BGBiogeosciencesBGBiogeosciences1726-4189Copernicus GmbHGöttingen, Germany10.5194/bg-11-7369-2014Components of near-surface energy balance derived from satellite soundings – Part 2: Noontime latent heat
fluxMallickK.kaniska.mallick@gmail.comJarvisA.WohlfahrtG.https://orcid.org/0000-0003-3080-6702KielyG.HiranoT.https://orcid.org/0000-0002-0325-3922MiyataA.YamamotoS.HoffmannL.Environmental Research and Innovation (ERIN), Luxembourg Institute of Science and Technology (LIST), L4422, Belvaux, LuxembourgLancaster Environment Centre, Lancaster University, Lancaster LA1 4YQ, UKInstitute of Ecology, University of Innsbruck, 6020 Innsbruck, AustriaHydrology Micrometeorology and Climate Investigation Centre, Department of Civil and Environmental Engineering, University College Cork, Cork, IrelandDivision of Environmental Resources, Research Faculty of Agriculture, Hokkaido University, Hokkaido, JapanNational Institute for Agro-Environmental Sciences, Tsukuba, JapanGraduate School of Environmental Science, Okayama University Tsushimanaka 3-1-1, Okayama 700-8530, JapanEuropean Academy of Bolzano, 39100, Bolzano, ItalyK. Mallick (kaniska.mallick@gmail.com)22December201411247369738227March20144June201431October201410November2014This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://www.biogeosciences.net/11/7369/2014/bg-11-7369-2014.htmlThe full text article is available as a PDF file from https://www.biogeosciences.net/11/7369/2014/bg-11-7369-2014.pdf
This paper introduces a relatively simple method for recovering global fields
of latent heat flux. The method focuses on specifying Bowen ratio estimates
through exploiting air temperature and vapour pressure measurements obtained
from infrared soundings of the AIRS (Atmospheric Infrared Sounder) sensor
onboard NASA's Aqua platform. Through combining these Bowen ratio
retrievals with satellite surface net available energy data, we have specified
estimates of global noontime surface latent heat flux at the 1∘×1∘ scale. These estimates were provisionally evaluated against data
from 30 terrestrial tower flux sites covering a broad spectrum of biomes.
Taking monthly average 13:30 data for 2003, this revealed promising
agreement between the satellite and tower measurements of latent heat flux,
with a pooled root-mean-square deviation of 79 Wm-2, and no
significant bias. However, this success partly arose as a product of the
underspecification of the AIRS Bowen ratio compensating for the underspecification of the AIRS net available energy, suggesting further refinement
of the approach is required. The error analysis suggested that the landscape
level variability in enhanced vegetation index (EVI) and land surface temperature
contributed significantly to the statistical metric of the predicted latent
heat fluxes.
Introduction
The spectre of increasing global surface temperatures means our
ability to both monitor and predict changes in the activity of the water
cycle becomes critical if we are to develop the adaptive capability needed to
manage the effects of this change (Lawford et al., 2004). As a result,
significant investments have been and are being made in developing both
monitoring and modelling capacity in the related areas of water resource
management (Nickel et al., 2005), flood and drought risk assessment (Lehner
et al., 2006), and weather and climate prediction (Irannejad et al., 2003;
Brennan and Lackmann, 2005). Of the various components of the water cycle,
the accuracy with which evaporative fluxes, E (or latent heat fluxes,
λE), are both measured and hence modelled at scales relevant to
decision making has been identified as an area where greater capacity is
needed, particularly in order to evaluate and hence better constrain model
performance (Chen and Dudhia, 2001; McCabe et al., 2008). These scales range
from 1 to 100 km (i.e. 0.01 to 1∘) in the spatial extent.
Satellites offer a potentially attractive source of data for calculating E
at scales directly relevant to model development (from 0.01 to 1∘;
Jiminez et al., 2009). Over the past 30 years a variety of schemes for
specifying E using remote sensing data have been developed and used to
evaluate the spatio-temporal behaviour of evaporation for field (Tasumi et
al., 2005), regional (Bastiaanssen et al., 1998; Su, 2002; Mu et al., 2007;
Mallick et al., 2007; Jang et al., 2010) and continental scales (Anderson et
al., 2007; Sahoo et al., 2011). The methods employed thus far can be
categorised based on the various approaches followed to determine E. The
most common approach centres on assuming a physical model of evaporation
given many of the variables required to compute evaporation using these
models are available directly as satellite products (e.g. land surface
temperature, vegetation index, albedo) (Choudhury and Di Girolamo,
1998; Mu et al., 2007, 2011). The Priestley–Taylor (Priestley and Taylor,
1972)-based model for estimating monthly global E relies on constraining
the Priestley–Taylor parameter with meteorological and satellite-based
biophysical variables (fractional vegetation cover, green canopy fraction,
vegetation index, etc.) (Fisher et al., 2008; Vinukollu et al., 2011). In
contrast, a number of studies have also tried to resolve E indirectly by
estimating the evaporative fraction from the relationship between satellite-derived albedo, vegetation indices and land surface temperature (Verstraeten
et al., 2005; Batra et al., 2006; Mallick et al., 2009). More recently,
Salvucci and Gentine (2013) proposed a novel method for determining E based
on minimising the vertical variance of relative humidity while simultaneously
estimating water vapour conductance and E. A list of the widely used global- and regional-scale satellite-based E models is listed in Table 1.
