Projectively simple rings

We introduce the notion of a projectively simple ring, which is an infinite-dimensional graded k-algebra A such that every 2-sided ideal has finite codimension in A (over the base field k). Under some (relatively mild) additional assumptions on A, we reduce the problem of classifying such rings (in the sense explained in the paper) to the following geometric question, which we believe to be of independent interest. Let X is a smooth irreducible projective variety. An automorphism f: X -> X is called wild if it X has no proper f-invariant subvarieties. We conjecture that if X admits a wild automorphism then X is an abelian variety. We prove several results in support of this conjecture; in particular, we show that the conjecture is true if X is a curve or a surface. In the case where X is an abelian variety, we describe all wild automorphisms of X. In the last two sections we show that if A is projectively simple and admits a balanced dualizing complex, then Proj(A) is Cohen-Macaulay and Gorenstein.Comment: Some new material has been added in Section 1; to appear in Advances in Mathematic

Temperature sensitivity of decomposition in relation to soil organic matter pools: critique and outlook

Knorr et al. (2005) concluded that soil organic carbon pools with longer turnover times are more sensitive to temperature. We show that this conclusion is equivocal, largely dependent on their specific selection of data and does not persist when the data set of Kätterer et al. (1998) is analysed in a more appropriate way. Further, we analyse how statistical properties of the model parameters may interfere with correlative analyses that relate the Q₁₀ of soil respiration with the basal rate, where the latter is taken as a proxy for soil organic matter quality. We demonstrate that negative parameter correlations between Q₁₀-values and base respiration rates are statistically expected and not necessarily provide evidence for a higher temperature sensitivity of low quality soil organic matter. Consequently, we propose it is premature to conclude that stable soil carbon is more sensitive to temperature than labile carbon

Influences of observation errors in eddy flux data on inverse model parameter estimation

Eddy covariance data are increasingly used to estimate parameters of ecosystem models. For proper maximum likelihood parameter estimates the error structure in the observed data has to be fully characterized. In this study we propose a method to characterize the random error of the eddy covariance flux data, and analyse error distribution, standard deviation, cross- and autocorrelation of CO<sub>2</sub> and H<sub>2</sub>O flux errors at four different European eddy covariance flux sites. Moreover, we examine how the treatment of those errors and additional systematic errors influence statistical estimates of parameters and their associated uncertainties with three models of increasing complexity – a hyperbolic light response curve, a light response curve coupled to water fluxes and the SVAT scheme BETHY. In agreement with previous studies we find that the error standard deviation scales with the flux magnitude. The previously found strongly leptokurtic error distribution is revealed to be largely due to a superposition of almost Gaussian distributions with standard deviations varying by flux magnitude. The crosscorrelations of CO<sub>2</sub> and H<sub>2</sub>O fluxes were in all cases negligible (<i>R</i><sup>2</sup> below 0.2), while the autocorrelation is usually below 0.6 at a lag of 0.5 h and decays rapidly at larger time lags. This implies that in these cases the weighted least squares criterion yields maximum likelihood estimates. To study the influence of the observation errors on model parameter estimates we used synthetic datasets, based on observations of two different sites. We first fitted the respective models to observations and then added the random error estimates described above and the systematic error, respectively, to the model output. This strategy enables us to compare the estimated parameters with true parameters. We illustrate that the correct implementation of the random error standard deviation scaling with flux magnitude significantly reduces the parameter uncertainty and often yields parameter retrievals that are closer to the true value, than by using ordinary least squares. The systematic error leads to systematically biased parameter estimates, but its impact varies by parameter. The parameter uncertainty slightly increases, but the true parameter is not within the uncertainty range of the estimate. This means that the uncertainty is underestimated with current approaches that neglect selective systematic errors in flux data. Hence, we conclude that potential systematic errors in flux data need to be addressed more thoroughly in data assimilation approaches since otherwise uncertainties will be vastly underestimated

Upscaled diurnal cycles of land–atmosphere fluxes: a new global half-hourly data product

