Subsurface Conduction Research Articles

Semi-implicit Solver for the Heat Equation with Stefan–Boltzmann Law Boundary Condition

The surface energy balance on an atmosphereless body consists of solar irradiance, subsurface heat conduction, and thermal radiation to space by the Stefan–Boltzmann law. Here we extend the semi-implicit Crank–Nicolson method to this specific nonlinear boundary condition and validate its accuracy. A rapid change in incoming solar flux can cause a numerical instability, and several approaches to dampen this instability are analyzed. A predictor based on the Volterra integral equation formulation for the heat equation is also derived and can be used to improve accuracy and stability. The publicly available implementation provides a fast and robust thermophysical model that has been applied to lunar, Martian, and asteroidal surfaces, on occasion to millions of surface facets or parameter combinations.

Subsurface heat conduction along the CHINARE traverse route, East Antarctica

AbstractUsing data from three automatic weather stations (LGB69, Eagle and Dome A) from distinctly different climatological zones along the CHINARE (Chinese National Antarctic Research Expedition) traverse route from Zhongshan Station to Dome A, we investigated the characteristics of meteorological conditions and subsurface heat conduction. Spatial analysis indicated decreasing trends in air temperature, relative humidity and wind speed from the coastal katabatic wind zone to the inland plateau region, and air temperatures clearly showed a strong daily variability in winter, suggesting the effect from the fluctuation in the Antarctic atmospheric system. We also analyzed the optimal response time of the 1 and 3 m depth snow temperatures to the 0.1 m depth snow temperature for each site under clear/overcast and day/night situations. This showed an important enhancement to the heat transfer from shortwave radiation penetration. Using an iterative optimization method, we estimated the subsurface heat conduction variations along the transect. This was ~3–5 W m–2. Multiple maxima in daily mean subsurface fluxes were found in winter, with a typical value above 2 W m–2, while a single minimum value under –2 W m–2was found in summer. On an annual scale, a larger mean loss of subsurface heat conduction was observed in the inland plateau compared to in the coastal katabatic area. Finally, we discussed the possible influences of turbulent and radiant transport on the vertical heat response and confirmed the wind enhancement on the growth of thermal conductivity. This preliminary study provides a brief perspective and an important reference for studying subsurface heat conduction in inland areas of Antarctica.

On the importance of subsurface heat flux for estimating the mass balance of alpine glaciers

Glaciers, as massive freshwater reservoirs, support the planet's living systems and have an impact on our daily lives, even for communities living far away. Ongoing and future climate change is predicted to have strong impacts on the mass balance of alpine glacier around the world. To understand the relationship between climate and glacier dynamics, a range of mass balance models are currently used. Most of these models however, ignore subsurface heat fluxes as a component of glacier mass balance. Here, we set out to investigate the importance of subsurface heat flux for the mass balance of an alpine glacier using a surface energy mass balance model (SEM) coupled with a multilayer subsurface heat conduction model (MSHCM) that resolves the subsurface glacier temperature. As a case study, we investigate the Urumqi Glacier No.1 in the Tianshan Mountains (NW China), which has a long and continuous time series of surface and subsurface glacier temperature measurements. We evaluate the results of both glacier temperature models (SEM and MSHCM) using these in situ observations and investigate the sensitivity of mass balance to five meteorological factors: air temperature, precipitation, incoming shortwave radiation, relative humidity, and wind speed. The mass balance of the glacier was simulated first by including the influence of subsurface heat flux, and second, the subsurface heat flux was neglected. Observed and simulated mass balance and the englacial temperature were found to be reasonably close in both cases. Furthermore, the mass balance was simulated with a zero surface temperature assumption, which resulted in a 6% overestimation of the summer ablation. We concluded that the mass balance of Urumqi Glacier No.1 was most sensitive to variations in temperature, followed by precipitation. Furthermore, our results show that subsurface heat flux in the ablation area can generally be neglected in estimating the mass balance of alpine glaciers during ablation season.

