Spatial Coefficient Of Variation Research Articles

On the local well-posedness for the nonlinear Schrödinger equation with spatial variable coefficient

We study a new type of nonlinear Schrödinger equation where the coefficient of Laplacian depends on spatial variable. Based on a modified Hankel transform and delicate frequency estimates, we establish the local well-posedness of the NLS with spatial variable coefficient in the weighted Lebesgue space for n≥2, and extend the Strichartz estimates to the non-radially Schrödinger equation with spatial variable coefficient in 2D Euclidian space.

Spatial Variability and Distribution of the Metals in Surface Runoff in a Nonferrous Metal Mine.

The spatial variation and distribution features of the metals tested in the surface runoff in Xikuangshan Bao Daxing miming area were analyzed by combining statistical methods with a geographic information system (GIS). The results showed that the maximum concentrations of those five kinds of the metals (Sb, Zn, Cu, Pb, and Cd) in the surface runoff of the antimony mining area were lower than the standard value except the concentration of metal Ni. Their concentrations were 497.1, 2.0, 1.8, 22.2, and 22.1 times larger than the standard value, respectively. This metal pollution was mainly concentrated in local areas, which were seriously polluted. The variation coefficient of Sb, Zn, Cu, Ni, Pb, and Cd was between 0.4 to 0.6, wherein the Sb's spatial variability coefficient is 50.56%, indicating a strong variability. Variation coefficients of the rest of metals were less than 50%, suggesting a moderate variability. The spatial structure analysis showed that the squared correlation coefficient (R 2) of the models fitting for Sb, Zn, Cu, Ni, Pb, and Cd was between 0.721 and 0.976; the ratio of the nugget value (C 0) to the abutment value (C + C 0) was between 0.0767 and 0.559; the semivariogram of Sb, Zn, Ni, and Pb was in agreement with a spherical model, while semivariogram of Cu and Cd was in agreement with Gaussian model, and both had a strong spatial correlation. The trend and spatial distribution indicated that those pollution distributions resulting from Ni, Pb, and Cd are similar, mainly concentrated in both ends of north and south in eastern part. The main reasons for the pollution were attributed to the residents living, transportation, and industrial activities; the Sb distribution was concentrated mainly in the central part, of which the pollution was assigned to the mining and the industrial activity; the pollution distributions of Zn and Cu were similar, mainly concentrated in both ends of north and south as well as in west; the sources of the metals were widely distributed.

Boundary control method to identification of elastic modulus of string equation from Neumann-Dirichlet map

This paper considers identification for the spatial variable coefficient of a vibrating string with Neumann boundary control from the measured boundary displacement. The reconstruction algorithm consists of two steps: The first step is to recover the spectral data from the measured boundary displacement by showing that the system is spectral controllable; the second step is to reconstruct the coefficient from the recovered spectral data using the boundary control method, for which the required exact controllability is also verified.

Design and characterization of spatial units for monitoring global impacts of environmental factors on major crops and food security

AbstractThis paper describes the design and characterization of a limited number of areas to be used as spatial monitoring and reporting units (MRU) by CropWatch, the global crop monitoring system ( http://www.cropwatch.com.cn/) hosted by the Chinese Academy of Sciences. The MRUs are modified and adapted from an existing standard vegetation zoning map. They are designed to be areas of uniform vulnerability as assessed by three sets of variables: environmental (such as climate and NDVI), seasonality (such as intra‐annual climate variations and interannual NDVI variability) and agronomy (such as presence/absence of major crops and their yield). The paper pays due attention to within‐zone spatial variability for each of the three groups of variables: in general, the variability measured as the average of the spatial coefficient of variation inside MRUs, is much larger for agronomic variables (330%) than for environmental variables (38%) and seasonality (55%). The MRUs provide a rather coherent picture of the variations of global agriculture, for instance, the links between the distribution of crops, agricultural production potential, and environmental variability (over space and time). They closely delineate the distribution of the major nonsugar food crops (barley, cassava, maize, potatoes, rice, soybean, and wheat). The discussion focuses on the relations between the size of the MRUs and the within‐MRU variability (spatial heterogeneity) of cropping, and environmental conditions including seasonality. The conclusion stresses that spatial variability in agriculture is bound to be larger than the variability in the environmental variables used to define the units, regardless of the units’ size. The size of the spatial units (and therefore their number) is not a very critical constraint for operational impact reporting, especially if impact indicators focus on agricultural areas inside MRUs.

