downward heat transfer. Comparison to local Monin–Obukhov similarity theory (MOST) reveals that scaled velocity and temperature gradients in homogeneous stably stratified channel flow at $Re_\tau =550$ agree reasonably well with empirical correlations obtained from meteorological data. For thermally heterogeneous cases with strips of finite length, the similarity functions only collapse higher above the surface, where dispersive fluxes are negligible. Lastly, we show that mean profiles of all simulations collapse when using outer-layer scaling based on displacement thickness.