What is common to all these approaches is that they rely to a greater or
lesser extent on parameterisation of surface characteristics in order to
derive the estimates of E and therefore the products from these
approaches are conditional on these parameterisations. For example, in
schemes which exploit the Penman–Monteith equation, both the aerodynamic and
surface resistance terms require some form of calibration of surface
characteristics, often involving vegetation indices, whether empirically (Mu
et al., 2007) or through linking to photosynthesis (Anderson et al., 2008).
This is obviously a confounding factor when one attempts to use these data to
evaluate surface parameterisations in weather, climate and hydrological
models, particularly when the models we wish to evaluate may contain very
similar model descriptions for E. What is required, therefore, are methods
for deriving E estimates from satellite data that do not rely unduly on
surface parameterisations, and thus they become a valid and valuable data
source for model evaluation. One approach that appears to fulfil this
requirement is where λE is estimated from satellite data as a
residual term in the energy balance equation (Tasumi et al., 2005; Mallick et
al., 2007). However, this approach suffers from the effects of error
propagation because all errors, including any lack of observed closure of the
regional energy budget, are lumped into the estimate of λE (Foken et
al., 2006). From this we can see that something more akin to a satellite
“observation” would be attractive.
Global polar-orbiting sounders like AIRS (Atmospheric Infrared Sounder)
provide profiles of air temperature and relative humidity at different
pressure levels from the surface to the upper troposphere, along with several
other geophysical variables (for example, surface temperature, near-surface
air temperature, precipitable water, cloudiness, surface emissivity,
geopotential height). Profile information like this points to the
possibility of exploring gradient-based methods such as Bowen ratio (Bowen,
1926) to produce large-scale estimates of E. Despite having been used to
refine estimate of near-surface air temperature over the oceans (e.g. Hsu,
1998), the use of Bowen ratio methods in conjunction with satellite sounder
data somewhat surprisingly appears to have been overlooked as a method for
estimating E. The reasons for this are probably twofold. Firstly, the
resolutions of the temperature and humidity retrievals are assumed to be
inadequate for differential methods like this. Secondly, there can be
reservations over the applicability of the underlying assumptions of gradient
methods on this scale. Although these appear valid concerns, there are also
important counter-arguments to consider. Firstly, the degree of signal
integration going on at the scale of the satellite sounding should help relax
the requirement on signal resolution. Sounders integrate signal horizontally
over scales of thousands of square kilometres and hence benefit from strong
spatial averaging characteristics in the measurement, despite suffering from
ambiguities in the vertical integration of signal. However, this later
drawback is aided by an effectively large sensor separation in the vertical
(Thompson and Hou, 1990). Secondly, studies over both ocean and land indicate
that the Bowen ratio method can be relatively robust under non-ideal
conditions (Tanner, 1961; Todd et al., 2000; Konda, 2004). Given the
potential benefits of having non-parametric estimates of E at the scales
and spatial coverage offered by the satellites, we argue that the possibility
of using sounder products within a Bowen ratio framework merits
investigation.
This paper presents the development and evaluation of 1∘×1∘
AIRS sounder–Bowen ratio-derived latent heat flux, λE. We focus on
terrestrial systems because of the availability of an extensive tower-based
flux measurement network against which we can evaluate the various satellite-derived components.
A list of satellite-based evapotranspiration models.
Model nameModelling approachInput variablesReferenceALEXI/TSEBTwo-source aerodynamic modelRN, G, TS, WS, LAI, fCAnderson et al. (2007),Norman et al. (1995)SEBSSingle-source aerodynamic modelRN, G, TS, TA, WS, LAI, fCSu (2002)SEBALSingle-source aerodynamic modelRN, G, TS, TA, WS, LAI, fCBastiaanssen et al. (1998)METRICSingle-source aerodynamic modelRN, G, TS, TA, WS, LAI, fCTasumi et al. (2005)RH varianceSingle-source Penman–Monteith modelRN, G, RH, TA, WSSalvucci and Gentine (2013)PM-MOD16Three-source Penman–Monteith modelRN, G, RH, TA, LAI, fCMu et al. (2007)PTJPLThree-source Priestley–Taylor modelRN, G, RH, TA, LAI, fCFisher et al. (2008)EFVI-TSTwo-dimensional scatter between TS and VIRN, G, TS, TA, VIBatra et al. (2006)EFalb-TSTwo-dimensional scatter between TS and albedoRN, G, TS, TA, albedoVerstraeten et al. (2005)
RN: net radiation; G: ground heat flux;
TS: land surface temperature; VI: vegetation index;
LAI: leaf area index; fC: fractional vegetation
cover; TA: air temperature; RH: relative
humidity; WS: wind speed.
MethodologyBowen ratio methodology
The Bowen ratio (β) is the ratio of sensible, H (Wm-2),
to latent, λE (Wm-2), heat flux (Bowen, 1926),
β=HλE,
where λ is the latent heat of vaporisation of water
(Jkg-1) and surface to atmosphere fluxes are positive. If the
instantaneous energy balance of the plane across which H and λE
are being considered is given by
Φ=RN-G=λE+H,
where Φ (Wm-2) is known as the net available energy,
RN (Wm-2) is the net radiation across that plane and
G (Wm-2) is the rate of system heat accumulation below that
plane; then, combining Eqs. (1) and (2), one gets
λE=Φ1+β.
Therefore, if Φ and β are available, λE can be computed
(Dyer, 1974). The estimation of Φ from satellite data is covered in a
companion paper (Mallick et al., 2014). β was estimated as follows.