Studying the spatial variability of methane flux with five eddy covariance towers of varying height

In this study, the spatial representativeness of eddy covariance (EC) methane (CH4) measurements was examined by comparing parallel CH4 fluxes from three short (6m) towers separated by a few kilometres and from two higher levels (20m and 60m) at one location. The measurement campaign was held on an intensively managed grassland on peat soil in the Netherlands. The land use and land cover types are to a large degree homogeneous in the area.The CH4 fluxes exhibited significant variability between the sites on 30-min scale. The spatial coefficient of variation (CVspa) between the three short towers was 56% and it was of similar magnitude as the temporal variability, unlike for the other fluxes (friction velocity, sensible heat flux) for which the temporal variability was considerably larger than the spatial variability. The CVspa decreased with temporal averaging, although less than what could be expected for a purely random process (1/N), and it was 14% for 26-day means of CH4 flux. This reflects the underlying heterogeneity of CH4 flux in the studied landscape at spatial scales ranging from 1ha (flux footprint) to 10km2 (area bounded by the short towers). This heterogeneity should be taken into account when interpreting and comparing EC measurements. On an annual scale, the flux spatial variability contributed up to 50% of the uncertainty in CH4 emissions. It was further tested whether EC flux measurements at higher levels could be used to acquire a more accurate estimate of the spatially integrated CH4 emissions. Contrarily to what was expected, flux intensity was found to both increase and decrease depending on measurement height. Using footprint modelling, 56% of the variation between 6m and 60m CH4 fluxes was attributed to emissions from local anthropogenic hotspots (farms). Furthermore, morning hours proved to be demanding for the tall tower EC where fluxes at 60m were up to four-fold those at lower heights. These differences were connected with the onset of convective mixing during the morning period.

Variability in shortwave irradiance caused by forest gaps: Measurements, modelling, and implications for snow energetics

Solar irradiance in and around forest gaps plays a key role in determining the snowmelt patterns that shape how forest gaps influence spring snow cover retention relative to open or continuously forested landscapes. To reduce uncertainty in forest gap snowmelt estimation, a new canopy solar transmittance model was developed to include the effects of shading and enhanced transmittance. The model couples a new a ray tracing approach with an existing canopy solar radiation extinction and transmission model. The new model analytically solves for the path length of a solar ray (beam) through a forest canopy and potential intersection(s) with a forest gap conceptualized as an upright circular cylinder surrounded by homogeneous forest. The model was tested alongside simpler transmittance models that ignored shading and treated the canopy as either a binary (open or forested) classification or that used proximal canopy descriptors. The models were evaluated using measurements of shortwave radiation from 20 pyranometers in and around a 56 m diameter gap in a coniferous forest. Errors from ignoring shading were greatest in the gap near the forest edge and in the forest nearest the northern gap edge. The new model reduced these errors; at the 20 pyranometer locations, individual biases up to +356Wm−2 and average biases up to +101Wm−2 were reduced to better than ±5Wm−2. Results suggest that an accurate description of spatial variability of solar irradiance in and around a forest gap requires explicit treatment of the effects of shading into a gap and enhanced transmittance beyond the gap extent; this is dependent upon solar position, gap and forest geometry, and location relative to the gap. A sensitivity experiment with the forest gap – ray trace model in which gap size, latitude, and day of year were varied under clear-sky conditions showed that cumulative daily solar irradiance has high spatiotemporal variability. The maximum of the spatial coefficient of variation (CV) of cumulative daily irradiance was a function of gap size and solar angles; smaller (larger) gaps and lower (higher) solar elevation angle ranges were more diffuse- (direct beam-) dominated with reduced (increased) spatial variability relative to the mean. It is found that there is no standard impact of a forest gap on shortwave irradiance – the impact of gap size on clear sky solar irradiance depends on forest structure, date, and latitude.

