Difference between revisions of "Evapotranspiration"

Revision as of 21:31, 24 January 2018

Evaporation[edit]

Evaporation is the phase transfer of water into atmospheric vapour. It occurs from all wet surfaces, including the leaves of plants and damp soil. The climatic factors which influence the rate of evaporation include net radiation (i.e. sunshine), wind speed, and vapour pressure or relative humidity.

Transpiration[edit]

This is process of water being removed from the soil and being vaporised into the atmosphere by plants. Upwards flow is created within the plant tissues via osmotic potential. Water evaporates from each leaf's stomata, so that the sap becomes more concentrated. Water is drawn upwards through the stems to equalise this pressure.

Transpiration is typically able to remove water from deeper within the soil profile than evaporation. The depth will depend upon the plants root structure and depth, and its inherent transpiration rate.

Calculation[edit]

Thornthwaite Mather method[edit]

The Thornthwaite Mather method of calculating water balance^[1] 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.^[2]. 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 How to contribute.

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: $\alpha =6.75\times 10^{-7}I^{3}-7.71\times 10^{-5}I^{2}+0.0179I+0.49$

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[edit]

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

↑ Thornthwaite, C. W., and Mather, J. R., Instructions and Tables for Computing Potential Evapotranspiration and the Water Balance, Drexel Institute of Technology, Laboratory of Climatology, 1957. Thornthwaite1957
↑ Sellinger,C.E. Computer Program for Estimating Evapotranspiration using the Thornthwaite Method NOAA Technical Memorandum ERL GLERL-101, Great Lakes Environmental Research Laboratory 1996 [1] Accessed 8 Jan 2018

[1] Thornthwaite, C. W., and Mather, J. R., Instructions and Tables for Computing Potential Evapotranspiration and the Water Balance, Drexel Institute of Technology, Laboratory of Climatology, 1957. Thornthwaite1957

[2] Sellinger,C.E. Computer Program for Estimating Evapotranspiration using the Thornthwaite Method NOAA Technical Memorandum ERL GLERL-101, Great Lakes Environmental Research Laboratory 1996 [1] Accessed 8 Jan 2018

[1]

[2]

@@ Line 15: / Line 15: @@
 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 [[How to contribute]].
-'''Step 1.''' Calculate the monthly heat index ('i'):
+'''Step 1.''' Calculate the monthly heat index (''i''):
 <math>i=\left ( \frac{T}{5} \right )^{1.514}</math>
 where:
-'T' = mean monthly temperature.
+''T'' = mean monthly temperature.
-'''Step 2.''' Calculate the annual heat index ('I'):
+'''Step 2.''' Calculate the annual heat index (''I''):
 <math>I=\sum_{i=1}^{12}i</math>
-'''Step 3.''' Calculate an uncorrected Potential Evapotranspiration ('PET<sub>uncorrected</sub>'):
+'''Step 3.''' Calculate an uncorrected Potential Evapotranspiration (''PET<sub>uncorrected</sub>''):
 <math>PET_{uncorrected}=16\cdot \left ( \frac{10\cdot T}{I} \right )^{\alpha }</math>
@@ Line 29: / Line 29: @@
 <math>\alpha=6.75\times10^{-7}I^{3}-7.71\times10^{-5}I^{2}+0.0179I+0.49</math>
-'''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'):
+'''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''):
 <math>PET=PET_{uncorrected}\cdot\frac{N}{12}\cdot\frac{daylight\ hours}{30}</math>