H and λE are assumed to be linearly related to the vertical
gradients in air temperature and partial pressure of water vapour, ∂T/∂z and ∂p/∂z, through assuming similarity in the
pathways for the two fluxes.
λE=ρλεkE∂p∂z
and
H=ρcPkH∂T∂z,
where ε is the ratio of the molecular weight of water vapour to
that of dry air, ρ is air density (kgm-3), cp is
air specific heat (Jkg-1K-1), and kE and
kH are the effective transfer coefficients for water vapour and
heat, respectively (ms-1) (Fritschen and Fritschen, 2005). If heat
and water vapour occupy the same transfer pathway and mechanism through a
plane, then kE≈kH (Verma et al., 1978) and
Eqs. (1) and (4) reduce to
β=cPλε∂T∂p,
suggesting β can be estimated from the relative vertical gradient in
T and p (Bowen, 1926). In the turbulent region of the atmosphere, eddy
diffusivities for all the conserved scalars are generally assumed equal
because they are carried by the same eddies and, therefore, are associated at
source (Swinbank and Dyer, 1967). There is evidence to suggest kH
is greater than kE under stable (early morning and late
afternoon) conditions when heat gets transferred more efficiently than the
water vapour (Katul et al., 1995) and when the effects of lateral advection of
heat are significant (Verma et al., 1978). For non-neutral atmospheric
conditions the turbulent efficiency for transporting water vapour is more than
that for heat (Katul et al., 1995), and under such conditions kE
is greater than kH. For the near-convective conditions (early to
mid-afternoon) the ratio of kH to kE is unity (Katul
et al., 1995).
AIRS soundings for T and p are available for a range of pressure levels
in the atmosphere (Tobin et al., 2006). Assuming the lowest available two
pressure levels p1,2 occur within a region of the planetary boundary
layer within which Eqs. (4a) and (b) hold, then a finite difference
approximation of Eq. (5) gives
β=cPλεT1-T2+Γp1-p2,
where Γ accounts for the adiabatic lapse rate in T, which in this
case will be significant. Here we specify Γ following Eq. (6.15) in
Salby (1996), which when rearranged gives
Γ=lnT2/T1Γdlnp2/p1κ,
where Γd is the dry adiabatic lapse rate (∼9.8Kkm-1) and κ is the ratio of the specific gas
constant (Jkg-1K-1) to the isobaric specific heat capacity
(Jkg-1K-1).
There are typically three dominant assumptions affecting the applicability of
Bowen ratio methods, and the validity of these is important in the present
context. The first is that the observations of the vertical gradients are
dominated by vertical transport, and hence the effects of advective fluxes are
minimal. This is a real problem in traditional, small-scale, near-surface
applications because the length of the vertical flux path being sampled is
similar to that of many of the turbulent fluxes involved in near-surface heat
and mass exchange. As a result, the observed vertical gradient can become
partially distorted by the lateral advection of heat and water vapour (Wilson
et al., 2001). In contrast, the satellite sounding data sample a radically
different space with a horizontal extent varying from 0.5 to 1∘. In
this preliminary investigation we have opted to use the AIRS sounding data
where the horizontal footprint is 1∘× 1∘ (or approximately
100km×100km). For the vertical profile we exploit
the 1000 and 925 mb pressure level soundings, corresponding to heights of
approximately 10 and 500 m. Therefore the vertical scale is nearly 3.5 orders of magnitude smaller than the horizontal. Although
advective fluxes occur across a range of scales in space, they are slow
relative to the vertical exchange on these scales and hence should tend to
distort the vertical gradient to a lesser extent than traditional Bowen
towers.
The second assumption is related to the first in that the lateral advective
fluxes become particularly important when the underlying land surface is
heterogeneous because lateral import of heat or mass into the observation
space from adjacent land patches will again distort the gradient
measurements. For the reasons expressed above on the relative scales of the
vertical and horizontal footprint of the sounding observations, such “edge
effects” should be diminished, although it is important to appreciate that
the landscape heterogeneity is likely to increase with scale. Therefore,
although the satellite-based method we are proposing shows promise as an
observation platform, relating these observations to unique surface
characteristics is likely to be problematic (despite an attempt being made
(Fig. 6) to explain the retrieval errors in light of the vegetation
biophysical heterogeneity).
The final assumption is that the land–atmosphere system is in some form of
dynamic equilibrium so that the vertical gradients representing vertical
fluxes and changes in storage are trivial. The soundings we utilise are for a
13:30 overpass time. Although not universally so, the turbulent boundary
layer tends to be approaching its most mature by this time of day and the
average depth of the turbulent boundary layer should extend well beyond the
925 mb level (Fisch et al., 2004). Therefore, the steady-state assumption
implicit in Bowen ratio methods (Fritschen and Simpson, 1989) is probably
closest to being fulfilled. That said, the development of the turbulent
boundary layer depends on the nature of the (radiative) forcing it is
experiencing and there may be many circumstances when it is still evolving at
the 13:30 overpass time. Although this has implications for the steady-state
assumption, it probably has bigger implications for the assumption that the
boundary layer has developed beyond the lowest two available soundings and
hence can be considered fully turbulent.
Although the system we are sampling is not the constant flux region near the
surface, in effect we have a surface source region (sampled by the 1000 mb
sounding) exchanging with a well-mixed volume (sampled by the 925 mb
sounding). The flux exchange between these two should be approximately linear
and equivalent in the concentration differences between the two, providing we
are near dynamic equilibrium (i.e. the turbulent boundary layer is not
growing/contracting excessively) and that additional fluxes into and out of
the boundary layer (including phase changes) are small relative to the
surface sourced fluxes of heat and water vapour.
