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An Assessment of Potential
Evapotranspiration
for the Northern Lake States
Mark A. White and George E. Host,
Natural Resources Research Institute
University of Minnesota
Duluth, MN 55811
Potential Evapotranspiration
(PET) is the amount of water that could be evaporated from land, water, and
plant surfaces if soil water were in unlimited supply. PET calculations are
based on standard weather station data (or in our case, interpolated climatic
data from our previous study), and correlate well with the distribution of
forest types, and, to some degree, the susceptibility of the landscape to
fire.
We calculated PET for Minnesota,
Wisconsin and Michigan using the Thornthwaite water balance method at a
resolution of 1 kilometer (Thornthwaite 1948).
The Thornthwaite method is based on an empirical relationship between
potential evapotranspiration and mean air temperature.
While this method is not the most accurate, and may lack theoretical
basis, it can provide reasonably accurate estimates of potential
evapotranspiration (Palmer and Havens 1958).
Potential evapotranspiration can be calculated using
the Thornthwaite water balance method using the following formula.
E= 1.6 (10T/I)a
Where:
E= monthly potential
evapotranspiration (cm).
T= mean monthly temperature
(C).
I= a heat index for a given area which is the sum of 12 monthly index values
i. i
is derived from mean monthly temperatures using the following formula:
i= (T/5)1.514
a= an empirically derived exponent
which is a function of I, a
= 6.75*10-7I3
– 7.71*10-5I2
+ 1.79* 10-2I
+ 0.49
We applied this formula to
mean monthly temperature data with a grid cell resolution of approximately 1 km2.
Mean monthly temperatures were calculated by averaging mean monthly
minimum and maximum temperatures. Climate
data used in this analysis was acquired from ZedX, Inc. Temperature data were
derived from 30 year (1961-1990) climatological summaries published by the
National Climatic Data Center. Climate
station data were interpolated at a 1km grid cell resolution using a multiple
regression model based on latitude, longitude and elevation (ZedX 1995).
PET was calculated for April through October, and as
mean PET for the growing season months (May through September).
Latitudinal Scaling of PET Values
PET values were scaled on a latitudinal gradient based in
mean duration of sunlight in 12-hour units.
We created a grid encompassing the study region, which ranged from 40
degrees north to 50 degrees north latitude and from 78 degrees west to 99
degrees west longitude. Sunlight duration was scaled in 0.2 degree latitude
increments. Values were assigned to
each cell assuming a linear trend from south to north.
For example, values from April ranged from 1.11 at 40
degrees north, to 1.15 at 50 degrees north latitude. Values increased from the minimum, (1.11) at a rate of .0008,
for every 0.2 degrees of latitude. Raw
monthly PET values were multiplied by the latitudinal day length scalar to yield
adjusted PET values.
PET maps
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| 30 year mean June PET |
30 year mean August PET |
30 year mean Growing Season PET |
Potential Evaporation Minus Precipitation
PET – P (precipitation) can be calculated to
estimate monthly or seasonal water balance.
Positive values indicate that PET exceeds precipitation, negative values
show moisture surplus. PET-P was calculated for April through October and as mean
PET-P for the growing season months (May through September).|
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| 30 year mean May PET-P |
30 year mean June PET-P |
30 year mean August PET-P |
Uses
Given the need for need for regional level planning across ownership’s,
databases such as PET which reveal fundamental properties of landscape and
ecosystems will become increasingly useful.
PET
and PET-P data for the Lake States will be a useful resource for analysis of
large-scale biophysical phenomena in this region.
Since soil moisture often has a strong influence on the distribution of
plant and animal species, on the productivity of ecosystems, and on disturbance
regimes, coarse-scale PET data will allow for regional analysis of these
important landscape and ecosystem characteristics.
Caveats
The input data used to create PET values for the Lake States does have
distinct limitations that should be considered when using this data.
The climate variables were interpolated from climatological summaries
from weather station data. The
distribution of weather stations probably does not represent the variability of
the landscape, as many parts of the landscape are undersampled. In
addition, all modeled data has inherent levels of error.
Thus the accuracy of this data is likely variable across the region,
particularly at fine spatial scales, Interpretations
based on these analysis should be restricted to regional scale assessments.
Literature Cited
Palmer, W. C.,
and A. V. Havens. 1958.
A graphical technique for determining evapotranspiration by the
Thornthwaite method. Monthly
Weather Review 86:123-128.
Thornthwaite, C.
W. 1948. An approach toward a rational classification of climate.
Geographic Review 38:55-94
ZedX.
1995. Database description:
Minnesota, Michigan, and Wisconsin. Hi
Rez Data Climatological series, ZedX, Boalsburg PA, USA.
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