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NASA NTRS2020

Uncertainties in CERES Top-of-Atmosphere Fluxes Caused by Changes in Accompanying Imager

The Clouds and the Earth’s Radiant Energy System (CERES) project provides observations of Earth’s radiation budget using measurements from CERES instruments on board the Terra, Aqua, Suomi National Polar-orbiting Partnership (S-NPP), and NOAA-20 satellites. The CERES top-of-atmosphere (TOA) fluxes are produced by converting radiance measurements using empirical angular distribution models, which are functions of cloud properties that are retrieved from imagers flying with the CERES instruments. As the objective is to create a long-term climate data record, not only calibration consistency of the six CERES instruments needs to be maintained for the entire time period, it is also important to maintain the consistency of other input data sets used to produce this climate data record. In this paper, we address aspects that could potentially affect the CERES TOA flux data quality. Discontinuities in imager calibration can affect cloud retrieval which can lead to erroneous flux trends. When imposing an artificial 0.6 per decade decreasing trend to cloud optical depth, which is similar to the trend difference between CERES Edition 2 and Edition 4 cloud retrievals, the decadal SW flux trend changed from −0.3 5 ± 0.18 Wm −2 to 0.61 ± 0.18 Wm −2 . This indicates that a 13% change in cloud optical depth results in about 1% change in the SW flux. Furthermore, different CERES instruments provide valid fluxes at different viewing zenith angle ranges, and including fluxes derived at the most oblique angels unique to S-NPP (>66 ∘ ) can lead to differences of 0.8 Wm −2 and 0.3 Wm −2 in global monthly mean instantaneous SW flux and LW flux. To ensure continuity, the viewing zenith angle ranges common to all CERES instruments (<66 ∘ ) are used to produce the long-term Earth’s radiation budget climate data record. The consistency of cloud properties retrieved from different imagers also needs to be maintained to ensure the TOA flux consistency.

Wenying Su↗

NASA NTRS2020

Attribution of Chemistry-Climate Model Initiative (CCMI) Ozone Radiative Flux Bias from Satellites

The top-of-atmosphere (TOA) outgoing longwave flux over the 9.6-μm ozone band is a fundamental quantity for understanding chemistry-climate coupling. However, observed TOA fluxes are hard to estimate as they exhibit considerable variability in space and time that depend on the distributions of clouds, ozone (O3), water vapor (H2O), air temperature (Ta), and surface temperature (Ts). Benchmarking present day fluxes and quantifying the relative influence of their drivers is the first step for estimating climate feedbacks from ozone radiative forcing and predicting radiative forcing evolution. To that end, we constructed observational instantaneous radiative kernels (IRKs) under clear-sky conditions, representing the sensitivities of the TOA flux in the 9.6-μm ozone band to the vertical distribution of geophysical variables, including O3, H2O, Ta, and Ts based upon the Aura Tropospheric Emission Spectrometer (TES) measurements. Applying these kernels to present-day simulations from the Chemistry-Climate Model Initiative (CCMI) project as compared to a 2006 reanalysis assimilating satellite observations, we show that the models have large differences in TOA flux, attributable to different geophysical variables. In particular, model simulations continue to diverge from observations in the tropics, as reported in previous studies of the Atmospheric Chemistry Climate Model Inter-comparison Project (ACCMIP) simulations. The principal culprits are tropical mid and upper tropospheric ozone followed by tropical lower tropospheric H2O. Five models out of the eight studied here have TOA flux biases exceeding 100 mWm-2 attributable to tropospheric ozone bias. Another set of five models have flux biases over 50 mWm-2 due to H2O. On the other hand, Ta radiative bias is negligible in all models (no more than 30 mWm-2). We found that AM3 and CMAM have the lowest TOA flux biases globally but are a result of cancellation of opposite biases due to difference processes. Overall, the multi-model ensemble mean bias is –133±98 mWm-2, indicating that they are too atmospherically opaque due to trapping too much radiation in the atmosphere by overestimated tropical tropospheric O3 and H2O. Having too much O3 and H2O in the troposphere would have different impacts on the sensitivity of TOA flux to O3 and these competing effects add more uncertainties on the ozone radiative forcing. We find that the inter-model TOA outgoing longwave radiation (OLR) difference is well anti-correlated with their ozone band flux bias. This suggests that there is significant radiative compensation in the calculation of model outgoing longwave radiation.