PROFIL VERTIKAL HANTARAN PANAS BAWAH PERMUKAAN MANIFESTASI PANAS BUMI DI BAGIAN BARAT GUNUNG TAMPUSU

Indonesia is an area that has enormous geothermal potential. In North Sulawesi itself, there are three geothermal locations, including Lahendong, which is the first geothermal field in Eastern Indonesia to produce electricity, then other locations, namely in Tompaso and Kotamobagu. Strategically, Tampusu Mount is located between Tondano Lake and Linow Lake where the two lakes are the largest types of manifestation in North Sulawesi. This manifestation occurs due to the conduction of heat transfer from subsurface rock to surface rock. This study aims to analyze the distribution of temperature at shallow depths to predict the vertical profile of the thermal conductivity of geothermal manifestations in the western part of Tampusu Mount. By using surfur 11 software, it was found that the subsurface temperature distribution at shallow depths was dominated by high temperatures ranging from 30ºC - 43ºC. The lowest temperature ranges from 20ºC - 23ºC and the vertical profile of subsurface heat conduction in the western part of Tampusu Mount is not evenly distributed in each soil layer, because the temperature data obtained varies.

Application of an improved surface energy balance model to two large valley glaciers in the St. Elias Mountains, Yukon

AbstractGlacier surficial melt rates are commonly modelled using surface energy balance (SEB) models, with outputs applied to extend point-based mass-balance measurements to regional scales, assess water resource availability, examine supraglacial hydrology and to investigate the relationship between surface melt and ice dynamics. We present an improved SEB model that addresses the primary limitations of existing models by: (1) deriving high-resolution (30 m) surface albedo from Landsat 8 imagery, (2) calculating shadows cast onto the glacier surface by high-relief topography to model incident shortwave radiation, (3) developing an algorithm to map debris sufficiently thick to insulate the glacier surface and (4) presenting a formulation of the SEB model coupled to a subsurface heat conduction model. We drive the model with 6 years of in situ meteorological data from Kaskawulsh Glacier and Nàłùdäy (Lowell) Glacier in the St. Elias Mountains, Yukon, Canada, and validate outputs against in situ measurements. Modelled seasonal melt agrees with observations within 9% across a range of elevations on both glaciers in years with high-quality in situ observations. We recommend applying the model to investigate the impacts of surface melt for individual glaciers when sufficient input data are available.

Mars: Quantitative Evaluation of Crocus Melting behind Boulders

Abstract The possibility of liquid water on present-day Mars has been debated for half a century. Melting is physically difficult under Martian environmental conditions, because with the total pressure of the atmosphere near the triple point pressure of water, evaporative cooling of ice is high near the melting point. Here, a suite of quantitative models is used to investigate whether melting of seasonal water frost can occur on present-day Mars. An updated and generalized parameterization is derived for the turbulent convective heat flux that results from the buoyancy of water vapor. A three-dimensional surface energy balance model is used to calculate surface temperatures; it includes terrain shadowing, self heating, and subsurface conduction. Protruding topography creates locations that experience a rapid transition from conditions where water frost accumulates to high solar energy input. Beyond the pole-facing side of a boulder, CO2 and frost can accumulate seasonally, and once the Sun reemerges and the CO2 frost disappears, the water frost is heated to near melting temperature within one or two sols. Dust contained in the CO2 frost facilitates the formation of a protective sublimation lag. Temperatures within about 10 K of the melting point are reached within one or two sols after the end of water frost accumulation. For expected sublimation lag thicknesses, evaporative cooling is not significantly reduced. Overall, melting of pure water ice is not expected under present-day Mars conditions. However, at temperatures that are readily reached, seasonal water frost can melt on a salt-rich substrate. Hence, crocus melting behind boulders can lead to the formation of brines under present-day Mars conditions.

Large-eddy simulation of the impact of urban trees on momentum and heat fluxes

Trees in urban environment have a profound impact on the microclimate and environmental sustainability. Realistically representing them in urban models is an ongoing area of research in urban environmental study. In this paper, we develop a novel large-eddy simulation (LES) model (LES-UrbanTree) that resolves the buildings and parameterizes urban trees by accounting for their aerodynamic impact. The shading effect of trees is explicitly taken into account in LES-UrbanTree by a subsurface conduction model coupled to LES. Two-dimensional street canyons with trees in the middle of the street are used as a prototype for case studies. It is found that under moderate canyon aspect ratio (i.e. height/width being 0.5 and 1), trees taller than the mean building height leads to the strongest modification of the flow and temperature fields. Tall trees strongly impact the downward transport of high momentum (i.e. sweeping events) and therefore alter the momentum and heat fluxes most significantly through direct interaction with the strong shear layer near the roof top. Simulations of street canyons of different aspect ratios also produce physically consistent results, thus demonstrating the application potential of LES-UrbanTree. The study overall highlights the importance of representing both the aerodynamic and thermodynamic changes due to trees in urban models.

