Search results for "Functional type"

Fully reliable a posteriori error control for evolutionary problems

2015

Relationships between vegetation, air and soil temperatures on Norwegian mountain summits

2017

ABSTRACTGeographic variations in air and soil temperatures are dependent on several biotic and abiotic factors. Air temperature has mostly been used to characterize thermal conditions for plant life, and studies of bioclimatic gradients. From a biological point of view, it is also essential to know to what extent soil temperature is coupled with air temperature. In this study, we have quantified the deviations between soil and air temperatures along gradients in latitude, altitude, and possible effects of the vegetation. Sixteen different temperature variables were estimated from 49 vegetation plots on 19 mountain summits along the high mountain range in Norway, ranging from 230 to 1780 m a…

Integrating Decomposers, Methane-Cycling Microbes and Ecosystem Carbon Fluxes Along a Peatland Successional Gradient in a Land Uplift Region

2021

AbstractPeatlands are carbon dioxide (CO2) sinks that, in parallel, release methane (CH4). The peatland carbon (C) balance depends on the interplay of decomposer and CH4-cycling microbes, vegetation, and environmental conditions. These interactions are susceptible to the changes that occur along a successional gradient from vascular plant-dominated systems to Sphagnum moss-dominated systems. Changes similar to this succession are predicted to occur from climate change. Here, we investigated how microbial and plant communities are interlinked with each other and with ecosystem C cycling along a successional gradient on a boreal land uplift coast. The gradient ranged from shoreline to meadows…

Mesh-adaptive methods for viscous flow problem with rotation

2007

In this paper, new functional type a posteriori error estimates for the viscous flow problem with rotating term are presented. The estimates give guaranteed upper bounds of the energy norm of the error and provide reliable error indication. We describe the implementation of the adaptive finite element methods (AFEM) in the framework of the functional type estimates proposed. Computational properties of the estimates are investigated on series of numerical examples.

An Ecohydrological Cellular Automata Model Investigation of Juniper Tree Encroachment in a Western North American Landscape

2016

Woody plant encroachment over the past 140 years has substantially changed grasslands in western North American. We studied encroachment of western juniper (Juniperus occidentalis var. occidentalis) into a previously mixed shrub–grassland site in central Oregon (USA) using a modified version of Cellular Automata Tree–Grass–Shrub Simulator (CATGraSS) ecohydrological model. We developed simple algorithms to simulate three encroachment factors (grazing, fire frequency reduction, and seed dispersal by herbivores) in CATGraSS. Local ecohydrological dynamics represented by the model were first evaluated using satellite-derived leaf area index and measured evapotranspiration data. Reconstruc…

A Unified Approach to Measuring Accuracy of Error Indicators

2014

In this paper, we present a unified approach to error indication for elliptic boundary value problems. We introduce two different definitions of the accuracy (weak and strong) and show that various indicators result from one principal relation. In particular, this relation generates all the main types of error indicators, which have already gained high popularity in numerical practice. Also, we discuss some new forms of indicators that follow from a posteriori error majorants of the functional type and compare them with other indicators. Finally, we discuss another question related to accuracy of error indicators for problems with incompletely known data.

Functional A Posteriori Error Estimate for a Nonsymmetric Stationary Diffusion Problem

2015

In this paper, a posteriori error estimates of functional type for a stationary diffusion problem with nonsymmetric coefficients are derived. The estimate is guaranteed and does not depend on any particular numerical method. An algorithm for the global minimization of the error estimate with respect to an auxiliary function over some finite dimensional subspace is presented. In numerical tests, global minimization is done over the subspace generated by Raviart-Thomas elements. The improvement of the error bound due to the p-refinement of these spaces is investigated.

Understanding the uncertainty in global forest carbon turnover

2020

Abstract. The length of time that carbon remains in forest biomass is one of the largest uncertainties in the global carbon cycle, with both recent historical baselines and future responses to environmental change poorly constrained by available observations. In the absence of large-scale observations, models used for global assessments tend to fall back on simplified assumptions of the turnover rates of biomass and soil carbon pools. In this study, the biomass carbon turnover times calculated by an ensemble of contemporary terrestrial biosphere models (TBMs) are analysed to assess their current capability to accurately estimate biomass carbon turnover times in forests and how these times a…

Two-Sided Guaranteed Estimates of the Cost Functional for Optimal Control Problems with Elliptic State Equations

2014

In the paper, we discuss error estimation methods for optimal control problems with distributed control functions entering the right-hand side of the corresponding elliptic state equations. Our analysis is based on a posteriori error estimates of the functional type, which were derived in the last decade for many boundary value problems. They provide guaranteed two-sided bounds of approximation errors for any conforming approximation. If they are applied to approximate solutions of state equations, then we obtain new variational formulations of optimal control problems and guaranteed bounds of the cost functional. Moreover, for problems with linear state equations this procedure leads to gu…

Global Upscaling of the MODIS Land Cover with Google Earth Engine and Landsat Data

2021

Image classification has become one of the most common applications in remote sensing yielding to the creation of a variety of operational thematic maps at multiple spatio-temporal scales. The information contained in these maps summarizes key characteristics related with the physical environment and provides fundamental information of the Earth for vegetation monitoring or land use status over time. However, high spatial resolution land cover maps are usually only produced for specific small regions or in an image tile. We present a general methodology to obtain a high spatial resolution land cover maps using Landsat spectral information, the powerful Google Earth Engine platform, and oper…