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We investigate how effective surface length scales (Le f f ) and atmospheric boundary layer stability modulate surface-induced secondary circulations over a realistic heterogeneous sur- face. The evolution of the circulations and their impact on surface-atmosphere fluxes are studied using coupled large eddy simulations of the CHEESEHEAD19 field campaign. The heterogeneity-induced circulations were diagnosed using time and ensemble averaging of the atmospheric fields. Simulations were performed for summer (August) and autumn (Septem- ber) Intensive Observation Periods of the field campaign, characterised differently in terms of normalised surface length scales and ABL stability. Quasi-stationary and persistent cir- culations were diagnosed in the daytime ABL that span the entire mixed layer height (zi ). Their variation in time and space are presented. Homogeneous control runs were also per- formed to compare and contrast spatial organisation and validate the time-ensemble averaging operation. In the convective boundary layers simulated during the summer time simulations, wavelengths that scale as the effective surface heterogeneity length scales contribute the most to the heterogeneity-induced transport. Contributions from surface-induced circulations were lower in the simulated near-neutral BL for the autumn simulations. We find that both Le f f /zi and ABL static stability control the relative contribution of surface-induced circulations to the area averaged vertical transport. This scale analysis supports prior work over the study domain on scaling tower measured fluxes by including low frequency contribution. We believe that the conceptual framework presented here can be extended to include the effects of sub-grid land surface heterogeneity in numerical weather prediction and climate models and also to further explore scale-aware scaling methodologies for near surface-atmosphere exchanges. 

Abstract In the last decades the energy-balance-closure problem has been thoroughly investigated from different angles, resulting in approaches to reduce but not completely close the surface energy balance gap. Energy transport through secondary circulations has been identified as a major cause of the remaining energy imbalance, as it is not captured by eddy covariance measurements and can only be measured additionally with great effort. Several models have already been developed to close the energy balance gap that account for factors affecting the magnitude of the energy transport by secondary circulations. However, to our knowledge, there is currently no model that accounts for thermal surface heterogeneity and that can predict the transport of both sensible and latent energy. Using a machine-learning approach, we developed a new model of energy transport by secondary circulations based on a large data set of idealized large-eddy simulations covering a wide range of unstable atmospheric conditions and surface-heterogeneity scales. In this paper, we present the development of the model and show first results of the application on more realistic LES data and field measurements from the CHEESEHEAD19 project to get an impression of the performance of the model and how the application can be implemented on field measurements. A strength of the model is that it can be applied without additional measurements and, thus, can retroactively be applied to other eddy covariance measurements to model energy transport through secondary circulations. Our work provides a promising mechanistic energy balance closure approach to 30-min flux measurements. 

Abstract. Long-term tall-tower eddy-covariance (EC) measurements have been recently established in three European pilot cities as part of the ICOS-Cities project. We conducted a comparison of EC software to ensure a reliable generation of interoperable flux estimates, which is the prerequisite for avoiding methodological biases and improving the comparability of the results. We analyzed datasets covering 5 months collected from EC tall-tower installations located in urbanized areas of Munich, Zurich, and Paris. Fluxes of sensible heat, latent heat, and CO2 were calculated using three software packages (i.e., TK3, EddyPro, and eddy4R) to assess the uncertainty of flux estimations attributed to differences in implemented postprocessing schemes. A very good agreement on the mean values and standard deviations was found across all three sites, which can probably be attributed to a uniform instrumentation, data acquisition, and preprocessing. The overall comparison of final flux time series products showed a good but not yet perfect agreement among the three software packages. TK3 and EddyPro both calculated fluxes with low-frequency spectral correction, resulting in better agreement than between TK3 and the eddy4R workflow with disabled low-frequency spectral treatment. These observed flux discrepancies indicate the crucial role of treating low-frequency spectral loss in flux estimation for tall-tower EC systems. 

Single point eddy covariance measurements of the Earth’s surface energy budget frequently identify an imbalance between available energy and turbulent heat fluxes. While this imbalance lacks a definitive explanation, it is nevertheless a persistent finding from single-site measurements; one with implications for atmospheric and ecosystem models. This has led to a push for intensive field campaigns with temporally and spatially distributed sensors to help identify the causes of energy balance non-closure. Here we present results from the Chequamegon Heterogeneous Ecosystem Energy-balance Study Enabled by a High-density Extensive Array of Detectors 2019 (CHEESEHEAD19)—an observational experiment designed to investigate how the Earth’s surface energy budget responds to scales of surface spatial heterogeneity over a forest ecosystem in northern Wisconsin. The campaign was conducted from June–October 2019, measuring eddy covariance (EC) surface energy fluxes using an array of 20 towers and a low-flying aircraft. Across the domain, energy balance residuals were found to be highest during the afternoon, coinciding with the period of surface heterogeneity-driven mesoscale motions. The magnitude of the residual varied across different sites in relation to the vegetation characteristics of each site. Both vegetation height and height variability showed positive relationships with the residual magnitude. During the seasonal transition from latent heat-dominated summer to sensible heat-dominated fall the magnitude of the energy balance residual steadily decreased, but the energy balance ratio remained constant at 0.8. This was due to the different components of the energy balance equation shifting proportionally, suggesting a common cause of non-closure across the two seasons. Additionally, we tested the effectiveness of measuring energy balance using spatial EC. Spatial EC, whereby the covariance is calculated based on deviations from spatial means, has been proposed as a potential way to reduce energy balance residuals by incorporating contributions from mesoscale motions better than single-site, temporal EC. Here we tested several variations of spatial EC with the CHEESEHEAD19 dataset but found little to no improvement to energy balance closure, which we attribute in part to the challenging measurement requirements of spatial EC. 