Stability of ice on the Moon with rough topography

The heat flux incident upon the surface of an airless planetary body is dominated by solar radiation during the day, and by thermal emission from topography at night. Motivated by the close relationship between this heat flux, the surface temperatures, and the stability of volatiles, we consider the effect of the slope distribution on the temperature distribution and hence prevalence of cold-traps, where volatiles may accumulate over geologic time. We develop a thermophysical model accounting for insolation, reflected and emitted radiation, and subsurface conduction, and use it to examine several idealized representations of rough topography. We show how subsurface conduction alters the temperature distribution of bowl-shaped craters compared to predictions given by past analytic models. We model the dependence of cold-traps on crater geometry and quantify the effect that while deeper depressions cast more persistent shadows, they are often too warm to trap water ice due to the smaller sky fraction and increased reflected and reemitted radiation from the walls. In order to calculate the temperature distribution outside craters, we consider rough random surfaces with a Gaussian slope distribution. Using their derived temperatures and additional volatile stability models, we estimate the potential area fraction of stable water ice on Earth’s Moon. For example, surfaces with slope RMS ∼15° (corresponding to length-scales ∼10 m on the lunar surface) located near the poles are found to have a ∼10% exposed cold-trap area fraction. In the subsurface, the diffusion barrier created by the overlaying regolith increases this area fraction to ∼40%. Additionally, some buried water ice is shown to remain stable even beneath temporarily illuminated slopes, making it more readily accessible to future lunar excavation missions. Finally, due to the exponential dependence of stability of ice on temperature, we are able to constrain the maximum thickness of the unstable layer to a few decimeters.

Geometric MCMC for infinite-dimensional inverse problems

Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank–Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.

Analytical simulation of groundwater flow and land surface effects on thermal plumes of borehole heat exchangers

Abstract Download : Download high-res image (76KB) Download : Download full-size image A new analytical model is presented for simulation of ground thermal effects from vertical borehole heat exchangers (BHEs). It represents an extension of the moving line source equation and efficiently describes the coupled transient effects from geothermal energy extraction, subsurface heat conduction, horizontal groundwater flow and spatially variable land use. It is successfully verified by comparison with an equivalent numerical model and validated by application to a field case with detailed long-term temperature monitoring. Non-dimensional sensitivity analysis reveals the coupled influence of advection and conduction for different assumptions of the land surface. Especially accelerated heat flux from asphalt or buildings at the land surface is shown to have a remarkable impact on the thermal conditions in the ground. Together with the flow velocity of the groundwater, it determines the intensity, form and steady-state of the thermal anomaly induced from BHE operation.

On the mystery of the perennial carbon dioxide cap at the south pole of Mars

A perennial ice cap has long been observed near the south pole of Mars. The surface of this cap is predominantly composed of carbon dioxide ice. The retention of a CO2 ice cap results from the surface energy balance of the latent heat, solar radiation, surface emission, subsurface conduction, and atmospheric sensible heat. While models conventionally treat surface CO2 ice using constant ice albedos and emissivities, such an approach fails to predict the existence of a perennial cap. Here we explore the role of the insolation‐dependent ice albedo, which agrees well with Viking, Mars Global Surveyor, and Mars Express albedo observations. Using a simple parameterization within a general circulation model, in which the albedo of CO2 ice responds linearly to the incident solar insolation, we are able to predict the existence of a perennial CO2 cap at the observed latitude and only in the southern hemisphere. Further experiments with different total CO2 inventories, planetary obliquities, and surface boundary conditions suggest that the location of the residual cap may exchange hemispheres favoring the pole with the highest peak insolation.

Transient thermal effects in Alpine permafrost

Abstract. In high mountain areas, permafrost is important because it influences the occurrence of natural hazards, because it has to be considered in construction practices, and because it is sensitive to climate change. The assessment of its distribution and evolution is challenging because of highly variable conditions at and below the surface, steep topography and varying climatic conditions. This paper presents a systematic investigation of effects of topography and climate variability that are important for subsurface temperatures in Alpine bedrock permafrost. We studied the effects of both, past and projected future ground surface temperature variations on the basis of numerical experimentation with simplified mountain topography in order to demonstrate the principal effects. The modeling approach applied combines a distributed surface energy balance model and a three-dimensional subsurface heat conduction scheme. Results show that the past climate variations that essentially influence present-day permafrost temperatures at depth of the idealized mountains are the last glacial period and the major fluctuations in the past millennium. Transient effects from projected future warming, however, are likely larger than those from past climate conditions because larger temperature changes at the surface occur in shorter time periods. We further demonstrate the accelerating influence of multi-lateral warming in steep and complex topography for a temperature signal entering the subsurface as compared to the situation in flat areas. The effects of varying and uncertain material properties (i.e., thermal properties, porosity, and freezing characteristics) on the subsurface temperature field were examined in sensitivity studies. A considerable influence of latent heat due to water in low-porosity bedrock was only shown for simulations over time periods of decades to centuries. At the end, the model was applied to the topographic setting of the Matterhorn (Switzerland). Results from idealized geometries are compared to this first example of real topography, and possibilities as well as limitations of the model application are discussed.

