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We present a numerical solver for the incompressible Navier–Stokes equations that combines fourth-order-accurate discrete approximations and an adaptive tree grid (i.e. h-refinement). The scheme employs a novel compact-upwind advection scheme and a 4th-order accurate projection algorithm whereby the numerical solution exactly satisfies the incompressibility constraint. Further, we introduce a new refinement indicator that is tailored to this solver. We show tests and examples to illustrate the consistency, convergence rate and the application for the adaptive solver. The combination of the solver scheme and the proposed grid adaptation algorithm result in fourth-order convergence rates whilst only tuning a single grid-refinement parameter. The speed performance is benchmarked against a well-established second-order accurate adaptive solver alternative. We conclude that the present 4th order solver is an efficient design for problems with strong localization in the spatial-temporal domain and where a high degree of convergence for the solution statistics is desired., Atmospheric Remote Sensing

Despite the importance of forests in the water and carbon cycles, accurately measuring their contribution remains challenging, especially at night. During clear-sky nights current models and theories fail, as non-turbulent flows and spatial heterogeneity become more important. One of the standing issues is the ‘decoupling’ of the air masses in and above the canopy, where little turbulent exchange takes place, thus preventing proper measurement of atmospheric fluxes. Temperature inversions, where lower air is colder and thus more dense, can be both the cause and result of this decoupling. With Distributed Temperature Sensing (DTS) it is now possible to detect these temperature inversions, and increase our understanding of the decoupling mechanism. With DTS we detected strong inversions within the canopy of a tall Douglas Fir stand. The inversions formed in on clear-sky nights with low turbulence, and preferentially formed in the open understory. A second inversion regularly occurred above the canopy. Oscillations in this upper inversion transferred vertically through the canopy and induced oscillations in the lower inversion. We hypothesize that the inversions could form due to a local suppression of turbulent motions along the height of the canopy. This was supported by a 1-D conceptual model, which showed that a local inversion layer would always form within the canopy if the bulk inversion (over the full canopy) was strong enough. Due to the near-continuous vertical motion and specific height the inversions occur at, a very high measurement density (better than ∼2 m) and measurement frequency (>0.1 Hz) are required to detect them. Consequently, it could be possible that the observed inversions are a regular feature in similarly structured forests, but are generally not directly observed. With DTS it is possible to detect and describe these types of features, which will aid in improving our understanding of atmospheric flows over complex terrain such as fores, Atmospheric Remote Sensing, Water Resources

Data-driven quantification and parameterization of cloud physics in general, and of aerosol-cloud interactions in particular, rely on input data from observations or detailed simulations. These data sources have complementary limitations in terms of their spatial and temporal coverage and resolution; simulation data has the advantage of readily providing causality but cannot represent the full process complexity. In order to base data-driven approaches on comprehensive information, we therefore need ways to integrate different data sources. We discuss how the classical statistical technique of Gaussian-process emulation can be combined with specifically initialized ensembles of detailed cloud simulations (large-eddy simulations, LES) to provide a framework for evaluating data-driven descriptions of cloud characteristics and processes across different data sources. We specifically illustrate this approach for integrating LES and satellite data of aerosol-cloud interactions in subtropical stratocumulus cloud decks. We furthermore explore the extension of our framework to ground-based observations of Arctic mixed-phase clouds., Atmospheric Remote Sensing

Mixed-phase clouds play an important role in the Arctic climate system. However, accurate climate projections are seriously hampered due to uncertainties in representing these clouds. Understanding their dynamical behavior based on first principles is a challenging task which requires the disentanglement of mixed-phase micro-physical complexities and a multitude multitude of cloud--surface--boundary layer interactions. Here we take an alternative route towards describing the cloud system and adopt a dynamical-systems perspective. Such an approach has already been successfully applied to describe and model a wide range of complex systems. This research focuses on data obtained at the permanent observatory in Ny-Alesund, Svalbard. We present our results concerning the analysis of distinct signatures of two preferred states. Further, preliminary results on the interdependence of the key variables and their temporal evolution are presented., Atmospheric Remote Sensing

Weather and climate influence life in many ways; varying climatic conditions can be associated with varying human cultures and on a day-to-day basis, the weather influences our plans and mood. As such, a proper prediction of the weather is of great importance. Ultimately, the weather is fueled by solar irradiation, which changes sharply over the course of the day. The relative position of the sun is directly influencingthe meteorological properties in the atmosphere closest to the surface. The atmospheric state in the lowest few kilometers, known as the troposphere, is therefore characterized by a daily cycle: during daytime, the sun heats the air and at night, the atmosphere typically cools down and the wind settles a bit. In spite of its omnipresence and importance, this diurnal cycle in weather patterns is still not fully understood by the meteorological community. Consequently, it is also hard to describe and predict the weather properly. The challenges emerge from the fact that the weather is continuously evolving, and is therefore never ‘in balance’, which would simplify analysis of the processes., Atmospheric Remote Sensing

