Transcript 4dvar presentation

Surface Analysis (II)
M. Drusch
DA 22.-31.3. 2006
Room TT 063, Phone 2759
Overview
1.
Motivation
2.
Screen level analysis (2 m T and relative humidity)
3.
Operational soil moisture analysis (‘local’ Optimum Interpolation)
- Motivation
- OI technique
DA 22.-31.3. 2006
- Evaluation of the analysis and the impact on the forecast
4.
Satellite observations and future developments
- Remote sensing aspects
- Results from a Nudging experiment
- Design of the future surface analysis
Screen-level analysis:
2D univariate statistical interpolation
1. Increments Xi are estimated at each observation location i from the
observation and the interpolated background field (6 h or 12 h forecast).
2. Analysis increments Xia at each model grid point j are calculated from:
X   w i  Xi
N
a
j
i 1
3. The optimum weights wi are given by: (B + O) w = b
DA 22.-31.3. 2006
b : error covariance between observation i and model grid point j
(dimension of N observations)
B : error covariance matrix of the background field (N × N observations)
B(i1,i2) = 2b ×(i1,i2) with the horizontal correlation coefficients (i1,i2)
and b = 1.5 K / 5 % rH the standard deviation of background errors.
 1  ri i  2 
μi1 , i 2   exp   1 2  
 2 d  


O : covariance matrix of the observation error (N × N observations):
O = 2o × I with o = 2.0 K / 10 % rH the standard deviation of
obs. errors
Screen-level analysis:
Quality controls and technical aspects
1. Number of observations N = 50, scanned radius r = 1000 km.
2. Gross quality checks as rH  [2,100] and T > Tdewpoint
3. Observation points that differ more than 300 m from model
orographie are rejected.
DA 22.-31.3. 2006
4. Observation is rejected if it satisfies:
X i  γ σ o2  σ 2b with  = 3
5. Number of used observations varies from 4000 to 6000 (40% of the
available observations) every 6 hours.
6. Increments are computed:
q = (B + O)-1 X and bTq
Overview
1.
Motivation
2.
Screen level analysis (2 m T and relative humidity)
3.
Operational soil moisture analysis (‘local’ Optimum Interpolation)
- Motivation
- OI technique
DA 22.-31.3. 2006
- Evaluation of the analysis and the impact on the forecast
4.
Satellite observations and future developments
- Remote sensing aspects
- Results from a Nudging experiment
- Design of the future surface analysis
3: Motivation
Evaporation and the Hydrological ‚Rosette‘
DA 22.-31.3. 2006
Rainfall ends
Rainfall starts
DA 22.-31.3. 2006
Motivation
Motivation Climate
Simulated July surface temperature for
A) wet soil case
(actual evapotranspiration is set
to potential evapotranspiration)
B) dry soil case
(no evapotranspiration)
GLAS atmospheric GCM , Shukla and Mintz [1982]
ECMWF long-term forecasts
3. Motivation
(from ENSEMBLES project)
volumetric soil moisture
2 m temperatures
soil moisture
temperature
soil moisture 1&2
root zone soil moisture
28
30
25
[º Celsius]
C
24
O
[%]
26
22
20
15
10
5
0
20
-5
T2m
dew point temp
-10
DA 22.-31.3. 2006
18
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
(monthly averages for North America)
Systematic errors in the land surface scheme result in a (dramatic) dry down
with summer values close to the permanent wilting point.
The corresponding 2 m temperature forecasts show a strong warm bias
exceeding 10 K during summer and 5 K during winter.
ECMWF long-term forecasts
turbulent surface fluxes
fractional cloud coverage
cloud cover
heat fluxes
0
0.65
-20
0.6
-40
0.55
[%]
[W m-2]
3. Motivation
(from ENSEMBLES project)
-60
0.5
0.45
-80
0.4
-100
0.35
latend heat
sensible heat
-120
DA 22.-31.3. 2006
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
(monthly averages for North America)
Latent heat flux is substantially reduced during summer, sensible heat
flux is almost doubled. Due to less moisture in the atmosphere cloud coverage
is also reduced. Surface pressure is reduced (not shown).
The model has to be re-initialized with analysed soil moisture to prevent
from drifting into an unrealistic state.
3. OI technique
Operational OI soil moisture analysis
The analysis increments from the screen level analysis are used to
produce increments for the water content in the first three soil layers
(root zone):

 
ΔΘi  a i Ta  Tb  bι rHa  rHb

and for the first soil temperature layer:

