One-dimensional Energy Balance Model Research Articles

Permafrost evolution in the Swiss Alps in a changing climate and the role of the snow cover

The snow cover plays a decisive role on Alpine permafrost distribution with respect to its insulating properties and strong short-wave reflectivity. The complex interaction processes between atmosphere, snow cover and permafrost complicate direct predictions of the effect of changing climate parameters on ground temperatures and permafrost distribution with respect to snow cover thickness and snow period variations. In this study, the soil-extended version of the one-dimensional mass and energy balance model SNOWPACK was applied to study the ground thermal influence of realistic climate change scenarios of changing mean annual air temperatures, and summer and winter precipitation. The increasing air temperatures of two climate scenarios combined with the effect of earlier snow disappearance in spring cause warmer ground temperatures throughout the whole soil profile and steadily increasing active layer depth. From the resulting mean annual ground surface temperature changes under these climate scenarios, the lower limit of permafrost occurrence in the Swiss Alpine region is estimated to be raised between 170 m and 580 m over a period of 80 years. The presented simulation results provide an estimation of the magnitudes of climate change impact on permafrost distribution, including the complex interaction processes between atmosphere, snow cover and permafrost.

Simulations of Snow, Ice, and Near-Surface Atmospheric Processes on Ice Station Weddell

The 4-month drift of Ice Station Weddell (ISW) produced over 2000 h of nearly continuous measurements in the atmospheric surface layer and in the snow and sea ice in the western Weddell Sea. This paper reports simulations, based on these data, of processes in the air, snow, and sea ice at ISW using SNTHERM, a onedimensional mass and energy balance model. An earlier version of SNTHERM had to be adapted, however, to treat the flooding that often occurs on sea ice in the western Weddell Sea. To treat this layer of slush and brine, SNTHERM holds the brine salinity constant at its initial value of 31.5 psu until 80% of this slush layer freezes. The current version of SNTHERM also incorporates a new parameterization for the roughness length for wind speed, z 0, derived from analyses of ISW eddy-covariance data. SNTHERM’s simulations are validated with temperature measurements within the ice and snow and with eddy-covariance measurements of the surface momentum and sensible and latent heat fluxes. The simulated turbulent fluxes agree fairly well with the measured fluxes, except the simulated sensible heat flux is biased low by 4‐5 W m 22 for both stable and unstable stratification. The simulated temperature profiles in the snow and ice also agree well with the measured temperatures. In particular, allowing seawater to flush the slush layer until it is 80% frozen delays the freezing of this layer such that its behavior mirrors the data.

Earth-like worlds on eccentric orbits: excursions beyond the habitable zone

Many of the recently discovered extrasolar giant planets move around their stars on highly eccentric orbits, and some with e [ges ] 0·7. Systems with planets within or near the habitable zone (HZ) will possibly harbour life on terrestrial-type moons if the seasonal temperature extremes resulting from the large orbital eccentricities of the planets are not too severe. Here we use a three-dimensional general-circulation climate model and a one-dimensional energy-balance model to examine the climates of either bound or isolated earths on extremely elliptical orbits near the HZ. While such worlds are susceptible to large variations in surface temperature, long-term climate stability depends primarily on the average stellar flux received over an entire orbit, not the length of the time spent within the HZ.

One-dimensional snow water and energy balance model for vegetated surfaces

We developed and evaluated a three-layer snow model for application in general circulation models. This one-dimensional snow model has many features of the detailed physically based model SNTHERM, yet is computationally much simpler. We have also extended the point model to vegetated areas using the parameterization concepts of the Biosphere-Atmosphere Transfer Scheme (BATS). Results of model applications for two types of vegetated fields—a short grassland in the French Alps and an old aspen forest in the southern study area of BOREAS—were presented. The results, on one hand, indicate the suitability of the model structure and parameter setting; on the other hand, the results explore the limitation of using ‘point’ field observations to evaluate an area model. Copyright © 1999 John Wiley & Sons, Ltd.

