Estimating Daily Evapotranspiration for Forests in Atlantic … · 2013. 12. 7. · ASPRS 2006...

ASPRS 2006 Annual Conference Reno, Nevada May 1-5, 2006

ESTIMATING DAILY EVAPOTRANSPIRATION FOR FORESTS IN ATLANTIC MARITIME CANADA: APPLICATION OF MODIS IMAGERY

Quazi K. Hassan*

Charles P.-A. Bourque Faculty of Forestry and Environmental Management

P.O. Box 44555, University of New Brunswick, Fredericton, NB E3B 6C2, Canada * 506-453-4509; Fax – 506-453-3538;

[email protected] ABSTRACT Daily evapotranspiration (ET), a key ecological variable, is calculated over the Canadian Province of New Brunswick (NB) from (i) optical and thermal band information extracted from the MODIS (Moderate Resolution Imaging Spectroradiometer) sensor on board of the TERRA satellite; and (ii) daily mean air temperatures from several first-order weather stations across NB. The MODIS data are used to derive a number of spatially explicit variables, such as albedo, emissivity, surface temperature, and normalized vegetation index (NDVI) important in the calculation of ET. A triangular relationship between NDVI and surface temperature is used to derive an estimate of evaporative fraction (EF); i.e., ratio of ET to net available energy. The daily net radiation, RN24 also spatially defined, constitutes the net available energy and is calculated mainly as a function of latitude, day of year, surface albedo, and air temperature. The multiplication of EF and RN24 provides spatial estimates of actual daily ET. Tower measurements of (i) incident and outgoing shortwave (solar) and longwave (terrestrial) radiation (and net radiation), and (ii) latent heat fluxes taken on a half-hourly basis at two sites are integrated into daily values and compared to MODIS-based values. The comparison for daily net radiation yields reasonably good agreement with a coefficient of determination (r2) = 92.6%. Comparisons of MODIS-derived estimates of ET and flux-tower measurements also provide reasonable agreement, with an r2 of 68.3%.

INTRODUCTION

Evapotranspiration (ET) is the process by which water vapour is released from plants, soils, and water bodies

and enters into the atmosphere. Evapotranspiration is an important component of both the water and energy balance. Evapotranspiration plays a vital role in determining forest-water conditions and is a good indicator of forest growth, regeneration, carbon sequestration, and forest fire hazard.

Since the 1990’s, eddy-covariance (EC) techniques have been widely used for measuring biospheric exchange of water vapour, energy, and gases, principally carbon dioxide. The EC approach is based on (i) rapid measurement of instantaneous fluctuations in the vertical wind speed, temperature, humidity, and carbon dioxide concentration fields (at rates of 10-20 Hz) as eddies move between the ecosystem and the atmosphere, (ii) statistical averaging of values, and (iii) determination of covariances, in particular those based on the vertical wind speed. Since 2003, four EC towers (flux-towers) have been operating as part of the Fluxnet-Canada Research Network (FCRN) project in New Brunswick. These flux towers provide a fine temporal resolution (30-minute resolution) of ecosystem functioning (i.e., photosynthesis, evapotranspiration, and respiration). Unfortunately, these installations only provide point measurements, which fail to give the spatial information needed for effective forest and land management applications. In contrast, remote sensing images provide reliable spatial information covering large spatial scales.

Optical remote sensing data has been used for estimating ET since the 1970’s. In general, ET can be estimated from several methodologies, such as (i) the residual term in the energy balance equation (e.g., Bastiaanssen et al. 1998), (ii) Priestly-Taylor equation (e.g., Jiang and Islam, 2001), (iii) Penman’s equation (e.g., Ganger, 1997), (iv) Penman-Monteith equation (e.g., Moran et al., 1996), (v) biophysically-based models (e.g., Choudhury, 2000), and (vi) hydrological models (e.g., Chen et al., 2005). Table 1 provides a brief description of some of these methods.


Table 1. Commonly used methodologies for estimating ET using optical images: for definition of notation refer to the footnote.

Source Methodologya Commentsa Jackson et al. (1977)

Estimates ET as a residual term of the energy balance, where H is defined as a function of the difference between Ta and Ts, surface roughness, and wind speed. This method produces reasonable results (e.g., Seguin and Itier, 1983; Moran et al., 1996).

As to Leblon, (2001): (i) Ts is used as a surrogate for the required aerodynamic Ts, so the vertical temperature difference increases with displacement from aerodynamically-rough surfaces; (ii) Ta and rs (aerodynamic resistance) need to be estimated at the image pixel level; and (iii) Ts does not depend solely on vegetation cover.

Bastiaanssen et al. (1998) Surface Energy Balance Algorithm for Land (SEBAL)

Computes ET as the residual term of the energy balance, where H does not depend on Ta, but on the vertical gradient in Ta between the surface roughness and a reference height above the surface. Also, Q is derived from Ts, NDVI, and s.

