Simulation of oasis breeze circulation in the arid region of the Northwestern China

In this paper, the process of oasis-desert circulation (ODC) is simulated by MM5V3.5 model through designing an ideal oasis-desert scheme and assuming that initial atmosphere is at rest (V = 0). The findings showed that the key of forming special oasis boundary structure is the difference of energy and water between oasis and desert. The evaporation of oasis surface consumes heat energy, and the low temperature of oasis causes an oasis breeze circulation (OBC), which drives an ODC with a downdraft over the oasis and an updraft over the desert. Later, the cold, dry and stable boundary over oasis is gradually formed, on the contrary,the atmospheric boundary over desert on the edge of oasis is hot, humid and unstable and its height is about 600 hPa. The updraft over the desert forms a wet ring that acts as a vertical wall weakening the low-level moisture exchange between the oasis and desert. The downdraft of OBC increases the atmospheric stability that reduces the oasis evaporation. The low-level outflow from the oasis (into the desert) prevents the dry, hot air flowing from the desert into the oasis.Thus an oasis self-preservation mechanism may be formed due to OBC. The horizontal area influenced by oasis is twice as oasis area and the vertical range is four times as oasis. The ODC is strong in the daytime and reaches the strongest at 17:00, and the influenced area is the largest at 20:00.     

Simulation of oasis breeze circulation in the arid region of the Northwestern China

In this paper, the process of oasis-desert circulation (ODC) is simulated by MM5V3.5 model through designing an ideal oasis-desert scheme and assuming that initial atmosphere is at rest (V= 0). The findings showed that the key of forming special oasis boundary structure is the difference of energy and water between oasis and desert. The evaporation of oasis surface consumes heat energy, and the low temperature of oasis causes an oasis breeze circulation (OBC), which drives an ODC with a downdraft over the oasis and an updraft over the desert. Later, the cold, dry and stable boundary over oasis is gradually formed, on the contrary, the atmospheric boundary over desert on the edge of oasis is hot, humid and unstable and its height is about 600 hPa. The updraft over the desert forms a wet ring that acts as a vertical wall weakening the low-level moisture exchange between the oasis and desert. The downdraft of OBC increases the atmospheric stability that reduces the oasis evaporation. The low-level outflow from the oasis (into the desert) prevents the dry, hot air flowing from the desert into the oasis. Thus an oasis self-preservation mechanism may be formed due to OBC. The horizontal area influenced by oasis is twice as oasis area and the vertical range is four times as oasis. The ODC is strong in the daytime and reaches the strongest at 17:00, and the influenced area is the largest at 20:00.     

Disposition of rainwater under creosotebush

In desert shrubland ecosystems water and nutrients are concentrated beneath shrub canopies in ‘resource islands’. Rain falling on to these islands reaches the ground as either stemflow or throughfall and then either infiltrates into the soil or runs off as overland flow. This study investigates the partitioning of rainwater between stemflow and throughfall in the first instance and between infiltration and runoff in the second. Two series of 40 rainfall simulation experiments were performed on 16 creosotebush shrubs in the Jornada Basin, New Mexico. The first series of experiments was designed to measure the surface runoff and was performed with each shrub in its growth position. The second series was designed to measure stemflow reaching the shrub base and was conducted with the shrub suspended above the ground. The experimental data show that once equilibrium is achieved, 16% of the rainfall intercepted by the canopy or 6·7% of the rain falling inside the shrub area (i.e. the area inside the shrub's circumscribing ellipse) is funnelled to the shrub base as stemflow. This redistribution of the rainfall by stemflow is a function of the ratio of canopy area (i.e. the area covered by the shrub canopy) to collar area (i.e. a circular area centred on the shrub base), with stemflow rate being positively correlated and throughfall rate being negatively correlated with this ratio. The surface runoff rate expressed as a proportion of the rate at which rainwater arrives at a point (i.e. stemflow rate plus throughfall rate) is the runoff coefficient. A multiple regression reveals that 75% of the variance in the runoff coefficient can be explained by three independent variables: the rainfall rate, the ratio of the canopy area to the collar area, and the presence or absence of subcanopy vegetation. Although the last variable is a dummy variable, it accounts for 66·4% of the variance in the runoff coefficient. This suggests that the density and extent of the subcanopy vegetation is the single most important control of the partitioning of rainwater between runoff and infiltration beneath creosotebush. Although these findings pertain to creosotebush, similar findings might be expected for other desert shrubs that generate significant stemflow and have subcanopy vegetation. Copyright © 2003 John Wiley & Sons, Ltd.     

