土壤中有效态镉与籽实中镉含量的关系

污水灌溉农田,在我国已有几十年的历史。未经处理的污水,长期灌溉农田,已造成各种污染物在土壤、作物中的累积。较为明显的是重金属镉对土壤、作物的污染。镉在生态系统中的迁移转化规律,土壤中全量镉与籽实中镉含量的关系,在国内外多有报道。本文主要通过盆栽试验水稻、大豆及污灌区的水稻来阐述土壤有效态镉与作物籽实中镉含量的关系。一、材料与方法1.土壤盆栽试验所需要的土壤,取材于沈阳市新民县胡台村,属非污染区草甸土,土体中游离碳酸钙全部淋     

稻鸭、稻鱼共作生态系统土壤可溶性有机N的动态和损失

通过田间试验研究了稻鸭、稻鱼共作生态系统土壤可溶性有机N(SON)的动态和损失,及其与土壤微生物量N和水稻吸N量的相关性.结果表明,(1)土壤SON是稻田土壤主要的可溶性N,其中处理CK,RD和RF土壤SON库分别为121.16, 109 30 和113.71 kg/hm2,高于土壤无机N库.(2)土壤SON与土壤可溶性无机N显著正相关(p<0.01);在水稻生育期间,土壤SON含量随水稻的生长而逐渐降低;同时由于鸭和鱼的存在,处理RD和RF土壤SON含量显著低于处理CK;土壤SON与水稻累积吸N量呈显著负相关(p<0.01),表明水稻生长强烈影响着土壤SON.(3)在水稻生长前期,渗漏水各形态N含量最大;溶解性有机N(DON)是稻田渗漏水N素的主要形态;同时,统计分析显示,相对于处理CK,RF土壤SON的下渗淋失量显著降低,RD土壤SON的下渗淋失量则略为降低.(4)水稻生育期间,土壤微生物量N不断地变化着,此外,由于鸭和鱼的存在,相对与处理CK,处理RD和RF土壤显著的提高了土壤MBN.同时,由于水稻吸收和N的淋失,土壤微生物量N与土壤SON不相关.总之,在水稻生长期间,土壤可溶性有机N受水稻吸N、微生物吸N与分解和N淋失的共同作用.     

长期施用有机肥和过磷酸钙对潮土有效磷积累与淋溶的影响

利用20年定位试验研究了施用化肥和有机肥对潮土耕层土壤有效磷（Olsen-P）含量与作物产量的关系及土壤Olsen-P积累和垂直移动规律的影响.结果表明：土壤Olsen-P含量在10～40 mg·kg^-1能保证小麦、玉米有较高的产量,土壤Olsen-P含量大于40 mg·kg^-1发生显著淋溶,轻壤质潮土Olsen-P发生淋溶的阈值为40 mg·kg^-1.连续施用化肥（NPK）和秸秆还田处理（SNPK）施磷量在77～90 kg·hm^-2,平均每100 kg P·hm^-2使耕层土壤Olsen-P提高0.63～0.72 mg·kg^-1,每年提高0.49～0.65 mg·kg^-1,达到淋失阈值需要45～60年.有机肥与化肥结合（MNPK、MNPK2和1.5 MNPK）,年施磷量为210 kg·hm^-2时,土壤Olsen-P（Y）与施肥年度（x）的关系为：Y_{1.5 MNPK}=4.506x+6.4464 (R²=0.8862),平均每年增加4.5 mg·kg^-1,连续施用8年可使耕层土壤Olsen-P达到淋失阈值;年施磷量为125和140 kg·hm^-2时,土壤Olsen-P与施肥年度的关系为：Y_MNPK2=2.4765x+13.563 (R²=0.9307)和Y_MNPK=3.1097x+6.9615 (R²=0.8562),平均每年增加2.47和3.1 mg·kg^-1,连续施用11年可使耕层土壤Olsen-P达到淋失阈值.有机无机肥结合处理土壤Olsen-P积累速度是化肥处理的3.5倍,过量施用有机肥增加了土壤Olsen-P的积累和淋失.     

