Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

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.

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.

Experimental warming shows that decomposition temperature sensitivity increases with soil organic matter recalcitrance

Soil C decomposition is sensitive to changes in temperature, and even small increases in temperature may prompt large releases of C from soils. But much of what we know about soil C responses to global change is based on short-term incubation data and model output that implicitly assumes soil C pools are composed of organic matter fractions with uniform temperature sensitivities. In contrast, kinetic theory based on chemical reactions suggests that older, more-resistant C fractions may be more temperature sensitive. Recent research on the subject is inconclusive, indicating that the temperature sensitivity of labile soil organic matter (OM) decomposition could either be greater than, less than, or equivalent to that of resistant soil OM. We incubated soils at constant temperature to deplete them of labile soil OM and then successively assessed the CO2-C efflux in response to warming. We found that the decomposition response to experimental warming early during soil incubation (when more labile C remained) was less than that later when labile C was depleted. These results suggest that the temperature sensitivity of resistant soil OM pools is greater than that for labile soil OM and that global change-driven soil C losses may be greater than previously estimated.

Sensitivity of organic matter decomposition to warming varies with its quality

The relationship between organic matter (OM) lability and temperature sensitivity is disputed, with recent observations suggesting that responses of relatively more resistant OM to increased temperature could be greater than, equivalent to, or less than responses of relatively more labile OM. This lack of clear understanding limits the ability to forecast carbon (C) cycle responses to temperature changes. Here, we derive a novel approach (denoted Q(10-q)) that accounts for changes in OM quality during decomposition and use it to analyze data from three independent sources. Results from new laboratory soil incubations (labile Q(10-q)=2.1 +/- 0.2; more resistant Q(10-q)=3.8 +/- 0.3) and reanalysis of data from other soil incubations reported in the literature (labile Q(10-q)=2.3; more resistant Q(10-q)=3.3) demonstrate that temperature sensitivity of soil OM decomposition increases with decreasing soil OM lability. Analysis of data from a cross-site, field litter bag decomposition study (labile Q(10-q)=3.3 +/- 0.2; resistant Q(10-q)=4.9 +/- 0.2) shows that litter OM follows the same pattern, with greater temperature sensitivity for more resistant litter OM. Furthermore, the initial response of cultivated soils, presumably containing less labile soil OM (Q(10-q)=2.4 +/- 0.3) was greater than that for undisturbed grassland soils (Q(10-q)=1.7 +/- 0.1). Soil C losses estimated using this approach will differ from previous estimates as a function of the magnitude of the temperature increase and the proportion of whole soil OM comprised of compounds sensitive to temperature over that temperature range. It is likely that increased temperature has already prompted release of significant amounts of C to the atmosphere as CO2. Our results indicate that future losses of litter and soil C may be even greater than previously supposed.

Soil management effects on organic carbon in isolated fractions of a Gray Luvisol

Agricultural management affects soil organic matter, which is important for sustainable crop production and as a greenhouse gas sink. Our objective was to determine how tillage, residue management and N fertilization affect organic C in unprotected, and physically, chemically and biochemically protected soil C pools. Samples from Breton, Alberta were fractionated and analysed for organic C content. As in previous report, N fertilization had a positive effect, tillage had a minimal effect, and straw management had no effect on whole-soil organic C. Tillage and straw management did not alter organic C concentrations in the isolated C pools, while N fertilization increased C concentrations in all pools. Compared with a woodlot soil, the cultivated plots had lower total organic C, and the C was redistributed among isolated pools. The free light fraction and coarse particulate organic matter responded positively to C inputs, suggesting that much of the accumulated organic C occurred in an unprotected pool. The easily dispersed silt-sized fraction was the mineral-associated pool most responsive to changes in C inputs, whereas the microaggregate-derived silt-sized fraction best preserved C upon cultivation. These findings suggest that the silt-sized fraction is important for the long-term stabilization of organic matter through both physical occlusion in microaggregates and chemical protection by mineral association.

Acid hydrolysis of easily dispersed and microaggregate-derived silt- and clay-sized fractions to isolate resistant soil organic matter

The current paradigm in soil organic matter (SOM) dynamics is that the proportion of biologically resistant SOM will increase when total SOM decreases. Recently, several studies have focused on identifying functional pools of resistant SOM consistent with expected behaviours. Our objective was to combine physical and chemical approaches to isolate and quantify biologically resistant SOM by applying acid hydrolysis treatments to physically isolated silt- and clay-sized soil fractions. Microaggegrate-derived and easily dispersed silt- and clay-sized fractions were isolated from surface soil samples collected from six long-term agricultural experiment sites across North America. These fractions were hydrolysed to quantify the non-hydrolysable fraction, which was hypothesized to represent a functional pool of resistant SOM. Organic C and total N concentrations in the four isolated fractions decreased in the order: native > no-till > conventional-till at all sites. Concentrations of non-hydrolysable C (NHC) and N (NHN) were strongly correlated with initial concentrations, and C hydrolysability was found to be invariant with management treatment. Organic C was less hydrolysable than N, and overall, resistance to acid hydrolysis was greater in the silt-sized fractions compared with the clay-sized fractions. The acid hydrolysis results are inconsistent with the current behaviour of increasing recalcitrance with decreasing SOM content: while %NHN was greater in cultivated soils compared with their native analogues, %NHC did not increase with decreasing total organic C concentrations. The analyses revealed an interaction between biochemical and physical protection mechanisms that acts to preserve SOM in fine mineral fractions, but the inconsistency of the pool size with expected behaviour remains to be fully explained.

