半干旱草地地表土壤热通量的计算及其对能量平衡的影响

利用2008年7月兰州大学半干旱气候与环境观测(SACOL)站的观测资料,对比分析了地表土壤热通量的三种计算方法,即谐波法、温度预报校正法(TDEC法)以及结合自校正热通量板(HFP01SC)测量的温度积分法(ITHP法);进而分析了三种不同方法的计算结果对地表能量平衡的影响。比较5cm深度处谐波法和TDEC法的计算结果与HFP01SC的实测结果,三者的相位基本一致,相互之间均具有很好的线性关系;谐波法与TDEC法的计算值较为接近,但分别比HFP01SC的实测值偏大了2%和6%(主要发生在夜间)。对于地表的土壤热通量(G0),谐波法与TDEC法两者的计算结果仅偏差约1%;TDEC法与ITHP法的计算结果之间也具有很好的线性关系(R2=0.99),但偏差达到9%左右。相对于HFP01SC的实测结果,由谐波法和TDEC法计算的G0可将SACOL站的地表能量闭合率分别提高6%和7%左右;利用温度积分法将HFP01SC的实测结果校正到地表后,地表能量闭合率也提高了约6%。因此,在对涡动相关通量做了常规订正的情况下,当充分考虑了土壤热存储后,SACOL站的地表能量闭合率可提高6%～7%,达到82%～83%左右。     

半干旱草原下垫面能量平衡特征及土壤热通量对能量闭合率的影响

土壤热通量在半干旱草原下垫面能量平衡研究中极为重要,土壤热通量估计不够准确是导致地表能量不平衡的一个重要原因。利用2008年6—9月锡林郭勒草原主生长期地表辐射、通量和土壤温度梯度观测资料,研究中纬度半干旱草原下垫面地表能量平衡特征。首先,在分析能量平衡各分量月平均日变化特征的基础上,通过对土壤热流量板观测的5 cm深度土壤热通量(G)的相位前移,研究了土壤热通量相位滞后对地表能量平衡产生的影响;其次,利用谐波分析方法,通过计算地表土壤热通量(Gs),分析了地表到热流量板之间的土壤热量储存对地表能量平衡的影响。结果表明:(1)将土壤热通量相位前移30 min,湍流通量与可利用能量(Rn-G)线性回归的斜率从0.835增加到0.842,地表能量闭合率提高了0.7%,但仍有15.8%的能量不闭合;(2)考虑了地表到热流量板之间的土壤热量储存之后,湍流通量与可利用能量之间的回归斜率达到0.979,能量不闭合程度仅为2.1%。     

土壤热异常对地表能量平衡影响初探

将来自土壤深部的热通量引入off line的陆面过程模式 (NCAR—LSM ) ,通过长达 2a的数值试验对比分析了它对各层次土壤温度和地表能量平衡的影响。　　在土壤底部引入 5W /m2 的热通量使底层土壤显著升温 ,但升温随着接近表层而迅速衰减。积分 3个月后 ,由地下进入地表的热流量增幅可达 1W/m2 以上 ,并持续增大到 5W /m2 ,地表最大升温约 0 .5K ,同时地表感热、蒸发潜热及长波辐射通量均有 1W /m2 左右的正异常 ;若将土壤热传导系数放大一个量级以加速热量交换 ,则地表升温提高到 1K以上 ,长波辐射增加 3W /m2 以上 ,超过了气溶胶全球平均的辐射效应。结果表明 :一定量值的土壤热异常对地表能量平衡和短期气候变化 (10 -1～ 10 1a)有着不可忽略的影响。同时 ,深入的资料分析、完善的陆面过程模式以及它与大气模式的耦合试验也是亟待进行的相关工作。     

