Introduction
Many observational and modelling studies suggest strong coupling between the
atmosphere and the land surface. The land surface states such as soil
moisture, temperature and snow play an important role in land-atmosphere
coupling. The very high albedo of snow, as well as the water storage and
insulation properties means that snow can have a significant impact on
numerical weather prediction (NWP) and seasonal forecasting. Soil moisture
and temperature have a significant impact on screen level temperature and
humidity, low clouds and precipitation, by influencing the exchange of heat
and moisture between the land surface and the atmosphere
. Soil moisture is important
for the prediction of summer-time precipitation at mid-latitudes over land
and plays an important role in the development of convective storms
. The land surface is also very important for the seasonal
prediction of extreme events such as heat waves and drought
.
Data assimilation (DA) is extremely important for NWP since errors in the
model initial conditions can grow rapidly and seriously degrade forecasts.
The initial land surface state can have a significant impact on forecasts of
screen level temperature and humidity as well as forecasts of precipitation.
Specifying the model initial soil moisture and temperature state is
especially difficult since there are few near real-time ground based
observations of soil moisture and temperature. Therefore, indirect
observations are usually used by land surface DA schemes to initialise the
model soil moisture and temperature . The
true information content of soil moisture data is in the relative values
(such as temporal variations or percent of saturation) and not in the
absolute magnitudes . Consequently, model soil moisture is
highly model specific. For example, show that direct
transfer of soil moisture values from one land surface model to a different
land surface model is inappropriate and likely to lead to problems.
Therefore, any land surface DA scheme must be consistent with the land
surface model used by the NWP system. Inconsistencies in the analysed land
surface fields could introduce spurious, long lived shocks to the NWP system
and degrade forecasts.
To make fuller use of the available global remotely sensed measurements of
the land surface as well as screen level observations an Extended Kalman
Filter (EKF) based land surface data assimilation system has been developed
in collaboration between the Bureau of Meteorology (Bureau) and the Met
Office . Such EKF land DA systems can make more
statistically optimal use of a wide variety of observation types, such as
screen level observations and satellite based estimates such as retrieved
Surface Soil Moisture, retrieved skin temperature, Leaf Area Index (LAI) and
Fraction of Photosynthetically Active Radiation. Indirect measurements can be
used and information propagated from the surface into the deeper soil layers.
For example an EKF based land DA system may: (a) use observations of screen
level temperature and humidity to analyse soil temperature and moisture. (b) Use
satellite estimates of surface soil moisture to analyse surface and
root-zone soil moisture. (c) Use satellite estimates of skin temperature to
analyse soil temperature and moisture. (d) Assimilate satellite estimates of
LAI .
Land surface analysis
A number of new space-borne remote sensing systems have been developed that
provide information on surface soil moisture and temperature. However, most
NWP centres still only use screen level observations of temperature and
humidity for the operational analysis of soil moisture and temperature, e.g. ECMWF European Centre for Medium range Weather Forecasts;, Meteo-France and the German Weather Service
. The Met Office operationally uses satellite derived
measurements of surface soil wetness together with screen level observations
for the analysis of soil moisture. find that
assimilation of remotely sensed surface soil wetness measurements improves
the agreement of the soil moisture analyses with ground based soil moisture
observations and improves forecasts of screen level temperature and humidity.
The extended Kalman filter
The DA problem is kept manageable by assuming that the model land columns are independent of each other (a 1-dimensional approach).
This assumption is also made by most land surface models, including JULES .
The standard EKF equations for each land column are given by
xa(ti)=xb(ti)+Kio(ti)-hi(xb)
Ki=BHiTHiBHiT+R-1.
x(ti) represents the state vector of a land column at time ti
with superscripts a and b standing for analysis and background.
o(ti) is the observation vector. Ki is the Kalman
gain matrix at time ti. B is the background error covariance
matrix. R is the observation error covariance matrix.
Hi is the linearised observation operator matrix
and is defined using
hi(x+Δ)≃hi(x)+HiΔ,
where Δ is a small perturbation to the model state x and
hi(x) is the non-linear observation operator.
