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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. 

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 The water vapor transport associated with latent heat flux (LE) in the planetary boundary layer (PBL) is critical for the atmospheric hydrological cycle, radiation balance, and cloud formation. The spatiotemporal variability of LE and water vapor mixing ratio (r_v) are poorly understood due to the scale‐dependent and nonlinear atmospheric transport responses to land surface heterogeneity. Here, airborne in situ measurements with the wavelet technique are utilized to investigate scale‐dependent relationships among LE, vertical velocity (w) variance (), andr_vvariance () over a heterogeneous surface during the Chequamegon Heterogeneous Ecosystem Energy‐balance Study Enabled by a High‐density Extensive Array of Detectors 2019 (CHEESEHEAD19) field campaign. Our findings reveal distinct scale distributions of LE, , and at 100 m height, with a majority scale range of 120 m–4 km in LE, 32 m–2 km in , and 200 m–8 km in . The scales are classified into three scale ranges, the turbulent scale (8–200 m), large‐eddy scale (200 m–2 km), and mesoscale (2–8 km) to evaluate scale‐resolved LE contributed by and . The large‐eddy scale in PBL contributes over 70% of the monthly mean total LE with equal parts (50%) of contributions from and . The monthly temporal variations mainly come from the first two major contributing classified scales in LE, , and . These results confirm the dominant role of the large‐eddy scale in the PBL in the vertical moisture transport from the surface to the PBL, while the mesoscale is shown to contribute an additional ∼20%. This analysis complements published scale‐dependent LE variations, which lack detailed scale‐dependent vertical velocity and moisture information. 

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. 

The Chequamegon Heterogeneous Ecosystem Energy-Balance Study Enabled by a High-Density Extensive Array of Detectors 2019 (CHEESEHEAD19) is an ongoing National Science Foundation project based on an intensive field campaign that occurred from June to October 2019. The purpose of the study is to examine how the atmospheric boundary layer (ABL) responds to spatial heterogeneity in surface energy fluxes. One of the main objectives is to test whether lack of energy balance closure measured by eddy covariance (EC) towers is related to mesoscale atmospheric processes. Finally, the project evaluates data-driven methods for scaling surface energy fluxes, with the aim to improve model–data comparison and integration. To address these questions, an extensive suite of ground, tower, profiling, and airborne instrumentation was deployed over a 10 km × 10 km domain of a heterogeneous forest ecosystem in the Chequamegon–Nicolet National Forest in northern Wisconsin, United States, centered on an existing 447-m tower that anchors an AmeriFlux/NOAA supersite (US-PFa/WLEF). The project deployed one of the world’s highest-density networks of above-canopy EC measurements of surface energy fluxes. This tower EC network was coupled with spatial measurements of EC fluxes from aircraft; maps of leaf and canopy properties derived from airborne spectroscopy, ground-based measurements of plant productivity, phenology, and physiology; and atmospheric profiles of wind, water vapor, and temperature using radar, sodar, lidar, microwave radiometers, infrared interferometers, and radiosondes. These observations are being used with large-eddy simulation and scaling experiments to better understand submesoscale processes and improve formulations of subgrid-scale processes in numerical weather and climate models. 

Abstract Surface‐atmosphere fluxes and their drivers vary across space and time. A growing area of interest is in downscaling, localizing, and/or resolving sub‐grid scale energy, water, and carbon fluxes and drivers. Existing downscaling methods require inputs of land surface properties at relatively high spatial (e.g., sub‐kilometer) and temporal (e.g., hourly) resolutions, but many observed land surface drivers are not continuously available at these resolutions. We evaluate an approach to overcome this challenge for land surface temperature (LST), a World Meteorological Organization Essential Climate Variable and a key driver for surface heat fluxes. The Chequamegon Heterogenous Ecosystem Energy‐balance Study Enabled by a High‐density Extensive Array of Detectors (CHEESEHEAD19) field experiment provided a scalable testbed. We downscaled LST from satellites (GOES‐16 and ECOsystem Spaceborne Thermal Radiometer Experiment on Space Station [ECOSTRESS]) with further refinement using airborne hyperspectral imagery. Temporally and spatially downscaled LST compared well to independent observations from a network of 20 micrometeorological towers and piloted aircrafts in addition to Landsat‐based LST retrieval and drone‐based LST observed at one tower site. The downscaled 50‐m hourly LST showed good relationships with tower (r² = 0.79, RMSE = 3.5 K) and airborne (r² = 0.75, RMSE = 2.4 K) observations over space and time, with precision lower over wetlands and lakes, and some improvement for capturing spatio‐temporal variation compared to a geostationary satellite. Further downscaling to 10 m using hyperspectral imagery resolved hot and cold spots across the landscape as evidenced by independent drone LST, with significant reduction in RMSE by 1.3 K. These results demonstrate a simple pathway for multi‐sensor retrieval of high space and time resolution LST.