Land data assimilation with satellite me
WATER RESOURCES RESEARCH, VOL. 37, NO. 6, PAGES 1713–1722, JUNE 2001
Land data assimilation with satellite measurements for
the estimation of surface energy balance components
and surface control on evaporation
Giorgio Boni
Centro di Ricerca in Monitoraggio Ambientale, Savona, Italy
Dara Entekhabi
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology
Cambridge, Massachusetts
Fabio Castelli
Dipartimento di Ingegneria Civile, Università degli Studi di Firenze, Florence, Italy
Abstract. A variational land data assimilation system is used to estimate latent heat flux
and surface control on evaporation. The dynamic equation for surface temperature with
energy balance is used as a constraint on the estimation using the adjoint technique.
Measurements of land surface temperature from satellite remote sensing are assimilated
over two subregions within the Southern Great Plains 1997 hydrology field experiment.
The performance of the estimation is linked to the timing of the satellite overpass. During
days when the measurements close to the time of peak ground temperature are available,
the estimation is adequate. The approach shows that satellite remote sensing of land
temperature may be used to provide estimates of components of the surface energy
balance and land surface control on evaporation. The latter parameter is related to
surface soil moisture, and here they are compared with independent values derived from
ground measurements.
1.
Introduction
Satellite platforms provide valuable source of remotely
sensed data for land surface hydrology principally because of
their spatial coverage. The introduction of these data require a
reformulation of both conceptual frameworks and operational
models in hydrology [Entekhabi et al., 1999]. The goal is to
devise and implement retrieval techniques that derive information on land surface hydrology states and parameters based
on measurements of radiation intensity in several narrow spectral ranges.
Since the remote sensing measurements are not direct observations of land surface hydrologic states and parameters,
the retrieval is often an under-determined inverse problem. An
emerging approach to solving such problems is data assimilation that can take advantage of the synergy of multisensor/
multiplatform (satellites as well as in situ) observations. Furthermore, they can effectively impose dynamical constraints by
using a model of the system as part of the statistical estimation.
In this paper a land data assimilation system is introduced
that includes a system model constraint and a measurement
component. Neither components are perfect, therefore noise
and structured error are ascribed to each. The system is directed towards providing statistically optimal estimates of land
surface turbulent flux (latent and sensible heat) and an index of
land surface (moisture) control on evaporation based on merging the data assimilation components. Satellite remote sensing
Copyright 2001 by the American Geophysical Union.
Paper number 2001WR900020.
0043-1397/01/2001WR900020$09.00
data from two low Earth orbit platforms are used as the measurements. The system is applied to a hydrology field experiment (the Southern Great Plains 1997 or SGP 97; see below)
where validation data on surface fluxes and near-surface soil
moisture are available.
Data assimilation has a long heritage in meteorology, oceanography, and geophysics [Bennett, 1992]. There is also extensive application of this approach in subsurface hydrology
[McLaughlin, 1995]. A review of applications in surface hydrology using remote sensing data is presented in section 2. In
section 3 the construct of the land data assimilation is presented, and in section 4 the testing and validation data for a
field experiment site are described. The results of the land data
assimilation system application with measurements from two
operational satellites are presented in section 5. Finally, section 6 contains a summary of the study.
2.
Land Data Assimilation
A land data assimilation system is composed of a dynamic
system (hereafter “forward model”) and a measurement system. The forward model is used to restrict the estimation
procedure by providing dynamical constraints. It further serves
to link estimates at various times which allow information
content of sequential observations to be extracted.
In data assimilation systems it is assumed that neither the
forward model nor the measurements are perfect descriptors
of the system states and parameters. Therefore the chief characteristic of data assimilation systems is the estimation of errors associated with each of these components. A land data
assimilation system must include both a propagation (based on
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BONI ET AL.: LAND DATA ASSIMILATION
the forward model) and an update (based on the measurement
system) component. The error structure of each of these components, frameworks for the propagation of errors, and their
estimation constitute an assimilation system. Finally, the estimation scheme is ideally designed to be statistically optimal,
for example in terms of minimizing sums of squared errors
(L 2 -norm). There are various alternatives to formulating an
estimation system that have all these characteristics.
An example is the sequential estimation technique that
marches states and associated measures of errors structures
(e.g., variance) forward in time. The Kalman-Bucy filter (hereafter Kalman filter) is a one such sequential estimation technique that is statistically optimal for linear problems. A key
requirement of the Kalman filter is that the model forecasts
result from the linearized forward model. R. D. Reichle et al.
(Hydrologic data assimilation with the ensemble Kalman filter,
submitted to Monthly Weather Review, 2000) recently applied
an ensemble Kalman filter to land data assimilation that alleviates the constraints associated with model forecast error covariance propagation in the presence of strong nonlinearity.
They also demonstrate that ensemble Kalman filters are capable of incorporating a wider range of uncertainty characterizations for the forward model. For linear and extended Kalman
filters, errors are assumed Gaussian; therefore the forecast
states are also expected to be Gaussian distributed. The update
step for all Kalman filter use covariances of the forecast errors
and the covariance of measurement errors to form a weighted
estimate of the expectation of states or parameters conditioned
on past observations. For Gaussian systems the use of second
moments for the update results in statistically optimal estimates. For systems with nonlinear forward models the linearization of the problem renders the system slightly suboptimal.
Furthermore, Kalman filter approaches are generally computationally demanding for distributed systems. Examples of Kalman
filter applications in land data assimilation for soil moisture
and/or surface energy balance are Entekhabi et al. [1994] and
Galantowicz et al. [1998] for state estimation and Katul et al.
[1993] for parameter estimation.
There are other estimation approaches for data assimilation
that do not require reliance on using a linearized system for
developing model forecasts. Variational approaches and specifically adjoint techniques (where the forward model is adjoined to a quadratic objective function minimizing squared
retrieval errors) are key among these techniques. A key requirement of the adjoint technique is the tangent-linear form
of the forward model for use in estimating the adjoint variable.
The derivation of the tangent-linear form is sometimes an
involved step especially if the forward model contains switches
or discontinuities. An important advantage of variational techniques is that they are batch estimators in that they use all the
measurements in the assimilation period to estimate the states
and parameters. In this respect, they are often superior to
sequential approaches such as the Kalman filter where only the
measurement up to the update time are used. If the system is
linear, the variational approach and the Kalman filter should
yield identical results at the time of the last measurement. Both
variational and Kalman filter approaches assume Gaussian errors in model and measurements. As mentioned earlier the
Kalman filter is a statistically optimal estimator of the conditional expectation for linear problems (it is suboptimal for
nonlinear problems). The variational approach optimality is
with respect to a slightly different criterion. The variational
approach estimates the conditional mode of the posteriori
probability density function. Only for linear problems do the
two estimates converge exactly and obey the same optimality
criterion. Examples of application of variational approaches to
soil moisture and/or surface energy balance are Reichle et al.
[2000], R. D. Reichle et al. (Downscaling of radiobrightness
measurements for soil moisture estimation: A four-dimensional variation data assimilation approach, submitted to Water
Resources Research, 2000), and Castelli et al. [1999]. Variational
approaches with adjoints require the formulation of the tangent-linear model for the forward model but the nonlinear
system equation is used to estimate the model prediction of
states. This approach is statistically optimal, computationally
efficient, and effective in extracting the information content of
both observations and sequences of observations.
Other approaches to merging model predictions and observations include statistically suboptimal techniques such as direct insertion (where model states predicted by the forward
model are replaced by observations when available) and nudging techniques (where predicted states are relaxed toward observations) [Houser et al., 1998].
In this paper a variational approach to land data assimilation
is presented that is based on adjoint-state formulation. The
land heat equation and surface energy balance constitute the
forward model to predict ground temperature. Here ground
temperature refers to the effective land surface temperature
that is the implicit variable in surface energy balance that
includes the turbulent heat flux and radiative losses. Measurements of ground temperature derived from satellite observations are assimilated and land surface control on evaporation
and components of the surface energy balance are estimated.
Data from the Southern Great Plains 1997 hydrologic field
experiment are applied and in situ observations that are withheld from the land data assimilation system are used for validation. Additionally, the dimensionless measure of land control on evaporation is compared with independent in situ
estimates of surface soil moisture. Micrometeorological forcing (air temperature, humidity, and wind speed) are used in the
forward model. The satellite data are derived from passes of
the five-channel (visible to infrared) Advanced Very High Resolution Radiometers (AVHRR) on board the NOAA 12 and
14 low-Earth orbit satellites.
3. Formulation of the Land Data Assimilation
System
3.1.