Aura Tropospheric Emission Spectrometer (TES) meas↗

NASA NTRS2021

Integrating continuous atmospheric boundary layer and tower-based flux measurements to advance understanding of land-atmosphere interactions

The atmospheric boundary layer mediates the exchange of energy, matter, and momentum between the land surface and the free troposphere, integrating a range of physical, chemical, and biological processes and is defined as the lowest layer of the atmosphere (ranging from a few meters to 3 km). In this review, we investigate how continuous, automated observations of the atmospheric boundary layer can enhance the scientific value of co-located eddy covariance measurements of land-atmosphere fluxes of carbon, water, and energy, as are being made at FLUXNET sites worldwide. We highlight four key opportunities to integrate tower-based flux measurements with continuous, long-term atmospheric boundary layer measurements: (1) to interpret surface flux and atmospheric boundary layer exchange dynamics and feedbacks at flux tower sites, (2) to support flux footprint modelling, the interpretation of surface fluxes in heterogeneous and mountainous terrain, and quality control of eddy covariance flux measurements, (3) to support regional-scale modeling and upscaling of surface fluxes to continental scales, and (4) to quantify land-atmosphere coupling and validate its representation in Earth system models. Adding a suite of atmospheric boundary layer measurements to eddy covariance flux tower sites, and supporting the sharing of these data to tower networks, would allow the Earth science community to address new emerging research questions, better interpret ongoing flux tower measurements, and would present novel opportunities for collaborations between FLUXNET scientists and atmospheric and remote sensing scientists.

Manuel Helbig↗

NASA NTRSDate not supplied

Towards a More Realistic Representation of NASA CERES-derived Surface Radiative Fluxes during Polar Night: A Comparison with the MOSAiC Field Campaign

The Arctic remains one of the more difficult regions observe, and so satellite observations are a critical tool for observing the region, such as those from Clouds and the Earth’s Radiant Energy System (CERES). But validating the satellite surface radiative flux estimates is difficult because of the lack of in situ measurements. The extensive high-quality surface radiative flux and meteorological measurements collected from MOSAiC provide a useful check on flux retrievals from CERES instruments. We compare MOSAiC and CERES surface radiative fluxes during October through March of 2019-2020 using the large set of meteorological measurements also collected by MOSAiC, specifically cloud properties. Previous work identified a significant source of error in the CERES estimate of surface downwelling longwave flux as the estimate of low level cloud amount when compared with MOSAiC W-band radar measurements. Continuing this work, we examine the effects of errors in cloud water path on surface radiative fluxes. When using all cloud conditions, errors in cloud water are also significantly correlated with surface radiative flux errors, though the size off the effect is only about half that of cloud amount. But when considering low cloud conditions only, the effects of cloud water and cloud amount are comparable. We compare MOSAiC and CERES surface radiative fluxes during October through March of 2019-2020 using the large set of meteorological measurements also collected by MOSAiC, specifically cloud properties. Previous work identified a significant source of error in the CERES estimate of surface downwelling longwave flux as the estimate of low level cloud amount when compared with MOSAiC W-band radar measurements. We further examine this source of error by examining selected case studies in which the disagreements in radiative fluxes and clouds are large.

J Brant Dodson↗

NASA NTRS2023

The Eruption of A Magnetic Flux Rope Observed By Solar Orbiter and Parker Solar Probe

Magnetic flux ropes are a key component of coronal mass ejections, forming the core of these eruptive phenomena. However, determining whether a flux rope is present prior to eruption onset and, if so, the rope's handedness and the number of turns that any helical field lines make is difficult without magnetic field modeling or in situ detection of the flux rope. We present two distinct observations of plasma flows along a filament channel on 2022 September 4 and 5 made using the Solar Orbiter spacecraft. Each plasma flow exhibited helical motions in a right-handed sense as the plasma moved from the source active region across the solar disk to the quiet Sun, suggesting that the magnetic configuration of the filament channel contains a flux rope with positive chirality and at least one turn. The length and velocity of the plasma flow increased from the first to the second observation, suggesting evolution of the flux rope, with the flux rope subsequently erupting within ∼5 hr of the second plasma flow. The erupting flux rope then passed over the Parker Solar Probe spacecraft during its encounter (13), enabling in situ diagnostics of the structure. Although complex and consistent with the flux rope erupting from underneath the heliospheric current sheet, the in situ measurements support the inference of a right-handed flux rope from remote-sensing observations. These observations provide a unique insight into the eruption and evolution of a magnetic flux rope near the Sun.

