Evapotranspiration estimation using energy balance algorithm for pyramid-based spatially enhanced thermal infrared image.
Gowri, V. ; Thirumalaivasan, D.
Introduction
Evapotranspiration (ET) is the combination of evaporation from the
soil surface and transpiration from vegetation. Conventional methods of
ET estimation are based on point measurements, which could provide
accurate results over the areas surrounding instruments, but the results
are not applicable to large heterogeneous areas. With the advent of
satellite remote sensing various models concerning the derivation of
evapotranspiration using satellite data have been published [1,2,3,4],
which provides with spatial estimation of ET. Gowda [5] discusses remote
sensing based regional ET prediction algorithms and their limitations,
data needs and availability, knowledge gaps, and future opportunities
and challenges with respect to agriculture. Remote sensing based
Evapotranspiration is presently developed along two types of approach:
(a) land surface energy balance and (b) reflectance based crop
coefficient.
Remote sensing images exhibit usually either high spectral
resolution and low spatial resolution or low spectral resolution and
high spatial resolution. The spatial and temporal remote sensing data
from the existing set of earth observing satellite platform are not
sufficient enough to be used in the estimation of spatially distributed
ET. Evaporation is generally estimated by using thermal infrared data
acquired by satellite and ground based meteorological data as inputs
[1]. The coarse spatial resolution of thermal bands has caused the
current ET estimates of little use for analyzing its spatial
distribution.
However research opportunities exist to improve the spatial and
temporal resolution of ET developing algorithms to increase the spatial
resolution of reflectance and surface temperature data derived from
Landsat/ASTER/MODIS images using same/other-sensor high resolution
multi-spectral images [5]. Due to the tradeoff between spatial and
spectral resolution, spatial enhancement of coarser resolution data is
desirable [6]. One possible solution comes from the field of data
fusion.
Data fusion/merging techniques take advantage of the complementary
spatial/spectral resolution characteristics of imaging sensors to
spatially enhance the acquired images. Multi resolution techniques are
extremely attractive for image understanding since they provide a
thorough yet multi fold, description of the imaged scene. Wavelets,
subbands and Gaussian/Laplacian Pyramids are most suitable
representations to allow spatial analysis to be carried out on multiple
scales [7].
Some studies have been published where images acquired in thermal
infrared bands have been synthesized with a better spatial resolution
with a satisfactory quality by means of images acquired in the visible
range [8,9,10,11]. Data fusion based on multi resolution analysis,
requires a model to describe about how the spatial details of high
resolution image are to be injected into the coarse resolution image.
Goal of this work is to highlight the use of Enhanced Laplacian
Pyramids (ELP) as a multi resolution data processing technique for
spatial enhancement of thermal infrared image. The spatially enhanced
thermal band is subsequently utilized for determining evapotranspiration
by means of surface energy balance method.
Materials and Methods
Landsat-7 ETM+ imagery is used for the analysis. There are a total
of 8 spectral bands from 15 m (Panchromatic), 30 m (Visible and
Short-wave infrared) and 60 m (Thermal). A cloud free Landsat 7 ETM+
data (Path/Row 143/53) for the date 15 May 2001 is obtained from the
GLCF University of Maryland website
(http://glcfapp.umiacs.umd.edu:8080/esdi/) in GeoTIFF format and are in
the UTM Zone 44 N projection and WGS 84 datum. Fig 1 shows the study
area selected for this analysis. The image has been analysed for
determination of different components of surface energy balance.
[FIGURE 1 OMITTED]
Multiresolution Image Analysis
Data merging techniques have been designed not only to allow
integration of different information sources, but also to take advantage
of complementary spatial and spectral resolution characteristics [11].
The visible bands exhibit a high spatial resolution compared to the
multispectral observations of the same sensor. The goal is to obtain
fused bands as similar as possible to what the multispectral sensor
would image at the resolution of visible band. Data merging requires the
definition of a model describing, how the missing high pass details to
be injected into the resampled MS bands, is extracted from visible
bands. Since the high-pass filtering technique [12] fusion methods based
on injecting high frequency components into resampled versions of MS
data have been demonstrated a superior performance. The algorithm
proposed in the following work is Enhanced Laplacian Pyramid [13] which
is a variant of HPF. Aiazzi [7], reports about the pyramid-based
multisensor image data fusion of data from remote sensing images having
different ground resolutions. The Enhanced Laplacian Pyramid method is
adopted for this study and is described below.