Surface Energy Balance Model
Since land surface temperature estimates from satellite remote sensing are assimilated, the relevant system equation is
the heat diffusion equation at the surface and subsurface
rCs
T
5
t
z
S D
ks
T
z
(1)
with boundary conditions
limz3` T~z, t! 5 T#
T
ks
~0, t! 5 2G~0, t!,
z
(2)
where T( z, t) is the soil temperature at depth z and time t, T#
is the deep ground temperature, k s is the soil thermal conductivity, and r s C s is the soil volumetric heat capacity given by the
product of soil density and specific heat capacity. The ground
BONI ET AL.: LAND DATA ASSIMILATION
heat flux or heat flux across the surface is G(0, t) (positive
upward).
The system (1)–(2) may be approximated by a single ordinary differential equation, provided that the soil thermal properties are nearly constant with depth and that the surface
forcing term G(t) has a strong single-frequency (e.g., diurnal)
component with period (vp)21. This approximation is known
as the force-restore equation [Deardorff, 1977; Hu and Islam,
1995]. Using the nondimensional variables,
T
u5 #
T
t 5 2 pv t
G5
G
s T# 4
c5
s T# 3
P Î vp
(3)
,
ence height. The land data assimilation system is directed toward estimating the time-varying parameter a and ground temperature T. The land control on evaporation is contained in
the dynamic parameter a and it is effective for both the entire
soil and vegetation continuum. All the land resistances to
moisture flux are effectively captured by a without componentby-component distinction. Once a and ground temperature are
known, the terms in the land surface energy balance, including
latent and sensible heat flux partitioning of available energy,
may be estimated.
3.2.
Adjoint State Formulation
The measurement component is composed of M discrete (in
time) observations of normalized ground temperature with
zero-mean errors « i :
(4)
where s is the Stefan-Boltzmann constant and P 5 =r s C s k s
is the thermal inertia [Castelli et al., 1999].
The normalized ground heat flux term G includes the components of the surface energy balance
G~ a , u ! 5 R@~ u 2 u a! 1 L~q g 2 q a!# 1 u 4 2 b,
(5)
where R is the dimensionless ratio of radiative to aerodynamic
resistances, L is the dimensionless ratio of specific latent heat
of vaporization to specific heat capacity of air at constant
pressure and multiplied by the reference temperature T# . The
variable b is the available surface radiation, normalized by
surface grey-body thermal radiation at reference temperature.
It does not include the outgoing thermal radiation which has u
dependence and is modeled using the Stefan-Boltzmann relationship in (5). The surface latent heat flux is proportional to
the difference between ground and air specific humidity q g 2
q a . Similarly, the surface sensible heat flux is proportional to
the difference between normalized ground and air temperatures u 2 u a 5 (T/T# ) 2 (T a /T# ). In both cases of surface
turbulent flux a similar aerodynamic resistance formulation is
used to establish the flux rates.
The aerodynamic resistance is based on a log-linear wind
profile in the surface atmospheric layer with an aerodynamic
roughness length scale z 0 . This parameterization is valid for
near-neutral conditions. Assumption of near-neutral conditions is convenient for the estimation scheme because it reduces the places where there is ground temperature dependence in the equations. When minimizing the objective
function, fewer terms have ground temperature dependence.
There are no obstacles to including stability correction except
for the effort. The near-neutral assumption probably causes a
damping of the diurnal cycle of turbulent flux efficiencies in
dissipating the surface available energy that translate to slight
degradation of the data assimilation system performance.
In the latent heat flux formulation, following Castelli et al.
[1999], the specific humidity at the ground surface, q g , is estimated by reducing the temperature-dependent saturation specific humidity (q*( u )) through a multiplicative and dimensionless index (a), which represents soil control on evaporation
q g 5 a q* ~ u !.
i 5 1, . . . , M.
u iobs 5 u i 1 « i
which can be written as simply
du
5 1 1 u 2 cG,
dt
1715
(6)
Latent heat flux is proportional to the difference between
this value of specific humidity and that in the air, q a , at refer-
(7)
The surface or soil control on evaporation has the true
(unknown) value a(t) in time and it can only be estimated with
zero-mean error m(t) such that the best estimate a9(t) is
(8)
a 9~ t ! 5 a ~ t ! 1 m ~ t !
The error covariances of « i and m(t) are positive-symmetric
functions K 21
and K 21
3
2 . The errors « i and m(t) are assumed to
be Gaussian, and they are therefore fully characterized by their
mean values and covariances.
An objective function J( u , a ) for the estimation problem
over the period [0, t1] has the following individual terms Boni
et al. [2001]:
M
M
1. Squared measurement error ¥ j51
¥ i51
« i K 2 i, j « j over
the entire period (separately include the value at terminal time
t1 as K 2 M,M « 2 ( t 1 )).
2. Squared estimation error of the parameter a over the
entire assimilation period [0, t1] as in * 0t 1 * 0t 1 m ( t ) K 3 ( t ,
t 9) m ( t 9) d t 9 d t .
3. The forward model (4) constraint that is adjoined using a
Lagrange multiplier l(t) as in 2 *t01 l[(du/dt) 2 1 1 u 1 cG] dt.
It is important to note that the uncertainty in the forward
model is contained in the a(t) component in this choice of
formulation.
Taking the first variation of J( u , a ), using the symmetry of
K 2 and K 3 , applying integration by-parts, and grouping the
independent variations results in Euler-Lagrange equations
that need to be integrated in time forward and backward [Castelli et al., 1999; Boni et al., 2001]. These equations are
S
dl
G
5l 11c
dt
u
D OO
M
M
1
~ u 2 u obs! tiK 2~ t i, t ! d ~ t 2 t j!
i51 j51
(9)
(10)
l ~ t 1! 5 K 1~ u obs 2 u ! t1
a 5 a9 2
E
t1
K 321~ t , t 0! l c
G
d t 0.
a
(11)
0
When there are sparsely sampled measurements (in time),
the full covariance of the prediction and estimation errors is
important [Boni et al., 2001]. In such a case a suitable covariance function must be defined that takes into account both
temporal decorrelation and periodic diurnal cycle effects. Such
a function is defined by
1
K 321~ t , t 0! 5 2 @1 1 cos ~u t 2 t 0u!# e 2
where t0 is the decorrelation scales.
ut2t0u
t0
,
(12)
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BONI ET AL.: LAND DATA ASSIMILATION
The data assimilation scheme iteratively improves estimates
of a starting from an initial guess a9. In this iteration the
forward model (4) is integrated in time with the initial guess a9.
The predicted values of normalized ground temperature u(t)
are used to integrate (9) backward in time starting with the end
condition (10). The forcing for the dynamic equation for the
Lagrange multiplier (9) is the prediction misfit (u 2 uobs)t i
whenever measurements are made (denoted by the delta function d ( t 2 t j ) at times of observation j 5 1, z z z , M). The
Lagrange multiplier l(t) is then used to update the estimate of
a using (11). The iteration continues until a desirable level of
convergence is reached.
4.
Data
The assimilation scheme is tested using data from the Southern Great Plains 1997 (SGP 97) hydrology field experiment
(available at http://hydrolab.arsusda.gov/sgp97/). SGP 97 experiment includes in situ, airborne, and space-borne data collection. The field experiment area covered ;10,000 km2 across
northeastern Oklahoma. Two intensive data collection subfields (Central Facility and El Reno) that contained surface
flux stations are used in this study.
The forcing of the data assimilation system is taken from
micrometeorological stations and aggregated to nominal 30
min time steps covering a 29 days period in June and July of
1997. The variables include air relative humidity, air pressure,
and air temperature at reference height (1.5 m), wind speed at
10 m, and incident solar radiation.
In the first assimilation example (the reference case for
comparisons), in situ soil temperature measurements at different depths (5 and 10 cm under bare soil, 5, 10, and 30 cm under
natural sod cover) are used. Soil temperature observations at
different depths (5 and 10 cm under bare soil, 5, 10, and 30 cm
under natural sod cover) are used to estimate ground surface
temperature to be assimilated. The method used in Boni et al.
[2001] is applied to inferring surface ground temperature. It is
based on a solution to the heat diffusion equation with periodic
boundary condition:
T~ z, t! 5 T~l, t! 1 A Te z/l sin ~ v t 2 z/l !,
(13)
where l is the e-folding depth of diurnal heat waves. The length
scale l can be estimated from the phase shift between time
series of soil temperature at two different depths. Soil temperature at the e-folding depth T(l, t) is approximated to be the
mean value of the observed diurnal cycle. The amplitude of the
surface ground temperature A T can be simply evaluated from
the available time series once l and T(l, t) are known. The
method has been successfully tested using the field experiment
measurement at the USDA Beltsville Agricultural Research
Center (BARC) conducted during 1994, where three different
depths of observations and radiometric surface ground observations were simultaneously available. The root-mean-squared
error (RMSE) of reconstructed ground surface temperature at
half-hour resolution was found to be of the order of 18C over
a 16 days period.