This method overcomes the first two limitations of the methodology of Jackson et al. (1997), described above. However, it is generally too complex to implement and the accuracy of the estimated ET is highly dependent on how well the other energy fluxes are computed.

Verstraeten et al. (2005)

Combines SEBAL, S-SEBI (Roerink et al., 1999) and SEBS (Su, 2002). ET is computed as a function of Rn, Q and EF, where EF is estimated from s and Ts.

Use of EF eliminates the complexity of H as EF is computed from s and Ts. However, estimation of EF is rendered more difficult over excessively humid areas (Roerink et al., 1999).

Granger (1997, 2000)

ET is computed by extending the Penman approach (Penman, 1948) by establishing a linear relationship between VPD and ET.

Applicable over forests as VPD is considered independent of cover type, but requires long-term mean Ta and surface roughness length as input variables; roughness length is not readily available.

Jiang and Islam (2001)

Computes actual ET by modifying the advection parameter of the Priestley-Taylor equation, i.e., (Priestley and Taylor, 1972); where is derived from a two-step linear relationship between NDVI and Ts.

The advantages over other methods are: (i) it avoids the complexity of estimating H from rs and (ii) it can be made operational without having ground data readily available.

a ET - evapotranspiration, where ET is its energy equivalent or latent heat flux ( is the latent of vaporization); Rn - net radiation; H - sensible heat flux; Q - soil heat flux; Ta - air temperature; Ts - surface temperature; rs - aerodynamic resistance; s - surface albedo; EF- evaporative fraction (ratio of ET to either the sum of ET and H or Rn); NDVI - normalized difference vegetation index; VPD - vapor pressure deficit; - advection parameter of the Priestley-Taylor equation; S-SEBI - Simplified Surface Energy Balance Index; SEBS - Surface Energy Balance System; SEBAL - Surface Energy Balance Algorithm for Land

This paper deals with the development of a methodology for estimating daily actual ET using MODIS by

calculating (i) the instantaneous EF-value based on an expression relating EF to surface temperature and NDVI, and (ii) the daily net radiation (RN24). Spatial calculations of daily ET are then compared with point measurements of the same variables measured by two flux-towers. Our goal with respect to this research is to understand the interactions among ecosystem compartments (e.g., aboveground forest vegetation, atmosphere, and soil) in the Acadian and boreal forests of southeastern, Atlantic Maritime Canada.


STUDY AREA

The Province of New Brunswick (NB) occupies about 35% of the Atlantic Maritime ecozone (Figure 1a). Figure 1b shows the location of the flux-tower sites, namely the Nashwaak Lake (NWL) and Charlie Lake (CL) sites, from which all of the validation, field measurements come from. The study area has a total area of 73,440 km2. The northern area is dominated by the Appalachian Mountains, sloping into a rolling plateau in the interior. The eastern portion of the study area is mostly flat. The southern is significantly more rugged. The climate is largely influenced by the proximity to the Atlantic Ocean. The area experiences a cool-moist climate, where the range of mean annual temperature and precipitation are from 3.5-6.5oC and 900-1500 mm, respectively.

Figure 1. Location of the Atlantic Maritime ecozone in Canada (a), and eddy-covariance flux-tower sites (yellow stars) and first-order weather stations in NB (yellow crosses; b).

In NB, the forest is a mixture of both coniferous and deciduous species (typical of Acadian forests) and

occupies about 85% of the NB landbase (Dept. of Natural Resources, New Brunswick, 2006). The dominating deciduous species are red maple (Acer rubrum L.), sugar maple (Acer saccharum Marsh), white birch (Betula papyrifera Marsh), yellow birch (Betula alleghaniensis Britton), and beech (Fagus grandifolia Ehrh.). The coniferous species are balsam fir (Abies balsamea (L.) Mill.), black spruce (Picea mariana (Mill.) B.S.P.), white spruce (Picea glauca (Moench) Voss), red spruce (Picea rubens Sarg.), eastern white cedar (Thuja occidentalis L.), and eastern hemlock (Tsuga canadensis (L). Carr.).

This study uses remote sensing images from the MODIS sensor, weather data from Environment Canada, and energy fluxes from the FCRN flux-towers (Figure 1; Table 2). Among the 36 available bands (channels) of the MODIS images, the visible and near infrared bands (optical bands 1 and 2) and the thermal bands (bands 31 and 32) are selected for this research. The visible and near infrared bands capture visual detail of the earth’s surface appropriate for estimating surface variables, such as NDVI, albedo and emissivity; while the thermal bands are useful for estimating surface temperature. The optical and thermal bands, however, come at different spatial resolutions: 250 m for the optical bands, and 1 km for the thermal bands.


Table 2. Data used in the research.

