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Published byLesley Summers Modified over 3 years ago

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Daisy World 2 sets of verbal/qualitative statements 2 graphical representations 2 mathematical formulae

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In words… 1.Biological statements: At low temperatures daisies cannot survive at all. As temperature increases they begin to survive and thrive, until the temperature reaches an “optimum”, where they are most prolific. As temperature increases past the optimum, they are less and less able to thrive. At very high temperatures the cannot survive at all. 1.Physical statements: Because daisy coverage corresponds to the planet’s albedo (daisies are white so the more daisies, the more reflective the planet), more daisies means lower temperature.

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Graphically… 1.Daisy response to temperature:

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Graphically… 2.Temperature response to daisy coverage:

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Mathematics… 1.Daisy coverage (d) is a function of temperature (T):

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Mathematics… 1.Daisy coverage (d) is a function of temperature (T): optimum temperature

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Mathematics… 1.Daisy coverage (d) is a function of temperature (T): parameter that controls how sensitive daisies are to temperature optimum temperature

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Mathematics… 1.Daisy coverage (d) is a function of temperature (T): daisy coverage at optimum temperature parameter that controls how sensitive daisies are to temperature optimum temperature

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Mathematics… 2.Temperature (T) is a function of albedo (α), and therefore of daisy coverage (d):

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Mathematics… 2.Temperature (T) is a function of albedo (α), and therefore of daisy coverage (d): Stefan-Boltzmann constant σ = 5.67x10 -8 Wm -2 K -4

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Mathematics… 2.Temperature (T) is a function of albedo (α), and therefore of daisy coverage (d): Solar “constant” Stefan-Boltzmann constant σ = 5.67x10 -8 Wm -2 K -4

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Bottom line… It’s difficult to sort out equilibrium climate of this “Daisy World” with just verbal/qualitative statements. It’s a bit easier if we can represent the verbal description of the climate graphically. It’s most straightforward if we just bite the bullet and do the math! All three methods are useful in their own right, though!

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So how do we find equilibria and examine stability? Verbal solution: Can’t really do much with the qualitative statements… Mathematical solution: Don’t want to dwell on the math, but it’s just algebra: 2 equations in 2 unknowns solve the system Graphical solution: overlay the two plots and the equilibria are the points of intersection (Can you see why?) Let’s try again today quickly…

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Aim: What are the higher degree function and equation? Do Now: a) Graph f(x) = x 3 + x 2 – x – 1 on the calculator b) How many times does the graph intersect.

Aim: What are the higher degree function and equation? Do Now: a) Graph f(x) = x 3 + x 2 – x – 1 on the calculator b) How many times does the graph intersect.

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