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.

Representative parameters of the scan geometry are empirically determined for the Global Precipitation Measurement (GPM) Microwave Imager (GMI). Effective fields of view (EFOVs) are computed for the GMI's 13 channels, taking into account the blurring effect of the measurement interval on the instantaneous fields of view (IFOVs). Using a Backus–Gilbert procedure, coefficients are derived that yield an approximate spatial match between synthetic EFOVs of different channels, using the 18.7 GHz channels as a target and with due consideration of the tradeoff between the quality of the fit and noise amplification and edge effects. Modest improvement in resolution is achieved for the 10.65 GHz channels, albeit with slight ringing in the vicinity of coastlines and other sharp brightness temperature gradients. For all other channels, resolution is coarsened to approximate the 18.7 GHz EFOV. It is shown that the resolution matching procedure reduces nonlinear correlations between channels in the presence of coastlines as well as enables the more efficient separation of large brightness temperature variations due to coastlines from the much smaller variations due to other geophysical variables. As a byproduct of this work, we report accurate EFOV resolutions as well as a self-consistent set of parameters for modeling the scan geometry of the GMI.

Shannon entropy has long been accepted as a primary basis for assessing the information content of sensor channels used for the remote sensing of atmospheric variables. It is not widely appreciated, however, that Shannon information content (SIC) can be misleading in retrieval problems involving nonlinear mappings between direct observations and retrieved variables and/or non-Gaussian prior and posterior PDFs. The potentially severe shortcomings of SIC are illustrated with simple experiments that reveal, for example, that a measurement can be judged to provide negative information even in cases in which the postretrieval PDF is undeniably improved over an informed prior based on climatology. Following previous authors’ writing mainly in the data assimilation and climate analysis literature, the Kullback–Leibler (KL) divergence, also commonly known as relative entropy, is shown to suffer from fewer obvious defects in this particular context. Yet, even KL divergence is blind to the expected magnitude of errors as typically measured by the error variance or root-mean-square error. Thus, neither information metric can necessarily be counted on to respond in a predictable way to changes in the precision or quality of a retrieved quantity.

An idealized synthetic database loosely resembling 3-channel passive microwave observations of precipitation against a variable background is employed to examine the performance of a conventional Bayesian retrieval algorithm. For this dataset, algorithm performance is found to be poor owing to an irreconcilable conflict between the need to find matches in the dependent database versus the need to exclude inappropriate matches. It is argued that the likelihood of such conflicts increases sharply with the dimensionality of the observation space of real satellite sensors, which may utilize 9 to 13 channels to retrieve precipitation, for example. An objective method is described for distilling the relevant information content from N real channels into a much smaller number (M) of pseudochannels while also regularizing the background (geophysical plus instrument) noise component. The pseudochannels are linear combinations of the original N channels obtained via a two-stage principal component analysis of the dependent dataset. Bayesian retrievals based on a single pseudochannel applied to the independent dataset yield striking improvements in overall performance. The differences between the conventional Bayesian retrieval and reduced-dimensional Bayesian retrieval suggest that a major potential problem with conventional multichannel retrievals – whether Bayesian or not – lies in the common but often inappropriate assumption of diagonal error covariance. The dimensional reduction technique described herein avoids this problem by, in effect, recasting the retrieval problem in a coordinate system in which the desired covariance is lower-dimensional, diagonal, and unit magnitude.

A high-resolution (1.25 m) large eddy simulation (LES) of the nocturnal cloud-topped marine boundary layer is used to evaluate random error as a function of continuous track length L for virtual aircraft measurements of turbulent fluxes of sensible heat, latent heat, and horizontal momentum. Results are compared with the widely used formula of Lenschow and Stankov (1986). In support of these comparisons, the relevant integral length scales and correlations are evaluated and documented. It is shown that for heights up to approximately 100 m ($z/z_i=\mathrm{0.12}$ ), the length scales are accurately predicted by empirical expressions of the form I_f=Az^b. The Lenschow and Stankov expression is found to be remarkably accurate at predicting the random error for shorter (7–10 km) flight tracks, but the empirically determined errors decay more rapidly with L than the $L^{-\mathrm{1}/\mathrm{2}}$ relationship predicted from theory. Consistent with earlier findings, required track lengths to obtain useful precision increase sharply with altitude. In addition, an examination is undertaken of the role of uncertainties in empirically determined integral length scales and correlations in flux uncertainties as well as of the flux errors associated with crosswind and along-wind flight tracks. It is found that for 7.2 km flight tracks, flux errors are improved by factor of approximately 1.5 to 2 for most variables by making measurements in the crosswind direction.