On the parameterisation of oceanic sensible heat loss to the atmosphere and to ice in an ice-covered mixed layer in winter

In high-latitude oceans with seasonal ice cover, the ice and the low-salinity mixed layer form an interacting barrier for the heat flux from the ocean to the atmosphere. The presence of a less dense surface layer allows ice to form, and the ice cover reduces the heat loss to the atmosphere. The ice formation weakens the stability at the base of the mixed layer, leading to stronger entrainment and larger heat flux from below. This heat transport retards, and perhaps stops, the growth of the ice cover. As much heat is then entrained from below as is lost to the atmosphere. This heat loss further reduces the stability, and unless a net ice melt occurs, the mixed layer convects. Two possibilities exist: (1) A net ice melt, sufficient to retain the stability, will always occur and convection will not take place until all ice is removed. The deep convection will then be thermal, deepening the mixed layer. (2) The ice remains until the stability at the base of the mixed layer disappears. The mixed layer then convects, through haline convection, into the deep ocean. Warm water rises towards the surface and the ice starts to melt, and a new mixed layer is reformed. The present work discusses the interactions between ice cover and entrainment during winter, when heat loss to the atmosphere is present. One crucial hypothesis is introduced: “When ice is present and the ocean loses sensible heat to the atmosphere and to ice melt, the buoyancy input at the sea surface due to ice melt is at a minimum”. Using a one-dimensional energy-balance model, applied to the artificial situation, where ice melts directly on warmer water, it is found that this corresponds to a constant fraction of the heat loss going to ice melt. It is postulated that this partitioning holds for the ice cover and the mixed layer in the high-latitude ocean. When a constant fraction of heat goes to ice melt, at least one deep convection event occurs, before the ice cover can be removed by heat entrained from below. After one or several convection events the ice normally disappears and a deep-reaching thermal convection is established. Conditions appropriate for the Weddell Sea and the Greenland Sea are examined and compared with field observations. With realistic initial conditions no convection occurs in the warm regime of the Weddell Sea. A balance between entrained heat and atmospheric heat loss is established and the ice cover remains throughout the winter. At Maud Rise convection may occur, but late in winter and normally no polynya can form before the summer ice melt. In the central Greenland Sea the mixed layer generally convects early in winter and the ice is removed by melting from below as early as February or March. This is in agreement with existing observations.

A spatial analysis of snow-surface energy exchanges over the northern Great Plains of the United States in relation to synoptic scale forcing mechanisms

The northern Great Plains of the US is a region that experiences extensive winter snow covers. Meltwater provided by this snow is an important source of freshwater for agriculture, domestic uses and hydroelectric power. The geographic location of the region, however, makes it subject to a variety of meteorological influences that can induce rapid ablation episodes and flooding. A study of the synoptic scale weather patterns that induce large snowmelt events can provide a useful insight into the processes that contribute to ablation. The first objective of this study is to identify distinct regional circulation patterns that are associated with snow depth changes of greater than 2.54 cm (1 in.). Detailed case studies representing each synoptic type are then examined and used to illustrate the spatial relationships between synoptically induced meteorological variations and snow–surface energy fluxes. A one-dimensional mass and energy balance model is used to compute the surface energy fluxes and snow depth changes. The use of modeled fluxes in lieu of measured values allows for a more spatially extensive analysis as surface fluxes over the entire study region can be analyzed in conjunction with the prevailing synoptic scale weather patterns. Three synoptic patterns are associated with large midwinter snowmelt episodes in the northern Great Plains. All three patterns involve a midlatitude cyclone moving through the region and the advection of warm air into the region. The case studies reveal that subtle differences in the location and the strength of the cyclones lead to variations in cloud cover, wind speed, temperature and humidity among the different synoptic types. These differences when combined with variations in surface cover can greatly affect the magnitude and spatial distribution of radiative and turbulent energy exchanges. Copyright © 1999 Royal Meteorological Society

Periodic Solutions in Low-Dimensional Climatic Models

Classic climatic models use constitutive laws without any response time. A more realistic approach to the natural processes governing climate dynamics must introduce response time for heat and radiation fluxes. Extended irreversible thermodynamics (EIT) is a good thermodynamical framework for introducing nonclassical constitutive laws. In the present study EIT has been used to analyze a Budyko‐Sellers one-dimensional energybalance model developed by G. R. North. The results present self-sustained periodic oscillations when the response time is greater than a critical value. The high-frequency (few kiloyears) damped and nondamped oscillations obtained can be related to abrupt climatic changes without any variation in the external forcing of the system.