富营养化河水灌溉对稻田土壤氮磷养分贡献的影响——以太湖地区黄泥土为例

以太湖地区主要稻田土壤类型黄泥土为对象,利用当地富营养化河水对回填土柱和植稻原状土渗漏池进行模拟稻田灌溉试验,系统研究了灌溉水对稻田土壤氮磷营养的贡献.在回填土柱灌溉试验中,在试验初期,不同形态的氮素均有较高的淋失量,以后逐渐降低,表明初期淋失的氮素主要来自土壤,而不是灌溉河水.在整个水稻生长季,均观测到有可溶性有机氮淋失,表明富营养化河水灌溉条件下可溶性有机氮是稻田土壤主要的氮素淋失形态.在本试验中,磷素的淋失动态与氮素的淋失动态截然相反,淹水后很长一段时间内均没有土壤磷素淋失,但在淹水灌溉后期有大量的土壤磷素淋失损失,这可能是淹水后期土壤对磷的吸持已达到饱和状态,不能继续固持土壤中多余的磷所致.与回填土柱模拟灌溉淋洗试验相比,在当前供肥条件下,原状土渗漏池试验氮磷淋失量远低于回填土柱试验,而灌溉水对土壤氮磷养分的贡献远高于回填土柱.通过富营养化河水灌溉带入当季稻田的N量达到每公顷56.3 kg,其中有55.8 kg N可被土壤吸持和作物吸收,表明太湖地区稻田土壤对氮磷养分来说是一个环境友好的生态系统.在利用当地富营养化河水进行稻田土壤灌溉时可适量减少肥料施用量、优化氮磷肥料管理.     

绿洲农田氮素积累与淋溶研究述评

作物对氮素的吸收利用及氮素在土壤中的积累和运移,制约着绿洲农田生产力并对农田环境造成影响,是绿洲农田生态系统可持续发展和绿洲稳定性研究的一个重要方面。针对农田氮素积累和淋溶这一绿洲资源消耗量增加、耕作方式粗放结果下的环境问题,对其特征及引发的环境效应进行了详细阐述,并从不同的角度综述了缓减绿洲氮素淋失及环境污染的对策。指出在未来还需加强绿洲地下水氮污染调查及农田氮素积累和淋溶现状的区域评价,并针对一些在绿洲大面积推广的农田管理技术开展其对农田氮素积累和淋溶影响的研究,并强调人文因素在绿洲农田氮素积累与淋溶调控中的重要性。     

半干旱地区农田生态系统中硝态氮的淋失

在不同深度的渗漏池,连续6年(11季作物)研究了半干旱地区农田生态系统中硝态氮的淋失.结果表明,在半干旱地区,硝态氮的淋失仍可发生.淋失量和降水量有密切关系:降水多,淋失量大,不同降水年际间表现出显著差异.氮肥用量决定着淋失量的大小,而尿素和碳酸氢铵的淋失量却无本质差别.不同深度的土壤有着不同的贮水量,因而也有着不同的淋失量.实行夏季休闲,会增加硝态氮淋失的潜在危险.     

咸水灌溉条件下土壤水盐分布特征

通过设置3种灌水量水平（100%ET_c、80%ET_c、60%ET_c）和3种灌水水质水平（0.7、3和6 g·L^-1）,研究了咸水灌溉条件下春小麦120 cm土层内水分动态和盐分累积特征.结果表明：水分在农田土壤中的分布主要受灌水量和土壤质地的影响,充分灌溉使水分存贮在较深土层中,而非充分灌溉则使水分存贮在表层;在相同灌水量的条件下,土体内的盐分积累程度随着灌溉水矿化度的增大而加剧;在相同矿化度条件下,土体内的盐分含量及积盐深度随着灌水量的增加而增大.在作物整个生育期内,连续使用咸水灌溉将导致土壤积盐,且非充分灌溉较充分灌溉更易使土壤表层积盐.     

