Sequential Assimilation of ISBA’s Prognostic Variables
(Global Version)
Stéphane Bélair and François Lemay
Meteorological Service of Canada
Through the representation of the main physical processes occuring at the surface,
land surface schemes calculate the surface fluxes of heat, moisture, and momentum. In
order to do so, the effect of soil hydraulic and thermal conductivities, vegetation
transpiration, snow on the ground, and freezing of soil water, are represented in these
schemes.
In the last few years, the ISBA surface scheme (Interactions Surface Biosphere
Atmosphere, see Noilhan and Planton 1989) has been used operationally at the Canadian
Meteorological Centre (CMC) for short-range regional weather forecast, and it is now
being considered for operational implementation in the global medium-range forecasting
system. A large number of surface variables are prognostically evaluated in ISBA: the
superficial and mean surface temperatures (TS and T2), the soil liquid water contents for
superficial and deep layers (wg and w2), the soil frozen water content (wf), the water
retained on the vegetation canopy (Wr), the snow water equivalent (WS), the snow density
(S), the snow albedo (S), and the liquid water retained in the snow canopy (Wl).
As should be expected, the surface fluxes greatly depend on the values of these
prognostic variables, and their initial values should be carefully specified.
In this
document, the specification of the initial values of the surface temperatures (TS and T2)
and soil liquid water contents (wg and w2) through a sequential assimilation technique is
described. The other surface variables are either cycled from day-to-day simulations
without any modifications (wf, Wr, Wl) or obtained from a combination of cycled and
analysed fields (WS, S, S, the analysed field being the snow depth).
The sequential assimilation technique
The basic idea of the sequential assimilation technique, first proposed by Mahfouf
(1991), is to relate errors in soil moisture contents to model errors on low-level air
temperature (T) and relative humidity (RH), following the linear equations:
 wg  wga  wgf
(1)
 1 T o  T f   2  RH o  RH f 
 w2  w2a  w2f
(2)
 1  T o  T f   2  RH o  RH f 
where the superscripts a, f, and o refers to “analyzed”, “forecast”, and “observed”.
The problem therefore consists in evaluating the 1, 2, 1, and 2 coefficients, and
this for all types of soils, vegetation, and meteorological conditions. Based on the work
of Mahfouf (1991), who estimated the statistical distribution of these coefficients at each
local solar time using a Monte-Carlo method, Bouttier et al. (1993) proposed an analytical
formulation of the coefficients (continuous functions of the surface characteristics), which
was later modified by Giard and Bazile (2000) to yield:
1  f (txt )1  veg a0T (t )  a1T (t ) veg  a2T veg 2 
(3)
2  f (txt )1  veg a0H (t )  a1H (t ) veg  a2H veg 2 
(4)

1  f (txt ) 1  vegb0T (t )  b1T (t ) veg  b2T (t ) veg 2   vegc0T (t )  c1T (t ) veg


LAI 
 (5)
Rs min 
2  f (txt ) 1  vegb0H (t )  b1H (t ) veg  b2H (t ) veg 2   vegc0H (t )  c1H (t ) veg

f (txt ) 
 w(txt )
 w(loam)
;
LAI 
 (6)
Rs min 
 w  w fc  wwilt
(7)
where txt is the soil texture (e.g., sand, clay, etc.), veg is the fraction of vegetation
covering a model grid area, LAI is the leaf area index (area of leaves coverage per surface
area unit), Rsmin is the minimum stomatal resistance, and wfc and wwilt are the volumetric
water contents at the field capacity and wilting point. Finally, the aiT, aiH, biT, and biH
coefficients were calculated to fit the continuous functions to a large sample of  and 
coefficients computed exactly using the Monte-Carlo method (see Bouttier et al. 1993 for
more details). Values for these coefficients are obtained by linearly interpolating hourlytabulated values (not shown here) to the local solar time of each model grid point.
For the surface temperatures, the increments are directly related to model errors at
the anemometer level (i.e., 2 m), following:
 TS  TSa  TSf  T2om  T2 fm
 T2  T  T2
a
2
f
T

o
2m
 T2 fm 
(8)

where   2 for ISBA.
Calculations of TSa , T2a , w ga , and w 2a are straightforward, except for a few tests
that must be done in order to avoid unrealistic and unphysical modifications to the surface
variables.
First, because low-level air temperature errors are not entirely due to soil moisture
and temperature (even with the most favorable atmospheric conditions), historical longterm temperature errors ( Tbias ) are carried on from one assimilation cycle to the next and
are subtracted from the model errors at low levels:
T
0
 T f   T 0  T f  mod  Tbias
(9)
with