Surface Radiance Temperature Variability Analysis through Multi-Level Cell Matrix (MLCM) and Statistical Techniques

The global inclination towards the urbanization enlightens the evolving concern for study on variation of the urban climate due to the heat island effect and global warming. Surface radiance temperature (SRT) is undoubtedly one of the most significant parameters in urban. The work presents the thermal image processing techniques to retrieve the SRT from the LandSat ETM+ data. The spatial variability was analyzed to illustrate their indigenous spatial distribution over urban-rural (Rurban) areas contributing to heat island. The results apparently indicate the increasing spatial thermal configuration along Rurban areas and vice versa. The percentage of urban landscape patches with high, sub high and low densities indicates their inherent characteristics. High temperature type was the dominant class in urban core, while sub medium temperature and low temperature type was the main heat landscape type in rural area. In the urban fringe, temperature variability showed very complex result from the various land use. Statistical tools such as spatial coefficient of variation, the correlogram and Semivariograms are introduced to characterize the spatial variability for each of the directional attribute. These tools also helped in detecting and quantifying the major to minor scales of spatial variability. The study also validates that the approach of integration of spatial variability with statistics for a reliable tool to monitor the thermal dynamics. The present paper addresses the role of urban behavior in the study of thermal variability for understanding energy demand.

Preliminary analysis of spatiotemporal pattern of global land surface water

Land surface water (LSW) is one of the most important resources for human survival and development, and it is also a main component of global water recycling. A full understanding of the spatial distribution of land surface water and a continuous measuring of its dynamics can support to diagnose the global ecosystem and environment. Based on the Global Land 30-water 2000 and Global Land 30-water 2010 products, this research analyzed the spatial distribution pattern and temporal fluctuation of land surface water under scale-levels of global, latitude and longitude, continents, and climate zones. The Global Land 30-water products were corrected the temporal inconsistency of original remotely sensed data using MODIS time-series data, and then calculated the indices such as water area, water ration and coefficient of spatial variation for further analysis. Results show that total water area of land surface is about 3.68 million km2 (2010), and occupies 2.73% of land area. The spatial distribution of land surface water is extremely uneven and is gathered mainly in mid- to high-latitude area of the Northern Hemisphere and tropic area. The comparison of water ratio between 2000 and 2010 indicates the overall fluctuation is small but spatially differentiated. The Global Land 30-water products and the statistics provided the fundamental information for analyzing the spatial distribution pattern and temporal fluctuation of land surface water and diagnosing the global ecosystem and environment.

Estimating the spatial means and variability of root-zone soil moisture in gullies using measurements from nearby uplands

Root-zone soil moisture is of critical importance to vegetation restoration, runoff and erosion processes in gullies, especially in arid and semiarid areas. Nevertheless, data relating to soil moisture in gullies are rare, since it is difficult to record in such environments. We hypothesize that mean soil moisture and its spatial variability within gullies could be estimated reliably on the basis of measurements from adjacent uplands, where data are much easier to collect. In this study, we proposed five different strategies to estimate root-zone (0–20, 20–40, 40–60 and 60–80 cm) spatial mean soil moisture in gullies and three different strategies to estimate soil moisture spatial variability at the corresponding depths, using measurements collected from nearby uplands, based on 2-year soil moisture data collection campaigns in the Yuanzegou gully catchment on the Chinese Loess Plateau. The estimation errors were quantified for each strategy. The results showed that spatial mean soil moisture (θ¯g) at each depth in gullies was reliably estimated from observations collected at a single upland location when previous soil moisture data collected simultaneously for gullies and uplands were available. The upland locations that were within a ±5% relative bias error for the estimation of θ¯g had similar average percentage clay content (16.1%) in the surface layer (0–20 cm) to that in the gullies (15.7%), and moderately steeper slopes (from 36.6% to 53.1%) compared to the upland average (39.4%). When previous soil moisture data were not available, the estimation was much less accurate. Furthermore, when different number of upland locations were randomly selected to estimate θ¯g, the estimation accuracy was only improved slightly when more than 10 locations were used. Based on the best estimated θ¯g and the quantitative relationship between spatial means and spatial variability of soil moisture in gullies, we were able to obtain the estimates of spatial soil moisture variability (standard deviation and coefficient of variation) with a certain level of accuracy (R2 from 0.300 to 0.625) in gullies at each depth. However, when the quantitative relationship was not available, there were much greater estimation errors. Our results demonstrated that spatial means and variability of soil moisture could be reliably estimated using measurements from nearby uplands provided previous soil moisture datasets for gullies and upland locations are simultaneously available.