塔克拉玛干沙漠不同区域土壤热通量变化比较

选取塔克拉玛干沙漠腹地塔中地区和北缘过渡带肖塘地区2013年土壤热通量观测资料,初步比较分析了塔克拉玛干沙漠两种下垫面的土壤热通量变化特征。结果表明：(1)在日变化尺度上,两个站点都有明显的日变化特征,1月份塔中站土壤热通量日平均变化幅度小于肖塘站,日较差分别为58.9 W.m2和72.4 W.m2,4月份两站土壤热通量变化幅度较为接近,日较差分别为88.1W.m2、100.1 W.m2。7、10月份塔中站土壤热通量变化幅度明显高于肖塘站,日较差分别为99.0 W.m2、53.7W.m2,100.3 W.m2、73.3W.m2。(2)不同天气条件下两个站点土壤热通量变化都有很大差异。晴天,塔中站和肖塘站土壤热通量变化都呈现出单峰型,变化幅度较一致,日较差分别为119.7 W.m2、119.1 W.m2。沙尘天和雨天受云层或降水的影响土壤热通量变化波动较大,沙尘天塔中站变化幅度小于肖塘站,日较差分别为83.6 W.m2、133.1 W.m2;雨天塔中站和肖塘站变化幅度都很剧烈,日较差分别为70.6 W.m2、66.6 W.m2。(3)年变化尺度上,塔中站土壤热通量在7月份达到最大值(7.7 W.m2),在11月出现最小值(-5.3 W.m2),肖塘站7月份出现最大值(4.2 W.m2),11月份出现最小值(-10.2 W.m2)。塔中站和肖塘站土壤热通量年总量差异很大,塔中站为16.8 W.m2,能量由大气向土壤传递,土壤为热汇,而肖塘站则为-34.9 W.m2,能量由土壤向大气传播,土壤表现为热源。     

陇中黄土高原地表能量不平衡特征及其影响机制研究

利用兰州大学半干旱气候与环境观测站(SACOL)2008年夏季的观测资料,分析了陇中黄土高原地表能量不平衡特征及其影响机制,计算了地表和5 cm深处土壤热通量板之间的热储存,并对地表能量不平衡特征重新进行了计算和评价。当把土壤热储存作为地表能量收支的一部分考虑后,不平衡差额绝对值平均降低了23 W.m-2,能量不闭合度平均减小了0.104,利用最小二乘法(OLS)进行线性回归得到的平均不闭合度减小了0.085。从白天和晚上的能量不闭合度频率分布也能够看出,土壤热储存对地表能量收支平衡有很大改善。但即使考虑了土壤热储存项,地表能量不闭合仍然很明显。除了土壤热储存,边界层大气不同形式的输送能力作为对地气能量通量交换过程中的重要因素,对能量不平衡也会产生深远影响。结果显示,地表能量不闭合度分别与垂直速度w、水平风速u和对流速度尺度w*有较密切的关系。涡动相关法通量计算中常通过坐标旋转强迫垂直速度变为零,然而非零的垂直速度和垂直平流是真实存在的,忽略垂直平流热量输送是产生地表能量不平衡的重要原因。     

估算地表热通量和近地层土壤含水量的变分方法

提出一种反演地表感热通量、潜热通量和近地层土壤含水量的变分方法,该方法把不同高度上的风速、位温以及湿度梯度的观测资料与Monin-Obukhov相似理论计算值的偏差、土壤水分蒸发参数化方案估算的蒸发潜热与由相似理论导出值的偏差在地表能量平衡的约束下融合到一个目标泛函数中,采用最优化算法寻求问题的解。利用2001年6月中国暴雨试验与研究项目在安徽肥西观测资料进行了数值验证,结果表明:该方法估算的通量值与Bowen比法具有很好的相关性且又能克服当Bowen比等于-1时计算通量出现的不稳定;同时能克服用廓线法求解热通量与地表能量平衡条件有较大出入的缺点。对观测误差的敏感性试验也表明变分方法是3类方法中最稳定的。反演的近地层土壤含水量对降水具有很好的响应并与观测的0—15 cm深度上平均土壤湿度的变化趋势具有很好的一致性,其绝对偏差小于0.03 m3/m3。     