Tbias  1  r  Tbias
 r T 0  T f  mod
(10)

in which Tbias
is the long-term tendency from the previous assimilation cycle, and r=0.5.
Thus, only the low-level temperature errors that differ from the long-term values, which
represent the model bias that is not related to surface characteristics, are taken into
account in the sequential assimilation. Note that the same temporal filtering of the model
low-level errors is not done for relative humidity, due to the more hectic behavior of this
variable.
Finally, minimum and maximum values are imposed on the analysed soil moistures:
01
. wwilt  wga  w fc
. wwilt
veg wwilt  w2a  w fc and w2a  01
(11)
(12)
Conditions for assimilation
The link between soil moisture and low-level air characteristics is stronger in
certain atmospheric conditions. For instance, air temperature and humidity will be more
influenced by soil moisture during the afternoon of a beautiful, calm, sunny summertime
day, as compared to a windy, cloudy day. Therefore, the sequential assimilation proposed
here is only performed once a day, at the time of maximum insolation.
And the
increments TS , T2 , wg , and w2 are multiplied by a rejection factor rej, which depends
on the following conditions:
a)
Increments are calculated only for tiles
If only water, then rej = 0.
which contain soil
b)
No increments are applied to snowy
surfaces
 W

rej MAX 1  S ,0
 Wsrej 
where Wsrej is a critical rejection value
for the snow mass
c)
No increments are applied if the soil is
frozen (even partially)

freez 
rej  MAX 1 
,0
 freezrej 
where freez 
wf
w f  w2
and freezrej is a critical rejection value
for the fraction of frozen soil water
content
d)
snowed in the 6 hours preceding the
 precip mod 
rej  MAX 1 
,0
precip rej 

analysis time
where precipmod is an average value of
No increments are applied if it rained or
predicted precipitation accumulation
in the 6-h period preceding the
analysis time, and preciprej is a critical
rejection value for precipitation
e)
level wind is too strong (advective

wind mod 
rej  MAX 2 
,0
wind rej 

effects)
where windrej is a critical rejection
No increments are applied if the low-
value for low-level wind
f)
No increments are applied if solar
radiation is attenuated too much in the
atmosphere (possible effect of clouds)
rej  2
solarground
where solarground
solartop
and solartop are the incident solar
radiation fluxes at the surface and at
the top of the atmosphere
g)
Apply increments only under daylight
 solartop
rej  min 
;
 solar
ref


1


where
solarref  750 W / m2 is a reference
value for the solar radiation at the top
of the atmosphere and solartop is the
inward radiation at the top of the
atmosphere.
The global assimilation cycle
The technique described above was set up in the assimilation cycle of the shortrange regional weather forecast model and its medium-range global weather forecast
version is currently in development. The global model is launched twice a day, for 240-h
integrations at 0000 and for 144-h integrations at 1200 UTC.
The model initial
conditions are obtained from a 3DVAR global cycle, in which data are assimilated every
6 h.
The increments TS , T2 , wg , and w2 are calculated every 6 hours, covering parts
of the world that are under daylight, using global analyses of low-level temperature and
humidity (TS and ES), as well as the results from the last global 6h-integration (see figure
1). The increments are then applied to the soil fields before the next 6h-integration.
Model GEM global-meso
800x600x58
6h forecast
I0, I1
PR, UU, VV, I0, I1, I2, I5,
FB, IV, P0, TT, HR
Soil temperature
and moisture
pseudo-analysis
TT, ES, UU, VV, PN
TS, ES
Screen level
temperature and
moisture
analysis
Fig. 1 Schematic of the global pseudo-analysis interaction with the 6h-integration and the
low-level analysis
References
Giard, D., and E. Bazile, 2000: Implementation of a new assimilation scheme for soil and
surface variables in a global NWP model. Mon. Wea. Rev., 128, 997-1015.
Laroche, S., P. Gauthier, J. St-James, and J. Morneau, 1999: Implementation of a 3D
variational data assimilation system at the Canadian Meteorological Centre. Part II:
The regional analysis. Atmos.-Ocean, 37, 281-307.
Mahfouf, J.-F., 1991:
Analysis of soil moisture from near-surface parameters: A
feasibility study. J. Appl. Meteor., 30, 1534-1547.
Noilhan, J., and S. Planton, 1989: A simple parameterization of land surface processes
for meteorological models. Mon. Wea. Rev., 117, 536-549.