Modeling the Earth System: Different Approaches for Different Problems James Kasting Department of Geosciences Penn State University

What is the Earth System? The Earth contains many different ‘systems’ that we might wish to simulate. These include (but are not limited to): – The climate system – Atmospheric composition – Geochemical cycles – Human populations – Human economic systems I’ll talk about modeling the first two of these systems

Talk Outline Part 1: Modeling the climate system Part 2: (Very brief) Modeling atmospheric composition and photochemistry

Hierarchies of Climate Models First, one needs to define the problem in which one is interested – Is it global or regional? – What is the time scale of interest? Decades? Centuries? Millennia? Billions of years? – How firm are the constraints? Are we simulating observations? Predicting the future? Speculating about other Earth-like planets? High levels of modeling complexity are justified only when the constraints are tight and/or the stakes are large (as in modern global warming)

Hierarchies of Climate Models I’ll talk about three levels of climate models 1.1-D radiative-convective models These are what I’ve spent most of my own time studying 2.Energy-balance models (EBMs) These are useful for a limited class of problems in which latitudinal resolution is needed, as well as long time scales 3.3-D global climate models (GCMs) These are how climate really ought to be modeled, but they are time-consuming to construct, expensive to run, and they contain many parameters (e.g., continental geography) that need to be known

Hierarchies of Climate Models I’ll talk about three levels of climate models 1.1-D radiative-convective models These are what I’ve spent most of my own time studying 2.Energy-balance models (EBMs) These are useful for a limited class of problems in which latitudinal resolution is needed, as well as long time scales 3.3-D global climate models (GCMs) These are how climate really ought to be modeled, but they are time-consuming to construct, expensive to run, and they contain many parameters (e.g., continental geography) that need to be known

Hierarchies of Climate Models I’ll talk about three levels of climate models 1.1-D radiative-convective models These are what I’ve spent most of my own time studying 2.Energy-balance models (EBMs) These are useful for a limited class of problems in which latitudinal resolution is needed, as well as long time scales 3.3-D global climate models (GCMs) These are how climate really ought to be modeled, but they are time-consuming to construct, expensive to run, and they contain many parameters (e.g., continental geography) that need to be known

1-D Radiative-convective models For many problems of interest, it is sufficient to calculate globally averaged vertical temperature profiles One needs to include both radiation and convection Radiation Convection

1-D Radiative-convective models One problem that these models can be used for, for example, is to determine what greenhouse gas, or combination of gases, could have compensated for the faint young Sun problem 

The faint young Sun problem Kasting et al., Scientific American (1988) T e = effective radiating temperature = [S(1-A)/4  ] 1/4 T S = average surface temperature

But we know that the early Earth was not frozen. Indeed, if anything the climate was generally warmer than today 

Geologic time Rise of atmospheric O 2 (Ice age) First shelly fossils (Cambrian explosion) Snowball Earth ice ages Warm (The ‘Boring Billion’) Ice ages Warm (?) Origin of life ‘Conventional’ interpretation of the Precambrian climate record

Greenhouse gases and CO 2 - climate feedbacks So, one needs more greenhouse gases, especially during the Archean CO 2 is a prime candidate because it is part of a negative feedback loop (see panel at right) Atmospheric CO 2 increases when the climate cools because of slower rates of silicate weathering on land Diagram illustrating the (modern) carbonate-silicate cycle

Is CO 2 the solution to the FYS problem? 1-D radiative-convective climate model calculations can be used to estimate past CO 2 concentrations that would be consistent with the geologic record Unfortunately, geochemists have made this problem more difficult by attempting to measure paleo-CO 2 concentrations  J. F. Kasting, Science (1993)

Precambrian pCO 2 from paleosols At first, these paleosol studies showed significantly lower Precambrian CO 2 levels If Sheldon and Driese are right about Precambrian CO 2 levels, then other greenhouse gases would have been needed to keep the early Earth from freezing But, more recent analyses show less of a discrepancy… N. Sheldon, Precambrian Res. (2006) Driese et al., 2011 (10-50 PAL)

Precambrian pCO 2 from paleosols If the new paleosol analysis is correct, then CO 2 could have been high enough to solve the faint young Sun problem by itself I’ll return to this story at the end because it remains unlikely that CO 2 was the only important greenhouse gas during the Archean Atmospheric O 2 levels were low, and so reduced greenhouse gases (e.g., CH 4 ) should have been more abundant Kanzaki & Murakami, GCA (2015)

1-D models of the habitable zone Another problem that can be addressed with 1-D climate models is to try to define the habitable zone around the Sun and other stars Definition: The habitable zone (HZ) is the region around a star in which liquid water can exist on a planet’s surface Figure based on Kasting et al. (Icarus, 1993)

Calculating HZ boundaries The inner edge of the HZ is defined by either a runaway or moist greenhouse –Runaway greenhouse: The planet’s ocean evaporates entirely –‘Moist ‘greenhouse: The ocean remains present, but water is lost anyway because the stratosphere becomes wet, allowing H 2 O to be photodissociated, after which the H escapes to space The outer edge of the HZ is defined by the ‘maximum greenhouse’ limit, beyond which the surface can no longer be warmed above the freezing point by a CO 2 - H 2 O atmosphere

Calculating HZ boundaries Calculating the boundaries of the habitable zone is difficult because one must be able to deal with dense H 2 O-rich atmospheres on the inner edge and dense CO 2 -rich atmospheres on the outer edge Both CO 2 and H 2 O have hundreds of thousands of absorption lines across the thermal- and near- infrared Including these in a climate model requires that they be parameterized using correlated-k coefficients

