Browsing by Author "Williams, Mathew"

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Biosphere-atmosphere exchange of CO2 in relation to climate: a cross-biome analysis across multiple time scales
(2009-10) Stoy, Paul C.; Richardson, Andrew D.; Baldocchi, Dennis D.; Katul, Gabriel G.; Stanovick, J.; Mahecha, M. D.; Reichstein, M.; Detto, Matteo; Law, Beverly E.; Wohlfahrt, Georg; Arriga, N.; Campos, J.; McCaughey, J. H.; Montagnani, Leonardo; Paw U, Kyaw Tha; Sevanto, S.; Williams, Mathew
The net ecosystem exchange of CO2 (NEE) varies at time scales from seconds to years and longer via the response of its components, gross ecosystem productivity (GEP) and ecosystem respiration (RE), to physical and biological drivers. Quantifying the relationship between flux and climate at multiple time scales is necessary for a comprehensive understanding of the role of climate in the terrestrial carbon cycle. Orthonormal wavelet transformation (OWT) can quantify the strength of the interactions between gappy eddy covariance flux and micrometeorological measurements at multiple frequencies while expressing time series variance in few energetic wavelet coefficients, offering a low-dimensional view of the response of terrestrial carbon flux to climatic variability. The variability of NEE, GEP and RE, and their co-variability with dominant climatic drivers, are explored with nearly one thousand site-years of data from the FLUXNET global dataset consisting of 253 eddy covariance research sites. The NEE and GEP wavelet spectra were similar among plant functional types (PFT) at weekly and shorter time scales, but significant divergence appeared among PFT at the biweekly and longer time scales, at which NEE and GEP were relatively less variable than climate. The RE spectra rarely differed among PFT across time scales as expected. On average, RE spectra had greater low frequency (monthly to interannual) variability than NEE, GEP and climate. CANOAK ecosystem model simulations demonstrate that "multi-annual" spectral peaks in flux may emerge at low (4+ years) time scales. Biological responses to climate and other internal system dynamics, rather than direct ecosystem response to climate, provide the likely explanation for observed multi-annual variability, but data records must be lengthened and measurements of ecosystem state must be made, and made available, to disentangle the mechanisms responsible for low frequency patterns in ecosystem CO2 exchange.
Improving land surface models with FLUXNET data
(2009-07) Williams, Mathew; Richardson, Andrew D.; Reichstein, M.; Stoy, Paul C.; Peylin, Phili; Verbeeck, Hans; Carvalhais, N.; Jung, Martin; Hollinger, David Y.; Kattge, J.; Leuning, R.; Luo, Yiqi; Tomelleri, E.; Trudinger, C.; Wang, Ying-Ping
There is a growing consensus that land surface models (LSMs) that simulate terrestrial biosphere exchanges of matter and energy must be better constrained with data to quantify and address their uncertainties. FLUXNET, an international network of sites that measure the land surface exchanges of carbon, water and energy using the eddy covariance technique, is a prime source of data for model improvement. Here we outline a multi-stage process for "fusing" (i.e. linking) LSMs with FLUXNET data to generate better models with quantifiable uncertainty. First, we describe FLUXNET data availability, and its random and systematic biases. We then introduce methods for assessing LSM model runs against FLUXNET observations in temporal and spatial domains. These assessments are a prelude to more formal model-data fusion (MDF). MDF links model to data, based on error weightings. In theory, MDF produces optimal analyses of the modelled system, but there are practical problems. We first discuss how to set model errors and initial conditions. In both cases incorrect assumptions will affect the outcome of the MDF. We then review the problem of equifinality, whereby multiple combinations of parameters can produce similar model output. Fusing multiple independent and orthogonal data provides a means to limit equifinality. We then show how parameter probability density functions (PDFs) from MDF can be used to interpret model validity, and to propagate errors into model outputs. Posterior parameter distributions are a useful way to assess the success of MDF, combined with a determination of whether model residuals are Gaussian. If the MDF scheme provides evidence for temporal variation in parameters, then that is indicative of a critical missing dynamic process. A comparison of parameter PDFs generated with the same model from multiple FLUXNET sites can provide insights into the concept and validity of plant functional types (PFT) – we would expect similar parameter estimates among sites sharing a single PFT. We conclude by identifying five major model-data fusion challenges for the FLUXNET and LSM communities: (1) to determine appropriate use of current data and to explore the information gained in using longer time series; (2) to avoid confounding effects of missing process representation on parameter estimation; (3) to assimilate more data types, including those from earth observation; (4) to fully quantify uncertainties arising from data bias, model structure, and initial conditions problems; and (5) to carefully test current model concepts (e.g. PFTs) and guide development of new concepts.