Rainfall Interception by Sacramento's Urban Forest

A one-dimensional mass and energy balance model was developed to simulate rainfall interception in Sacramento County, California. The model describes tree interception processes: gross precipitation, leaf drip, stem flow, and evaporation. Kriging was used to extend existing meteorological point data over the region. Regional land use/ land cover and tree canopy cover were parameterized with data obtained by remote sensing and ground sampling. Annual interception was 1.1% for the entire county and 11.1% of precipitation falling on the urban forest canopy. Summer interception at the urban forest canopy level was 36% for an urban forest stand dominated by large, broadleaf evergreens and conifers (leaf area index = 6.1) and 18% for a stand dominated by medium-sized conifers and broadleaf deciduous trees (leaf area index = 3.7). For 5 precipitation events with return frequencies ranging from 2 to 200 years, interception was greatest for small storms and least for large storms. Because small storms are responsible for most pollutant washout, urban forests are likely to produce greater benefits through water quality protection than through flood control.

The Laptev Sea flaw lead—detailed investigation on ice formation and export during 1991/1992 winter season

The main objective of this research paper is to estimate the new-ice production in the Laptev Sea flaw lead during the 1991/1992 winter season. A one-dimensional energy balance model was applied to calculate ocean-to-atmosphere heat flux and the resulting new-ice formation over open water. For a detailed estimate of regional ice production, the flaw lead was divided into 14 sections based on the analysis of NOAA-satellite images and Russian ice charts. Opening and maintenance of the lead sections are controlled by offshore winds, whereas closing of open water is caused by onshore winds. Since the orientation of the lead varies from section to section, the same regional wind forcing can cause different local lead behavior. Model results reveal that the seasonally accumulated thickness of new ice formed in the different lead sections—under the assumption of instantaneous lateral new-ice removal from the water surface—varies from 1.3 m to 13 m over temporarily open water and may reach 20 m over permanently open water. The corresponding ice volume produced in the sections varies between 3.4 km 3 and 59 km 3 and amounts to 258 km 3 for the entire lead. The significant regional variations in new-ice production are due to differences in (i) the number of days that a lead section is open (open-lead days), (ii) the oceanic heat loss during open-lead days, and (iii) the areal extent of the lead sections. As compared to other studies,—at least during 1991/1992 winter season—the Laptev Sea flaw lead produced between 28 and 617% more initial sea ice than the Kara, Barents, East Siberian and Chukchi leads. Despite its limited areal extent of roughly 36,000 km 2, which represents only 8% of the entire Laptev Sea, the flaw lead produces about 32% of the annual shelf ice. The ice production in the flaw lead is 5.3 times higher than the remainder of the shelf (7.4 m vs. 1.4 m). Furthermore, the Laptev Sea flaw lead produces 2.6% of the ice annually formed the entire Arctic Mediterranean Sea and contributes about 9% to the volume of the Siberian branch of the Transpolar Drift Ice System. This makes the Laptev Sea flaw lead a significant producer of Arctic sea ice on local and regional scales, whereas the contribution of lead ice to the entire volume of annually formed pack in high northern latitudes amounts only to roughly 1.3%.

Modeling of Solid Particle Flow and Heat Transfer in Rotary Kiln Calciners

Contaminated solid wastes exist in many industrial sites, gas plants, and oil refineries. One method of decontaminating the soil is to subject it to high temperatures in a rotary calciner in an anaerobic environment. Preliminary results from a computational model are presented in this paper for the flow and heat transfer from granular solid particles under treatment in a rotary kiln calciner. A fluidization model using kinetic theory of granular flow has been employed to solve the particle flow and heat transfer problem. While a two-dimensional model is used to predict the rotation induced flow of the solid particles, a pseudo three-dimensional model for heat transfer is developed where the axial bulk temperature gradient is obtained from a one-dimensional energy balance model. The model predictions indicate interesting features of the flow and temperature fields in the bed material. Future tasks include the development of a devolatilization model to study the decontamination of waste soil in the rotary calciner.

