Chapter 11, Global Climate Models Video Solutions, Global physical climatology

Problem 1

Suppose that the air temperature above the Arctic Ocean is $-30^{\circ} \mathrm{C}$ and the water temperature is $-2^{\circ} \mathrm{C}$. Solve for the sensible heat flux to the atmosphere if the bulk aerodynamic formula for heat flux (4.26) applies with surface pressure $10^5 \mathrm{~Pa}, C_{\mathrm{DH}}=10^{-3}$, and $U_{\mathrm{r}}=5 \mathrm{~m} \mathrm{~s}^{-1}$. Assume a steady state with no heat storage and ignore radiative and latent heat fluxes. Consider three cases: (a) no sea ice, (b) $1 \mathrm{~m}$ of sea ice, and (c) $3 \mathrm{~m}$ of sea ice. Solve for the temperature of the surface in those cases with sea ice. Use (11.3) with $k_1=2 \mathrm{~W} \mathrm{~m}^{-1} \mathrm{~K}^{-1}$ to solve for the flux through the ice.

Keshav Singh

Numerade Educator

05:21

Problem 2

Repeat problem 1 for the case of $1 \mathrm{~m}$ of sea ice with $10 \mathrm{~cm}$ of snow on top. Use $k_s=0.3 \mathrm{~W} \mathrm{~m}^{-1} \mathrm{~K}^{-1}$.

Surendra Kumar

Numerade Educator

05:21

Problem 3

Calculate the surface temperature and sea ice thickness in equilibrium under the following conditions: polar darkness, air temperature $-40^{\circ} \mathrm{C}$, The downward longwave flux is $100 \mathrm{~W} \mathrm{~m}^{-2}$, and the surface has unit longwave emissivity. Consider cases where the ocean supplies heat to the base of the ice at the rate of (a) $10 \mathrm{~W} \mathrm{~m}^{-2}$ and (b) $20 \mathrm{~W} \mathrm{~m}^{-2}$. Hint: Use the energy balance at the surface and at the base of the ice and linearize the Stefan-Boltzmann emission about the air temperature. Ignore latent cooling.

Surendra Kumar

Numerade Educator

04:18

Problem 4

What would be the equilibrium sea ice thickness for the two cases of problem 3 if the sea ice were covered by $20 \mathrm{~cm}$ of snow with $k_{\mathrm{s}}=0.3 \mathrm{~W}$ $\mathrm{m}^{-1} \mathrm{~K}^{-1}$ ?

Banhishikha Sinha

Numerade Educator

00:44

Problem 5

Look in the tropical Pacific at the cloud changes in Fig. 11.8 and at the precipitation changes in Fig. 11.14. Explain how these are consistent with each other.

Kevin Chimex

Numerade Educator

03:41

Problem 6

Compare the relative humidity changes in Fig. 11.12 with the zonal mean wind changes in Fig. 11.13. Explain how these are consistent with the general circulation of the atmosphere described in Chapter 6, and the modes of natural variability described in Fig. 8.4.

Sarah Mccrumb

Numerade Educator

00:57

Problem 7

In Fig. 11.15, the January warming is much greater over Hudson Bay than over the surrounding land regions of North American. Can you explain this?

Dading Chen

Numerade Educator