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Accurately quantifying air‐sea fluxes is important for understanding air‐sea interactions and improving coupled weather and climate models. This study introduces a probabilistic framework to represent the highly variable nature of air‐sea fluxes, which is missing in deterministic bulk algorithms. Assuming Gaussian distributions conditioned on the input variables, we use artificial neural networks and eddy‐covariance measurement data to estimate the mean and variance by minimizing negative log‐likelihood loss. The trained neural networks provide alternative mean flux estimates to existing bulk algorithms, and quantify the uncertainty around the mean estimates. A stochastic parameterization of air‐sea turbulent fluxes can be constructed by sampling from the predicted distributions. Tests in a single‐column forced upper‐ocean model suggest that changes in flux algorithms influence sea surface temperature and mixed layer depth seasonally. The ensemble spread in stochastic runs is most pronounced during spring restratification.

We propose the multivariate locally stationary wavelet (mvLSW) process to analyze surface turbulent fluxes in nonstationary atmospheric conditions. Using theoretical spectral characteristics, we generated synthetic data representing stationary and nonstationary turbulence time series. This data enables us to explore the impact of mesoscale atmospheric flows on the stationary microscale turbulence field and detect the spectral gap in the time-varying cospectra. Applying this approach to experimental data collected in Fairbanks, Alaska and Bogota, Colombia, we demonstrated the ability to detect cospectral gaps and compute bandwidth-limited turbulent fluxes arising from stationary components of the atmospheric flow. These findings underscore the importance of considering scale-dependent atmospheric forcing when comparing model and experimental data.

In this study, a systematic mathematical analysis has been presented for the extent of applicability of various non-linear similarity functions for momentum (φm) and heat (φh) under stable conditions to compute surface turbulent fluxes in numerical models. The investigation is carried out for equal and unequal momentum (z0) and heat (zh) roughness lengths. The study reveals that φm and φh 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 and zh to the height (z) from the surface (i.e., z0z and zhz) lie in the range (0.2,1), the functions are valid for a limited range of ζ (stability parameter) in strong stable conditions ζ>1; however, when z0z≤0.2 and zhz≤0.2, the validity of functions is unrestricted. In terms of bulk Richardson number RiB, 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 and RiB. The efforts have also been made to implement these functions in the Weather Research and Forecasting as well as global scale models.

Non‐stationarity challenges the applicability of turbulent similarity theory and flux estimation, especially in urban areas with highly heterogeneous underlying surfaces. Based on the observational data in Beijing, we investigated the characteristics and potential physical mechanisms of turbulent non‐stationarity in a megacity area. The results show that the proportion of non‐stationary turbulence in Beijing reached 52.41% in 2017. Strongly non‐stationary turbulence mainly occurs under strongly‐stable/strongly‐unstable stratification conditions. Strong non‐stationarity reduces the turbulent transport efficiency. This is characterized by the disintegration of turbulent coherent structures and the dominance of submeso motions. Furthermore, it was found that submeso motions (e.g., internal gravity waves and convective circulations) are the main cause of non‐stationary turbulence. After removing the influence of submeso motions based on the Hilbert‐Huang transform, the non‐stationary level is effectively reduced. The results are significant for accurately estimating turbulent fluxes and improving the parameterization of turbulent exchange processes in megacity areas.