The elements of Hi are estimated using finite difference
by individually perturbing each component of x by a a small scalar amount δj.
A given element of Hi is calculated using
Hkj=yk(x+δj)-yk(x)δj.
yk(x+δj) is a short model forecast of observation type k (e.g. screen level temperature)
starting from perturbed initial conditions x+δj.
The sensitivity of the calculated Jacobians to the magnitude of the perturbations, δ, is described in a
later subsection.
The number of perturbed forecasts required increases with the number of model variables to be analyses and the number of soil layers.
For example, to analyse skin temperature and soil moisture and temperature on four soil levels would require
ten perturbed forecasts, including the control y(x).
The length of a perturbed forecast is typically a few hours long.
The major computational cost of the EKF land DA system is the cost of running the perturbed forecasts.
ECMWF use the fully coupled land/atmosphere model for the perturbed forecasts.
Meteo France use an off-line land surface model (uncoupled to the atmosphere model) for the perturbed forecasts.
Consequently the Meteo France EKF land DA system is computationally several orders of magnitude cheaper.
The Bureau EKF land DA system also uses an off-line land surface model for the perturbation forecasts.
and have shown that the off
line land surface model can be used to reliably calculate Hi.
The
forcing data for the off-line land surface model (precipitation, surface longwave and shortwave
radiation, air temperature and humidity, wind speed and surface pressure) are obtained
from forecasts of the NWP model. Air
temperature and humidity forcing are applied at a height of 20 m (which is above the screen level).
This allows the EKF land DA system to also assimilate observations of screen level
temperature and humidity (see Fig. 1 of , for a fuller explanation).
The land surface model
The Bureau EKF land DA system uses JULES to represent the land surface
processes. The soil is discretised into four layers of 0.1, 0.25, 0.65 and
2 m thickness (from top to bottom). The soil hydrology is based on a finite
difference form of the Richards equation and Darcy's law. The
equations are used to describe the relationship of soil
hydraulic conductivity and soil suction to the unfrozen volumetric
soil moisture. Currently, there is no vertical variation of
the soil hydraulic parameters in the model.
The freezing and melting of soil water are also represented and the
associated latent heat is included in the thermodynamic calculations.
The JULES model uses 5 vegetation tiles (broadleaf trees, needleleaf trees,
C3 (temperate) grass, C4 (tropical) grass and shrubs) and 4 non-vegetation
tiles (urban, inland open water, bare soil and land ice). Transpiration by
plants extracts soil water directly from the soil layers via the plant roots
while bare soil evaporation extracts soil water from the top soil layer only.
The ability of plants to access water from each soil layer is determined by
the root density distribution and soil moisture availability. The broadleaf
trees are assumed to have a root depth of dr=3m, needleleaf trees have
dr=1m, grasses and shrubs have dr=0.5m and the total depth of the
model soil zt=3m. The bulk stomatal resistance in the absence of soil
moisture stress is calculated by a photosynthesis model and
depends on incident radiation, vegetation type, surface air temperature and
humidity deficit. The bulk stomatal resistance includes a dependency on the
soil moisture content via a soil moisture availability factor.
Experiments and results
In order to avoid compensating effects through temporal averaging, results
are presented for one time period only; the off-line perturbed forecasts are
started from initial conditions valid at 3Z 16 January 2011. The length of the
perturbed forecasts is three hours. Perturbed forecasts with shorter (longer)
lengths of one (five) hour(s) have also been tried. Figure shows
the model initial conditions for snow amount and level 1 soil temperature.
During January much of the Northern Hemisphere land is covered by snow. The
initial land surface model states (e.g. soil moisture, soil temperature and
snow) used in the experiments are obtained from the operational weather
forecasting system and are as accurate as possible. Although the model
initial conditions are likely to affect the magnitude of the computed
Jacobians, they do not affect the conclusions.
