Consider a peat (organic rich soil) with k = 0.12 mm²/s and a mineral soil with k = 0.98 mm²/s. 

a) Calculate z* for the annual temperature wave for each of these soils.

b) Which soil will have the greatest decline in temperature fluctuations with depth (tightest annual temperature maximum envelope)?

c) Prove your prediction by calculating the ratio of the amplitude of the annual temperature fluctuations at 1 m depth to the amplitude at the surface for both soils. If T_amp = 10°C at the surface, what is the amplitude of fluctuations at 1 m depth for the two soils?

d) Calculate the lag, in days, of the annual temperature wave at 1 m depth for each soil.