C.P.J. Mitchell

Assignment #3: Modelling the Soil Water Budget and Sensitivity Analysis (38 marks total; worth 10% of grade)

The objectives of the assignment are to:

  1. Learn to construct a basic water balance model given basic climatological data.
  2. Explore sensitivity analysis (adjusting parameters sequentially and looking at effects).
  3. Improve on your presentation and interpretation of hydrologic data.


You need to construct a water budget at a monthly timescale given only some basic climatological variables.  The scale of measurement is a 1 m x 1 m x 1 m block of loam soil. ET is to be estimated using the Thornthwaite Method (learned in class, but your TA’s will go over it as well).  I’ve included a very detailed “tips sheet” about how to go through the other numbers, literally step by step. 

You will also have to do some sensitivity analysis (tweaking of parameters and looking at effects).  This is almost always done in modelling.  Make sure you are familiar with the “copy worksheet” function in Excel as your workbook will end up with several embedded worksheets. This saves an enormous amount of time.  Your TA’s will show you how in tutorial. 

Assignment format and submission instructions: Submit both your assignment questions (as a Word document using 12-point font) and your spreadsheet model (as an Excel file) via Quercus. To submit your assignment, click on the assignment for your particular tutorial section in the week 7 module tab and then click on the submit button in the upper right corner. Where an answer requires a graph, copy the graph from your spreadsheet and paste into the Word document (suggest “paste special” and choose pdf or picture). Organize your assignment according to the order of the questions below.

Specific to this assignment: Simply refer to your model for your answers to questions 1 through 4. The rest of the assignment should be submitted as one Word document with embedded graphs.

Assignment Questions

  1. Access the data from the file “soil moisture water balance.xls” and calculate average daily precipitation for each month. Also, calculate the Heat Index (i) for each month as is done for the Thornthwaite method of ET estimation.  Calculate the overall Heat Index for the year (I) and calculate the a coefficient.  (3 marks)
  • Calculate PET (unadjusted) on a monthly basis using the Thornthwaite method.  Then, adjust that value for the days in each month and the daylight hours in each month (termed PETadjusted).  (3 marks)
  • Calculate the soil water surplus/deficit, the soil water storage, and actual evapotranspiration, as outlined in your “tips sheet” and as shown by your TA’s.  Make sure the field capacity of the soil is set at 220 mm/m.  (3 marks)
  • Calculate Soil recharge/withdrawal for each month and finally runoff for each month.  (2 marks)
  • Create a graph with monthly precipitation (bar/column), adjusted PET and AET (line) all on the same graph.  Don’t forget to label everything correctly.  Comment on the relationships observed in this graph among the 3 variables.  (8 marks)
  • Create a line graph of monthly soil water storage and runoff from your spreadsheet of calculated data.  Again, label everything properly. Comment on the relationships observed in this graph between the 2 variables.  (6 marks)
  • Rerun your model using a mean daily temperature of 15°C every month and a mean sunlight hours of 12 hours per day for every month.  Show the new graphs.  What are the main differences you observe?  (5 marks)
  • Go back to your model completed in questions 1 through 4. Explain what happens to your model outputs when you adjust field capacity in increments of 50 mm from 150 mm to 300 mm (sensitivity analysis).  No need to show new graphs, although you’ll have to make some to comment properly. To help in your interpretation, I suggest you keep your y-axis scale of your soils moisture/runoff graphs constant at 0-300 mm.  (5 marks)
  • Again, start with your model completed in questions 1 through 4. Explain what happens to your model outputs when you adjust initial soil moisture in increments of 50 mm from 0 mm to 200 mm (while keeping field capacity constant at 220 mm).  No need to show new graphs, although you’ll have to make some to comment properly.  (3 marks)
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