Seasonal bryophyte productivity in the sub‐Arctic: a comparison with vascular plants
(2012-04) Street, Lorna E.; Stoy, Paul C.; Sommerkorn, Martin; Fletcher, Benjamin J.; Sloan, Victoria L.; Hill, Timothy C.; Williams, Mathew
1. Arctic ecosystems are experiencing rapid climate change, which could result in positive feedbacks on climate warming if ecosystem carbon (C) loss exceeds C uptake through plant growth. Bryophytes (mosses, liverworts and hornworts) are important components of Arctic vegetation, but are currently not well represented in terrestrial C models; in particular, seasonal patterns in bryophyte C metabolism compared to vascular plant vegetation are poorly understood. 2. Our objective was to quantify land-surface CO2 fluxes for common sub-Arctic bryophyte patches (dominated by Polytrichum piliferum and Sphagnum fuscum) in spring (March–May) and during the summer growing season (June–August) and to develop a simple model of bryophyte gross primary productivity fluxes (PB). We use the model to explore the key environmental controls over PB for P. piliferum and S. fuscum and compare seasonal patterns of productivity with those of typical vascular plant communities at the same site. 3. The modelled total gross primary productivity (ΣPB) over 1 year (March – November) for P. piliferum was c. 360 g C m−2 ground and for S. fuscum c. 112 g C m−2 ground, c. 90% and 30% of total gross primary productivity for typical vascular plant communities (ΣPV) over the same year. In spring (March–May), when vascular plant leaves are not fully developed, ΣPB for P. piliferum was 3 × ΣPV. 4. Model sensitivity analysis indicated that bryophyte turf water content does not significantly affect (March–November) ΣPB for P. piliferum and S. fuscum, at least for periods without sustained lack of precipitation. However, we find that seasonal changes in bryophyte photosynthetic capacity are important in determining ΣPB for both bryophyte species. 5. Our study implies that models of C dynamics in the Arctic must include a bryophyte component if they are intended to predict the effects of changes in the timing of the growing season, or of changes in vegetation composition, on Arctic C balance.
Topographic controls on the leaf area index and plant functional type of a Fennoscandian tundra ecosystem
(2008-11) Spadavecchia, Luke; Williams, Mathew; Bell, Robert; Stoy, Paul C.; Huntley, Brian; van Wijk, Mark T.
Leaf area index (LAI) is an emergent property of vascular plants closely linked to primary production and surface energy balance. LAI can vary by an order of magnitude among Arctic tundra communities and is closely associated with plant functional type. 2. We examined topographic controls on vegetation type and LAI distribution at two different scales in an Arctic tundra ecosystem in northern Sweden. ‘Micro-scale’ measurements were made at 0.2-m resolution over a 40 m × 40 m domain, while ‘macro-scale’ data were collected at approximately 10-m resolution over a 500 m × 500 m domain. Tundra LAI varied from 0.1–3.6 at the micro-scale resolution, and from 0.1–1.6 at the macro-scale resolution. 3. The correlation between dominant vascular species and LAI at the micro-scale ( r 2 = 0.40) was greater than the correlation between dominant vegetation and LAI at the macro-scale ( r 2 = 0.14).At the macro-scale, LAI was better explained by topographic parameters and spatial auto-correlation (pseudo r 2 = 0.32) than it was at the micro-scale ( r 2 = 0.16). Exposure and elevation were significantly but weakly correlated with LAI at the micro-scale, while on the macro-scale the most significant explanatory topographic variable was elevation ( r 2 = 0.12). 4. The distribution of plant communities at both scales was significantly associated with topography. Shrub communities, dominated by Betula nana , were associated with low elevation sites at both scales, while more exposed and/or high elevation sites were dominated by cryptogams. 5. Synthesis. Dominant vegetation, topography and LAI were linked at both scales of investigation but, for explaining LAI, topography became more important and dominant vegetation less important at the coarser scale. The explanatory power of dominant species/functional type for LAI variation was weaker at coarser scales, because communities often contained more than one functional type at 10 m resolution. The data suggest that remotely sensed topography can be combined with remotely sensed optical measurements to generate a useful tool for LAI mapping in Arctic environments.