The scalar front generated by the horizontal self advection of a dipolar vortex through a mod-est scalar gradient is investigated. This physical scenario is an idealization of the emergenceof strong temperature ramps in the stable atmospheric boundary layer. The proposed mecha-nism is discussed and a two-dimensional analogy is studied in depth using direct numericalsimulation. More specifically, the scalar-gradient sharpening is investigated as a function ofthe Reynolds number. It appears that the process of gradient sharpening at large-eddy scalesmay be challenging for turbulence-resolving methods applied to the stable-boundary-layerregime., Atmospheric Remote Sensing

Wind machines are used in the agricultural sector to prevent or mitigate the adverse effects of night frost in spring. In this study we aim to quantify the impact of wind machine operation on the local temperature field in an orchard. To this end, a field experiment is conducted and experimental analysis is combined with numerical simulation studies in order to assess the functional relations between wind machine performance and the dominating physical processes occurring during radiative frost events. Experimental observations showed that the temperature response strongly depends on the radial distance to the fan and the height above the surface. In agreement with previous studies, the wind machine was able to achieve rotation-averaged temperature increases of up to 50% of the inversion strength ( ≈ 3 K) in an area of 3–5 ha at 1 m height. Furthermore, it was observed that even weak ambient winds (<1 m/s) already may cause strong upwind-downwind asymmetries in the protected area, the downwind area being larger. The numerical model, inspired by the field experiment, showed similar spatial temperature responses as compared to observations. Interestingly, it was found that slower rotation times of the wind machine (3 to 6 min) lead to a significant increase of affected area, while the temperature enhancement itself stayed relatively constant. Variation of the horizontal tilt angle showed that, in our model, temperature enhancement was maximized between 8∘ and 16∘. This nearly horizontal flow already facilitates efficient vertical mixing of momentum and heat, presumably due to generation of shear instabilities at the lower edge of the jet. Finally, like in the observations also the numerical result showed strong upwind-downwind asymmetry in the affected area due to background wind., Atmospheric Remote Sensing, Water Resources

We present a conceptual model for the diurnal cycle of the dry atmospheric boundary layer (ABL). It may serve as a framework for future numerical studies on the transitional dynamics that characterize the ABL over land. The conceptual model enables us to define expressions for relevant physical scales as a function of the most prominent forcing parameters and the low degree of complexity facilitates a dimensionless description. This is useful to help generalize boundary layer dynamics that occur on a diurnal time scale. Further, the model’s application for numerical studies is illustrated herein with two examples: a single-column-model study that assesses the effect of wind forcing on the main characteristics of the diurnal cycle, and a large-eddy-simulation study on the daily evolution of turbulence under weak-wind-forcing conditions. The results from these studies sketch the general evolution of the present set of diurnal-cycle systems in more detail. We discuss how the setups are able to reproduce well-known dynamical features of the ABL and also highlight limitations, where the simple conceptual system is unable to describe realistic ABL behavior. We conclude that the present conceptual model has an interesting balance between model-system complexity and physical realism, such that it is useful for future idealized studies on the diurnal cycle of the ABL., Atmospheric Remote Sensing

The Netherlands is characterized by highly variable land use within a small area, and a strong influence of the North Sea on national climate. Devoid of significant topography, it is an excellent location for assessing the relative influence of various factors on fog occurrence in the absence of terrain effects. Using observations from a dense network of weather stations throughout the country, the climatology of fog in the Netherlands is assessed over a period of 45 years. On a national scale, interannual variability is linked to changes in synoptic pressure-gradient forcing. Within the country, a comprehensive in-depth analysis of regional differences between fog occurrence is made, together with an assessment of local physical factors which could bias fog formation in one location over another. Regional variability is shown to be strongly related to the mesoscale influences of urbanization and the North Sea. In fact, some locations experience over twice as much fog as others. From this finding, a simple index is presented, which combines the water and urban fraction surrounding a station. This “Regionally Weighted Index” (RWI) is able to accurately sort the stations according to their relative fogginess. Its practical use is encouraged for assessing a given site's climatological favourability, even when in situ meteorological observations are unavailable., Atmospheric Remote Sensing