Habitable zone updates Within the past two years, our group has recalculated HZ boundaries using updated 1-D climate models The main thing that has changed is the development of a new HITEMP database for H 2 O absorption coefficients (replacing the older HITRAN database) –The new database gives more absorption of incoming sunlight at visible/near-IR wavelengths, thereby lowering a planet’s albedo Goldblatt et al., Nature Geosciences (2013)

Revised conventional HZ limits The runaway and moist greenhouse limits on the inner edge of the HZ have recently been revised. They now lie perilously close to Earth’s orbit Note that the horizontal axis has been changed to show effective stellar luminosity, S eff = S/S 0 Kasting et al., PNAS, 2014 (Figure by Sonny Harman)

But these 1-D climate model calculations may be too pessimistic, for at least two reasons 1.They typically assume that the troposphere is fully saturated 2.Cloud feedback is typically ignored (Neither of these processes can be modeled effectively in 1-D)

3-D modeling of habitable zone boundaries Fortunately, new studies using 3-D climate models predict that the runaway greenhouse threshold is increased by ~10% because the tropical Hadley cells act like radiator fins –This behavior was pointed out 20 years ago by Ray Pierrehumbert (JAS, 1995) in a paper dealing with Earth’s tropics We have adjusted our (1-D) HZ inner edge inward to account for this behavior Leconte et al., Nature (2013) Outgoing IR radiation

Updated habitable zone (Kopparapu et al., 2013, 2014) When the 3-D climate calculations are taken into account, the inner edge of the HZ moves back to ~0.95 AU around the Sun Credit: Sonny Harman

Tidal locking for planets around M stars 3-D models are also needed to simulate tidally locked planets orbiting M stars Such planets are likely to be syncronously rotating, i.e., they always show the same face to the star –The 1-D approximation is not very good in this case Figure based on Kasting et al. (1993)

3-D climate model calculations for M- and K-star planets Clouds dominate the sunny side of tidally locked planets orbiting M and late-K stars, raising their albedos The inner edge of the HZ is therefore pushed way in –S eff  2 for a synchronously rotating planet around a K star (dark blue curves) Yang et al., ApJ Lett (2013)

Most recent habitable zone Thus, our current estimate of the habitable zone looks something like this. The inner edge is still highly uncertain Kopparapu et al., ApJ Lett (2014)

Recent work shows that the outer edge of the HZ may be similarly complex, requiring the use of climate models of at least EBM complexity…

A new paper by Kristen Menou shows that planets near the outer edge of the habitable zone should not have stable, warm climates, despite the influence of the carbonate-silicate cycle See also Kadoya and Tajika (ApJ, 2014), along with earlier papers by Tajika, referenced therein Energy balance models (EBMs) are needed to simulate this behavior because it involves polar glaciation

Limit cycling near the HZ outer edge Our own EBM predicts limit cycles near the outer edge of the HZ A planet in this region remains frozen much of the time, but warms occasionally near the equator Calculation of the ice line is needed to study this phenomenon Haqq-Misra et al., PNAS, submitted

Limit cycling near the HZ outer edge This phenomenon may have implications for the existence of complex (animal) life, including intelligent life It is hard to see how such life could evolve in a limit-cycling environment

Part 2: (Very brief) Modeling atmospheric composition and photochemistry Finally, on long time scales, the composition of the atmosphere may change in ways that affect the Earth’s climate. This requires the use of a photochemical model..

1-D photochemical models Divide the atmosphere into vertical layers (typically 100  1 km) Calculate absorption and scattering of incident solar UV radiation Calculate photochemical reaction rates and (vertical) transport for the relevant atmospheric species (typically 50-60) Integrate the model in time until it converges using an implicit an implicit numerical method, such as the reverse Euler method Segura et al., Astrobiology (2003)

1-D photochemical models For example, one can calculate the vertical profiles of CH 4 and N 2 O for different atmospheric O 2 levels A constant upward flux of each gas is assumed Segura et al., Astrobiology (2003)

1-D photochemical models Segura et al., Astrobiology (2003) One can also calculate vertical ozone profiles Then, by feeding this output back into the 1-D climate model, and iterating back and forth, one can calculate the effect on vertical temperature profiles

The faint young Sun problem revisited Finally, to return briefly to the faint young Sun problem, mentioned earlier, it is easy to demonstrate that atmospheric CH 4 concentrations could have been up to 1000 times higher than today (~1000 ppmv, compared to 1.7 ppmv today) prior to the rise of atmospheric O 2 This could have provided an additional degrees of greenhouse warming A. A. Pavlov et al., JGR (2001) Volume mixing ratio

Archean CH 4 -CO 2 greenhouse Diagram shows a hypothetical Archean atmosphere at 2.8 Ga The black curves show predicted surface temperatures with zero and 1000 ppm of CH 4 The loss of much of this CH 4 at ~2.5 Ga could plausibly have triggered the Paleoproterozoic glaciations 2.8 Ga S/S o = 0.8 J.F. Kasting, Science (2013) Driese et al. (2011)

Geologic time Rise of atmospheric O 2 (Ice age) First shelly fossils (Cambrian explosion) Snowball Earth ice ages Warm (The ‘Boring Billion’) Ice ages Warm (?) Origin of life ‘Conventional’ interpretation of the Precambrian climate record

Conclusions Different types of climate models are useful for different problems – 1-D models are useful for studying weakly constrained problems like the faint young Sun problem and the boundaries of the circumstellar habitable zone – 3-D models are useful for refining such calculations and for investigating problems like modern day global warming, for which both tight constraints and lots of funding are available – EBMs are useful for long-timescale problems for which latitudinal information, e.g. ice lines, are essential 1-D photochemical models, sometimes coupled to 1-D climate models, are useful for studying problems (like the faint young Sun problem) in which changes in atmospheric composition are important