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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. 

Abstract. Fluxes of nitrogen oxides (NOx=NO+NO2) and carbon dioxide (CO2) were measured using eddy covariance at the British Telecommunications (BT) Tower in central London during the coronavirus pandemic. Comparing fluxes to those measured in 2017 prior to the pandemic restrictions and the introduction of the Ultra-Low Emissions Zone (ULEZ) highlighted a 73 % reduction in NOx emissions between the two periods but only a 20 % reduction in CO2 emissions and a 32 % reduction in traffic load. Use of a footprint model and the London Atmospheric Emissions Inventory (LAEI) identified transport and heat and power generation to be the two dominant sources of NOx and CO2 but with significantly different relative contributions for each species. Application of external constraints on NOx and CO2 emissions allowed the reductions in the different sources to be untangled, identifying that transport NOx emissions had reduced by >73 % since 2017. This was attributed in part to the success of air quality policy in central London but crucially due to the substantial reduction in congestion that resulted from pandemic-reduced mobility. Spatial mapping of the fluxes suggests that central London was dominated by point source heat and power generation emissions during the period of reduced mobility. This will have important implications on future air quality policy for NO2 which, until now, has been primarily focused on the emissions from diesel exhausts. 

The Cahn–Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic boundary conditions for the Cahn–Hilliard equation have been proposed and investigated in recent times. Of particular interests are the model by Goldstein et al . [ Phys. D 240 (2011) 754–766] and the model by Liu and Wu [ Arch. Ration. Mech. Anal. 233 (2019) 167–247]. Both of these models satisfy similar physical properties but differ greatly in their mass conservation behaviour. In this paper we introduce a new model which interpolates between these previous models, and investigate analytical properties such as the existence of unique solutions and convergence to the previous models mentioned above in both the weak and the strong sense. For the strong convergences we also establish rates in terms of the interpolation parameter, which are supported by numerical simulations obtained from a fully discrete, unconditionally stable and convergent finite element scheme for the new interpolation model. 

Nature-based Climate Solutions (NbCS) are managed alterations to ecosystems designed to increase carbon sequestration or reduce greenhouse gas emissions. While they have growing public and private support, the realizable benefits and unintended consequences of NbCS are not well understood. At regional scales where policy decisions are often made, NbCS benefits are estimated from soil and tree survey data that can miss important carbon sources and sinks within an ecosystem, and do not reveal the biophysical impacts of NbCS for local water and energy cycles. The only direct observations of ecosystem-scale carbon fluxes, e.g., by eddy covariance flux towers, have not yet been systematically assessed for what they can tell us about NbCS potentials, and state-of-the-art remote sensing products and land-surface models are not yet being widely used to inform NbCS policy making or implementation. As a result, there is a critical mismatch between the point- and tree- scale data most often used to assess NbCS benefits and impacts, the ecosystem and landscape scales where NbCS projects are implemented, and the regional to continental scales most relevant to policy making. Here, we propose a research agenda to confront these gaps using data and tools that have long been used to understand the mechanisms driving ecosystem carbon and energy cycling, but have not yet been widely applied to NbCS. We outline steps for creating robust NbCS assessments at both local to regional scales that are informed by ecosystem-scale observations, and which consider concurrent biophysical impacts, future climate feedbacks, and the need for equitable and inclusive NbCS implementation strategies. We contend that these research goals can largely be accomplished by shifting the scales at which pre-existing tools are applied and blended together, although we also highlight some opportunities for more radical shifts in approach. 

Abstract. During March–June 2017 emissions of nitrogen oxides were measured via eddy covariance at the British Telecom Tower in central London, UK. Through the use of a footprint model the expected emissions were simulated from the spatially resolved National Atmospheric Emissions Inventory for 2017 and compared with the measured emissions. These simulated emissions were shown to underestimate measured emissions during the daytime by a factor of 1.48, but they agreed well overnight. Furthermore, underestimations were spatially mapped, and the areas around the measurement site responsible for differences in measured and simulated emissions were inferred. It was observed that areas of higher traffic, such as major roads near national rail stations, showed the greatest underestimation by the simulated emissions. These discrepancies are partially attributed to a combination of the inventory not fully capturing traffic conditions in central London and both the spatial and temporal resolution of the inventory not fully describing the high heterogeneity of the urban centre. Understanding of this underestimation may be further improved with longer measurement time series to better understand temporal variation and improved temporal scaling factors to better simulate sub-annual emissions.