The second assimilation case is provided with land surface
temperatures from satellite remote sensing instead. These
measurements are estimated from NOAA 12 and 14 low Earth
orbit satellites. Overpasses occur at 0730 and 1930 6 ;1 hour
for NOAA 12 and at 0230 and 1430 p.m. 6 ;1 hour for NOAA
14, all in local time. The AVHRR instrument on board these
platforms makes measurements in discrete visible to infrared
spectral bands. The nominal spatial resolution of the satellite
measurements are 1.1 km at nadir.
To calculate ground temperature from satellite brightness
temperatures (T b ) a split-window algorithm for multichannel
infrared data has been applied [Wan and Dozier, 1996]. This
particular method relates ground temperature to AVHRR
brightness temperature measurements in channels 4 and 5
(T b 4 and T b 5 ). Satellite brightness temperature measurements are averaged over an 11 km2 area. In both cases the
estimated ground temperature values are related to ground
truth with less than 18C RMSE. Averaged brightness temperature values that are contaminated by cloud cover are discarded. The criterion for detecting clouds is based on 50% or
more pixels brightness temperature colder than 108C indicating cloud tops rather than the surface as the emitting body.
obs
For validation half-hourly latent and sensible heat flux (Q E
obs
and Q H
) from eddy-correlation systems are used. Groundtruth values of a may also be estimated for validation from
these measurements. This may be done by inverting the resistance expression for latent heat flux for a. However, using the
definition of evaporative fraction EF
EF ;
Q obs
E
Q 1 Q Hobs
(14)
obs
E
allows for inverting sensible and latent heat fluxes simultaneously so that the estimates of observed a or aobs do not
directly depend on specification of an aerodynamic resistance
r a . With the definition 14, solving for a gives
a obs 5
S
u 2 ua
L
q*~T!~1 2 EF!
q a~1 2 EF! 1
D
EF
.
(15)
In assimilation experiments besides the value of surface
aerodynamic roughness z 0 , solar albedo, surface thermal emissivity, and deep ground temperature T# also need to be specified. Here an aerodynamic roughness length equal to 3 3 1024
m is used. This is consistent with the observed latent and
sensible heat fluxes. The solar albedo and surface thermal
emissivity are estimated from the radiative flux measurements
at the Central Facility site. Also, the deep ground temperature
T# is set to the mean of daily ground temperature at 0.1 m
below the surface over the simulation period.
Finally, daily estimates of surface (within top 0.06 m) volumetric moisture content at three sites (one at the Central
Facility and two at the El Reno fields) are used for comparison
with the estimated values of a which represent the land surface
control on evaporation. The daily estimates of soil moisture
have been derived by impedance point measurements on a
regularly spaced grid around each site [Famiglietti et al., 1999].
5.
Results
Two sites within the SGP 97 experiment area (El Reno and
Central Facility) are selected for application and validation of
the data assimilation approach. These sites were chosen because the El Reno and Central Facility sites had installed
systems to measure latent and sensible heat flux, and field soil
moisture. The El Reno site is principally range land or cultivated with winter wheat. It has flat terrain and generally silty
loam soils. During the 1997 experiment this site was moist and
BONI ET AL.: LAND DATA ASSIMILATION
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Figure 1a. Time series of in situ measured ground temperature for the SGP97 experiment period at the El
Reno site (line). Estimates derived from NOAA 12 and NOAA 14 satellite overpasses based on AVHRR
instrument are represented as symbols. The closed symbols are those satellite estimates that fall within the
three hours period around the time of the maximum ground temperature occurrence.
experienced major rain events. The Central Facility site also in
a flat region with silty loam soils. The regional land cover is
principally cultivated winter wheat.
Only ground surface temperature (in the first assimilation
case only), deep ground temperatures, and surface air micrometeorology (air temperature, humidity, and wind speed)
are provided to the data assimilation system. The remainder of
observations such as precipitation, measured latent and sensible heat fluxes, and soil moisture are withheld for validation.
The entire period of the SGP 97 experiment (amounting to a
total of 29 days) is the window for the assimilation system.
Two cases are studied at each site. In the first case half-
Figure 1b. Same as Figure 1a but for the Central Facility site.
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BONI ET AL.: LAND DATA ASSIMILATION
Figure 2a. Data assimilation results at the El Reno site. In this case the half-hourly in situ ground temperature measurements are assimilated. (top) Time series of half-hourly errors in the estimation of ground
temperature. (middle) Measurement (dashed line) and assimilation (solid line) estimates of surface latent
heat flux. Also included in this panel are the trace records of precipitation. (bottom) Estimates of a based on
measured EF (dashed line) and assimilation (solid line) are shown. The daily a and latent heat values are
averages over six hours around noon. Missing values in the measured EF sequence correspond to days when
the measured fluxes yielded a values far outside of the expected [0, 1] range.
hourly in situ observations of ground temperature are used as
the measurements for the data assimilation in a nearly ideal,
albeit rarely available configuration. Such a configuration is
similar to the one considered in the study of Castelli et al.
[1999] where validation was performed with data from First
International Satellite Land Surface Climatology Project
(ISLSCP) Field Experiment (FIFE). The quality of FIFE validation data is likely to be superior to SGP 97 because several
Figure 2b. Same as Figure 2a but for the Central Facility site.
BONI ET AL.: LAND DATA ASSIMILATION
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Figure 3a. The assimilation with half-hourly in situ ground temperature measurements at El Reno are used
for comparison with assimilation with satellite data only: (top) Time series of half-hourly errors in the
estimation of ground temperature; (middle) Base case (solid line) and assimilation with satellite data estimates of surface latent heat flux. Also included are the trace records of precipitation. (bottom) Estimates of
a based on the base case assimilation (solid line) and assimilation with satellite data alone are shown. The
daily a and latent heat values are averages over 6 hours around noon. The solid symbols are those satellite
estimates that fall within the 3 hours period around the time of the maximum ground temperature occurrence
(as in Figures 1a and 1b).
surface flux measurement stations were used to form area
averages. The data assimilation system performed with an
RMSE of ;30 W m22 for daily latent heat flux estimation,
which may be considered to be on the same order as the
turbulent flux measurement uncertainty. In SGP 97 the availability of surface heat flux stations is considerably more limited. For this reason we take the assumption that data assimilation with half-hourly in situ measured ground temperature
Figure 3b. Same as Figure 3a but for the Central Facility site.
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BONI ET AL.: LAND DATA ASSIMILATION
provides a reasonable reconstruction of ground-truth for SGP
97. This reconstruction is therefore used as the base case for
comparison of data assimilation with infrequently sampled satellite data.
Figure 1a for El Reno and Figure 1b for Central Facility
show the time series of in situ measured ground temperature.
The symbols represent estimates made based on the satellite
brightness temperatures measurements through the Wan and
Dozier [1996] algorithm. Estimates from those satellite measurements that fall within a 3-hour window of the time of peak
daily ground temperature (NOAA 14 1430 LT overpass) are
solid symbols. This distinction will prove to be important when
the satellite data are assimilated, and it will be discussed later
in this section.
The application of the data assimilation system with halfhourly ground temperature in situ observations as measurements is shown in Figure 2a (El Reno) and Figure 2b (Central
Facility). Figures 2a and 2b (top) shows the error in the estimation of ground temperature which is the state of the system
(4). The errors are plotted for each half hour of the 29 days. In
both cases the errors are small (RMSE values are 0.648C at the
El Reno and 0.258C at the Central Facility sites). The surface
heat balance is reconstructed closely in the case of assimilation
with half-hourly ground temperature observations. Figures 2a
and 2b (middle) show the performance of the system in terms
of latent heat flux. The estimation values are averaged over the
6 hours centered around noon (solid lines). The values derived
from observations are represented by the dashed lines and
rainfall events are included as bars. At the El Reno site (Figure
2a) the data assimilation and observed values of surface latent
heat flux have day-to-day fluctuations that track closely but the
values based on the EBBR system at the site are consistently
above the data assimilation results with peaks reaching 600 W
m22.
In order to assess whether there are possible biases in the
turbulent heat flux measurements at each site, we make some
scale comparisons with the possibly more reliable pyranometer
measurements. The half-hourly measured peak net radiation
observed at the El Reno is 730 W m22. At the time of this peak
the ground heat flux is changing sign and it is therefore near
zero. With 730 W m22 of peak net radiation a half-hour peak
surface latent flux measurement at El Reno of 760 W m22 may
indicate positive bias and/or noise in the surface flux measuring
system at this site. At Central Facility the peak net radiation
experienced during the SGP 97 period was 650 W m22, which
is close to the observed peak latent heat flux of 625 W m22.
