Midterm Exam

When will the midterm examination will take place?

The mid-term exam will be an in-person exam on Wednesday, Feb 26th during our regular class period.

What topics does the midterm include?

Topics 1-19 (note we skipped Topics 13 & 14 so they are not included), namely:

all content of slides on Topics 1 to 19
all assigned readings for Topics 1 to 19

What type of questions will be part of the midterm.

There will be a number of multiple-choice questions (36% of total score), short answer questions (24%) and a set of a few more complex problems where you must use your background knowledge to observe, interpret and explain a particular phenomena or process (42%). Total possible marks are 102%.

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)
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)
\(I_{u} = \sigma_{u}/M\)
\(I_{v} = \sigma_{v}/M\)
\(I_{w} = \sigma_{w}/M\)
\(M = \sqrt{\overline{u}^{2}+\overline{v}^{2}+\overline{w}^{2}}\)
The average eis called mean turbulent kinetic energy (TKE): \(\bar{e} = \frac{1}{2} \left( \overline{u'^2} + \overline{v'^2} + \overline{w'^2} \right)\) (Lecture 18)
Correlation coefficient: \(r_{uw} = \frac{\overline{u' w'}}{\sigma_u \sigma_w}\) (Lecture 18)
Reynolds stress: \(\tau = -\rho{\overline{u'w'}}\) (Lecture 19)
Friction velocity: \(u_{*} = \sqrt{-\overline{u'w'}}\) (Lecture 19)

Are there examples from previous years?

Yes. There are midterms from previous year, which have similar types of questions and overall structure. You can solve midterms from 2014, 2013, 2011, and 2010 and check your answers using the answer keys for 2014, 2013, 2011, and 2010. 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.