The Netherlands is characterized by highly variable land use within a small area, and a strong influence of the North Sea on national climate. Devoid of significant topography, it is an excellent location for assessing the relative influence of various factors on fog occurrence in the absence of terrain effects. Using observations from a dense network of weather stations throughout the country, the climatology of fog in the Netherlands is assessed over a period of 45 years. On a national scale, interannual variability is linked to changes in synoptic pressure-gradient forcing. Within the country, a comprehensive in-depth analysis of regional differences between fog occurrence is made, together with an assessment of local physical factors which could bias fog formation in one location over another. Regional variability is shown to be strongly related to the mesoscale influences of urbanization and the North Sea. In fact, some locations experience over twice as much fog as others. From this finding, a simple index is presented, which combines the water and urban fraction surrounding a station. This “Regionally Weighted Index” (RWI) is able to accurately sort the stations according to their relative fogginess. Its practical use is encouraged for assessing a given site's climatological favourability, even when in situ meteorological observations are unavailable.

It is well known that the representation of certain atmospheric conditions in climate and weather models can still suffer from the limited grid resolution that is facilitated by modern-day computer systems. Herein we study a simple one-dimensional analogy to those models by using a single-column model description of the atmosphere. The model employs an adaptive Cartesian mesh that applies a high-resolution mesh only when and where it is required. The so-called adaptive-grid model is described, and we report our findings obtained for tests to evaluate the representation of the atmospheric boundary layer, based on the first two GEWEX ABL Study (GABLS) inter-comparison cases. The analysis shows that the adaptive-grid algorithm is indeed able to dynamically coarsen and refine the numerical grid whilst maintaining an accurate solution. This is an interesting result as in reality, transitional dynamics (e.g. due to the diurnal cycle or due to changing synoptic conditions) are the rule rather than the exception., Atmospheric Remote Sensing

We present a proof-of-concept for the adaptive mesh refinement method applied to atmospheric boundary-layer simulations. Such a method may form an attractive alternative to static grids for studies on atmospheric flows that have a high degree of scale separation in space and/or time. Examples include the diurnal cycle and a convective boundary layer capped by a strong inversion. For such cases, large-eddy simulations using regular grids often have to rely on a subgrid-scale closure for the most challenging regions in the spatial and/or temporal domain. Here we analyze a flow configuration that describes the growth and subsequent decay of a convective boundary layer using direct numerical simulation (DNS). We validate the obtained results and benchmark the performance of the adaptive solver against two runs using fixed regular grids. It appears that the adaptive-mesh algorithm is able to coarsen and refine the grid dynamically whilst maintaining an accurate solution. In particular, during the initial growth of the convective boundary layer a high resolution is required compared to the subsequent stage of decaying turbulence. More specifically, the number of grid cells varies by two orders of magnitude over the course of the simulation. For this specific DNS case, the adaptive solver was not yet more efficient than the more traditional solver that is dedicated to these types of flows. However, the overall analysis shows that the method has a clear potential for numerical investigations of the most challenging atmospheric cases., Atmospheric Remote Sensing, Atmospheric Physics

We present a proof-of-concept for the adaptive mesh refinement method applied to atmospheric boundary-layer simulations. Such a method may form an attractive alternative to static grids for studies on atmospheric flows that have a high degree of scale separation in space and/or time. Examples include the diurnal cycle and a convective boundary layer capped by a strong inversion. For such cases, large-eddy simulations using regular grids often have to rely on a subgrid-scale closure for the most challenging regions in the spatial and/or temporal domain. Here we analyze a flow configuration that describes the growth and subsequent decay of a convective boundary layer using direct numerical simulation (DNS). We validate the obtained results and benchmark the performance of the adaptive solver against two runs using fixed regular grids. It appears that the adaptive-mesh algorithm is able to coarsen and refine the grid dynamically whilst maintaining an accurate solution. In particular, during the initial growth of the convective boundary layer a high resolution is required compared to the subsequent stage of decaying turbulence. More specifically, the number of grid cells varies by two orders of magnitude over the course of the simulation. For this specific DNS case, the adaptive solver was not yet more efficient than the more traditional solver that is dedicated to these types of flows. However, the overall analysis shows that the method has a clear potential for numerical investigations of the most challenging atmospheric cases.