The Central Facility latent heat flux estimation is also biased
(but less than in the case of El Reno). Nonetheless, the covariability between the data assimilation and measurements
show close tracking in Figure 2b (middle). The third panels in
Figures 2a and 2b contain the daily values of a averaged for the
6 hours centered at noon in the diurnal cycle. Again the results
based on measurements are denoted by dashed lines; they are
estimated using (15). The values resulting from data assimilation are represented by solid lines. Because of inconsistencies
and errors in observations of latent and sensible heat flux and
surface micrometeorology, some of the values of aobs fall outside of the expected [0, 1] range. Biases in the turbulent heat
flux measurements may cause other, largely unknown, errors in
the estimation of aobs. These errors can truly only be characterized using a synthetic case study where the true condition is
better known.
The values of a from the data assimilation of half-hourly in
situ measured ground temperature are closer to the available
observation estimates for the Central Facility site (Figure 2b)
when compared with the El Reno site (Figure 2a). This is
consistent with the performances when surface latent heat flux
is compared. Notably, in the case of Central Facility the dayto-day fluctuations, especially increases in the values of a following surface wetting by rain events, are captured well in the
data assimilation results.
Use of low-Earth orbit satellite measurements in data assimilation is constrained by the temporal sampling problem.
The AVHRR instrument on board the NOAA 12 and 14
satellite platforms are used here to provide the measurements
in data assimilation. No other source of ground temperature
observations are used. Figure 3a and 3b show the results of the
data assimilation. The symbols represent the results of the data
assimilation with measurements provided by AVHRR only.
Again, the solid symbols are used to indicate those satellite
ground temperature estimates that are made with available
NOAA 14 1430 LT pass measurements. Figures 3a and 3b
(top) contain the time series of errors in the estimation of
half-hourly ground temperature with respect to the base case.
The RMSE in the case of El Reno is 2.7 8C and in the case of
Central Facility 2.48C. There also appears to be a slight bias
during the period when midday satellite observations are
sparse, but over the entire assimilation period the bias is small.
The values are larger than the case in Figures 2a and 2b (even
when compared to in situ measurements) mostly due to inadequate sampling of the diurnal cycle in ground temperature.
Figures 3a and 3b (middle) show the daytime surface latent
heat flux. In both cases (El Reno in Figure 3a and Central
Facility in Figure 3b) on days when the satellite overpass near
the time of the peak daily ground temperature is available
(identified by solid squares) the data assimilation estimates of
surface latent heat flux are close to the base case. On days
when no NOAA 14 1430 overpass measurements are available
(identified by open squares), the performance is considerably
worse. This indicates the importance of satellite sampling
times for land data assimilation [Boni et al., 2001]. The maximum surface ground temperature results from cumulative
heating and hence it is sensitive to the partitioning of available
energy into sensible and latent turbulent heat fluxes during the
day. For this reason it is particularly important to have measurements near the time of maximum ground temperature
(early afternoon) for land data assimilation of hydrologic variables such as a. Boni et al. [2001] showed how the assimilation
performance rapidly degrades when temperature sampling is
done outside a three hours window around the time of diurnal
peak. Some of the shortcomings in the estimation of a is also
related to the error model used for it. We have assumed that
errors in a are Gaussian distributed. The parameter a is
bounded between zero and unity, and such an error model is
convenient but can certainly pose some problems when errors
are large. Furthermore we make comparisons with midday
values of aobs because during this period the turbulent fluxes
are strong and their measurement errors are a smaller fraction
of the signal. Furthermore, during this period radiation is often
not the limiting factor for surface evaporation, and therefore
the day-to-day land control is more clearly evident.
In situ soil moisture measurement offer an independent data
set to validate the retrieved values of a. Data on volumetric
moisture content collected at El Reno and Central Facility
sites are reported by Famiglietti et al. [1999]. The values are
normalized by soil porosity reported by Famiglietti et al. [1999]
BONI ET AL.: LAND DATA ASSIMILATION
Figure 4a. Comparison of soil moisture based on estimate a
and application of the model of Noilhan and Planton [1989] at
El Reno site. The ordinate is soil moisture observed in situ
together with spatial standard deviation [Famiglietti et al.,
1999]. Data assimilation with satellite data are stratified according to whether there are available satellite data near the
peak of the diurnal ground temperature (closed circles for
available measurements near the peak and open circles for lack
of measurements near the peak). A characteristic soil porosity
of 0.45 is used to compare relative soil saturation values.
for the sites (near 0.45) in order to estimate relative soil saturation in the normalized range [0, 1]. The standard deviation
associated with the daily mean values reported by Famiglietti et
al. [1999] refer to spatial variability at the data collection sites
in El Reno and Central Facility. In order to compare the a
index of soil water to these in situ measurements the parameterization of Noilhan and Planton [1989] is used to transform
a into relative soil saturation. The parameterization is a simple
empirical model of relative humidity at the ground surface
related to the surficial soil moisture [Noilhan and Planton,
1989, equation (28)]. It is only an approximation in order to
translate the a values into a reasonable expected surficial soil
moisture. Figures 4a and 4b show the plot of estimated relative
soil saturation (based on the data assimilation system with
satellite measurements of ground temperature) and those
measured at the El Reno and Central Facility sites, respectively. Again the open symbols are used to indicate days during
which NOAA 14 1430 LT measurements are not available.
Solid symbols represent estimated values during days when the
available satellite data falls within the 3-hours window around
the peak of diurnal ground temperature. Plot-scale spatial variability of in situ soil moisture measurements are denoted by
the one standard deviation error whiskers around the mean
values in Figures 4a and 4b. The value estimated by data
assimilation corresponds to the effective value within the
ground resolution of the satellite measurements. Nonetheless,
in both Figures 4a and 4b it is evident that estimates during
days when the satellite data for ground temperature near the
time of diurnal peak is available, the correspondence of assim-
1721
Figure 4b. Same as Figure 4a but for the Central Facility
site.
ilation estimate of surface relative soil saturation and in situ
measurements are superior to days when such data are missing.
6.
Summary
A statistically optimal land data assimilation system to minimize the error of estimation when both model and measurements contain uncertainty is applied to two sites within the
Southern Great Plains 1997 hydrology field experiment in
northeast Oklahoma. The model consists of ground heat flow
with surface energy balance at the land surface. It is used to
provide dynamically consistent constraints on the estimation.
Two case studies are considered, each with a different input
stream of measurements. In the first and ideal case that also
serves as the reference for subsequent comparisons, halfhourly in situ ground temperature observations are the measurements in the data assimilation. In the second case, satellite
data from two low-Earth orbit satellite are the only source of
measurements for ground temperature. Data from surface flux
measuring stations and in situ soil moisture observations are
used to validate the estimation results with ground-truth. It is
shown that the data assimilation system performs well in capturing the day-to-day variations in the components of surface
energy balance, ground temperature, and soil moisture or surface control on evaporation. Even though the precipitation
data are withheld from the assimilation system, the wetting and
drydown events are estimated and their effects on land control
on evaporation are captured. On days when satellite data are
available close to the time of peak diurnal ground temperature,
the estimation is considerably improved over days when the
cumulative daily heating is unknown.
Use of remotely sensed land surface temperature in a data
assimilation framework to estimate fields of energy balance
components and surface control on evaporation is feasible but
considerably more refinements need to be made. The advantage of using land surface temperature data for this application
in hydrology is that the satellite remote sensing of this variable
1722
BONI ET AL.: LAND DATA ASSIMILATION
has a long heritage, and it is possible to construct long-period
data sets based on past and current sensors and platforms. The
areas where the assimilation system can be improved include
the following: (1) revised formulation of the uncertainty in the
forward model and incorporation of more suitable characterization of errors for the bounded parameter a, (2) extensions
to spatial fields so that the spatial covariance in the forcing and
parameter fields can effectively condition the estimation, and
(3) use of the synergy provided by multiple satellite platforms
in order to better characterize the diurnal cycle of land temperatures.
Acknowledgments. This study was supported by NASA grant
NAG8-1524, the MIT-CNR cooperative agreement, and sabbatical
leave granted by MIT.
References
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165–172, 2001.
Castelli, F., D. Entekhabi, and E. Caporali, Estimation of surface heat
flux and an index of soil moisture using adjoint-state surface energy
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processes for meteorological models, Mon. Weather Rev., 117, 536 –
549, 1989.
Reichle, R., D. B. McLaughlin, and D. Entekhabi, Variational data
assimilation of microwave radiobrightness observations for land surface hydrologic applications, IEEE Trans. Geosci. Remote Sens., in
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Reichle, R., D. B. McLaughlin, and D. Entekhabi, Hydrologic data
assimilation with the ensemble Kalman Filter, Mon. Weather Rev., in
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G. Boni, Centro di Ricerca in Monitoraggio Ambientale, Savona,
Italy ([email protected])
F. Castelli, Dipartimento di Ingegneria Civile, Università degli Studi
di Firenze, Florence, Italy.