The principle difficulty as far as we can ascertain is the effect of phase
changes associated with cloud formation, producing latent warming of the
boundary layer whilst removing water vapour. Providing this happens above the
925 mb sounding, we anticipate it being less of a problem, but if it happens
below this level then clearly this is problematic. Of course, this also
impacts on the estimation of the net available energy.
The reliability of the estimates of β also depends on the accuracy and
resolution of the measurements of the temperature and humidity gradients. The
AIRS products are quoted as having resolutions and accuracies of ±1Kkm-1 for T and ±10%km-1 for p
(Aumann et al., 2003; Tobin et al., 2006). Given Bowen ratio studies are
invariably applied to small sensor separations of the order of metres, and at
the point scale, precisions of ±0.01∘C for temperature and
±0.01kPa for vapour pressure are required (Campbell Scientific,
2005), making the AIRS sensitivities appear untenable. However, as mentioned
above, the effective sensor separation of the order of hundreds of metres
allied to the sounding integrating at the 10 000 km2 scale should
help lift these restrictions. There are missing data segments in the AIRS
sounder profiles, which are particularly prominent at high latitudes, where
presumably it is difficult to profile the atmosphere reliably near the
surface, and over the mountain belts, where the lower pressure levels are
intercepted by the ground.
A general sensitivity–uncertainty analysis was carried out to assess the
propagation of uncertainty through the calculation scheme onto the estimates
of λE (see Mallick et al., 2014, for details).
Satellite data sources
The AIRS sounder is carried by NASA's Aqua satellite, which was launched into
a Sun-synchronous low Earth orbit on 4 May 2002 as part of NASA's Earth
Observing System (Tobin et al., 2006). It gives global, twice-daily coverage
at 01:30–13:30 from an altitude of 705 km. In the present study we
have used AIRS level 3 standard monthly products from 2003, with a spatial
resolution of 1∘×1∘. The monthly products are simply the
arithmetic mean, weighted by counts, of the daily data of each grid box. The
monthly merged products have been used here because the infrared retrievals
are not cloud-proof and the monthly products gave decent spatial cover in
light of missing cloudy-sky data. The data products were obtained in
hierarchical data format (HDF4) with associated latitude–longitude
projection from NASA's Mirador data holdings
(http://mirador.gsfc.nasa.gov/). These data sets included all the
meteorological variables required to realise Eqs. (6) and (7).
Tower evaluation data
The satellite estimates of β, λE and H were evaluated
against 2003 data from 30 terrestrial FLUXNET eddy covariance towers
(Baldocchi et al., 2001) covering 7 different biome classes. These tower
sites were selected to cover a range of hydro-meteorological environments in
South America, North America, Europe, Asia, Oceania and Africa. A
comprehensive list of the site characteristics and the site locations are
given in a companion paper (Mallick et al., 2014), which describes the
specification of the satellite net available energy used here.
Eddy covariance has largely replaced gradient-based methods like the Bowen
ratio as the preferred method for tower measurements of terrestrial water
vapour and sensible heat flux. Because eddy covariance is not a gradient
method it is an attractive source of evaluation data. Sensible and latent
heat flux measurements were used as reported in the FLUXNET data base; in
other words no corrections for any lack in energy balance closure (Foken,
2008; Wohlfahrt et al., 2009) were applied. The spatial scale of the tower
eddy covariance footprint is of the order of ∼1km2 and is
hence on a scale approximately 4 orders of magnitude smaller than the
10 000 km2 satellite data, which obviously has implications in
heterogeneous environments (see above). The most important implication for
spatial heterogeneity in the present context is that, in addition to
complicating comparison with tower data, relating these observations to
unique surface characteristics is likely to be problematic.
ResultsBowen ratio – evaporative fraction evaluation
Figure 1a shows the global distribution of annual average, 13:30 h estimates
for β for the year 2003 derived using the sounder method. The missing
data segments are due to two data rejection criteria, one of which is already
mentioned in Sect. 2.1. We have additionally imposed our own data rejection
for β when there is reversal of the vertical vapour pressure gradient
under high radiative load. This condition is often encountered in hot, arid
settings when large-scale advection causes the assumptions behind Bowen ratio
methodology to become invalid (Rider and Philip, 1960; Perez et al., 1999).
This condition was particularly prevalent over Australia in summer 2003 (Feng
et al., 2008) and hence this region is not covered particularly well.
The first thing to note from Fig. 1a is that there is a clear land–sea
contrast with β being relatively low and uniform over the sea as
expected. The values of β over the oceans are in the region of 0.1, in
line with commonly quoted figures for the sea (Betts and Ridgway, 1989; Hoen
et al., 2002). Over the tropical forest regions of Amazonia and the Congo,
β is in the range of 0.1 to 0.3, which also compares with values
reported for these areas (da Rocha et al., 2004, 2009; Russell and
Johnson, 2006). The more arid areas are also clearly delineated. Although
somewhat variable, the Sahara gives a range of 1.5–3.5, which corresponds to
the results of Kohler et al. (2010) and Wohlfahrt et al. (2009) for the
Mojave Desert. The South American savanna gives a range between 0.5 and 1,
which corresponds to values reported by Giambelluca et al. (2009). One
notable feature is the homogeneity of the β fields over the Americas in
contrast to the heterogeneity over Eurasia. The year 2003 was associated with
widespread drying over Europe (Fink et al., 2004), which may explain this
feature.
