Final Exam

When will the final examination will take place?

The mid-term exam will be an in-person exam on Tuesday, April 22nd from 2pm-5pm in BH 306 (our regular classroom).

What topics does the final include?

Topics 1-32 (note we skipped Topics 13, 14 & 28 so those are not included), namely all content of slides and all assigned readings.

What type of questions will be part of the final.

There will be a number of (A) multiple-choice questions, (B) short-answer questions, (C) comparison questions and (D) problem questions similar to the midterm.

Is the exam open book?

No. Although you are allowed one 2-sided sheet with notes.

Note that with respect to equations, it is more important for you to understand the concept of any formula rather than the pure arrangement of symbols. For example you should know if a variable is linearly proportional or inversely proportional to another variable (a possible multiple-choice question) and what the constant of proportionality is called (a possible short-answer question). You should have some ideas about the typical range of variables in the atmosphere and the order of magnitude of constants rather than their exact value.

Can I use a calculator?

Yes, although the questions are designed to be completed without needing one.

Which equations should I focus on?

Energy fluxes at Earth’s surface – ideal surface: \(Q* = Q_{H} + Q_{E} + Q_{G}\) (Topic 3)
Cosine law of illumination: \(S = S_{i}cosZ\) (Topic 4)
Conservation of incident radiation: \(\psi_{\lambda} + \alpha_{\lambda} + \zeta_{\lambda} = 1\) (Topic 5 & 7)
Spectral reflectivity: \(\alpha_{\lambda}\) = Radiation reflected/Radiation incident (Topic 6)
Albedo: = \(K\uparrow/K\downarrow\)
Stefan-Boltzmann’s law: \(E = \sigma T_{0}^{4}\) (and \(E = \sigma \varepsilon T_{0}^{4}\)) (Topic 7)
Kirchhoff’s law: \(\zeta_{\lambda} = \varepsilon_{\lambda}\) (Topic 7)
Net longwave radiation: \(L* = L\downarrow - L\uparrow = L\downarrow - (\varepsilon_{o}T_{o}^{4} +(1-\varepsilon_{o}))L\downarrow)\) (Topic 8)
Net (absorbed) solar: \(K* = K\downarrow - K\uparrow = K\downarrow(1 -\alpha)\) (Topic 8)
Net all-wave radiation: \(Q* = K* + L * = K\downarrow(1 -\alpha) + \varepsilon_{o}L\downarrow - \varepsilon_{o}T_{o}^{4}\) (Topic 8)
The heat capacity of a mixture: \(C_{s} = C_{m}\theta_{m}+C_{o}\theta_{o}+C_{w}\theta_{w}+C_{a}\theta_{a}\) (Topic 10)
Rate of temperature change in a soil: \(\frac{\Delta T}{\Delta t} = \frac{1}{C_{s}}\frac{\Delta Q}{\Delta z}\) (Topic 10)
Fourier’s law: \(Q_{G} = -k\Delta T/\Delta z = -k(T_{2}-T_{1})/(z_{2}-z_{1})\) (Topic 10 & 11)
Thermal diffusivity: \(\kappa = k/C\) (Topic 10)
Thermal admittance: \(\mu = (kC)^{1/2}\) (Topic 11)
Damping depth: \(D=\sqrt{\frac{2\kappa}{\omega}}=\sqrt{\frac{\kappa P}{\pi}}\) (Topic 12)
Beer’s law: \(I_{\lambda(z)} = I_{\lambda(o)}e^{-kz}\) (Topic 13)
The energy balance of snow and ice: \(Q* = Q_{H} + Q_{s} + Q_{M}\)
Sensible heat flux through LBL: \(Q_{H} = C_{a}(T_{0} -T_{a})/r_{b}\) (Topic 15)
