Agricultural and Forest Meteorology 117 (2003) 125–144
Methods of estimating CO2 , latent heat and sensible heat fluxes
from estimates of land cover fractions in the flux footprint
Segun O. Ogunjemiyo a,∗ , Samuel K. Kaharabata c , Peter H. Schuepp b ,
Ian J. MacPherson d , Ray. L. Desjardins c , Dar A. Roberts a
b
a Department of Geography, University of California, Santa Barbara, CA 93106-4060, USA
Department of Natural Resource Sciences, McGill University, Macdonald Campus, Ste-Anne-de Bellevue, Que., Canada
c Research Branch, Agriculture and Agri-Food Canada, Ottawa, Ont., Canada
d Institute for Aerospace Research, National Research Council of Canada, Ottawa, Ont., Canada
Received 12 December 2002; received in revised form 11 February 2003; accepted 18 February 2003
Abstract
We present a description of the process of estimating surface fluxes of CO2 , latent heat and sensible heat from estimates
of fractions of satellite-based land cover types in the flux footprint. The study is conducted at two heterogeneous sites in the
boreal forest of Central Canada. Using a Twin Otter aircraft, fluxes were measured in a grid pattern during three Intensive
Field Campaigns (IFCs) and Landsat thematic mapper data were used for land cover classification. Using a footprint function
developed from tracer gas release experiments in the boreal forest, the fractions of cover types within the footprint were
determined, and used in a regression analysis against observed fluxes. The results showed that the surface cover types within
the flux footprint accounted for about 90% of the variations in the measured airborne fluxes of CO2 , sensible heat and latent
heat, at two different study sites. The attempted validation of the regression models, by comparing flux estimates over regional
transects outside the grid area for which the regression model had been developed or over site-specific runs within the grid
area against observed fluxes, based on fractional distributions of surface cover types, were encouraging. They indicate the
potential for extrapolating models developed for a given location to another location, based simply on the fractions of cover
types, at least for similar land cover types.
© 2003 Elsevier Science B.V. All rights reserved.
Keywords: Flux footprint; Sensible heat; Latent heat; Intensive Field Campaigns
Abbreviations: BOREAS, Boreal Ecosystem Atmosphere Study; BORIS, BOREAS Information System; C, CO2 flux; CODE, California
Ozone Deposition Experiment; FIFE, First International Satellite Land Surface Climatology Project Field Experiment; H, sensible heat
flux; IFC, Intensive Field Campaigns; LE, latent heat flux; NOWES, Northern Wetland Study; NSA, Northern Study Area; P, flux footprint;
RSS, remote sensing science; SSA, Southern Study Area; TE, terrestrial ecosystem; TO, Twin Otter
Land cover class abbreviations: As, aspen; Cd, conifer dry; Cr, conifer regeneration; Cw, conifer wet; De, deciduous; Di, disturbed; Dr,
deciduous regeneration; Fe, fen; Cl, clearing; Pi, pine; Sp, spruce; Sh, shrub; Wt, water
∗ Corresponding author. Tel.: +1-805-893-4519; fax: +1-805-893-7782.
E-mail address: segun@geog.ucsb.edu (S.O. Ogunjemiyo).
0168-1923/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0168-1923(03)00061-3
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S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
1. Introduction
The need to further understand the processes
governing the transfer of heat, mass and energy
between the terrestrial ecosystems and the atmosphere and to improve process model predictions of
surface–atmosphere exchange has been a subject of
great concern in recent years. It has motivated the
design and execution of multi-scale projects such as
HAPEX-MOBILHY (André et al., 1996), the First
International Satellite Land Surface Climatology
Project Field Experiment (FIFE) (Sellers et al., 1989),
the Northern Wetland Study (NOWES) (Glooschenko
et al., 1994), the California Ozone Deposition Experiment (CODE) (Pederson, 1995) and the Boreal
Ecosystem Atmosphere Study (BOREAS) (Sellers
et al., 1995). Most coupled boundary-layer surface
energy balance models estimate surface fluxes on
the basis of a known relationship between fluxes and
easily derived or remotely sensed parameters such as
radiative surface temperature, which reflects the combined effects of surface energy balance, atmospheric
state and the character of the local land surface (Diak,
1990; Carlson et al., 1994; Norman and Becker,
1995), and vegetation indices such as the normalized
difference vegetation index (NDVI), greenness index
(GI) or simple ratio (SR), leaf area index (LAI), which
are related to variables such as vegetation structure
and density (e.g. Hall et al., 1992; Bonan, 1993).
The coupled boundary-layer surface energy balance
models are known to have produced mixed results.
An example is the use of remotely sensed data to infer surface sensible heat flux on a regional scale. For
land surfaces composed of either dense vegetation or
bare soils, remote-sensing-based land surface energy
balance models have been used with reasonable accuracy (Kustas et al., 1989; Diak, 1990; Abareshi and
Schuepp, 1998). Over areas with incomplete canopy
cover, however, less satisfactory results have been reported, probably because such areas do not support the
assumption of coupling between sensible heat flux and
radiative temperature. Grid flight data from BOREAS
(Ogunjemiyo et al., 1997, 1999) revealed a poor agreement between aircraft-based estimates of sensible heat
flux and surface radiative temperature, and also between flux estimates and those obtained from satellite derived surface temperature (Ogunjemiyo et al.,
1998). This is mainly attributed to the fact that the
downward looking radiometer sees largely the surfaces
between the spindly trees and the shaded subcanopy
surfaces, which occupy part of its field of view, while
heat exchange takes place primarily from the top of the
trees, which have a small radiometric cross-section.
The same problem was identified by Hall et al. (1992),
and Sun and Mahrt (1995).
