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103
CALIBRATING SATELLITE-BASED VEGETATION INDICES TO
ESTIMATE EVAPOTRANSPIRATION AND CROP COEFFICIENTS
Masahiro Tasumi1
Richard G. Allen2
Ricardo Trezza3
ABSTRACT
This paper presents a procedure to estimate actual evapotranspiration (ET) using a
satellite-derived vegetation index. Actual ET is computed in a traditional manner
using the crop coefficient (Kc) and reference ET (ETref) procedure (i.e., ET = Kc
x ETref) with Kc estimated from the satellite-based NDVI. This study calibrated
relationships between Kc and NDVI using satellite-based ET determined by
surface energy balance. This unique approach enables calibration of the Kc vs
NDVI equations using large numbers of sampled fields (in this case, more than
3000). Thus the calibration represents a regional average Kc estimate. The study
was conducted for alfalfa, beans, sugar beet, corn, potatoes, and small grain crops,
which are the major crops in southern Idaho. Estimation accuracy for ET was
statistically evaluated. Average error of seasonal ET was within 5 percent of the
energy balance (EB) determined ET for most crop types. Error in seasonal ET
from individual fields is expected to be within 10 percent. NDVI based ET was
compared with lysimeter measurements of ET from grass and sugar beets. The
seasonal error of the NDVI based method was only 2 percent for grass and 6
percent for the sugar beets, as compared to lysimeter measurements. Statistical
accuracy assessments suggest that NDVI based ET estimation can be a robust,
simple and inexpensive tool to estimate ET from irrigated agricultural crops with
reasonable good accuracy.
INTRODUCTION
Evapotranspiration (ET) is the major consumptive use of irrigation water and thus,
spatial and temporal quantification of ET is important in agricultural water
management, especially in areas experiencing scarcity in total fresh water
resources. ET has traditionally been estimated at regional and field-scales using
the crop coefficient (Kc) method (ASCE - EWRI 2005):
1 Associate Professor, University of Miyazaki, 1-1, Gakuen Kibanadai-Nishi,
Miyazaki-shi, Miyazaki 889-2192, JAPAN; tasumi@kimberly.uidaho.edu.
2 Professor, University of Idaho, 3793N, 3600E, Kimberly ID 83341;
rallen@kimberly.uidaho.edu.
3 Visiting Associate Professor, University of Idaho, 3793N, 3600E, Kimberly ID
83341; rtrezza@kimberly.uidaho.edu.
104 Ground Water and Surface Water Under Stress
refc ETKET ×= (1)
where ETref is reference ET (alfalfa (ETr) or clipped grass (ETo) reference).
Using recently developed techniques, accurate ET estimation, spatially and
temporally, is possible via satellite-based energy balance (e.g. Anderson et al.,
1997; Bastiaanssen et al., 1998; Kustas and Norman, 2000; Allen et al., 2007a).
However, this approach requires surface temperature imagery along with a
relatively high knowledge level of near-surface energy exchange physics and
aerodynamics, which prevents many general water resources professionals from
applying the technique. The Kc-based ET estimation method is often preferred for
operational applications because of its simplicity (Duchemin et al., 2005). Simpler
ET estimation approaches based on correlation of crop ET and NDVI from
satellite images have been investigated by Allen et al., (2003), Hunsaker (2003)
and Duchemin et al., (2005), where NDVI is the normalized difference vegetation
index and is computed from red and near infrared bands of the satellite. While this
approach is simple, accuracy of ET estimation can be limited because vegetation
indices do not provide information on the soil evaporation portion of ET in
irrigated agriculture. Earlier work on Kc vs. NDVI based on aerial imagery
included that by Neale et al. (1989) and Bausch et al. (1989).
In this paper, we attempt to determine mean Kc by NDVI, where the NDVI- Kc
relationship is calibrated using satellite based energy balance. This approach
requires a one-time application of the energy balance for each area of interest to
calibrate the local Kc vs NDVI function. Once the Kc is locally calibrated by
NDVI, ET for the following years can be estimated with reasonable accuracy as:
()
ref
ETbNDVIaET ×+⋅= (2)
where a and b are regional constants calibrated by surface energy balance, NDVI
is at-satellite or at-surface NDVI from satellite image, and ETref is alfalfa or grass
reference ET calculated by weather data. Other vegetation indices besides NDVI,
for example SAVI, have been explored for estimating Kc. However, it appears
that NDVI exhibits a desirable tendency to ‘saturate’ at about the same leaf area
index as does Kc, thus reaching an upper limit at the same time as Kc (Allen et al.,
2007c). The ‘at-satellite’ NDVI (computed with no atmospheric correction to
bands) appears to be as consistent in estimating Kc as an at-surface NDVI (Allen
et al., 2007c). Satellite based ET maps provide a robust means to analyze Kc,
because the method can cover large numbers of sampled fields (Tasumi et al.,
2005, Tasumi and Allen, 2006).