David M. Long↗

NASA NTRS2023

Investigating the Role of Incident Ion Flux in Solar Wind Space Weathering of Carbon-Rich Asteroidal Regolith Via H+ and He+ Irradiation of the Murchison Meteorite

We present results from a set of low and high flux 1 keV/amu H + and He + irradiation experiments performed on slabs of the Murchison CM2 carbonaceous chondrite. The low flux conditions for H + and He + irradiation were ~1-1.5 orders of magnitude lower than the high flux conditions, and each experiment was irradiated to a total fluence between ~3 × 10 16 to ~6 × 10 16 ions/cm 2 . Irradiation-induced changes in the surface chemistry and optical properties of the Murchison samples were evaluated using in situ X-ray photoelectron spectroscopy (XPS) and visible and near-infrared spectroscopy (VNIR). We characterized the microstructure and composition of ion damaged rims in focused ion beam (FIB) cross-sections extracted from olivine and matrix material in each irradiated Murchison slab using transmission electron microscopy (TEM). XPS results suggest that both low flux and high flux H + and He + irradiation cause minor sputtering of surface carbon as well as a reduction in the valence state of iron, from Fe 3+ to Fe 2+ . Slope bluing is observed in VNIR spectra of the irradiated samples which may reflect carbonization and dehydrogenation of organic species and contrasts with reddening trends associated with npFe 0 formation. Although we do not observe a strong flux-dependence on the crystallinity of ion-damaged olivine, TEM analyses reveal a variety of microstructures in all olivine FIB-sections, suggesting that crystallographic orientation affects amorphization efficiency. Analyses of matrix FIB-sections indicate that phyllosilicate alteration is mainly driven by He+ irradiation, where the higher incident flux leads to greater amorphization and the formation of more distinct ion-damaged layers, similar to smooth layers in returned Ryugu particles. TEM results also provide some evidence that higher ion flux leads to greater vesiculation, with He + irradiation being more efficient at vesiculation than H + irradiation, and that higher ion flux may promote the segregation of Mg and Si into laterally extensive lenses and layers in olivine samples. We discuss the implications of these findings for constraining the role that ion flux plays in the development of space weathering characteristics in silicate phases present in carbonaceous asteroidal regoliths. These results will be important for understanding the complexity of this process and how it operates on carbon-rich airless bodies like asteroids Bennu and Ryugu.

meteorites↗

NASA NTRSDate not supplied

How Auroral Electron Precipitations Contribute to the Formation of Electron Heat Fluxes to the Ionosphere?

Electron heat fluxes (also called electron thermal fluxes) in the ionosphere are carried by thermal electrons whose energy is below a few eV. Electron heat fluxes greatly impact on electron temperature, which is a fundamental parameter in the ionospheric dynamics. At the high latitude in the auroral regions electron heat flux is originated dominantly from the magnetosphere through high-energy electron energy fluxes. High-energy electron fluxes in the diffuse auroral region can undergo multiple backscatters between the magnetically conjugated regions of both hemispheres, and different kind of wave-particle interactions along the magnetic field line. High-energy electron fluxes in discrete auroral region can be trapped below the auroral acceleration region and can also undergo backscatter and multiple reflection. These processes, in turn, amplify super-thermal electrons (<~500-600 eV) that dominantly form electron heat fluxes through Coulomb collision between thermal electrons. Such electron heat fluxes play an important role to determine electron temperature profile in the ionosphere, which is one of the key parameters that controls the ionospheric dynamics. Thus, it is necessary to include electron heat flux as a topside energy input in all global ionospheric models. We demonstrate all above results based on Superthermal Electron Transport (STET), Superthermal Proton, Electron and Atomic Hydrogen tRansport in the Ionosphere and Thermosphere (SPEAH-RIT), and Comprehensive Inner Magnetosphere and Ionospheres (CIMI) codes developed at NASA Goddard Space Flight Center.