Enhanced Laplacian Pyramids
The basis of the pyramid is the original image. Each level of the
pyramid is an approximation of the original image computed from the
original image. The Laplacian pyramid (LP) originally proposed in P. J.
Burt [14] is a band-pass image decomposition derived from the Gaussian
Pyramid (GP), which is a multi resolution image representation obtained
through a recursive reduction (low pass filtering and decimation) of the
image dataset.
Let [G.sub.o] (i, j) be the original gray-scale image, where i = 0,
..., M-1 and j = 0, ..., N-1, M = u x [2.sup.k], N = v x [2.sup.k]. The
GP is defined as [G.sub.k] (i,j) = [reduce.sub.2] [[G.sub.k-1]] (i, j) =
[Lr.summation over (m=-Lr)] [Lr.summation over (n=-Lr)]
r(m)r(n)[G.sub.k-1] (2i + m, 2j + n)
for k = 1, ..., K, i = 0, 1, ..., M/[2.sup.k]-1 and j = 0, 1, ...,
N/[2.sup.k]-1; in which k identifies the level of pyramid, K being the
top or base band approximation. Burts parametric kernel {r(m),m =
[-L.sub.r], ..., [L.sub.r]} ([L.sub.r] = 2) has been widely used [14,
13]. The 2D reduction low-pass filter stems from a linear symmetric 1-D
kernel, generally odd sized.
From the GP, the Enhanced LP (ELP) [13] is determined, for k =
0,.., k-1, as [L.sub.k] (i, j) = [G.sub.k] (i, j)-exp [and.sub.2]
[[G.sub.k+1]] (i, j) in which exp [and.sub.2] [[G.sub.k+1]] denotes the
(k+1)st GP level expanded by 2 to match the underlying kth level:
exp [and.sub.2] [[G.sub.k+1]] (i, j) = [Le.summation over (m=-Le)
(i + m)] [Le.summation over (n=-Le)] e(m)e(n)[G.sub.k+1] (i + m/2, j +
n/2)
for i = 0, ..., M/[2.sup.k] - 1, j = 0, ..., N/[2.sup.k] - 1, and k
= 0, ... K-1. the 2-D low-pass filter for expansion is given as the
outer product of a linear symmetric odd sized kernel {e(m), m =
[-L.sub.e], ..., [L.sub.e]}. Summation terms are taken to be null for
non-integer values of (i+m)/2 and (j+n)/2, corresponding to interleaving
zeros. The base band approximation is added to the band pass ELP ie.,
[L.sub.K] (m, n) [equivalent to] [G.sub.K] (m, n), to yield a complete
image description.
The detail is given as the difference between the original image
and an expanded version of the low pass approximation. The detail
injection model describes the relationship between the detail observed
in high resolution band and the ones that should appear in the enhanced
band [11]. The spectral distortion minimisation (SDM) model [15] is
adopted here to preserve the spectral information.
Algorithm for Evapotranspiration estimation
Remote sensing has long been recognized as the most feasible means
to provide spatially distributed regional ET information on the land
surfaces. There are many remote sensing algorithms for estimating the
energy balance fluxes on the surface, each algorithm has its own
advantages and disadvantages. The surface energy balance for land
(SEBAL) is used to estimate the evapotranspiration and other energy
balance terms. The processing of the SEBAL model has been done after the
standard method described in Bastiaanssen [1] to calculate energy
partitioning at the regional scale with an effort to use minimum ground
data.
In the SEBAL model, ETa is calculated from satellite images and
local weather station data using surface energy balance equation. Since
the satellite image provides information for the satellite overpassing
time only, the SEBAL computes an instantaneous ET flux for the image
time. The instantaneous ET flux is calculated for each pixel of the
image as a residual of the surface energy balance equation:
[lambda]E = [R.sub.n] - [G.sub.0] - H (1)
where; [lambda]E is the latent heat flux (measure of
evapotranspiration) in [Wm.sup.-2], [R.sub.n] is the net radiation flux
at the surface in [Wm.sup.-2], [G.sub.0] is the soil heat flux in
[Wm.sup.-2] and H is the sensible heat flux to the air in [Wm.sup.-2].
