This study presents the development of a TKE-l parameterization of the diffusion coefficients for the representation of turbulent diffusion in neutral and stable conditions in large-scale atmospheric models. The parameterization has been carefully designed to be completely tunable in the sense that all adjustable parameters have been clearly identified and their number minimized as much as possible to help the calibration and to thoroughly assess the parametric sensitivity. We choose a mixing length formulation that depends on both static stability and wind shear to cover the different regimes of stable boundary layers. We follow a heuristic approach for expressing the stability functions and turbulent Prandlt number in order to guarantee the versatility of the scheme and its applicability for planetary atmospheres composed of an ideal and perfect gas such as that of Earth and Mars. Particular attention has also been paid to the numerical stability at typical time steps used in General Circulation Models. Test, parametric sensitivity assessment and preliminary tuning are performed on single-column idealized simulations of the weakly stable boundary layer. The robustness and versatility of the scheme are also assessed through its implementation in the LMDZ General Circulation Model and the Mars Planetary Climate Model and by running simulations of the Antarctic and Martian nocturnal boundary layers.

We demonstrate a new approach for climate model tuning in a realistic situation. Our approach, described in detail in Part I, systematically uses a single-column configuration of a global atmospheric model on a series of test cases for which reference large-eddy-simulations are available. The space of free parameters is sampled running the single-column model from which metrics are estimated in the full parameter space using emulators. The parameter space is then reduced by retaining only the values that are consistent with the metrics computed on large eddy simulations within a given tolerance to error. The approach is applied to the recently designed 6A version of the LMDZ model, itself the result of a long investment in the development of physics parameterizations and by-hand tuning. The boundary layer is revisited by increasing the vertical resolution and varying parameters that were kept fixed so far. The approach allows us to automatically reach a tuning as good as that of the 6A version, after some improvements are done at process scale. This approach helps accelerate the introduction of new parameterizations, by avoiding a tedious manual tuning process and preventing some of the error compensations that could occur if calibration was carried out directly with the full atmospheric model. This way of using machine learning techniques allows us to maintain the physical foundations of the model and to ensure that the improvement of global metrics is obtained for a reasonable behavior at process level. That is, we get things right for the right reasons.

Process-scale development, evaluation and calibration of physically-based parameterizations are key to improve weather and climate models. Cloud–radiation interactions are a central issue because of their major role in global energy balance and climate sensitivity. In a series of papers, we propose papers a strategy for process-based calibration of climate models that uses machine learning techniques. It relies on systematic comparisons of single-column versions of climate models with explicit simulations of boundary-layer clouds (LES). Parts I and II apply this framework to the calibration of boundary layer parameters targeting first boundary layer characteristics and then global radiation balance at the top of the atmosphere. This third part focuses on the calibration of cloud geometry parameters that appear in the parameterization of radiation. The solar component of a radiative transfer scheme (ecRad) is run in offline single-column mode on input cloud profiles synthesized from an ensemble of LES outputs. A recent version of ecRad that includes explicit representation of the effects of cloud geometry and horizontal transport is evaluated and calibrated by comparing radiative metrics to reference values provided by Monte Carlo 3D radiative transfer computations. Errors on TOA, surface and absorbed fluxes estimated by ecRad are computed for an ensemble of cumulus fields. The average root-mean-square error can be less than 5 Wm$^{-2}$ provided that 3D effects are represented and that cloud geometry parameters are well calibrated. A key result is that configurations using calibrated parameters yield better predictions than those using parameter values diagnosed in the LES fields.

The development of parameterizations is a major task in the development of weather and climate models. Model improvement has been slow in the past decades, due to the difficulty of encompassing key physical processes into parameterizations, but also of calibrating or â\euro˜tuningâ\euro™ the many free parameters involved in their formulation. Machine learning techniques have been recently used for speeding up the development process. While some studies propose to replace parameterizations by data-driven neural networks, we rather advocate that keeping physical parameterizations is key for the reliability of climate projections. In this paper we propose to harness machine learning to improve physical parameterizations. In particular we use Gaussian process-based methods from uncertainty quantification to calibrate the model free parameters at a process level. To achieve this, we focus on the comparison of single-column simulations and reference large-eddy simulations over multiple boundary-layer cases. Our method returns all values of the free parameters consistent with the references and any structural uncertainties, allowing a reduced domain of acceptable values to be considered when tuning the 3D global model. This tool allows to disentangle deficiencies due to poor parameter calibration from intrinsic limits rooted in the parameterization formulations. This paper describes the tool and the philosophy of tuning in single-column mode. Part 2 shows how the results from our process-based tuning can help in the 3D global model tuning.