Improved methods of estimating root length using a photocopier,a light box and a bar code reader

Photocopying was found to be a rapid method of making a permanent record of a root sample. The method used produced a copy with white roots against a black background. Manual estimates of root length were made from photocopies using a light box. The number of intersections visible when laid over a copy of a white on black regular square grid was counted. Automated estimates of root length were made by scanning a photocopy with a bar code reader in place of a pen in a computer-driven graph plotter. Roots >0.2 mm diameter were resolved with precision and speed.     

Responses of root length/leaf area ratio and specific root length of an understory herb, Pteridophyllum racemosum, to increases in irradiance

The understory evergreen perennial Pteridophyllum racemosum Sieb. et Zucc. (Papaveraceae) has the ability to increase root mass per unit transpiring leaf area (RMA) if irradiance increases gradually over several years. In this study, we examined how P. racemosum changes its root length/leaf area ratio and specific root length when the species encounters abrupt increases in irradiance, such as sudden and unexpected canopy openings. Plants were transplanted from a low light condition in a subalpine wave-regenerating forest (photon flux density on the forest floor relative to the full sun (RPFD) was 2.7%) to a high light condition in a glasshouse (30% RPFD) (LH treatment). Transplantation from the low light condition in the forest to a low light condition in the glasshouse (LL) and transplantation from a high light condition in the forest (33% RPFD) to a high light condition in the glasshouse (HH) were also conducted as controls. Compared to the LL plants, the LH plants exhibited significant increases in RMA and root length/leaf area ratio from 30 to 70 days after transplantation. On the other hand, the effect of increased irradiance on specific root length (SRL) was weak, and both the LL and LH plants showed increased SRL from 30 to 70 days after transplantation. Increased SRL results from longer root length per unit construction cost. We concluded that increased root length/leaf area ratio of P. racemosum in response to abrupt increases in irradiance was caused by a combination of enhanced carbon allocation to roots with increased SRL.     

水曲柳根系生物量、比根长和根长密度的分布格局

采用连续钻取土芯法在生长季内对东北林业大学帽儿山实验林场17年生水曲柳人工林根系取样,研究水曲柳不同直径根系现存生物量、比根长和根长密度及垂直分布状况.结果表明,水曲柳人工林根系总生物量为1 637.6 g·m^-2,其中活根生物量占85%,死根占15%.在活根生物量当中,粗根(直径5～30 mm)占的比例最高（69.95%）,其次为活细根（直径<1 mm,13.53%）,小根(1～2 mm)和中等直径的根(2～5 mm)比例较小（分别为7.21%和9.31%）.直径<1 mm活细根的比根长为32.20 m·g^-1,直径5～30 mm粗根的比根长为0.08 m·g^-1.单位面积上活根的总长度为6 602.54 m·m^-2,其中直径<1 mm的细根占92.43%,其它直径等级则不到活根总长度的8%.直径<1 mm的细根生物量与根长密度具显著线性关系（R²=0.923）,但与比根长无显著相关关系（R²=0.134）.     

Sieve size effects on root length and biomass measurements of maize (Zea mays) and Grevillea robusta

The purpose of this study was to investigate the effects of different mesh sizes on the recovery of root length and biomass and to determine whether the degree of recovery was influenced by plant species and sample location. Sieves of 2.0, 1.0, 0.5 and 0.25 mm (4.0, 1.0, 0.25 and 0.06 mm2) mesh sizes were used to recover and measure the root length and biomass of Zea mays L. (maize) at 0–15 cm and 30–45 cm depths and of Grevillea robusta A. Cunn. ex R. Br. (grevillea) at the same depths 1.0 m and 4.5 m from a line of grevillea trees. At 0–15 cm, the coarser sieves (sum collected with 2.0 and 1.0 mm sieves) recovered approximately 80% of the total root biomass measured, but only 60% of the root length. The proportion of total maize root length and biomass recovered by the coarser sieves decreased with soil depth. The proportion of total grevillea root length recovered by the coarser sieves was similar at the two soil depths, but increased slightly with distance from the tree line. The ≥ 0.5 mm sieves recovered between 93 and 96% of grevillea and maize root biomass and between 73 and 98% of their root length, depending on the sample location. Roots passing through the 0.5 mm sieve, but recovered by the 0.25 mm sieve were about 20% of total maize root length and grevillea root length at 1.0 m from the tree line but < 5% of the total grevillea root length at 4.5 m from the tree. Roots passing through the 0.5 mm sieve but recovered by the 0.25 mm sieve contributed only slightly to root biomass. Although the ≥ 0.5 mm sieves provided adequate measurements of root biomass, the ≥ 0.25 mm sieves were required for accurate measurement of fine root length. There was no universal correction for root length and biomass underestimation when large sieve sizes were used because the proportions of length and biomass recovered depended on the plant species and on soil depth and distance from the plant. This revised version was published online in August 2006 with corrections to the Cover Date.     