青藏高原典型下垫面地表能量通量的模型估算与验证

青藏高原地区地表能量通量的估算与验证对高原及其周边地区能量和水循环研究具有重要意义,地表能量平衡系统SEBS(Surface Energy Balance System)模型为研究高原非均匀地表区域地表能量通量提供了一种行之有效的方法。基于中国科学院那曲高寒气候环境观测研究站(简称那曲站)、中国科学院纳木错多圈层综合观测研究站(简称纳木错站)和中国科学院珠穆朗玛大气与环境综合观测研究站(简称珠峰站) 2008年辐射资料、大气边界层塔站观测资料,结合MODIS卫星数据,利用SEBS模型估算地表能量通量,并用站点地表能量通量观测资料进行验证。结果表明,模型估算的感热通量和土壤热通量与站点实测值具有较好的一致性,且感热通量和土壤热通量的估算精度明显优于潜热通量;感热通量的估算精度最高,那曲站、纳木错站和珠峰站的均方根误差分别为54. 98,37. 37和27. 10 W·m~(-2);而模型估算的潜热通量验证结果偏差较大和站点实测数据存在"能量不闭合"问题相关。鉴于在地表能量通量观测中广泛存在"能量不闭合"的问题,利用波文比校正方法校正站点实测潜热通量。研究表明波文比校正方法可以明显改善地表通量观测数据"能量不闭合"的问题,那曲站、纳木错站和珠峰站的能量闭合率分别提高了19. 4%,21. 4%和19. 1%;与原始站点实测潜热通量相比,校正后的潜热通量与SEBS模型估算结果一致性较好,3个站点潜热通量的均方根误差分别减少了6. 78,33. 48和29. 30 W·m~(-2)。     

珠峰北坡地区地表辐射和能量季节变化的初步分析

对青藏高原地区地表能量的研究是一个十分重要的问题.利用中国科学院珠穆朗玛峰大气与环境综合观测研究站2006年5月至2007年4月一年的观测资料,分析了青藏高原珠峰地区的地表能量,即净辐射通量、感热通量、潜热通量和土壤热通量,得到了一些有关珠峰地区地表能量的结果,即太阳总辐射、大气长波辐射、地面长波辐射和净辐射呈现出明显的年变化特征,净辐射、感热通量、潜热通量和土壤热通量得到的日变化是很明显的.并且讨论了计算地表能量通量的方法及其优缺点.     

塔中地面加热场强度变化特征分析

利用塔克拉玛干沙漠大气环境综合观测试验站塔中西站10 m梯度自动气象站2009年1、4、7、10月观测数据,基于土壤的一维热扩散方程计算四季自然沙地下垫面的地表土壤热通量和地面加热场强度,从而分析沙漠下垫面的地面加热场强度变化特征。结果表明:(1)春季和夏季地表土壤热通量日总量为正值,热通量方向向下,沙层相对大气是热汇,秋季和冬季则相反;日较差最大值出现在秋季,最小值出现在冬季;除冬季以外土壤热通量只占净辐射通量的很小一部分;(2)1、4、7、10月地面加热场强度分别为-33.20～87.39 W/m~2、-36.92～274.16 W/m~2、-7.59～244.78W/m~2、-24.90～170.42 W/m~2,地面加热场强度日平均值均为正值,地面为热源,夏季最强,春季次之,冬季最弱;(3)与大气相较,白天地面为强热源,夜间为弱冷源,春季地面加热场强度峰值出现在12时(地方时),夏季、秋季、冬季均出现在13时(地方时)。因此,塔克拉玛干沙漠腹地地面加热场强度具有独特的日变化和季节变化特征。     

华南农田下垫面地气交换和能量收支的观测研究

利用2004年11月至12月在广东省惠州地区进行的湍流连续观测资料,分析非均匀农田近地面层的基本气象要素特征以及水汽和CO2的浓度与通量输送规律,作为今后深入探讨地表非均匀性效应的基础.通过各辐射分量和感热、潜热与土壤热通量的特征分析,研究能量收支的基本状况,并讨论了造成显著能量"不平衡"的原因.观测的基本结果是:(1)近地面1.8 m高度处以北风为主,风速大多低于2 m/s,正午入射太阳辐射约700 W/m2;CO2浓度的日变化范围为600～900 mg/m3,水汽为5～25 g/m3.(2)各气象要素呈现明显的日变化,当地温度日较差约10℃,相对湿度始终高于50%.CO2和水汽的浓度在夜间较白天高,二者的日平均值为713.7 mg/m3和15.9 g/m3;利用涡旋相关法,测得二者的通量在白天高于夜间,日平均值为25.3 mg·m-2·s-1和-4.7×10-2mg·m-2·s.当地的日平均波文(Bowen)比仅为0.04,这主要是由于当地的高湿度造成的.(3)当地存在显著的能量"不平衡"现象,正午时的差额热通量可高达150 W/m2,这可能与平均垂直运动输送的作用、观测误差以及通量和辐射观测的"源地"不匹配等原因有关.研究结果与荒漠、城市和稻田下垫面的观测事实进行了定量比较.     

