Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Integrity determination of RTK solutions in precision farming applications

Integrity of Real Time Kinematic (RTK) positioning solutions relates to the confidential level that can be placed in the information provided by the RTK system. It includes the ability of the RTK system to provide timely valid warnings to users when the system must not be used for the intended operation. For instance, in the controlled traffic farming (CTF) system that controls traffic separates wheel beds and root beds, RTK positioning error causes overlap and increases the amount of soil compaction. The RTK system’s integrity capacity can inform users when the actual positional errors of the RTK solutions have exceeded Horizontal Protection Levels (HPL) within a certain Time-To-Alert (TTA) at a given Integrity Risk (IR). The later is defined as the probability that the system claims its normal operational status while actually being in an abnormal status, e.g., the ambiguities being incorrectly fixed and positional errors having exceeded the HPL. The paper studies the required positioning performance (RPP) of GPS positioning system for PA applications such as a CTF system, according to literature review and survey conducted among a number of farming companies. The HPL and IR are derived from these RPP parameters. A RTK-specific rover autonomous integrity monitoring (RAIM) algorithm is developed to determine the system integrity according to real time outputs, such as residual square sum (RSS), HDOP values. A two-station baseline data set is analyzed to demonstrate the concept of RTK integrity and assess the RTK solution continuity, missed detection probability and false alarm probability.

Bioavailability of soil organic carbon and Fe as influenced by forestry practices in a subtropical coastal catchment

Potential impacts of plantation forestry practices on soil organic carbon and Fe available to microorganisms were investigated in a subtropical coastal catchment. The impacts of harvesting or replanting were largely limited to the soil top layer (0–10 cm depth). The thirty-year-old Pinus plantation showed low soil moisture content (Wc) and relatively high levels of soil total organic carbon (TOC). Harvesting and replanting increased soil Wc but reduced TOC levels. Mean dissolved organic carbon (DOC) and microbial biomass carbon (MBC) increased in harvested or replanted soils, but such changes were not statistically significant (P > 0.05). Total dithionite-citrate and aqua regia-extractable Fe did not respond to forestry practices, but acid ammonium oxalate and pyrophosphate-extractable, bioavailable Fe decreased markedly after harvesting or replanting. Numbers of heterotrophic bacteria were significantly correlated with DOC levels (P < 0.05), whereas Fe-reducing bacteria and S-bacteria detected using laboratory cultivation techniques did not show strong correlation with either soil DOC or Fe content.

Soil Carbon Turnover Measurement by Physical Fractionation at a Forest-to-Pasture Chronosequence in the Brazilian Amazon

The effect of conversion from forest-to-pasture upon soil carbon stocks has been intensively discussed, but few studies focus on how this land-use change affects carbon (C) distribution across soil fractions in the Amazon basin. We investigated this in the 20 cm depth along a chronosequence of sites from native forest to three successively older pastures. We performed a physicochemical fractionation of bulk soil samples to better understand the mechanisms by which soil C is stabilized and evaluate the contribution of each C fraction to total soil C. Additionally, we used a two-pool model to estimate the mean residence time (MRT) for the slow and active pool C in each fraction. Soil C increased with conversion from forest-to-pasture in the particulate organic matter (> 250 mu m), microaggregate (53-250 mu m), and d-clay (< 2 mu m) fractions. The microaggregate comprised the highest soil C content after the conversion from forest-to-pasture. The C content of the d-silt fraction decreased with time since conversion to pasture. Forest-derived C remained in all fractions with the highest concentration in the finest fractions, with the largest proportion of forest-derived soil C associated with clay minerals. Results from this work indicate that microaggregate formation is sensitive to changes in management and might serve as an indicator for management-induced soil carbon changes, and the soil C changes in the fractions are dependent on soil texture.

Does physical protection of soil organic matter attenuate temperature sensitivity?

Global climate change may induce accelerated soil organic matter (SOM) decomposition through increased soil temperature, and thus impact the C balance in soils. We hypothesized that compartmentalization of substrates and decomposers in the soil matrix would decrease SOM sensitivity to temperature. We tested our hypothesis with three short-term laboratory incubations with differing physical protection treatments conducted at different temperatures. Overall, CO2 efflux increased with temperature, but responses among physical protection treatments were not consistently different. Similar respiration quotient (Q(10)) values across physical protection treatments did not support our original hypothesis that the largest Q(10) values would be observed in the treatment with the least physical protection. Compartmentalization of substrates and decomposers is known to reduce the decomposability of otherwise labile material, but the hypothesized attenuation of temperature sensitivity was not detected, and thus the sensitivity is probably driven by the thermodynamics of biochemical reactions as expressed by Arrhenius-type equations.

Soil carbon saturation : implications for measurable carbon pool dynamics in long-term incubations

The efficiency of agricultural management practices to store SOC depends on C input level and how far a soil is from its saturation level (i.e. saturation deficit). The C Saturation hypothesis suggests an ultimate soil C stabilization capacity defined by four SOM pools capable of C saturation: (1) non-protected, (2) physically protected, (3) chemically protected and (4) biochemically protected. We tested if C saturation deficit and the amount of added C influenced SOC storage in measurable soil fractions corresponding to the conceptual chemical, physical, biochemical, and non-protected C pools. We added two levels of C-13- labeled residue to soil samples from seven agricultural sites that were either closer to (i.e., A-horizon) or further from (i.e., C-horizon) their C saturation level and incubated them for 2.5 years. Residue-derived C stabilization was, in most sites, directly related to C saturation deficit but mechanisms of C stabilization differed between the chemically and biochemically protected pools. The physically protected C pool showed a varied effect of C saturation deficit on C-13 stabilization, due to opposite behavior of the POM and mineral fractions. We found distinct behavior between unaggregated and aggregated mineral-associated fractions emphasizing the mechanistic difference between the chemically and physically protected C-pools. To accurately predict SOC dynamics and stabilization, C Saturation of soil C pools, particularly the chemically and biochemically protected pools, should be considered. (C) 2008 Elsevier Ltd. All rights reserved.