Gross Evaporation Calculations and Database
Presentation at PPWB Prairie Hydrology Workshop
January 29, 2013
Overview
•
•
•
•
Why is gross evaporation data required by the PPWB?
How is Gross Evaporation Calculated?
The Meyer Formula
The Future?
Why is gross evaporation data required by the PPWB?
•
•
•
Net evaporative losses from reservoirs are considered a
consumptive use in calculating net depletion to natural flow for
apportionment monitoring purposes
Various methods are currently used:
• Meyer Formula – Lake Diefenbaker, Reid Lake,
Tobin Lake, St. Mary Reservoir, Waterton Reservoir,
Moosomin Reservoir, Pipestone Lake
• Morton’s Model – Glennifer Lake
• Penman’s (recently replaced Evaporation Pan station) – Lodge,
Middle and Battle Creek basins
Various attempts over the years to assess the most appropriate
methodology for computing gross evaporation for operational
needs
• Discussion in PPWB Report No. 162 (Hopkinson, 2003)
How is Gross Evaporation Calculated?
•
•
•
•
•
Mass Transfer
Energy Budget
Water Budget
Empirical Formulae (Meyer, Penman, etc.)
Direct Measurement (pan)
Use of the Meyer Formula on the Canadian Prairies
•
•
•
•
•
1962 study by McKay and Stichling on Weyburn Reservoir compared
seven methods for evaporation determination including water
budget, energy budget, pan and empirical formulae
Recommended the Meyer Formula for operational purposes
because of data availability and simplicity
PPWB used the Meyer Formula to estimate gross evaporation for
the period 1921 to 1950 at 15 locations (PPWB Report No. 5, 1952)
SNBB used the Meyer Formula to calculate gross evaporation for the
period 1912 to 1967 at 17 locations
PFRA refined the Meyer Formula for Prairie conditions and published
updated data (Hydrology Reports #113, 121, 133 and 143)
•
Data and maps are widely distributed and are used by federal and provincial
governments, consultants and academia in the Canadian Prairies
Meyer Formula
Requires only monthly:
•
Air Temperature
•
Wind Speed
•
Dew Point Temperature or Relative Humidity
Water temperature data is estimated from air temperature as:
TW = 0.60TA + B
where: TW =
monthly mean surface water temperature, in oC,
TA = monthly mean air temperature, in oC, and
B =
intercept value corresponding to the month under
consideration and location
Meyer Formula
EG = CK(Vw - Va)(1 + 6.2139x10-2W)(1 + 3.28084x10-5A) .............................
where:
EG =
C =
K =
Vw =
Va =
W
=
A
=
(1)
monthly gross evaporation, in millimetres, at the meteorological station,
coefficient of 11 if saturated vapour pressure is based on two observations of relative
humidity per day; a coefficient of 10.1 if saturated vapour pressure is based on either
two, four or 24 observations of dew point temperature per day; and a coefficient of 10.2
if saturated vapour pressure is based on three observations of dew point temperature
per day,
metric conversion factor of 0.750062,
saturated vapour pressure, in millibars, corresponding to the estimated monthly mean
water temperature at the surface of a hypothetical open body of water at the station
site,
actual monthly mean vapour pressure, in millibars, in the atmosphere at 7.62 metres
above the ground level at the station,
monthly mean wind speed, in kilometres per hour, at 7.62 metres above the ground
level at the station, and
elevation, in metres above mean sea level, of ground level at the station.