不同施肥条件下玉米田土壤养分淋溶规律的原位研究

利用排水采集器法结合田间原位试验,研究了夏玉米不同施肥处理对棕壤土养分淋失的影响.结果表明:在夏玉米生长期内,影响玉米田土壤水分淋溶的主要因素是大量降雨和灌溉,夏玉米生长前期的土壤淋溶水量较大,但随夏玉米生育进程的推进而递减,各处理差异也逐渐减小;与施氮肥处理相比,秸秆还田配施氮肥处理可加剧土壤水淋溶.在夏玉米生长期内,施肥处理的土壤淋溶水硝态氮浓度均呈"双峰"曲线变化趋势,而铵态氮浓度则呈先升后降的变化趋势.玉米田土壤氮素淋失以硝态氮形式为主,其累计淋失量为12.90～46.53 kg·hm-2,铵态氮的累计淋仅为1.66～5.11 kg·hm-2,两种形态氮的淋失量都随施氮量的增加而升高.秸秆还田配施氮肥处理的氮素淋失率比单施氮肥处理高6.53%～13.07%,低氮处理的氮素淋失率比高氮处理高3.66%～10.10%;玉米田土壤速效磷的累计淋失量较小,仅为0.148～0.235 kg·hm-2,而速效钾的累计淋失量较大,为7.08～13.00 kg·hm-2.在夏玉米生长后期,秸秆还田配施氮肥处理使土壤速效磷淋失量升高,并可加剧土壤速效钾的淋失,而单施氮肥处理作用不明显.     

施用猪粪对油麦菜产量、硝酸盐含量及土壤养分的影响

应用盆栽试验方法,研究了施用猪粪对西南地区黄壤和紫色土中油麦菜产量、硝酸盐含量及土壤养分的影响.结果表明:施用猪粪能显著提高油麦菜产量,且黄壤中油麦菜增产幅度大于紫色土;油麦菜中硝酸盐、氮磷钾含量与土壤类型及猪粪施用量密切相关,以中国农业科学院制定的蔬菜中硝酸盐污染程度评价标准为依据,在紫色土对照(CK)及1倍猪粪(相当于施纯N 200 kg·hm^-2)处理下油麦菜硝酸盐含量较低,符合一级标准(≤432 mg·kg^-1,轻度污染);其他处理多超过二级标准(≤758 mg·kg^-1,中度污染),但均未超过三级标准(≤1440 mg·kg-¹,重度污染);黄壤中除化肥和8倍猪粪(相当于施纯N 1600 kg·hm^-2)处理下油麦菜硝酸盐含量超过二级标准外,其他各处理均符合一级标准;黄壤和紫色土中表征磷素淋失风险的有效磷临界值分别为96.3和107.7 mg·kg^-1.黄壤的猪粪环境安全容量较紫色土高.施用猪粪能显著提高两种土壤的有机碳和全氮含量.     

土壤优先水流及溶质优先迁移的研究

通过土壤原状土柱和填充土柱实验,研究了土壤优先水流的特征和非吸附性离子Br^-和NO3^-在土壤中的优先迁移。结果表明,土壤优先水流存在优先穿透、穿透曲线不对称性、偶向入渗和拖尾等特征,原状土柱中Br^-标记的优先水流在实验开始后24h出现穿透,穿透时的孔隙体积仅0.04,在原状土柱中以Br^-标记的土壤优先水流占土壤出流总量的26％,所引起的Br^-累积淋出量占总淋出量的86.7％,说明土壤优先水流虽只占出流总量较小的比例,却可造成较大比例的溶质迁移,优先水流可使NO3^－快速向下迁移,在仅1倍孔隙体积时,其出流中可收获投加量的11％,优先水流可使Br^-和NO3^-向土壤较深层次迁移的同时,发生径向扩散。     

宁夏黄灌区稻田冬春休闲期硝态氮淋失量

对宁夏黄灌区稻田设置不同有机肥处理：常规施肥（CK）;常规施肥条件下分别施用4500 kg/hm2（T1）与9000 kg/hm2猪粪（T2）,采用树脂芯法测定了稻田冬春休闲期30 cm、60 cm、90 cm处的硝态氮流失量。结果表明,常规施肥条件下,90 cm处硝态氮淋失量最大,分别为T1、T2的1.10与1.13倍;在常规施肥基础上增施猪粪,硝态氮最大淋失量出现在60 cm土层,T1、T2的流失量分别为4.47 kg/hm2与4.21 kg/hm2,分别为该层CK淋失量的1.50与1.42倍。灌区稻田常规施肥基础上增施有机肥,能够减少硝态氮向深层淋失;但60 cm土层处硝态氮淋失量增加,为硝态氮的深层淋失提供了基础,但在灌区水旱轮作模式下,下季旱作灌水量明显减少,加之作物吸收,硝态氮淋失也将明显降低。     

Biotic versus hydrologic control over seasonal nitrate leaching in a floodplain forest