Relationships between root diameter,root length and root branching along lateral roots in adult,field-grown maize

Background and Aims Root diameter, especially apical diameter, plays an important role in root development and function. The variation in diameter between roots, and along roots, affects root structure and thus the root system’s overall foraging performance. However, the effect of diameter variation on root elongation, branching and topological connections has not been examined systematically in a population of high-order roots, nor along the roots, especially for mature plants grown in the field.Methods A method combining both excavation and analysis was applied to extract and quantify root architectural traits of adult, field-grown maize plants. The relationships between root diameter and other root architectural characteristics are analysed for two maize cultivars.Key Results The basal diameter of the lateral roots (orders 1–3) was highly variable. Basal diameter was partly determined by the diameter of the bearing segment. Basal diameter defined a potential root length, but the lengths of most roots fell far short of this. This was explained partly by differences in the pattern of diameter change along roots. Diameter tended to decrease along most roots, with the steepness of the gradient of decrease depending on basal diameter. The longest roots were those that maintained (or sometimes increased) their diameters during elongation. The branching density (cm^–1) of laterals was also determined by the diameter of the bearing segment. However, the location of this bearing segment along the mother root was also involved – intermediate positions were associated with higher densities of laterals.Conclusions The method used here allows us to obtain very detailed records of the geometry and topology of a complex root system. Basal diameter and the pattern of diameter change along a root were associated with its final length. These relationships are especially useful in simulations of root elongation and branching in source–sink models.     

A comparison of methods for converting rhizotron root length measurements into estimates of root mass production per unit ground area

Rhizotrons provide valuable information about plant root production, but measurements are usually made in units of root length per unit surface area of observation window surface. These measurement units are not easily comparable to above-ground plant growth. To address this deficiency, several techniques have been developed to convert rhizotron measurement units into root mass production per unit ground area. In this study, four different conversion methods were applied to the same dataset of rhizotron measurements. This data was used to reveal the effect of conversion method upon estimates of the temporal variation in, and annual magnitude of, gross root mass production. Application of four different conversion methods resulted in gross root production estimates ranging between 2.1 and 11.4 t ha⁻¹ year⁻¹. Temporal variation in gross root mass production also varied between methods. All current methods for quantifying root production are likely to cause some disturbance and bias. Based upon a comparison of the sources of error present in each conversion method, we assess which methods are likely to produce the most reliable estimates of root biomass production per unit ground area, and propose additional measurements which could further improve accuracy.     

Seasonal dynamics of fine root biomass,root length density,specific root length,and soil resource availability in a Larix gmelinii plantation

