Parametrization of peatland hydraulic properties for the Canadian land surface scheme

Abstract

A hydraulic parametrization is developed for peatland environments in the Canadian Land Surface Scheme (CLASS). Three ‐wetland soil classes account for the typical variation in the hydraulic characteristics of the uppermost 0.5 m of organic soils. Review of the literature reveals that saturated hydraulic conductivity varies from a median of 1.0 × 10^?7m/s in deeply humified sapric peat to 2.8 × 10^?4 m/s in relatively undecomposed fibric peat. Average pore volume fraction ranges from 0.83 to 0.93. Parameters have been designed for the soil moisture characteristic curves for fibric, hemic and sapric peat using the Campbell (1974) equation employed in CLASS, and the van Genuchten (1980) formulation. There is little difference in modelled soil moisture between the two formulations within the range of conditions normally found in peatlands. Validation of modelled water table depth and peat temperature is performed for a fen in northern Québec and a bog in north‐central Minnesota. The new parametrization results in a more realistic simulation of these variables in peatlands than the previous version of CLASS, in which unrealistic mineral soil “equivalents “ were used for wetland soil climate modelling.     

一个用于气候模式的简单冻土过程参数化方案的建立和检验

在NCAR／LSM的基础上，发展了一个简单的冻土过程参数化方案，并使用苏联6个站的水气象观测资料考察了耦合了新方案模式的气候效应。在新方案中，加入了对含冰量的求解和在相变过程中的能量变化;并使用Johanson的方案替代了模式中原有的土壤导热率的参数化方案，考虑了含冰量对土壤水热性质的影响。原模式和改进后模式的模拟结果的比较得到，冻土过程方案能够合理的模拟土壤列中的能量收支及水热性质随含冰量的变化。随着入渗的减少和径流的增加，春季的土壤湿度减小。因此，热通量的分配和土壤温度也产生了相应的变化。     

Improving CLM4.5 simulations of land–atmosphere exchange during freeze–thaw processes on the Tibetan Plateau

Soil is heterogeneous and has different thermal and hydraulic properties, causing varied behavior in heat and moisture transport. Therefore, soil has an important effect on land–atmosphere interactions. In this study, an improved soil parameterization scheme that considers gravel and organic matter in the soil was introduced into CLM4.5 (Community Land Model). By using data from the Zoige and Madoi sites on the Tibetan Plateau, the ability of the model to simultaneously simulate the duration of freeze–thaw periods, soil temperature, soil moisture, and surface energy during freeze–thaw processes, was validated. The results indicated that: (1) the new parameterization performed better in simulating the duration of the frozen, thawing, unfrozen, and freezing periods; (2) with the new scheme, the soil thermal conductivity values were decreased; (3) the new parameterization improved soil temperature simulation and effectively decreased cold biases; (4) the new parameterization scheme effectively decreased the dry biases of soil liquid water content during the freezing, completely frozen, and thawing periods, but increased the wet biases during the completely thawed period; and (5) the net radiation, latent heat flux, and soil surface heat flux of the Zoige and Madoi sites were much improved by the new organic matter and thermal conductivity parameterization.     

CLM3.0模式中冻土过程参数化的改进及模拟试验

对NCAR CLM3.0(Community Land Model)的冻土过程参数化进行了改进.根据平衡态的热力学关系和考虑含冰量的土壤基质势的经验公式定义了冰点下的最大液态水含量,超过最大液态水含量的部分冻结为冰,并在水导率的计算中加入了冰的阻挡作用.利用青藏高原改则站2003年4月1日至2004年12月31日的观测...     