George V. Khazanov↗

NASA NTRS2021

On the Relationship Between CYGNSS Surface Heat Fluxes and the Life Cycle of Low-Latitude Ocean Extratropical Cyclones

Surface latent and sensible heat fluxes are important for extratropical cyclone evolution and intensification. Because extratropical cyclone genesis often occurs at low-latitude, CYGNSS surface latent and sensible heat flux retrievals are composited to provide a mean picture of their spatial distribution in low-latitude oceanic extratropical cyclones. CYGNSSn heat fluxes are not affected by heavy precipitation and offer observations of storms with frequent revisit times. Consistent with prior results obtained for cyclones in the Gulf Stream region, the fluxes are strongest in the wake of the cold fronts, and weakest to negative in the warm sector in advance of the cold fronts. As cyclone strength increases, or mean precipitable water decreases, the maximum in surface heat fluxes increases while the minimum decreases. This impacts the changes in fluxes during cyclone intensification: the post-cold frontal surface heat flux maximum increases due to the increase in near surface winds. During cyclone dissipation, the fluxes in this sector decrease, due to the decrease in winds and in temperature and humidity contrast. The warm sector minimum decreases throughout the entire cyclone lifetime and is mostly driven by sea-air temperature and humidity contrast changes. However, during cyclone dissipation, the surface heat fluxes increase along the cold front in a narrow band to the east, independently from changes in the cyclone characteristics. This suggests that, during cyclone dissipation, energy transfers from the ocean to the atmosphere are linked to frontal in addition to synoptic-scale processes.

CYGNSS↗

NASA NTRSDate not supplied

Bridging Current Indirect and Future Direct Estimates of Convective Mass Flux Toward Quantifying the Role of Convective Cores on Anvil Area Time Tendencies

Anvil cloud spatial extent is strongly driven by convective mass flux. However, the lack of convective mass flux observations precludes global analyses of the functional relationship between anvil cloud area growth tendencies and convective areal coverage and vertical mass flux. Partly informed by analyses of a hierarchy of WRF mesoscale convective system (MCS) simulations, in this presentation, we discuss new work on estimating convective mass flux by way of an approach that casts the problem of quantifying convective mass flux into terms related to diabatic heating vertical structure, convective area and tropospheric stability. We demonstrate the usefulness of this approach at the MCS spatial scale via development of a simple, robust model that analytically connects system-scale convective mass flux and anvil cloud area growth rates. We show that the model predicts anvil area size changes in agreement with those observed in a global convective system tracking database (TOOCAN). An additional advantage of this approach for estimating convective mass flux is that it bridges future satellite mission plans for directly observing convective mass flux (e.g., AOS) with longer-record observations made by TRMM, GPM and satellite sounder mission data (the latter used for estimating stability) that, when combined, can be used for inferring convective mass fluxes at the MCS spatial scale spanning slowly changing, diverse environments. An evaluation and bridging of both direct and indirect approaches supports convective process analyses varying over longer time periods in this “era of convection.”

convective mass flux↗

NASA NTRSDate not supplied

Bridging current indirect and future direct estimates of convective mass flux toward quantifying the role of convective cores on anvil area time tendencies

convective mass flux↗

NASA NTRS2021

Changes in TOA SW Fluxes over Marine Clouds When Estimated via Semiphysical Angular Distribution Models

Top-of-atmosphere (TOA) shortwave (SW) angular distribution models (ADMs) approximate—per angular direction of an imagined upward hemisphere—the intensity of sunlight scattered back from a specific Earth–atmosphere scene. ADMs are, thus, critical when converting satellite-borne broadband radiometry into estimated radiative fluxes. This paper applies a set of newly developed ADMs with a more refined scene definition and demonstrates tenable changes in estimated fluxes compared to currently operational ADMs. Newly developed ADMs use a semiphysical framework to consider cloud-top effective radius (¯¯R_e) and above-cloud water vapor (ACWV), in addition to accounting for surface wind speed and clouds’ phase, fraction, and optical depth. In effect, instantaneous TOA SW fluxes for marine liquid-phase clouds had the largest flux differences (of up to 25 W m−2) for lower solar zenith angles and cloud optical depth greater than 10 due to extremes in ¯¯R_e or ACWV. In regions where clouds had persistently extreme levels of ¯¯R_e (here mostly for ¯¯R_e < 7μm and ¯¯R_e > 15μm) or ACWV, instantaneous fluxes estimated from Aqua, Terra, Meteosat-8, and Meteosat-9 satellites using the two ADMs differed systematically, resulting in significant deviations in daily mean fluxes (up to ±10 W m^(−2)) and monthly mean fluxes (up to ±5 W m^(−2)). Flux estimates using newly developed, semiphysical ADMs may contribute to a better understanding of solar fluxes over low-level clouds. It remains to be seen whether aerosol indirect effects are impacted by these updates.