Accurate representation of the turbulent exchange of carbon, water, and heat between the land surface and the atmosphere is critical for modelling global energy, water, and carbon cycles in both future climate projections and weather forecasts. Evaluation of models' ability to do this is performed in a wide range of simulation environments, often without explicit consideration of the degree of observational constraint or uncertainty and typically without quantification of benchmark performance expectations. We describe a Model Intercomparison Project (MIP) that attempts to resolve these shortcomings, comparing the surface turbulent heat flux predictions of around 20 different land models provided with in situ meteorological forcing evaluated with measured surface fluxes using quality-controlled data from 170 eddy-covariance-based flux tower sites. Predictions from seven out-of-sample empirical models are used to quantify the information available to land models in their forcing data and so the potential for land model performance improvement. Sites with unusual behaviour, complicated processes, poor data quality, or uncommon flux magnitude are more difficult to predict for both mechanistic and empirical models, providing a means of fairer assessment of land model performance. When examining observational uncertainty, model performance does not appear to improve in low-turbulence periods or with energy-balance-corrected flux tower data, and indeed some results raise questions about whether the energy balance correction process itself is appropriate. In all cases the results are broadly consistent, with simple out-of-sample empirical models, including linear regression, comfortably outperforming mechanistic land models. In all but two cases, latent heat flux and net ecosystem exchange of CO2 are better predicted by land models than sensible heat flux, despite it seeming to have fewer physical controlling processes. Land models that are implemented in Earth system models also appear to perform notably better than stand-alone ecosystem (including demographic) models, at least in terms of the fluxes examined here. The approach we outline enables isolation of the locations and conditions under which model developers can know that a land model can improve, allowing information pathways and discrete parameterisations in models to be identified and targeted for future model development.

Horizontal grid spacings of numerical weather prediction models are rapidly approaching O (1 km) and have become comparable with the dominant length scales of flows in the boundary layer; within such “gray-zone”, conventional planetary boundary layer (PBL) parameterization schemes start to violate basic design assumptions. Scale-aware PBL schemes have been developed recently to address the gray-zone issue. By performing WRF simulations of Hurricane Earl (2010) at sub-kilometer grid spacings, this study investigates the effect of the scale-aware Shin-Hong (SH) scheme on the tropical cyclone (TC) intensification and structural changes in comparison to the non-scale-aware YSU scheme it is built upon. Results indicate that SH tends to produce a stronger TC with a more compact inner core than YSU. At early stages, the scale-aware coefficients in SH gradually decrease as the diagnosed boundary layer height exceeds the horizontal grid spacing. This scale-aware effect is most prominent for the nonlocal subgrid-scale vertical turbulent fluxes, in the non-precipitation regions radially outside of the convective rainband, and from the early stage through the middle of rapid intensification (RI) phase. Both the scale awareness and different parameterization of the nonlocal turbulent heat flux in SH reduce the parameterized vertical turbulent mixing, which further induces stronger radial inflows and helps retain more water vapor in the boundary layer. The resulting stronger moisture convergence and diabatic heating near the TC center account for the faster inner-core contraction before RI onset and the higher intensification rate during the RI period. Potential issues of applying these two PBL schemes in TC simulations and suggestions for improvements are discussed.

Surface turbulent fluxes constitute key energy exchanges in the atmospheric boundary layer (ABL). Accurate prediction of variations in the ABL is essential for agricultural ecology and climate studies. Existing prediction methods include those based on Monin–Obukhov similarity theory (MOST) and machine learning (ML). However, the MOST method requires experimental parameters and empirical equations, while the ML method considerably relies on manual feature extraction. Given the potential of deep learning (DL) in time series prediction, an inverted Transformer (iTransformer) model is employed in this study to predict friction velocity, kinematic sensible heat flux, and kinematic latent heat flux values across different seasons. The iTransformer model encodes the data via transposed encoding, and a multivariate self‐attention module is employed to capture the correlations between variables. The feed‐forward neural networks leverage these correlations to predict surface turbulent fluxes. Compared with other methods, including the Transformer and ML methods, the iTransformer model can not only improve the prediction correlations but also reduce the errors in surface turbulent fluxes. Moreover, the model can effectively capture the trends in various fluxes within 1 month or even one day. In summary, the iTransformer model can significantly increase the predictive performance for surface turbulent fluxes. Plain Language Summary Surface turbulent fluxes are vital in atmospheric boundary layer (ABL) research, with significant implications for agricultural production and related studies. Traditional Monin–Obukhov similarity theory (MOST) and existing machine learning (ML) methods exhibit notable biases in predicting surface turbulent fluxes. Deep learning (DL) provides a novel approach for surface turbulent fluxes prediction. In this study, an inverted transformer (iTransformer) model and data from the Shanghuang and Xilinhot sites in Zhejiang Province are employed, and surface turbulent fluxes during the four seasons are predicted. The experimental results reveal that the iTransformer model outperforms the MOST and ML methods in predicting surface turbulent fluxes, highlighting its significant potential. Key Points A deep learning model based on iTransformer is established for predicting surface turbulent fluxes The model utilizes transpose encoding and multi‐variate self‐attention to capture correlations among variables of surface turbulent fluxes The iTransformer model achieves significantly improved prediction correlations and reduced prediction errors relative to previous models