Parametrization schemes of incident radiation in the North Water polynya

Abstract

An evaluation of the Canadian Land Surface Scheme (CLASS) 3.1 snow cover simulations at four sites included in the Snow Model Intercomparison Project (SnowMIP) revealed that CLASS was able to provide realistic representations of snow cover accumulation, melt and physical properties over a range of snow cover climates. The modified snow aging parametrization in CLASS 3.1 provided improved simulations of snowpack density which resulted in a marked reduction in the root‐mean‐square (rms) error for daily snow depth, and slight improvements in snow surface temperature. CLASS 3.1 still exhibited a tendency to overestimate snow cover duration which is attributed to the way shallow snow ablation is treated. CLASS provided generally realistic simulations of daily and seasonal variation in snow albedo although cold snow albedo was underpredicted by 0.10 to 0.15 at a site with a deep (> 2 m) cold snowpack. CLASS also exhibited a tendency to overpredict late spring snow albedo which was reduced by the addition of a snow layer subroutine that kept track of snow albedo by precipitation event. CLASS had a noticeable cold bias averaging 3°–4°C at two mountain sites included in the comparison. The bias was closely linked to atmospheric stability and could exceed 10°C under conditions of strong radiative cooling and low wind speeds. The CLASS energy deficit under these conditions was determined to be ～20–40 W m^?2 and was mostly accounted for by introducing a windless exchange coefficient into the calculation of sensible heat fluxes following the approach used in a number of other physical snowpack models. CLASS provided realistic simulations of daily snowmelt runoff with the exception of the Weissfluhjoch site which was characterized by a deep cold snowpack. A preliminary assessment of snow water equivalent (SWE) rms error for the 23 models participating in SnowMIP showed that CLASS was one of the better single layer snow models included in the comparison. CLASS performance was comparable to the multi‐layer CROCUS snowpack model in the evaluations carried out in this study.     

陆面模式CLM对若尔盖站冻融期模拟性能的检验与对比

陆面模式CLM(Community Land Model)是目前国际上发展较为完善并被广泛应用的陆面过程模式。本文使用中国科学院寒区旱区环境与工程研究所位于青藏高原东部的若尔盖高原湿地生态系统研究站的观测资料,对CLM3.0版本及CLM4.0版本在上述地区的模拟性能进行了检验与对比。通过比较观测值与模拟值,验证了模式在高原季节性冻土地区的适用性,发现CLM4.0较CLM3.0在模拟结果上有了一定提高。CLM4.0加入了未冻水参数化方案,使模式可以模拟到冬季土壤冻结后存留的未冻水,显著增加了冻融期间土壤含水量的模拟,同时减小了土壤含冰量的模拟值。并因此增大了模拟的冻土热容量,减小了热导率,使冻融期间土壤温度的模拟也有了一定改善。但是模拟中也发现对于较深层土壤,温度模拟值在冻融期间较观测显著偏低。另外,在消融(冻结)过程阶段CLM4.0模拟的土壤含水量骤增(骤降)的时间均较观测提前。消融过程、冻结过程阶段模拟时间偏短,而完全冻结、完全消融阶段模拟时间偏长。因此CLM对于高原冻土地区的模拟仍是其需要重点改进的地方之一。     

Introduction of a sub-grid hydrology in the ISBA land surface model

In atmospheric models, the partitioning of precipitation between infiltration and runoff has a major influence on the terrestrial water budget, and thereby on the simulated weather or climate. River routing models are now available to convert the simulated runoff into river discharge, offering a good opportunity to validate land surface models at the regional scale. However, given the low resolution of global atmospheric models, the quality of the hydrological simulations is much dependent on various processes occurring on unresolved spatial scales. This paper focuses on the parameterization of sub-grid hydrological processes within the ISBA land surface model. Five off-line simulations are performed over the French Rhône river basin, including various sets of parameterizations related to the sub-grid variability of topography, precipitation, maximum infiltration capacity and land surface properties. Parallel experiments are conducted at a high (8 km by 8 km) and low (1° by 1°) resolution, in order to test the robustness of the simulated water budget. Additional simulations are performed using the whole package of sub-grid parameterizations plus an exponential profile with depth of saturated hydraulic conductivity, in order to investigate the interaction between the vertical soil physics and the horizontal heterogeneities. All simulations are validated against a dense network of gauging measurements, after the simulated runoff is converted into discharge using the MODCOU river routing model. Generally speaking, the new version of ISBA, with both the sub-grid hydrology and the modified hydraulic conductivity, shows a better simulation of river discharge, as well as a weaker sensitivity to model resolution. The positive impact of each individual sub-grid parameterization on the simulated discharges is more obvious at the low resolution, whereas the high-resolution simulations are more sensitive to the exponential profile with depth of saturated hydraulic conductivity.     

