Austin Long
Department of Geosciences and Hydrology and Water Resources
University of Arizona
Tucson, AZ 85721-0077

J. R. Sturgul
Department of Mining and Metallurgical Engineering
University of Idaho
Moscow, ID 83843

A primary consideration in a long-term risk assessment of a geological repository for radioactive waste is the likelihood that contaminants will migrate into the inhabited environment. Selection or rejection of a repository may hinge on its long-term penetrability by infiltrating water, which has the potential of corroding the storage containers and carrying radioactive materials into surrounding areas. Yucca Mountain, in Southern Nevada, USA, is the only site still under consideration for long-term storage of spent nuclear fuel rods from U.S. reactors. An assessment of the long-term environmental risk of storing radioactive waste in Yucca Mountain must account for soil type, geomorphology and rock structure, and all reasonably likely geological and climatological processes related to movement of water and contaminants into the environment.

This study addresses the question of future precipitation and temperature at Yucca Mountain over the next one million years. The framework for climate change during the next million years is based on patterns of past climates and on how industrial activity may affect climate. Present and future precipitation is simulated with models. As net infiltration, particularly in arid and semi-arid zones, depends on rainfall event patterns as well as annual amounts; the models produce daily rain events in 30-day simulations. Any number of months (100, 1000, or more) of simulated precipitation, representing different seasons and climate conditions, can be quickly produced, then rerun to check the stability of the output. The "modern" rainfall model simulates the instrument-based daily record for current conditions at Yucca Mountain for winter-type and summer-type precipitation. Similar models simulate probable future conditions for "greenhouse" conditions, and for varying degrees of wetter "pluvial" conditions likely to occur during the next million years. Several possible future climatic scenarios are presented, and their relative probabilities are estimated based on available evidence.

Of the many elements in the chain of processes involved in modeling the potential for introducing harmful materials into the environment near Yucca Mountain, the first is net infiltration of precipitation. Infiltration is complex in itself, involving present and future amounts of precipitation, characteristics of the topography, surface and subsurface features of the soil and rocks, vegetation cover, and present and future evapotranspiration. The portion of water that evapotranspires depends on temperature, humidity, seasonal and temporal distribution of precipitation, plant cover and wind velocities as well as the physical characteristics controlling infiltration and runoff.

Here we address some of these variables controlling net infiltration: present and future temperature and present and future seasonal and temporal variations of precipitation at Yucca Mountain and vicinity. Both temperature and precipitation will change in the future, as they have in the past. Future climate variations will have both natural and anthropogenic driving forces. Anthropogenic greenhouse gases, primarily CO₂ and CH₄, will continue to increase for a few centuries and are likely to influence climate for the next 25,000 years. Natural variability will eventually resume dominance of the climate, resulting in repeated patterns of glacial and interglacial cycles.

Inferences for future precipitation and temperatures for Yucca Mountain are based on present conditions, documented recurrence of past conditions, and future effects of greenhouse gases inferred from general circulation models (GCM's). This study incorporates available climate information in the form of daily rainfall and temperature records and summaries in the case of current climate conditions, and seasonal summaries in the case of past climate conditions. It also utilizes greenhouse climate simulations by GCM's for near-future greenhouse conditions, and climate inferences from the geological record for probable future more intense greenhouse conditions. In the extended future, past conditions are assumed to follow a pattern established during the Quaternary geological period (approximately the past 3 million years), and recorded in flora and fauna.

Pre-historical climate inferences are typically in the form of average temperature and precipitation differences compared to present conditions. In some cases seasonal climate data are estimated. GCM simulations of future climates are available as seasonal or monthly summaries, usually in the form of differences from current climates. These differences are most relevant to the present case because this is a site-specific study, and the spatial resolution of the current generation of GCM's limits their ability to model exact temperatures and precipitation amounts for specified local conditions.

Although seasonal averages for temperature are useful in the present study, seasonal average values for precipitation are of little value in modeling net infiltration. This is because infiltration depends strongly on the pattern of precipitation, especially in arid and semiarid climates in which the potential evaporation exceeds, sometimes greatly exceeds the precipitation. This is the case for Yucca Mountain now, where net infiltration evidently occurs only if precipitation events are extended in time, or sufficiently closely spaced to allow water to seep down deep enough to continue downward without complete evapotranspiration. Only event-based (stochastic) precipitation models are applicable to infiltration simulation under such conditions.

The present study is an extension of previous work [1,2], which considered climate and infiltration for the next 10,000 years. We now focus on precipitation and temperature changes expected at Yucca Mountain during the next million years. In addition, the present study takes advantage of recent advances in the understanding of past climates and modeling of future climates. Three notable differences between the previous work and the present one are: 1) the extended time frame, from 10,000 years to 1,000,000 years; 2) the modeled precipitation better matches actual precipitation patterns, and 3) more deterministic climate scenarios in time steps. Additional improvements over [1,2] include a new precipitation model capable of simulating different storm types, and the integration of Markov chains into the recurrence probabilities of winter-type storms. The model's time base is now in the form of days of the month. A day may or may not experience precipitation. This allows more straightforward calibration with standard reports of meteorological data, and verification with independent datasets. Model parameters are adjusted to match precipitation during the various climate modes identified for future climates expected for Yucca Mountain.

Seasonal precipitation amounts and temperatures for future climates at Yucca Mountain are estimated from existing GCM outputs in the case of near-future greenhouse conditions, from geological evidence of the Earth's response to even greater levels of CO₂ for the extended future, and for the post-greenhouse conditions at Yucca Mountain. Seasonal precipitation and temperature are inferred from paleobotanical responses to past glacial conditions. The intensity and duration of future greenhouse conditions depends strongly on future technological advances in energy production and societal responses to production technologies, energy use and control of CO₂ emissions. The most likely climatic pathway taken in the greenhouse model is the more pessimistic "business as usual" scenario in which developing countries resist emissions controls. It is also assumed likely that the greenhouse climates will affect somewhat the timing of resuming the next glacial-interglacial cycle and the degree of maximum cooling during this cycle.

