Post on 16-Dec-2015
Single Column Modeling: Sensitivity Analysis, Parameter Estimation,
and Land-Atmosphere Interactions
Yuqiong Liu University of Arizona, USAHoshin Gupta University of Arizona, USA
Luis Bastidas Utah State University, USASoroosh Sorooshian University of California, Irvine, USA
GABLS/GLASS WorkshopDe Bilt, The Netherlands, September 19-21, 2005
GABLS/GLASS Workshop 2De Bilt, The Netherlands Sept. 19-21, 2005
“Systems” Description of a Model
Model Structure MXt = fx ( Xt-1, , It-1 )Ot = fo (Xt, )
IInput
sX
State VariablesOutput
s
O
Parameters(time-invariant properties of the system)
Xo
Initial States
(Time-variant quantities)
B.C.
Each model component has some uncertainty associated with it …
Parameter Estimation
GABLS/GLASS Workshop 3De Bilt, The Netherlands Sept. 19-21, 2005
Parameter Estimation
Real World
Model ({})
Measured Inputs
Measured Outputs
Computed Outputs
t
Yt
Error
Parameter
Tuning
Parameter Optimization
{}: Parameters
Parameter Sensitivity Analysis
Parameter Estimation
GABLS/GLASS Workshop 4De Bilt, The Netherlands Sept. 19-21, 2005
Context
TOA Radiation
Land Surface Model
(www.arm.gov)A Single Column Model
Single Column Model
GABLS/GLASS Workshop 5De Bilt, The Netherlands Sept. 19-21, 2005
Single Column Model (SCM)
ATMO (, xA)
LAND ( , xL)
P RL R
S E
H RSR
L
B. C.B. C.
RTOA
Everything may have an error in it: , , XA, XL, B.C. …. Everything may have an error in it: , , XA, XL, B.C. ….
GABLS/GLASS Workshop 6De Bilt, The Netherlands Sept. 19-21, 2005
Biophysical fluxes• radiative transfer• sensible/latent heat• stomatal physiology• momentum flux• soil heat/snow melt• temperatures
Column hydrology• interception• throughfall/stemflow• snow hydrology• infiltration/surface runoff• soil water redistribution• capillary rise/drainage
Integrated surface albedo• direct albedo (VIS, NIR)• diffuse albedo (VIS, NIR)
Dry convectionDry adiabatic adjustment on T, q
Moist convection• Deep conv. (zhang- McFarlane, 1996)• shallow/mid-level conv. (Hack, 1994)=> Convective precip
Large-scale condensation
• super-saturation=> largescale precip
Cloud fraction • convective cloud - convective moisture flux • (high+mid)layer clouds - brunt-vaisalla frequency q threshold• low clouds - fixed q threshold (0.9 or 0.8)
=> Total cloud
Radiation • solar (VIS+NIR) - -Eddington scheme • long wave radiation - absorbtivity and emissivity - direct solar (VIS, NIR)- diffuse solar (VIS,NIR)- downward longwave
DRIVER
Initializationu, v, T, q etc.
If nstep=1
• surface pressure• atm pressure• wind (u, v)• temperature• specific humidity
• convective precip. • large-scale precip. • downward longwave• bottom layer height
• direct incident solar (VIS, NIR)• diffuse incident solar (VIS, NIR)
• latent/sensible heat• water vapor flux• momentum flux• emitted longwave• direct albedo (VIS, NIR)• diffuse albedo (VIS, NIR)
• Vertical diffusion and boundary layer process• Rayleigh friction (u,v tendency)• Gravity wave drag - u, v, T tendencies• Semi-Lagrangian transport for vertical advection• forecast (u, v, T, q)
nstep +1
MODEL – NCAR SCM
GABLS/GLASS Workshop 7De Bilt, The Netherlands Sept. 19-21, 2005
Observations
P: precipitationRnet: net surface radiationE: latent HeatH: Sensible Heat
Ta: Air temperatureqa: air specific humidityTg: ground temperatureS: Soil moisture
Boundary Conditions
85%: Crops %15: bare ground
DATA – ARM SGP IOP Datasets
GABLS/GLASS Workshop 8De Bilt, The Netherlands Sept. 19-21, 2005
Impacts of Land-Atmosphere Interactions
-100
0
100
200
300
400
observation default
-50
0
50
100
150
200
20 40 60 80 100 120 140 160 180 200296
298
300
302
304
306
Gro
un
d
Te
mp
era
ture
Se
ns
ible
He
at
La
ten
t H
ea
t
default: simulation with the default parameter set
calibrated
calibrated: simulation with an optimal parameter set from multi-objective calibration
-200
0
200
400
600
800
-100
0
100
200
300
Se
ns
ible
He
at
La
ten
t H
ea
t
Offline
Coupled
GABLS/GLASS Workshop 9De Bilt, The Netherlands Sept. 19-21, 2005
Part I:
Parameter Sensitivity Analysis (SA)
Purpose:
• Understand model behavior with respect to each parameter
• Reduce dimensionality of parameter space to facilitate parameter optimization
Two-step process:
• One-at-A-Time (OAT) independent analysis for first screening
• multi-parameter, multi-objective analysis for further reduction
GABLS/GLASS Workshop 10De Bilt, The Netherlands Sept. 19-21, 2005
One-at-A-Time (OAT) Independent SA
# of Parameters (59 40):
Land 45 32 Vegetation: 12 Soil: 16 Init. Soil water: 4
Atmo 14 8 convection: 4 clouds: 4
GABLS/GLASS Workshop 11De Bilt, The Netherlands Sept. 19-21, 2005
Multi-parameter, Multi-objective Sensitivity Analysis
Multi-Objective Generalized Sensitivity Analysis (MOGSA)
3 Cases to explore the impacts of land-atmo interactions:
• offline LSM (32 land par)
• coupled SCM (32 land par only)
• coupled SCM (32 land par + 8 atmo par = 40)
RMSE of latent heat, sensible heat, and ground temperature
4 kinds of sensitivities: Multi-criteria E H Tg
Parameters
Objectives
Algorithm
Calculates both multi-objective and single-objective sensitivities
GABLS/GLASS Workshop 12De Bilt, The Netherlands Sept. 19-21, 2005
Multi-parameter, multi-objective SA results (1)M
ult
i-
Cri
teri
a
Late
nt
Heat
Sen
sib
le
Heat
Gro
un
d
Tem
p.