Towards closing the vertical water balance in Canadian atmospheric models: Coupling of the land surface scheme class with the distributed hydrological model watflood

Abstract

Second generation land surface schemes are the subject of much development activity among atmospheric modellers. This work is aimed at, among other things, improving the representation of the soil water balance in order to simulate, more properly, exchanges with the atmosphere and to permit the use of model output to generate streamflow for model validation. The Canadian development program is centred on CLASS, the Canadian Land Surface Scheme, developed at Environment Canada. This paper focuses on the improvement of hydrology in CLASS. This was accomplished by designing a two‐way interface to WATFLOOD, a distributed hydrologic model developed at the University of Waterloo. The two models share many features, which facilitated the coupling procedure.

The interface retains the three‐layer vertical moisture budget representation in CLASS but adds three horizontal runoff possibilities. Runoff from the surface water follows Manning's equation for overland flow. Interflow is generated from the near‐surface soil layer using a parametrization of Richard's equation and base flow is produced by Darcian flow from the bottom of layer 3. An approximation of the internal topography of grid elements is used to supply horizontal gradients for the runoff components.

Tests are in progress in four Canadian study areas. Initial results are presented for the summer of 1993 for the Saugeen River in southwestern Ontario. The new scheme produces realistic hydrographs, whereas the old scheme did not. Bare ground evaporation is reduced by about 17% as a consequence of reduced water availability in layer 1. Evapotranspiration is not affected because the rooting depth extends into layer 3, in which soil moisture does not change appreciably with the new scheme. These results suggest that the new scheme improves the representation of streamflow in WATFLOOD/CLASS and of the soil moisture budget in CLASS. Work is in progress to validate this result over basins, such as the BOREAS study watersheds, where both runoff and evapotranspiration measurements are available.     

陆面过程模型中垂直非均匀土壤的水分传输及相变的模拟

土壤湿度在陆气相互作用中的重要性体现在它既能影响陆地和大气之间水循环的速率, 又能改变地表的能量分配。本文针对陆面过程模型中描述土壤湿度变化的方程进行了理论分析, 指出在非均匀土壤和冻土中采用土壤水势梯度描述垂直非均匀土壤水分流动的合理性。基于描述土壤内部水热传输的统一土壤模型, 并利用推广的表征土壤水分特征的Clapp-Hornberger关系式, 研究了非冻结和冻结的土壤湿度对于垂直非均匀土壤的敏感性。结果表明, 由土壤质地决定的土壤水势和导水率对土壤湿度的模拟有重要的影响。具体地, 在决定土壤性质的Clapp-Hornberger关系式中, 与土壤质地有关的饱和水势、饱和导水率以及土壤孔隙大小分布指数B, 对土壤湿度的模拟起到了关键作用。参数B的重要性尤为突出, 它的增加会引起导水率的大大下降, 从而对水分在土壤中的垂直分布产生重要影响。饱和水势的绝对值和参数B的增加会使得土壤水势绝对值增加明显, 使土壤的结冰(融化)过程延迟, 土壤温度因为没有结冰(融化)释放(吸收)的潜热加热(冷却)而持续下降(上升), 因此在冻融时期土壤温度会比观测值振幅偏大。上述结果揭示了考虑土壤垂直非均匀性并采用有效的土壤特性参数对于陆面过程模型的重要性。     

Study Of `Soft' Night-Time Surface-Layer Decoupling Over Forest Canopies In A Land-Surface Model

