Day 31 in math modeling

Here are some specific goals that I've thought of for each group. You will hopefully have some goals of your own! Think of mine as a starter set, at any rate.

• Data Quality

  • We need to have a checkout system in place by Friday.

  • We need to get the best data we have, end of Friday, to the modeling group. That will be their starting set.

  • Then, any time there's a change, the word needs to go out to the modeling group so that they can upload the corrected data set(s).

  • Jacob put out a call for error Identification: every city group should look at their city's data, and answer his call by Friday -- for either "errors", or "outliers". Then the Data Quality group teams can begin investigating each value.

    Assignment for all: please have a member of each city's group email Jacob with a summary of identified issues in the three reports prepared so far (and any other issues identified since).

  • Outlier and data error groups need to develop protocols, so that we can explain exactly why and how data are either removed, replaced, or flagged.

    I might suggest that two separate pairs of eyes examine each issue.

• Modeling

  • We need to get a preliminary model for Max/Min Temperature (at least -- we can hold off on rainfall, as far as I'm concerned, but go for it if you want).

  • I suggest generalizing the local model, of the form

    \[ M(t)= a+b(t-1961)+\sum_{i=1}^{n}\left(\alpha_i \cos\left(\frac{2 \pi (t-1961)}{T_i}\right)+\beta_i \sin\left(\frac{2 \pi (t-1961)}{T_i}\right)\right) \]

    to include elevation, latitude, and longitude.

    Including them linearly would be a good start. That makes the parameters easy to interpret.

  • How do you choose the periods? You might do a fit with a single pair, but continuously varying period, to see which periods are most fruitful, would produce a nice plot. Perhaps our software groups can create those plots, graphing $R^2(s)$, say as we vary the period (see KeelingFrequencyAnalysis.nb):

    \[ M(t)= a+b(t-1961)+ \alpha_i \cos\left(\frac{2 \pi (t-1961)}{T_0+s}\right) + \beta \sin\left(\frac{2 \pi (t-1961)}{T_0+s}\right) \]

    where $T_0$ is the smallest reasonable period (e.g. Nyquist limit).

    (again, incorporating elevation, latitude, and longitude as well).

  • We'll see what interesting frequencies pop up, but one question is whether we get long periods (perhaps due to solar activity, or ENSO, or other long period effects) that we might want to include.

  • Once the preliminary model (and any other models) are created, they need to be shared with all city groups, so that each city group can begin to analyse the Togo model with respect to their individual city, to check for "local fit".

• Research and Writing

  • We've submitted questions to the Togolese, and once we have those responses we can write the data collection methods section.

  • At this point research is a priority: what is known in the literature about
    1. Togolese climate

    2. Modeling monthly temperatures in general, in particular extremes

    3. Temperatures and West Africa

    4. Modeling monthly rainfall in general

    5. Rainfall and West Africa
    If you can conduct your preliminary searches before Friday, our experts should be able to help decipher the mathematics, if unfamiliar.

  • We've asked the Togolese for mean temperatures -- perhaps they have those (don't know why they wouldn't!). That would be a useful addition -- and more work for the modeling team.

  • We need to get latex working, and bibtex (the bibliography tool related to latex). By the end of the day, Friday (if not before), we should get the paper into a format that the group can use to produce your own copy of the "final paper" (so you can wrestle it from my hands!:).

  • Bibliography folks can be getting references and citations into place -- in the text, and in the bibliography.