Strong seasonal increases in aquatic (stream, ground and hyporheic water) nitrate have been observed in a variety of ecosystems. In most cases, changes in hydrological and vegetative activity occur contemporaneously, making it difficult to determine whether soil leaching is being driven by increases in the availability of leachable N or is simply due to flushing of N that has accumulated over longer periods. Three studies were conducted to better determine controls on soil nitrate leaching in a near-pristine temperate floodplain ecosystem receiving large N inputs via N-fixation by red alder: 1) an artificial rainfall experiment was conducted to estimate N-leaching potential during the summer, when plant uptake is high and new inputs of organic matter are low; 2) soil solution, groundwater and surface water were sampled during a major autumn storm to document exchanges at the seasonal transition, when plant uptake is low and inputs of senescent organic matter are high; and 3) monthly samples of soil and aquatic nitrogen were collected in 1997 and 1998 to document seasonal patterns of N exchanges. Collectively, these studies demonstrate the importance of hydrologic factors in controlling N flux. Nitrate was rapidly leached from soils during actual and simulated rainstorms. Two pathways of nitrate leaching were identified. Localized flooding and direct leaching of streamside soils into surface waters contributed to high solute concentrations in peak flows. Nitrate that leached into interstitial waters was subject to various factors that could delay or reduce its delivery to surface waters. Greater residence time may increase the influence of this component of stormflow on ecosystem productivity. While soil nitrate pools were rapidly depleted during rainstorms, accumulation of soil nitrate occurred over summer dry periods. Large differences in soil and aquatic nitrate concentrations between two years with contrasting rainfall highlight the potential for inter-annual hydrologic variability to affect ecosystem nutrient cycling.     

降水变化对科尔沁沙地樟子松人工林土壤氮矿化和淋溶的影响

为研究降水量减少对沙地森林土壤氮循环过程的影响,以科尔沁沙地15年生樟子松人工林为研究对象,野外模拟不同降水量（自然降水、减少30%和50%）对沙地樟子松人工林土壤无机氮（SIN）含量、氮矿化速率和淋溶动态的影响。研究结果发现,沙地樟子松人工林SIN主要以硝态氮形态存在,模拟降水减少降低土壤硝态氮含量（P<0.05）和硝态氮/SIN值（P<0.001）,而增加土壤铵态氮含量（P<0.05）。与自然降水相比,降水减少降低土壤净硝化速率和净矿化速率（P=0.002）,但不同降雨处理的土壤净氨化速率差异不显著（P=0.86）。科尔沁沙地樟子松人工林土壤以硝态氮淋溶为主,不同降雨处理土壤硝态氮淋溶量差异不显著（P=0.09）,但模拟降水减少降低土壤铵态氮淋溶（P=0.04）。此外,沙地樟子松人工林SIN含量、净氮矿化速率和淋溶量具有明显月动态特征,与降雨月动态规律基本一致。降水处理和采样时间对SIN含量和净氮矿化速率具有显著交互作用,但土壤氮淋溶量的交互作用不显著。可见,降水变化能够显著影响科尔沁沙地樟子松人工林土壤氮有效性、氮矿化速率和淋溶等过程,未来干旱加剧可能降低科尔沁沙地樟子松人工林土壤氮的可利用性。     

河套灌区秋浇对不同类型农田土壤氮素淋失的影响

研究了河套灌区秋浇对不同类型农田 NO3 - N淋失的影响。结果表明 ,秋浇前小麦和白菜地 NO3 - N含量最高 ,玉米地和小麦 -玉米套种地次之 ,葵花地最低。秋浇后土壤剖面 NO3 - N的损失量按照表层 (0～40 cm)、中层 (40～ 80 cm)、深层 (80～ 1 2 0 cm)依次递减 (玉米地除外 )。不同农田 NO3 - N淋失量按照小麦地、白菜地、玉米地、葵花地、小麦 -玉米地依次递减。这说明 ,发展套种耕作将有利于减少氮素淋失。土壤 NO3 -N的淋失还直接导致地下水质的恶化。在当前的耕作制度及秋浇定额下 ,河套灌区每年可损失约 2 .6× 1 0 7kg N。因此 ,需要科学地确定秋浇方式和秋浇量 ,减少氮素淋失 ,减少地下水污染     