The modern precipitation model was tested by comparing its output with a precipitation dataset different from the one it was calibrated against. Agreement was excellent. Not included in this model is the probability of extreme, very rare events, which may not appear in meteorological records, but are recorded in the geological record [3,4,5,6]. These will be the focus of work in progress.

Our foresight for climate at Yucca Mountain for the next million years is far from clear, and expert opinion is far from unanimous (see, for example, [7]). However, several lines of evidence reveal a pattern of past climate change with probable triggering mechanisms. These mechanisms will continue into the future, and here it is assumed that the climate system will respond to them as in the past. Thus, the approach taken here to the problem of estimating future climates at Yucca Mountain assumes that future climates will most probably be a replay of patterns during the past 3 million years, with an important interruption. This interruption will be in the form of a greenhouse climate brought on by industrial activity. The impact of the industrial greenhouse effect on natural climate is problematic, but the relative probabilities of different scenarios can be estimated. The difficulties lie in interpreting the geological and paleobotanical records in terms of climate, evaluating past patterns and the uncertainties involved in applying past climate data to the future.

Geologic, paleobotanical and isotopic records reveal both global and local variability in past climates. The major climate changes during the Pleistocene affected Yucca Mountain vicinity. With present understanding of driving forces and mechanisms, past patterns of change can be extrapolated into the future with a high level of certainty. Even anthropogenic global climatic driving forces have analogs in the past which we assume to be relevant to future climates.

The present global climates are a moderate, relatively warm interlude in the context of the entire geological record. The Earth has been much cooler and much warmer than in the present and historical times. This present-day so-called "post glacial" period existed on Earth during perhaps only 10% of the past million years. Even during the past 10,000 years of post glacial climates the Earth has undergone extended times of somewhat cooler and somewhat warmer climates. (See Figure 1, after ref. [8]).

Records of past climates are written in the flora, fauna, and in stable isotopes in geological deposits. Past climates are also registered in ocean sediments, polar ice sheets, glacial and alluvial deposits, lake sediments, bogs, ancient shorelines and tree rings. Short-term climate changes, both on global and local levels, show elements of both deterministic and chaotic behavior. For example, the causes of seasonal climate changes are well understood, but, why an unusually wet winter may be followed by an unusually dry one is less well understood. Similarly, climate changes that occur on a longer time scale have components of both deterministic and chaotic behavior. Convincing evidence supports an astronomically-driven hypothesis for glacial-interglacial recurrences on a 10,000 to 3,000,000-year time frame. Periodicities appear at 100,000 year, 43,000 year, 24,000 year and 19,000 year time intervals, corresponding to periodicities of the Earth's orbit eccentricity, precession and tilt with respect to the orbital plane [9]. Thus the astronomical forcing of glacial periodicity appears to be related to periodic changes in the seasonal and latitude distribution of solar energy impinging on the Earth. Yet the 100,000-year cycles of d ¹⁸O in foraminifera are not exact images of each other, indicating that other factors as well control the Earth's long-term climate changes [10]. What triggered the initiation of these cycles some 3 million years ago, and when these cycles will terminate is controversial, though crustal plate movements, possibly the rise of the Tibetan Plateau, and changes in ocean circulation were likely involved.

Figure 2, after [11], illustrates the variations in global climate, inferred from changes in stable oxygen isotope ratios in microfaunal species over the past three million years, the approximate time span of the Pleistocene era. The more positive values correspond to times of maximum glacial extent in Europe and North America. A 500,000-year oxygen isotope sequence in groundwater-deposited calcite from Devil's Hole near Yucca Mountain [10,12] reveals a pattern similar to that found in ocean cores for the last 500,000 years.

On a longer time frame, stable isotopes of hydrogen in silicates may be interpreted as revealing past climate information for the area near Yucca Mountain. Winograd et al.[13] found that hydrogen isotope ratios (dD values in permil, l) in calcite fluid inclusions became progressively depleted in the heavy isotope from 2.5 million years toward the present. They interpreted this as due more to the progressive uplift of the Sierras, and increasing rain-shadow effect than to temperature. Their data connect with those of Arehart and O'Neil [14] who reported d D and d ¹⁸O values in supergene (produced by infiltrating water) alunites from Nevada. Their data span 29 to 5.3 million years ago, and show a 25 permil decrease in d D from 15 to 8 million years ago. These data suggest that southern Nevada climates during the mid Miocene (15 million years ago), were a few degrees C warmer than today's climates. This is consistent with Lamb's compilation of temperature inferences in Northern Europe for the past 30 million years, which shows a gradual downward trend of about 10° C ([15], p. 305). Berner's CO₂ model [16] shows a corresponding downward trend over the same time period. Figure 3, after [17] summarizes general trends of global temperatures over the past 100 million years, the present, and the likely future.

Atmospheric CO₂ levels have evidently affected the Earth's temperatures in the geological past. Intense volcanic activity associated with tectonic processes in the geological past has increased levels of atmospheric CO₂ and produced warm global temperatures. A geological example with high levels of CO₂ possible in the next few hundred years occurred during the Cretaceous 150 to 60 million years ago. During this time atmospheric CO₂ levels may have exceeded 6 times the present level, and the temperatures rose on average 8EC higher than today's. These atmospheric CO₂ levels and temperatures are from Berner's models [16]. Cerling [18], based on isotopic data from paleosoils, independently arrived at a comparable or even higher CO₂ level (up to 10 times the 300 ppmv level during the Cretaceous. Yapp and Poths [19] inferred similar high levels of atmospheric CO₂.