Modeling of Millimeter Wave Backscatter of Time-Varying Snowcover — Summary

The temporal variation of millimeter wave backscatter signature of snowcover is studied based on a dense medium radiative transfer (DMRT) theory and a one-dimensional mass and energy balance model of snow named SNTHERM. The multilayer DMRT scattering model of snowcover developed in this work takes into account the reflection and refraction at the snow-snow interfaces. Appropriate boundary conditions, quadrature points and weights are selected for using the discrete-ordinate eigenanalysis method to solve the multilayer DMRT equations. It shows that the inclusion of reflection and refraction at the snow-snow interfaces may affect the model prediction. Cohesive spherical particles are applied to account for the clustering feature of snow grains. To model the time-varying behavior of snowcover, SNTHERM is employed to simulate the aging process of snow. SNTHERM provides pertinent snow parameters, such as grain size, density, liquid water content, and stratification with a high resolution in time and depth. These snow properties are then used in modeling the temporal radar signatures of snowcover. The comparisons of temporal model responses with time series polarimetric backscatter data at 35 and 95 GHz are presented. Good agreement is demonstrated between model and measurements in both timing and magnitude. The results indicated that the coupled DMRT and SNTHERM model can be useful in studying the electromagnetic interactions with time-varying snow microstructure.

The small ice cap instability in seasonal energy balance models

Results from a two-dimensional energy balance model with a realistic land-ocean distribution show that the small ice cap instability exists in the Southern Hemisphere, but not in the Northern Hemisphere. A series of experiments with a one-dimensional energy balance model with idealized geography are used to study the roles of the seasonal cycle and the land-ocean distribution. The results indicate that the seasonal cycle and land-ocean distribution can influence the strength of the albedo feedback, which is responsible for the small ice cap instability, through two factors: the temperature gradient and the amplitude of the seasonal cycle. The land-ocean distribution in the Southern Hemisphere favors the small ice cap instability, while the land-ocean distribution in the Northern Hemisphere does not. Because of the longitudinal variations of land-ocean distribution in the Northern Hemisphere, the behavior of ice lines in the Northern Hemisphere cannot be simulated and explained by the model with zonally symmetric land-ocean distribution. Model results suggest that the small ice cap instability may be a possible mechanism for the formation of the Antarctic icesheet. The model results cast doubt, however, on the role of the small ice cap instability in Northern Hemisphere glaciations.

A numerical simulation of supraglacial heat advection and its influence on ice melt

AbstractEnergy exchange between the atmosphere and a melting glacier surface is mediated by the presence of a water layer. Under conditions of rapid melt and/or heavy rainfall, the possibility exists that a supraglacial run-off layer can advect sensible heat and influence the spatial variations of melt. The potential magnitude of such advection was investigated by numerically solving differential equations expressing the mass and energy balances of a two-dimensional run-off layer. Solutions were obtained for conditions typical of rainfall events, in which the potential for supraglacial heat advection should be maximal. The solutions indicate that advection cannot influence macro-scale melt patterns and surface morphology, except perhaps under heavy rainfall and/or rapid melt conditions, but can possibly cause micro-scale variations in ice melt. One-dimensional energy-balance models, which have normally been applied over glacier surfaces, should remain valid for most conditions.

A numerical simulation of supraglacial heat advection and its influence on ice melt

AbstractEnergy exchange between the atmosphere and a melting glacier surface is mediated by the presence of a water layer. Under conditions of rapid melt and/or heavy rainfall, the possibility exists that a supraglacial run-off layer can advect sensible heat and influence the spatial variations of melt. The potential magnitude of such advection was investigated by numerically solving differential equations expressing the mass and energy balances of a two-dimensional run-off layer. Solutions were obtained for conditions typical of rainfall events, in which the potential for supraglacial heat advection should be maximal. The solutions indicate that advection cannot influence macro-scale melt patterns and surface morphology, except perhaps under heavy rainfall and/or rapid melt conditions, but can possibly cause micro-scale variations in ice melt. One-dimensional energy-balance models, which have normally been applied over glacier surfaces, should remain valid for most conditions.