Fine root tumover is a major pathway for carbon and nutrient cycling in terrestrial ecosystems and is most likely sensitive to many global change factors.Despite the importance of fine root turnover in plant C allocation and nutrient cycling dynamics and the tremendous research efforts in the past,our understanding of it remains limited.This is because the dynamics processes associated with soil resources availability are still poorly understood.Soil moisture,temperature,and available nitrogen are the most important soil characteristics that impact fine root growth and mortality at both the individual root branch and at the ecosystem level.In temperate forest ecosystems,seasonal changes of soil resource availability will alter the pattern of carbon allocation to belowground.Therefore,fine root biomass,root length density(RLD)and specific root length(SRL)vary during the growing season.Studying seasonal changes of fine root biomass,RLD,and SRL associated with soil resource availability will help us understand the mechanistic controls of carbon to fine root longevity and turnover.The objective of this study was to understand whether seasonal variations of fine root biomass,RLD and SRL were associated with soil resource availability,such as moisture,temperature,and nitrogen,and to understand how these soil components impact fine root dynamics in Larix gmelinii plantation.We used a soil coring method to obtain fine root samples(≤2 mm in diameter)every month from Mav to October in 2002 from a 17-year-old L.gmelinii plantation in Maoershan Experiment Station,Northeast Forestry University,China.Seventy-two soil cores(inside diameter 60 mm;depth intervals:0-10 cm,10-20 cm,20-30 cm)were sampled randomly from three replicates 25 m×30 m plots to estimate fine root biomass(live and dead),and calculate RLD and SRL.Soil moisture,temperature,and nitrogen(ammonia and nitrates)at three depth intervals were also analyzed in these plots.Results showed that the average standing fine root biomass(live (32.2 g.m-2.a-1)in the middle(10-20 cm)and deep layer (20-30cm),respectively.Live and dead fine root biomass was the highest from May to July and in September,but lower in August and October.The live fine root biomass decreased and dead biomass increased during the growing soil layer.RLD and SRL in May were the highestthe other months,and RLD was the lowest in Septemberdynamics of fine root biomass,RLD,and SRL showed a close relationship with changes in soil moisture,temperature,and nitrogen availability.To a lesser extent,the temperature could be determined by regression analysis.Fine roots in the upper soil layer have a function of absorbing moisture and nutrients,while the main function of deeper soil may be moisture uptake rather than nutrient acquisition.Therefore,carbon allocation to roots in the upper soil layer and deeper soil layer was different.Multiple regression analysis showed that variation in soil resource availability could explain 71-73% of the seasonal variation of RLD and SRL and 58% of the variation in fine root biomass.These results suggested a greater metabolic activity of fine roots living in soil with higher resource availability,which resulted in an increased allocation of carbohydrate to these roots,but a lower allocation of carbohydrate to those in soil with lower resource availability.     

Accurate root length and diameter measurement using NIH Image: use of Pythagorean distance for diameter estimation

This report describes an image analysis algorithm to estimate the length versus diameter of washed root samples accurately. Image analysis was performed using a Macintosh computer and the public domain NIH Image program. The binary image of the roots was processed to get the thinned image to calculate the length of the roots. The pixels of the root in a binary image were then stripped off from around the periphery based on the pixel's Pythagorean distance from the nearest background pixel. The length of the remaining root in each stripping off process was calculated after the image was thinned. Images (300 dpi) of copper wire of 0.23, 0.5, 1.0 mm diameter were analyzed for verification of the usefulness of the procedure. The results showed that more than 93% of the wires in each diameter wire were calculated to be in diameter classes including the true diameter and its adjoining classes: 93.6% of the wires of 0.23 mm diameter appeared in the 0.098–0.38 mm diameter classes, 96.19% of the wires of 0.5 mm diameter appeared in the 0.38–0.61 mm diameter classes, and 96.17% of the wires of 1 mm diameter appeared in the 0.85–1.08 mm diameter classes. The proposed method was tested for primary and secondary roots of water-cultured rice (Oryza sativa L.) and it was proven that the method could provide accurate length and diameter measurements for each root order. In addition, it was found that the method could provide the lengths of the thick primary, thin primary, and secondary roots. The effectiveness of applying sharpening for the grayscale image before making the binary image is also discussed.     

A rapid quantitative measurement of root length and root branching by microcomputer image analysis

A computer program was made for fast and reliable measurement of root length and for estimating the number of root tips and branching points. Image-processing procedures available in a program package for image analysis by means of a personal computer were used. The method is described in this paper and some results of tests on variance and systematic errors (bias) are discussed.Time required for analysis of an evenly spread root (sub-)sample with a total length of max. 300 cm was reduced to less than 20 seconds. Random deviations from the real length, determined by measuring known lengths of wire, did not exceed 5%, after correction for length density dependent bias. Counts of root tips appeared to be unreliable, but branching ratios could be determined fairly accurately, after correction for the length density dependent number of pseudo-branches (e.g. crossings). Rhizotron root photographs were also analysed satisfactorily, after modification of a few steps in the program.     