Because land cover reflects the combined effects of
vegetation, climate, soil and topography, some relationship should be expected between it and airborne
measured fluxes of sensible heat, latent heat and
CO2 . The development of a land cover-based model
for estimation of surface fluxes could then provide a
more attractive alternative to flux estimation based on
remotely sensed surface characteristics. The lack of
studies in this area are due to the specific (but seldom
satisfied) requirements for establishing a relationship
between fluxes and land cover: (a) high-resolution
land cover data; (b) aircraft flux measurements; (c)
tower flux measurements for specific cover types;
(d) a mechanism for delineating the cover types that
contribute significantly to the measured flux. The
data acquisition in BOREAS was designed to meet
such requirements. The project produced Landsat
thematic mapper (TM)-based land cover data of the
BOREAS study areas, and airborne flux data of the
area on a regional scale and the development of the
footprint concept provided a refined method for relating eddy fluxes to areas upwind of the measurement
platform.
The focus of this study is to explore the potential
of estimating surface fluxes of heat, water and CO2
from a heterogeneous ecosystem given the proportion
of cover types that constitute the ecosystem. The study
was conducted at two 16 km × 16 km heterogeneous
grid sites in the study areas of BOREAS in 1994. The
subject is approached by multiple regression analysis,
through which flux estimates can be deduced from the
fractions of cover types within the flux footprint under the given meteorological conditions. Chen et al.
(1999) is the only study known by the authors to have
been done in this area for a heterogeneous and complex terrain as the boreal forest, where as much as 13
different cover types have been identified (Hall et al.,
1997). This study provides a simpler alternative to
Chen et al. (1999) approach, which is mathematically
complex in practical application and too-heavily based
on normalizing the ‘response function’ (of fluxes to
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
surface characteristics) based on tower data and works
only if the latter are really representative of the overall
terrain, which is precisely questionable in a complex
surface like BOREAS.
2. Materials and methods
2.1. Site description
The study sites are 16 km × 16 km heterogeneous grid areas located in the Southern Study Area
(SSA) and Northern Study Area (NSA) of BOREAS.
The diagonal corners of the SSA grid are located
at 53.92◦ N/104.81◦ W and 53.78◦ N/104.56◦ W and
those of the NSA grid site at 55.94◦ N/98.65◦ W
and 55.80◦ N/98.40◦ W. The land cover maps of the
grids are given in Ogunjemiyo et al. (1997) and
Barr et al. (1997). The number of cover type ranges
from 6 to 13, depending on the classification scheme
(Hall et al., 1997; Ranson et al., 1997). The dominant cover type is conifer, which consists mainly of
black spruce (Picea mariana) and jack pine (Pinus
banksiana). Black spruce is found primarily in poorly
drained areas, and jack pine stands are associated with
well-drained and relatively dry areas, concentrated in
the north-central and lower half center of the SSA
grid, where the effects of logging with new regeneration can be observed. The deciduous species include
quaking aspen (Populus tremuloides), balsam poplar
(Populus balsamifera), and tamarack (Larix laricina).
In the poorly drained areas throughout the grid, bogs
support black spruce with some tamarack. The fen
areas are composed mostly of sedge vegetation with
discontinuous cover of tamarack or swamp birch. The
distinct feature of the NSA grid is the abundance
of mature conifer stands in the northern half and a
mixture of conifers and deciduous stands at different stages of regeneration in the lower half of the
grid.
2.2. Aircraft-based data
The flux data were acquired using the Canadian Twin Otter (TO) aircraft (MacPherson, 1996;
Ogunjemiyo et al., 1999). The principal role of the
TO in BOREAS was to make low-altitude flux measurements for use in scaling up fluxes from tower
127
scales to the regional scales observable by satellite.
The TO aircraft was operated in all the three Intensive Field Campaigns (IFCs) in 1994: IFC-1 from 23
May to 13 June, IFC-2 from 20 July to 8 August, and
IFC-3 from 30 August to 19 September. At the NSA,
five grid flights were flown in IFC-1, four in IFC-2,
and five in IFC-3 while the corresponding numbers
for the SSA were three, four and two.
The flight patterns included site-specific runs, regional runs and grid patterns (MacPherson, 1996).
Model development in our study was based on
data from grid patterns, with some regional and
site-specific runs used for model validation (Section
4.5). The grid patterns were flown at an approximate altitude of 30 m a.g.l., at a mean air speed of
60 m s−1 . Each grid flight consisted of nine parallel
straight lines 16 km in length, spaced 2 km apart, with
each line sampled twice in a time-centered sequence.
Flight trajectories (East–West or North–South) were
chosen for closest approach to crosswind conditions.
All flights were flown around solar noon, under
mostly clear weather conditions (cloud cover < 10%)
characterized by unstable thermal stratification of the
atmosphere.
The aircraft was instrumented to measure about
64 different variables. Data were digitized at 16 Hz.
Observed data used in this study include the three
components of the wind speed, air temperature, surface temperature, incident and reflected solar radiation, reflected red and near-infrared radiation and
mixing ratios of CO2 and H2 O. Parameters derived
from measured variables include, friction velocity
(u∗ ), Obukhov length (L), net radiation, and potential
temperature (θ). Detailed descriptions of the aircraft
instrumentations and data, including the weather conditions are given by Ogunjemiyo et al. (1997, 1999)
and MacPherson and Betts (1997).
2.3. Satellite-based data
The description of surface cover types used the
land classification maps based on Landsat TM data.
The TM-based imagery in BOREAS was classified
with two schemes by the Terrestrial Ecosystem team
and one by the Remote Sensing Science team (Sellers
and Hall, 1994). These datasets are henceforth identified as TE-1, TE-2 and RSS, respectively. The images
were obtained from the BOREAS Information System
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S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
(BORIS) database and stored in the BOREAS grid
projection based on the ellipsoidal version of the Albers Equal Area Conic Projection (AEAC). The spatial coverage of TE-1 and TE-2 for the NSA and TE-1
for the SSA was approximately 129 km × 86 km, and
TE-2 for the SSA approximately 144 km × 114 km.