The Jacobians for screen level observations
Figure shows an example of the computed Jacobians
HT2m,θl≡ΔT2m/Δθl which are
elements of the linearised observation operator matrix for screen level
temperature with respect to soil moisture in the four model soil layers
(l). For soil layers two to four, the coupling between screen level
temperature and soil moisture is primarily through transpiration by
vegetation. Consequently the coupling occurs during daylight. The vertical
variation of the coupling is discussed in the next subsection. The negative
values means that an increase in soil moisture leads to a cooling of the
screen level. For the surface soil layer, the picture is more complicated as
there is strong coupling both during the day and at night. The Jacobians have
a positive value in some places and a negative value in others.
The Jacobians of screen level specific humidity with respect to soil moisture
(Δq2m/Δθl)
are shown in Fig. .
The spatial pattern shown in Fig. is similar to Fig. . However, for screen level specific humidity,
the Jacobian values are primarily positive meaning that an increase in soil moisture leads to an increase in screen level humidity.
The Jacobians of screen level temperature with respect to soil temperature
(ΔT2m/ΔTl) are shown in Fig. . The
Jacobians are largest for soil level 1 and become very small for soil levels 3
and 4. The Jacobians are largest during the night and generally positive in
value. This is consistent with the experience of ECMWF who find that their
soil temperature nudging scheme is more effective during the night and winter
when screen level errors are less likely to be related to soil moisture
.
Effect of land surface parameterisations
To investigate the impact of the land surface model parameterisations on the
calculation of the Jacobians, experiments are performed where the
parameterisations are modified or switched off. Figure
shows the effect of switching off bare soil evaporation. Comparing Fig. with the top panel of Fig. shows that
bare soil evaporation can produce strong coupling between screen level
temperature and surface soil moisture, both during the day and night.
Switching off bare soil evaporation reduces the magnitude of ΔT2m/Δθ1 in the interior of Australia, the Sahara and parts of
south America. In some night time regions, switching off bare soil
evaporation causes ΔT2m/Δθ1 to swap sign and have
positive instead of negative values. With bare soil evaporation switched off,
ΔT2m/Δθ1 is predominantly negative in the daytime
region and predominantly positive in the night time region.
The soil thermal conductivity can be strongly affected by soil moisture and could be responsible for the positive values of ΔT2m/Δθ1 in night-time regions,
observed in Fig. . The JULES soil thermal conductivity (λs) is calculated using
λs=(λsat-λdry)Ke+λdry
where λsat is the soil thermal conductivity when the soil is
saturated and λdry when the soil is dry. Ke is the Kersten
number given by
Ke=log10θθs+1.0θθs≥0.10otherwise.
For investigation, the parameterisation of soil thermal conductivity is modified to becomes independent of soil moisture,
λsmodified=(λsat+λdry)/2.
Figure shows ΔT2m/Δθ1 when the soil
thermal conductivity parameterisation is modified and bare soil evaporation
is switched off. Comparing Figs. and
shows that modifying soil thermal conductivity significantly reduces the
coupling between screen level temperature and topmost level soil moisture in
many regions, both during the day and night. However, some night-time regions
with positive values of ΔT2m/Δθ1 still persist. This
suggests that other processes, such as the relation between soil heat
capacity and soil moisture, are also important.
The coupling between the root zone soil moisture and the screen level is
primarily through transpiration by plants and is only significant during the
day. The vertical variation of the coupling is significantly affected by the
vegetation root depths. Figure shows the computed Jacobians
ΔT2m/Δθl when the vegetation root depths are doubled.
Increasing the vegetation root depth causes stronger coupling with the deeper
soil layers, i.e. increases the magnitude of ΔT2m/Δθ4
and reduces the magnitude of ΔT2m/Δθ2.
The Jacobians for the assimilation of surface soil moisture measurements
Several new space-borne
remote sensing systems have been
developed that provide global retrievals of surface soil
moisture (SSM), e.g. SMOS Soil Moisture Ocean Salinity,,
ASCAT Advanced SCATterometer, and
SMAP Soil Moisture Active Passive,.
Measurements of SSM can be assimilated to update both the model surface and
root zone soil moisture by using Eq. () to compute Δθ1/Δθl≡Hθ1,θl. Example results
are shown in Fig. . Generally, for JULES, the coupling
between the surface and root zone soil moisture is weak. Δθ1/Δθ3 and Δθ1/Δθ4 are close to zero.