Global fields of yearly average 13:30 derived from AIRS sounder
observations for 2003. (a) Bowen ratio β
(Wm-2/Wm-2). (b) Net available energy, Φ
(Wm-2). (c) Latent heat flux, λE
(Wm-2). (d) Sensible heat flux, H (Wm-2).
Missing data are marked in grey.
In an attempt to reassure the reader about the validity of the assumptions we
are making, we have first tested the proposed methodology over a surface flux
measurement site of SMEX02 experiment (Kustas et al., 2005) in the central
United States, where both the radiosonde measurements and eddy covariance
flux observations were available. The Bowen ratio was estimated from the air
temperature and dewpoint temperature measurements of the radiosonde
observations using the same methodology as described in the current
manuscript. We have elected to evaluate β in terms of evaporative
fraction (Λ) (=(1+β)-1) (Shuttleworth et al., 1989)
because, unlike β, Λ is bounded and more linearly related to
the tower fluxes from which it is derived (λE=ΛΦ, cf.
Eq. 3). Figure 2 shows the relationship between the radiosonde- and
tower-derived estimates of Λ and reveals a fair degree of
correspondence between the two. This analysis produces a significant and
modest correlation (r=0.69±0.101), reasonably low RMSE (0.11) and
mean absolute percent deviation (14 %) between radiosonde-derived
Λ and tower-observed Λ.
Evaluation of the radiosonde-derived evaporative fraction,
Λ. This produces a correlation of 0.69 (R2=0.48) and a
regression line (solid black line) of Λ(radiosonde) =1.12(±0.24)Λ(tower) -0.08(±0.16).
The evaluation of the AIRS-derived monthly 13:30 surface flux
components against their tower equivalent. (a) Evaporative fraction,
Λ. Here, the solid regression line denotes Λ(satellite) =0.31(±0.02)Λ(tower) +0.49(±0.04). (b) Net available
energy, Φ. Here, the solid regression line denotes Φ(satellite) =0.90(±0.03)Φ(tower) -2.43(±8.19) (see Mallick et al., 2014).
(c) Latent heat flux, λE. (d) Sensible heat flux,
H. For regression statistics see Table 3. The 1:1 line is shown for
reference.
(+ EBF; × MF; ○ GRA; * CRO; ∇ ENF; ◊ DBF;
□ SAV)
EBF: evergreen broadleaf forest; MF: mixed forest; GRA: grassland;
CRO: cropland; ENF: evergreen needleleaf forest; DBF: deciduous
broadleaf forest; SAV: savanna
Scatter plot showing the slope of regression (M) between the
observed and estimated λE as a function of the corresponding
λE measurement height (tower height, ht) for different
biome classes. The tower heights of similar biomes are averaged. The solid
line is the best-fit relationship (M=0.003ht+0.84, R2=0.46) after removing the SAV biome type. This shows that M approaches unity
with ht.
(+ EBF; × MF; ○ GRA; * CRO; ∇ ENF; ◊ DBF;
□ SAV)
Figure 3a shows the relationship between the satellite- and tower-derived
estimates of Λ. The evaluation in Fig. 3a reveals a significant
correlation (r=0.34±0.06
All uncertainties are expressed as
±one standard deviation unless otherwise stated.
) between Λ(satellite) and Λ(tower), albeit one corrupted by significant
variability. This is to be expected given β is defined as a ratio of
either four uncertain soundings (for the satellite) or two uncertain fluxes
(for the tower). Assuming both measures are co-related through some “true”
intermediate-scale variable, then the slope and intercept of the regression
relationship between the AIRS- and tower-observed Λ are 0.31 (±0.02) and 0.49 (±0.04), respectively.
Sensitivity analysis results of Λ, Φ and λE.
The forcing data are taken for mid-summer, Southern Great Plains, US.
Sensitivities are locally linear-averaged across the ensemble response and
expressed as dimensionless relative changes. Only absolute sensitivities >0.1 are shown. N=105 realisations.
τA: atmospheric transmissivity; f: cloud
cover fraction; α: surface albedo;
εS: surface emissivity;
εA: air emissivity; TS: land surface
temperature; T925: air temperature at 925 mb sounding;
T1000: air temperature at 1000 mb sounding; p925: partial
pressure of water vapour at 925 mb sounding; p1000: partial pressure
of water vapour at 1000 mb sounding.
The sensitivity analysis results are given in Table 2 and show a
differentially higher sensitivity to the vapour pressure observations than for
temperature, and a standard deviation of 0.11 on the estimates of Λ(satellite), although these results are dependent on the level of the input
data given the inverse nonlinearity in Eq. (6).
Latent and sensible heat evaluation
Figures 1b and 3b show the geographical distribution of the average noontime
net available energy and its evaluation for the year 2003 taken from Mallick
et al. (2014). The corresponding geographical distributions of λE
and H are shown in Fig. 1c and d. Figure 3c shows the relationship between
the satellite and tower λE for all 30 evaluation sites. This gives
an overall correlation of r=0.75(±0.04). Assuming both the tower and
satellite data are linearly co-related, linear regression between the
satellite and tower λE gave λE(satellite) =0.98(±0.02)λE(tower) (offset not significant) with a root-mean-square deviation
(RMSD) of 79 Wm-2 (see Fig. 3c). The biome-specific statistics
for λE are given in Table 3, which reveals correlations ranging from
r=0.41(±0.22) (SAV, savanna) to r=0.76(±0.10) (ENF, evergreen needleleaf forest), RMSD ranging from
61 (MF) to 141 (SAV) Wm-2 and regression gains ranging from
0.85(±0.08) (CRO, crops) to 2.00(±0.28) (SAV). Higher correlations (r=0.65-0.76) were evident over the forest sites where the tower height ranged
from 40 to 65 m, followed by moderate correlation over crops (CRO)
and grasses (GRA) (r=0.59-0.67) with tower height of 5–10 m
(Table 3). Similarly, the slope of the correlation was close to unity for the
forests and less than unity for CRO and GRA (Table 3) (Fig. 4). The only
exception was found in savanna (SAV), which showed significant overestimation
and low correlation (Table 3, Fig. 4; reasons discussed later).