angular distribution models (ADMs)↗

NASA NTRS2022

Constraining Arctic Climate Projections of Wintertime Warming With Surface Turbulent Flux Observations and Representation of Surface-Atmosphere Coupling

The drivers of rapid Arctic climate change—record sea ice loss, warming SSTs, and a lengthening of the sea ice melt season—compel us to understand how this complex system operates and use this knowledge to enhance Arctic predictability. Changing energy flows sparked by sea ice decline, spotlight atmosphere-surface coupling processes as central to Arctic system function and its climate change response. Despite this, the representation of surface turbulent flux parameterizations in models has not kept pace with our understanding. The large uncertainty in Arctic climate change projections, the central role of atmosphere-surface coupling, and the large discrepancy in model representation of surface turbulent fluxes indicates that these processes may serve as useful observational constraints on projected Arctic climate change. This possibility requires an evaluation of surface turbulent fluxes and their sensitivity to controlling factors (surface-air temperature and moisture differences, sea ice, and winds) within contemporary climate models (here Coupled Model Intercomparison Project 6). The influence of individual controlling factors and their interactions is diagnosed using a multi-linear regression approach. This evaluation is done for four sea ice loss regimes, determined from observational sea ice loss trends, to control for the confounding effects of natural variability between models and observations. The comparisons between satellite- and model-derived surface turbulent fluxes illustrate that while models capture the general sensitivity of surface turbulent fluxes to declining sea ice and to surface-air gradients of temperature and moisture, substantial mean state biases exist. Specifically, the central Arctic is too weak of a heat sink to the winter atmosphere compared to observations, with implications to the simulated atmospheric circulation variability and thermodynamic profiles. Models were found to be about 50% more efficient at turning an air-sea temperature gradient anomaly into a sensible heat flux anomaly relative to observations. Further, the influence of sea ice concentration on the sensible heat flux is underestimated in models compared to observations. The opposite is found for the latent heat flux variability in models; where the latent heat flux is too sensitive to a sea ice concentration anomaly. Lastly, the results suggest that present-day trends in sea ice retreat regions may serve as suitable observational constraints of projected Arctic warming.

turbulent fluxes↗

NASA NTRS1984

The magnetic non-equilibrium of buoyant flux tubes in the solar corona

The magnetic field in the convection zone and photosphere of the sun exists mostly as concentrated tubes of magnetic flux. It is, therefore, necessary to study the basic properties of magnetic flux tubes to obtain a basis for understanding the behavior of the sun's magnetic field. The present investigation is concerned with the global equilibrium shape of a flux tube in the stratified solar atmosphere. A fundamental property of isolated flux tubes is magnetic buoyancy. Attention is given to flux tubes with external field, and twisted flux tubes. It is shown that the analysis of Parker (1975, 1979) and Spruit (1981) for calculating the equilibrium of a slender flux tube in a stratified atmosphere may be extended to more general situations. The slender tube approximation provides a method of solving the problem of modeling the overall curvature of flux tubes. It is found that for a twisted flux tube, there can be two possible equilibrium values of the height.

Browning, P. K.↗

NASA NTRS1990

A comparison of surface sensible and latent heat fluxes from aircraft and surface measurements in FIFE 1987

Surface fluxes of sensible and latent heat over a tall-grass prairie in central Kansas, as measured by 22 surface stations during FIFE 1987, are compared with values gained indirectly by linear extrapolation of aircraft-measured flux profiles to the surface. The results of 33 such comparisons covering the period 26 June to 13 October 1987 indicate that the sensible heat flux profiles were generally more linear with less scatter in the measurements at each level than were the latent heat flux profiles, the profile extrapolations of sensible heat flux in general underestimate the surface averages by about 30 percent, with slightly better agreement during periods of small flux, and the profile extrapolations of latent heat flux in general underestimate the surface averages by about 15 percent, with overestimates during periods of small fluxes (dry conditions) and overestimates during periods of large fluxes (moist conditions). Possible origins of the differences between the two sets of measurements are discussed, as directions for further research.