Validation of the Canadian land surface scheme (class) for a subarctic open woodland

Abstract

This study reports on testing of the peatland version of the Canadian Land Surface Scheme (CLASS) for simulating the energy balance of subarctic open woodland terrain. Model results are compared against several years of measured data from a site near Churchill, Manitoba. In contrast to most forest environments, the floor of the open forest plays a large role in total ecosystem energy exchange. This behaviour presents a significant challenge for land surface models like CLASS and their simplified treatment of vegetation canopies.

Simulations of summer energy balance for seven years encompassing a wide range of meteorological conditions produced consistent results. Root mean square errors for sensible and latent heat fluxes fell between 11 and 28 W m^?2. CLASS consistently underestimated slightly the daily latent heat flux and overestimated the sensible heat flux, average mean bias errors being ‐7.6 and 9.1 W m^?2, respectively. The soil heat flux was less well represented. In general, CLASS was able to capture the diurnal and seasonal behaviour of the measured fluxes under a range of conditions with reasonable accuracy.

In a full year simulation, CLASS reproduced the annual variations in energy balance with some discrepancies associated with snow accumulation and ablation periods. The model performance was sensitive to both snow density and specification of the surface cover. Recommendations for improving the model for subarctic woodlands and terrain types with similar features are discussed.     

An Assessment of Storage Terms in the Surface Energy Balance of a Subalpine Meadow in Northwest China

The heat storage terms in the soil-vegetation-atmosphere system may play an important role in the surface energy budget.In this paper,we evaluate the heat storage terms of a subalpine meadow based on a ficld experiment conducted in the complex terrain of the eastern Qilian Mountains of Northwest China and their impact on the closure of the surface energy balance under such non-ideal conditions.During the night, the average sum of the storage terms was -5.5 W m^-2,which corresponded to 10.4%of net radiation.The sum of the terms became positive at 0730 LST and negative again at about 1500 LST,with a maximum value of 19 W m^-2 observed at approximately 0830 LST.During the day,the average of the sum of the storage terms was 6.5 W m^-2,which corresponded to 4.0%of net radiation.According to the slopes obtained when linear regression of the net radiation and partitioned fluxes was forced through the origin,there is an imbalance of 14.0%in the subalpine meadow when the storage terms are not considered in the surface energy balance.This imbalance was improved by 3.4%by calculating the sum of the storage terms.The soil heat storage flux gave the highest contribution（1.59%）,while the vegetation enthalpy change and the rest of the storage terms were responsible for improvements of 1.04%and 0.77%,respectively.     

Towards Closing the Surface Energy Budget of a Mid-latitude Grassland

Observations for May and August, 2005, from a long-term grassland meteorological station situated in central Netherlands were used to evaluate the closure of the surface energy budget. We compute all possible enthalpy changes, such as the grass cover heat storage, dew water heat storage, air mass heat storage and the photosynthesis energy flux, over an averaging time interval. In addition, the soil heat flux was estimated using a harmonic analysis technique to obtain a more accurate assessment of the surface soil heat flux. By doing so, a closure of 96% was obtained. The harmonic analysis technique appears to improve closure by 9%, the photosynthesis for 3% and the rest of the storage terms for a 3% improvement of the energy budget closure. For calm nights (friction velocity u _* < 0.1 m s⁻¹) when the eddy covariance technique is unreliable for measurement of the vertical turbulent fluxes, the inclusion of a scheme that calculates dew fluxes improves the energy budget closure significantly.     

The Surface Energy Budget and Its Impact on the Freeze-thaw Processes of Active Layer in Permafrost Regions of the Qinghai-Tibetan Plateau