沙漠陆面过程参数化与模拟

沙漠地区植被稀疏、干旱少雨,其陆面物理过程具有与全球其它地区显著不同的特点.本文利用巴丹吉林沙漠观测资料,分析和计算了地表反照率、比辐射率、粗糙度和土壤热容量、热传导系数等关键陆面过程参数,建立了适合于沙漠地区的陆面过程模式DLSM (Desert Land Surface Model),并与NOAH陆面过程模式的模拟结果和观测资料进行了比较.结果表明:巴丹吉林沙漠地表反照率为0.273,比辐射率为0.950,地表粗糙度为1.55×10^-3 m,土壤热容量和热扩散系数分别为1.08×10⁶ J·m^-3·K^-1和3.34×10^-7 m²·s.辐射传输、感热输送和土壤热传导过程是影响沙漠地区地表能量平衡的主要物理过程.通过对这三种过程的准确模拟检验,DLSM能够较准确地模拟巴丹吉林沙漠地气能量交换特征;短波辐射、长波辐射和感热通量的模拟结果与观测值间的标准差分别为7.98,6.14,33.9 W·m^-2,与NOAH陆面过程模式的7.98,7.72,46.6 W·m^-2的结果接近.地表反照率是沙漠地区最重要的陆面过程参数,地表反照率增大5%,向上短波辐射通量随之增加5%,感热通量则减小2.8%.本文研究结果对丰富陆面过程参数化方案,改进全球陆面过程模式、气候模式具有参考意义.     

沙漠绿洲地区夏季地表能量收支的数值模拟

本文在MSPAS(Modified Soil-Plant-Atmosphere Scheme)的基础上,引入了一个有效的晴天大气辐射传输方案,建立了一个能在物理上真实地模拟陆气相互作用及其反馈机制的二维模式MLAIM（Modified Land Atmosphere Interaction Model）.本文利用HEIFE实验的观测资料对MLAIM的模拟结果进行了检验,对其中不合理的部分进行了分析,指出了在干旱半干旱区陆面过程参数修正的必要性,对干旱半干旱区土壤水分传输以及大气近地面层湍流输送的参数化方案进行了改进.改进后的模式能够较好地模拟夏季连续晴天条件下沙漠的地表能量收支,因此,本文利用MLAIM研究了绿洲对其周围沙漠地表能量收支的影响,并对地表能量收支各分量之间的相互作用进行了分析.结果表明,绿洲向其下风向沙漠的水汽输送是导致其上下风向沙漠间地表能量收支差异的最重要的因子.     

Evaluation of remote sensing‐based evapotranspiration estimates using a water transfer numerical simulation under different vegetation conditions in an arid area

Daily actual evapotranspiration (AET) and seasonal AET values are of great practical importance in the management of regional water resources and hydrological modelling. Remotely sensed AET models and Landsat satellite images have been used widely in producing AET estimates at the field scale. However, the lack of validation at a high spatial frequency under different soil water conditions and vegetation coverages limits their operational applications. To assess the accuracies of remote sensing‐based AET in an oasis‐desert region, a total of 59 local‐scale daily AET time series, simulated using HYDRUS‐1D calibrated with soil moisture profiles, were used as ground truth values. Of 59 sampling sites, 31 sites were located in the oasis subarea and 28 sites were located in the desert subarea. Additionally, the locally validated mapping evapotranspiration at high resolution with internalized calibration surface energy balance model was employed to estimate instantaneous AET values in the area containing all 59 of the sampling sites using seven Landsat subimages acquired from June 5 to August 24 in 2011. Daily AET was obtained using extrapolation and interpolation methods with the instantaneous AET maps. Compared against HYDRUS‐1D, the remote sensing‐based method produced reasonably similar daily AET values for the oasis sites, while no correlation was observed for daily AET estimated using these two methods for the desert sites. Nevertheless, a reasonable monthly AET could be estimated. The correlation analysis between HYDRUS‐1D‐simulated and remote sensing‐estimated monthly AET values showed relative root‐mean‐square error values of 15.1%, 12.1%, and 12.3% for June, July, and August, respectively. The root mean square error of the summer AET was 10.0%. Overall, remotely sensed models can provide reasonable monthly and seasonal AET estimates based on periodic snapshots from Landsat images in this arid oasis‐desert region.     