Δθ1/Δθ2 is non-zero in regions where the soil is
wet and consequently the hydraulic conductivity is high. Δθ1/Δθ1≡Hθ1,θ1 is close to unity in most
regions, the exceptions are where the soil is wet and Jacobian values as low
as 0.5 can occur. Increasing the length of the perturbation forecasts is
found to significantly increase the coupling between the surface and root
zone soil moisture. has found similar results when using
JULES.
The equations describe the relationship between the soil hydraulic
conductivity (KVG) and the unfrozen volumetric soil moisture θu.
KVG=KsSeL1-(1-Se1/m)m2,
where the soil wetness Se=(θu-θr)/(θs-θr), L=0.5
and m=1-1/n. θs, θr, Ks, α and n are the van
Genuchten soil parameters and assumed to depend on soil type. The hydraulic
conductivity is very sensitive to changes in soil moisture. Small changes in
soil moisture can lead to order of magnitude changes in soil hydraulic
conductivity. For example, when Se=1, KVG=Ks while when Se=0.9
and n=1.18, KVG=Ks×10-2. In addition, Ks is strongly
affected by soil type and has a high spatial variability see for
example. For coarse textured soils the model
assumes Ks=1.95×10-2mms-1 while for medium textured soils
Ks=2.8×10-3mms-1. also show that the
uncertainty in predicted Ks is about one order of magnitude. Consequently,
uncertainty in soil type and pedotransfer functions can also lead to order of
magnitude uncertainty in soil hydraulic conductivity.
Figure shows the computed Jacobians Δθ1/Δθ2
when the soil hydraulic conductivity is increased by a factor of ten. The coupling between the SSM and the root zone has increased significantly.
Using four different land surface models with different coupling strengths
and synthetic observations of SSM, find that the potential
of SSM assimilation to improve root zone soil moisture is higher when the
coupling between the SSM and root zone soil moisture is stronger. Given that
the true strength of coupling between the SSM and root zone soil moisture is
unknown, the non-identical twin, assimilation experiments of
suggest that it is better to over-estimate rather than
under-estimate the coupling between the SSM and root zone soil moisture.
Therefore, artificially increasing the model soil hydraulic conductivity by a
factor of ten may be an effective technique to improve the assimilation of
satellite derived SSM. However, careful and comprehensive testing will be
required to fully validate all the consequences of such an approach.
The Jacobians of the observation operator for surface skin temperature
show that in unstable conditions, to a good approximation
ΔT*=ΔT2m/1-μra,2m/ra.
Where ra (ra,2m) is the aerodynamic resistance between the surface and first model level (screen level) and
μ≃0.9. Therefore, it is expected that the computed Jacobians between surface skin temperature and
soil moisture (ΔT*/Δθl) should show a similar spatial pattern to the Jacobians
between screen level temperature and soil moisture (ΔT2m/Δθl) but have a larger magnitude
(since the denominator in Eq. () is less than 1).
Figure shows the computed Jacobians ΔT*/Δθl and that there is
significant coupling between surface skin temperature and soil moisture.
Therefore, it may be possible to assimilate satellite measurements of T*
to analyse soil moisture. However, for a variety of reasons, model and
satellite derived surface skin temperature exhibit very different
climatologies and consequently bias correction will be required
. As expected, comparing Figs. and
shows that, the spatial variation of ΔT*/Δθl is very similar to ΔT2m/Δθl and the
magnitudes are much larger. Figure shows the computed Jacobians
ΔT*/ΔTl and that there is significant coupling between
surface skin temperature and model level 1 soil temperature. There are also
strong similarities between ΔT*/ΔTl and ΔT2m/ΔTl. have assimilated measurements of surface skin
temperature for the Africa region using the JULES land surface model and
found improvements to model surface fluxes and soil moisture.