D. Entekhabi, Department of Civil and Environmental Engineering,
Massachusetts Institute of Technology, 48-331 Ralph M. Parsons Laboratory, Cambridge, MA 02139. ([email protected])
(Received February 24, 2000; revised December 23, 2000;
accepted January 12, 2001.)
Land data assimilation with satellite measurements for
the estimation of surface energy balance components
and surface control on evaporation
Giorgio Boni
Centro di Ricerca in Monitoraggio Ambientale, Savona, Italy
Dara Entekhabi
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology
Cambridge, Massachusetts
Fabio Castelli
Dipartimento di Ingegneria Civile, Università degli Studi di Firenze, Florence, Italy
Abstract. A variational land data assimilation system is used to estimate latent heat flux
and surface control on evaporation. The dynamic equation for surface temperature with
energy balance is used as a constraint on the estimation using the adjoint technique.
Measurements of land surface temperature from satellite remote sensing are assimilated
over two subregions within the Southern Great Plains 1997 hydrology field experiment.
The performance of the estimation is linked to the timing of the satellite overpass. During
days when the measurements close to the time of peak ground temperature are available,
the estimation is adequate. The approach shows that satellite remote sensing of land
temperature may be used to provide estimates of components of the surface energy
balance and land surface control on evaporation. The latter parameter is related to
surface soil moisture, and here they are compared with independent values derived from
ground measurements.
1.
Introduction
Satellite platforms provide valuable source of remotely
sensed data for land surface hydrology principally because of
their spatial coverage. The introduction of these data require a
reformulation of both conceptual frameworks and operational
models in hydrology [Entekhabi et al., 1999]. The goal is to
devise and implement retrieval techniques that derive information on land surface hydrology states and parameters based
on measurements of radiation intensity in several narrow spectral ranges.
Since the remote sensing measurements are not direct observations of land surface hydrologic states and parameters,
the retrieval is often an under-determined inverse problem. An
emerging approach to solving such problems is data assimilation that can take advantage of the synergy of multisensor/
multiplatform (satellites as well as in situ) observations. Furthermore, they can effectively impose dynamical constraints by
using a model of the system as part of the statistical estimation.
In this paper a land data assimilation system is introduced
that includes a system model constraint and a measurement
component. Neither components are perfect, therefore noise
and structured error are ascribed to each. The system is directed towards providing statistically optimal estimates of land
surface turbulent flux (latent and sensible heat) and an index of
land surface (moisture) control on evaporation based on merging the data assimilation components. Satellite remote sensing
Copyright 2001 by the American Geophysical Union.
Paper number 2001WR900020.
0043-1397/01/2001WR900020$09.00
data from two low Earth orbit platforms are used as the measurements. The system is applied to a hydrology field experiment (the Southern Great Plains 1997 or SGP 97; see below)
where validation data on surface fluxes and near-surface soil
moisture are available.
Data assimilation has a long heritage in meteorology, oceanography, and geophysics [Bennett, 1992]. There is also extensive application of this approach in subsurface hydrology
[McLaughlin, 1995]. A review of applications in surface hydrology using remote sensing data is presented in section 2. In
section 3 the construct of the land data assimilation is presented, and in section 4 the testing and validation data for a
field experiment site are described. The results of the land data
assimilation system application with measurements from two
operational satellites are presented in section 5. Finally, section 6 contains a summary of the study.
2.
Land Data Assimilation
A land data assimilation system is composed of a dynamic
system (hereafter “forward model”) and a measurement system. The forward model is used to restrict the estimation
procedure by providing dynamical constraints. It further serves
to link estimates at various times which allow information
content of sequential observations to be extracted.
In data assimilation systems it is assumed that neither the
forward model nor the measurements are perfect descriptors
of the system states and parameters. Therefore the chief characteristic of data assimilation systems is the estimation of errors associated with each of these components. A land data
assimilation system must include both a propagation (based on
1713
1714
BONI ET AL.: LAND DATA ASSIMILATION
the forward model) and an update (based on the measurement
system) component. The error structure of each of these components, frameworks for the propagation of errors, and their
estimation constitute an assimilation system. Finally, the estimation scheme is ideally designed to be statistically optimal,
for example in terms of minimizing sums of squared errors
(L 2 -norm). There are various alternatives to formulating an
estimation system that have all these characteristics.
An example is the sequential estimation technique that
marches states and associated measures of errors structures
(e.g., variance) forward in time. The Kalman-Bucy filter (hereafter Kalman filter) is a one such sequential estimation technique that is statistically optimal for linear problems. A key
requirement of the Kalman filter is that the model forecasts
result from the linearized forward model. R. D. Reichle et al.
(Hydrologic data assimilation with the ensemble Kalman filter,
submitted to Monthly Weather Review, 2000) recently applied
an ensemble Kalman filter to land data assimilation that alleviates the constraints associated with model forecast error covariance propagation in the presence of strong nonlinearity.
They also demonstrate that ensemble Kalman filters are capable of incorporating a wider range of uncertainty characterizations for the forward model. For linear and extended Kalman
filters, errors are assumed Gaussian; therefore the forecast
states are also expected to be Gaussian distributed. The update
step for all Kalman filter use covariances of the forecast errors
and the covariance of measurement errors to form a weighted
estimate of the expectation of states or parameters conditioned
on past observations. For Gaussian systems the use of second
moments for the update results in statistically optimal estimates. For systems with nonlinear forward models the linearization of the problem renders the system slightly suboptimal.
Furthermore, Kalman filter approaches are generally computationally demanding for distributed systems. Examples of Kalman
filter applications in land data assimilation for soil moisture
and/or surface energy balance are Entekhabi et al. [1994] and
Galantowicz et al. [1998] for state estimation and Katul et al.
[1993] for parameter estimation.
There are other estimation approaches for data assimilation
that do not require reliance on using a linearized system for
developing model forecasts. Variational approaches and specifically adjoint techniques (where the forward model is adjoined to a quadratic objective function minimizing squared
retrieval errors) are key among these techniques. A key requirement of the adjoint technique is the tangent-linear form
of the forward model for use in estimating the adjoint variable.
The derivation of the tangent-linear form is sometimes an
involved step especially if the forward model contains switches
or discontinuities. An important advantage of variational techniques is that they are batch estimators in that they use all the
measurements in the assimilation period to estimate the states
and parameters. In this respect, they are often superior to
sequential approaches such as the Kalman filter where only the
measurement up to the update time are used. If the system is
linear, the variational approach and the Kalman filter should
yield identical results at the time of the last measurement. Both
variational and Kalman filter approaches assume Gaussian errors in model and measurements. As mentioned earlier the
Kalman filter is a statistically optimal estimator of the conditional expectation for linear problems (it is suboptimal for
nonlinear problems). The variational approach optimality is
with respect to a slightly different criterion. The variational
approach estimates the conditional mode of the posteriori
probability density function. Only for linear problems do the
two estimates converge exactly and obey the same optimality
criterion. Examples of application of variational approaches to
soil moisture and/or surface energy balance are Reichle et al.
[2000], R. D. Reichle et al. (Downscaling of radiobrightness
measurements for soil moisture estimation: A four-dimensional variation data assimilation approach, submitted to Water
Resources Research, 2000), and Castelli et al. [1999]. Variational
approaches with adjoints require the formulation of the tangent-linear model for the forward model but the nonlinear
system equation is used to estimate the model prediction of
states. This approach is statistically optimal, computationally
efficient, and effective in extracting the information content of
both observations and sequences of observations.
Other approaches to merging model predictions and observations include statistically suboptimal techniques such as direct insertion (where model states predicted by the forward
model are replaced by observations when available) and nudging techniques (where predicted states are relaxed toward observations) [Houser et al., 1998].
In this paper a variational approach to land data assimilation
is presented that is based on adjoint-state formulation. The
land heat equation and surface energy balance constitute the
forward model to predict ground temperature. Here ground
temperature refers to the effective land surface temperature
that is the implicit variable in surface energy balance that
includes the turbulent heat flux and radiative losses. Measurements of ground temperature derived from satellite observations are assimilated and land surface control on evaporation
and components of the surface energy balance are estimated.
Data from the Southern Great Plains 1997 hydrologic field
experiment are applied and in situ observations that are withheld from the land data assimilation system are used for validation. Additionally, the dimensionless measure of land control on evaporation is compared with independent in situ
estimates of surface soil moisture. Micrometeorological forcing (air temperature, humidity, and wind speed) are used in the
forward model. The satellite data are derived from passes of
the five-channel (visible to infrared) Advanced Very High Resolution Radiometers (AVHRR) on board the NOAA 12 and
14 low-Earth orbit satellites.