The cause of a night-time land-surface model cold bias over forest canopies at threedifferent sites is studied in connection with various formulations of turbulent transferand the phenomenon of decoupling between the surface and the boundary layer. Themodel is the Canadian Land Surface Scheme (CLASS), a leading internationally knownmodel that has been tested over a variety of instrumented sites. The bias was first attributed to a deficient turbulent transfer and a few formulations were compared. One formulation is the classical log-linear profile with a sharp cut-off of the fluxes at a critical Richardsonnumber around 0.2, while in the other ones the flux decreases less rapidly with increasingstatic stability. While the surface-layer formulations have an impact on the modelled canopy temperature, other causes were found for the negative bias. The CLASS model neglected the heat capacity of the air trapped inside the canopy and its inclusion multiplied theeffective heat capacity of the canopy, by a factor ranging from 2.3 to 3.4 for the canopies studied, and reduced the error. A correction was also made to the air specific humidity at canopy level and the topsoil thermal conductivity was changed from that of organic matter to that of mineral soil. With these modifications, and using the incoming longwave radiative flux instead of the net longwave flux, the bias almost completely disappeared. Using ascheme with more heat transfer at large static stability, obtained by assuming that thefluxes decrease in magnitude with height in the surface layer, reduced the original biaswhile using the log-linear formulation amplified the cold bias. The impact of the turbulent transfer formulations is much reduced when they are applied to model runs in which the other above modifications have been made.The phenomenon of decoupling is presented and its understanding is complementedwith the new notions of `hard' versus `soft' decoupling and complete versus incompletedecoupling, depending on the impact decoupling has on the model and on the effectiveness of the model in achieving the decoupling. The geostrophic wind speed is a determiningfactor in separating cases of hard decoupling (rare) from the soft cases (frequent) while the completeness of the decoupling primarily depends on the form of the turbulent transfer curve as a function of static stability.     

陆面过程模式CLASS径流模拟的改进和应用

针对陆面过程模式CLASS(Canadian Land Surface Scheme)产流模拟方面的不足,提出考虑壤中流产流机制的产流模拟方案。利用淮河流域能量和水分循环试验(HUBEX)资料,在史灌河流域对改进前后的模型进行了对比试验。结果表明,产流模拟改进方案大大提高了CLASS的径流模拟能力,同时改善了模式对土壤含水量的模拟。     

Simulating the role of gravel in freeze–thaw process on the Qinghai–Tibet Plateau

Soils containing gravel (particle size ≥2 mm) are widely distributed over the Qinghai–Tibet Plateau (QTP). Soil mixed with gravel has different thermal and hydrological properties compared with fine soil (particle size <2 mm) and thus has marked impacts on soil water and heat transfer. However, the most commonly used land models do not consider the effects of gravel. This paper reports the development of a new scheme that simulates the thermal and hydrological processes in soil containing gravel and its application in the QTP. The new scheme was implemented in version 4 of the Community Land Model, and experiments were conducted for two typical sites in the QTP. The results showed that (1) soil with gravel tends to reduce the water holding capacity and enhance the hydraulic conductivity and drainage; (2) the thermal conductivity increases with soil gravel content, and the response of the temperature of soil mixed with gravel to air temperature change is rapid; (3) the new scheme performs well in simulating the soil temperature and moisture—the mean biases of soil moisture between the simulation and observation reduced by 25–48 %, and the mean biases of soil temperature reduced by 9–25 %. Therefore, this scheme can successfully simulate the thermal and hydrological processes in soil with different levels of gravel content and is potentially applicable in land surface models.

     

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.     

A regional climate model simulation over West Africa: parameterization tests and analysis of land-surface fields

The West African Monsoon has been simulated with the regional climate model PROMES, coupled to the land-surface model ORCHIDEE and nested in ECMWF analysis, within AMMA-EU project. Three different runs are presented to address the influence of changes in two parameterizations (moist convection and radiation) on the simulated West African Monsoon. Another aim of the study is to get an insight into the relationship of simulated precipitation and 2-m temperature with land-surface fluxes. To this effect, data from the AMMA land-surface model intercomparison project (ALMIP) have been used. In ALMIP, offline simulations have been made using the same land-surface model than in the coupled simulation presented here, which makes ALMIP data particularly relevant for the present study, as it enables us to analyse the simulated soil and land-surface fields. The simulation of the monsoon depends clearly on the two analysed parameterizations. The inclusion of shallow convection parametrization affects the intensity of the simulated monsoon precipitation and modifies some dynamical aspects of the monsoon. The use of a fractional cloud-cover parameterization and a more complex radiation scheme is important for better reproducing the amplitude of the latitudinal displacement of the precipitation band. This is associated to an improved simulation of the surface temperature field and the easterly jets. However, the parameterization changes do not affect the timing of the main rainy and break periods of the monsoon. A better representation of downward solar radiation is associated with a smaller bias in the surface heat fluxes. The comparison with ALMIP land-surface and soil fields shows that precipitation and temperature biases in the regional climate model simulation are associated to certain biases in land-surface fluxes. The biases in soil moisture seem to be driven by atmospheric biases as they are strongly affected by the parameterization changes in atmospheric processes.     