Sensitivity to magnitude of perturbations
Figure shows the sensitivity of the calculated Jacobians for screen
level temperature to the magnitude of the volumetric soil moisture
perturbations, for the Australia region. The results indicates that the
system is well behaved for perturbation values in the range of
10-4 to 10-2m3m-3, a perturbation value of 10-3m3m-3
is found to be close to optimal. A similar analysis using the calculated
Jacobians for screen level specific humidity also shows that a soil moisture
perturbation value of 10-3m3m-3 is close to optimal (results not
shown). The Jacobians for screen level specific humidity are less sensitive
to the magnitude of the soil moisture perturbation. For skin and soil
temperature, results indicate that the system is well behaved for
perturbation values in the range of 10-2 to 1K, a perturbation
value of 10-1K is found to be close to optimal.
Conclusions
To take full advantage of the available global satellite measurements of the
land surface as well as screen level observations an EKF based land surface
data assimilation system has been developed at the Bureau in collaboration
with the Met Office. Such a system is flexible and can make more
statistically optimal use of a wide variety of observation types. The most
important aspect of the system is the calculation of the Jacobians that
describe the link between the observations and the land surface model
variables. The Jacobians are computed using finite difference by perturbing
each model variable to be analysed, in-turn, and performing short model
forecasts. The number of perturbed forecasts required increases with the
number of model variables to be analyses and the number of soil layers. Other
works such as and have also looked at
the calculation of the Jacobians. However, this work examines the Jacobians
in much greater detail than before. In addition, this is the first work to
use the JULES land surface model to compute the Jacobians for screen level
observations and measurements of surface skin temperature.
Results show that the computed Jacobians can be sensitive to the size of the perturbations used.
Perturbations that are too small cause problems due to numerical rounding while perturbations that are
too large cause problems due to non-linearities in the model. Experiments show
that volumetric soil moisture perturbation values in the
range of 10-4 to 10-2m3m-3 give good results and a perturbation value of 10-3m3m-3 is close to optimal.
For skin and soil temperature perturbations, experiments indicate that a perturbation value of 10-1K is close to optimal.
This is the first work to look at the effect of land surface parameterisations on the computed Jacobians.
As expected, the parameterisation details have a significant impact. Experiments are performed where the parameterisations are
modified or switched off.
Results show that the coupling between the soil moisture in the topmost model layer and the screen level is due to a number of
processes including bare soil evaporation, soil thermal conductivity, soil thermal capacity as well as transpiration by plants.
The coupling between the soil moisture in the lower model layers and the screen level is due to transpiration by plants.
This result is significant as it explains why the coupling with the soil moisture in the topmost model layer is much stronger than the
coupling with the soil moisture in the lower model layers. Consequently, soil moisture increments in the topmost model layer will be larger
than would be the case if the coupling were only due to transpiration. In addition, improving the analysis of topmost model layer
soil moisture will have a significant impact on forecasts of screen level temperature and humidity.
The Jacobians linking observations of surface soil moisture with soil
moisture in the lower model layers have been computed. Experiments show that
artificially increasing the soil hydraulic conductivity by a factor of ten
significantly increases the coupling between the surface and root zone soil
moisture. Otherwise, for JULES, the coupling between the surface and root
zone soil moisture is weak. Small uncertainty in soil moisture or soil type
can lead to order of magnitude uncertainty in soil hydraulic conductivity. In
addition, suggest that it is better to over-estimate rather
than under-estimate the coupling between the surface and root zone soil
moisture. Consequently, artificially increasing the model soil hydraulic
conductivity by a factor of ten may be an effective technique to improve the
assimilation of satellite derived surface soil moisture.
The Jacobians linking observations of skin temperature to model soil temperature
and moisture have also been computed. These Jacobians have a similar spatial pattern to
the Jacobians linking observations of screen level temperature to model soil temperature and
moisture but are larger in magnitude. Consequently, assimilation of satellite derived skin temperature
may also significantly improve the analysis of model soil temperature and moisture.
It is well known that model soil moisture is model specific . Results indicate that the
Jacobians are also model specific. Consequently, careful examination of the Jacobians might allow
significant insight into the behaviour of land surface models.
It is intended that the CABLE land surface model will be integrated into the JULES
framework . Therefore, it would be instructive to examine and compare the Jacobians computed using
CABLE, JULES and other land surface models.