Stability of banded vegetation patterns under seasonal rainfall and limited soil moisture storage capacity

The delicate equilibrium of soil moisture and biomass may become unstable under water scarcity conditions causing banded vegetation patterns to form on hillsides of semi-arid catchments. Soil related processes that induce instability (namely: soil moisture advection and diffusion), have been evaluated numerically for different rainfall regimes. This study addresses the combined influence of some relevant soil characteristics, and the effect of seasonal precipitation on vegetation patterns, advancing the comprehension of those mechanisms that cause shifts toward banded vegetation patterns or bare states.     

Influence of variation of soil spatial heterogeneity on vegetation restoration

Ecological restoration as a new research field of applied ecology can be traced back to the 1950s, it mainly focuses on the studies of ecological restoration of mine fields, tropical forests, wetlands and indus-try-polluted ecosystems[1-4]. Following the raising of the conception of “restoration ecology”[5], the holding of a series of international conferences and the found-ing of the International Association for Restoration Ecology, the studies of ecological restoration has be-come a quit…     

The impact of using area-averaged land surface properties —topography, vegetation condition, soil wetness—in calculations of intermediate scale (approximately 10 km) surface-atmosphere heat and moisture fluxes

It is commonly assumed that biophysically based soil-vegetation-atmosphere transfer (SVAT) models are scale-invariant with respect to the initial boundary conditions of topography, vegetation condition and soil moisture. In practice, SVAT models that have been developed and tested at the local scale (a few meters or a few tens of meters) are applied almost unmodified within general circulation models (GCMs) of the atmosphere, which have grid areas of 50–500 km². This study, which draws much of its substantive material from the papers of Sellers et al. (1992c, J. Geophys. Res., 97(D17): 19033–19060) and Sellers et al. (1995, J. Geophys. Res., 100(D12): 25607–25629), explores the validity of doing this. The work makes use of the FIFE-89 data set which was collected over a 2 km × 15 km grassland area in Kansas. The site was characterized by high variability in soil moisture and vegetation condition during the late growing season of 1989. The area also has moderate topography.

The 2 km × 15 km ‘testbed’ area was divided into 68 × 501 pixels of 30 m × 30 m spatial resolution, each of which could be assigned topographic, vegetation condition and soil moisture parameters from satellite and in situ observations gathered in FIFE-89. One or more of these surface fields was area-averaged in a series of simulation runs to determine the impact of using large-area means of these initial or boundary conditions on the area-integrated (aggregated) surface fluxes. The results of the study can be summarized as follows:

1. 1. analyses and some of the simulations indicated that the relationships describing the effects of moderate topography on the surface radiation budget are near-linear and thus largely scale-invariant. The relationships linking the simple ratio vegetation index (SR), the canopy conductance parameter (_F) and the canopy transpiration flux are also near-linear and similarly scale-invariant to first order. Because of this, it appears that simple area-averaging operations can be applied to these fields with relatively little impact on the calculated surface heat flux.

2. 2. The relationships linking surface and root-zone soil wetness to the soil surface and canopy transpiration rates are non-linear. However, simulation results and observations indicate that soil moisture variability decreases significantly as an area dries out, which partially cancels out the effects of these non-linear functions.In conclusion, it appears that simple averages of topographic slope and vegetation parameters can be used to calculate surface energy and heat fluxes over a wide range of spatial scales, from a few meters up to many kilometers at least for grassland sites and areas with moderate topography. Although the relationships between soil moisture and evapotranspiration are non-linear for intermediate soil wetnesses, the dynamics of soil drying act to progressively reduce soil moisture variability and thus the impacts of these non-linearities on the area-averaged surface fluxes. These findings indicate that we may be able to use mean values of topography, vegetation condition and soil moisture to calculate the surface-atmosphere fluxes of energy, heat and moisture at larger length scales, to within an acceptable accuracy for climate modeling work. However, further tests over areas with different vegetation types, soils and more extreme topography are required to improve our confidence in this approach.