The RSS imagery covered a smaller area, but large
enough to encompass most of the tower sites and the
TO grid sites. Each pixel in the images represents a
30 m × 30 m area of ground. Subsets of the images,
representing the 16 km ×16 km TO grid site were produced from the bigger images.
TE-1 and TE-2 classifications were based solely
on TM data, while a combination of Shuttle Imaging Radar-C (SIR-C) and TM data were used for RSS
classification. The scene for the TE-1 dataset was acquired on 20 August 1988 for the NSA, and 6 August
1990 for the SSA. For TE-2, the imagery scene was
acquired on 21 June 1995 for the NSA, and 2 September 1994 for the SSA. The scene for RSS was acquired
on 2 September 1995, for the SSA and on 13 April
1994 for the NSA.
Table 1 shows the cover class categories as defined
by the three classification schemes. A detailed description of the data and the procedures used to classify
TE-1, TE-2 and RSS are given in Hall and Knapp
(1999), Hall et al. (1997) and Ranson et al. (1997),
respectively.
3. Data processing
To estimate the vertical turbulent fluxes of sensible heat (H), latent heat (LE) and CO2 (C) at the
flight level, the scalars and the vertical component of
the wind were detrended as outlined in Ogunjemiyo
et al. (1997), to obtain the fluctuations of the variables.
Fluxes were then computed from the time-averaged
covariance between fluctuations of the vertical wind
and the scalar of interest. The fluxes were averaged
over 2 km data windows along each of the nine 16 km
runs, and the segment values averaged over the two
repeated passes of each grid line, creating a matrix,
Fij , of 8 × 9 data points per grid. In this study, the
contributions to the flux by scales larger than 2 km
were considered negligible based on the findings by
Ogunjemiyo et al. (1999), which showed that they did
not exceed 10% of the turbulent flux on any given
segment flight and far less when composited over an
IFC. For this reason the data used for analysis were
composited over multiple grid flights. We assume that
the segment averaged fluxes are due to flux density
contributions from all the cover types within the flux
footprint, i.e.
Fij =
K
ψijk dijk
(1)
k=1
Table 1
Land cover classes at the grid sites as defined by the three classification schemes
ClassID
1
2
3
4
5
6
7
8
9
10
11
12
13
TE1
TE2
RSS
Cover type
NSA
(%)
SSA
(%)
Cover type
NSA
(%)
SSA
(%)
Cover type
NSA
(%)
SSA
(%)
Conifer wet
Conifer dry
Mixed
Deciduous
Fen
Water
Disturbed
Regeneration (young)
Regeneration (medium)
Regeneration (older)
Recent Burn
–
–
36.0
15.0
10.0
2.0
5.0
4.0
3.0
0
14.0
11.0
0
–
–
57.9
4.7
11.7
2.1
6.4
0.2
1.2
4.7
2.1
8.7
0.3
–
–
Conifer wet
Conifer dry
Mixed
Deciduous
Fen
Water
Disturbed
Fire blackened
New regeneration conifer
Medium-age regeneration conifer
New regeneration deciduous
Medium-age regeneration deciduous
Grass
3.1
2.3
4.2
15.0
14.4
1.1
5.6
0.2
9.3
11.7
32.1
0.7
0.3
45.0
3.1
9.7
4.5
12.1
0.2
4.1
0.1
5
12.4
3.6
0.1
0.1
Spruce
Pine
Aspen
Shrub
Clearing
Fen
Water
–
–
–
–
–
–
33.0
15.2
8.5
37.9
1.3
3.6
0.5
–
–
–
–
–
–
39.2
38.9
7.7
8.1
3.5
2.5
0.1
–
–
–
–
–
–
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
where dijk is the spatially averaged flux density and
ψijk is the weighting function for cover type k in
segment i of grid line j. The flux density dijk is
difficult to measure even in a homogeneous area
because of its dependence on ecophysiological factors and biophysical properties of the cover types.
In the absence of independent information on this
parameter, a relationship was developed between Fij
and ψijk through a multiple regression model of the
form
2
Fij = β0 + β1 ψij1 + η1 ψij1
+ · · · + βk ψijk
2
+ηk ψijk
+ε
(2)
where β is the coefficient for the linear term, η is the
coefficient for the quadratic term for each of the independent variable, and ε is the error associated with
this model. Estimated values of ψijk were checked
for possible colinearity or multi-colinearity. Meteorological variables were purposely excluded from this
regression analysis, not only because meteorological
conditions were similar within the database for each
IFC, but in order to highlight the role of surface cover
on spatial flux distribution.
To estimate the land cover fractions, the footprint
extent, including up to 98% of total estimated contribution to the flux, was superimposed over the land
cover classification image, which consisted of rows of
30 m pixels in the upwind direction, i.e. perpendicular to the flight track. If αx is the weight given to the
pixel at upwind horizontal distance x from the pixel
corresponding to the flight path (x = 0), and Imxk is
an indicator for the presence or absence of cover type
k for the pixel at distance x and row m in the segment,
then
ψijk =
X
P
1 Imxk αx
R
(3)
m=1 x=0
where R is the number of rows in the segment, X is
the maximum upwind extent of the footprint which
contributes 98% of the measured flux. The value of
Imxk is 1 if cover type k is represented by the pixel
at distance x and column m, otherwise Imxk is 0. The
weight of the pixels, αx , was determined from the flux
footprint function (P) developed for the grid sites by
Kaharabata et al. (1997), i.e.
xn+1
x=xn P
dx
x=0 P
dx
αx = X
129
(4)
where xn+1 and xn are upwind and downwind distances, respectively, of the pixel in the nth column,
and P is defined as
s
P(x, z) =
u∗ k
szs e−(z/Bσz )
Φ(z/L) (Bσz )s Aσz u(x)
(5)
where A = s−1 Γ(1/s)3/2 Γ(3/s)−1/2 and B =
Γ(1/s)1/2 Γ(s/3)−1/2 (Γ , the gamma function) are
diffusion parameters, s is the vertical shape exponent
of the diffusing scalar’s plume and ranges from 1 (instability) to 2 (stable stratification), Φ is the stability
correction, and z (m) is the observation height.