Does the acid hydrolysis-incubation method measure meaningful soil organic carbon pools?

The literature was reviewed and analyzed to determine the feasibility of using a combination of acid hydrolysis and CO2-C release during long-term incubation to determine soil organic carbon (SOC) pool sizes and mean residence times (MRTs). Analysis of 1100 data points showed the SOC remaining after hydrolysis with 6 M HCI ranged from 30 to 80% of the total SOC depending on soil type, depth, texture, and management. Nonhydrolyzable carbon (NHC) in conventional till soils represented 48% of SOC; no-till averaged 56%, forest 55%, and grassland 56%. Carbon dates showed an average of 1200 yr greater MRT for the NHC fraction than total SOC. Longterm incubation, involving measurement of CO2 evolution and curve fitting, measured active and slow pools. Active-pool C comprised 2 to 8% of the SOC with MRTs of days to months; the slow pool comprised 45 to 65% of the SOC and had MRTs of 10 to 80 yr. Comparison of field C-14 and (13) C data with hydrolysis-incubation data showed a high correlation between independent techniques across soil types and experiments. There were large differences in MRTs depending on the length of the experiment. Insertion of hydrolysis-incubation derived estimates of active (C-a), slow (C-s), and resistant Pools (C-r) into the DAYCENT model provided estimates of daily field CO2 evolution rates. These were well correlated with field CO2 measurements. Although not without some interpretation problems, acid hydrolysis-laboratory incubation is useful for determining SOC pools and fluxes especially when used in combination with associated measurements.

Impact of soil texture on the distribution of soil organic matter in physical and chemical fractions

Previous research on the protection of soil organic C from decomposition suggests that soil texture affects soil C stocks. However, different pools of soil organic matter (SOM) might be differently related to soil texture. Our objective was to examine how soil texture differentially alters the distribution of organic C within physically and chemically defined pools of unprotected and protected SOM. We collected samples from two soil texture gradients where other variables influencing soil organic C content were held constant. One texture gradient (16-60% clay) was located near Stewart Valley, Saskatchewan, Canada and the other (25-50% clay) near Cygnet, OH. Soils were physically fractionated into coarse- and fine-particulate organic matter (POM), silt- and clay-sized particles within microaggregates, and easily dispersed silt-and clay-sized particles outside of microaggregates. Whole-soil organic C concentration was positively related to silt plus clay content at both sites. We found no relationship between soil texture and unprotected C (coarse- and fine-POM C). Biochemically protected C (nonhydrolyzable C) increased with increasing clay content in whole-soil samples, but the proportion of nonhydrolyzable C within silt- and clay-sized fractions was unchanged. As the amount of silt or clay increased, the amount of C stabilized within easily dispersed and microaggregate-associated silt or clay fractions decreased. Our results suggest that for a given level of C inputs, the relationship between mineral surface area and soil organic matter varies with soil texture for physically and biochemically protected C fractions. Because soil texture acts directly and indirectly on various protection mechanisms, it may not be a universal predictor of whole-soil C content.

Stabilization mechanisms of soil organic matter: Implications for C-saturation of soils

The relationship between soil structure and the ability of soil to stabilize soil organic matter (SOM) is a key element in soil C dynamics that has either been overlooked or treated in a cursory fashion when developing SOM models. The purpose of this paper is to review current knowledge of SOM dynamics within the framework of a newly proposed soil C saturation concept. Initially, we distinguish SOM that is protected against decomposition by various mechanisms from that which is not protected from decomposition. Methods of quantification and characteristics of three SOM pools defined as protected are discussed. Soil organic matter can be: (1) physically stabilized, or protected from decomposition, through microaggregation, or (2) intimate association with silt and clay particles, and (3) can be biochemically stabilized through the formation of recalcitrant SOM compounds. In addition to behavior of each SOM pool, we discuss implications of changes in land management on processes by which SOM compounds undergo protection and release. The characteristics and responses to changes in land use or land management are described for the light fraction (LF) and particulate organic matter (POM). We defined the LF and POM not occluded within microaggregates (53-250 mum sized aggregates as unprotected. Our conclusions are illustrated in a new conceptual SOM model that differs from most SOM models in that the model state variables are measurable SOM pools. We suggest that physicochemical characteristics inherent to soils define the maximum protective capacity of these pools, which limits increases in SOM (i.e. C sequestration) with increased organic residue inputs.

Spatial variability of soil organic carbon in grasslands: implications for detecting change at different scales

Extensive data used to quantify broad soil C changes (without information about causation), coupled with intensive data used for attribution of changes to specific management practices, could form the basis of an efficient national grassland soil C monitoring network. Based on variability of extensive (USDA/NRCS pedon database) and intensive field-level soil C data, we evaluated the efficacy of future sample collection to detect changes in soil C in grasslands. Potential soil C changes at a range of spatial scales related to changes in grassland management can be verified (alpha=0.1) after 5 years with collection of 34, 224, 501 samples at the county, state, or national scales, respectively. Farm-level analysis indicates that equivalent numbers of cores and distinct groups of cores (microplots) results in lowest soil C coefficients of variation for a variety of ecosystems. Our results suggest that grassland soil C changes can be precisely quantified using current technology at scales ranging from farms to the entire nation. (C) 2001 Elsevier Science Ltd. All rights reserved.