3. Formulation of the Land Data Assimilation
System
3.1.
Surface Energy Balance Model
Since land surface temperature estimates from satellite remote sensing are assimilated, the relevant system equation is
the heat diffusion equation at the surface and subsurface
rCs
T
5
t
z
S D
ks
T
z
(1)
with boundary conditions
limz3` T~z, t! 5 T#
T
ks
~0, t! 5 2G~0, t!,
z
(2)
where T( z, t) is the soil temperature at depth z and time t, T#
is the deep ground temperature, k s is the soil thermal conductivity, and r s C s is the soil volumetric heat capacity given by the
product of soil density and specific heat capacity. The ground
BONI ET AL.: LAND DATA ASSIMILATION
heat flux or heat flux across the surface is G(0, t) (positive
upward).
The system (1)–(2) may be approximated by a single ordinary differential equation, provided that the soil thermal properties are nearly constant with depth and that the surface
forcing term G(t) has a strong single-frequency (e.g., diurnal)
component with period (vp)21. This approximation is known
as the force-restore equation [Deardorff, 1977; Hu and Islam,
1995]. Using the nondimensional variables,
T
u5 #
T
t 5 2 pv t
G5
G
s T# 4
c5
s T# 3
P Î vp
(3)
,
ence height. The land data assimilation system is directed toward estimating the time-varying parameter a and ground temperature T. The land control on evaporation is contained in
the dynamic parameter a and it is effective for both the entire
soil and vegetation continuum. All the land resistances to
moisture flux are effectively captured by a without componentby-component distinction. Once a and ground temperature are
known, the terms in the land surface energy balance, including
latent and sensible heat flux partitioning of available energy,
may be estimated.
3.2.
Adjoint State Formulation
The measurement component is composed of M discrete (in
time) observations of normalized ground temperature with
zero-mean errors « i :
(4)
where s is the Stefan-Boltzmann constant and P 5 =r s C s k s
is the thermal inertia [Castelli et al., 1999].
The normalized ground heat flux term G includes the components of the surface energy balance
G~ a , u ! 5 R@~ u 2 u a! 1 L~q g 2 q a!# 1 u 4 2 b,
(5)
where R is the dimensionless ratio of radiative to aerodynamic
resistances, L is the dimensionless ratio of specific latent heat
of vaporization to specific heat capacity of air at constant
pressure and multiplied by the reference temperature T# . The
variable b is the available surface radiation, normalized by
surface grey-body thermal radiation at reference temperature.
It does not include the outgoing thermal radiation which has u
dependence and is modeled using the Stefan-Boltzmann relationship in (5). The surface latent heat flux is proportional to
the difference between ground and air specific humidity q g 2
q a . Similarly, the surface sensible heat flux is proportional to
the difference between normalized ground and air temperatures u 2 u a 5 (T/T# ) 2 (T a /T# ). In both cases of surface
turbulent flux a similar aerodynamic resistance formulation is
used to establish the flux rates.
The aerodynamic resistance is based on a log-linear wind
profile in the surface atmospheric layer with an aerodynamic
roughness length scale z 0 . This parameterization is valid for
near-neutral conditions. Assumption of near-neutral conditions is convenient for the estimation scheme because it reduces the places where there is ground temperature dependence in the equations. When minimizing the objective
function, fewer terms have ground temperature dependence.
There are no obstacles to including stability correction except
for the effort. The near-neutral assumption probably causes a
damping of the diurnal cycle of turbulent flux efficiencies in
dissipating the surface available energy that translate to slight
degradation of the data assimilation system performance.
In the latent heat flux formulation, following Castelli et al.
[1999], the specific humidity at the ground surface, q g , is estimated by reducing the temperature-dependent saturation specific humidity (q*( u )) through a multiplicative and dimensionless index (a), which represents soil control on evaporation
q g 5 a q* ~ u !.
i 5 1, . . . , M.
u iobs 5 u i 1 « i
which can be written as simply
du
5 1 1 u 2 cG,
dt
1715
(6)
Latent heat flux is proportional to the difference between
this value of specific humidity and that in the air, q a , at refer-
(7)
The surface or soil control on evaporation has the true
(unknown) value a(t) in time and it can only be estimated with
zero-mean error m(t) such that the best estimate a9(t) is
(8)
a 9~ t ! 5 a ~ t ! 1 m ~ t !
The error covariances of « i and m(t) are positive-symmetric
functions K 21
and K 21
3
2 . The errors « i and m(t) are assumed to
be Gaussian, and they are therefore fully characterized by their
mean values and covariances.
An objective function J( u , a ) for the estimation problem
over the period [0, t1] has the following individual terms Boni
et al. [2001]:
M
M
1. Squared measurement error ¥ j51
¥ i51
« i K 2 i, j « j over
the entire period (separately include the value at terminal time
t1 as K 2 M,M « 2 ( t 1 )).
2. Squared estimation error of the parameter a over the
entire assimilation period [0, t1] as in * 0t 1 * 0t 1 m ( t ) K 3 ( t ,
t 9) m ( t 9) d t 9 d t .
3. The forward model (4) constraint that is adjoined using a
Lagrange multiplier l(t) as in 2 *t01 l[(du/dt) 2 1 1 u 1 cG] dt.
It is important to note that the uncertainty in the forward
model is contained in the a(t) component in this choice of
formulation.
Taking the first variation of J( u , a ), using the symmetry of
K 2 and K 3 , applying integration by-parts, and grouping the
independent variations results in Euler-Lagrange equations
that need to be integrated in time forward and backward [Castelli et al., 1999; Boni et al., 2001]. These equations are
S
dl
G
5l 11c
dt
u
D OO
M
M
1
~ u 2 u obs! tiK 2~ t i, t ! d ~ t 2 t j!
i51 j51
(9)
(10)
l ~ t 1! 5 K 1~ u obs 2 u ! t1
a 5 a9 2
E
t1
K 321~ t , t 0! l c
G
d t 0.
a
(11)
0
When there are sparsely sampled measurements (in time),
the full covariance of the prediction and estimation errors is
important [Boni et al., 2001]. In such a case a suitable covariance function must be defined that takes into account both
temporal decorrelation and periodic diurnal cycle effects. Such
a function is defined by
1
K 321~ t , t 0! 5 2 @1 1 cos ~u t 2 t 0u!# e 2
where t0 is the decorrelation scales.
ut2t0u
t0
,
(12)
1716
BONI ET AL.: LAND DATA ASSIMILATION
The data assimilation scheme iteratively improves estimates
of a starting from an initial guess a9. In this iteration the
forward model (4) is integrated in time with the initial guess a9.
The predicted values of normalized ground temperature u(t)
are used to integrate (9) backward in time starting with the end
condition (10). The forcing for the dynamic equation for the
Lagrange multiplier (9) is the prediction misfit (u 2 uobs)t i
whenever measurements are made (denoted by the delta function d ( t 2 t j ) at times of observation j 5 1, z z z , M). The
Lagrange multiplier l(t) is then used to update the estimate of
a using (11). The iteration continues until a desirable level of
convergence is reached.
4.
Data
The assimilation scheme is tested using data from the Southern Great Plains 1997 (SGP 97) hydrology field experiment
(available at http://hydrolab.arsusda.gov/sgp97/). SGP 97 experiment includes in situ, airborne, and space-borne data collection. The field experiment area covered ;10,000 km2 across
northeastern Oklahoma. Two intensive data collection subfields (Central Facility and El Reno) that contained surface
flux stations are used in this study.
The forcing of the data assimilation system is taken from
micrometeorological stations and aggregated to nominal 30
min time steps covering a 29 days period in June and July of
1997. The variables include air relative humidity, air pressure,
and air temperature at reference height (1.5 m), wind speed at
10 m, and incident solar radiation.
In the first assimilation example (the reference case for
comparisons), in situ soil temperature measurements at different depths (5 and 10 cm under bare soil, 5, 10, and 30 cm under
natural sod cover) are used. Soil temperature observations at
different depths (5 and 10 cm under bare soil, 5, 10, and 30 cm
under natural sod cover) are used to estimate ground surface
temperature to be assimilated. The method used in Boni et al.
[2001] is applied to inferring surface ground temperature. It is
based on a solution to the heat diffusion equation with periodic
boundary condition:
T~ z, t! 5 T~l, t! 1 A Te z/l sin ~ v t 2 z/l !,
(13)
where l is the e-folding depth of diurnal heat waves. The length
scale l can be estimated from the phase shift between time
series of soil temperature at two different depths. Soil temperature at the e-folding depth T(l, t) is approximated to be the
mean value of the observed diurnal cycle. The amplitude of the
surface ground temperature A T can be simply evaluated from
the available time series once l and T(l, t) are known. The
method has been successfully tested using the field experiment
measurement at the USDA Beltsville Agricultural Research
Center (BARC) conducted during 1994, where three different
depths of observations and radiometric surface ground observations were simultaneously available. The root-mean-squared
error (RMSE) of reconstructed ground surface temperature at
half-hour resolution was found to be of the order of 18C over
a 16 days period.