DA 22.-31.3. 2006
T  c  Ta - T b

Superscripts a and b denote analysis and background ( = forecast),
respectively, i denotes the soil layer.
Coefficients ai and bi are defined as the product of optimum
coefficients i and i minimizing the variance of analysis error
and of empirical functions F1, F2, F3.
[Douville et al. (2000), Mahfouf (1991)]
3. OI technique
Operational OI soil moisture analysis:
Optimum coefficients
Coefficients a, b and c can be written as:
F1F2F3
b = Cv ×  ×
F1F2F3
c = (1 - F2)F3
with:
DA 22.-31.3. 2006
a = Cv ×  ×
b 
afraction
 (clow +chigh), 
Cvσvegetation


σ


Θ
rH
2
1   b  ρT,Θ  ρT,rHρ rH, Θ 
Φσ   σ rH  




2
b
a



 σT  
σΘ 





β
1

ρ

ρ
ρ
rH, Θ
T,rH T,Θ 
b 
b 

ΦσrH   σ T  




α
b
T
  σa 2    σa 2 
2


  1   Tb   1   rH
ρ
T,rH
b 
  σ T     σ rH  
F1, F2, F3 empirical functions
From univariate
statistical interpolation
theory (Daley, 1991).
 errors,  correlation
of background errors
between variables x
and y.
3. OI technique
Operational OI soil moisture analysis:
Statistics of background errors
σθb
σa
Based on forecast differences between day 1 and 2 of the net surface
σθb  0.01m3m3
water budget.
Standard deviation of analysis error:
1
σ
a2

1
σ
b2

1
σ
o2
σ aT  1.2 K
σarH  4.47%
DA 22.-31.3. 2006
Statistics of background errors for soil moisture derived from the
Monte Carlo Experiments
coefficient
ρTθ1
ρTθ2
ρTθ3
ρrHθ1
ρrHθ2
ρrHθ3
ρrHT
value
-0.82
-0.92
-0.90
0.83
0.93
0.91
-0.99
3. OI technique
Operational OI soil moisture analysis:
Empirical functions
1. Winter / night time correction: F1  1  tanh λμ M  0.5
2
M : cos mean solar zenith angle
1
 Rg 

2. Weak radiative forcing correction: τ r  
 S0μ M 
r : atmospheric transmittance


DA 22.-31.3. 2006
rmin: 0.2
rmax: 0.9
S0 : solar constant
F2 =
M : cos mean solar zenith angle
R g : mean dw surface solar radiation
forecast
μΜ
r < rmin
0
τ r  τ rmin
τ rmax  τ rmin
rmin < r < rmax
r > rmax
1
0
3. Mountain correction:
Z : model orographie
Zmin : 500 m
Zmax: 3000 m
=7
Z > Zmax
2
F3 =
 Z  Z max 