Calibrating Satellite-Based Vegetation Indices 105
METHODOLOGY
ET images and related field data produced by surface energy balance by Tasumi et
al. (2005) and Tasumi and Allen (2006) were used to evaluate relationships
between alfalfa-reference Kc (Kcr) and at-satellite NDVI (NDVIas). The study
area is the Magic Valley in Idaho, a large irrigated agricultural area in
south-central Idaho having a semi-arid climate (Figure 1). The major crops of the
area are alfalfa, dry, edible beans, field and sweet corn, small grains, peas,
potatoes and sugar beets. Typical field sizes in the region are 400 m by 400 m to
800 m by 800 m, thus, ET from individual fields is amenable to sampling from
Landsat images having 30 m by 30 m spatial resolution.
During previous studies, twelve Landsat images from March through October,
2000, were processed for the study area using the METRIC model to estimate ET
and Kcr. The METRIC program and applications are described in Allen et al,
(2007a, b). METRIC Kcr was developed for each Landsat image on a 16 to 32
day frequency. Kcr values were interpolated between satellite-image dates using a
spline function (Excel Cubic Spline 1.01 by SRS1 Software) applied pixel by
pixel. A crop-type classification was conducted for the same year using the
Landsat images and independent ground truth information. In total 3420 fields
were sampled that included eight crop types (Table 1).
Figure 2 shows the NDVIas vs. Kcr relationships from March to October. NDVIas
vs. Kcr relationships tended to be linear and converged after NDVI > 0.7 (i.e.
maximum cover season). The general relationships (solid lines) in Figure 2 were
drawn past the point of NDVIas vs Kcr convergence, and the intercept was
determined so that the average estimation error is zero when ET is estimated using
equation 2. Using the general calibration developed in Figure 2, equation 2 can be
reexpressed as:
()
ras ETNDVIET ×+⋅= 04.018.1 (3)
106 Ground Water and Surface Water Under Stress
02550
km
TwinFalls weather station
42.66oN/114.45oW (Elev.1195m)
Figure 1. Agricultural Study Area in Magic Valley, Idaho (Circled by Dotted Line)
and Location of Weather Station Used to Calculate Reference ET Used as a Basis
of the Surface Energy Balance and Derivation of Crop Coefficients
Table 1. Investigated Crops and Numbers of Sampled Fields.
Crop type Alfalfa Bean Corn Potato(S)
*
Potato(L)
*
Sugar
Beet
Spring
Grain
Winter
Grain Total
Sample field
number 325 432 451 396 221 495 536 564 3420
* Potato(S) and Potato(L) are potato crops having short (S) and long (L) full cover periods respectively.
Calibrating Satellite-Based Vegetation Indices 107
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1
NDVI
as
K
cmr
Alfalfa Beans Beet Corn Potato-S
Potato-L Sgrain Wgrain
K
cr
= 1.18 NDVI
as
+ 0.04
A
verage line
Figure 2. Mean Kcr vs. NDVIas by Crop Type from March to October (5 day
average).
RESULTS AND DISCUSSION
ET was estimated using equation 3 for the twelve Landsat images of southern
Idaho, 2000. Figure 3 shows the result image for 7/5/2000. Figure 4 shows daily
ET averaged over multiple fields of sugar beets where ET was estimated using
NDVIas and Kcr. The ET estimated from NDVIas corresponds well with
METRIC results for all evaluated crops.
Seasonal ET was calculated for average field conditions (i.e. using NDVI
averaged over all sampled fields having the same crop type) by employing a
spline curve to interpolate daily between average NDVI from each Landsat date.
Daily ET was calculated by multiplying Kcr computed for each day of the season
via the spline by alfalfa-reference ET (ETr) for that day. Seasonal ET was then
calculated by summing daily values across the growing season, which in this case
was defined as March 15 – October 17 for all crops (these were the first and last
dates for Landsat coverage for 2000).
Mean differences between seasonal ET estimated by NDVI and seasonal ET
determined directly from METRIC for the same groups of fields are compared in
Table 2. Results indicate that, in general, equation 3 estimates ET with reasonable
accuracy for the primary crops grown in southcentral Idaho, with average error
108 Ground Water and Surface Water Under Stress
within 5 percent in most crop types. Also, error of seasonal ET estimation is
within 10 percent for most individual fields as compared to ET derived directly
from the METRIC energy balance.
ET (mm/d)
0
2
4
6
8
10
Figure 3. ET Estimated by NDVIas on 7/5/2000, (Landsat 5, path 40, row 30).