The surface energy budget is closely related to freeze-thaw processes and is also a key issue for land surface process research in permafrost regions.In this study,in situ data collected from 2005 to 2015 at the Tanggula site were used to analyze surface energy regimes,the interaction between surface energy budget and freeze-thaw processes.The results confirmed that surface energy flux in the permafrost region of the Qinghai-Tibetan Plateau exhibited obvious seasonal variations.Annual average net radiation(R_n)for 2010 was 86.5 W m^-2,with the largest being in July and smallest in November.Surface soil heat flux(G₀)was positive during warm seasons but negative in cold seasons with annual average value of 2.7 W m^-2.Variations in R_n and G₀ were closely related to freeze-thaw processes.Sensible heat flux(H)was the main energy budget component during cold seasons,whereas latent heat flux(LE)dominated surface energy distribution in warm seasons.Freeze-thaw processes,snow cover,precipitation,and surface conditions were important influence factors for surface energy flux.Albedo was strongly dependent on soil moisture content and ground surface state,increasing significantly when land surface was covered with deep snow,and exhibited negative correlation with surface soil moisture content.Energy variation was significantly related to active layer thaw depth.Soil heat balance coefficient K was>1 during the investigation time period,indicating the permafrost in the Tanggula area tended to degrade.     

THE ENERGY BUDGETS UNDER DIFFERENT SYNOPTIC CONDITIONS OVER HUAIHE RIVER BASIN DURING HUBEX FIELD OBSERVATION PERIODS IN 1999*

In different synoptic conditions and at different time scales,the analysis of the energy budgets by Bowen Ratio Method and Bulk Schemes over Huaihe River Basin during the field observation periods of HUBEX in 1999 shows that,(1) the averaged latent heat flux is an order of magnitude more than the averaged sensible heat flux during the observation period:(2) the variation of totalcloud amount is out of phase with the terms of energy budgets except for the downward longwave radiation which maybe is related to the cloud's height and class:(3) the values of sensible and latent heat fluxes are small during rain episodes,but thereafter,the values become high and then up to maximum.It is similar to the other terms of the energy budgets except for the downward longwave radiation.The diurnal variation of energy budgets indicates that the daytime precipitation exerts great influence to the energy budgets,but the nighttime precipitation makes little influence;(4) the variation of the latent heat flux is in phase with the evaporation,which indicates that the latent heat flux calculated by bulk schemes is reliable:(5) the means of the sensible and latent heat flux and momentum flux by bulk schemes for the time period from May to August are,respectively,30.71W/m².116.81W/m².2.86×10^-2N/m² in 1998 and 30.28W/m²,107.35W/m²,2.74×10^-2N/m² in 1999.The values of these two years are similar.During summer in 1999 the magnitude and activity of sensible heat flux are strongest in June and those of the latent heat flux are in August.     

江苏省人为热排放现状及未来变化趋势分析

依据1990~2013年江苏省能源消费统计资料和1990、1995、2000、2005、2010年的人口空间分布数据,估计江苏省人为热排放量、探讨其时空分布特征并预测其未来变化趋势。研究结果表明,20多年来江苏省的人为热排放量持续增长,从1990年全省平均的0.59 W/m~2增加到2013年的2.85 W/m~2。排放的空间分布也不均匀,总体上江苏南部地区的排放通量高于江苏北部。近些年江苏省的人为热排放已成为区域问题,高值区已连接成片,2010年江苏省大部分地区的人为热排放高于2.5 W/m~2,南部主要城市排放通量大于10 W/m~2、北部城市也多大于5 W/m~2。江苏各城市的城区人为热排放通量稳步增长,2002年后增长加速、增量最高可达到2 W m~(-2) a~(-1)。在2030年和2050年江苏省的平均人为热排放通量将分别达到5.7 W/m~2和9.1 W/m~2,可能对中国东部的气候和大气环境产生重要影响。     

Calibration of soil heat flux transducers

Summary Soil heat flux transducer calibration, according to theory, is influenced by the thermal conductivity difference between the transducer and the calibration medium and the geometry of the transducer. This study was conducted to compare the influence of these parameters on the calibration factors of two types of commercial soil heat flux transducers with different material thermal conductivities and different geometries. A theoretical calibration equation was developed and evaluated. Calibrations of 14 transducers representing two commercial types were conducted in the laboratory using steady-state conductive methods over a range of heat fluxes from 40 W/m² to 200 W/m². The calibration medium was dry and saturated sand with a thermal conductivity varying from 0.3 to 3 W m^–1°C^–1. The mean calibration factor for one type of transducer was 12% lower than the mean manufacturer's calibration factor instead of the 26 to 36% lower value predicted by theory. The other type of transducer had a mean calibration factor 7% greater than the mean manufacturer's calibration factor in contrast to the 1 to 11% larger value predicted from theory. The computed geometric factors were 1.07 and 0.89 for the circular and square transducers, respectively. These factors were less than the theoretical value of 1.70 for each shape of transducer but similar to experimental values of 1.02 to 1.31 from previous studies reported in the literature. The thermal conductivity of the calibration medium and the geometry of the transducer affects the calibration factors of soil heat flux transducers, basically according to theory.Contribution from USDA-Agricultural Research Service, Southern Plains Area.With 4 Figures     