GROSS
EVAPORATION
(MILLIMETRES)
--JAN
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
FEB
WINNIPEG
MAR
APR
MAY
JUNE
JULY
AUG
SEPT
OCT
NOV
DEC
TOTAL
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
31.4
41.4
44.6
45.0
43.8
41.2
50.8
52.9
22.5
40.6
37.7
37.8
45.3
41.3
47.8
45.1
59.9
38.5
47.6
38.5
54.1
39.3
52.3
58.4
43.0
51.8
42.8
56.9
53.5
50.1
33.7
42.1
61.6
54.5
41.9
64.0
44.7
38.9
48.4
42.3
50.1
76.8
54.7
48.1
52.2
45.5
46.5
71.8
57.9
47.3
52.3
42.8
49.3
54.8
47.9
49.8
47.1
59.1
56.7
43.7
50.2
43.5
62.5
39.4
49.9
56.1
93.0
62.1
42.5
81.4
64.9
63.3
54.9
70.1
55.5
51.9
63.5
78.1
54.3
56.5
63.0
47.8
56.0
69.4
44.5
40.7
45.4
65.4
66.7
68.9
52.2
54.2
77.0
56.2
53.8
58.4
72.4
65.4
44.1
76.8
120.5
132.8
130.8
150.9
144.9
118.9
163.2
127.7
101.1
120.9
129.4
116.5
144.7
135.9
136.6
153.3
127.3
130.6
140.4
119.3
126.3
159.5
144.9
170.3
140.5
151.3
144.2
134.2
137.5
134.1
124.5
123.6
127.3
119.5
115.9
136.9
126.5
138.4
131.8
101.5
156.2
143.3
124.9
131.7
147.6
126.8
164.3
173.2
141.2
152.1
159.5
119.1
129.3
156.1
147.7
133.4
140.1
135.8
131.5
124.5
147.9
136.7
146.0
112.9
131.7
146.9
167.5
166.8
118.0
192.2
156.9
148.3
143.6
148.3
131.1
126.5
151.4
158.5
160.5
135.4
133.7
160.9
139.7
144.8
124.1
120.1
140.8
120.9
134.7
138.2
129.3
158.5
155.2
123.4
120.8
120.0
133.2
134.9
132.2
124.5
110.6
175.4
184.7
188.4
149.3
120.7
179.5
159.0
95.0
127.7
141.1
158.8
159.2
162.7
129.0
168.6
153.0
127.7
164.9
134.4
160.5
133.1
184.5
159.5
157.9
165.0
168.5
172.5
140.9
156.0
124.8
143.7
128.0
118.7
145.6
157.6
148.3
147.1
158.1
156.2
155.3
163.7
134.9
144.7
143.6
174.8
141.8
179.6
158.7
166.4
226.2
151.1
146.8
153.4
197.5
163.9
171.5
171.8
148.2
153.2
128.8
169.3
147.4
185.7
132.9
155.9
144.6
153.8
171.4
194.3
151.3
164.4
149.8
134.1
143.2
150.4
152.5
190.4
142.8
122.6
157.0
141.2
161.5
141.7
164.9
163.1
175.3
114.3
133.7
135.0
133.9
150.3
127.6
155.7
125.2
151.0
132.3
141.6
145.9
109.4
141.8
145.0
164.6
172.8
172.2
132.0
161.7
157.1
147.6
168.2
151.6
160.7
149.6
180.3
180.4
173.7
145.7
118.9
181.0
142.3
172.8
158.2
184.7
193.8
151.9
185.8
175.0
153.2
205.1
170.8
143.0
159.2
160.1
167.9
151.7
175.6
161.8
152.7
175.2
142.7
180.3
164.5
165.8
145.5
167.4
142.7
171.1
163.9
182.7
217.2
181.8
159.7
174.0
161.7
164.3
158.4
176.1
169.6
146.3
180.5
157.0
151.7
161.9
208.0
173.0
197.5
170.8
154.6
179.3
202.8
171.8
162.7
169.6
155.4
154.4
140.5
135.8
184.5
156.0
149.0
168.3
134.0
135.4
143.0
164.5
143.9
153.3
140.7
141.3
142.2
138.0
165.9
153.8
142.0
153.1
195.7
160.1
154.2
144.3
141.9
104.0
122.3
119.1
150.8
160.8
123.1
156.4
136.8
107.9
137.0
126.9
109.2
159.7
157.6
149.8
146.9
162.1
125.3
186.2
130.9
161.4
157.7
191.0
175.2
159.8
168.4
169.3
193.2
159.1
168.0
143.3
143.1
155.8
157.9
161.7
172.7
137.0
145.9
159.7
143.5
142.1
167.1
156.7
134.7
190.7
149.5
155.1
170.2
176.3
174.1
216.9
150.8
157.2
191.5
157.1
154.7
181.7
139.6
163.0
187.5
166.9
150.8
144.6
163.7
137.3
179.0
143.6
163.5
150.7
135.2
148.1
163.9
174.6
175.4
127.8
153.2
141.3
182.8
164.5
184.4
194.8
146.7
128.6
132.2
167.2
138.9
146.9
156.0
144.0
156.8
155.5
143.6
187.6
128.3
154.7
185.8
165.7
164.1
118.1
130.9
81.7
82.8
69.9
96.7
76.5
104.3
71.3
92.2
91.9
78.6