The temperature and precipitation we estimate for the future at Yucca Mountain and vicinity assume that future climates will be greenhouse conditions superimposed on continued natural glacial/interglacial (pluvial/interpluvial) climate modes. The specific site estimates, in terms of degrees Celsius and % differences in precipitation are based on paleobotanical evidence and general circulation models (GCM's). It is important to realize that climate is very location specific. It depends not just on latitude, storm tracks and elevation, but on nearby topography and bodies of water. Paleobotanical climatic inferences must therefore be based on local studies, and should take into account landscape differences. GCM's do not yet have sufficient spatial resolution to produce satisfactory results in mountainous terrain. Meteorologically, Yucca Mountain lies in the rain shadow of the Sierra-Nevada mountain range. Consequently, inferences from the geological past must consider that the Sierras have been rising during the past few million years. Correspondingly, estimates of future climate must consider possible future landscape changes. Future tectonic uplift of the Sierras, based on the consensus opinion of geophysicists at the University of Arizona, is likely to continue to be slow, possibly compensated by erosion, with little net change in altitude during the next few hundred thousand years.

Paleobotanical remains are also valuable records of past climates. Wolf [20] summarized plant distributions during the Tertiary—the approximately 65 million years prior to the Pleistocene— and inferred climates. Spaulding [21] compared plant species now growing in mountain ranges in southern Nevada near Yucca Mountain with fossil plants that grew 18,000 years ago at similar elevations. We assume here that temperature and precipitation differences between climate conditions are not significantly altitude dependent, and that the same D t between full glacial and post glacial in nearby mountain ranges applies to Yucca Mountain.

The seasonal climate differences for full glacial conditions Spaulding [21] reported are, with respect to present-day climates:

Note that these conditions apply to maximum glacio-pluvial climate conditions. Stable isotope trends in ice-cores and marine microfauna indicate that the Earth spent only a fraction of the Glacial Era in the full glacial mode (see figure 3). Accordingly, the future climate values suggested in the present study are scaled proportionally with the stable isotope values to infer climates in a time sequence.

Only for brief intervals in the future are climates at Yucca Mountain likely to be the same as they have been during the instrumentally recorded past. The future will be a continuation of the pluvial (glacial) and interpluvial (interglacial) pattern interrupted during the immediate future by an industrially induced greenhouse episode. The challenge lies in predicting to what extent the industrial gases will affect the present climate and the timing of the resumption of the pluvial conditions.

Our estimates of the greenhouse effects are based on GCM outputs; estimates of pluvial conditions are based on geological and paleobotanical evidence in the area; interpluvial conditions are assumed to resemble the past 100 years of climate in the Yucca Mountain vicinity.

General circulation climate models attempt to simulate present and future climate. These models operate on the same principles as weather-forecasting models. They incorporate the physics of solar heating of the atmosphere, continents and oceans, the exchange of heat and water between oceans and atmosphere, the circulation of water and air masses, and heat and water mass exchange between the atmosphere and continents. In these models seasons change, and water evaporates and precipitates. Topography and air and water circulation attempt to simulate the operation of the Earth's climate and weather systems, driven as naturally as possible by solar energy, gravity and Earth's rotation.

In principle, these models could simulate the climate system as an artificial alternate Earth. In practice, the available computing power (they presently run on workstations and super computers) limits spatial resolution, and some important details of atmospheric dynamics. Also, an inherent characteristic of air circulation precludes a deterministic prediction of weather: seemingly minor perturbations can result in major changes in the overall system behavior. Atmospheric chaos requires the circulation system to make a series of probabilistic decisions in a time-space progression. This is why weather forecasts in many temperate zones (where chaotic processes are common) are often valid for only a few days into the future. Thus the argument that if we cannot predict the weather more than a few days in advance, how can we use similar models to predict climate decades or centuries ahead?

Although the day-to-day behavior of the weather in temperate zones is not responsive to long-range forecasts, the general trends of seasonal changes are predictable. It is still not possible to predict with certainty that next winter will be unusually cold or wet, but probabilities can be stated based on past experience. In the case of very long-range predictions, as are attempted here, long-term climatic trends of the past and GCM outputs are called upon to estimate future climates and climate changes. The predictions are in terms of general trends, not specific forecasts.

The GCM experiment outputs available in the literature, and utilized in this study, have modeled the climate perturbations induced by increased atmospheric CO₂ contents and by the return of glacial/pluvial climate conditions [22]. The results of GCM runs for future climate, like weather forecasts, must be taken with an understanding that though they are the best now available, they are far from perfect, and not in complete agreement among various models. For example, of the four GCM outputs examined for the present study (as summarized in [23]), all showed wide differences in their conclusions on the temperature and precipitation effects greenhouse warming would have on Yucca Mountain. It was concluded that for this analysis the best approach was a non-judgmental one: take the average. Another deficiency with the GCM's is their near universal overestimation of precipitation [23,24]. Evidently, this follows from the fact that the models produce precipitation as soon as humidity reaches 100%. In reality, clouds are clusters of suspended droplets, or potential rain. Therefore, our analysis uses only differences in GCM-produced precipitation between present and modeled conditions, as did Hostetler and Giorgi [24] and Wigley [25].

Virtually all GCM's that estimate climate conditions influenced by enhanced atmospheric CO₂ assume a CO₂ level twice that of pre-industrial levels. The atmospheric CO₂ level may well exceed, possibly by far, the 2xCO₂ level. Carbon-cycle models predict that unless severe restrictions are soon placed on global emissions of CO₂, the atmospheric levels of CO₂ will exceed 4 times the pre-industrial level [26,27,28]. Although GCM outputs are not available at this time for higher levels, the real-Earth experiment has already been performed. Unfortunately, it was performed millions of years ago when the geography, both global and near Yucca Mountain, was different. Some geological evidence suggests that at least the temperature part of the climate response is positive with respect to CO₂ levels, and that responses are linear with respect to CO₂ levels in the atmosphere [29]. Temperatures increase, and winter precipitation increases while summer precipitation decreases with increasing CO₂ forcing. To a certain extent these principles can be applied to the study of paleoclimates. Taylor [30] gives an excellent summary of several classes of climate models as applied to past climates. Broccoli [31] discusses the application of climate models to future climates.