Data type Description Date (DOYa) Optical satellite data MODIS data from NASA

• Bands 1 and 2 • Bands 31 and 32

Flux-tower data; half hour resolution

• Incoming and outgoing shortwave radiation • Incoming and outgoing longwave radiation • Air and surface temperature

Environment-Canada meteorological data

Daily mean air temperature at several weather stations across NB

10 June 2004 (162) 12 July 2004. (194) 25 August 2004 (238) 15 September 2004 (259)

a DOY=day of year

METHODLOGY

The optical remote sensing data from MODIS are major input in the calculation of ET, through their expression in the calculations of surface albedo, surface emissivity, and normalized difference vegetation index, NDVI. Their use and relationship to other input variables (including surface temperature) are highlighted in Figure 2. The NDVI and surface temperature are used in the formulation of EF. Daily net radiation (RN24) is calculated as a function of incoming shortwave and net longwave radiation, surface albedo, and surface emissivity. Multiplication of EF and RN24 provides a spatial estimate of actual daily ET. A brief description of the calculation procedure is provided below.

Figure 2. Flow diagram for computing ET using MODIS image data as primary input.

Pre-processing of MODIS Images The radiance values of the MODIS level 1B data for both the visible and near infrared bands are converted as

top of atmosphere (TOA) reflectance values using the reflection scales specified in the header file and the solar zenith angle. The TOA reflectance is used here in the calculation of NDVI (Eq. 1) and the albedo at TOA, TOA (Eq. 2; Valiente et al., 1995).


rrrrNDVI TOA1

TOA2

TOA1

TOA2

+−= , and (1)

TOA2

TOA1

TOA r32.0r545.0035.0 ++=α , (2)

where NDVI and TOA are dimensionless quantities, and r1

TOA and r2TOA are the TOA reflectance from the visible

band and near infrared band (dimensionless). Surface albedo, s (dimensionless) is then estimated from the albedo at TOA (Chen and Orhing, 1984), i.e.,

baTOA

s−α=α , (3)

where a is the mean albedo at the top of a clear atmosphere above a non-reflecting surface, and b is the mean effective “two-way” transmittance through a clear atmosphere (both dimensionless).

Surface emissivity is the most important variable for calculating surface temperature, Ts and the outgoing longwave radiation component. It is estimated as a linear function of NDVI and is valid for NDVI values between 0.16 – 0.74 (van de Griend and Owe, 1993; Cihlar et al., 1997). The emissivity for band 31, 31, and the difference in emissivity between bands 31 and 32 ( = 31 - 32) are calculated according to:

)NDVI( ln029.09897.031 +=ε , and (4)

(NDVI)ln 0.013440.01019 +=εΔ . (5)

Evaluation of Eq.’s 4 and 5 are subsequently used to estimate Ts (K; shown below). Surface emissivity, s, is also calculated as a linear function of NDVI (van de Griend and Owe, 1993), i.e.,

)NDVI( ln0047.0009.1s +=ε , (6) which is then used to estimate the outgoing longwave radiation. Emissivities in Eq.’s 4 through 6 are all dimensionless.

The radiance from bands 31 and 32 (thermal infrared) are converted into brightness temperatures using radiance scales and offsets specified in the header file and Planck’s function (Houghton, 2002). Surface temperature, Ts is calculated as a function of brightness temperature and emissivities using a split-window algorithm described in Coll et al. (1994):

εΔ−ε−+−−++= 40)1(45)TT)}(TT(28.029.1{TT 313231323131s , (7)

where T31 and T32 are the brightness temperatures from bands 31 and 32, in K. Evaporative Fraction (EF)

Evaporative fraction is calculated based on an expression relating EF to Ts and NDVI. A number of studies in the literature use the relationship between NDVI and Ts to derive various surface variables. For example, Moran et al. (1994) develop a water deficit index; Carlson et al. (1995) estimate soil water content; Jiang and Islam (2001)


derive a modified Priestley-Taylor coefficient for estimating actual ET; and Sandholt et al. (2002) derive a temperature-vegetation dryness index (TDVI) for estimating surface moisture. Instead of estimating TDVI (i.e., a land surface dryness index for estimating soil moisture based on an empirical parameterisation of the relationship between NDVI and Ts), we use a triangular relationship of NDVI-Ts to estimate EF. Figure 3 shows the concept of estimating EF using the NDVI-Ts relationship. The dry edge, Td (the line where the surface temperature is highest in relation to NDVI; Figure 3), represents the case where water is not available for evapotranspiration, and as a result EF possesses the lowest value (~ 0.0). The Td is determined as a linear fit of the highest surface temperature in relation to NDVI (i.e., Td = a + b*NDVI, where a and b are the intercept and slope of the linear fit). In contrast, the wet edge, Ts min (the line where the surface temperature is lowest in relation to NDVI; Figure 3), represents the case where water is freely available for evapotranspiration and EF is highest (~ 1.0). Pixel-calculation of EF is as follows:

min s

sT)NDVI*ba(

T)NDVI*ba( EF−+

−+= , (8)

where EF is a dimensionless quantity, and Ts min is in K.