The Summer Surface Energy Balance of the High Antarctic Plateau

The summertime surface energy balance (SEB) at Kohnen station, situated on the high Antarctic plateau (75°00′ S, 0°04′ E, 2892m above sea level) is presented for the period of 8 January to 9 February 2002. Shortwave and longwave radiation fluxes were measured directly; the former was corrected for problems associated with the cosine response of the instrument. Sensible and latent heat fluxes were calculated using the bulk method, and eddy-correlation measurements and the modified Bowen ratio method were used to verify these calculated fluxes. The calculated sub-surface heat flux was checked by comparing calculated to measured snow temperatures. Uncertainties in the measurements and energy-balance calculations are discussed. The general meteorological conditions were not extraordinary during the period of the experiment, with a mean 2-m air temperature of −27.5°C, specific humidity of 0.52×10⁻³kg kg⁻¹ and wind speed of 4.1ms⁻¹. The experiment covered the transition period from Antarctic summer (positive net radiation) to winter (negative net radiation), and as a result the period mean net radiation, sensible heat, latent heat and sub-surface heat fluxes were small with values of −1.1, 0.0, −1.0 and 0.7 Wm⁻², respectively. Daily mean net radiation peaked on cloudy days (16 Wm⁻²) and was negative on clear-sky days (minimum of −19 W m⁻²). Daily mean sensible heat flux ranged from −8 to +10 Wm⁻², latent heat flux from −4 to 0 Wm⁻² and sub-surface heat flux from −8 to +7 Wm⁻².     

The atmospheric energy budget and implications for surface fluxes and ocean heat transports

Comprehensive diagnostic comparisons and evaluations have been carried out with the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) and European Centre for Medium Range Weather Forecasts (ECMWF) reanalyses of the vertically integrated atmospheric energy budgets. For 1979 to 1993 the focus is on the monthly means of the divergence of the atmospheric energy transports. For February 1985 to April 1989, when there are reliable top-of-the-atmosphere (TOA) radiation data from the Earth Radiation Budget Experiment (ERBE), the implied monthly mean surface fluxes are derived and compared with those from the assimilating models and from the Comprehensive Ocean Atmosphere Data Set (COADS), both locally and zonally integrated, to deduce the implied ocean meridional heat transports. While broadscale aspects and some details of both the divergence of atmospheric energy and the surface flux climatological means are reproducible, especially in the zonal means, differences are also readily apparent. Systematic differences are typically ∼20 W m⁻². The evaluation highlights the poor results over land. Land imbalances indicate local errors in the divergence of the atmospheric energy transports for monthly means on scales of 500 km (T31) of 30 W m⁻² in both reanalyses and ∼50 W m⁻² in areas of high topography and over Antarctica for NCEP/NCAR. Over the oceans in the extratropics, the monthly mean anomaly time series of the vertically integrated total energy divergence from the two reanalyses correspond reasonably well, with correlations exceeding 0.7. A common monthly mean climate signal of about 40 W m⁻² is inferred along with local errors of 25 to 30 W m⁻² in most extratropical regions. Except for large scales, there is no useful common signal in the tropics, and reproducibility is especially poor in regions of active convection and where stratocumulus prevails. Although time series of monthly anomalies of surface bulk fluxes from the two models and COADS agree very well over the northern extratropical oceans, the total fields all contain large systematic biases which make them unsuitable for determining ocean heat transports. TOA biases in absorbed shortwave, outgoing longwave and net radiation from both reanalysis models are substantial (>20 W m⁻² in the tropics) and indicate that clouds are a primary source of problems in the model fluxes, both at the surface and the TOA. Time series of monthly COADS surface fluxes are shown to be unreliable south of about 20^∘N where there are fewer than 25 observations per 5^∘ square per month. Only the derived surface fluxes give reasonable implied meridional ocean heat transports. Received: 21 March 2000 / Accepted: 21 June 2000