The vertical spread of the diffusing scalar plume σ z
(m) is a function of the mean plume height Z (m) and
has been defined as
σz =
Γ(1/s)1/2 Γ(3/s)1/2
Z
Γ(2/s)
(6)
according to Pasquill and Smith (1983). To estimate Z,
which is a function of upwind distance x, van Ulden’s
(1994) expression for dZ/dx is numerically integrated
as in Kaharabata et al. (1997).
The horizontal wind velocity at mean plume height
u(x) (m s−1 ), expressed as a function of Z, was estimated by
c(Z − d)
u∗
cZ
ln
u(Z) =
−Ψ
(7)
k
z0
L
where Ψ is the stability correction for momentum,
d (m) is the displacement height, u∗ is the friction
velocity, and z0 (m) is the roughness length. The stability component in the flux footprint function was
represented by the Obukhov length, L (m).
4. Results and discussion
4.1. Comparison between the classifications
Table 1 shows the land cover classes at the grid sites
as defined by the three classification schemes. The
classes range from 7 in RSS to 13 in TE-2. The classes
common to TE-1 and TE-2 include water, fen, deciduous, mixed, conifer wet (primarily black spruce growing on peat or poorly drained mineral soils) and conifer
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dry (primarily jack pine stands in a well-drained area
with sandy soils). The mixed class describes an area
that contains coniferous and deciduous trees, with the
dominant species <80%. The main difference between
TE-1 and TE-2 is in the subdivision of the regeneration classes, which is more refined in TE-2 than in
TE-1. This difference may be more likely due to the
year of data acquisition than to the classification techniques. The 7 years separating the two datasets at the
NSA, and 4 years at the SSA, may have produced successional changes in the vegetation, as well as other
temporal differences due to clear cutting and other
man-induced change, making it possible to distinguish
between regenerating conifers and deciduous.
The spruce, pine and shrub classes in RSS scheme
are similar to conifer wet, conifer dry and the regeneration classes in TE-1 and TE-2. The RSS classification
differs from others by the absence of a mixed conifer
(spruce and pine) or mixed trees (conifer and deciduous) class, which was known to be present at the sites.
This appears as the main weakness of this classification. The major discrepancy between the classification
schemes is evident from the comparison of the percentage composition of their classes. For example, at
the NSA grid the composition of regeneration class
varies from 24% in TE-1 to 52% in TE-2; the fen class
varies from 4.3% in TE-1 to 14% in TE-2; and the
spruce or conifer wet class varies from 3.3% in TE-2
to 37% in TE-1. There is better agreement between
the maps at the SSA than the NSA.
Despite the different classification methods with
their associated errors, and the variation in the class
definitions, some noticeable agreements can be observed. For example, at the NSA grid the maps show
a well defined contrast in biophysical properties between the northern half and the southern half, which
exhibits the signature of an area recovering from fire
events. The area is dominated by regenerating plants,
mainly deciduous (aspen), which are interspersed with
bare soils and rock outcroppings. In the center of this
area is a pocket of unburned mature stands. On the
other hand, the northern half of the grid is typical of a
mature temperate forest, i.e. tall conifers with closed
canopy. The species in this area occur in mixtures,
and in patches of pure stands, as is the case with the
jack pine and black spruce. The most distinct distribution patterns common to all the SSA maps are the
occurrence of fen at the SW quadrant of the grid, the
cluster of deciduous patches along the NW–SE diagonal, the regenerating areas and jack pine that are confined to the north of the diagonal, and the black spruce
which appears to be everywhere in the grid, but with
highest concentration in an elongated strip below the
diagonal.
4.2. Footprint function and estimates
Over heterogeneous terrain, the turbulence characteristics may not be in equilibrium with the local
surface but will reflect the surface conditions some
distance upwind. This problem is particularly relevant
in the case of flux observations by aircraft. In order
to relate aircraft-measured fluxes to satellite-derived
vegetation indices or cover types, it is therefore important to identify the areas (pixels) upwind that actually
contributed to the fluxes, i.e. the flux footprints. Flux
footprint have been studied extensively (Leclerc and
Thurtell, 1990; Schuepp et al., 1990, 1992; Horst and
Weil, 1992, 1994; Schmid, 1994; Baldocchi, 1997;
Kaharabata et al., 1997; Amiro, 1998).
The footprint model used in this study (Kaharabata
et al., 1997) was based on a tracer gas experiment conducted at the sites, and had input parameters which
include: the Obukhov Length, L; friction velocity u∗ ;
roughness length, z0 ; and the displacement height, d.
The sensitivity test of the model by Kaharabata et al.
(1997) showed the model less sensitive to u∗ than to
z0 , such that <1% average difference was observed in
the footprint for changes in u∗ from 0.53 to 1.0 m s−1
for both neutral and unstable stratification, while the
footprint was found to increase fairly uniformly by
about 23% for the unstable and 17% for the neutral case as the roughness length changed from 0.7
to 0.4 m. To examine the impact of this sensitivity on
the cover types, footprint functions based on values
of L = −100 m, u∗ = 0.50 m s−1 , and z0 = 0.4,
0.7, 1.0 m, typical for BOREAS noontime, clear-sky
conditions, were applied to TE-1 data for N–S grid
flight trajectory with west wind in the NSA grid, and
E–W grid flight trajectory with south wind in the
SSA grid.