The net radiation flux at the surface (Rn) is the actual radiant
energy available at the surface. It is given by the surface radiation
balance equation:
[R.sub.n] = (1 - [alpha])[R.sub.S] [down arrow] + [R.sub.L] [down
arrow] - [R.sub.L] [up arrow] - (1 [[epsilon].sub.0])[R.sub.L] [down
arrow] (2)
where; [R.sub.S] [down arrow] is the incoming shortwave radiation
([Wm.sup.-2]), [alpha] is the surface albedo (dimensionless), [R.sub.L]
[down arrow] is the incoming longwave radiation ([Wm.sup.-2]), [R.sub.L]
[up arrow] is the outgoing longwave radiation ([Wm.sup.-2]), and
[[epsilon].sub.0] is the surface thermal emissivity (dimensionless).
The next step of the SEBAL is to compute the soil heat flux (G) and
the sensible heat flux to air (H). Soil heat flux is the rate of heat
storage into the soil and vegetation due to conduction. In the SEBAL,
the ratio G/Rn is calculated using the following empirical equation
developed by Bastiaanssen:
C/[R.sub.n] = [T.sub.S]/[alpha] (0.0038[alpha] +
0.0074[[alpha].sup.2]) (1 - 0.98[NDVI.sup.4] (3)
where Ts is the surface temperature (in [degrees]C); [alpha] is the
surface albedo and NDVI is the Normalized Difference Vegetation Index.
Sensible heat flux is the rate of heat loss to the air by
convection and conduction due to temperature difference. The computation
of H requires more attention because of the strong dependence upon the
type of surface and height of vegetation and local meteorological
conditions [16]. It is computed using the following equation for heat
transport:
H = ([[rho].sub.a] x [C.sub.p]dT)/[r.sub.ah] (4)
where [[rho].sub.a] is air density (1.15 kgm-3), [C.sub.p] is air
specific heat (1004.16 Jkg-1K-1), dT is the temperature difference
([T.sub.S] - [T.sub.a]) and rah is the stability corrected aerodynamic
resistance to heat transport (s/m). [r.sub.ah] varies with wind speed,
and intensity and direction of the H. Therefore, rah could be determined
through several iterations.
[r.sub.ah] = 1n([Z.sub.h] - d/[Z.sub.oh]) - [[psi].sub.h]/u * x k
(5)
u * = k x [u.sub.z]/1n([Z.sub.m] - d/[Z.sub.om]) - [[psi].sub.m]
(5)
where [Z.sub.m] and [Z.sub.h] are heights in meters above the zero
plane displacement (d) of the vegetation, u * is the friction velocity
(m/s) which quantifies the turbulent velocity fluctuations in the air
and k is von karman's constant (0.41), k is von Karman's
constant, [u.sub.z] is the wind speed (m/s) at height [Z.sub.m] and
[Z.sub.om] is the momentum roughness length (m). [[psi].sub.m] and
[[psi].sub.h] are stability correction factors for momentum and heat
transfer, respectively which are functions of Monin-Obukhov stability
parameters.
The actual evapotranspiration, [ET.sub.a] (mm/day) is determined as
[ET.sub.a] = 8.64 x [10.sub.7] [LAMBDA](24[integral]0
[R.sub.n])/([[lambda][rho].sub.w]) (7)
where [LAMBDA] = evaporative fraction [[LAMBDA] =
[[lambda]E/([lambda]E + H)] on the instantaneous time basis (-);
[lambda] are latent heat of vaporization (J/Kg) and [[rho].sub.w] =
density of water (Kg/[m.sup.3]).
Approach
In Landsat ETM+ the visible band are acquired at 30m resolution
while the thermal band is acquired at a coarser resolution of 60m. The
spectral radiances of the visible and thermal infra red band were
calculated using the calibration equations for the sensors [17]. The
image based atmospheric correction (Dark object subtraction) is carried
out for the optical remote sensing data [18]. The atmospheric correction
for thermal band is applied as described by Barsi et al., [19]. The
atmospherically corrected TIR is resampled to the spatial resolution of
the visible band (30m).
Evaporation is generally estimated using the thermal infrared data
acquired by satellite data and ground based meteorological data inputs.
The SEBAL is carried out as discussed in the section 2.2. The components
involved in the ET computation are modeled in a series of steps using
ERDAS Imagine 8.6 Model Maker tool. For insight of the practical
procedure, Tasumi [20], provide extensive details of step-by-step
considerations applied. The actual ET maps derived are at the spatial
resolution of the visible bands.
In the next attempt the spatial resolution of the thermal band is
enhanced from 60m to 30m by applying the multi resolution approach. Fig
2 reports the scheme for spatial enhancement of the TIR image with
spatial details obtained from VNIR image. The ELP was performed, and the
spatial detail to be injected into the thermal band was extracted from
the visible band (band2). The high-pass details are obtained as the
difference between the high resolution image and its low-pass version
achieved through low pass filtering. These details are then added to the
expanded versions of the low resolution thermal band. The 7 taps kernel
is applied to yield a bicubic interpolation for low pass filtering.