Temporal and spatial variation of seedfall in a broad-leaved evergreen forest in Gutianshan Nature Reserve of Zhejiang Province, China

Aims Seedfall of woody plants often fluctuates considerably from year to year and from site to site. These varia- tions may have strong effects not only on the recruitment of the plant populations themselves, but also on the community composition and structure. Our objective was to elucidate seasonal, annual and spatial variations of seedfall in broad-leaved evergreen forest in Gutianshan Nature Reserve of Zhejiang Province over four years. Methods Seed rain was censused weekly since June 2006, using 130 seed traps set along 2.3 km of trails within the Gutianshan 24 hm 2 subtropical evergreen forest plot. Each seed trap consisted of a square, 0.5 m 2 Poly Vinyl Chloride (PVC) frame supporting a shallow, open-topped, 1-mm nylon mesh bag suspended 0.8 m above the ground. Because of heavy snowfall in February 2008, seed traps were damaged, and all seed traps were reset. Therefore, seed rain data were absent from February to April 2008. We summarized four years of seed rain data from June 2006 to August 2010. Important findings There were a total of 124 227 seeds over the four years, belonging to 63 species, 51 genera and 29 families, and the Pearson correlation between adult tree basal area and seed production was significant. There was a marked peak in the number of seeds and species in each year in the dry season (autumn), but there were also ten species that dispersed their seeds in the wet season. Different species had different fruiting dates. Based on four years of seed rain data, annual variation in seedfall (CVyears) on Gutianshan was substantial (CVyears > 75% for almost all species), and the median coefficient of variation of annual seedfall was 1.72. Spatial varia- tion was also great, and the median coefficient of spatial variation in seedfall among traps was 8.06. Spatial varia- tion in seedfall density was greater than annual variation for almost all species. The rarity of seed-bearing adults, variation in seed deposition with distance, and different topography might be the most important sources of this spatial variation. Comparing with Barro Colorado Island tropical forest seed rain, Gutianshan data supported the

Interannual variability of snowmelt in the Sierra Nevada and Rocky Mountains, United States: Examples from two alpine watersheds

The distribution of snow and the energy flux components of snowmelt are intrinsic characteristics of the alpine water cycle controlling the location of source waters and the effect of climate on streamflow. Interannual variability of these characteristics is relevant to the effect of climate change on alpine hydrology. Our objective is to characterize the interannual variability in the spatial distribution of snow and energy fluxes of snowmelt in watersheds of a maritime setting, Tokopah Basin (TOK) in California's southern Sierra Nevada, and a continental setting, Green Lake 4 Valley (GLV4) in Colorado's Front Range, using a 12 year database (1996–2007) of hydrometeorological observations and satellite‐derived snow cover. Snowpacks observed in GLV4 exhibit substantially greater spatial variability than in TOK (0.75 versus 0.28 spatial coefficient of variation). In addition, modeling results indicate that the net turbulent energy flux contribution to snowmelt in GLV4 is, on average, 3 times greater in magnitude (mean 29% versus 10%) and interannual variability (standard deviation 17% versus 6%) than in TOK. These energy flux values exhibit strong seasonality, increasing as the melt season progresses to times later in the year (R2 = 0.54–0.77). This seasonality of energy flux appears to be associated with snowmelt rates that generally increase with onset date of melt (0.02 cm d−2). This seasonality in snowmelt rate, coupled to differences in hydrogeology, may account for the observed differences in correspondence between the timing of snowmelt and timing of streamflow in these watersheds.