     

Seasonal variation in albedo and radiation exchange between a burned and unburned forested peatland: implications for peatland evaporation

Forested boreal peatlands represent a precipitation‐dependent ecosystem that is prone to wildfire disturbance. Solar radiation exchange in forested peatlands is modified by the growth of a heterogeneous, open‐crown tree canopy, as well as by likely disturbance from wildfire. Radiation exchange at the peat surface is important in peatlands, as evaporation from the peat surface is the dominant pathway of water loss in peatlands of continental western North America. We examined shortwave and longwave radiation exchange in two forested ombrotrophic peatlands of central Alberta, Canada: one with (>75 years since wildfire; unburned) and another without a living spruce canopy (1–4 years since wildfire; burned) between the autumn of 2007 and 2010. Above‐canopy winter albedo was nearly two times greater in the recently burned peatland than the unburned peatland. Incoming shortwave radiation at the peat surface was much higher at the burned peatland, which increases the amount of energy available for evaporation. This is especially true for hollow microforms that are generally shaded by the tree canopy in unburned peatlands. Snow‐free albedo was similar between peatlands, although an increase in longwave losses at the burned site resulted in slightly greater net radiation at the unburned site. Copyright © 2015 John Wiley & Sons, Ltd.     

Evapotranspiration and its main controlling mechanism over the desert riparian forests in the lower Tarim River Basin

Evapotranspiration(ET) and its controlling mechanism over the desert riparian forests in arid regions are the important scientific basis for the water resources managements of the lower reaches of the inland rivers of China. Nearly three years of continuous measurements of surface ET, soil water content at different depths and groundwater table over a typical Tamarix spp. stand and a typical Populus euphratica stand were conducted in the lower reach of the Tarim River. The ET seasonal trends in the growing season were controlled by plant phenology, and ET in non-growing season was weak. The diurnal variations of ET resulting from the comprehensive effects of all atmospheric factors were significantly related with reference ET. The spatial pattern of ET was determined by vegetation LAI, more vegetation coverage, more ET amount. Groundwater is the water source of surface ET, and the soil water in shallow layers hardly took part in the water exchange in the groundwatersoil-plant-air system. The temporal processes of ET over the Tamarix stand and the Populus stand were similar, but the water consumption of the well-grown Populus euphratica was higher than that of the well-grown Tamarix spp. Further analysis indicates that plant transpiration accounts for most of the surface ET, with soil evaporation weak and negligible; groundwater table is a crucial factor influencing ET over the desert riparian forests, groundwater influences the processes and amounts of ET by controlling the growth and spatial distribution of desert riparian forests; quantifying the water stress of desert riparian forests using groundwater table is more appropriate, rather than soil water content. Based on the understanding of ET and water movements in the groundwater-soil-plant-air system, a generalized framework expressing the water cycling and its key controlling mechanism in the lower reaches of the inland rivers of China is described, and a simple model to estimate water requirements of the desert riparian forests is presented.     

Inversion of the asymmetry factor for desert areas of China

Deserts,which have high surface albedo and wide area,are important components of the earth system.It is very important for the research of surface radiation and energy balance to understand the anisotropic scattering of desert areas.The emergence and development of multi-angle remote sensing made possible the inversion of the anisotropic scattering of desert areas at the regional or global scale.Firstly,this paper explored the accuracy of the inversion of asymmetry factor using the Hapke model and the simul...     