On the role of subsurface heat conduction in glacier energy-balance modelling

AbstractWe discuss the inclusion of the subsurface heat-conduction flux into the calculation of the energy balance and ablation at the glacier–atmosphere interface. Data from automatic weather stations are used to force an energy-balance model at several locations on alpine glaciers and at one site in the dry Andes of central Chile. The heat-conduction flux is computed using a two-layer scheme, assuming that 36% of the net shortwave radiation is absorbed by the surface layer and that the rest penetrates into the snowpack. We compare simulations conducted with and without subsurface heat flux. Results show that assuming a surface temperature of zero degrees leads to a larger overestimation of melt at the sites in the accumulation area (10.4–13.3%) than in the ablation area (0.5–2.8%), due to lower air temperatures and the presence of snow. The difference between simulations with and without heat conduction is also high at the beginning and end of the ablation season (up to 29% for the first 15 days of the season), when air temperatures are lower and snow covers the glacier surface, while they are of little importance during periods of sustained melt at all the locations investigated.

Reconciling different observations of the CO2 ice mass loading of the Martian north polar cap

The GRS measurements of the peak mass loading of the north polar CO2 ice cap on Mars are about 60% lower than those calculated from MGS TES radiation data and those inferred from the MOLA cap thicknesses. However, the GRS data provide the most accurate measurement of the mass loading. We show that the TES and MOLA data can be reconciled with the GRS data if (1) subsurface heat conduction and atmospheric heat transport are included in the TES mass budget calculations, and (2) the density of the polar deposits is ∼600 kg m−3. The latter is much less than that expected for slab ice (∼1600 kg m−3) and suggests that processes unique to the north polar region are responsible for the low cap density.

Recent gullies on Mars and the source of liquid water

Geologic features resembling terrestrial water‐carved gullies imply that liquid water has flowed recently on the surface of Mars and challenge our views of the present‐day low‐temperature environment. We evaluate two possible mechanisms for the formation of liquid water under environmental conditions that we expect to have existed on Mars in its recent past. First, we examine the stability of ground ice in the permafrost and the potential for melting near‐surface ground ice (in the top few meters of soil) by solar heating and subsurface conduction. Second, we examine the potential for melting and refreezing of ice at shallow depths due to geothermal heating. We find that near‐surface ground ice does not reach the melting point of water under a range of conditions of soil thermophysical properties, latitudes, obliquities, and surface slopes. The atmosphere remains too dry for the ground ice to melt, even at high obliquity; instead, ice sublimates before reaching melting temperatures. However, the presence of salts in concentrations of 15–40% can adequately lower the melting point to allow melting to occur. We also find that a combination of a global average geothermal heat flux and a thick, low‐conductivity, unconsolidated regolith raises the depth of the melting isotherm to less than a few hundred meters from the surface. Orbitally induced oscillations in the mean annual surface temperature can cause freezing cycles in a confined aquifer at this depth. Freezing pressures generated are adequate to fracture ice‐cemented ground and allow water to escape to the surface, similar to the formation and evolution of terrestrial pingos in shallow permafrost. Both mechanisms are possible; however, the geothermal mechanism is consistent with the observations of the distribution of gullies, while the salty near‐surface ground ice mechanism is not. Further observational tests that can be performed with existing and future spacecraft are suggested.