Kelly, Robert D.↗

NASA NTRS1992

An airborne study of boundary layer heat and moisture fluxes for project FIFE

A summary of work accomplished during the first International Satellite Cloud Climatology Project (ISLSCP) Field Experiment is presented. The Wyoming King Air participated in Intensive Field Campaigns (IFCs) 3 and 4 in 1987, which were committed to a combination of airborne sensible and latent heat flux measurements and soil moisture mappings, with the University of Kansas' X-band side-looking airborne radar (SLAR). A total of 9 flux missions were flown in 1987 using several different flight designs. A critical decision in the first round of aircraft flux analyses, agreed to by all the flux aircraft investigators, was to pass the aircraft data through a high-pass filter prior to the eddy-correlation flux calculations. Several conclusions were drawn from this study: (1) boundary layer (BL) profiles of heat fluxes were usually linear; (2) high-pass filtering applied to the aircraft data did not add to the disagreement between the profile; (3) undersampling at high frequencies could have accounted for as much as a 15 percent underestimate of surface fluxes; (4) disagreement between the aircraft and surface latent heat fluxes changed signs between summer and fall; (5) magnitude and sign of disagreement between aircraft and surface heat fluxes varied systematically with BL depth or height of aircraft profile; and (6) Bowen ratios from both detrended and filtered aircraft data agreed with surface values better for moist, summer cases than for dry cases.

Kelly, Robert D.↗

NASA NTRS1992

A comparison of surface sensible and latent heat fluxes from aircraft and surface measurements in FIFE 1987

Kelly, Robert D.↗

NASA NTRS1992

Adjustment of footprint correction for airborne flux mapping over the FIFE site

A meaningful interpretation of airborne flux estimates over nonuniform terrain must consider local advection from nonhomogeneous source distributions (footprint correction). An empirical procedure for footprint correction of airborne flux data obtained in the First ISLSCP Field Experiment (FIFE) 1989 is presented, based on simple analytical solutions of the diffusion equation which have been adjusted to approximate more realistic solutions. Optimized estimates of surface flux 'maps' derived from airborne observations are then constructed for maximum correlation between flux estimates and independently observed surface characteristics. This paper also includes an analysis of resolution for the given procedure, in terms of amplitude recovery of hypothetical square-wave distributions of surface flux density, and discusses its implications for the interpretation of the optimized estimates of FIFE surface flux maps. Results show that corrected spatial sink distributions are obtained by the current empirical procedure at the cost of considerable reduction in amplitude recovery of small-scale variations in surface flux density. The high spatial correlation observed between corrected flux maps and surface characteristics such as greenness or surface temperature excess is ascribed to the approximately correct positioning of the main flux gradients across the site, which can be expected to have been reproduced with amplitude recovery equal to or greater than 60 percent.

Schuepp, P. H.↗

NASA NTRS1992

Soil surface CO2 fluxes and the carbon budget of a grassland

Measurements of soil surface CO2 fluxes are reported for three sites within the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE) area, and simple empirical equations are fit to the data to provide predictions of soil fluxes from environmental observations. A prototype soil chamber, used to make the flux measurements, is described and tested by comparing CO2 flux measurements to a 40-L chamber, a 1-m/cu chamber, and eddy correlation. Results suggest that flux measurements with the prototype chamber are consistent with measurements by other methods to within about 20 percent. A simple empirical equation based on 10-cm soil temperature, 0- to 10-cm soil volumetric water content, and leaf area index predicts the soil surface CO2 flux with a rms error of 1.2 micro-mol sq m/s for all three sites. Further evidence supports using this equation to evaluate soil surface CO2 during the 1987 FIFE experiment. The soil surface CO2 fluxes when averaged over 24 hours are comparable to daily gross canopy photosynthetic rates. For 6 days of data the net daily accumulation of carbon is about 0.6 g CO2 sq m/d; this is only a few percent of the daily gross accumulation of carbon by photosynthesis. As the soil became drier in 1989, the net accumulation of carbon by the prairie increased, suggesting that the soil flux is more sensitive to temperature and drought than the photosynthetic fluxes.

Norman, J. M.↗