The relationship between the satellite and tower H for all 30 evaluation
sites is shown in Fig. 3d. Here, r=0.56(±0.05) and the regression
between the satellite-predicted and tower-observed H produced a regression
line of H(satellite)=0.59(±0.02)H(tower) with an RMSD of
77 Wm-2 for the pooled data. Again, the biome-specific
statistics for H are given in Table 3 and reveal correlations ranging from
0.43(±0.15) (GRA) to 0.79(±0.11) (CRO), RMSD ranging from 52 (CRO)
to 149 (SAV) Wm-2 and regression gains ranging from 0.45(±0.05) (SAV) to 0.93(±0.06) (CRO). Figure 5 shows some examples of
monthly time series of λE for both the satellite and the towers for
a range of sites. This reveals that the seasonality in λE(tower) is
relatively well captured in λE(satellite) in the majority of cases
with the exception of Vielsalm, Tsukuba and Skukuza. Therefore, the
individual site statistics given in Table 3 largely reflect the seasonality
in the tower data.
The sensitivity–uncertainty results for λE are given in Table 2,
revealing a standard deviation on the estimate of λE from the
ensemble of 60 Wm-2 and significant sensitivity to the range of
inputs used to calculate both β and Φ.
Discussion
The results in Fig. 3a may be interpreted through considering the effect of
noise in the satellite sounding observations on the estimation of β and
hence Λ. From Table 2 we see the ensemble distribution of Λ
has a significant negative skew due to taking the inverse of the noise on
p1 and p2 (cf. Eq. 6). As a result, there will be a tendency to overspecify Λ from the sounding data given the “true” value will be
less than the mode. Both the likelihood and the magnitude of this overspecification will increase as p1-p2→0 (i.e. as Λ→0)
because of a decreasing signal-to-noise ratio. This explains why
Λ(satellite) and Λ(tower) diverge as Λ→0. An
additional reason for this divergence is provided by the fact that
H(satellite) <H(tower) due to the effects of warm air entrainment (see
later).
The retrieval of λE depends heavily on Φ, hence the increase in
the satellite-to-tower correlation seen for λE relative to
Λ. Indeed, Λ is a relatively stable characteristic within
site, and so the variance of λE is dominated by seasonal and diurnal
variations in RN and Φ (da Rocha et al., 2004; Kumagai et
al., 2005). For a detailed discussion of the efficacy of the satellite-derived values of Φ we have used here, the reader is referred to Mallick
et al. (2014). To summarise, in comparing the satellite-derived Φ with
the tower H+λE, Mallick et al. (2014) found that their satellite
estimate underestimated the tower value by, on average, approximately
10 %, i.e. Φ(satellite) ≈0.90Φ(tower) (see Fig. 3b).
Therefore, the 2 % underestimate in λE(satellite) seen here
would indicate that we are getting an approximately 8 % compensation
error in λE, introduced by the overspecification of Λ(satellite) seen in Fig. 3a.
Given that there appears to be a widespread lack of energy balance closure of the
order of 20 % observed at most FLUXNET sites (Wilson et al., 2002), this
implies a potential systematic underspecification of λE(tower)
(and/or H(tower)). However, by the same argument the evaluation between
satellite and tower for Φ would change by a similar amount, leading to
little or no net change in the overall evaluation for λE. Mallick et
al. (2014) found that accommodating a 20 % imbalance in Φ(tower)
gave Φ(satellite) ≈0.72Φ(tower) and that this lack of
agreement could be explained by the underspecification of the downwelling
shortwave radiation component of Φ(satellite). It is unlikely that the
entire energy imbalance is attributable solely to λE(tower) (Foken,
2008). As a result, the likely range for the pooled gain between the
satellite and tower λE is between 0.8 and 1.0, determined by the
combination of underspecification of the satellite downwelling shortwave
combined with overspecification of satellite Λ.
The monthly infrared products of AIRS are, by definition, a sample of
relatively cloud-free conditions whilst the tower fluxes are for a mixture of
clear and cloudy atmospheric conditions. The inclusion/omission of cloudy
conditions should have little or no impact on energy partitioning ratios such
as β (Grimmond and Oke, 1995; Balogun et al., 2009). Furthermore,
despite being biased low, the shortwave component of Φ specified by
Mallick et al. (2014) was for all-sky conditions, whilst the IR components of
Φ appeared to be somewhat insensitive to the clear-sky sampling bias. As
a result, the primary motivation for attempting to recover satellite
estimates for all-sky conditions would appear to be for increasing the
temporal resolution of the data, and not for removing bias from the monthly
satellite estimates.
Error analysis of AIRS-derived λE and H over diverse
plant functional types (biomes) of the FLUXNET eddy covariance network. Values in
the parenthesis are ± 1 standard deviation unless otherwise stated.