 Zmin < Z < Zmax
 Z min  Z max 
1
Z < Zmin
3. OI technique
Operational OI soil moisture analysis:
Further limitations
Soil moisture increments are set to 0 if:
1. The last 6 h precipitation exceeds 0.6 mm.
2. The instantaneous wind speed exceeds 10 m s-1.
DA 22.-31.3. 2006
3. The air temperature is below freezing.
4. There is snow on the ground.
Analysed screen level parameters are used as proxy ‘observations’ for the root
zone soil moisture analysis. The relationship between 2 m temperature and
relative humidity and soil moisture is often rather weak and intermittent.
3. Evaluation
Impact study: Soil moisture increments
experiment 1: Optimal Interpolation, atmospheric 4DVar
vs
experiment 2: Open Loop (no analysis), atmospheric 4DVar
[mm]
160°W
140°W
120°W
100°W
80°W
60°W
40°W
20°W
0°
20°E
40°E
60°E
80°E
100°E
120°E
140°E
160°E
250
80°N
80°N
70°N
70°N
60°N
60°N
50°N
50°N
40°N
40°N
30°N
30°N
20°N
20°N
10°N
10°N
200
150
DA 22.-31.3. 2006
0°
100
50
10
0°
10°S
10°S
20°S
20°S
30°S
30°S
40°S
40°S
50°S
50°S
60°S
60°S
70°S
70°S
80°S
80°S
-10
-50
-100
-150
-200
-250
160°W
140°W
120°W
100°W
80°W
60°W
40°W
20°W
0°
20°E
40°E
60°E
80°E
100°E
120°E
140°E
160°E
OI
3. Evaluation
Humidity increments
160°W
140°W
120°W
100°W
80°W
60°W
40°W
20°W
0°
20°E
40°E
60°E
80°E
100°E
120°E
140°E
160°E
15
80°N
80°N
70°N
70°N
60°N
60°N
50°N
50°N
40°N
40°N
30°N
30°N
20°N
20°N
10°N
10°N
0°
OI
mean humidity
increments [%]
10
7.5
5
2.5
0.5
0°
10°S
10°S
20°S
20°S
30°S
30°S
40°S
40°S
50°S
50°S
60°S
60°S
70°S
70°S
80°S
80°S
-0.5
-2.5
-5
-7.5
-10
-15
160°W
140°W
120°W
100°W
80°W
60°W
40°W
20°W
0°
160°W
20°E
140°W
40°E
120°W
60°E
100°W
80°E
80°W
100°E
60°W
120°E
40°W
140°E
20°W
160°E
0°
20°E
40°E
60°E
80°E
100°E
120°E
140°E
[%]
160°E
DA 22.-31.3. 2006
5
80°N
80°N
70°N
70°N
60°N
60°N
50°N
50°N
40°N
40°N
30°N
30°N
20°N
20°N
10°N
10°N
0°
OL – OI difference
of mean humidity
increments [%]
2
1.5
1
0.5
0.1
0°
10°S
10°S
20°S
20°S
30°S
30°S
40°S
40°S
50°S
50°S
60°S
60°S
70°S
70°S
80°S
80°S
-0.1
-0.5
-1
-1.5
-2
-5
160°W
140°W
120°W
100°W
80°W
60°W
40°W
20°W
0°
20°E
40°E
60°E
80°E
100°E
120°E
140°E
160°E
3. Evaluation
Forecast skills
Root-mean-square error E
Ej 
f
j  a
2
Significance levels for the Sign test
area
height
24 h
72 h
120 h
168 h
216 h
Northern
Hemisphere
1000
0.1
0.1
0.5
10.0
1.0
850
0.1
0.1
5.0
-
5.0
700
5.0
1.0
-
-
10.0
1000
0.1
0.1
0.1
-
-
850
0.1
0.1
5.0
-
-
700
-
10.0
-
-
-
1000
0.1
0.1
5.0
5.0
0.5
850
0.1
0.1
-
-
0.2
700
-
-
-
-
5.0
1000
0.1
0.1
-
-
-
Europe
East Asia
DA 22.-31.3. 2006
Temperature at 1000 hPa
North
America
grey: OI
850
0.1
0.1
black: OL
700
5.0
solid: North America
Thedotted:
proxyEurope
‘observations’ are efficient in improving the turbulent surface fluxes
dashed: East Asia
and consequently the weather forecast on large geographical domains.
DA 22.-31.3. 2006
3. Evaluation
Validation against OK Mesonet
observations
DA 22.-31.3. 2006
3. Evaluation
Validation of forcing data
area averages for Oklahoma
daily precipitation
daily downward shortwave radiation
model forecast (OI)
observations
model forecast (OI)
observations
total amount of rainfall:
June
July
87.3 mm model
on
87.8 mm observations on
110. mm model
on
79. mm observations on
19 days
9 days
26 days
20 days
Correlation
Bias
: 0.85
: - 0.7 Wm-2
DA 22.-31.3. 2006
3. Evaluation
Validation of soil moisture
area averages for Oklahoma
surface soil moisture
root zone soil moisture
model forecast (OI)
model forecast (OL)
model forecast (OI)
model forecast (OL)
observations
observations
• Too quick dry downs (model problem).
• Too much precip in July (model problem).
• Too little water added in wet conditions
(analysis problem).
• NO water removed in dry conditions
(analysis problem).
• Precipitation errors propagate to the
root zone.
• Analysis constantly adds water.
• The monthly trend is underestimated.
The current analysis fails to produce more accurate soil moisture estimates.
Overview
1.
Motivation
2.
Screen level analysis (2 m T and relative humidity)
3.
Operational soil moisture analysis (‘local’ Optimum Interpolation)
- Motivation
- OI technique
DA 22.-31.3. 2006
- Evaluation of the analysis and the impact on the forecast
4.
Satellite observations and future developments
- Remote sensing aspects
- Results from a Nudging experiment
- Design of the future surface analysis
DA 22.-31.3. 2006
4. Remote sensing aspects
Wavelengths and soil moisture
Wavelength
IR
Microwave
(scatterometer)
Microwave
(radiometer)
pros
good temporal
resolution
• good spatial
resolution
•
acceptable temporal
resolution
• acceptable spatial
resolution
• all weather tool
•