S.Beet
0.0
2.0
4.0
6.0
8.0
10.0
3/1
4/1
5/1
6/1
7/1
8/1
9/1
10/1
11/1
ET (mm/day)
Figure 4. Comparisons Between Daily ET (5-day Mov. Avg.) Determined by
METRIC and ET Determined from the General Kcr vs. NDVIas Relationship,
Averaged Over All Sugar Beet Sampled Fields
Calibrating Satellite-Based Vegetation Indices 109
Table 2. METRIC Seasonal ET (March 15-October 17) and Error in Seasonal ET
Estimated Using NDVI (Averaged Over Multiple Fields of the Same Crop), and
Estimation Error for Individual Fields for year 2000
Crops Alfalfa Beans Beet Corn Potato(S) Potato(L) S.Grain W.Grain
METRIC ET
(mm/season) 1001 479 904 846 733 846 720 837
Average
error* (%) 5 7 -2 -7 1 -2 -2 -2
Error range*
(%, 1σ)+1 to +8 0 to +14 -7 to +1 -12 to -2 -3 to +6 -6 to +3 -7 to +3 -8 to +3
* Positive values indicate over estimation by the NDVI-based method. Error range represents
differences between seasonal METRIC ET and ET by Eq. 3 for individual fields.
Performance of NDVI based ET estimation was tested at two fields equipped with
precision weighing lysimeters near Kimberly, Idaho. The lysimeter ET data were
collected by Dr. J.L.Wright at the USDA Agricultural Research Service facility
during the 1970’s and 1980’s (Wright, 1982; Wright, 1991). Daily and seasonal
NDVI based ET was estimated for the Lysimeter field from eight clear-sky
Landsat 5 images in 1989 (4/18, 5/4, 5/20, 6/5, 6/21, 7/7, 7/23 and 9/25) using
equation 3. NDVIas values used in this analysis were averages taken from three
pixels near the center of the grassed lysimeter field (i.e. for the center 120m by
30m area), and from four pixels near the center of the sugar beet lysimeter field
(i.e. for the center 60m by 60m area). NDVIas computed for each satellite image
date was then interpolated for days between dates using a cubic spline function.
The NDVI-based ET estimations corresponded relatively well with the actual
lysimeter measurements for both the grass and sugar beet fields. The standard
error of daily ET estimates as compared to lysimeter measurements was 0.6 mm
d-1 and 1.3 mm d-1 for grass and sugar beets, respectively. On a seasonal basis,
the NDVIas-based ET estimates using the general equation developed for
southern Idaho using year 2000 date (i.e. equation 3) estimated seasonal ET
relatively accurately for the two lysimeter fields during 1989. The estimation error
for seasonal ET was 2 percent for grass and 6 percent for sugar beets, both of
which were underestimated. The expected error range for grass is unknown, but
the observed error for sugar beet was within the expected error range determined
in Table 2 (i.e. from 7 percent underestimation to 1 percent overestimation). This
comparison study demonstrates a good potential for using NDVI based ET
estimates, even for applications to individual fields.
110 Ground Water and Surface Water Under Stress
SUMMARY AND CONCLUSIONS
This study developed a simple vegetation index-based equation to estimate total
ET via satellite. The empirical NDVI based Kc relationship was calibrated using
ET information developed by satellite-based energy balance, so that the
calibration represents mean Kc vs. NDVI relationships and conditions over large
number of fields (3420 individual agricultural fields). Accuracy of ET estimated
using the calibrations is expected to have similar accuracy, when averaged over
enough fields to average out differences in ET caused by individual irrigation
events, to the original ET maps developed from METRIC.
Alfalfa, beans, sugar beets, corn, two variety groups of potatoes, and spring and
winter grains in south-central Idaho were evaluated. Results indicated that one
single equation was sufficient to estimate ET for all of the investigated crop types.
This means that crop classification is not required to estimate ET via the
NDVI-based method, which is a strong advantage and permits low expense and
rapid application.
Average error of seasonal ET was within +/-5 percent for most crop types. Error
in seasonal ET estimated for any individual field lies within 10 percent in most
cases. In the comparison with Lysimeter-measured ET, the seasonal error for the
NDVI based method was only 2 percent for grass, and 6 percent for sugar beets.
The statistical assessment of accuracy, including comparisons with actual
lysimeter measurements, suggests that NDVI based ET estimation may represent
a dependable tool to estimate ET over large areas. Achieving the accuracy levels
reported herein using the traditional ET estimation methods without the aid of
satellites is difficult. The high accuracy reported herein was achieved partly
because the NDVI based ET equation was calibrated to the particular region using
ET derived using a reliable energy balance (METRIC). The NDVI based ET
approach is empirically based, thus, specific calibration may be necessary for
other regions.
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Calibrating Satellite-Based Vegetation Indices 111
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