Data from the Idealized Planar-Array experiment for Quantifying Spatial heterogeneity are used to perform a control volume analysis (400 × 400 × × 2 m^3) on the total derivative of the temperature tendency equation. Analysis of the heat-flux imbalance, which is defined as the ratio of the sum of advective, dispersive, and turbulence-flux terms to the turbulence-flux term, are presented. Results are divided amongst free-convective and forced-convective days, as well as high-wind-speed and quiescent nocturnal periods. Findings show that the median flux imbalance is greater on forced-convective days (a 168% turbulence-flux overestimation, or relative importance of the advection to dispersive flux to the turbulence flux) when compared to free-convective periods (79% turbulence-flux overestimation). During nocturnal periods, a median turbulence-flux underestimation of 146% exists for quiescent nights and a 43% underestimation of the flux for high-wind-speed nights. These results support the existing literature, suggesting that mean air-temperature heterogeneities lead to strong bulk advection and dispersive fluxes. A discussion of the impact of the flux imbalance on the surface energy balance and numerical-weather-prediction modelling is presented. 

Abstract Large-eddy simulations (LES) are an important tool for investigating the longstanding energy-balance-closure problem, as they provide continuous, spatially-distributed information about turbulent flow at a high temporal resolution. Former LES studies reproduced an energy-balance gap similar to the observations in the field typically amounting to 10–30% for heights on the order of 100 m in convective boundary layers even above homogeneous surfaces. The underestimation is caused by dispersive fluxes associated with large-scale turbulent organized structures that are not captured by single-tower measurements. However, the gap typically vanishes near the surface, i.e. at typical eddy-covariance measurement heights below 20 m, contrary to the findings from field measurements. In this study, we aim to find a LES set-up that can represent the correct magnitude of the energy-balance gap close to the surface. Therefore, we use a nested two-way coupled LES, with a fine grid that allows us to resolve fluxes and atmospheric structures at typical eddy-covariance measurement heights of 20 m. Under different stability regimes we compare three different options for lower boundary conditions featuring grassland and forest surfaces, i.e. (1) prescribed surface fluxes, (2) a land-surface model, and (3) a land-surface model in combination with a resolved canopy. We show that the use of prescribed surface fluxes and a land-surface model yields similar dispersive heat fluxes that are very small near the vegetation top for both grassland and forest surfaces. However, with the resolved forest canopy, dispersive heat fluxes are clearly larger, which we explain by a clear impact of the resolved canopy on the relationship between variance and flux–variance similarity functions. 

Abstract. The observing system design of multidisciplinary fieldmeasurements involves a variety of considerations on logistics, safety, andscience objectives. Typically, this is done based on investigator intuitionand designs of prior field measurements. However, there is potential forconsiderable increases in efficiency, safety, and scientific success byintegrating numerical simulations in the design process. Here, we present anovel numerical simulation–environmental response function (NS–ERF)approach to observing system simulation experiments that aidssurface–atmosphere synthesis at the interface of mesoscale and microscalemeteorology. In a case study we demonstrate application of the NS–ERFapproach to optimize the Chequamegon Heterogeneous Ecosystem Energy-balanceStudy Enabled by a High-density Extensive Array of Detectors 2019(CHEESEHEAD19). During CHEESEHEAD19 pre-field simulation experiments, we considered theplacement of 20 eddy covariance flux towers, operations for 72 h oflow-altitude flux aircraft measurements, and integration of various remotesensing data products. A 2 h high-resolution large eddy simulationcreated a cloud-free virtual atmosphere for surface and meteorologicalconditions characteristic of the field campaign domain and period. Toexplore two specific design hypotheses we super-sampled this virtualatmosphere as observed by 13 different yet simultaneous observing systemdesigns consisting of virtual ground, airborne, and satellite observations.We then analyzed these virtual observations through ERFs to yield an optimalaircraft flight strategy for augmenting a stratified random flux towernetwork in combination with satellite retrievals. We demonstrate how the novel NS–ERF approach doubled CHEESEHEAD19'spotential to explore energy balance closure and spatial patterning scienceobjectives while substantially simplifying logistics. Owing to its modularextensibility, NS–ERF lends itself to optimizing observing system designs alsofor natural climate solutions, emission inventory validation, urban airquality, industry leak detection, and multi-species applications, among otheruse cases.