In-situ root extent measurements by electrical capacitance methods

A conceptual model is presented that provides a rational basis for using plant root capacitance as an in-situ measurement for assessing plant root development. This method is based on measuring the electricla capacitance of an equivalent parallel resistance-capacitance circuit formed by the interface between soil-water and the plant root surface. Nutrient solution studies using tomato (Lycopersicon esculentum Mill.) showed a good correlation between plant root capacitance and root mass. Stage of development studies showed plant root capacitance measurements capable of detecting root development rate and suggested the method to be sensitive to root function. Soil water content was shown to have a significant effect on plant root capacitance measurement. The possibility of using this technique to assess relative root function is discussed. Positioning of the plant shoot electrode was shown to also have a significant effect on measurement of plant root capacitance, demonstrating the need for using consistent measurement techniques. The electrical capacitance method shows considerable promise. More research is needed before it can be used routinely.     

青杨人工林根系生物量、表面积和根长密度变化

在植物生长季节,采用钻取土芯法对秦岭北坡50年生青杨人工林根径≤2 mm和2～5 mm根系的生物量、表面积和根长密度进行测定.结果表明：在青杨人工林根系(＜5 mm)中,根径≤2 mm根系占总生物量的77.8%,2～5 mm根系仅占22.2%;根径≤2 mm根系表面积和根长密度占根系总量的97%以上,而根径2～5 mm根系不足3%.随着土层的加深,根径≤2 mm根系生物量、表面积和根长密度数量减少,根径2～5 mm根系生物量、表面积和根长密度最小值均分布在20～30 cm土层.≤2 mm根系生物量、表面积和根长密度与土壤有机质、有效氮呈极显著相关,而根径2～5 mm根系的相关性不显著.     

Seasonal dynamics of fine root biomass, root length density, specific root length, and soil resource availability in a Larix gmelinii plantation

Fine root turnover is a major pathway for carbon and nutrient cycling in terrestrial ecosystems and is most likely sensitive to many global change factors. Despite the importance of fine root turnover in plant C allocation and nutrient cycling dynamics and the tremendous research efforts in the past, our understanding of it remains limited. This is because the dynamics processes associated with soil resources availability are still poorly understood. Soil moisture, temperature, and available nitrogen are the most important soil characteristics that impact fine root growth and mortality at both the individual root branch and at the ecosystem level. In temperate forest ecosystems, seasonal changes of soil resource availability will alter the pattern of carbon allocation to belowground. Therefore, fine root biomass, root length density (RLD) and specific root length (SRL) vary during the growing season. Studying seasonal changes of fine root biomass, RLD, and SRL associated with soil resource availability will help us understand the mechanistic controls of carbon to fine root longevity and turnover. The objective of this study was to understand whether seasonal variations of fine root biomass, RLD and SRL were associated with soil resource availability, such as moisture, temperature, and nitrogen, and to understand how these soil components impact fine root dynamics in Larix gmelinii plantation. We used a soil coring method to obtain fine root samples (⩽2 mm in diameter) every month from May to October in 2002 from a 17-year-old L. gmelinii plantation in Maoershan Experiment Station, Northeast Forestry University, China. Seventy-two soil cores (inside diameter 60 mm; depth intervals: 0–10 cm, 10–20 cm, 20–30 cm) were sampled randomly from three replicates 25 m × 30 m plots to estimate fine root biomass (live and dead), and calculate RLD and SRL. Soil moisture, temperature, and nitrogen (ammonia and nitrates) at three depth intervals were also analyzed in these plots. Results showed that the average standing fine root biomass (live and dead) was 189.1 g·m⁻²·a⁻¹, 50% (95.4 g·m⁻²·a⁻¹) in the surface soil layer (0–10 cm), 33% (61.5 g·m⁻²·a⁻¹), 17% (32.2 g·m⁻²·a⁻¹) in the middle (10–20 cm) and deep layer (20–30cm), respectively. Live and dead fine root biomass was the highest from May to July and in September, but lower in August and October. The live fine root biomass decreased and dead biomass increased during the growing season. Mean RLD (7,411.56 m·m⁻³·a⁻¹) and SRL (10.83 m·g⁻¹·a⁻¹) in the surface layer were higher than RLD (1 474.68 m·m⁻³·a⁻¹) and SRL (8.56 m·g⁻¹·a⁻¹) in the deep soil layer. RLD and SRL in May were the highest (10 621.45 m·m⁻³ and 14.83m·g⁻¹) compared with those in the other months, and RLD was the lowest in September (2 198.20 m·m⁻³) and SRL in October (3.77 m·g⁻¹). Seasonal dynamics of fine root biomass, RLD, and SRL showed a close relationship with changes in soil moisture, temperature, and nitrogen availability. To a lesser extent, the temperature could be determined by regression analysis. Fine roots in the upper soil layer have a function of absorbing moisture and nutrients, while the main function of deeper soil may be moisture uptake rather than nutrient acquisition. Therefore, carbon allocation to roots in the upper soil layer and deeper soil layer was different. Multiple regression analysis showed that variation in soil resource availability could explain 71–73% of the seasonal variation of RLD and SRL and 58% of the variation in fine root biomass. These results suggested a greater metabolic activity of fine roots living in soil with higher resource availability, which resulted in an increased allocation of carbohydrate to these roots, but a lower allocation of carbohydrate to those in soil with lower resource availability. __________ Translated from Acta Phytoecologica Sinica, 2005, 29(3): 403–410 [译自: 植物生态学报, 2005, 29(3): 403–410]     

