There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We upscaled FLUXNET observations of carbon dioxide, water, and energy fluxes to the global scale using the machine learning technique, model tree ensembles (MTE). We trained MTE to predict site-level gross primary productivity (GPP), terrestrial ecosystem respiration (TER), net ecosystem exchange (NEE), latent energy (LE), and sensible heat (H) based on remote sensing indices, climate and meteorological data, and information on land use. We applied the trained MTEs to generate global flux fields at a 0.5 degrees x 0.5 degrees spatial resolution and a monthly temporal resolution from 1982 to 2008. Cross-validation analyses revealed good performance of MTE in predicting among-site flux variability with modeling efficiencies (MEf) between 0.64 and 0.84, except for NEE (MEf = 0.32). Performance was also good for predicting seasonal patterns (MEf between 0.84 and 0.89, except for NEE (0.64)). By comparison, predictions of monthly anomalies were not as strong (MEf between 0.29 and 0.52). Improved accounting of disturbance and lagged environmental effects, along with improved characterization of errors in the training data set, would contribute most to further reducing uncertainties. Our global estimates of LE (158 +/- 7 J x 10(18) yr(-1)), H (164 +/- 15 J x 10(18) yr(-1)), and GPP (119 +/- 6 Pg C yr(-1)) were similar to independent estimates. Our global TER estimate (96 +/- 6 Pg C yr(-1)) was likely underestimated by 5-10%. Hot spot regions of interannual variability in carbon fluxes occurred in semiarid to semihumid regions and were controlled by moisture supply. Overall, GPP was more important to interannual variability in NEE than TER. Our empirically derived fluxes may be used for calibration and evaluation of land surface process models and for exploratory and diagnostic assessments of the biosphere.

Global patterns of land-atmosphere fluxes of carbon dioxide, latent heat, and sensible heat derived from eddy covariance, satellite, and meteorological observations

. Flux footprint models are often used for interpretation of flux tower measurements, to estimate position and size of surface source areas, and the relative contribution of passive scalar sources to measured fluxes. Accurate knowledge of footprints is of crucial importance for any upscaling exercises from single site flux measurements to local or regional scale. Hence, footprint models are ultimately also of considerable importance for improved greenhouse gas budgeting. With increasing numbers of flux towers within large monitoring networks such as FluxNet, ICOS (Integrated Carbon Observation System), NEON (National Ecological Observatory Network), or AmeriFlux, and with increasing temporal range of observations from such towers (of the order of decades) and availability of airborne flux measurements, there has been an increasing demand for reliable footprint estimation. Even though several sophisticated footprint models have been developed in recent years, most are still not suitable for application to long time series, due to their high computational demands. Existing fast footprint models, on the other hand, are based on surface layer theory and hence are of restricted validity for real-case applications. To remedy such shortcomings, we present the two-dimensional parameterisation for Flux Footprint Prediction (FFP), based on a novel scaling approach for the crosswind distribution of the flux footprint and on an improved version of the footprint parameterisation of Kljun et al. (2004b). Compared to the latter, FFP now provides not only the extent but also the width and shape of footprint estimates, and explicit consideration of the effects of the surface roughness length. The footprint parameterisation has been developed and evaluated using simulations of the backward Lagrangian stochastic particle dispersion model LPDM-B (Kljun et al., 2002). Like LPDM-B, the parameterisation is valid for a broad range of boundary layer conditions and measurement heights over the entire planetary boundary layer. Thus, it can provide footprint estimates for a wide range of real-case applications. The new footprint parameterisation requires input that can be easily determined from, for example, flux tower measurements or airborne flux data. FFP can be applied to data of long-term monitoring programmes as well as be used for quick footprint estimates in the field, or for designing new sites.

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A simple two-dimensional parameterisation for Flux Footprint Prediction (FFP)

. With the eddy covariance (EC) technique, net fluxes of carbon dioxide (CO2) and other trace gases as well as water and energy fluxes can be measured at the ecosystem level. These flux measurements are a main source for understanding biosphere–atmosphere interactions and feedbacks through cross-site analysis, model–data integration, and upscaling. The raw fluxes measured with the EC technique require extensive and laborious data processing. While there are standard tools1 available in an open-source environment for processing high-frequency (10 or 20 Hz) data into half-hourly quality-checked fluxes, there is a need for more usable and extensible tools for the subsequent post-processing steps. We tackled this need by developing the REddyProc  package in the cross-platform language R that provides standard CO2-focused post-processing routines for reading (half-)hourly data from different formats, estimating the u* threshold, as well as gap-filling, flux-partitioning, and visualizing the results. In addition to basic processing, the functions are extensible and allow easier integration in extended analysis than current tools. New features include cross-year processing and a better treatment of uncertainties. A comparison of REddyProc  routines with other state-of-the-art tools resulted in no significant differences in monthly and annual fluxes across sites. Lower uncertainty estimates of both u* and resulting gap-filled fluxes by 50 % with the presented tool were achieved by an improved treatment of seasons during the bootstrap analysis. Higher estimates of uncertainty in daytime partitioning (about twice as high) resulted from a better accounting for the uncertainty in estimates of temperature sensitivity of respiration. The provided routines can be easily installed, configured, and used. Hence, the eddy covariance community will benefit from the REddyProc  package, allowing easier integration of standard post-processing with extended analysis. 1 http://fluxnet.fluxdata.org/2017/10/10/toolbox-a-rolling-list-of-softwarepackages-for-flux-related-data-processing/ , last access: 17 August 2018