Crowley [17,33] convincingly argues that although the geologic past presents no exact analogs for the future greenhouse climates, at least the geologic record demonstrates that times in the past that were significantly warmer than at present corresponded to higher atmospheric CO₂ levels. This is consistent with the hypothesis that increased levels of atmospheric CO₂ trap a larger fraction of infra-red energy in the troposphere. Although the Earth was formed about 4.5x10⁹ years ago, the geologic record of a clear sequence of life forms begins with the Paleozoic, about 0.6x10⁹ years ago. During this extensive time range, liquid water existed on the Earth's surface, as did primitive life forms. It now seems likely [34] that the Earth's atmosphere contained CO₂, which maintained the Earth's surface temperature within limits throughout most of its existence, despite an increasing solar energy output with time. Atmospheric CO₂ levels reached at least 6 times pre-industrial levels as recently as during the Cretaceous Period 100 million years ago, as discussed above [16,17,18].

Crowley [17,33] and Covey et al. [29] have discussed the necessity and validity of employing geologic analogs to estimating future impacts of industrial greenhouse gases on the Earth's climates. Geological analogs are valuable to show not only that the Earth has seen much higher levels of CO₂ and survived, but also indicate the general climate changes that were associated with such high levels. The present study uses the geological analogs to extrapolate the conclusions of GCM's.

Wigley [25] placed an upper limit of CO₂ concentration at 1000 ppmv. The reason given for this was that the higher concentrations would dissolve shell materials, thus would destroy marine ecology. The basis for this statement was not clear in this reference. However, the abundance of fossil shells in the Cretaceous Period, (100 million years ago) when the atmospheric levels were "probably on the order of between 1500 and 3000 ppmv" (Cerling, [18]), and in the Cambrian Period (early Paleozoic, 550 million years ago). During this time Berner [16] suggested atmospheric CO₂ levels most likely reached 18 times present-day levels. Cerling's conclusions are based on stable isotopes in soil carbonates, whereas Berner's data are based on tectonic models. These two independent approaches agree on the Cretaceous levels. Cerling's study did not extend beyond (older than) the Cretaceous.

Because the Sun is the source of virtually all of the Earth's energy, variability of its output on a scale of decades to centuries, or even millennia would be of interest in forecasting future climates. Changes on a much longer, solar evolution time scale are theoretically likely, but probably minor for the next million years, and not considered here. In the case of long-term changes (on a scale of billions of years) in solar energy output are probably not important if on these time scales, the Earth’s global tectonic and sedimentation processes [16,34] regulate climate.

Correlation of climate with sunspot occurrences has been a tempting exercise. Kerr (35) reviewed briefly the history of correlations of climate with 11-year Sunspot cycles. He summarizes recent reports of observations of pressure increases and greater ozone production with increased solar energy output. He also notes that solar energy output was minimal during the "Little Ice Age" of the 17^th century. Most who are familiar with the field agree that solar energy differences shown in the 11-year cycles are of minor importance in affecting global climates (e.g., [36]). However, Haigh [37] noted that solar energy arrives in specific wavelengths, which can induce specific photochemical reactions, which in turn may affect the hydrological cycle, planetary waves, or atmospheric circulation. Haigh tested this with an atmospheric circulation model, and concluded that the 11-year solar cycle did produce shifts in storm tracks similar to but smaller in magnitude than those observed in nature. Crowley and Kim [38] found statistically significant positive correlations between solar irradiance changes and northern hemisphere temperature changes over the past 400 years. They suggest that solar energy output may be responsible for a significant portion of the temperature changes during the Little Ice Age (AD 1350 to 1850). A stronger energy variation of solar origin comes from solar flares [39]. Projections of the periodicities of solar-flare output indicate that solar-energy changes will enhance the greenhouse effect well into the next century. The present study did not account for this source of weather and possibly climate variability as it appears to be a second-order climate forcing function.

Karl, et al. [40] discussed recent trends in climate indicators, specifically those believed to respond to forcing by greenhouse gases. GCM's predict that in addition to increasing temperatures, a cluster of other meteorological parameters would be expected to accompany increasing greenhouse gases. These include:

• The increase in mean surface temperature would be more pronounced in the winter,
• An increase in precipitation in the winter,
• More severe and longer-lasting droughts, particularly in the warm season,
• A small, but significant increase in nighttime temperature compared with daytime temperature, particularly during the warm season,
• A greater portion of warm-season precipitation derived from heavy convective rainfall, compared with gentler, longer-lasting rainfalls,
• A decrease in the day-to-day variability of temperature.

These authors evaluated these criteria in light of recent weather records. They concluded that the chances that the meteorological trend observed in recent years is due to statistical chance alone is only 5 or 10%. That is, the chance these changes are due to greenhouse gases is 90 to 95%. Mitchell, et al. [41] reached a similar conclusion.

It is not known how far into the future that industrial gases will affect climates. Several relevant questions are simply unanswerable now. What is known is that CO₂, which warms the troposphere, has a long residence time in the atmosphere, and SO₂, which cools the troposphere, has a relatively short residence time. This means that in the more unlikely future climate pathway, a technological innovation introduces an alternate energy source, which emits no problem gases, or toxic products, and which is cheaper than fossil fuels and would be available to developing countries, and changeover is essentially instantaneous, then the cooling effect of SO₂ will rapidly decline, allowing the warming effect of CO₂ to continue uninhibited [42]. The long natural residence time of CO₂ in the atmosphere will maintain the greenhouse effect for hundreds or thousands of years. Thus, the question of the future rate and amount of industrial emissions is unanswerable. A more likely pathway is that developing societies will continue to industrialize, resist external controls on their expansion and consumption of fossil fuels, and continue to produce industrial gases until their costs and availability become prohibitive. Estimates of fossil fuel consumption for the next century range from optimistic (slight increase or decrease) to factor-of-ten increase. Resulting atmospheric CO₂ trajectories would fall between leveling off near present levels and rising to 1500 parts per million by volume (ppmv) (about 5xCO₂) within the next 100 years [25]. The ultimate impact depends on how soon and how effectively the industrial nations will take action. Schneider [43] raises the question of how certain must we be to take action. What are the consequences of waiting until we are 99% rather than only the present 90 to 95% certain?