Pluto's Non-isothermal Surface

We report on repeated far-infrared photometric observations of the Pluto–Charon system conducted in 1997 with the Infrared Space Observatory (ISO). These observations have led to the first detection of the system at 150 and 200 μm and to the first clear detection of its thermal lightcurve at 60 μm (and more marginally at 100 μm). They definitely prove that Pluto's surface is not isothermal. The thermal lightcurve is, as expected, roughly anticorrelated with the visible lightcurve, but not exactly. The data are fit by physical models including Charon and three separate units on Pluto, respectively dominated by (1) N 2-ice (2) CH 4-ice, and (3) tholins. These models are constructed in accordance with information from visible imaging and lightcurves, visible spectroscopy and infrared spectroscopy, and considerations on the thermal balance of N 2 and CH 4, and they include a thermophysical description of subsurface conduction and infrared beaming. Charon's contribution, which cannot be separated from Pluto's in the observations, is assumed to be independent of longitude and equivalent to that of a ∼52 K body. The main implications are that Pluto's surface in units 2 and 3 has a thermal inertia Γ=(1.5–10)×10 4 erg cm −2 s −1/2 K −1, comparable to that of other icy satellites, and relatively high bolometric emissivities (not lower than 0.5 and most likely 0.8–1). Diurnal temperature variations must be significant, with maximum dayside temperatures in the range 54–63 K. The value of thermal inertia may be indicative of porosity in the top centimeters of Pluto's surface. The observations further confirm that the far-IR brightness temperatures, though somewhat smaller than indicated by IRAS, are higher than in the millimeter/submillimeter range. Extending the models to longer wavelengths suggests that a low radio emissivity, as opposed to a mixing of temperatures or a subsurface sounding effect, is the correct explanation. Finally, in spite of large error bars, the 150-μm fluxes indicated by ISO seem unexpectedly high given the spectral properties of ices in the far-IR. These, and the expected lightcurves of the Pluto–Charon system at λ=15–60 μm should be priority measurements for SIRTF.

Simulations of the general circulation of the Martian Atmosphere: 2. Seasonal pressure variations

We have simulated the CO2 seasonal cycle of the Martian atmosphere and surface with a hybrid energy balance model that incorporates dynamical and radiation information from a large number of general circulation model (GCM) runs. This information includes heating due to atmospheric heat advection, the seasonally varying ratio of the surface pressure at the two Viking landing sites to the globally averaged pressure (rk), the rate of CO2 condensation in the atmosphere, and solar heating of the atmosphere and surface. The GCM runs collectively covered a full set of seasonal dates and a large range of dust optical depths. We have compared the predictions of the energy balance model with the seasonal pressure variations measured at the two Viking landing (VL)sites and the springtime retreat of the seasonal polar cap boundaries. Numerical experiments with the energy balance model indicate that the following quantities have a strong influence on the VL seasonal pressures: albedo Ais of the seasonal CO2 ice deposits, emissivity eis of this deposit, atmospheric heat advection, and the pressure ratio rk. This last factor does not enter into the seasonal CO2 condensation/sublimation cycle in a significant way. The numerical experiments also indicate that the following factors have only a minor effect on the VL pressures: (1) the net radiative effects (solar plus thermal) of atmospheric dust at the latitudes of the polar caps, and (2) the subsurface heat conduction. The significant influence of the pressure ratio rk on the VL seasonal pressures is due to large seasonal variations in the global distribution of surface pressure. At low and mid‐latitudes, these “weather” variations are engendered by seasonal changes in the Hadley circulation and by seasonal changes in the atmospheric scale height close to the surface. Comparison of the VL1 and VL2 pressures with one another provide direct evidence for the presence of such a “weather component” in the measured pressures. The differential weather component (VL2‐VL1) derived from the data is reproduced approximately by the energy balance model. We find that the seasonal weather variations account for about 20% and 30% of the seasonal pressure variations measured at VL1 and VL2, respectively, that dynamical and scale height variations make comparable contributions to the weather component during years without global dust storms, and that the dynamical contribution is the larger one during years with global dust storms. Interannual variations in the weather component, rather than variations in CO2 condensation rates, are the dominant sources of the observed interannual variations of pressure during the season of global dust storms. Optimum fits to the Viking pressure measurements and the data on the polar cap boundaries are achieved with values of about 0.45 and 0.75 for Ais and eis, respectively. The former value is consistent with available photometric determinations of the albedo of the seasonal caps, while the latter value, especially in light of infrared thermal mapper brightness temperatures at high latitudes, may reflect, in part, the influence of the polar hood on the radiation balance of the winter polar regions.

