EESB04 Tips for Calculating Monthly Water Budgets for Assignment #3
1. The monthly heat index (i) for each month is calculated using the equation:
where T is the mean monthly temperature in Celsius. If T<0, then i = 0. A Boolean conditional is best used here (“IF” statement in Excel). Your TA will go over this in tutorial.
To get the Heat Index (I) for the year, simply sum the i values for every month. This brings the overall equation from #1 above to what we learned in class:
2. The a coefficient is calculated as:
a = 6.75 x 10-7*I3 – 7.71×10-5*I2 + 0.0179*I + 0.49
(Use this formula, not the slightly less precise one shown in lecture)
3. Calculate the monthly unadjusted PET using:
However, when Tmonth< 0, PET = 0
It will more convenient if you use a conditional statement here as well.
4. To calculate the monthly adjusted PET, use the following formula:
This makes adjustments for the length of the month and the average daily number of daylight hours in eachmonth. As learned in lecture, this adjustment is the b coefficient. This “monthly adjusted PET” is the full version of the Thornthwaite Equation.
5. Calculate the Water Surplus/Deficit, which is the difference betweenPrecipitation and adjusted PET. Think about what a positive or negative number mean?
6. Calculate the soil water storage, assuming a 220 mm/m maximum soil water storage (that the field capacity is 220 mm/m). Start out with the assumption that the soil is holding 130 mm/m of water prior to your first month’s data. Think of the soil as a tank that can hold a maximum of 220 mm of water, and cannot go below 0 mm.You need to calculate the amount of water that the soil is holding. First, use the 130mm you presume is already there. This will be your temporary starting soil water. So for January, you add the “Water Surplus/Deficit” to this current storage, and if this is larger than 220 mm, then the rest runs off. The value cannot be less than 0, so if it is, change the value to zero.
You’ll need another nested conditional Boolean statement to ensure that soil moisture storage neither exceeds 220 mm NOR falls below 0 mm. In other words, if the Soil Water from the previous month plus the Surplus is larger than 220 mm, then the soil staysat 220 mm. If Soil Water from the previous month plus the Deficit is less than zero (in otherwords, water needed is greater than what is in the soil), then the soil water goes to zero. Otherwise, theextra water simply recharges the soil and is available the next month.
7. Actual Evapotranspiration (the next row) is limited by either energy available (PET) or the wateravailable. You’ve calculated the adjusted PET already, so that is the energy limit. The water limit is theprecipitation for the month plus the soil water from the previous month. Therefore, AET is theminimum of PET and the sum of the soil water from the previous month and precipitation.
In other words:
=MIN(PETADJ,(precip+ previous month’s soil water storage))
For January, you can use the initial soil water storage as the “previous”.
8. Soil water Recharge/Withdrawal will keep track of the water going in or out of the soil. Youhave implicitly calculated this already; it is just a difference between the current soil water and in thesoil water from the preceding month. Calculate this for each month. Think about this. Whatdoes a positive number mean? What does a negative number mean?
9. Runoff is calculated as the residual (what’s left over) in the water balance equation, specifically as the difference between precipitation and the sum of AET and soil waterrecharge/withdrawal.
10. As a check, make sure all the water is accounted for each month. Precipitation minus AET, recharge,and runoff should equal zero for every month.
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