Another unanswerable question is what impact will greenhouse warming have on natural climate cycles? If global temperatures rise well beyond levels experienced during the Pleistocene interglacials, as now seems likely, will the Greenland ice sheet and/or the West Antarctic ice sheet disappear, thus possibly interrupting the glacial/interglacial cycles? Or will the increased heat and atmospheric water vapor content create much greater high-latitude precipitation and a net accumulation of snow, producing a permanent ice age? Most probably the impact of high atmospheric CO₂ levels lies between the extremes. The greenhouse effect will most likely subdue the next scheduled glacial period, but allow eventual resumption of the natural cycle. The present study attempts to evaluate probabilities of each of these climatic scenarios.

Goodess and Palutikokof [44] presented three future climate scenarios as possible responses to increasing CO₂ and its impact on the continuation of the glacial/interglacial cycle. Although these scenarios are written for the United Kingdom, and details of temperature and precipitation apply to that region, the fundamental driving forces are global. It is possible to infer how these global processes would likely affect climate at Yucca Mountain. The present assessment accepts what Goodess and Palutikokof consider the Earth system's most likely response to excess atmospheric carbon dioxide, the intermediate one (number 2, below), and customizes it for Yucca Mountain (Table 1). The extreme Goodess and Palutikokof climate responses, (numbers 1 & 3, below) are given as less probable scenarios. Their three scenarios are:

1. The greenhouse effect will be relatively short, about 1000 years, then the climate will resume according to the climate pattern established in the past several hundred-thousand years.
2. The greenhouse effect will, for several thousand years, affect the resumption of the glacial/interglacial pattern by suppressing the next full-glacial. Subsequent glacial/interglacial cycles will be unaffected.
3. The greenhouse effect will cause the Earth's climate system to fall into an irreversible permanent greenhouse state. Pleistocene glaciations will terminate.

Other responses, here considered unlikely, include: 1) that high levels of CO₂ will increase the amount of atmospheric water vapor, whose precipitation will feed polar ice sheets faster than they can melt, thus triggering a permanent glaciation [45], and 2) the Earth will respond in an organic manner to compensate for whatever additional stresses are placed on it, a simplified statement of the Gaia hypothesis [46].

Regarding the permanent ice sheet suggestion, this cannot be disproved. The Earth has not run this exact experiment before (continents were not in the same position during the Cretaceous, when atmospheric CO₂ levels were several times present level); however, a modeling exercise [47] suggests this is unlikely to happen.

Regarding the Earth's organic response to increasing CO₂, this will happen in an inorganic sense, but it will take a long time. The Earth has evidently been self-regulating its atmospheric CO₂ level through the tectonic/volcanic (CO₂-producing) vs. CaCO₃-precipitation/sedimentation (CO₂-sequestering) cycle. The concept is that volcanogenic CO₂ warms the air, creates more precipitation, thus enhances the weathering rate of calcium, which promotes the formation of CaCO₃, which, in turn, reduces the CO₂. Enting et al. [28] summarize the results of 18 models for the response of atmospheric CO₂ to various industrial output scenarios. All the models reveal limits to the ocean's absorptive rate and short-term capacity. The Earth can control the CO₂ level, but on a much longer time-scale (millions of years) than would be useful to preserve the current conditions comfortable for humans.

The most imminent climate change, which may already be underway, is that induced by industrial activity. Simply stated, carbon dioxide, among some other trace gases in the atmosphere, have the property of being nearly transparent to incoming visible and ultraviolet solar energy, but absorb infrared energy radiated by the Earth's surface. This has the effect of warming the lower layer (troposphere) of the atmosphere. Increasing industrial output has the potential of, and may already have begun, affecting global climate in several ways. The assumption taken here is the more pessimistic "business as usual" scenario in which developing countries resist CO₂ emissions controls. Wigley et al. [48] discuss the tradeoff's required to maintain various levels of atmospheric CO₂. It is optimistic to assume that people will voluntarily reduce emissions, or that the major energy-consuming countries will impose drastic reductions at the risk of reducing their competitiveness. (See, for example, [49].) The so-called >runaway greenhouse', in which excess greenhouse warming terminates the clacial/interglacial cycles, is also a possible scenario. This may have happened on the planet Venus [50]. Goodess and Palutikof [44] consider this the least likely for the Earth’s near future. Modeling by Berger, et al., [51] suggests that the Greenland ice sheet is robust. Even if a significant portion melts under severe greenhouse conditions, it is likely to reform when CO₂ levels fall.

Event-based, or stochastic models are appropriate for input to infiltration or flood-frequency simulations because they more closely emulate natural processes than do values for average seasonal or monthly precipitation. This is especially important in cases of arid and semi-arid climates in which the potential evaporation exceeds annual precipitation. In these cases, if precipitation were evenly distributed throughout the year, season or month, little or no infiltration or flooding would occur. It is the clustering of precipitation events that enables infiltration. Thus, hypothetically, at a particular site, with a given average annual rainfall, a wide range of infiltration amounts is possible, depending on the time distribution of precipitation. For this reason, the stochastic model must, inasmuch as possible, mimic natural rainfall distributions.

Most continental temperate zones have complex meteorology. The Yucca Mountain vicinity is no exception. Hevesi, et al. [52] identified 5 distinct storm types that contribute precipitation to Yucca Mountain. Each of these types can have distinctive properties in terms of recurrence intervals, persistence characteristics, mean rainfall amount per day, and season of occurrence. Thus the model should contain a selected mixture of mathematical functions to simulate the various storm types in the appropriate seasons. A model must also be able to produce the year-to-year variability found in nature. For example, Hevesi, J. A. and Flint, A. L. (personal communication, 1996) in an analysis of 53 years of rain-gauge records at 12 stations in the Nevada Test Site area, found the total precipitation for individual years ranged from 70 to 370 mm/yr.

