PHY392 : PHYSICS OF CLIMATE Assignment 4
物理作业代写 What temperature change is needed to offset the doubling of methane (assuming CO2 remains at the present day value)?
1. In the n-layer greenhouse model, Ts = (n + 1)1/4Te , the increase of the surface temperature with the number of layers reflects the influence of increased abundances of greenhouse gases in the atmosphere on the surface temperature. Let’s assume that the number of layers is a power of the surface temperature
This captures, for example, the rapid increase of the saturation vapour pressure of water in the atmosphere
(a) [4 points] Determine the values of α appropriate for current conditions Ts = 288K and Te = 255K , for β = 2 and β = 4.
(b) [4 points] Using these values of α, determine whether β = 2 or β = 4 causes the surface temperature to rapidly increase as Te is increased. If Ts increases much faster than Te the atmosphere might experience an uncontrolled ’runaway’ greenhouse, as a result of increasing the amount of greenhouse absorber. You can answer this question by plotting Ts as a function of Te over a suitable range, or by calculating a range of values of both temperatures. Calculate/plot the results for both β = 2 and β = 4. Is either case an example of a runaway greenhouse effect?
(The saturation vapour pressure of water actually increases exponentially with temperature, not a polynomial!)
(c) [3 points] The high surface temperature on Venus is often described as an example of a runaway greenhouse. Calculate the emission temperature of Venus assuming a planetary albedo of 0.15, which might be expected in the absence of clouds early in the planet’s history.
(d) [4 points] Figure 1 shows the evolution of temperatures in the early atmospheres of Venus and Earth, together with the phase diagram for water. Using this figure, explain why the Earth did not experience a runaway greenhouse as water accumulated in the atmosphere from outgassing from the planet’s interior.
2. Parts of this assignment involve using the MODTRAN (MODerate resolution atmospheric TRANmission) model that can be found at http://climatemodels.uchicago.edu/modtran/. 物理作业代写
(a) [4 points] Using the default setup for MODTRAN (70km looking down, tropical atmosphere), under current conditions what is the net radiative forcing effect of doubling carbon dioxide (CO2) or doubling methane (CH4)?
(b) [2 points] According to the IPCC, methane is more than 25 times stronger as a greenhouse gas than carbon dioxide. Does this information help explain your answer to the above question? why or why not?
(c) [3 points] What change in carbon dioxide concentration would have the same effect as doubling methane concentration?
(d) [2 points] What temperature change is needed to offset the doubling of methane (assuming CO2 remains at the present day value)? (Change the “Ground T offset” value to make the fluxes cancel again).
(e) [2 points] What temperature change is needed to offset the doubling of carbon dioxide (assuming methane remains at the present day value)? (Change the “Ground T offset” value to make the fluxes cancel again).
Figure 1: Saturation vapor pressure curve for water, plotted with the evolution of water vapor and temperature history of Earth and Venus.
3. Figure 2 shows the concentration of carbon dioxide in the lower atmosphere as a function of time since 1960. The figure shows measurements from the top of Mauna Loa on the island of Hawaii, from a monitoring station at the South Pole, and from Alert in Nunavut.
(a) [4 points] What is the cause of the cyclical signal observed at some stations? Why does the amplitude of the cycle change with station?
(b) [3 points] What is the cause of the increase in the measured amount of carbon dioxide since 1960? What is the rate of growth?
(c) [4 points] The calculated emission of carbon dioxide from anthropogenic sources is 9 Gigatonnes of carbon atoms per year. How much would this emission change the concentration of carbon dioxide (measured in ppmv) in the atmosphere each year?
(d) [3 points] Explain the difference between your answers to part b and c.
4. Burning carbon based fuels releases carbon dioxide into the atmosphere, contributing to the warming of the atmosphere. Each year, approximately 8 GtC (gigatonnes of carbon) contained in fossil fuels is burned and converted into 2.2 ppm of carbon dioxide in the atmosphere. In 2017 the atmospheric concentration of carbon dioxide was 405 ppm. Assume 220ppm of atmospheric carbon dioxide is added over 100 years.
(a) [5 points] For small changes in the radiative forcing (e.g. from greenhouse gases) we can define a Climate Sensitivity parameter λ defined as
where Ts is the surface temperature, F is the radiative forcing. The value for ∆F can be experimentally
Figure 2: Carbon dioxide concentration measured using flask or in–situ instruments. (left) Measurements from the Mauna–Loa observation site (latitude 19.5◦S, grey), and the south pole carbon monitoring site (latitude 90◦S, black). Data exists for almost every month since 1960. (right) Measurements from Mauna–Loa, the south pole, and Alert, Nunavut (latitude 82.5◦N, dashed black) from 1985 to 1995.
found for greenhouse gases, for carbon dioxide a suitable approximation is given by
where ∆F is in units of W /m2 , C is the concentration of carbon dioxide, and C0 is a reference concentration of CO2. Derive an expression for the change in surface temperature caused by a change in the concentration of carbon dioxide. Use this equation to calculate the surface temperature change after 100 years caused by
the constant emission scenario above. Assume that λ = 0.8K/(W /m2). Compare your values with the estimates from the The Intergovernmental Panel on Climate Change (IPCC), which predicts surface temperature will rise by 1°C – 4°C in the next 100 years.
(b) [5 points] Estimate the value of ∂T ∂F you would get from the Stefan–Boltzmann law F = σT4, using an appropriate value for T . Explain the difference between this value for and the value for λ given is part a of 0.8K/(W /m2).
5. Consider the instruments and platforms used to observe climate. 物理作业代写
(a) [4 points] Atmospheric temperature and cloud cover are observed using satellites orbiting the Earth in downward looking satellites in Low Earth Orbit (LEO, at an altitude of <1000km). Some newer satellites are being placed in Geostationary Orbit (GEO, at an altitude of ≈30,000km). Briefly describe the differences between the two methods, and give two advantages of each geometry.
(b) [6 points] The composition of the atmosphere is measured using balloons launched the ground, solar observing ‘column’ measurements, and from orbit using satellites. Briefly describe the advantages and disadvantages of each method.