The surface temperature images were generated from original TIR
band resampled to 30 m and from spatially enhanced TIR image. The values
obtained are statistically compared. The SEBAL is applied with the above
derived surface temperature maps at 30 m spatial resolution. The flux
estimates and evapotranspiration for both the analysis are compared. The
Evapotranspiration estimates are also validated using the conventional
Penman Monteith method [21].
[FIGURE 2 OMITTED]
Quality Assessment of Spatially Enhanced Image
The ELP has been experimented on Landsat ETM+ image. The similarity
of the images to be merged is to be studied before deciding on the
selection of VNIR band for obtaining the spatial details. The VNIR band
2 and band 3 are reduced to the resolution of the original TIR image
(60m). The correlation analysis is carried out and correlation
coefficients are used to quantitatively evaluate the data merging
results. The correlation matrix in table 1 reports the similarity which
has been computed between original TIR and reduced VNIR bands. The
analysis of the table 1 reveals that band 2 is strongly correlated with
the TIR band. Since band 2 is most similar to the TIR band, the spatial
details to be injected in the expanded TIR band is obtained from band 2.
Quality assessment of the data merging is assessed by visual analysis
from Fig 3.
[FIGURE 3 OMITTED]
The result of the spatially enhanced TIR image with the band 2 is
reported in the table 2. The original 60m TIR has been expanded to the
scale of VNIR bands (30m) and are compared with the TIR images merged by
means of VNIR band 2 and VNIR band 3. From the correlation matrix
reported in table 2 expanded TIR image is similar to the image merged by
means of VNIR band 2. Fig 4 shows the expanded original TIR image along
with the spatially enhanced image of TIR by means of VNIR band2 and 3.
[FIGURE 4 OMITTED]
The each merged image is reduced to the original resolution (60m)
and then compared with the original TIR image. From the results are
reported in table 3, the TIR image merged by band 2 is considered for
estimating surface temperature image.
Comparison of Surface Temperature Images
The surface temperature images were estimated using the simplified
plank function for the resampled TIR image and spatially enhanced TIR
image. Table 4 reports the statistical results of surface temperature
obtained from resampled TIR image and spatially enhanced TIR image.
Table 5 shows the surface temperature of the different landuse/cover.
Fig 5 reports the variation in surface temperature for different
landuse. The images of the surface temperature for resampled TIR and
spatially enhanced TIR image is shown in Fig 6.
[FIGURE 5 OMITTED]
Estimation of Energy Balance and ET.
Surface energy balance algorithm for land (SEBAL) is used to
estimate the daily evapotranspiration and the different terms of surface
energy balance at the time of satellite overpass. Table 6 depicts the
energy balance and daily ET for agricultural landuse type. The table
reports the instantaneous values for SEBAL analysis on resampled TIR
image and spatially enhanced TIR image.
The spatial variation in the evapotranspiration can be visually
read from the Fig 7. The mean values of the different terms calculated
from SEBAL analysis are reported in table 8. Prior to the generation of
the [ET.sub.a] image, an evaporative fraction image is generated. The
statistical analysis indicates the range between 0 and 1 and the mean
values are tabulated in table 7. The low evaporative fraction is
observed for bareland and high evaporative fraction is observed for
water bodies. The agricultural fields closer to the river show high
evaporative fraction compared to the nonagricultural land.
The range of [ET.sub.a] for cropped areas is observed between 1.9
and 3.1 mm/day (mean 2.5mm/day) for the image analysed with original 60m
TIR image. For the analysis with spatially enhanced TIR image the range
of [ET.sub.a] for cropped areas is observed between 3.2 and 4.5 mm/day
(mean 3.85 mm/day). In the absence of ground information on energy
fluxes the reliability of the estimated [ET.sub.a] by the SEBAL model is
checked with conventional evapotranspiration equation using
meteorological data. The CROPWAT model is used for the estimation of
evapotranspiration from climatic data. The average [ET.sub.a] by using
the CROPWAT model (Penman-Monteith equation) is calculated as 2.8 mm/day
and satellite based estimation of evapotranspiration show that values
are higher than the values computed using CROPWAT.