The previous precipitation model [2] served to illustrate the stochastic approach to precipitation/infiltration modeling at Yucca Mountain. This previous model addressed the question of climates for the next 10,000 years. Its precipitation component was limited, however, in that it assumed a simple exponential amount and distribution for all events, with spacing between events exponentially distributed as well. It did not incorporate Markov chains for modeling persistent storms. It was able to simulate the average modern rainfall, but it imperfectly simulated the distribution of different depths of events; it overestimated the midrange and small events. A further disadvantage of this model was that it did not have a straightforward daily precipitation output that could be compared with the standard daily meteorology station precipitation records.

The present model is completely new. It was constructed using GPSS/H [53], a language designed for modeling event sequences and queuing in industrial processes. The model now incorporates most features associated with precipitation events, including persistence of storms over a sequence of days (Markov chains), as well as several different functions corresponding to the different storm types in the Nevada Test Site area. The annual rainfall model is actually two separate models, one each for Winter and Summer.

The winter model is the more complex in that it contains four functions that represent four storm types. Each can be adjusted for relative probability of occurrence and for mean rainfall for all events that follow that function. The fraction of days without rain is adjustable as well. Using Markov chains, as was done here, the probability of and the amount of rainfall is a function of both the occurrence and the amount of rainfall on the previous day.

A fourth-order Markov chain in the winter model allows for the possible occurrence of a sequence of up to 4 days with rain. The summer model produces events with depths following a simple exponential function, and Poisson distributed in time, as L. Duckstein (personal communication, 1996) finds summer-type storms to follow in southern Arizona. The model's time base is day-by-day for one month at a time. This allows simple calibration with existing meteorological data, which typically are available on a daily (24-hour) basis. The model was calibrated and adjusted for Yucca Mountain elevation using the most comprehensive and lengthy (maximum record about 100 years) meteorological database available for southern Nevada [54, 55, 56].

The modern output was tested on a dataset produced by Alan Flint and Joseph Hevesi [pers. Com., 1996] from rain gauges on the Nevada Test site near Yucca Mountain. This is an independent dataset from the one used to calibrate the precipitation model. The new precipitation model was able to reproduce the depth/recurrence pattern of the Flint and Hevesi Yucca Mountain dataset.

Table 1 summarizes the most probable temperatures and seasonal precipitation amounts expected for a sequence of time frames during the next 1 million years. Twelve stochastic precipitation models were developed, corresponding to winter and summer for each of the 6 climatic scenarios. These six include modern (same as interglacial), 1/3 full glacial, 2/3 full glacial, 3/3 full glacial, 500ppm CO₂ greenhouse and 900ppm CO₂ greenhouse. Model outputs, consisting of 924 months (» 150 years) for each climate mode, were transferred to the infiltration model.

The present model of future climates at Yucca Mountain extends the time frame to 1,000,000 years. The stochastic precipitation is quite flexible, in that it can easily be modified as better information on different storm types and extreme precipitation events become available. It matches present precipitation in terms of annual averages and distribution in time of daily precipitation depths. It also matches actual precipitation in terms of summer and winter averages. The precipitation model simulates four distinct storm patterns for winter, for four assumed meteorological conditions leading to precipitation. Note that the present version has an empirical fit, rather than identifying a specific mathematical function with specific meteorological conditions. The work of Hevesi, Ambos and Flint [52] will soon enable such specific matches. The summer precipitation model is simpler than the winter model, in that it has only one function. Here, summer precipitation is assumed to behave similar to that of southern Arizona, and to be dominated by convective storms that are Poisson distributed. The precipitation model feeds directly into a net infiltration model for Yucca Mountain, then into a regional flow model to evaluate the possible transfer of radioactive material into the groundwater system [57].

All but a small minority of skeptics agree that the next global climate phase will be dominated by the greenhouse response to industrial products, primarily CO₂ and CH₄. The degree of response depends on how effective will be worldwide reduction of these products. After several centuries, natural processes will subsume these gases, and the glacial/interglacial cycles will most probably resume control of climate, as they did for the million or so years before industrial interference. It is slightly possible that the greenhouse conditions will so overwhelm the conditions that set the stage for glacial cycles, that glacial cycles will be long delayed, or will stop entirely.

Each of the future climate phases has characteristic seasonal temperatures and precipitation amounts. This study illustrates how these temperatures can be inferred, and precipitation events can be simulated in a manner that represents the most probable future conditions. These simulations are compatible with the infiltration simulation protocol of Childs and Long [58].

Future precipitation simulations are possible based on past precipitation records and best estimates of the effects of greenhouse and post-greenhouse climates. We assume future climates will continue the patterns established during the Pleistocene. The model output is in the form of daily precipitation, i.e., which days of the month it rains, and how much. Because these resemble meteorological station daily records, the simulated data are easily compared with actual records.

Daily precipitation records over an extended time period, in the present case up to 100 years, serve as a basis for an empirical match with the computer simulations. Seasonal differences in patterns of precipitation can also be matched, although only winter-type and summer-type were simulated in this study. Daily precipitation values, combined with diurnal temperature estimates enable net infiltration modeling.

This study was supported by the Electric Power Research Institute, Palo Alto, CA., and Risk Engineering, Boulder CO.