WRF单柱模式中单参数方法对热带对流模拟能力的影响

利用耦合Milbrandt 2-mon(MY)双参数微物理方案的WRF中的单柱模式,对TWP-ICE试验(Tropical Warm Pool International Cloud Experiment)期间的个例进行数值模拟和敏感性试验。通过与观测资料和云分辨率模式的模拟结果进行对比发现:MY方案默认的双参数版本和单参数版本均能够再现TWP-ICE期间的热带云系的总体宏观和微观特征。MY方案的双参数版本模拟的降水率的演变特征同观测十分吻合,冰相粒子的微观特征同观测事实较为一致。单参数默认版本的降水率、液态云的构成及冰相粒子微观特征方面同观测事实存在明显差距。然而实际业务应用中单参数方案由于计算量较小应用更为广泛,但模拟效果有待改善。为了使方案保持计算量较为合理的同时具有较好的模拟效果,参考双参数控制试验中的冰相物质的微观特征,尝试对单参数方案中冰相粒子的单参数方法进行改进。冰晶单参数改进试验中虽然对于冰晶数浓度采用两种不同的处理方法,但模拟效果均未明显改善。其中冰云总含量更加接近观测,且冰云构成发生显著变化,主要归因于冰晶有效半径的减小间接削弱了雪和霰的发展。云滴含量的异常增强导致液态水含量比观测偏高约一个量级,暖云异常增厚则与上升运动的增强直接相关。雨水含量明显增强及雨滴有效半径减小综合导致了降水率仅有微弱改善。雪的单参数改进试验中,雪的截距值增加及环境场过饱和条件改善促进了冰云的发展。通过适当调整雪的截距的经验诊断公式,雪的截距、液态水含量以及降水率均得到较好的改善;而指定雪截距为常数的处理方式使液态云更为偏厚,降水率演变细节同观测仍然差异显著。改进试验结果表明,单参数方案中采用适当的经验公式诊断雪的截距的处理方法对改善单参数方案的模拟能力具有一定的可行性。     

Soil moisture prediction over the Australian continent

Summary This paper describes an attempt to model soil moisture over the Australian continent with an integrated system of dynamic models and a Geographic Information System (GIS) data base. A land surface scheme with improved treatment of soil hydrological processes is described. The non-linear relationships between soil hydraulic conductivity, matric potential and soil moisture are derived from the Broadbridge and White soil model. For a single location, the prediction of the scheme is in good agreement with the measurements of the Hydrological and Atmospheric Pilot Experiment (HAPEX). High resolution atmospheric and geographic data are used in soil moisture prediction over the Australian continent. The importance of reliable land surface parameters is emphasized and details are given for deriving the parameters from a GIS. Predicted soil moisture patterns over the Australian continent in summer, with a 50 km spatial resolution, are found to be closely related to the distribution of soil types, apart from isolated areas and times under the influence of precipitation. This is consistent with the notion that the Australian continent in summer is generally under water stress. In contrast, predicted soil temperatures are more closely related to radiation patterns and changes in atmospheric circulation. The simulation can provide details of soil moisture evolution both in space and time, that are very useful for studies of land use sustainability, such as plant growth modelling and soil erosion prediction.With 12 Figures     

Effect of surface layer thickness on simultaneous transport of heat and water in a bare soil and its implications for land surface schemes

Abstract

A physically‐based multi‐layer numerical model is developed to determine the coupled transport of heat and water in the soil and in the soil‐atmosphere boundary layer. Using inputs of standard weather data and initial soil conditions the model is capable of predicting the surface energy balance components as well as water content and temperature profiles in the soil. It is used to predict these variables for a bare silt loam soil under two tillage treatments, viz. culti‐packed and left loose after disc‐harrowing, and the predicted results are compared with measurements. Very good agreement between the model predictions and measured evaporation and heat fluxes and soil water and temperatures for a ten‐day period shows that the model is capable of simulating the coupled transport of soil heat and soil water and their transfer across the soil surface‐atmosphere interface adequately.