Mass dynamics of coarse woody debris in an old-growth deciduous forest of Gwangneung, Korea

We investigated the mass dynamics of coarse woody debris (CWD) in an old-growth deciduous forest dominated by Quercus serrata, Carpinus laxiflora, and C. cordata in a 1 ha permanent plot of the Gwangneung Experiment Forest, Korea, from 2002 through 2010. CWD mass varied from 16.8 to 34.2 Mg ha−1, and the ratio of CWD mass to stand biomass varied from 0.06 to 0.13. The mean CWD mass input and loss rates were 4.81 Mg ha−1 yr−1 and 2.28 Mg ha−1 yr−1, respectively. A large heterogeneity of CWD mass, as represented by the spatial coefficient of variation (127.2%) and annual coefficient of variation (178.5%), might be inherent in the old-growth temperate forest, which consisted of large biomass trees. The decay rate constant, as estimated from the wood density change, was 0.049yr−1. However, the large variation of annual CWD mass input could cause the overestimation of decay rate constant (0.167 yr−1) as calculated from the ratio of CWD mass input to CWD mass. According to the CWD decay class classification, class II (72.8%) comprised the majority of CWD mass. The proportion of CWD mass to total CWD mass was 57.5% for Q. serrata, 25.0% for C. laxiflora, and 10.4% for C. cordata, respectively, and corresponded to the proportion of stem biomass to total stem biomass. These data support the stability of the current status in this old-growth deciduous forest as representing the climax stage. Due to the relatively short-term measurement of CWD mass compared with the whole life span of CWD, additional long-term studies with various approaches are required to enhance the knowledge of CWD mass dynamics in this forest.

The Impact of Pharmacologic Sympathetic and Parasympathetic Blockade on Atrial Electrogram Characteristics in Patients with Atrial Fibrillation

Ablation of atrial autonomic inputs exerts antifibrillatory effects. However, because ablation destroys both myocardium and nerve cells, the effect of autonomic withdrawal alone remains unclear. We therefore examined the effects of pharmacologic autonomic blockade (PAB) on frequency and fractionation in patients with atrial fibrillation (AF). Esmolol and atropine were administered and electrograms were recorded simultaneously from both atria and the coronary sinus. In 17 patients, AF was recorded for 5 minutes and dominant frequency (DF) and continuous activity (CA) were compared before and during PAB. Examination of the pooled data (537 sites, 17 patients) revealed a statistically significant decrease in mean DF (5.61–5.43Hz, P < 0.001) during PAB. Site-by-site analysis showed that 67% of sites slowed (0.45 ± 0.59 Hz), whereas 32% accelerated (0.49 ± 0.59Hz). Fractionation was reduced: median CA decreased from 31% to 26% (P < 0.001). In patient-by-patient analysis, mean DF/median CA decreased in 13 of 17 patients and increased in four. The spatial heterogeneity of DF decreased in nine of 17 patients (spatial coefficient of variation of DF at "nondriver sites" decreased by a mean of 2%). PAB decreases DF and CA in the majority of sites. Given the complexity of interactions between atrial cells during AF, the effects of PAB on DF and fractionation are more heterogeneous than the effects of PAB on isolated cells.

Spatial variability and diffuse attenuation coefficient of remote sensing inversion in Lake Chaohu