Figure 3. Estimation of EF using an NDVI-Ts relationship (modified after Sandholt et al., 2002) Daily Net Radiation

Daily net radiation, RN24 (W m-2) is estimated from the sum of the daily shortwave and longwave radiation, i.e.,

RRRRR 24L24L24S24S24N ↑−↓+↑−↓= , (9)

where RS24 and RS24 are the daily incoming and outgoing shortwave radiation; RL24 and RL24 are the daily incoming and outgoing longwave radiation (all in W m-2). The RS24 can be considered as a product of RS24 and s. Both RL24 and RL24 are estimated as a function of daily mean air temperature ( aT ) and daily mean surface


temperatures ( sT ) and the application of the Stefan-Boltzmann equation. Here, we assume aT sT , so Eq. 9 can be re-written as:

)(TR)1( R sa

4a24Ss24N ε−εσ+↓α−= , (10)

where a is the atmospheric emissivity and is calculated as a function of air temperature (Swinbank, 1963); is the Stefan–Boltzmann constant, i.e., 5.6697×10-8 (in W m-2K-4). The RS24 is calculated as a function of day of year, latitude, solar declination, and daily atmospheric transmittance (set here at 0.75 for clear-skies; following Allen et al., 1998; Bourque and Gullison, 1998; Iqbal, 1983).

Based on our assumption of aT sT (Figure 4), we use aT instead of sT in our modeling effort. This hypothesis is evaluated by comparing the aT and sT for the period Jan.-Oct., 2004 using the data obtained from the FCRN flux-towers. However, sT is evaluated as a function of daily average outgoing longwave radiation using the Stefan-Boltzmann’s equation. A linear regression through the paired data (air vs. surface temperature) generally show excellent agreement, r2=0.99, with a sample size, n=299 (Figure 4).

Figure 4. Comparison between daily mean air and surface temperature. Actual Daily Evapotranspiration

Actual daily evapotranspiration is estimated based on two assumptions: (i) soil heat flux is zero over a 24-hour period, and (ii) instantaneous values of EF can be considered constant over a full day (Shuttleworth et al., 1989; Crago, 1996). Given these assumptions, ET24 is estimated according to Bastiaanssen (2000):

588.28R*EFET 24N

24 = , (10)

where ET24 is the actual daily evapotranspiration (in mm d-1).


RESULTS

We perform a sensitivity analysis of the modelled daily net longwave radiation given that aT sT . Our analysis reveals that the modelled daily net longwave radiation is insensitive (variation < 3.52 W m-2) if the accuracy of aT is within ±1 K over a broad range of temperature values (i.e., 243-303 K). The results are shown in Figure 5.

Figure 5. Modelled daily net longwave radiation under clear-sky conditions as a function of aT (±1 K accurracy).

Figure 6 shows a comparison between the modelled and measured daily net radiation at the flux-towers. The

data points provide a reasonable agreement (i.e. r2 = 92.6%).

Figure 6. Modelled versus measured daily net radiation shown with a linear fit with corresponding 95% CI.


Figure 7 provides a comparison between modelled and measured daily ET values. A reasonably good agreement exists between the two quantities (r2 = 68.3%).

Figure 7. Modelled versus measured daily ET shown with a linear fit with corresponding 95% CI.

Figure 8 shows daily ET values for 12 July 2004. The red areas represent the lowest ET values, as these are urban areas with little to no available water for evaporation. In contrast, the blue areas represent the highest ET values, as these are low-lying and well-watered areas.

Figure 8. MODIS-based estimates of daily ET values for 12 July 2004 for the study area.


CONCLUSION

The methodology developed in this paper demonstrates the potential of using MODIS data in estimating actual daily ET over forest ecosystems. Comparisons of estimated and measured values show reasonably good agreement. This work provides a simplified protocol for analysis that can be readily used for other forest-areas of Canada and possibly elsewhere. We like to extend this research to examine soil water content and/or carbon dioxide uptake in forest ecosystems. This work will lead to a better understanding of the interactions among forest, energy, water, and soil; and provide a basis for further research in the sequestration of atmospheric carbon and climate change impacts at regional scales.

ACKNOWLEDGEMENTS

This study is partially funded by the FCRN Project and funds from a Discovery Grant awarded to CPAB from the Natural Science and Engineering Council of Canada. The MODIS data were made available at free of charge from NASA. We are grateful for the meteorological data received from Environment Canada and the help received from Mr. William Richards (meteorologist, Environment Canada) in accessing these data.

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Estimating Daily Evapotranspiration for Forests in Atlantic … · 2013. 12. 7. · ASPRS 2006...

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