Water vapour flux through LBL: \(Q_{E} = L_{v}(\rho_{vo}-\rho_{va})/r_{b}\) (Topic 15)
Reynold’s number: \(Re = \frac{\mu d}{\nu}\) (Topic 16)
Reynold’s decomposition: \(a(t) = a'(t) - \overline{a}\) (Lecture 18)
The variance of \(a\) (variable of interest) in a turbulent time series: \(\overline{a^{'2}} = \frac{1}{N}\sum_{i = 0}^{N-1}{a^{'2}(t_{i},x_{0})}\) (Lecture 18)
The standard deviation of a (variable of interest) in a turbulent time series: \(\sigma_{a} = \sqrt{\overline{a^{'2}}}\)
Turbulence intensities: (Lecture 18)
\(I_{u} = \sigma_{u}/M\)
\(I_{v} = \sigma_{v}/M\)
\(I_{w} = \sigma_{w}/M\)
\(M = \sqrt{\overline{u}^{2}+\overline{v}^{2}+\overline{w}^{2}}\)
Reynolds stress: \(\tau = -\rho{\overline{u'w'}}\) (Lecture 19)
Friction velocity: \(u_{*} = \sqrt{-\overline{u'w'}}\) (Lecture 19)
The logarithmic wind law: \(\overline{u}_{(z)} = \frac{u_{*}}{k}ln\frac{z}{z_{0}}\) or if we include the zero-plane displacement (\(z_{d}\)) \(\overline{u}_{(z)} = \frac{u_{*}}{k}ln\frac{z-z_{d}}{z_{0}}\) (Lecture 20)
Estimate of the roughness length (\(z_{0}\)): \(z_{0} \approx 0.1z_{h}\) (Lecture 20)
Flux-gradient equations (i.e., K-theory) for momentum flux density: \(\tau = \rho K_{m} \frac{\partial \overline{u}}{\partial z}\), Water vapour flux density: \(E = K_{V} \frac{\partial \overline{\rho_{v}}}{\partial z}\), sensible heat flux density: \(Q_{H} = C_{a} K_{H} \frac{\partial \overline{\theta}}{\partial z}\), trace gas flux density: \(F_{c} = K_{c} \frac{\partial \overline{\rho_{c}}}{\partial z}\) (Lecture 21)
Reynold’s analogy: \(K_{M} = K_{H} = K_{V} = K_{C}\) (Lecture 21)
Sensible heat flux density measured via eddy covariance: \(Q_{H} = \rho c_{p} \overline{w'T'}\) (Lecture 22)
Latent heat flux density measured via eddy covariance: \(Q_{E} = L_{v} \overline{w' \rho_{v}'}\) (Lecture 22)
Trace gas flux density measured via eddy covariance: \(F_{c} = \overline{w' \rho_{c}'}\) (Lecture 22)
Gradient Richardson number: \(R_{i} = \frac{g}{\overline{T}} \frac{\Delta \overline{\theta}/\Delta z}{(\Delta \overline{u}/\Delta z)^{2}}\) (Lecture 23)
Land-atmosphere water balance: \(P = E + I + \Delta R + \Delta S\) (Lecture 29)
Water balance of plant canopies: \(P = P_{T} + P_{S} + P_{I}\) (Lecture 29)
Net ecosystem productivity: NEP = GPP-ER (Lecture 30)
Ecosystem respiration: ER = AR + HR (Lecture 30)
Penman model for evapotranspiration: \(Q_{E} = \frac{s}{s + \gamma}(Q^{*} - Q_{G}) + \frac{C_{a} (vdd_{a} / r_H)}{s + \gamma}\) (Lecture 31)

Are there examples from previous years?

Yes. There are finals from previous year, which have similar types of questions and overall structure. You can solve finals from 2013, 2011, 2009, and 2007 and check your answers using the answer keys for 2013, 2011, 2009, and 2007. Note that you may not be able to answer all questions with your background. The order of topics has changed slightly from previous years when this course was taught by another instructor. Also note that lectures and slides referenced in the answer keys may no longer align with this year’s version of the course.