WINTER RADIATION EXTINCTION AND REFLECTION IN A BOREAL PINE CANOPY: MEASUREMENTS AND MODELLING

Predicting the rate of snowmelt and intercepted snow sublimation in boreal forests requires an understanding of the effects of snow-covered conifers on the exchange of radiant energy. This study examined the amount of intercepted snow on a jack pine canopy in the boreal forest of central Saskatchewan and the shortwave and net radiation exchange with this canopy, to determine the effect of intercepted snow and canopy structure on shortwave radiation reflection and extinction and net radiation attenuation in a boreal forest. The study focused on clear sky conditions, which are common during winter in the continental boreal forest. Intercepted snow was found to have no influence on the clear-sky albedo of the canopy, the extinction of short wave radiation by the canopy or ratio of net radiation at the canopy top to that at the surface snow cover. Because of the low albedo of the snow-covered canopy, net radiation at the canopy top remains positive and a large potential source of energy for sublimation. The canopy albedo declines somewhat as the extinction efficiency of the underlying canopy increases. The extinction efficiency of short wave radiation in the canopy depends on solar angle because of the approximately horizontal orientation of pine branches. For low solar angles above the horizon, the extinction efficiency is quite low and short wave transmissivity through the canopy is relatively high. As the solar angle increases, extinction increases up to angles of about 50°, and then declines. Extinction of short wave radiation in the canopy strongly influences the attenuation of net radiation by the canopy. Short wave radiation that is extinguished by branches is radiated as long wave, partly downwards to the snow cover. The ratio of net radiation at the canopy top to that at the snow cover surface increases with the extinction of short wave radiation and is negative for low extinction efficiencies. For the pine canopy examined, the daily mean net radiation at the snow cover surface became positive when daily mean solar angles exceeded 22° in late March. Hence, canopy structure and solar angle control the net radiation at the snow cover surface during clear sky conditions and will govern the timing and rate of snowmelt. Models of intercepted snow sublimation and forest snowmelt could beneficially incorporate the canopy radiation balance, which can be extrapolated to stands of various canopy densities, coverage and heights in a physically based manner. Such models could hence avoid ‘empirical’ temperature index measures that cannot be extrapolated with confidence.     

The effect of biological soil crusts on soil moisture dynamics under different rainfall conditions in the Tengger Desert,China

Rainfall is considered as the dominant water replenishment in desert ecosystems, and the conversion of rainfall into soil water availability plays a central role in sustaining the ecosystem function. In this study, the role of biological soil crusts (BSCs), typically formed in the revegetated desert ecosystem in the Tengger Desert of China, in converting rainfall into soil water, especially for the underlying soil moisture dynamics, was clarified by taking into account the synthetic effects of BSCs, rainfall characteristics, and antecedent soil water content on natural rainfall conditions at point scale. Our results showed that BSCs retard the infiltration process due to its higher water holding capacity during the initial stage of infiltration, such negative effect could be offset by the initial wet condition of BSCs. The influence of BSCs on infiltration amount was dependent on rainfall regime and soil depth. BSCs promoted a higher infiltration through the way of prolonged water containing duration in the ground surface and exhibited a lower infiltration at deep soil layer, which were much more obvious under small and medium rainfall events for the BSCs area compared with the sand area. Generally, the higher infiltration at top soil layer only increased soil moisture at 0.03 m depth; in consequence, there was no water recharge for the deep soil, and thus, BSCs had a negative effect on soil water effectiveness, which may be a potential challenge for the sustainability of the local deep‐rooted vegetation under the site specific rainfall conditions in northwestern China.     

沙漠-绿洲陆-气相互作用和绿洲效应的数值模拟

本文利用一个已发展的陆面过程参数化方案与大气边界层模式耦合,模拟了半干旱区绿洲戈壁非均匀下垫面的陆面过程及其与大气边界层的相互作用,给出了“绿洲效应”这一自然现象垂直剖面上更为清晰、准确和细致的结构特征.数值模拟的结果与早前的许多观测实验结论相吻合,即“绿洲效应”具有明显的“冷岛效应”和“湿岛效应”;它表现为在绿洲区域比戈壁沙漠区域环境温度低、湿度大、湍流动能输送弱,具有下沉气流而导致与周围戈壁沙漠区域产生水平输送环流.而更加细致地研究这些现象对于深入了解绿洲气候的形成和绿洲的维持机理具有重要的意义.     

Simulation of crop growth and energy and carbon dioxide fluxes at different time steps from hourly to daily