If we define X98 and Xmax as the upwind distances
corresponding to a cumulative 98% of the footprint,
and the distance of local maximum contribution, respectively, these footprint simulations showed X98 values of 739, 614 and 534 m, and Xmax values of 72,
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
131
Fig. 1. Ratio of the proportion of the cover types within the footprint (F) to the grid average value (G). The x-axis represents the cover
classID, as given in Table 1.
58 and 49 m, respectively, for z0 values of 0.4, 0.7
and 1.0 m. The impact of the changes in footprint on
cover types is demonstrated in Fig. 1, which represents
the ratio of the proportion of the cover types within
the footprint to grid average values, and shows that a
change in footprint from 534 to 739 m had little effect on the proportion of the cover types contributing
to the flux. It also demonstrates that the area effectively sampled by the aircraft was representative of the
grid, with the exception of class 6 in the SSA, which
is open water. However, since the surface coverage of
that class is <0.3%, this discrepancy is irrelevant for
the purpose of this analysis.
4.3. Choosing the most appropriate cover map
Visual inspection suggests systematic bias in some
of the classes for the various classifications, which
could affect the results of the regression analysis of
flux versus surface cover. In order to choose the land
cover map that will optimize the regression correlation between the surface cover and the surface fluxes,
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S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
Fig. 2. Maps showing abundance of (a) vegetation or shrub, (b) conifer wet or spruce and (c) conifer dry or pine.
a footprint function based on z0 = 0.65 m, d = 8 m,
u∗ = 0.56 m s−1 and L = −100 m, was applied to
TE-1, TE-2 and RSS using N–S grid flight trajectories. The estimates of each of the cover types within
the FP of the 2 km window along the flight lines were
used to produce maps of class abundance. Such maps
for the NSA, showing the abundance for regeneration
(shrub), conifer wet (spruce) and conifer dry (pine)
classes, are shown in Fig. 2. As seen from this figure, the regeneration class within the flux footprint
showed comparable values for all the maps, though
with greater spatial extent in RSS and TE-2 compared
to TE-1. However, the conifer wet or spruce class, and
the conifer dry or pine class, within the flux footprint
in TE-2 appeared nonrepresentative of the grid. This
is concluded because their percentage compositions
around the old black spruce and old jack pine towers
are only seen as 21 and 5%, respectively, compared
to 87 and 78% for RSS, and 69 and 65% for TE-1.
One of the criteria for locating the flux towers was
the presence of a (>60%) single vegetation type in an
area. For this reason, TE-2 was rejected for the analysis. Either RSS or TE-1 could be used for the analysis,
but RSS was chosen over TE-1 based on the more representative year of data acquisition. The species composition maps for the SSA grid (Fig. 3) are shown for
the regeneration, conifer wet and fen classes. In this
case, all the datasets were found appropriate for the
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
133
Fig. 3. Species composition maps for the SSA grid, showing the (a) regeneration, (b) conifer wet or spruce, and (c) fen classes.
analysis, but TE-2 was chosen because of its more detailed surface description.
4.4. Regression analysis
4.4.1. SSA grid
4.4.1.1. Model formulation. Regression models
were formulated for sensible heat, latent heat and CO2
fluxes, for each IFC, at the SSA. Spatially averaged
value of z0 and d, were obtained by spatial aggregation
based on the weighted value of the individual cover
types, using values of z0 and d for different cover
types at the grids as given in Kaharabata et al. (1997)
and Mahrt et al. (1997). The weight of the pixels, αx ,
were determined for all pixels within 98% of the flux
footprint, and applied on the TE-2 cover map. The
choice of X98 was made to ensure that the cover
types that contributed to the flux were adequately
represented.
The values of u∗ and L for the grid flights in the
three IFCs are given in Table 2. Also given in the
table are the values for Xmax and X98 . Average values
of u∗ for each of the IFCs were typical of our study
areas, which were covered with mature forest stands.
Highest variation in the values of L occurred during
134
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
Table 2
SSA grid flight conditions and footprint estimates
IFC
Date
Flight number
Flight direction (◦ )
Cross wind
u∗ (m s−1 )
L (m)
Xmin (m)
IFC-1
05/31
06/04
07
09
N–S
N–S
West
West
0.74
0.71
183.0
176.0
21
20
74
73
846
823
IFC-2
07/20
07/21
07/24
07/26
21
22
26
30
E–W
N–S
E–W
N–S
North
West
North
West
0.72
0.71
0.66
0.41
415.6
202.7
141.2
128.0
28
22
19
10
100
78
66
34
1242
884
730
365
IFC-3
09/13
09/16
49
53
E–W
N–S
South
West
0.65
0.72
187.0
258.0
21
24
75
85
850
998
Xmax (m)
X98 (m)
u∗ : friction velocity; L: Obukhov length; Xmin : minimum distance that contributes to the flux; Xmax : distance of maximum contribution to
the flux; X98 : the distance that contributes 98% of the measured flux.
IFC-2. On the average, the minimum distance from
which contribution was made to the measured flux,
Xmin , was about 20 m and an average about 28 pixels
on the cover maps (based on TM spatial resolution of
30 m) contributed 98% of the measured flux.
For the purpose of the regression analysis classes
in TE-2 were reclassified. New regeneration conifer
and medium-age regeneration conifer classes were
merged, and the new class named conifer regeneration. Also the new regeneration deciduous and
medium-age regeneration deciduous classes were
merged, and the new class named deciduous regeneration. The merging was done in order to prevent
undue fragmentation of the cover classes.