根据2009年6月巢湖32个样点的实测数据, 分析巢湖水体漫衰减系数光谱特征、主导因子、空间分布规律以及400-700nm各波段K_d与K_d(490)之间的关系, 并在此基础上, 建立了K_d的遥感反演模型.结果表明:巢湖水体K_d具有一致的光谱特征, 400-600nm之间K_d随波长的增加呈指数衰减趋势, 在600-700nm之间的变化较小, 部分点位在波长675nm附近出现峰值, 700-900nm之间K_d呈现出类似于纯水的吸收光谱特征;巢湖中无机颗粒物是水体漫衰减的主导因子, 有机悬浮物影响次之, CDOM的影响最小;巢湖东半湖区K_d(490)普遍高于西半湖区, 巢湖中部K_d(490)等值线分布较密集, 湖区其他部分则相对稀疏;利用591、702、842nm处的遥感反射率进行多元线性回归反演得到的K_d(490)与实测K_d(490)之间的平均相对误差为7.85%;同时, 400-550nm波段范围内, 可以利用线性关系和K_d(490)对K_d(λ, λ≠490nm)进行参数化表示, 在550-700nm波段范围则可采用常数与K_d(490)的乘积来表示K_d(λ, λ≠490mn).通过遥感反射率反演K_d(490), 进而推算K_d(λ), 其结果与实测K_d之间的平均相对误差为6.14%。;According to the in situ measured data on 32 sampling sites in Lake Chaohu in June 2009, the spectral characteristics of diffuse attenuation coefficient (K_d), dominant factors, spatial distribution, as well as the relationship between K_d and K_d (490) in 400-700nm bands were analyzed.On the basis of these analysis, remote sensing inversion model was developed to calculate K_d (490).The results indicate that presented the consistent spectral characteristics.The K_d in 400-600nm showed a exponential decay trend, but K_d from 600nm to 700nm didn't correlate with wavelength.Due to the higher concentration of phytoplankton in some locations, peak values of K_d appeared at 675nm;but K_d showed a feature that was similar to that of pure water in 700-900nm.The dominant factor of diffuse attenuation coefficient was inorganic particles in Lake Chaohu, organic particles took the second place, and CDOM held a minimal impact.In general, K_d(490) in the eastern part of the Lake Chaohu was higher than that in the western part.In the central part, the contour lines of K_d(490) were denser than those in other parts of the lake.K_d(490) was inversed by multivariate linear regression model established with R_rs(591), R_rs(702) and R_rs(842).And the average relative error between measured and in versed K_d (490) was 7.85%.At the same time, the relationship between K_d(λ, λ≠ 490nm) and K_d(490) could be parameterized with wavelength by linear formula in 400-550nm.From 550nm to 700nm K_d(λ, λ≠490nm) was obtained from multiplying K_d(490) by a constant.The relative error between the observed K_d and the K_d(λ), which was calculated by K_d(490) by inversing of the R_rs, was 6.14%.

Spatial and temporal variability of dissolved nitrous oxide in near‐surface groundwater and bubble‐mediated mass transfer to the unsaturated zone

AbstractUnderstanding spatial and temporal variability of dissolved nitrous oxide (N2O) is essential to process understanding of N2O emissions from near‐surface groundwater to the unsaturated zone and to the atmosphere. We propose a conceptual model of bubble‐mediated mass transfer within the exchange zone defined by the range of groundwater fluctuations. Based on this model, we discuss our experimental data collected over a period of 2 years from of a small‐scale test site (6.5 m × 2.5 m × 5 m, 20 observation wells), where we measured the dissolved gases N2O and O2 at five different depths ( 0.1, 0.5, 0.8, 1.5, and 2.5 m below groundwater level).We show by visualization of the spatially interpolated data and by descriptive statistics that the N2O concentration of near‐surface groundwater exhibits a significant anticorrelation to O2 concentration, a spatial coefficient of variation up to 260%, and a spatial‐correlation range at the meter‐scale. The temporal variation of the spatially averaged data is correlated to the temporal variation of the averaged groundwater level. The implications of high spatial and temporal variability on gradient‐based flux models like the steady state–flat interface model usually used in literature are discussed. Our main conclusion is that both the steady‐state assumption and the flat‐interface model are far from being realistic, because of (1) the highly transient behavior of the exchange zone and (2) the oversimplification of the gas–water interface that underestimates mass transfer by order of magnitudes compared to bubble‐mediated mass transfer.