Understanding the exchange processes of energy and carbon dioxide (CO₂) in the soil–vegetation–atmosphere system is important for assessing the role of the terrestrial ecosystem in the global water and carbon cycle and in climate change. We present a soil–vegetation–atmosphere integrated model (ChinaAgrosys) for simulating energy, water and CO₂ fluxes, crop growth and development, with ample supply of nutrients and in the absence of pests, diseases and weed damage. Furthermore, we test the hypotheses of whether there is any significant difference between simulations over different time steps. CO₂, water and heat fluxes were estimated by the improving parameterization method of the coupled photosynthesis–stomatal conductance–transpiration model. Soil water evaporation and plant transpiration were calculated using a multilayer water and heat‐transfer model. Field experiments were conducted in the Yucheng Integrated Agricultural Experimental Station on the North China Plain. Daily weather and crop growth variables were observed during 1998–2001, and hourly weather variables and water and heat fluxes were measured using the eddy covariance method during 2002–2003. The results showed that the model could effectively simulate diurnal and seasonal changes of net radiation, sensible and latent heat flux, soil heat flux and CO₂ fluxes. The processes of evapotranspiration, soil temperature and leaf area index agree well with the measured values. Midday depression of canopy photosynthesis could be simulated by assessing the diurnal change in canopy water potential. Moreover, the comparisons of simulated daily evapotranspiration and net ecosystem exchange (NEE) under different time steps indicated that time steps used by a model affect the simulated results. There is no significant difference between simulated evapotranspiration using the model under different time steps. However, simulated NEE produces large differences in the response to different time steps. Therefore, the accurate calculation of average absorbed photosynthetic active radiation is important for the scaling of the model from hourly steps to daily steps in simulating energy and CO₂ flux exchanges between winter wheat and the atmosphere. Copyright © 2007 John Wiley & Sons, Ltd.     

Responses of distribution pattern of desert riparian forests to hydrologic process in Ejina oasis

By using the theories and methods of landscape ecology and the technology of GIS and RS, a study has been carried out on the responses of distribution pattern of desert riparian forest to hydrologic process on the basis of the hydrologic data from 1990 to 2000 and the TM image of 2001 year. The results showed that: (1) there appears an even distribution pattern for the relative forest area in oasis, however, the degenerated forest diaplays an increasing tendency from west to east; (2) the desert riparian forest in Ejina is in completely degenerated process at the patch scale; (3) the number of patch is influenced not only by hydrologic process, but also by agricultural activity such as cultivation. The severe deterioration of the degraded vegetation in whole oasis initiates from lower reaches, and gradually impels to upstream; the fragmentation of landscape in the terminal site is more obvious, which is influenced by river shape and decreasing flux of water. It is found that the influence of surface hydrologic process to the ground hydrologic process of desert riparian forest in Ejina oasis is little for the recent ten years. The relative area of the degenerated forest increased with increasing ground water depth in the direction of parallel to river channel. On the contrary, in the direction perpendicular to river channel, there is a decreasing tendency for the average patch area of the forest and the degenerated forest with increasing ground water depth.     

Responses of distribution pattern of desert riparian forests to hydrologic process in Ejina oasis

By using the theories and methods of landscape ecology and the technology of GIS and RS, a study has been carried out on the responses of distribution pattern of desert riparian forest to hydrologic process on the basis of the hydrologic data from 1990 to 2000 and the TM image of 2001 year. The results showed that: (1) there appears an even distribution pattern for the relative forest area in oasis, however, the degenerated forest diaplays an increasing tendency from west to east; (2) the desert riparian forest in Ejina is in completely degenerated process at the patch scale; (3) the number of patch is influenced not only by hydrologic process,but also by agricultural activity such as cultivation. The severe deterioration of the degraded vegetation in whole oasis initiates from lower reaches, and gradually impels to upstream; the fragmentation of landscape in the terminal site is more obvious, which is influenced by river shape and decreasing flux of water. It is found that the influence of surface hydrologic process to the ground hydrologic process of desert riparian forest in Ejina oasis is little for the recent ten years. The relative area of the degenerated forest increased with increasing ground water depth in the direction of parallel to river channel. On the contrary, in the direction perpendicular to river channel, there is a decreasing tendency for the average patch area of the forest and the degenerated forest with increasing ground water depth.     

Spatial patterns and temporal stability of soil moisture across a range of scales in a semi‐arid environment

The antecedent soil moisture status of a catchment is an important factor in hydrological modelling. Traditional Hortonian infiltration models assume that the initial moisture content is constant across the whole catchment, despite the fact that even in small catchments antecedent soil moisture exhibits tremendous spatial heterogeneity. Spatial patterns of soil water distribution across three transects (two in a burnt area and one in an unburnt area) in a semi‐arid area were studied. At the transect scale, when the factors affecting soil moisture were limited to topographical position or local topography, spatial patterns showed time stability, but when other factors, such as vegetation, were taken into account, the spatial patterns became time unstable. At the point scale, and in the same areas, topographical position was the main factor controlling time stability. Scale dependence of time stability was studied and local topography and vegetation presence were observed to play an important role for the correlation between consecutive measures depending on the scale. Copyright © 2000 John Wiley & Sons, Ltd.