Interactions between the biosphere and the atmosphere can be well characterized by fluxes between the two. In particular, carbon and energy fluxes play a major role in understanding biogeochemical processes on an ecosystem level or global scale. However, the fluxes can only be measured at individual sites, e.g., by eddy covariance towers, and an upscaling of these local observations is required to analyze global patterns. Previous work focused on upscaling monthly, 8-day, or daily average values, and global maps for each flux have been provided accordingly. In this paper, we raise the upscaling of carbon and energy fluxes between land and atmosphere to the next level by increasing the temporal resolution to subdaily timescales. We provide continuous half-hourly fluxes for the period from 2001 to 2014 at 0.5° spatial resolution, which allows for analyzing diurnal cycles globally. The data set contains four fluxes: gross primary production (GPP), net ecosystem exchange (NEE), latent heat (LE), and sensible heat (H). We propose two prediction approaches for the diurnal cycles based on large-scale regression models and compare them in extensive cross-validation experiments using different sets of predictor variables. We analyze the results for a set of FLUXNET tower sites showing the suitability of our approaches for this upscaling task. Finally, we have selected one approach to calculate the global half-hourly data products based on predictor variables from remote sensing and meteorology at daily resolution as well as half-hourly potential radiation. In addition, we provide a derived product that only contains monthly average diurnal cycles, which is a lightweight version in terms of data storage that still allows studying the important characteristics of diurnal patterns globally. We recommend to primarily use these monthly average diurnal cycles, because they are less affected by the impacts of day-to-day variation, observation noise, and short-term fluctuations on subdaily timescales compared to the full half-hourly flux products. The global half-hourly data products are available at https://doi.org/10.17871/BACI.224.</p

Carbon balance assessment of a natural steppe of southern Siberia by multiple constraint approach

Steppe ecosystems represent an interesting case in which the assessment of carbon balance may be performed through a cross validation of the eddy covariance measurements against ecological inventory estimates of carbon exchanges (Ehman et al., 2002; Curtis et al., 2002). &lt;br&gt;&lt;br&gt; Indeed, the widespread presence of ideal conditions for the applicability of the eddy covariance technique, as vast and homogeneous grass vegetation cover over flat terrains (Baldocchi, 2003), make steppes a suitable ground to ensure a constrain to flux estimates with independent methodological approaches. &lt;br&gt;&lt;br&gt; We report about the analysis of the carbon cycle of a true steppe ecosystem in southern Siberia during the growing season of 2004 in the framework of the TCOS-Siberia project activities performed by continuous monitoring of CO&lt;sub&gt;2&lt;/sub&gt; fluxes at ecosystem scale by the eddy covariance method, fortnightly samplings of phytomass, and ingrowth cores extractions for NPP assessment, and weekly measurements of heterotrophic component of soil CO&lt;sub&gt;2&lt;/sub&gt; effluxes obtained by an experiment of root exclusion. &lt;br&gt;&lt;br&gt; The carbon balance of the monitored natural steppe was, according to micrometeorological measurements, a sink of carbon of 151.7±36.9 g C m&lt;sup&gt;&amp;minus;2&lt;/sup&gt;, cumulated during the growing season from May to September. This result was in agreement with the independent estimate through ecological inventory which yielded a sink of 150.1 g C m&lt;sup&gt;&amp;minus;2&lt;/sup&gt; although this method was characterized by a large uncertainty (±130%) considering the 95% confidence interval of the estimate. Uncertainties in belowground process estimates account for a large part of the error. Thus, in particular efforts to better quantify the dynamics of root biomass (growth and turnover) have to be undertaken in order to reduce the uncertainties in the assessment of NPP. This assessment should be preferably based on the application of multiple methods, each one characterized by its own merits and flaws

Extreme events in gross primary production: a characterization across continents

Climate extremes can affect the functioning of terrestrial ecosystems, for instance via a reduction of the photosynthetic capacity or alterations of respiratory processes. Yet the dominant regional and seasonal effects of hydrometeorological extremes are still not well documented and in the focus of this paper. Specifically, we quantify and characterize the role of large spatiotemporal extreme events in gross primary production (GPP) as triggers of continental anomalies. We also investigate seasonal dynamics of extreme impacts on continental GPP anomalies. We find that the 50 largest positive extremes (i.e., statistically unusual increases in carbon uptake rates) and negative extremes (i.e., statistically unusual decreases in carbon uptake rates) on each continent can explain most of the continental variation in GPP, which is in line with previous results obtained at the global scale. We show that negative extremes are larger than positive ones and demonstrate that this asymmetry is particularly strong in South America and Europe. Our analysis indicates that the overall impacts and the spatial extents of GPP extremes are power-law distributed with exponents that vary little across continents. Moreover, we show that on all continents and for all data sets the spatial extents play a more important role for the overall impact of GPP extremes compared to the durations or maximal GPP. An analysis of possible causes across continents indicates that most negative extremes in GPP can be attributed clearly to water scarcity, whereas extreme temperatures play a secondary role. However, for Europe, South America and Oceania we also identify fire as an important driver. Our findings are consistent with remote sensing products. An independent validation against a literature survey on specific extreme events supports our results to a large extent