Evapotranspiration

Calculation

Thornthwaite Mather method

The Thornthwaite Mather method of calculating water balance is recommended within the 2003 Ontario Stormwater Management Planning and Design Manual. The original paper (linked below) provides the required calculations as a series of lookup tables. The following equations are derived from these, and are widely documented elsewhere e.g.<ref>Sellinger,C.E. Computer Program for Estimating Evapotranspiration using the Thornthwaite Method . We are in the process of writing an xls tool to semi-automate these; please feel free request a draft copy, or to contribute your own.

Step 1. Calculate the monthly heat index (i): $i=\left({\frac {T}{5}}\right)^{1.514}$ where: T = mean monthly temperature.

Step 2. Calculate the annual heat index (I): $I=\sum _{i=1}^{12}i$

Step 3. Calculate an uncorrected Potential Evapotranspiration (PET_uncorrected): $PET_{uncorrected}=16\cdot \left({\frac {10\cdot T}{I}}\right)^{\alpha }$

where: α = 6.75 x 10^-7 I³ - 7.71 x 10^-5 I²+ 0.0179 I + 0.49

Step 4. A monthly correction is then applied to account for varying daylight hours and number of days in a month, to find the corrected potential evapotranspiration (PET): $PET=PET_{uncorrected}\cdot {\frac {N}{12}}\cdot {\frac {daylight\ hours}{30}}$

Example

For the town of Richmond Hill (Lat = 43.87)
For monthly calculations, data can be found in Environment Canada Climate Normals

	Jan	Feb	Mar	Apr	May	June	July	Aug	Sept	Oct	Nov	Dec
Declination (rad)	- 0.372	- 0.232	- 0.035	0.171	0.330	0.407	0.372	0.239	0.052	- 0.157	- 0.325	- 0.407
Day length (hr)	9	10	12	13	15	15	15	14	12	11	9	9
Temperature (°C)	- 6.20	- 4.90	- 0.30	6.90	13.30	18.70	21.40	20.30	15.90	9.10	3.10	- 2.70
Monthly heat index, i	0.00	0.00	0.00	1.63	4.40	7.37	9.04	8.34	5.76	2.48	0.48	0.00
PET (mm, uncorrected)	0.00	0.00	0.00	29.91	62.44	91.50	106.44	100.33	76.28	40.80	12.19	0.00
days in month	31	28	31	30	31	30	31	31	30	31	30	31
Corrected PET (mm)	0.0	0.0	0.0	33.1	78.3	116.4	136.9	119.3	78.7	38.1	9.6	0.0

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The accounting of inflow and outflow of water in a system according to the components of the hydrologic cycle.

The quantity of water transpired (given off). Retained in plant tissues, and evaporated from plant tissues and surrounding soil surfaces. Quantitatively it is usually expressed in terms of depth of water per unit area during a specified period. e.g. mm/day

The combined loss of water to the atmosphere from land and water surfaces by evaporation and from plants by transpiration.

The quantity of water transpired (given off). Retained in plant tissues, and evaporated from plant tissues and surrounding soil surfaces. Quantitatively it is usually expressed in terms of depth of water per unit area during a specified period. e.g. mm/day

The combined loss of water to the atmosphere from land and water surfaces by evaporation and from plants by transpiration.