Accurate root length measurement by image analysis

Algorithms for estimating root length by image analysis should lead to results that have no systematic error (bias), be insensitive to preferential root orientation, valid across a wide range of sample sizes and adjust for overlap between roots in samples, to reduce the effort needed in spreading out root systems. We propose a new algorithm that forms a compromise between small bias and robustness (insensitivity to variation in sample size and preferential root orientation), and provide a simple way of dealing with root overlap. Image analysis was performed on a Macintosh computer using the public domain NIH Image program. The digital image of the root was processed to get the thinned image (skeleton). The numbers of orthogonally and diagonally connected pairs of pixels (N _o and N _d, respectively) in the skeleton were counted separately and used for length (L) calculation. A new length calculation equation was introduced so that the effect of orientation on length calculation was minimized; L=[N d ²+(N _d+N _o/2)²]^1/2+N _o/2. The maximum error due to orientation of a single line was evaluated for an ideal line, and the analysis revealed that the new equation was less affected by orientation than previous equations. Copper wire and rice (Oryza sativa L.) roots containing both primary and fine secondary root were measured manually and with image analysis. The two methods showed good agreement within 1.5%. The proposed image analysis method yielded length estimates with CV from 0.23 to 0.88%, which was lower than the CVs of the line-intersect method. Moreover, the lengths of overlapping samples were calculated correctly because the image analysis method distinguished an overlapping pixel from a thinned image, while the calculation with the line-intersect method showed underestimation because overlaps were not considered in that method. This revised version was published online in June 2006 with corrections to the Cover Date.     

Scaling of root length density of maize in the field profile

Root length density is an important parameter in crop growth simulation and in evaluating consequences of root pattern on crop water and nutrient uptake. In this study, a scaling model was presented for estimating the profile distribution of root length density of maize (Zea mays L.). The model inputs are root length data of a reference profile and bulk densities of soil layers, as well as root length data in the first soil layer of a field profile to be investigated. Using the root length data of 10 soil profiles investigated over 2 years, the model was examined. The results show that the proposed scaling approach is effective in estimating the root length density of each layer of soil in the field profile. The relative root mean square error (RRMSE) of the developed scaling model was 25.28%, while that of the traditional exponential model was 39.53%. The scaling approach would facilitate determination of heterogeneous distributions of root length densities in the field.     

施用氮肥对落叶松人工林一级根外生菌根侵染及形态的影响

以落叶松人工林为研究对象,通过施N肥试验,对不同季节、不同土壤深度根系进行取样,研究了1级根外生菌根真菌侵染率和形态,及其与不同季节、土壤深度和土壤N有效性的关系.结果表明:外生菌根真菌对落叶松人工林1级根的侵染率显著受不同季节和土壤深度土壤N有效性的影响.在不同季节和土层之间,施N肥导致菌根真菌侵染率下降.与未侵染菌根真菌相比,菌根真菌侵染导致1级根形态发生明显改变,平均直径增加18.7%,平均根长缩短23.7%,比根长降低16.3%.这种根系形态变化在不同季节、不同土壤深度处理中表现明显.菌根真菌侵染改变了1级根形态,影响根系的生理生态过程.     