acceptable temporal
resolution
• all weather tool
• most direct signal
• radiative transfer
established
•
Cons
cloud free situations only
• model is needed to infer
the energy balance at the
surface (indirect
information)
•
strong dependency on
incidence angle
• effects of surface
roughness and vegetation
• radiative transfer complex
•
•
coarse spatial resolution
4. Remote sensing aspects
ERS-1/2 scatterometer derived soil moisture
Data set produced by:
Institute of Photogrammetry
and Remote Sensing,
Vienna University of Technology
Basis:
ERS scatterometer backscatter
measurements
DA 22.-31.3. 2006
Method:
change detection method for
extrapolated backscatter at
40º reference incidence angle
Output:
topsoil moisture content in relative
units (0 [dry] to 1 [wet])
http://ipf.tuwien.ac.at/radar/ers-scat/home.htm
4. Remote sensing aspects
AMSR-E derived soil moisture
Data set produced by:
National Snow and Ice Data Center
(NSIDC), Boulder, Colorado
Basis:
brightness temperatures at 10.7
and 18.7 GHz horizontal and
vertical polarization
Method:
DA 22.-31.3. 2006
change detection method for
normalized polarization ratios
Typical day with coverage of 28 half orbits.
Output:
(http://nsidc.org/data/docs/daac/ae_land_l2b_soil_moisture.gd.html)
surface soil moisture [g cm-3],
vegetation water content [kg m-3]
DA 22.-31.3. 2006
4. Remote sensing aspects
TMI Pathfinder Data Set
Data set produced by:
Dept. Civil and Environmental Engineering,
Princeton University, NJ
July 2nd, 1999
Basis:
brightness temperatures
at 10.65 GHz horizontal
polarization
Method:
physical retrieval based on
land surface microwave
emission model and
auxiliary data sets from the
North American Land Data
Assimilation Study project
Output:
surface soil moisture [cm3 cm-3],
0
5 10 15 20 25 30 35 40 45
(%)
(Gao et al. 2006)
DA 22.-31.3. 2006
4. Remote sensing aspects
Oklahoma data sets 2002
4. Remote sensing aspects
Bias correction / CDF matching
Cumulative
Distribution
Function
TMI
ECMWF
DA 22.-31.3. 2006
x
x’
CDFM(x’) = CDFS(x)
transfer funcion
03/2002-10/2002
• CDF matching reduces systematic errors:
The bias has been removed and the dynamic
range has been adjusted.
• The random error may increase.
r2 = 0.01
r2 = 0.18
x‘-x
4. Remote sensing aspects
TMI soil moisture transformation
r2 = 0.66
r2 = 0.69
DA 22.-31.3. 2006
Bias: -0.35 %
x
Bias: -11.67 %
4. Remote sensing aspects
Corrected TMI soil moisture
volumetric surface
soil moisture [%]
for 06/06/2004
the modelled first guess
DA 22.-31.3. 2006
TMI Pathfinder data
corrected TMI data set
DA 22.-31.3. 2006
4. TMI Nudging experiment
Nudging set up
00
03
06
09
12
AN
15
18
21
00
AN
FC
03
06
09
AN
FC
12
15
18
21
00
Delayed cut-off
4D-Var (12 h)
FC
TMI sampling
period (daily)
soil moisture
analysis
1/4
2/4
1/4
2/4
DA 22.-31.3. 2006
4. TMI Nudging experiment
Validation of soil moisture
area averages for Oklahoma
surface soil moisture
root zone soil moisture
• Nudging / satellite data remove water
effectively and produce a realistic dry
down.
• Nudging the satellite results in the most
accurate surface soil moisture estimate.
• The information introduced at the
surface propagates to the root zone.
• The monthly trend is well reproduced
using the nudging scheme.
Satellite derived soil moisture improve the soil moisture analysis and
results in the most accurate estimate.
DA 22.-31.3. 2006
4. TMI Nudging experiment
Forecast skill
correlation (observation / fc)
bias
OI
Nudging
OL
rH
rH
The impact of the satellite data on the forecast quality (of screen level
T
T
variables) is neutral (correlation).
The biases obtained from the nudging
experiment are slightly higher when compared against the OI and lower
when compared against the OL.
DA 22.-31.3. 2006
4. TMI Nudging experiment
Soil moisture increments
accumulated increments over June and July 2002
[mm]
Optimal
Interpolation
(2 m T and RH)
Nudging
(TMI
soil moisture)
4. Future surface analysis
The future Surface Data Assimilation
System
00
03
06
09
Delayed cut-off
4D-Var (12 h)
12
15
18
21
00
AN
06
09
12
15
18
21
AN
FC
FC
Early Delivery Analysis
4D-Var (6 h)
03
AN
AN
DA 22.-31.3. 2006
12 UTC FC
00 UTC FC
SDAS
00
DA 22.-31.3. 2006
4. Future surface analysis
Land Data Assimilation Systems LDAS
Development of advanced systems for the assimilation of satellite observations
to improve the analysis of the state of the land surface (and consequently the
numerical weather forecasts).
North America : NLDAS, Globe : GLDAS
(NASA GSFC, see http://ldas.gsfc.nasa.gov)
Canada: CLDAS
(Meteorological Service of Canada)
Europe: ELDAS
(KNMI, see http://www.knmi.nl/samenw/eldas)