Conclusions and perspectives• Reduced analysis increments at depth.• EKF assimilation independent of the time of the day.• Stronger coupling land-atmosphere during daytime → forecast errors reduced.• Forecast errors sensitivity decrease with soil depth.• Cycling forecast errors between assimilation cycles (no initialization of the forecast error matrix

at each assimilation cycle). Is it feasible for extended periods?• Investigation of the Q matrix role in the propagation of forecast errors.

BibliographyDrusch, M., K. Scipal, P. de Rosnay, G. Balsamo, E. Andersson, P. Bougeault, P. Viterbo, “Towards aKalman filter based soil moisture analysis system for the operational ECMWF Integrated ForecastSystem”, Geophys. Res. Let., submitted 2008.

Mahfouf, J.-F., K. Bergaoui, C. Draper, F. Bouyssel, F. Taillefer, and L. Taseva (2009), “A comparisonof two off-line soil analysis schemes for assimilation of screen-level observations”, J. Geophys. Res.,doi:10.1029/2008JD011077, in press. [PDF] (accepted 21 January 2009).

Soil moisture analysis at ECMWF using a SEKF scheme:recent developments and preliminary results

J. Muñoz Sabater (1) • P. de Rosnay (1)

M. Drusch (2) • G. Balsamo (1)

(1) ECMWF • (2) ESTEC, ESA

Operational OI vs. the new SEKF scheme at ECMWFOI, operational global soil moisture analysis at ECMWF:

• Designed to assimilate only conventional SYNOP observations, which are only weakly related tosoil moisture.

• Relies on strong land-atmospheric coupling (atmospheric switches).• Based on empirical (static) coefficients.• Not adapted to follow land surface developments.

Currently, implementation of a simplified EKF scheme:

• Allows assimilation of satellite data at “asynoptic” times, more directly related to soil moisture oftop surface layer.

• Computed gain is “optimal”.• Forecast errors depend on the weather regime and can be dynamically propagated between

assimilation cycles.

SEKF approacha) It consists of minimizing the general cost function J:

J(x) = ½ (x–xb)TB–1(x–xb) + ½ (y–H(xb))R–1(y–H(xb))

x: state vector (soil moisture in layer j).xb: background, modelled state vector (modelled soil moisture in layer j).y: observation vector (T2m and RH2m).H: non-linear observation operator (project state variables in the observation space).B: background error covariance matrix (forecast error of modelled soil moisture).R: observation error covariance matrix (T2m and RH2m observations errors).

b) Linear Tangent Hypothesis: Linearization of the non-linear observation operator H, by integratingthe model with perturbed initial conditions (one for each state variable). In this way no tangentlinear and adjoint models are needed.

c) For small estimation problems and under the linear tangent hypothesis, the minimum of J canbe obtained analytically. The solution for the state vector xa (soil moisture at layer j) at time i is:

xa(i) = xb(i) + K[i,i+12] (y[i,i+12] – H[i,i+12](xb))

where [i,i+12] refers to a 12h atmospheric 4D-VAR assimilation window operationally used atECMWF, and the gain matrix K[i,i+12] is:

K[i,i+12] = [B–1(i) + HT(i)[i,i+12]R–1 H(i)[i,i+12]]–1 HT(i)[i,i+12]R–1

d) The background values for the next assimilation window (i+12) are computed by:xb(i+12) = M[i,i+12] xa(i)

with M[i,i+12] being the forecast operator between two assimilation windows of 12h.

e) Cycling of the B-matrix: the background error evolves in time according to:

B(i+12) = M[i,i+12] A(i) MT[i,i+12] + Q(i)

with M[i,i+12] the tangent linear of the forecast operator M[i,i+12], Q is the model error covariancematrix and A is the analysis error covariance matrix computed as:

A(i) = [I – K[i,i+12] H(i)[i,i+12]] B–1(i)

The perturbed model runs needed to compute M[i,i-12] allow soil water transfer between the soil layers.

Perturbation of initial soilmoisture of layer j.

Perturbed integration j and computation ofmodelled perturbed increment in observationspace at observation times (δy(i)).

Construction of thelinearized observationoperator.

160°W 120°W 80°W 40°W 0° 40°E 80°E 120°E 160°E

80°S

60°S

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0°

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80°N

160°W 120°W 80°W 40°W 0° 40°E 80°E 120°E 160°E

160°W 120°W 80°W 40°W 0° 40°E 80°E 120°E 160°E

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40°N

60°N

80°N

160°W 120°W 80°W 40°W 0° 40°E 80°E 120°E 160°E

160°W 120°W 80°W 40°W 0° 40°E 80°E 120°E 160°E

80°S

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0°

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160°W 120°W 80°W 40°W 0° 40°E 80°E 120°E 160°E

0 0.0003 0.0005 0.0008 0.001 0.0013 0.0015 0.0018 0.002

a) 01 05 2007 12 UTC 02 05 2007 12 UTC

b)

c)

a)

b)

c)

OI SEKF–15 –1 –0.05 0 0.05 1 15

Analysis increment (in mm) from the OI (left) and SEKF (right) for 01-05-2007 at 12UTC. Panels refer to a) the top layer (0–0.07 m), b) theroot-zone (0.07–0.28 m) and c) the bottom layer (0.28–0.72 m).

1-day soil moisture analysis experiment at global scale• 24h soil moisture analysis from 01-05-2007 at 00 UTC containing two complete 12h

atmospheric 4D-Var analysis windows (from 21 to 09 UTC and from 09 to 21 UTC).• Background fields are computed from previous forecasts, based on analysis at 06 and 18 UTC.• Forecast errors are initialised at the beginning of each 4D-Var assimilation window

21 00 03 06 09 12 15 18 21 00

T2m

RH2m

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w00

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w06

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w12

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Observations

4D-Var 4D-Var

15h fc 15h fcBackground fields

Linearisedoperational operator

Analysis

00 00+12

Preliminary results propagating forecast errors between assimilation cycles

00+24

B00

B00 = M•A00–12•MT+Q00 B00+12 = M•A00

•MT+Q12 B00+24 = M•A00+12•MT+Q00+24

B00+12B00+24

A00 A00+12 A00+24

4D-Var 4D-Var

Error reduction in soil moisture forecast between two assimilation cycles: 01-05-2007 at 12 UTC (left) and 02-05-2007 at 00 UTC (right). The scaleshows the variance error. Panels refer to a) the top layer (0–0.07 m), b) the root-zone (0.07–0.28 m) and c) the bottom layer (0.28–0.72 m).