Tests of three urban energy balance models

Observations of surface characteristics, meteorological conditions and energy balance components from Vancouver, B.C. are used to test the validity of the output from three one-dimensional surface energy balance models. The results show that whereas all of the models provide good simulations of net radiation, none can consistently predict the turbulent fluxes of sensible and latent heat using easily available input data. Inability to handle the role of water availability and its impact on evapotranspiration is identified as the principal problem.

A simplified model for dioxin and furan formation in municipal-waste incinerators

We have used the temperature-time profile derived from a one-dimensional energy-balance model, in conjunction with the kinetic estimates of Shaub and Tsang, to estimate the production of dioxins from chlorinated precursors in the gas phase and on fly ash. In agreement with earlier studies, we find that dioxin production on particulates is much larger than gas-phase formation. The scaling relation for dioxin production on fly ash shows that the adsorbed concentration in ng/g is proportional to the square of the gas-phase precursor concentration and inversely proportional to the particulate radius. Calculated dioxin outputs for flue-gas-fly-ash mixtures and for bottom ash fall in the general range observed for some of the available municipal-waste incinerator data. We suggest modifications needed in the model parameters to obtain agreement with the best of the newer incinerators. Work by Vogg et al on dioxin production, after maintenance of fly ash with adsorbed precursors for 2 h at relatively low temperatures, is accounted for quantitatively with the Shaub-Tsang model by introducing minor changes in the kinetic parameters. This slow, low-temperature conversion to dioxin may occur in low-temperature furnace sections, the baghouse or the electrostatic precipitator and may contribute to the dioxin concentration in bottom ash.

Comparing Zero- and One-Dimensional Climate Models

Abstract Zero-dimensional energy balance climate models that have appeared in the literature do not exhibit the same physical behavior as one-dimensional energy balance models. Although numerical values of such predicted quantities as the globally averaged surface temperature and its sensitivity to a solar constant change can be made nearly the same in the two model types, the physical mechanisms leading, for example, to the white earth solution when the solar constant is decreased below some critical lower limit are different. It is possible to formulate a global albedo for use in certain zero-dimensional models such that results obtained from zero- and one-dimensional models are both physically. and mathematically identical.

Effect of Ice-Albedo Feedback on Global Sensitivity in a One-Dimensional Radiative-Convective Climate Model

Abstract The feedback between ice albedo and temperature is included in a one-dimensional radiative-convective climate model. The effect of this feedback on global sensitivity to changes in solar constant is studied for the current climate conditions. This ice-albedo feedback amplifies global sensitivity by 26 and 39%, respectively, for assumptions of fixed cloud altitude and fixed cloud temperature. The global sensitivity is not affected significantly if the latitudinal variations of mean solar zenith angle and cloud cover are included in the global model. The differences in global sensitivity between one-dimensional radiative-convective models and energy balance models are examined. It is shown that the models are in close agreement when the same feedback mechanisms are included. The one-dimensional radiative-convective model with ice-albedo feedback included is used to compute the equilibrium ice line as a function of solar constant. It is found that the fixed cloud temperature parameterization breaks ...

Structural and stochastic analysis of a zero-dimensional climate system

An ‘almost trivial’ climate system of geometrical dimension zero is analysed, the complexity of which has been reduced to a minimum. It can be simply described as the globally averaged energy flux balance between infrared emission and solar heat input, expanded by a linear albedo-temperature feedback. This nonlinear and time-dependent climate model is formulated as a gradient system of a potential and can be analysed without explicit time integration. It includes many of the results which are also exhibited by one-dimensional energy balance models. Two equilibrium solutions appear. The stable one is characterized by the interglacial, whereas the unstable equilibrium defines a lower bound for temperature (state variable) changes which the system can absorb. Beyond a threshold of an external parameter combination (fold catastrophe) no equilibria exist so that the system attains a ‘deep freeze’ climate situation. A −2 power law describes the linear response of the (internally stable) system to weather fluctuations.