Forty years ago, climate scientists predicted the Arctic to be on of Earth’s most sensitive climate regions and thus extremely vulnerable to increased CO2. The rapid and unprecedented changes observed in the Arctic confirm this prediction, which has consequences that ripple through the global climate system. Especially significant, sea ice loss is altering the exchange of mass, energy, and momentum between the atmosphere and Arctic Ocean. A thick, extensive, and multiyear ice cover has historically limited such exchanges, however, the summertime Arctic Ocean is expected to be nearly ice‐free within 15 years increasing the potential for air‐sea exchange. Changes in surface turbulent fluxes can alter the Arctic surface energy budget, sea ice, clouds, boundary layer temperature and humidity, and atmospheric and oceanic circulations. This paper reviews current knowledge of surface turbulent fluxes across the Arctic Ocean and the known effects on climate. We conclude that Arctic air‐sea energy exchanges are becoming an increasingly consequential factor driving Arctic climate. Arctic Ocean surface turbulent energy exchanges are not smooth and steady but rather irregular and episodic, considering this nature of air‐sea energy exchanges is essential for improving Arctic climate projections. New field data focusing on the episodic nature of air‐sea exchange will accelerate our understanding of Arctic climate change.

Wind turbines generate wakes, which can potentially influence the local microclimate near the ground. To verify and quantify such effects, the Vertical Enhanced Mixing (VERTEX) field campaign was conducted in late summer 2016 to measure near-surface turbulent fluxes, wind speed, temperature, and moisture under and outside of the wake of an operational wind turbine in Lewes, Delaware. We found that, in the presence of turbine wakes from a single wind turbine, friction velocity, turbulent kinetic energy, and wind speed were reduced near the ground under the wake, while turbulent heat flux was not significantly affected by the wake. The observed near-ground temperature changes were <0.4°C in magnitude. Near-ground temperature changes due to the wake correlated well with the temperature lapse rate between hub height and the ground, with warming observed during stable and neutral conditions and cooling during unstable conditions. Of the two properties that define a wake (i.e., wind speed deficit and turbulence), the wind speed deficit dominates the surface response, while the wake turbulence remains aloft and hardly ever reaches the ground. We propose that the mechanism that drives changes in near-ground temperature in the presence of turbine wakes is the vertical convergence of turbulent heat flux below hub height. Above hub height, turbulence and turbulent heat flux are enhanced; near the ground, turbulence is reduced and turbulent heat flux is unchanged. These conditions cause an increase (during stable/neutral stability) or decrease (during unstable stability) in heat flux convergence, ultimately resulting in warming or cooling near the ground, respectively.

This paper quantifies the impacts of approximations and assumptions in the parameterization of bulk formulas on the exchange of momentum, heat, and freshwater computed between the ocean and atmosphere. An ensemble of sensitivity experiments is examined. Climatologies of wind stress, turbulent heat flux, and evaporation for the period 1982–2014 are computed using SST and surface meteorological state variables from ERA-Interim. Each experiment differs from the defined control experiment in only one aspect of the parameterization of the bulk formulas. The wind stress is most sensitive to the closure used to relate the neutral drag coefficient to the wind speed in the bulk algorithm, which mainly involves the value of the Charnock parameter. The disagreement between the state-of-the-art algorithms examined is typically on the order of 10%. The largest uncertainties in turbulent heat flux and evaporation are also related to the choice of the algorithm (typically 15%) but also emerge in experiments examining approximations related to the surface temperature and saturation humidity. Thus, approximations for the skin temperature and the salt-related reduction of saturation humidity have a substantial impact on the heat flux and evaporation (typically 10%). Approximations such as the use of a fixed air density, sea level pressure, or simplified formula for the saturation humidity lead to errors no larger than 4% when tested individually. The impacts of these approximations combine linearly when implemented together, yielding errors up to 20% over mid- and subpolar latitudes.