1. LONG, "A probabilistic climate and rainfall model" in Demonstration of a Risk-Based Approach to High-Level Waste Repository Evaluation. EPRI TR-100384 Interim Report, May 1992, pp. 2-1 to 2-19 (1992).
2. LONG, and S. W. CHILDS, "Rainfall and net infiltration probabilities for future climate conditions at Yucca Mountain" Proceedings of the Fourth Annual International Conference on High-Level Radioactive Waste Management, Las Vegas, Nevada, pp. 112-121 (1993).
3. V.R BAKER, "Geomorphological understanding of floods" Geomorphology, vol. 10, pp. 139-156, (1994).
4. V. KLEMES "Probability of extreme hydrometeorological events¾ a different approach" in Extreme Hydrological Events: Precipitation, Floods and Droughts (Proceedings of the Yokohama Symposium, July 1993). IAHS Publ. no. 213, (1993).
5. Y. ENZEL, L. L. ELY, P. K. HOUSE, V. R. BAKER and R. H. WEBB "Paleoflood evidence for natural upper bound to flood magnitudes to flood magnitudes in the Colorado River basin", Water Resources Research, vol. 29, pp. 2287-2297 (1993).
6. MARES, and C. MARES, C. "On extreme events in the precipitation field" in Extreme Hydrological Events: Precipitation, Floods and Droughts (Proceedings of the Yokohama Symposium, July 1993). IAHS Publ. no. 213, (1993).
7. A.R. DeWISPELARE, L. T. HERREN, M. P. MIKLAS, and R. T. CLEMEN "Expert elicitation of future climate in the Yucca Mountain vicinity" Iterative Performance Assessment Phase 2.5, Center for Nuclear Waste Regulatory Analysis, San Antonio, Texas (1993).
8. T. CROWLEY, "Remembrance of things past: greenhouse lessons from the geological record" Consequences, vol. 2, no. 1, pp. 3-11 (1996).
9. J. IMBRIE, and K. P. IMBRIE, Ice Ages: Solving the Mystery, Enslow Publishers, Hillside, N.J., 224pp (1979).
10. I.J. WINOGRAD, J. M LANDWEHR, K. R. LUDWIG, T. B. COPLEN, and A. C. RIGGS "Duration and Structure of the Last Four Interglaciations", Quaternary Research, vol. 48, pp. 141-154 (1997).
11. I.KAYANE "Interactions Between the Biospheric Aspects of the Hydrological Cycle and Land Use/Cover Change" Global Change Newsletter, no. 25, pp. 8-9 (1996).
12. I.J. WINOGRAD, T. B. COPLEN, J. M. LANDWEHR, A. C. RIGGS, K. R. LUDWIG, B. J. SZABO, P. T. KOLESAR, K. M. REVESZ "Continuous 500,000-year climate record from vein calcite in Devil's Hole, Nevada", Science, vol. 258, pp. 255-260 (1992).
13. I.J.WINOGRAD, B. J. SZABO, T. B. COPLEN, A. C. RIGGS and P. T. KOLESAR "Two-million-year record of deuterium depletion in Great Basin ground waters", Science, vol. 227, pp. 519-522 (1985).
14. G.B. AREHART and J. R. O'NEIL "D/H ratios of supergene alunite as an indication of paleoclimate in continental settings" in Climate Change in Continental Isotopic Records, Geophysical Monograph 78, American Geophysical Union, pp. 277-284 (1993).
15. H.H. LAMB, Climate: Present, Past and Future. Vol. 1, 835 pp (1997).
16. R.A. BERNER, (1991) "A Model for Atmospheric CO₂ over Phanerozoic Time" American Journal of Science, vol. 291, pp. 339-376 (1991).
17. T.J. CROWLEY, "Are There Any Satisfactory Geologic Analogs for a Future Greenhouse Warming?" Journal of Climate, vol. 3, pp. 1282-1292 (1990).
18. T.E. CERLING "Carbon Dioxide in the Atmosphere: Evidence from Cenozoic and Mesozoic Paleosols" American Journal of Science, vol. 291, pp. 377-400 (1991)
19. C.L. YAPP, and H. POTHS "Carbon Isotopes in Continental Weathering Environments and Variations in Ancient Atmospheric CO₂ Pressure", Earth and Planetary Science Letters, vol. 137, pp. 71-82 (1996).
20. Wolfe, Jack A. (1985) "Distribution of major vegetational types during the Tertiary", in The Carbon Cycle and Atmospheric CO₂: Natural Variations Archean to Present. E. T. Sundquist and W. S. Broecker, eds. American Geophysical Union, Washington, D.C., 627 pp.
21. W.G. SPAULDING "Vegetation and Climates of the Last 45,000 Years in the Vicinity of the Nevada Test Site, South-Central Nevada" U. S. Geological Survey Professional Pater 1329, 83 pp (1985).
22. J.E. KUTZBACH, P. J. GUETTER, P. J. BEHLING and R. SELIN "Simulated Climatic Changes: Results of the COHMAP Climate-Model Experiments" in Global Climates Since the Last Glacial Maximum. University of Michigan Press, pp. 24-93 (1993).
23. P.J. ROBINSON "Yucca Mountain Nevada Vicinity Climate, the Next 10,000 Years" in Expert Elicitation of Future Climate in the Yucca Mountain Vicinity, Iterative Performance Assessment Phase 2.5. CNWRA 93-016, pp. G3 1-11 (1993).
24. S.W. HOSTETLER, and F. GIORGI "Effects of a 2xCO₂ Climate on Two Large Lake Systems: Pyramid Lake, Nevada, and Yellowstone Lake, Wyoming." Global and Planetary Change, vol. 10, pp. 43-54 (1995).
25. T.M.L. WIGLEY, "Future Climate of the Yucca Mountain Site" in Expert Elicitation of Future Climate in the Yucca Mountain Vicinity, Iterative Performance Assessment Phase 2.5. CNWRA 93-016, pp. G4 1-14 (1993).
26. J.R. TRABALKA, Atmospheric Carbon Dioxide and the Global Carbon Cycle DOE/ER-0239, Office of Energy Research, Office of Basic Energy Sciences, Carbon Dioxide Research Division, Washington DC 20545 (1985).
27. J.C.G. WALKER, Numerical Adventures with Geochemical Cycles. Oxford University Press, 192 pp (1991).