The second assimilation case is provided with land surface
temperatures from satellite remote sensing instead. These
measurements are estimated from NOAA 12 and 14 low Earth
orbit satellites. Overpasses occur at 0730 and 1930 6 ;1 hour
for NOAA 12 and at 0230 and 1430 p.m. 6 ;1 hour for NOAA
14, all in local time. The AVHRR instrument on board these
platforms makes measurements in discrete visible to infrared
spectral bands. The nominal spatial resolution of the satellite
measurements are 1.1 km at nadir.
To calculate ground temperature from satellite brightness
temperatures (T b ) a split-window algorithm for multichannel
infrared data has been applied [Wan and Dozier, 1996]. This
particular method relates ground temperature to AVHRR
brightness temperature measurements in channels 4 and 5
(T b 4 and T b 5 ). Satellite brightness temperature measurements are averaged over an 11 km2 area. In both cases the
estimated ground temperature values are related to ground
truth with less than 18C RMSE. Averaged brightness temperature values that are contaminated by cloud cover are discarded. The criterion for detecting clouds is based on 50% or
more pixels brightness temperature colder than 108C indicating cloud tops rather than the surface as the emitting body.
obs
For validation half-hourly latent and sensible heat flux (Q E
obs
and Q H
) from eddy-correlation systems are used. Groundtruth values of a may also be estimated for validation from
these measurements. This may be done by inverting the resistance expression for latent heat flux for a. However, using the
definition of evaporative fraction EF
EF ;
Q obs
E
Q 1 Q Hobs
(14)
obs
E
allows for inverting sensible and latent heat fluxes simultaneously so that the estimates of observed a or aobs do not
directly depend on specification of an aerodynamic resistance
r a . With the definition 14, solving for a gives
a obs 5
S
u 2 ua
L
q*~T!~1 2 EF!
q a~1 2 EF! 1
D
EF
.
(15)
In assimilation experiments besides the value of surface
aerodynamic roughness z 0 , solar albedo, surface thermal emissivity, and deep ground temperature T# also need to be specified. Here an aerodynamic roughness length equal to 3 3 1024
m is used. This is consistent with the observed latent and
sensible heat fluxes. The solar albedo and surface thermal
emissivity are estimated from the radiative flux measurements
at the Central Facility site. Also, the deep ground temperature
T# is set to the mean of daily ground temperature at 0.1 m
below the surface over the simulation period.
Finally, daily estimates of surface (within top 0.06 m) volumetric moisture content at three sites (one at the Central
Facility and two at the El Reno fields) are used for comparison
with the estimated values of a which represent the land surface
control on evaporation. The daily estimates of soil moisture
have been derived by impedance point measurements on a
regularly spaced grid around each site [Famiglietti et al., 1999].
5.
Results
Two sites within the SGP 97 experiment area (El Reno and
Central Facility) are selected for application and validation of
the data assimilation approach. These sites were chosen because the El Reno and Central Facility sites had installed
systems to measure latent and sensible heat flux, and field soil
moisture. The El Reno site is principally range land or cultivated with winter wheat. It has flat terrain and generally silty
loam soils. During the 1997 experiment this site was moist and
BONI ET AL.: LAND DATA ASSIMILATION
1717
Figure 1a. Time series of in situ measured ground temperature for the SGP97 experiment period at the El
Reno site (line). Estimates derived from NOAA 12 and NOAA 14 satellite overpasses based on AVHRR
instrument are represented as symbols. The closed symbols are those satellite estimates that fall within the
three hours period around the time of the maximum ground temperature occurrence.
experienced major rain events. The Central Facility site also in
a flat region with silty loam soils. The regional land cover is
principally cultivated winter wheat.
Only ground surface temperature (in the first assimilation
case only), deep ground temperatures, and surface air micrometeorology (air temperature, humidity, and wind speed)
are provided to the data assimilation system. The remainder of
observations such as precipitation, measured latent and sensible heat fluxes, and soil moisture are withheld for validation.
The entire period of the SGP 97 experiment (amounting to a
total of 29 days) is the window for the assimilation system.
Two cases are studied at each site. In the first case half-
Figure 1b. Same as Figure 1a but for the Central Facility site.
1718
BONI ET AL.: LAND DATA ASSIMILATION
Figure 2a. Data assimilation results at the El Reno site. In this case the half-hourly in situ ground temperature measurements are assimilated. (top) Time series of half-hourly errors in the estimation of ground
temperature. (middle) Measurement (dashed line) and assimilation (solid line) estimates of surface latent
heat flux. Also included in this panel are the trace records of precipitation. (bottom) Estimates of a based on
measured EF (dashed line) and assimilation (solid line) are shown. The daily a and latent heat values are
averages over six hours around noon. Missing values in the measured EF sequence correspond to days when
the measured fluxes yielded a values far outside of the expected [0, 1] range.
hourly in situ observations of ground temperature are used as
the measurements for the data assimilation in a nearly ideal,
albeit rarely available configuration. Such a configuration is
similar to the one considered in the study of Castelli et al.
[1999] where validation was performed with data from First
International Satellite Land Surface Climatology Project
(ISLSCP) Field Experiment (FIFE). The quality of FIFE validation data is likely to be superior to SGP 97 because several
Figure 2b. Same as Figure 2a but for the Central Facility site.
BONI ET AL.: LAND DATA ASSIMILATION
1719
Figure 3a. The assimilation with half-hourly in situ ground temperature measurements at El Reno are used
for comparison with assimilation with satellite data only: (top) Time series of half-hourly errors in the
estimation of ground temperature; (middle) Base case (solid line) and assimilation with satellite data estimates of surface latent heat flux. Also included are the trace records of precipitation. (bottom) Estimates of
a based on the base case assimilation (solid line) and assimilation with satellite data alone are shown. The
daily a and latent heat values are averages over 6 hours around noon. The solid symbols are those satellite
estimates that fall within the 3 hours period around the time of the maximum ground temperature occurrence
(as in Figures 1a and 1b).
surface flux measurement stations were used to form area
averages. The data assimilation system performed with an
RMSE of ;30 W m22 for daily latent heat flux estimation,
which may be considered to be on the same order as the
turbulent flux measurement uncertainty. In SGP 97 the availability of surface heat flux stations is considerably more limited. For this reason we take the assumption that data assimilation with half-hourly in situ measured ground temperature
Figure 3b. Same as Figure 3a but for the Central Facility site.
1720
BONI ET AL.: LAND DATA ASSIMILATION
provides a reasonable reconstruction of ground-truth for SGP
97. This reconstruction is therefore used as the base case for
comparison of data assimilation with infrequently sampled satellite data.
Figure 1a for El Reno and Figure 1b for Central Facility
show the time series of in situ measured ground temperature.
The symbols represent estimates made based on the satellite
brightness temperatures measurements through the Wan and
Dozier [1996] algorithm. Estimates from those satellite measurements that fall within a 3-hour window of the time of peak
daily ground temperature (NOAA 14 1430 LT overpass) are
solid symbols. This distinction will prove to be important when
the satellite data are assimilated, and it will be discussed later
in this section.
The application of the data assimilation system with halfhourly ground temperature in situ observations as measurements is shown in Figure 2a (El Reno) and Figure 2b (Central
Facility). Figures 2a and 2b (top) shows the error in the estimation of ground temperature which is the state of the system
(4). The errors are plotted for each half hour of the 29 days. In
both cases the errors are small (RMSE values are 0.648C at the
El Reno and 0.258C at the Central Facility sites). The surface
heat balance is reconstructed closely in the case of assimilation
with half-hourly ground temperature observations. Figures 2a
and 2b (middle) show the performance of the system in terms
of latent heat flux. The estimation values are averaged over the
6 hours centered around noon (solid lines). The values derived
from observations are represented by the dashed lines and
rainfall events are included as bars. At the El Reno site (Figure
2a) the data assimilation and observed values of surface latent
heat flux have day-to-day fluctuations that track closely but the
values based on the EBBR system at the site are consistently
above the data assimilation results with peaks reaching 600 W
m22.
In order to assess whether there are possible biases in the
turbulent heat flux measurements at each site, we make some
scale comparisons with the possibly more reliable pyranometer
measurements. The half-hourly measured peak net radiation
observed at the El Reno is 730 W m22. At the time of this peak
the ground heat flux is changing sign and it is therefore near
zero. With 730 W m22 of peak net radiation a half-hour peak
surface latent flux measurement at El Reno of 760 W m22 may
indicate positive bias and/or noise in the surface flux measuring
system at this site. At Central Facility the peak net radiation
experienced during the SGP 97 period was 650 W m22, which
is close to the observed peak latent heat flux of 625 W m22.