Homogenization of nonlinear reaction-diffusion equation with a large reaction term

This paper deals with the homogenization of a second order parabolic operator with a large nonlinear potential and periodically oscillating coefficients of both spatial and temporal variables. Under a centering condition for the nonlinear zero-order term, we obtain the effective problem and prove a convergence result. The main feature of the homogenized equation is the appearance of a non-linear convection term.

Macroscopic Rock Texture Image Classification Using a Hierarchical Neuro-Fuzzy Class Method

We used a Hierarchical Neuro-Fuzzy Class Method based on binary space partitioning (NFHB-Class Method) for macroscopic rock texture classification. The relevance of this study is in helping Geologists in the diagnosis and planning of oil reservoir exploration. The proposed method is capable of generating its own decision structure, with automatic extraction of fuzzy rules. These rules are linguistically interpretable, thus explaining the obtained data structure. The presented image classification for macroscopic rocks is based on texture descriptors, such as spatial variation coefficient, Hurst coefficient, entropy, and cooccurrence matrix. Four rock classes have been evaluated by the NFHB-Class Method: gneiss (two subclasses), basalt (four subclasses), diabase (five subclasses), and rhyolite (five subclasses). These four rock classes are of great interest in the evaluation of oil boreholes, which is considered a complex task by geologists. We present a computer method to solve this problem. In order to evaluate system performance, we used 50 RGB images for each rock classes and subclasses, thus producing a total of 800 images. For all rock classes, the NFHB-Class Method achieved a percentage of correct hits over 73%. The proposed method converged for all tests presented in the case study.

A numerical algorithm for the solution of an intermediate fractional advection dispersion equation

One of the main applications of fractional derivative is in the modeling of intermediate physical processes. In this work, the methodology of fractional calculus is used to model the intermediate process between advection and dispersion as an initial-boundary-value problem for a partial differential equation of fractional order with one spatial variable and constant coefficients. A numerical algorithm based on symbolic computations for the solution of the problem is suggested and tested with good results.

Approaches to objective assessment of differences in tissue textures by ultrasound equipment as a contribution to quality assurance

For clinical investigators the increasing number of ultrasonic machines with different technological equipment makes it difficult to reliably assess their ability to differentiate between the textures of various tissues. We investigated a procedure for a standardised method to measure the tissue texture when using different ultrasonic machines. The texture parameters concern brightness, standard deviation, coefficient of variation and spatial coefficient of variation. These were calculated for three tissue phantoms with changing levels of gain and distance. These parameters, well established in literature for speckle detection, texture differentiation and contrast monitoring were useful for rapid comparison of the texture differentiation achieved by several ultrasonic machines. A linear relationship between standard deviation and mean image brightness seems to be an important factor for the detection of small changes in ultrasonic textures. We noticed great differences between the various ultrasonic machines tested by us. The best parameter in our set was the spatial coefficient of variation. The method allows rapid orientation regarding the ability of a machine to distinguish between several textures depending on the brightness, and offers an opportunity of determining the best working point for a given machine.

Effects of forest floor organic layer and root biomass on soil respiration following boreal forest fire

Soil respiration and its spatial and temporal variation were studied at three boreal forest sites in central Saskatchewan, Canada, burned in 1998, 1989, and 1977. Soil respiration, soil temperature, and organic layer thickness were measured at 100 points in a grid pattern of 2 m × 2 m at each site in 2004 and 2005. The mean within-site spatial coefficient of variation was 35%, and the measurements were not spatially autocorrelated. We found no significant difference in variance between the two youngest sites (P &gt; 0.05), whereas the older site showed significantly lower variance (P &lt; 0.05). Soil respiration was not correlated with the forest floor organic layer thickness at any of the sites (R2 &lt; 0.1). Removal of the forest floor layer reduced the soil respiration by 17% to 38%, depending on the site. Thus, the respiration from the mineral soil seemed to contribute a major fraction of the total soil respiration (62%–83%). Soil respiration was positively linearly related to the fine root biomass (R2 = 0.63–0.85, P &lt; 0.05) at all sites. We conclude that variation in root biomass has a larger effect than differential forest floor organic layers on variation in soil respiration in young boreal postfire forests.