Using a classical example, the Lorenz‐63 model, an original stochastic framework is applied to represent large‐scale geophysical flow dynamics. Rigorously derived from a reformulated material derivative, the proposed framework encompasses several meaningful mechanisms to model geophysical flows. The slightly compressible set‐up, as treated in the Boussinesq approximation, yields a stochastic transport equation for the density and other related thermodynamical variables. Coupled to the momentum equation through a forcing term, the resulting stochastic Lorenz‐63 model is derived consistently. Based on such a reformulated model, the pertinence of this large‐scale stochastic approach is demonstrated over classical eddy‐viscosity based large‐scale representations.

Expanding on a wavelet basis the solution of an inverse problem provides several advantages. First of all, wavelet bases yield a natural and efficient multiresolution analysis which allows defining clear optimization strategies on nested subspaces of the solution space. Besides, the continuous representation of the solution with wavelets enables analytical calculation of regularization integrals over the spatial domain. By choosing differentiable wavelets, accurate high-order derivative regularizers can be efficiently designed via the basis's mass and stiffness matrices. More importantly, differential constraints on vector solutions, such as the divergencefree constraint in physics, can be nicely handled with biorthogonal wavelet bases. This paper illustrates these advantages in the particular case of fluid flow motion estimation. Numerical results on synthetic and real images of incompressible turbulence show that divergencefree wavelets and high-order regularizers are particularly relevant in this context.

Numerical simulations of industrial and geophysical fluid flows cannot usually solve the exact Navier-Stokes equations. Accordingly, they encompass strong local errors. For some applications-like coupling models and measurements-these errors need to be accurately quantified, and ensemble forecast is a way to achieve this goal. This paper reviews the different approaches that have been proposed in this direction. A particular attention is given to the models under location uncertainty and stochastic advection by Lie transport. Besides, this paper introduces a new energy-budget-based stochastic subgrid scheme and a new way of parameterizing models under location uncertainty. Finally, new ensemble forecast simulations are presented. The skills of that new stochastic parameterization are compared to that of the dynamics under location uncertainty and of randomized-initial-condition methods.

Abstract. Based on a wavelet expansion of the velocity field, we present a novel optical flow algorithm dedicated to the estimation of continuous motion fields such as fluid flows. This scale-space representation, associated to a simple gradient-based optimization algorithm, naturally sets up a well-defined multi-resolution analysis framework for the optical flow estimation problem, thus avoiding the common drawbacks of standard multi-resolution schemes. Moreover, wavelet properties enable the design of simple yet efficient high-order regularizers or polynomial approximations associated to a low computational complexity. Accuracy of proposed methods is assessed on challenging sequences of turbulent fluids flows.

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A motion estimation algorithm was applied to image sequences produced by a horizontally scanning elastic backscatter lidar. The algorithm, a wavelet-based optical flow estimator named Typhoon, produces dense two-component vector flow fields that correspond to the apparent motion of microscale aerosol features. To validate the efficacy of this approach for the remote measurement of wind fields in the lower atmosphere, an experiment was conducted in Chico, California, in 2013 and 2014. The flow fields, estimated every 17 s, were compared with measurements from an independent Doppler lidar. Time series of wind speed and direction, statistical assessment of the 10-min averages, and examples of wind fields are presented. The comparison of 10-min averages at 100 m AGL reveals excellent correlations between estimates from the Typhoon algorithm and measurements from the Doppler lidar. Power spectra and spectral transfer functions are computed to estimate the filtering effects of the algorithm in the spatial domain.

This article describes the implementation of a simple wavelet-based opticalflow motion estimator dedicated to continuous motions such as fluid flows. The wavelet representation of the unknown velocity field is considered. This scale-space representation, associated to a simple gradient-based optimization algorithm, sets up a welldefined multiresolution framework for the optical flow estimation. Moreover, a very simple closure mechanism, approaching locally the solution by high-order polynomials, is provided by truncating the wavelet basis at fine scales. Accuracy and efficiency of the proposed method is evaluated on image sequences of turbulent fluid flows.

Numerical and field experiments were conducted to test an optimized cross-correlation algorithm (CCA) for the remote sensing of two-component wind vectors from horizontally scanning elastic backscatter lidar data. Each vector is the result of applying the algorithm to a square and contiguous subset of pixels (an interrogation window) in the lidar scan area. Synthetic aerosol distributions and flow fields were used to investigate the accuracy and precision of the technique. Results indicate that in neutral static stability, when the mean flow direction over the interrogation window is relatively uniform, the random error of the estimates increases as the mean wind speed and turbulence intensity increases. In convective conditions, larger errors may occur as a result of the cellular nature of convection and the dramatic changes in wind direction that may span the interrogation window. Synthetic fields were also used to determine the significance of various image processing and numerical steps used in the CCA. Results show that an iterative approach that dynamically reduces the block size provides the largest performance gains. Finally, data from a field experiment conducted in 2013 in Chico, California, are presented. Comparisons with Doppler lidar data indicate excellent agreement for the 10-min mean wind velocity computed over a set of 150 h: the root-mean-square deviations (and slopes) for the u and υ components are 0.36 m s−1 (0.974) and 0.37 m s−1 (0.991), respectively, with correlation coefficients > 0.99.