55.9
68.6
119.3
101.3
81.8
100.1
97.2
96.0
104.5
101.6
80.0
118.2
110.6
105.0
104.2
109.6
103.2
133.3
101.4
105.0
94.8
106.3
120.3
79.6
103.7
115.9
111.6
134.6
110.5
98.7
91.3
125.5
101.0
96.9
122.8
104.6
100.6
123.0
104.3
122.5
108.3
119.3
119.0
129.6
99.4
120.8
158.4
103.6
96.7
103.5
114.4
117.1
111.9
105.4
108.3
144.0
91.2
117.7
114.5
107.0
112.4
124.2
118.4
104.1
94.3
90.8
100.5
119.8
120.6
118.8
134.6
115.3
103.4
94.1
101.6
93.8
115.9
107.2
95.9
105.7
106.6
101.1
103.3
81.1
104.4
112.1
112.5
95.3
96.1
93.6
26.4
43.9
34.7
20.2
43.3
43.6
43.2
44.9
45.2
48.2
19.1
35.2
54.8
49.9
43.6
43.4
41.1
48.2
41.2
40.3
37.6
47.3
50.7
48.0
59.6
62.1
53.6
62.4
50.1
47.9
46.7
56.2
64.9
47.5
51.5
51.3
55.2
66.6
52.3
49.4
46.1
64.6
50.6
54.7
58.4
59.0
51.1
54.3
44.3
67.1
63.8
49.1
71.5
70.9
64.0
53.2
49.7
51.0
44.6
57.5
43.9
55.8
44.7
63.6
54.9
67.7
65.0
56.1
57.0
54.6
58.3
43.3
46.7
46.3
56.2
50.2
52.9
57.4
59.0
64.9
60.0
55.1
57.5
47.6
39.9
55.4
50.1
40.2
54.5
61.6
64.5
51.3
49.9
46.5
41.9
60.9
43.9
48.6
35.7
52
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
617
744
749
825
791
684
826
770
611
721
662
687
833
829
769
831
786
685
866
707
793
813
919
910
817
894
857
906
848
832
711
774
818
746
772
874
785
824
836
734
821
905
789
756
883
803
830
936
866
947
1009
792
847
918
878
834
925
830
787
850
809
825
819
879
788
947
876
874
833
967
864
870
858
834
762
763
798
972
858
832
911
801
782
773
807
756
828
745
771
808
780
825
854
733
754
884
820
804
716
729
MIN
MAX
MEAN
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
22.5
93.0
52.5
101.1
192.2
137.9
95.0
226.2
152.1
118.9
217.2
162.1
104.0
216.9
155.1
55.9
158.4
104.8
19.1
71.5
51.1
0.0
0.0
0.0
0.0
0.0
0.0
611
1009
816
mean 1981-2010
0.0
0.0
0.0
59.7
138.3
145.4
153.2
155.4
105.9
51.7
0.0
0.0
810
Mean Annual Gross Evaporation for the Standard 30-Year Period 1971-2000
at Selected Locations in the Canadian Prairies
LOCATION
1971-2000
MEAN ANNUAL
GROSS
EVAPORATION
(mm)
BRITISH COLUMBIA
Fort Nelson
Fort St. John
419
805
ALBERTA
Calgary
Cold Lake
Coronation
Edmonton International
Edmonton Municipal
Edson
Fort McMurray
Grande Prairie
High Level
Jasper
Lethbridge
Lloydminster*
Medicine Hat
Peace River
Pincher Creek
Red Deer
Rocky Mountain House
Slave Lake*
Whitecourt
898
733
863
734
828
628
458
786
415
657
1071
787
1014
778
1083
765
618
712
619
SASKATCHEWAN
Broadview
Buffalo Narrows
817
452
LOCATION
Cree Lake*
Estevan
Kindersley
La Ronge
Meadow Lake
Moose Jaw
Nipawin*
North Battleford
Prince Albert
Regina
Saskatoon
Swift Current
Wynyard
Yorkton
1971-2000
MEAN ANNUAL
GROSS
EVAPORATION
(mm)
453
946
947
465
699
983
763
852
769
989
913
1026
828
810
MANITOBA
Brandon
Churchill
Dauphin
Flin Flon
Gillam
Gimli
Island Lake
Lynn Lake
Norway House
Pilot Mound*
Portage La Prairie
The Pas
Thompson
Winnipeg
791
440
803
466
475
660
433
480
444
767
790
487
432
834
What Does the Future Hold?
• Report with monthly gross evaporation data
updated to 2010 and new 30-year average maps
(1980 to 2010) for gross evaporation and
precipitation will be completed soon.
• ??????? – PFRA no longer exists, and there is no
mandate in the current organization to continue
gross evaporation updates.