The following abbreviations were used for the cover
classes: conifer wet (Cw), conifer dry (Cd), mixed
(Mi), deciduous (De), fen (Fe), disturbed (Di), conifer
regeneration (Cr), deciduous regeneration (Dr). The
fire blackened, water and grass classes were not used
in the regression analysis because of their small composition in the grid (each <0.3%), and the fact that
their estimated values in the flux footprint were often
not representative of the grid average.
The components of the regression models for the
fluxes are given in Table 5. A significant relationship
was obtained between CO2 flux and cover types in
each of the IFCs. The coefficients of determination,
r2 , were 0.70 for IFC-1 (Cifc1 ), 0.89 for IFC-2 (Cifc2 ),
and 0.91 for IFC-3 (Cifc3 ). Both H and LE showed
significant relationships in IFC-2 (Hifc2 , LEifc2 ) and
IFC-3 (Hifc3 and LEifc3 ) but no significant relationship in IFC-1. The r2 values for LEifc2 and LEifc3
were 0.92 and 0.87, respectively, and all cover types,
except Cd, made significant contributions to LE in
IFC-2. The r2 values for Hifc2 and Hifc3 were 0.84
and 0.93, respectively. The lack of relationship for
LE in IFC-1 could be that at this time of the year
LE is fairly uniform in space. The nonlinear nature
of the relationships between fluxes and cover types
is depicted by the quadratic terms in the models.
The variation in the number of cover types between
IFCs that made significant contributions to the fluxes,
even when similar numbers of pixels were within the
flux footprint, indicates the dependence of the fluxes
on biophysical and phenological properties of the
cover types.
4.4.1.2. Model evaluation. The data used for model
evaluation are from flights executed over a “regional
run” (Candle Lake run; MacPherson, 1996) either
overlapping or within 8 days from the timing of the
grid flights used in the regression model. The land
cover map of the SSA site showing the flight trajectory of the run relative to the grid site runs is given
in Barr et al. (1997). The track was chosen to cover
significant heterogeneity; it crossed aspen and black
spruce forests, a partially logged area, an old burn
and three lakes (Halkett, Candle and White Gull). The
track was divided into nine segments (as described in
Table 3), over which the mean fluxes were calculated.
Also, the values for z0 , d, u∗ and L were calculated
for each segment. The fraction of cover types within
the aircraft footprint, calculated for the segments, are
given in Table 4. To include the seasonal trend in
the fluxes, one run from each of the three IFCs was
used. The predicted fluxes for each segment, based
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
Table 3
Description of the segments along the Candle Lake run
Segment
Approximate length (km)
Description
A
B
C
D
E
F
G
H
I
19
2
14
17
17
11
12
4
18
Aspen (As)
Halkett Lake (Lk)
Mostly aspen (As)
Mixed (Mi)
Mixed (Mi)
Candle Lake (Lk)
Spruce (Sp)
White Gull Lake (Lk)
Spruce (Sp)
on the regression models in Table 5, are compared
in Figs. 4–6 against the observed fluxes from the TO
aircraft.
Comparisons of the predicted to measured flux estimates show a trend that represents a successful demonstration of the potential to scale up from local (grid)
observations to larger areas. The correlation coefficients for C are 0.79, 0.89 and 0.90 for IFC-1, IFC-2
and IFC-3, respectively. In IFC-2 and IFC-3, the coefficients are 0.92 and 0.90 for LE, 0.88 and 0.93 for
H, respectively. Results of a sensitivity analysis for
the regression coefficients showed r2 is more sensi-
135
tive to changes in the coefficients of the cover types
that have higher cover fraction values. Comparison between the flux types showed LE models to be most sensitive and C models to be least sensitive to changes in
coefficients.
The averaged predicted values of C and LE showed
a concomitant pattern with the forest LAI (Blanken
et al., 1997). This is more apparent for deciduous (predominantly aspen stands) C estimates, which increase
from a spring (25 May) value of −0.11 mg m−2 s−1
to a summer (25 July) of −0.68 mg m−2 s−1 and
then level off to an autumn (12 September) value of
−0.24 mg m−2 s−1 . The value of LE is also higher in
summer than in autumn, and while this is expected it
should be pointed out that the high values are associated with high soil moisture at the site. During IFC-2
in 1994, there were high rainfall events at the SSA
that caused water table level to rise, thereby increasing the canopy conductance to evapotranspiration and
plants uptake of CO2 .
A comparison between the predicted estimates of
C and LE for the aspen stands against the other cover
types (spruce and mixed vegetation) shows a pattern
that further highlights the success of the approach used
in this study to predict the dynamics of gas exchanges
in a complex forest ecosystem. In all cases where
Table 4
Fraction of cover types in the flux footprint along the Candle Lake run
Date
Fraction of cover types
Cw
Cd
Mi
De
Fe
Di
Cr
Dr
C (aspen)
05/25/94
07/25/94
09/12/94
0.02
0.03
0.04
0.01
0.01
0.01
0.15
0.18
0.19
0.51
0.49
0.49
0.03
0.02
0.02
0.02
0.01
0.01
0.04
0.04
0.04
0.18
0.18
0.17
D (mixed)
05/25/94
07/25/94
09/12/94
0.20
0.24
0.24
0.01
0.00
0.00
0.28
0.26
0.26
0.12
0.12
0.12
0.05
0.05
0.05
0.01
0.00
0.03
0.10
0.09
0.09
0.19
0.19
0.18
E (mixed)
05/25/94
07/25/94
09/12/94
0.25
0.23
0.22
0.00
0.00
0.00
0.21
0.19
0.18
0.17
0.18
0.17
0.07
0.07
0.07
0.03
0.02
0.01
0.13
0.16
0.16
0.11
0.14
0.14
G (spruce)
05/25/94
07/25/94
09/12/94
0.33
0.34
0.35
0.00
0.00
0.00
0.10
0.12
0.13
0.05
0.05
0.05
0.22
0.19
0.19
0.00
0.00
0.00
0.27
0.25
0.24
0.00
0.01
0.01
I (spruce)
05/25/94
07/25/94
09/12/94
0.30
0.30
0.30
0.00
0.01
0.01
0.06
0.06
0.07
0.06
0.06
0.06
0.22
0.22
0.21
0.00
0.00
0.00
0.32
0.32
0.31
0.02
0.03
0.03
The descriptions of the cover classes are given in the text.