[FIGURE 7 OMITTED]
Conclusions
The main objective of the paper was to apply multi resolution
technique for facilitating the spatial enhancement of the thermal
infrared image by exploiting the high spatial resolution visible image
as a complementary data. The application of the energy balance equation
to satellite remote sensing has matured over the past decades and can
bring practical results today. The combination of ground and remotely
sensed data is extremely important in areas with insufficient monitoring
of meteorological variables. Evapotranspiration at higher spatial
resolution is required than coarser resolution for better analysis in
various applications. In this study the daily evapotranspiration images
was generated from the original TIR image and for the spatially enhanced
TIR image. The adopted multi resolution technique of enhanced Laplacian
pyramid was working better and the other techniques like wavelet
analysis, subband analysis can also be studied.
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Appendix A: The theoretical basis of SEBAL," Final Report, The
Raytheon Systems Company, EOSDIS Project.
V. Gowri (1) and D. Thirumalaivasan (2)
(1) Visiting Faculty, Institute of Remote Sensing, Anna University,
Chennai, India. E-mail: gowrisenthilkumar@gmail.com
(2) Assistant professor Institute of Remote Sensing, Anna
University, Chennai, India. E-mail: dtvasan@annauniv.edu
Table 1: Correlation between reduced
VNIR band2 and 3 with original TIR.
Band 2 3 6
2 1 0.9 0.8437
3 0.9 1 0.6845
6 0.8437 0.6645 1
Table 2: Correlation of the merged TIR images (30m) with the Expanded
TIR image.
Band 6 enhanced Band 6 enhanced Expanded
Band by band 2 by band 3 Band 6
Band 6 enhanced by band 2 1 0.8963 0.8263
Band 6 enhanced by band 3 0.8963 1 0.6734
Expanded Band 6 0.8263 0.6734 1
Table 3: Correlation of the original TIR image and the reduced TIR
merged images.
Band 6 enhanced Band 6 enhanced
Band (60m) Band 6 by band 2 by band 3
Band 6 1 0.8198 0.6053
Band 6 enhanced by band 2 0.8198 1 0.7998
Band 6 enhanced by band 3 0.6053 0.7998 1
Table 4: Statistical result of the surface temperature (Ts).
Surface Temperature (Ts in K)
Spatially
Resampled TIR Enhanced TIR
Minimum 296.08 265.73
Maximum 318.29 355.26
Mean 306.448 309.368
Std deviation 3.406 6.617
Table 5: Surface temperature values for different
Landuse/cover types.
Surface Temperatur(Ts in K)
Spatially
Land use Resampled TIR Enhanced TIR
Agriculture 301.61 309.709
Urban 306.163 314.679
Water 299.018 298.693
Bare land 312.976 329.546
Table 6: Instantaneous parameter over agricultural landuse during
satellite overpass.
SEBAL with SEBAL with Spatially
Units Resampled TIR Enhanced TIR
Location: Latitude:10[degrees]
05' 25", Longitude: 77[degrees]
52' 22"
Surface Albedo -- 0.16 0.161
NDVI -- 0.688 0.695
Surface Emissivity -- 0.998 0.992
Surface temperature K 304.076 305.548
Instantaneous Rn [Wm.sup.-2] 300.903 290.630
Instantaneous G [Wm.sup.-2] 36.147 36.252
Instantaneous H [Wm.sup.-2] 59.308 56.24
Instantaneous LE [Wm.sup.-2] 205.448 198.138
Evaporative Fraction -- 0.776 0.778
Rn 24 Hours [Wm.sup.-2] 345.399 335.394
Daily ET mm/day 3.9 3.2
Table 7: Comparison of SEBAL analysis.
SEBAL with
Parameters resampled TIR
Min Max Mean
NDVI 0.092 0.752 0.411
Ts (K) 296.08 318.29 306.448
Rn ([Wm.sup.-2]) 137.23 424.91 267.431
G ([Wm.sup.-2]) 27.934 58.782 44.064
H ([Wm.sup.-2]) 45.083 219.065 83.737
24 hour ET
(mm/day) 0.62 4.5 2.6
SEBAL with
Parameters Spatially Enhanced TIR
Min Max Mean
NDVI 0.025 0.798 0.423
Ts (K) 265.73 355.26 309.368
Rn ([Wm.sup.-2]) 23.491 431.287 241.878
G ([Wm.sup.-2]) 18.55 66.49 42.85
H ([Wm.sup.-2]) 16.573 328.268 110.728
24 hour ET
(mm/day) 0.29 6.7 3.45