宁夏引黄灌区秸秆还田对麦田土壤硝态氮淋失的影响

以宁夏引黄灌区为例,探索秸秆还田条件下冬小麦土壤硝态氮淋失规律。试验设置常规施肥(CK)、常规施肥条件下施用4500kg/hm2(T1,半量还田)和9000 kg/hm2(T2,全量还田)秸秆3个处理。利用树脂芯法吸附10、20、30、60cm和90cm土层的硝态氮流失量。结果表明:硝态氮(纯N)淋失量6.26—12.85 kg/hm2,是冬小麦施用化肥氮量的2.78%—5.71%。与对照CK相比,T1和T2在10cm土层减少0.09%和3.97%;20cm土层减少8.51%和9.81%;30cm土层减少2.25%和10.34%;60cm土层减少23.85%和13.08%;90cm土层减少27.65%和20.73%。10cm和20cm土层,处理与对照以及处理之间均未到显著性差异(P0.05);30cm处理,T1与CK以及T1与T2未达到显著性差异,但T2与CK达到显著性差异表明全量还田效果最好;60cm土层,处理与对照、以及处理之间均达到显著性差异;90cm土层,处理与对照之间达到显著性差异,处理之间未达到显著性差异。硝态氮淋失主要发生在冬小麦返青至灌浆期间,占全生育期淋失量的52.95%—67.79%。T1、T2冬小麦产量增产率分别为10.11%与11.51%。可见,稻秆还田能够减少灌区土壤硝态氮淋失量。     

旱地小麦不同栽培条件对土壤硝态氮残留的影响

在陕西渭北旱塬进行了2a田间试验,研究不同栽培模式、施氮量和小麦种植密度对旱地硝态氮残留的影响。结果表明,种植小麦2a后0~200 cm土壤剖面中残留硝态氮58.6~283.9 kg/hm2,数量可观,短期内在渭北旱塬深厚的土壤中不会对地下水造成威胁,但夏季休闲期间容易下迁至作物无法吸收的土壤深度。与常规无覆盖模式相比,地膜覆盖和垄沟种植显著提高了作物对氮素的吸收,但同时也增加了土壤0~200 cm的硝态氮残留,这与地膜覆盖导致有机氮矿化增加有关;秸秆覆盖对作物氮素吸收和硝态氮残留均没有明显影响。施氮量低于120 kg/hm2时,各种栽培模式土壤剖面残留硝态氮的分布差异较小,只有地膜覆盖和垄沟种植处理在土壤表层有少量硝态氮累积;施氮量为240 kg/hm2时,无覆盖和秸秆覆盖土壤60~120 cm深度都有明显累积峰,地膜覆盖和垄沟种植土壤残留硝态氮则在60 cm以上土层累积较多。小麦种植密度也影响了各种栽培模式土壤硝态氮及其分布特点。垄沟种植条件下,从土壤表层到200 cm的深层,垄上土壤残留硝态氮均显著高于沟内土壤;上层差异最大,随着土壤深度的增加其差异逐渐降低;随着施氮量的增加,这种差异显著增大;随小麦种植密度的增加则显著降低。随着施氮量增加,小麦吸氮量和土壤中残留硝态氮量均显著提高;施氮增加的残留硝态氮占施氮量的0.3%~44.6%。垄沟种植模式施氮增加的残留硝态氮最多,地膜覆盖处理次之,垄沟种植处理垄上土壤增加量远远高于沟内土壤。施氮量提高1倍,增加的残留硝态氮量平均提高了3倍多。提高小麦种植密度,施氮增加的残留硝态氮平均减小13.2 kg/hm2。由于种植密度增加显著提高了小麦对氮素的吸收,因此硝态氮残留有降低的趋势。其中,秸秆覆盖模式80~140 cm土层降低显著;地膜覆盖条件下高密与低密残留硝态氮的差异主要在深层;垄沟模式中,低密度种植硝态氮残留量在整个土壤剖面都高于高密度处理;而无覆盖条件下,残留硝态氮则随种植密度的提高呈增加趋势。     

A methodology for measuring drainage and nitrate leaching in unevenly irrigated vegetable crops