136
Flux
Regression terms and their coefficients
Cw
De
Dr
Fe
Mi
Cw2
Di2
Dr2
Fe2
Mi2
–
17.3
65.2
–
5.7
28.6
–
−27.4
–
10.2
–
−58.2
–
−68
−115
−3.14
–29.2
–
249
899
–
18
–
–
−23
−135
–
–
177
239
β0
Cw
De
Dr
Fe
Mi
Cw2
Cd
Cr
Fe2
Mi2
Di
37.8 × 102
14.6 × 102
−22.7 × 102
–
−13.7 × 102
−12.9 × 102
144 × 102
–
−226 × 102
−119 × 102
287 × 102
−51.9 × 102
364 × 102
136 × 102
–
475 × 102
−67 × 102
–
1270 × 102
–
1060 × 102
–
302 × 102
–
β0
Cw
De
Fe
Mi
Cw2
Dr2
Fe2
Mi2
De2
18.3 × 102
38.3 × 102
72.5 × 102
−176 × 102
–
−74.5 × 102
99.9 × 102
–
–
77.3 × 102
117 × 102
184 × 102
105 × 102
–
−279 × 102
–
–
−24.9 × 102
–
β0
Cifc1
Cifc2
Cifc3
LEifc2
LEifc3
Hifc2
Hifc3
1.05
7.65
2.4
The subscripts are used to indicate the IFC.
49.9 × 102
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
Table 5
Regression model terms and coefficients obtained for CO2 flux (Cifc1 , Cifc2 , Cifc3 ), latent heat flux (LEifc2 , LEifc3 ), and sensible heat flux (Hifc2 , Hifc3 ) at the SSA
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
137
Fig. 4. Comparison of the airborne observed CO2 fluxes along the Candle Lake run against the regression model estimates.
model evaluations are made for LE and C, their values
for the mixed tree class fall between the extreme values
that are associated with aspen and black spruce. This is
not surprising considering that the mixed forest cover
class is a mixture of black spruce and aspen. While
there is no clear pattern in the estimates of H, the
seasonal dynamics of the shifting roles of LE and H
is exemplified by values of the Bowen ratio, which
138
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
Fig. 5. Comparison of the airborne observed latent heat fluxes (LE) along the Candle Lake run against the regression model estimates.
Table 6
Northern Study Area grid flight conditions and footprint estimates
IFC
Date
Flight number
Flight direction (◦ )
Cross wind
u∗ (m s−1 )
L (m)
Xmin (m)
Xmax (m)
X98 (m)
IFC-2
07/28
08/01
08/04
08/08
33
35
37
39
N–S
N–S
N–S
N–S
West
West
West
West
0.49
0.31
0.72
0.51
67.6
25.2
245.2
65.8
13
6
23
12
45
30
84
44
475
247
975
467
u∗ : friction velocity; L: Obukhov length; Xmin : minimum distance that contributes to the flux; Xmax : distance of maximum contribution to
the flux; X98 : the distance that contributes 98% of the measured flux.
are lower in IFC-2 than in IFC-3. For example the
Bowen ratio for aspen and black spruce increase from
0.26 and 0.78 in July to 1.37 and 1.01, respectively,
in September.
4.4.2. NSA grid
4.4.2.1. Model formulation. The regression analysis
for this site explored a situation where a single cover
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
139
Fig. 6. Comparison of the airborne observed sensible heat fluxes (H) along the Candle Lake run against the regression model estimates.
Table 7
Regression model terms and coefficients obtained for CO2 flux (Cn , Cs ), latent heat flux (LEn , LEs ) and sensible heat flux (Hn , Hs ) at the
NSA
Flux
Cn
Hn
LEn
Cs
Hs
Les
Regression terms and their coefficients
β0
Sh
As
Sp
Sp2
Pi
7.49
1200
−2090
−9.91
–
3340
–
−16700
−3930
−14.08
10600
6640
6.67
−12800
−4760
−4.49
−6850
–
–
–
–
−1.03
1001
666
–
–
–
2.19
–
–
−2.21
–
–
–
–
−16700
0.469
−746
−309
–
1570
−5760
Pi2
Fe2
Fe
–
–
–
−13.5
2450
–
–
–
–
–
–
7670
The subscripts are used to differentiate between the models developed for the northern half (n) and southern half (s) of the grid. The
variables (i.e. cover classes) are defined in the text.
140
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
Fig. 7. Plots of the observed against the regression estimates of (a) C, (b) H and (c) LE, for the black spruce run in the NSA.
type dominated each half of the grid area. Regression
equations were developed separately for the closed
canopy (predominantly black spruce) in the northern
half of the grid, and the sparse and open canopy regen-
erating area in the southern half. The flux data used
were from IFC-2. The conditions for the grid flights
and the associated footprint parameters are shown in
Table 6.
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
141
Fig. 8. Plots of the observed against the regression estimates of (a) C, (b) H and (c) LE, for the burn site run in the NSA.