N: number of data points falling under each biome category.EBF: evergreen broadleaf forest; MF: mixed forest; GRA: grassland;
CRO: cropland; ENF: evergreen needleleaf forest; DBF: deciduous
broadleaf forest; SAV: savanna.
Satellite (grey) and tower (black) time series of monthly average
13:30 latent heat flux, λE, for a selection of sites for 2003.
The numbers on the x axis are the month numbers, indicating January (
month number 1) to December (month number 12).
(a, b) Scatter plot showing the slope of regression between
the observed and estimated λE as a function of the mean variance of
EVI and TS for a 10km×10km area
surrounding the tower sites of each biome categories. Variances of individual
sites falling under each biome are averaged. The solid lines are the best-fit
relationships (M=-23.90µ(σEVI2)+1.03,
R2=0.37; M=-0.08µ(σTS2)+1.04,
R2=0.39) after removing the SAV biome type. This shows M approaches
unity with increasing homogeneity.
(+ EBF; × MF; ○ GRA; * CRO; ∇ ENF; ◊ DBF;
□ SAV)
The landscape-scale β (and hence Λ) estimated from sounder data
relate to a location some few hundred metres above the surface, whilst the
tower data relate to heights either metres (for GRA, CRO and SAV) or tens of
metres (for EBF, MF, DF, EF) above the surface. These towers are designed to
operate in the constant flux portion of the planetary boundary layer which,
as a rule of thumb, occupies the lower 10 % of the planetary boundary
layer and where fluxes change by less than 10 % with height (Stull,
1988). Above this layer there is a tendency of H to decrease with height
due to the entrainment of warm air from aloft down into the mixed layer
(Stull, 1988). This could partly explain the results in Fig. 3d, where
H(satellite) is significantly less than H(tower). In contrast, λE often tends to be preserved with height by the entrainment dry air from
aloft (Stull, 1988; Mahrt et al., 2001). While comparing ground eddy
covariance fluxes with aircraft fluxes over diverse European regions, Gioli
et al. (2004) found the value of H at an average height of 70 m was
35 % less that those at ground level, whereas no such trend in λE was observed. Similarly, Miglietta et al. (2009) found H lapsed by
36 % as one moved from the surface to a height of 100 m. The same
behaviour has also been frequently observed in both airborne and ground-based
eddy covariance measurements in the USA (e.g. Desjardins et al., 1992) and
Europe (Torralba et al., 2008; Miglietta et al., 2009). Because of the
differing lapse properties of λE and H, one would imagine
Λ(satellite) should, on average, be more than Λ(tower),
which, despite being somewhat uncertain, is what we observe both in Figs. 2
and 3a.
The Bowen ratio method has been seen to break down under hot, dry conditions.
This is due to large-scale regionally advected sensible heat desaturating the
surface and causing the vertical vapour pressure gradient to reverse (Perez et
al., 1999), a condition that appeared to persist in the AIRS soundings over
central Australia throughout the summer of 2003. Under these conditions
kH can become 2 to 3 times higher than kE, so
that kE≠kH (Verma et al., 1978; Katul et
al., 1995). Although we rejected all samples characterised by a reversal of
the AIRS vapour pressure gradient, a tendency for Λ(satellite)<Λ(tower) should be observed in the data particularly for the drier
biomes. However, for the SAV data Λ(satellite)>Λ(tower) on
average (see Fig. 3a), indicating this is not a dominant effect.
The satellite-derived fluxes aggregate sub-grid heterogeneity (surface
geometry, roughness, vegetation index, land surface temperature, surface
wetness, albedo, etc.) at the 10 000 km2, whereas the towers
aggregate at scales of ∼1km2. This mismatch on the scale of approximately four orders
of magnitude is an important potential source of disagreement
between the satellite- and tower-observed fluxes. Although towers are often
installed in relatively homogenous terrain at the local scale, rarely can
this be assumed for scales approaching the AIRS data. In addition,
characteristics such as surface wetness and temperature can still be highly
heterogeneous at the local tower scale (Kustas and Norman, 1999; McCabe and
Wood, 2006; Li et al., 2008) whilst also exerting significant nonlinear
effects on λE (Nykanen and Georgiou, 2001). If, for example, the
probability of a tower being located in either a cool/wet or hot/dry patch is
even, and yet the cool/wet regions contribute disproportionately to the
satellite-scale latent heat flux, then, on average, there clearly is a
tendency for the tower-observed flux to be less than its satellite
counterpart (Bastiaanssen et al., 1997). Because of the diversity of
nonlinear surface characteristics effects on λE, a detailed
evaluation of the scaling characteristics of λE lies beyond the
scope of this paper. However the slope of the regression between the observed
and estimated λE of individual biome category was significantly
related to the average variance of EVI (enhanced vegetation index) [μ(σEVI2)] and TS (land surface temperature) [μ(σTS2)] for a 10km×10km area
surrounding the tower sites (Fig. 6a and b) (R2=0.37 and 0.39,
respectively). The slope of regression varied systematically with the
landscape heterogeneity and the results are in agreement with Stoy et
al. (2013), who also found a systematic relationship between the surface
energy balance closure and landscape heterogeneity over 173 FLUXNET tower
sites. One general inference can be drawn, however; the degree of agreement we
see in the pooled evaluation would suggest that the spatial scaling from
tower to satellite appears somewhat conserved, a feature that is no doubt
greatly aided by investigating the monthly average data where the effects of
dynamic spatial heterogeneity (e.g. in surface wetness and surface
temperature) will tend to have been averaged out. However the results in
Table 3 and Fig. 4 suggest that the data from the taller, more extensive
forest towers are more closely related to their satellite counterparts,
although the higher correlations may also reflect the dominance of net
radiation in driving latent heat flux over these sites.