The objective of our study was to establish a methodology to determine drainage and nitrate leaching in unevenly irrigated vegetable crops. It was conducted in a tomato crop (Lycopersicum esculentum Mill) with drip irrigation in the summer of 2000 in the Ebro Valley, Spain. Two soil management techniques and two irrigation treatments were evaluated bare soil (S1) and soil mulched with black plastic (S2), with irrigation calculated according to the Crop Evapotranspiration (ETc) for bare soil (R1) and for mulched soil (R2). Volumetric soil water content (θv) was measured weekly to 1 m depth in six positions transverse to the drip line. Drainage was calculated by applying the water balance equation to the data from: (i) all six positions (method 1) and (ii) to the positions located under the plants and between the rows, respectively (method 2). Soil solution was extracted at 1 m depth with porous ceramic cups and analysed for nitrate. Nitrate leached to 1 m depth was calculated as the product of volume of drainage accumulated weekly and the nitrate concentration of the soil solution. Drainage and nitrate leaching were evaluated for two different crop periods crop establishment and crop growth. Method 2 produced results that were not significantly different from those from method 1. However, method 1 was more accurate and identified more differences between treatments. The greater drainage occurred during the crop establishment period, which also favoured the leaching of nitrates previously stored in the soil profile and later applied as fertilizer before planting. During establishment the crop was unable to use all available nitrate and the quality of groundwater deteriorated. The results suggest that further studies are required to adjust crop coefficients (Kc) to the actual needs of tomato crops grown with drip irrigation under bare soil and plastic mulching conditions.     

干旱区不同景观单元土壤盐分的变化特征

针对内陆河流域空间土壤盐渍化问题,以新疆三工河流域为例,通过调查、取样分析,研究了冲洪积扇和冲洪积平原2个水文地质带上一个生长季5-10月0～10、10～20cm土壤盐分积聚特征及其主导因素.结果表明:冲洪积扇土壤盐分含量明显低于冲洪积平原,盐分含量的变异系数均>100%,属于强变异性;灌溉景观土壤盐分的聚积在冲洪积扇和冲洪积平原相似,盐分含量均减小,而非灌溉景观的差异较大,冲洪积扇区土壤盐分含量减小,土壤盐渍化程度减弱;而冲洪积平原区土壤盐分含量升高,盐渍化程度增强.冲洪积扇区土层间盐分变化关系紧密相关(P<0.01),降雨和灌溉对盐分都具有淋洗作用,促进了盐分含量的减少;冲洪积平原区,蒸发对非灌溉景观0～10 cm土层盐分聚积起到促进作用,而10～20 cm土层盐分聚积受上层土壤盐分和地下水位共同作用.

Abstract：

Aiming at the problem of soil salinization in inland river basin, a case study was con-ducted in the Sangong River catchment of Xinjiang, China. The characteristics and dominant af-fecting factors of salt accumulation in 0-10 cm and 10-20 cm soil layers in two hydro-geological zones, i. e. , alluvial-proluvial delta and alluvial plain, were studied in a growth season (from May to October), and the precipitation, evaporation, groundwater table, and irrigation were also taken into account. The soil salt content was obviously lower in alluvial-proluvial delta than in al-luvial plain, but its coefficient of variation in the two zones was all higher than 100%, indicating a great variability. The soil salt accumulation in irrigated landscape in the two zones had a similar decreasing trend, but that in non-irrigated landscape had greater difference, with a decreased soil salinization in alluvial-proluvial delta, and an increased soil salinization in alluvial plain. In allu-vial-proluvial delta, the salt contents in 0-10 cm and 10-20 cm soil layers had a close relation-ship (P <0. 01), and there was a clear process of salt leaching by precipitation and irrigation, leading to the decrease of soil salt content. In alluvial plain, the salt accumulation in 0-10 cm soil layer in non-irrigated landscape was promoted by evaporation, and that in 10-20 cm soil lay-er was co-affected by the salt content in 0-10 cm soil layer and the groundwater table.     

Dynamic simulation of vertical non-adsorbed anion transport

Summary A model for the simulation of leaching of non-adsorbed anions is described. The model can also be used to study the degree of salinization by evaporation.The accent is laid on usefulness under practical conditions. In view of this it has been assumed that transport of ions is only caused by mass flow and hydrodynamic dispersion.Data about soil and profile, initial water and salt conditions and ground-water level must be known. Given a precipitation and evaporation distribution the model can compute the leaching or accumulation of nitrate or chloride during a long period ofe.g. 125 days.The results of a number of computations are compared with theoretical expectations and actual measurements. There is a passably good agreement.