The components of the regression equations for the
northern half (Cn , Hn and LEn ) and southern half (Cs ,
Hs and LEs ) are given in Table 7. Abbreviated class
name used are aspen (As), fen (Fe), spruce (Sp), pine
(Pi), clearing (Cl), shrub (Sh), and water (Wt). The
main difference between the two halves of the grid is in
the contributions due to Sp and Fe. At the northern half
there was no significant contribution due to Fe, and all
142
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
fluxes have a nonlinear relationship with Sp. However,
at the southern half, Fe contributions to all the fluxes
were significant, and its relationship to the fluxes of
moisture and CO2 is quadratic. It should be noted
that even though As is statistically significant to be
included in the regression equations for LE and H
(LEn and Hn ), it’s actual contribution to the fluxes is
very marginal. This is because As constitutes <6% of
the land cover compositions at the northern half of the
NSA grid for which the models were developed. The
same applies to Pi in the regression equation for LEs .
4.4.2.2. Model validation. Data from the sitespecific runs, were used to evaluate the NSA regression models. These data were independent of
those used to develop the regression models. The
smallest-scale site-specific runs were chosen to sample, and much as practicable, a single type vegetation.
Most of the runs were made to pass within about
100 m of one of the main BOREAS flux towers. In
the NSA, site-specific runs were made to pass the
towers at the old black spruce (OBS), old jack pine
(OJP) and young jack pine (YJP). Since regenerating,
burned-over areas dominated much of the NSA, an
additional site-specific run was flown over it, although
it had no flux tower. The runs varied in length from 3
or 4 to 14 km. The shorter runs were usually repeated
up to 10 times to improve the statistical reliability of
flux estimates. The YJP and burn site runs were flown
at slightly lower altitude than other runs to reduce the
flux footprint. The longer runs were typically flown
4–6 times on a given flight.
Cn , Hn and LEn , were evaluated using data from
the site-specific old black spruce run (MacPherson,
1996). The run was divided into four segments (A, B,
C and D), and fluxes were averaged over each of the
segments. Three flights flown on 29 July, 2 August and
8 August were used to test the regression models. Each
of the flights consisted of at east six passes. To evaluate
Cs , Hs and LEs , data from the site-specific burn run
(MacPherson, 1996) were used. The data, from two
flights flown on 29 July, and 02 August, consisted
of five and six passes, respectively. The flight length
was divided into five segments (A, B, C, D and E),
and fluxes were averaged over the segments. Figs. 7
and 8 show the plots of the observed fluxes against the
predicted flux estimates based on Cn , Hn , LEn , and
Cs , Hs , LEs , respectively.
A good agreement was observed between the predicted and observed estimates. For the burn run, the
correlation coefficients, r, for C, H, LE were 0.8, 0.82
and 0.91, respectively. For the old black spruce run
the model outputs compared very well with the observed fluxes, with r values for C, H, and LE of 0.94,
0.84 and 0.93. Both LE and C estimates for the burn
site are on the average higher than the black spruce
estimates, while H estimates are higher over the black
spruce. The high C estimates over the burn site are
primarily due to the presence of a mixture of young
growing plants, dominated by aspen, which is known
for its strong CO2 absorption. Evaporation from the
shallow pools of water scattered across the burn area
and the transpiration from the regenerating plants both
account for the high LE observed for the site. In general the estimates show greater variations compared to
SSA estimates.
The results from this study, as demonstrated by the
agreement between measured and predicted surface
fluxes, suggest that to a large extent the quadratic
terms have been able to capture the nonlinear interactions between the surface heat fluxes and the specified
variables.
5. Conclusions
The growing concern about global warming and its
impact on the environment requires that more large
scale experiments such as BOREAS be conducted to
provide data that will help to understand the exchange
processes over ecosystems at global scales. Our analysis of the BOREAS data focused on the relationship
between surface cover as described by satellites and
their relationship to aircraft-measured fluxes. Previous studies (Ogunjemiyo et al., 1997, 1999) demonstrated links between the flux distribution patterns
at the grid sites and the surface configuration of the
land cover and this study pursued the objective of
establishing quantitative relationships between cover
types and airborne flux measurements by multiple
linear regression.
The successful efforts in BOREAS in delineating
the footprint of airborne observations, i.e. the surface
source zones sampled by the flux systems, provided a
basis for correlating the airborne fluxes with surface
cover types. Our study demonstrates the importance of
S.O. Ogunjemiyo et al. / Agricultural and Forest Meteorology 117 (2003) 125–144
a physically and physiologically meaningful surface
classification in heterogeneous terrain for the prediction of scalar fluxes, and gives some indirect insight
into spatial scales that are of importance for such estimates. Where more than one land cover classification
schemes are available, as it is the case in this study, it
is difficult to tell if there is any benefit from seeking
the minimally complex land use map. However, what
this study has demonstrated is that the complexity of
the land cover maps is secondary to the accurate representation of the cover classes by the cover maps.
The method described in this study can be implemented for any region where the necessary data are
available. Where there is lack of adequate data, the
method can be implemented by using regression models developed over a site with similar surface conditions and land cover types. Because the models are
constrained by phenological status and physical condition (e.g. surface wetness) of the land cover, they
are not general enough for general application. We expect the expressions to perform well if extrapolated to
areas with similar cover type and surface conditions,
but considerable additional information about surface
and sub-surface conditions would have to be incorporated into a model fit for general application. It is
important to note that this is the first study of this
kind, and more studies might be required to corroborate the validity of this technique. Our study should
be seen as a necessary (but far from sufficient) condition for a model of general applicability in scaling-up
within a complex, heterogeneous landscape. Considering that until now no consistent results have been
reported from the use of boundary-layer models in
predicting fluxes over heterogeneous areas, and how
little effort has been made by modelers to relate fluxes
to cover types in these areas, the results from this
study will hopefully stimulate further research on this
problem.
Acknowledgements
The financial and technical support for these studies
from the Canadian Natural Science and Engineering
Council, Agricultural and Agri-Food Canada, the National Research Council and from the Atmospheric
Environment Service is gratefully acknowledged. The
first author is currently being supported through fund-
143
ing by the Western Regional Center (WESTGEC)
of the National Institute for Global Environmental
Change (NIGEC).
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