Michael and Francois,


   Excellent work on the final project. I was hoping that all of the projects would involve 
   doing some actual analysis of data, and so it's good that you actually dug so deeply
   into the temperature and precipitation data to understand trends affecting the 
   "Corn Belt" and corn farming in particular. I sense that you might be a bit disappointed
   that the results weren't more clear-cut -- that the growing season trends didn't turn
   out to be very significant for example.  But "that's life" in a way(!)  Statistical 
   tests like Mann-Kendall are set up so that we don't over-interpret the data and claim 
   that trends exist when the same results could be resulting purely from chance variations.  
   
   One interesting point that occurred to me in reading your paper was that, in addition
   to the overall trends, the more information about the occurrence of extremes such as 
   the worst drought years might be extremely useful for farmers.  For instance if there 
   was some sort of predictable climate pattern that was controlling when the extremely 
   dry years happened, knowing about it ahead of time would be immensely important.  Finding 
   anything like that (assuming it exists at all) would require a different sort of 
   analysis, though.  

   It's also interesting to ask what we could do to help corn farmers meet the demand
   for their products while making a reasonable living and profit from the farming
   business.  As you say, extremely favorable growing years produce huge harvests that
   drive down the price of corn and make the business essentially unsustainable.  The
   small farms of the past are much less common today, and food production has moved
   to large corporations partly for this reason.  It's much easier for a big company
   to absorb losses some years and make profits other years if necessary.  The US 
   government has also paid farmers not to plant crops on all of their land -- to keep 
   some growing capacity in reserve, so to speak -- and hence keep the prices from falling 
   so low.  But those price supports are not very popular politically (especially when
   they are going to big corporations, and outside of states with heavy farming areas). 
   No "easy answers" there either(!)   
  
   Specific writing comments:

   Page 2:  "day in age" should be "day and age."  But your first sentence would also
   be more direct and forceful if you just said "Climate change has become an increasingly 
   relevant and studied phenomena in the world."

   "While the crops that grow in this region are not limited to corn, it is in light of 
    the fact that this region having “soils [that] are deep, fertile, and rich in organic 
    material … [and receiving] well-distributed rainfall … during the growing season [that] 
    are ideal conditions for raising corn” 1 in particular that it was termed the Corn Belt"
   This is a rather wordy, complicated, and hard to parse sentence.  Something like this would 
   be more direct and clearer:  "This region is termed the Corn Belt even though other crops 
   are grown there.  With soils that are "deep, fertile, and rich in organic material"  
   "well-distributed rainfall ... during the growing season" the conditions are ideal
   for growing corn^1.  (The footnote can apply to this whole discussion, which 
   is paraphrasing something from your source, even when you are not placing it at 
   the end of the direct quotation.)    

   Page 3:  "It is economic consequences of this sort that wish to be avoided in the future, 
   and the analysis of precipitation and temperature data may prove useful in providing 
   predictions as it concerns to the climate."  It's not the consequences that wish anything,
   as your sentence seems to be saying.  You need a different subject in order to use this
   sentence, something like:  "If possible, farmers would prefer to avoid economic consequences
   of this sort in the future, and the analysis of precipitation and temperature data may 
   prove useful in providing climate predictions." 

   Page 6:  "The tk denotes the number of equal values as compared to a certain k in the data
   set."  Not exactly.  The k is just a summation index for the formula.  If there are 
   some number g of groups of "ties" in the data, then k ranges from 1 to g and t_k is 
   the number of data values in the kth group that are equal to each other.  

   "S - 1 / √V, for S = 0, Z = 0, and lastly for S < 0, Z = S+1 / √V"  Strictly speaking, 
   for formulas written "in-line" like this, you need parentheses around the whole 
   numerators:  (S - 1)/sqrt(V).  Your formula would usually be interpreted to mean,
   "subtract 1/sqrt(V) from S."  Also, in the formula for the seasonal MK test, I 
   don't believe the V_i's should have the +/- 1's.  Only the S's have those.

   Page 8:  "significantly significant at the α = 0.05 level"  -- don't need the first
   "significantly" here :)

   Final Project: 

   Annotated Bibliography -- 10/10
   
   Presentation -- 35/35

   Paper -- 53/55

   Total -- 98/100   (letter: A)