28. I.G. ENTING, T. M. L. WIGLY and M. HEIMANN Future Emissions and Concentrations of Carbon Dioxide: Key Ocean/Atmosphere/Land Analysis. CSIRO Division of Atmospheric Research Technical Paper No. 31, 120 pp (1994).
29. COVEY, L. C. SLOAN and M. I. HOFFERT "Paleoclimate Data Constraints on Climate Sensitivity: the Paleocalibration Method" Climate Change. Vol. 32, 165-184 (1996)
30. K.E. TAYLOR, "Climate Models for the Study of Paleoclimates", in Long-Term Climate Variations, J.-C. DUPLESSY and M.-T. SPYRIDAKIS, eds. Springer-Verlag, pp. 21-41 (1994).
31. A.J. BROCCOLI, A. J. AClimate Model Sensitivity, Paleoclimate and Future Climate Change" in Long-Term Climate Variations, J.-C. DUPLESSY and M.-T. SPYRIDAKIS, eds. Springer-Verlag, pp. 551-567 (1994).
32. COVEY "Using Paleoclimates to Predict Future Climate: How Far Can Analogy Go?" Climate Change, vol. 29, pp. 403-407 (1995).
33. T.J. CROWLEY "Geological Assessment of the Greenhouse Effect" Bulletin of the American Meteorological Society, vol. 74, no. 12, pp. 2363-2373 (1993).
34. J.F. KASTING, and O. B. TOON "Climate Evolution on the Terrestrial Planets" in Origin and Evolution of Planetary and Satellite Atmospheres, edited by S. K. Atreya, J. B. Pollack, and M. S. Matthews, 881 pp (1989).
35. R.A. KERR "A Fickle Sun Could be Altering Earth's Climate After All" Science, vol. 269, p. 633 (1995).
36. COVEY, "Sun-Climate Links" Science, vol. 272, p. 179 (1996).
37. J.D. HAIGH, "The Impact of Solar Variability on Climate" Science, vol. 272, pp. 981-984 (1996).
38. T.J. CROWLEY and K.-K. KIM "Comparison of Proxy Records of Climate Change and Solar Forcing", Geophysical Research Letters, vol. 23, no. 4, pp. 359-362 (1996).
39. P.E. DAMON, "Solar vs. Greenhouse Forcing of Twentieth Century Global Warming", Testimony to the U.S. Senate Committee on Commerce, Science and Transportation, 27 Feb, 1992.
40. T.R. KARL, R. W. KNIGHT, D. R. EASTERLING and R. G. QUAYLE "Trends in U.S. Climate During the Twentieth Century" Consequences, vol. 1. No. 1, pp. 3-12 (1995).
41. J.F.B. MITCHELL, T. C. JOHNS, J. M. GREGORY and S. F. B. TETT, "Climate Response to Increasing Levels of Greenhouse Gases and Sulphate Aerosols" Nature, vol. 376, pp. 501- 504 (1995).
42. M.O. ANDREAE, "Raising Dust in the Greenhouse" Nature, vol. 380, pp. 389-390 (1996).
43. S.H. SCHNEIDER, "Detecting Climatic Change Signals: Are There Any Fingerprints?" Science, vol. 263, pp. 341-347 (1994).
44. C.M. GOODESS and J. P. PALUTIKOF, "Studies of Climate Transition Periods Following the Present Temperate Climate State." Publ. by Climate Research Unit, School of Environmental Sciences, University of East Anglia, Norwich, NR4 7TJ. NIREX: NSS/R316, 64pp (1993).
45. G.H. MILLER, G. H. and A. de VEMAL, "Will Greenhouse Warming Lead to Northern Hemisphere Ice-Sheet Growth?" Nature, vol. 355, pp. 244-246 (1992).
46. J.E. LOVELOCK, Gaia, A New Look at Life on Earth. Oxford University Press, 157 pp. (1979)
47. T.S. LEDLEY and S. CHU "Can Greenhouse Warming Induce Ice-Sheet Growth?" Fourth Symposium on Global Change Studies, publ. by the American Meteorological Society, pp. 272-275 (1993).
48. T.M.L. WIGLEY, R. RICHARDS and J. A. EDMONDS "Economic and Environmental Choices in the Stabilization of Atmospheric CO₂ Concentrations" Nature, vol. 379, pp. 240-243 (1996).
49. MASGOOD "Industry Warms to 'Flexible' Carbon Cuts" Nature, vol. 383, p. 657 (1996).
50. S.K. ATREYA, J. B. POLLACK and M. S. MATTHEWS (editors) "Origin and Evolution of Planetary and Satellite Atmospheres" The University of Arizona Press, 881 pp. (1989)
51. A.H. BERGER, A., H. GALLEE, and J. L. MELICE "The Earth's Future Climate at the Astronomical Time Scale" in Proceedings of the International Workshop on Future Climate Change and Radioactive Waste Disposal, eds: C. M. Goodess and J. P. Palutikof, Nirex Safety Series, NSS/R257, pp. 148-165 (1991).
52. J.H. HEVESI, D. S. AMBOS and A. L. FLINT "Analysis of Regional Precipitation and Synoptic-Scale Weather Patterns During Water Years 1992 and 1993 for the Yucca Mountain Region, Nevada, California" USGS Prof. Pap. In review (1996).
53. Wolverine Software Corporation, 7617 Little River Turnpike, Suite 900, "nnandale. VA 22003-2603 USA / wolverine"intr.net
54. R.H. FRENCH, "A preliminary Analysis of Precipitation in Southern Nevada" Desert Research Institute Publication No. 45031, 39 p (1983).
55. R.H. FRENCH, (1985) "Daily, seasonal and annual precipitation at the Nevada Test Site , Nevada" Desert Research Institute 57 p. (1985).
56. R.H. FRENCH, "Estimation of dominant hydrometeorological variables and review of geotechnical data for the effluent disposal site, Buckeye Creek area, Douglas County, Nevada" Desert Research Institute Publication No. 45031, 39 p (1988).
57. S.W. CHILDS, and F. W. SCHWARTZ "Flow and Transport in the Unsaturated Zone: Net Infiltration and Deep Percolation" Chapter 3 in Yucca Mountain Total System Performance Assessment, Phase 3 EPRI TR(1996).
58. S.W. CHILDS and A. LONG "Model and Calculations for Net Infiltration", Proceedings of the 3^rd International High Level Radioactive Waste Conference, Las Vegas, Nevada. April 12-16, 1992.

BACK