Specific root length as an indicator of environmental change

Abstract

Specific root length (SRL, m g^?1) is probably the most frequently measured morphological parameter of fine roots. It is believed to characterize economic aspects of the root system and to be indicative of environmental changes. The main objectives of this paper were to review and summarize the published SRL data for different tree species throughout Europe and to assess SRL under varying environmental conditions. Meta-analysis was used to summarize the response of SRL to the following manipulated environmental conditions: fertilization, irrigation, elevated temperature, elevated CO₂, Al-stress, reduced light, heavy metal stress and physical disturbance of soil. SRL was found to be strongly dependent on the fine root classes, i.e. on the ectomycorrhizal short roots (ECM), and on the roots <0.5 mm, <1 mm, <2 mm and 1 – 2 mm in diameter SRL was largest for ECM and decreased with increasing diameter. Changes in soil factors influenced most strongly the SRL of ECM and roots <0.5 mm. The variation in the SRL components, root diameter and root tissue density, and their impact on the SRL value were computed. Meta-analyses showed that SRL decreased significantly under fertilization and Al-stress; it responded negatively to reduced light, elevated temperature and CO_2. We suggest that SRL can be used successfully as an indicator of nutrient availability to trees in experimental conditions.     

Experimental evaluation of an efflux-influx model of C exudation by individual apical root segments

The aim of this study was to evaluate if a model describing the efflux and the influx of C through the root surface could be fitted to experimental short-term kinetics of carbon (C) exudation by individual apical root segments in maize (Zea mays L.). The efflux of C was set constant or modelled by a power function of the distance from the apex to simulate the greater release of C around the root tip commonly reported in the literature. The influx was proportional to the C concentration in the external solution to simulate the active re-uptake of exudates by the root. Plants were exposed to full light or to shade to manipulate C allocation to roots. The model with a constant efflux gave satisfactory fits to the kinetics of exudation (average R(2)=0.66). The average gross efflux was then 2.1 mug C cm(-2) root surface h(-1). The model was improved if exudation was set more intense towards the root apex (average R(2)=0.74). The estimated gross efflux decreased then from 5.2 mug C cm(-2) h(-1) at the apex to 1.8 mug C cm(-2) h(-1) for the region located 5-25 cm from the root tip. The decrease in net exudation of individual roots due to the shading of plants was weak, which may indicate that the import of C by the primary roots studied was not reduced significantly. By describing the exudation of an apical root segment of variable length and diameter, the model is a first step in linking exudation to root system architecture models and to whole plant functioning.     

Relations between root length densities and root intersections with horizontal and vertical planes using root growth modelling in 3-dimensions

The root growth simulation model of Diggle (ROOTMAP; 1988) was modified to allow the numerical output of data on root intersections with horizontal and vertical planes. ROOTMAP was used to generate two three-dimensional model structures of fibrous root systems. The lateral roots were oriented randomly (geotropism index=0) but the main axes were positively gravitropic (geotropism index=0.6). The mean density of root intersections (n, cm^-2) with the sides of a series of 5×5×5 cm cubic volumes was related approximately linearly to the root length density (L_t cm^-2) within each volume by the equation L_t=2.3n (correlation coefficient, r=0.981). This compared with the relation of L_t=2n predicted theoretically for randomly oriented lines (Melhuish and Lang, 1968). Root length density was related to the intersection density by the equation L_t=2.43n_v (r=0.940) for the vertical faces and L_t=1.88n_h (r=0.984) for the horizontal faces. L_t/n_v was greater than L_t/n_h because of the preferential vertical orientation of the main root axes. The Melhuish and Lang (1968) equation does not generally give accurate prediction of root length density from field experiment data. Under field conditions, values have been reported in the ranges of 1.4 to 16 for L_t/n_h, and 3.8 to 9 for L_t/n_v. The most likely explanation for this difference is that only a small proportion (e.g. about 20–30%) of the actual number of roots are counted using the core-break and root mapping (including the trench wall) methods, due to the practical experimental difficulties of identifying individual fine roots under field conditions. Detailed experimental studies are needed to identify what portion of the root system is recorded using these field techniques (e.g. whether the main root axes are counted while the fine lateral roots remain undetected). Three-dimensional models of root growth provide a new method of studying the relations between L_t, n_v and n_h for root systems generated stochastically according to known geometrical rules. Using these models it will be possible to determine the effects of the degree of gravitropism and of root branching on the value and on the variability of L_t/n_h and L_t/n_v. The effectiveness of the statistical corrections that have been developed to correct for non-random root orientation can also be evaluated, as can the effects of sample position.