Model predictions were compared with those of CLASS (Canadian Land Surface Scheme). It is shown that CLASS, version 2.6, provides good estimates of evaporation and hence the latent heat flux density, Q_E, under wetter soil conditions, but overestimates Q_E at moderately wet soil conditions and underestimates it under dry soil conditions. Under dry to moderately wet soil conditions the calculation of evaporation from bare soil is very sensitive to the thickness of the top layer particularly as the thickness approaches 10 cm.     

MRI模式对华南春雨气候态及年际变率的模拟：不同模式分辨率的比较

本文利用日本气象研究所（MRI）参加第五次国际耦合模式比较计划（CMIP5）的大气环流模式在高、中、低三种分辨率下的AMIP试验结果,评估了其对华南春雨气候态和年际变率的模拟能力,比较了不同分辨率的模拟结果。结果表明,三种不同水平分辨率（120 km、60 km和20 km）的模式均能再现北半球春季位于中国东南部的降水中心。相较于120 km模式,20 km模式能够更为合理地模拟出华南春雨位于南岭—武夷山脉的降水中心。水汽收支分析表明,60 km、20 km模式高估了水汽辐合,使得华南春雨的降水强度被高估。在年际变率方面,在三种分辨率下,模式均能较好地再现观测中El Ni?o衰减年春季的西北太平洋反气旋以及华南春雨降水正异常。较之120 km模式,60 km、20 km模式模拟的降水正异常的空间分布和强度更接近观测,原因是后者模拟的El Ni?o衰减年春季华南地区的水平水汽平流异常更接近观测。本研究表明,发展高分辨率气候模式是提高华南春雨的气候态和年际变率模拟水平的有效途径之一。     

Evaluation of the hydrological components added to an atmospheric land-surface scheme

Summary Discharge from a small grassland catchment in Ireland is simulated with the atmospheric land-surface scheme SEWAB. Hydrological processes are parameterized to represent surface runoff and baseflow generation and soil moisture storage changes. Surface ponding and infiltration are explicitly described in order to account for the rapid response of streamflow to precipitation events. The annual discharge, the evapotranspiration and individual flood flows are accurately modelled. The simulation of soil moisture at various depths is close to the observations from time domain reflectometer measurements. An analysis of the significance of individual hydrological processes for discharge simulation from the small catchment found the ponding process to be essential for time periods of less than 12 hours. A depth dependent saturation hydraulic conductivity improves the simulations on all time scales. Received October 25, 2000/Revised February 16, 2001     

Trends in water demand and water availability for power plants—scenario analyses for the German capital Berlin

The availability of electric power is an important prerequisite for the development or maintenance of high living standards. Global change, including socio-economic change and climate change, is a challenge for those who have to deal with the long-term management of thermoelectric power plants. Power plants have lifetimes of several decades. Their water demand changes with climate parameters in the short and medium term. In the long term, the water demand will change as old units are retired and new generating units are built. The present paper analyses the effects of global change and options for adapting to water shortages for power plants in the German capital Berlin in the short and long term. The interconnection between power plants, i.e. water demand, and water resources management, i.e. water availability, is described. Using different models, scenarios of socio-economic and climate change are analysed. One finding is that by changing the cooling system of power plants from a once-through system to a closed-circuit cooling system the vulnerability of power plants can be reduced considerably. Such modified cooling systems also are much more robust with respect to the effects of climate change and declining streamflows due to human activities in the basin under study. Notwithstanding the possible adaptations analysed for power plants in Berlin, increased economic costs are expected due to declining streamflows and higher water temperatures.