Upscaling as ecological information transfer: A simple framework with application to arctic ecosystem carbon exchange
(2009-06) Stoy, Paul C.; Williams, Mathew; Prieto-Blanco, Ana; Huntley, Brian; Baxter, Robert; Lewis, Philip
Transferring ecological information across scale often involves spatial aggregation, which alters information content and may bias estimates if the scaling process is nonlinear. Here, a potential solution, the preservation of the information content of fine-scale measurements, is highlighted using modeled net ecosystem exchange (NEE) of an Arctic tundra landscape as an example. The variance of aggregated normalized difference vegetation index (NDVI), measured from an airborne platform, decreased linearly with log(scale), resulting in a linear relationship between log(scale) and the scale-wise modeled NEE estimate. Preserving three units of information, the mean, variance and skewness of fine-scale NDVI observations, resulted in upscaled NEE estimates that deviated less than 4% from the fine-scale estimate. Preserving only the mean and variance resulted in nearly 23% NEE bias, and preserving only the mean resulted in larger error and a change in sign from CO2 sink to source. Compressing NDVI maps by 70–75% using wavelet thresholding with the Haar and Coiflet basis functions resulted in 13% NEE bias across the study domain. Applying unique scale-dependent transfer functions between NDVI and leaf area index (LAI) decreased, but did not remove, bias in modeled flux in a smaller expanse using handheld NDVI observations. Quantifying the parameters of statistical distributions to preserve ecological information reduces bias when upscaling and makes possible spatial data assimilation to further reduce errors in estimates of ecological processes across scale.
Upscaling tundra CO2 exchange from chamber to eddy covariance tower
(2013-05) Stoy, Paul C.; Williams, Mathew; Evans, Jonathan G.; Prieto-Blanco, Ana; Disney, Mathias; Hill, Timothy C.; Ward, Helen C.; Wade, Thomas J.; Street, Lorna E.
Extrapolating biosphere-atmosphere CO2 flux observations to larger scales in space, part of the so-called “upscaling” problem, is a central challenge for surface-atmosphere exchange research. Upscaling CO2 flux in tundra is complicated by the pronounced spatial variability of vegetation cover. We demonstrate that a simple model based on chamber observations with a pan-Arctic parameterization accurately describes up to 75% of the observed temporal variability of eddy covariance—measured net ecosystem exchange (NEE) during the growing season in an Abisko, Sweden, subarctic tundra ecosystem, and differed from NEE observations by less than 4% for the month of June. These results contrast with previous studies that found a 60% discrepancy between upscaled chamber and eddy covariance NEE sums. Sampling an aircraft-measured normalized difference vegetation index (NDVI) map for leaf area index (L) estimates using a dynamic flux footprint model explained less of the variability of NEE across the late June to mid-September period, but resulted in a lower root mean squared error and better replicated large flux events. Findings suggest that ecosystem structure via L is a critical input for modeling CO2 flux in tundra during the growing season. Future research should focus on quantifying microclimate, namely photosynthetically active radiation and air temperature, as well as ecosystem structure via L, to accurately model growing season tundra CO2 flux at chamber and plot scales.
Using information theory to determine optimum pixel size and shape for ecological studies: Aggregating land surface characteristics in arctic ecosystems
(2009-03) Stoy, Paul C.; Williams, Mathew; Bell, Robert A.; Spadavecchia, Luke; Prieto-Blanco, Ana; Evans, J. G.; van Wijk, Mark T.
Quantifying vegetation structure and function is critical for modeling ecological processes, and an emerging challenge is to apply models at multiple spatial scales. Land surface heterogeneity is commonly characterized using rectangular pixels, whose length scale reflects that of remote sensing measurements or ecological models rather than the spatial scales at which vegetation structure and function varies. We investigated the ‘optimum’ pixel size and shape for averaging leaf area index (LAI) measurements in relatively large (85 m2 estimates on a 600 × 600-m2 grid) and small (0.04 m2 measurements on a 40 × 40-m2 grid) patches of sub-Arctic tundra near Abisko, Sweden. We define the optimum spatial averaging operator as that which preserves the information content (IC) of measured LAI, as quantified by the normalized Shannon entropy (E S,n) and Kullback–Leibler divergence (D KL), with the minimum number of pixels. Based on our criterion, networks of Voronoi polygons created from triangulated irregular networks conditioned on hydrologic and topographic indices are often superior to rectangular shapes for averaging LAI at some, frequently larger, spatial scales. In order to demonstrate the importance of information preservation when upscaling, we apply a simple, validated ecosystem carbon flux model at the landscape level before and after spatial averaging of land surface characteristics. Aggregation errors are minimal due to the approximately linear relationship between flux and LAI, but large errors of approximately 45% accrue if the normalized difference vegetation index (NDVI) is averaged without preserving IC before conversion to LAI due to the nonlinear NDVI-LAI transfer function.