The pooled RMSD of 79 Wm-2 for the λE evaluation is
comparable with the results reported elsewhere. Mecikalski et al. (1999)
reported RMSEs in daily λE estimates in the range of 37 to
59 Wm-2 while estimating continental scale fluxes over the USA
using GOES (Geostationary Operational Environmental Satellite) data. Anderson
et al. (2008) reported an RMSD for instantaneous λE estimates of
79 Wm-2 using a Bowen Ratio closure method and
66 Wm-2 using the residual surface energy balance method.
Another study of Anderson et al. (2007) reported an RMSD in hourly λE of 58 Wm-2 using 10 km2 scale GOES data over Iowa,
although this reduced to 1.7 Wm-2 when considering cumulative
daily data. Jiang et al. (2009) reported an RMSD of 23–40 Wm-2
for daily λE retrievals using NOAA (National Oceanic and Atmospheric
Administration) AVHRR (Advanced Very High Resolution Radiometer) data over
southern Florida. Interestingly, they also found a significant negative
correlation between satellite and ground-truth evaporative fraction. Jiang
and Islam (2001) and Batra et al. (2006) reported RMSDs for noontime λE retrievals from a series of studies over the Southern Great Plains of the
USA in the range of 25 to 97 Wm-2 using moderate-resolution
NOAA-16, NOAA-14 and MODIS-Terra optical and thermal data. In addressing the
effects of scaling and surface heterogeneity issues on λE, McCabe
and Wood (2006) obtained an RMSD of 64 Wm-2 when comparing
spatially aggregated LANDSAT (Land Remote-Sensing Satellite)-derived
instantaneous λE and MODIS Terra λE in central Iowa.
Finally, using the surface temperature vs. vegetation index triangle approach
with MSG (Meteosat Second Generation) SEVIRI (Spinning Enhanced Visible and
Infrared Imager) data, Stisen et al. (2008) obtained an RMSD of
41 Wm-2 for daily data over the Senegal River basin. Finally,
Prueger et al. (2005) obtained a disagreement of 45 Wm-2 in
instantaneous noontime λE while comparing 40 m aircraft and 2 m
ground eddy covariance λE measurements again in central Iowa. Some
additional studies also reported RMSDs of monthly fluxes (for example, Cleugh
et al., 2007; Mu et al., 2011). In these studies, daily λE was
modelled using daily radiation and meteorological variables and monthly
fluxes were generated from the daily averages. Cleugh et al. (2007) reported
RMSD of 27 Wm-2 over two contrasting sites in Australia using
tower meteorology and MODIS vegetation index over the eddy covariance
footprints. Mu et al. (2007, 2011) reported an RMSD of
8–180 Wm-2 on 8-day average λE and 12 mm on
monthly average λE.
Conclusions
We conclude that the combination of the satellite sounding data
and the Bowen ratio methodology shows significant promise for retrieving
spatial fields of λE when compared with tower ground-truth data, and
warrants further investigation and refinement. The specification of satellite
net available energy, and its shortwave component in particular, requires
further attention. There are also circumstances where the satellite Bowen
ratio method is inapplicable, but these conditions could be easily flagged by
internal checks on the sounding profiles. Where the method appears to work,
this provides estimates of λE that would prove valuable in a range
of applications. In particular, because no land surface model has been
involved in their derivation, the estimates of λE we show can be
used as independent data for evaluating land surface parameterisations in a
broad range of spatially explicit hydrology, weather and climate models.
Furthermore, the availability of sounding data at both 1∘ and 5 km
resolution in conjunction with tower and scintillometer surface flux data
would provide an excellent opportunity to explore robust scaling methods in
these same models.
Given that the Bowen ratio method should work best in the non-limiting water
environments, the sea estimates of latent heat we show here are potentially
more reliable than their terrestrial counterparts.
The advent of microwave sounding platforms such as Megha-Tropiques may
afford an opportunity to extend the methodology to persistent overcast
conditions, allowing for more detailed process studies. This approach could
also exploit high spatial and temporal resolution geostationary sounder
platforms like GOES and, in the near future, GIFTS (Geosynchronous
Interferometric Fourier Transform Spectrometer) and INSAT (Indian National
Satellite)-3D. We also expect that the high vertical resolution soundings
these platforms will provide will improve the accuracy of the current
approach, particularly over elevated terrain.
Acknowledgements
We would like to acknowledge Goddard Earth Sciences Data and Information
Services Center (GESS – DISC) and Atmosphere Archive and Distribution System
(LAADS) web interface, NASA, for making the AIRS and MODIS data available. We
gratefully acknowledge all the site PIs who provided terrestrial flux data
through the FLUXNET La Thuile data archive. The AmeriFlux regional network
component of this archive is supported with funding from the US Department of
Energy under its Terrestrial Carbon project. We also acknowledge National
Snow and Ice Data Center (NSIDC) for the SMEX02 radiosonde data. This work
was supported by Natural Environment Research Council (NERC) grant
NEE0191531. We thank Paul Stoy, Montana State University, for valuable
suggestions that helped in improving the manuscript. The authors declare no
conflict of interest.
Edited by: P. Stoy
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