Geostrophic wind speed data, derived from pressure observations, are used in combination with tower measurements to investigate the nocturnal stable boundary layer at Cabauw, the Netherlands. Since the geostrophic wind speed is not directly influenced by local nocturnal stability, it may be regarded as an external forcing parameter of the nocturnal stable boundary layer. This is in contrast to local parameters such as in situ wind speed, the Monin-Obukhov stability parameter (z/L), or the local Richardson number. To characterize the stable boundary layer, ensemble averages of clear-sky nights with similar geostrophic wind speeds are formed. In this manner, the mean dynamical behavior of near-surface turbulent characteristics and composite profiles of wind and temperature are systematically investigated. The classification is found to result in a gradual ordering of the diagnosed variables in terms of the geostrophic wind speed. In an ensemble sense the transition from the weakly stable to very stable boundary layer is more gradual than expected. Interestingly, for very weak geostrophic winds, turbulent activity is found to be negligibly small while the resulting boundary cooling stays finite. Realistic numerical simulations for those cases should therefore have a comprehensive description of other thermodynamic processes such as soil heat conduction and radiative transfer., Atmospheric Remote Sensing

Geostrophic wind speed data, derived from pressure observations, are used in combination with tower measurements to investigate the nocturnal stable boundary layer at Cabauw (The Netherlands). Since the geostrophic wind speed is not directly influenced by local nocturnal stability, it may be regarded as an external forcing parameter of the nocturnal stable boundary layer. This is in contrast to local parameters such as in situ wind speed, the Monin-Obukhov stability parameter (z/L) or the local Richardson number. To characterize the stable boundary layer, ensemble averages of clear-sky nights with similar geostrophic wind speed are formed. In this manner, the mean dynamical behavior of near-surface turbulent characteristics, and composite profiles of wind and temperature are systematically investigated. We find that the classification results in a gradual ordering of the diagnosed variables in terms of the geostrophic wind speed. In an ensemble sense the transition from the weakly stable to very stable boundary layer is more gradual than expected. Interestingly, for very weak geostrophic winds turbulent activity is found to be negligibly small while the resulting boundary cooling stays finite. Realistic numerical simulations for those cases should therefore have a comprehensive description of other thermodynamic processes such as soil heat conduction and radiative transfer.

A conceptual model is used in combination with observational analysis to understand regime transitions of near-surface temperature inversions at night as well as in Arctic conditions. The model combines a surface energy budget with a bulk parameterization for turbulent heat transport. Energy fluxes or feedbacks due to soil and radiative heat transfer are accounted for by a "lumped parameter closure," which represents the "coupling strength" of the system. Observations from Cabauw, Netherlands, and Dome C, Antarctica, are analyzed. As expected, inversions are weak for strong winds, whereas large inversions are found under weak-wind conditions. However, a sharp transition is found between those regimes, as it occurs within a narrow wind range. This results in a typical S-shaped dependency. The conceptual model explains why this characteristic must be a robust feature. Differences between the Cabauw and Dome C cases are explained from differences in coupling strength (being weaker in the Antarctic). For comparison, a realistic column model is run. As findings are similar to the simple model and the observational analysis, it suggests generality of the results. Theoretical analysis reveals that, in the transition zone near the critical wind speed, the response time of the system to perturbations becomes large. As resilience to perturbations becomes weaker, it may explain why, within this wind regime, an increase of scatter is found. Finally, the so-called heat flux duality paradox is analyzed. It is explained why numerical simulations with prescribed surface fluxes show a dynamical response different from more realistic surface-coupled systems., Atmospheric Remote Sensing, Atmospheric Physics

A conceptual model is used in combination with observational analysis to understand regime transitions of near-surface temperature inversions at night as well as in Arctic conditions. The model combines a surface energy budget with a bulk parameterization for turbulent heat transport. Energy fluxes or feedbacks due to soil and radiative heat transfer are accounted for by a "lumped parameter closure," which represents the "coupling strength" of the system. Observations from Cabauw, Netherlands, and Dome C, Antarctica, are analyzed. As expected, inversions are weak for strong winds, whereas large inversions are found under weak-wind conditions. However, a sharp transition is found between those regimes, as it occurs within a narrow wind range. This results in a typical S-shaped dependency. The conceptual model explains why this characteristic must be a robust feature. Differences between the Cabauw and Dome C cases are explained from differences in coupling strength (being weaker in the Antarctic). For comparison, a realistic column model is run. As findings are similar to the simple model and the observational analysis, it suggests generality of the results. Theoretical analysis reveals that, in the transition zone near the critical wind speed, the response time of the system to perturbations becomes large. As resilience to perturbations becomes weaker, it may explain why, within this wind regime, an increase of scatter is found. Finally, the so-called heat flux duality paradox is analyzed. It is explained why numerical simulations with prescribed surface fluxes show a dynamical response different from more realistic surface-coupled systems.