A thermal model for the seasonal nitrogen cycle on Triton

A Mars thermal model has been adapted to study the seasonal nitrogen cycle on Triton. Unlike other models published to date, it incorporates diurnal and seasonal subsurface heat conduction, and accounts for the heat capacity of N 2 frost deposits. Key observables that this model attempts to reproduce include Triton's atmospheric pressure and surface albedo features at the time of the Voyager encounter, as well as changes in Triton's disk-integrated spectral properties between 1977 and 1989. Subsurface heat conduction is found to have an important effect on the behavior of Triton's polar caps and atmospheric pressure fluctuations. The results of this model differ from those of previous studies in that they generally do not predict the catastrophic freeze-out of Triton's atmosphere on a seasonal basis. The model results indicate that even for a wide range of possible input parameters, it is unlikely that Triton's bright southern polar cap is a seasonal nitrogen deposit, because it would have largely sublimated before the Voyager encounter. However, these results do not rule out the possibility of a large bright permanent polar cap in Triton's southern hemisphere. The best agreement between the model results and the available observations is obtained when Triton's seasonal nitrogen frost deposits are assumed to be darker than the undelying substrate. Assuming a constant nitrogen frost albedo of 0.62, a frost emissivity of 0.5, a substrate albedo of 0.8, and a substrate thermal inertia of 7 × 10 −3 cal cm −2 K −1 sec −1 2 yields good agreement with the surface pressure and global albedo patterns observed during the Voyager encounter, as well as a rapid change in disk-integrated albedo from 1977 to 1989 due to the retreat and disappearance of a dark south seasonal polar cap. These results lend support to microphysical arguments for the presence of dark, or smooth, translucent nitrogen frost on the surface of Triton.

The influence of thermal inertia on temperatures and frost stability on Triton

Seasonal subsurface heat conduction can have a large influence on Triton's N 2 frost distribution. Increasing surface thermal inertia reduces the thickness and extent of seasonal N 2 frosts. If the thermal inertia of the nonvolatile substrate is greater than about 30% of the value for nonporous H 2O or CO 2, or if nonporous H 2O or CO 2 is overlaid by a porous regolith of low thermal inertia but less than a few meters thick, the northernmost latitudes visible to Voyager should have been frost-free at the time of the encounter, possibly accounting for their relatively low albedo. If the substrate in the northern hemisphere has sufficiently low albedo and/or emissivity and also has a thermal inertia comparable to that of nonporous H 2O or CO 2, there may be no seasonal or permanent N 2 deposits in the northern hemisphere at all. Because this model, like previous ones, predicts a monotonic recession of permanent N 2 deposits toward the poles and very limited seasonal N 2 frost in the southern hemisphere at Voyager time, and because of new spectroscopic evidence for nonvolatile CO 2 on Triton's bright southern hemisphere, we consider it possible that much of the bright material on Triton's southern hemisphere is not N 2. Bright nonvolatiles in the southern hemisphere may allow seasonal N 2 frosts to form there during the southern summer, possibly helping to explain Triton's spectroscopic changes during the past decade. All the models considered here predict 10-fold or greater seasonal variations in atmospheric pressure, with pressure currently increasing in high-thermal-inertia models and decreasing in models with low thermal inertia.

Subgrid Scale Physics in 1-Month Forecasts. Part I: Experiment with Four Parameterization Packages

Four packages of subgrid scale (SGS) physics parameterization are tested by including them in a general circulation model and by applying the four models to 1-month forecasts. The four models are formulated by accumulatively increasing the elaboration and the sophistication of the physics. The first is the reference model (the A-physics); the second model (the E-physics) uses the Monin–Obukhov similarity theory for the fluxes of surface boundary layer, the turbulence closure scheme for the fluxes in the entire atmosphere, and subsurface soil heat conduction; the third model (the F-physics) replaces the cumulus parameterization by the Arakawa–Schubert method; and the fourth model (the FM-physics) enhances the SGS orography. One-month integrations are performed for eight January cases, with each case consisting of three different forecasts. Originally the forecast performance was expected to be a stepwise improvement with the elaboration of the SGS physics from the A to the FM, but the forecast results do not show up in such a simple way. The impact of these processes on the 1-month integration is subtle and yet significant. The superiority of the F-model over the A- and the E-models is evident in the last 10 days of the 1-month forecasts, though the performance of the E-model is consistently good, in comparison with the other models, in terms of root-mean-square (rms) error of geopotential height. It is likely that 80% condensation criterion in the E (instead of 100%) is at least partly responsible for the forecast deterioration in the last 10 days, compared with the F. The FM-model gives the lowest rms error, but the predicted transient eddies are extremely low, probably due to the excessively enhanced orography. The simulated global precipitation patterns are presented for the different models, and the drawbacks are discussed. The F- and the FM-models produce spatially smooth distribution of tropical rainfall. The 30-day forecast performance appears to be more sensitive to the initial conditions, rather than the SGS physics. The systematic errors in all of the models are substantial in magnitude, though they vary with the SGS physics.