The Central Facility latent heat flux estimation is also biased
(but less than in the case of El Reno). Nonetheless, the covariability between the data assimilation and measurements
show close tracking in Figure 2b (middle). The third panels in
Figures 2a and 2b contain the daily values of a averaged for the
6 hours centered at noon in the diurnal cycle. Again the results
based on measurements are denoted by dashed lines; they are
estimated using (15). The values resulting from data assimilation are represented by solid lines. Because of inconsistencies
and errors in observations of latent and sensible heat flux and
surface micrometeorology, some of the values of aobs fall outside of the expected [0, 1] range. Biases in the turbulent heat
flux measurements may cause other, largely unknown, errors in
the estimation of aobs. These errors can truly only be characterized using a synthetic case study where the true condition is
better known.
The values of a from the data assimilation of half-hourly in
situ measured ground temperature are closer to the available
observation estimates for the Central Facility site (Figure 2b)
when compared with the El Reno site (Figure 2a). This is
consistent with the performances when surface latent heat flux
is compared. Notably, in the case of Central Facility the dayto-day fluctuations, especially increases in the values of a following surface wetting by rain events, are captured well in the
data assimilation results.
Use of low-Earth orbit satellite measurements in data assimilation is constrained by the temporal sampling problem.
The AVHRR instrument on board the NOAA 12 and 14
satellite platforms are used here to provide the measurements
in data assimilation. No other source of ground temperature
observations are used. Figure 3a and 3b show the results of the
data assimilation. The symbols represent the results of the data
assimilation with measurements provided by AVHRR only.
Again, the solid symbols are used to indicate those satellite
ground temperature estimates that are made with available
NOAA 14 1430 LT pass measurements. Figures 3a and 3b
(top) contain the time series of errors in the estimation of
half-hourly ground temperature with respect to the base case.
The RMSE in the case of El Reno is 2.7 8C and in the case of
Central Facility 2.48C. There also appears to be a slight bias
during the period when midday satellite observations are
sparse, but over the entire assimilation period the bias is small.
The values are larger than the case in Figures 2a and 2b (even
when compared to in situ measurements) mostly due to inadequate sampling of the diurnal cycle in ground temperature.
Figures 3a and 3b (middle) show the daytime surface latent
heat flux. In both cases (El Reno in Figure 3a and Central
Facility in Figure 3b) on days when the satellite overpass near
the time of the peak daily ground temperature is available
(identified by solid squares) the data assimilation estimates of
surface latent heat flux are close to the base case. On days
when no NOAA 14 1430 overpass measurements are available
(identified by open squares), the performance is considerably
worse. This indicates the importance of satellite sampling
times for land data assimilation [Boni et al., 2001]. The maximum surface ground temperature results from cumulative
heating and hence it is sensitive to the partitioning of available
energy into sensible and latent turbulent heat fluxes during the
day. For this reason it is particularly important to have measurements near the time of maximum ground temperature
(early afternoon) for land data assimilation of hydrologic variables such as a. Boni et al. [2001] showed how the assimilation
performance rapidly degrades when temperature sampling is
done outside a three hours window around the time of diurnal
peak. Some of the shortcomings in the estimation of a is also
related to the error model used for it. We have assumed that
errors in a are Gaussian distributed. The parameter a is
bounded between zero and unity, and such an error model is
convenient but can certainly pose some problems when errors
are large. Furthermore we make comparisons with midday
values of aobs because during this period the turbulent fluxes
are strong and their measurement errors are a smaller fraction
of the signal. Furthermore, during this period radiation is often
not the limiting factor for surface evaporation, and therefore
the day-to-day land control is more clearly evident.
In situ soil moisture measurement offer an independent data
set to validate the retrieved values of a. Data on volumetric
moisture content collected at El Reno and Central Facility
sites are reported by Famiglietti et al. [1999]. The values are
normalized by soil porosity reported by Famiglietti et al. [1999]
BONI ET AL.: LAND DATA ASSIMILATION
Figure 4a. Comparison of soil moisture based on estimate a
and application of the model of Noilhan and Planton [1989] at
El Reno site. The ordinate is soil moisture observed in situ
together with spatial standard deviation [Famiglietti et al.,
1999]. Data assimilation with satellite data are stratified according to whether there are available satellite data near the
peak of the diurnal ground temperature (closed circles for
available measurements near the peak and open circles for lack
of measurements near the peak). A characteristic soil porosity
of 0.45 is used to compare relative soil saturation values.
for the sites (near 0.45) in order to estimate relative soil saturation in the normalized range [0, 1]. The standard deviation
associated with the daily mean values reported by Famiglietti et
al. [1999] refer to spatial variability at the data collection sites
in El Reno and Central Facility. In order to compare the a
index of soil water to these in situ measurements the parameterization of Noilhan and Planton [1989] is used to transform
a into relative soil saturation. The parameterization is a simple
empirical model of relative humidity at the ground surface
related to the surficial soil moisture [Noilhan and Planton,
1989, equation (28)]. It is only an approximation in order to
translate the a values into a reasonable expected surficial soil
moisture. Figures 4a and 4b show the plot of estimated relative
soil saturation (based on the data assimilation system with
satellite measurements of ground temperature) and those
measured at the El Reno and Central Facility sites, respectively. Again the open symbols are used to indicate days during
which NOAA 14 1430 LT measurements are not available.
Solid symbols represent estimated values during days when the
available satellite data falls within the 3-hours window around
the peak of diurnal ground temperature. Plot-scale spatial variability of in situ soil moisture measurements are denoted by
the one standard deviation error whiskers around the mean
values in Figures 4a and 4b. The value estimated by data
assimilation corresponds to the effective value within the
ground resolution of the satellite measurements. Nonetheless,
in both Figures 4a and 4b it is evident that estimates during
days when the satellite data for ground temperature near the
time of diurnal peak is available, the correspondence of assim-
1721
Figure 4b. Same as Figure 4a but for the Central Facility
site.
ilation estimate of surface relative soil saturation and in situ
measurements are superior to days when such data are missing.
6.
Summary
A statistically optimal land data assimilation system to minimize the error of estimation when both model and measurements contain uncertainty is applied to two sites within the
Southern Great Plains 1997 hydrology field experiment in
northeast Oklahoma. The model consists of ground heat flow
with surface energy balance at the land surface. It is used to
provide dynamically consistent constraints on the estimation.
Two case studies are considered, each with a different input
stream of measurements. In the first and ideal case that also
serves as the reference for subsequent comparisons, halfhourly in situ ground temperature observations are the measurements in the data assimilation. In the second case, satellite
data from two low-Earth orbit satellite are the only source of
measurements for ground temperature. Data from surface flux
measuring stations and in situ soil moisture observations are
used to validate the estimation results with ground-truth. It is
shown that the data assimilation system performs well in capturing the day-to-day variations in the components of surface
energy balance, ground temperature, and soil moisture or surface control on evaporation. Even though the precipitation
data are withheld from the assimilation system, the wetting and
drydown events are estimated and their effects on land control
on evaporation are captured. On days when satellite data are
available close to the time of peak diurnal ground temperature,
the estimation is considerably improved over days when the
cumulative daily heating is unknown.
Use of remotely sensed land surface temperature in a data
assimilation framework to estimate fields of energy balance
components and surface control on evaporation is feasible but
considerably more refinements need to be made. The advantage of using land surface temperature data for this application
in hydrology is that the satellite remote sensing of this variable
1722
BONI ET AL.: LAND DATA ASSIMILATION
has a long heritage, and it is possible to construct long-period
data sets based on past and current sensors and platforms. The
areas where the assimilation system can be improved include
the following: (1) revised formulation of the uncertainty in the
forward model and incorporation of more suitable characterization of errors for the bounded parameter a, (2) extensions
to spatial fields so that the spatial covariance in the forcing and
parameter fields can effectively condition the estimation, and
(3) use of the synergy provided by multiple satellite platforms
in order to better characterize the diurnal cycle of land temperatures.
Acknowledgments. This study was supported by NASA grant
NAG8-1524, the MIT-CNR cooperative agreement, and sabbatical
leave granted by MIT.
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G. Boni, Centro di Ricerca in Monitoraggio Ambientale, Savona,
Italy ([email protected])
F. Castelli, Dipartimento di Ingegneria Civile, Università degli Studi
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D. Entekhabi, Department of Civil and Environmental Engineering,
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(Received February 24, 2000; revised December 23, 2000;
accepted January 12, 2001.)