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Basic and extensible post-processing of eddy covariance flux data with REddyProc

The magnitude and evolution of parameters that characterize feedbacks in the coupled carbon–climate system are compared across nine Earth system models (ESMs). The analysis is based on results from biogeochemically, radiatively, and fully coupled simulations in which CO2 increases at a rate of 1% yr−1. These simulations are part of phase 5 of the Coupled Model Intercomparison Project (CMIP5). The CO2 fluxes between the atmosphere and underlying land and ocean respond to changes in atmospheric CO2 concentration and to changes in temperature and other climate variables. The carbon–concentration and carbon–climate feedback parameters characterize the response of the CO2 flux between the atmosphere and the underlying surface to these changes. Feedback parameters are calculated using two different approaches. The two approaches are equivalent and either may be used to calculate the contribution of the feedback terms to diagnosed cumulative emissions. The contribution of carbon–concentration feedback to...

Carbon-concentration and carbon-climate feedbacks in CMIP5 Earth system models

Mapping surface-atmosphere exchange by using environmental response function for both turbulent and storage eddy-covariance fluxes

The Earth's surface is heterogeneous at multiple scales owing to spatial variability in various properties. The atmospheric responses to these heterogeneities through fluxes of energy, water, carbon, and other scalars are scale‐dependent and nonlinear. Although these exchanges can be measured using the eddy covariance technique, widely used tower‐based measurement approaches suffer from spectral losses in lower frequencies when using typical averaging times. However, spatially resolved measurements such as airborne eddy covariance measurements can detect such larger scale (meso‐β, meso‐γ) transport. To evaluate the prevalence and magnitude of these flux contributions, we applied wavelet analysis to airborne flux measurements over a heterogeneous mid‐latitude forested landscape, interspersed with open water bodies and wetlands. The measurements were made during the Chequamegon Heterogeneous Ecosystem Energy‐balance Study Enabled by a High‐density Extensive Array of Detectors intensive field campaign. We ask, how do spatial scales of surface‐atmosphere fluxes vary over heterogeneous surfaces across the day and across seasons? Measured fluxes were separated into smaller‐scale turbulent and larger‐scale mesoscale contributions. We found significant mesoscale contributions to sensible and latent heat fluxes through summer to autumn which would not be resolved in single‐point tower measurements through traditional time‐domain half‐hourly Reynolds decomposition. We report scale‐resolved flux transitions associated with seasonal and diurnal changes of the heterogeneous study domain. This study adds to our understanding of surface‐atmospheric interactions over unstructured heterogeneities and can help inform multi‐scale model‐data integration of weather and climate models at a sub‐grid scale.

Space‐Scale Resolved Surface Fluxes Across a Heterogeneous, Mid‐Latitude Forested Landscape

Mapping the flux field around eddy-covariance measurements

Arctic permafrost-associated wetlands and thawing permafrost emit the greenhouse gas methane (CH4), either as a product of recent microbial activity in the active layer or taliks, or from deeper geogenic sources where pathways through the permafrost exist. Current emission estimates vary strongly between different models and there is still disagreement between bottom-up estimates from local field studies and top-down estimates from atmospheric measurements. We use airborne flux data from two campaigns in the Mackenzie River Delta, Canada, in July 2012 and 2013 to directly quantify permafrost CH4 emissions on the regional scale, to analyse the regional pattern of CH4 fluxes and to estimate the contribution of geogenic emissions to the overall CH4 budget of the delta. CH4 fluxes were calculated with a time-frequency resolved version of the eddy covariance technique, resulting in a gridded 100 m x 100 m resolution flux map within the footprints of the flight tracks. We distinguish geogenic gas seeps from biogenic sources by their strength and show that they contribute strongly to the annual CH4 budget of the delta. Our study provides the first estimate of annual CH4 release from the Mackenzie River Delta and the adjacent coastal plain. We show that one percent of the covered area contains the strongest geogenic seeps which contribute disproportionately to the annual emission estimate. Our results show that geogenic CH4 emissions might need more attention, especially in areas where permafrost is vulnerable to thawing sufficiently to create pathways for geogenic gas migration. The presented map can be used as a baseline for future CH4 flux studies in the Mackenzie River Delta.

Stefan Metzger

Papers

Mapping surface-atmosphere exchange by using environmental response function for both turbulent and storage eddy-covariance fluxes

Space‐Scale Resolved Surface Fluxes Across a Heterogeneous, Mid‐Latitude Forested Landscape

Mapping the flux field around eddy-covariance measurements

Geogenic Sources Strongly Contribute to the Mackenzie River Delta’s Methane Emissions Derived From Airborne Flux Data

How many flux towers are enough? Energy balance closure and large eddy simulation as diagnostic tools for secondary circulations