1 2 3 4 5 6 7 8 9 10 11 12
.001
.01
0.1
1.0
1 2 3 4 5 6 7 8 9 10 11 12
.001
.01
0.1
1.0
1 2 3 4 5 6 7 8 9 10 11 12
.001
.01
0.1
1.0
1 2 3 4 5 6 7 8 9 10 11 12
.001
.01
0.1
1.0
z0m
vt
zp
dvt
bp
rho
l1
rho
l2
tau
l1
tau
l2 xl
ch
2o
p
hvt
avcm
x
co
ver
Vegetation Parameters
LSM
SCM (32 par)
SCM (40 par)
GABLS/GLASS Workshop 13De Bilt, The Netherlands Sept. 19-21, 2005
Multi-parameter, multi-objective SA results (2)
Soil Parameters
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
.001
.01
0.1
1.0
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
.001
.01
0.1
1.0
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
.001
.01
0.1
1.0
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
.001
.01
0.1
1.0
rlso
i
wats
at
hksat
sm
psat
bch
watd
ry
wato
pt
tkso
l
tkd
ry
cso
l
alb
sat1
alb
sat2
dzso
i1
dzso
i2
dzso
i3
dzso
i4
Mu
lti-
C
rite
ria
Late
nt
Heat
Sen
sib
le
Heat
Gro
un
d
Tem
p.
LSM
SCM (32 par)
SCM (40 par)
GABLS/GLASS Workshop 14De Bilt, The Netherlands Sept. 19-21, 2005
Multi-parameter, multi-objective SA results (3)
Initial Soil MoistureM
ult
i-
Cri
teri
a
Late
nt
Heat
Sen
sib
le
Heat
Gro
un
d
Tem
p.
29 30 31 32
.001
.01
0.1
1.0
29 30 31 32
.001
.01
0.1
1.0
29 30 31 32
.001
.01
0.1
1.0
29 30 31 32
.001
.01
0.1
1.0
h2osoi1 h2osoi2 h2osoi3 h2osoi4
LSM
SCM (32 par)
SCM (40 par)
GABLS/GLASS Workshop 15De Bilt, The Netherlands Sept. 19-21, 2005
Multi-parameter, multi-objective SA results (4)
Atmospheric Parameters
33 34 35 36 37 38 39 40
.001
.01
0.1
1.0
33 34 35 36 37 38 39 40
.001
.01
0.1
1.0
33 34 35 36 37 38 39 40
.001
.01
0.1
1.0
33 34 35 36 37 38 39 40
.001
.01
0.1
1.0
capelmt tau fmax alfa rhminl rhminh Cconv rhccn
Mu
lti-
C
rite
ria
Late
nt
Heat
Sen
sib
le
Heat
Gro
un
d
Tem
p.
SCM (40 par)
GABLS/GLASS Workshop 16De Bilt, The Netherlands Sept. 19-21, 2005
Part I Summary
land-atmosphere interactions may have significant influences on parameter sensitivities
Parameter sensitivities depend on the flux/variable being analyzed (H, E, Tg, or multi-criteria)
For vegetation parameters, land-atmosphere interactions seem to have much less influence on H than E and Tg
Sensitivities of soil thickness and initial soil water decrease with depth into soil
Some atmospheric parameter are very sensitive and should be considered in coupled calibration studies
Sensitivity Analysis
GABLS/GLASS Workshop 17De Bilt, The Netherlands Sept. 19-21, 2005
Part II:
Parameter Optimization 31 parameters (23 land, 8 atmosphere) to be optimized
Calibration case design: which parameters and fluxes/variables to focus on
Use a modified Shuffled Complex Evolution algorithm for multi-objective, multi-parameter optimization
GABLS/GLASS Workshop 18De Bilt, The Netherlands Sept. 19-21, 2005
Calibration case design
Objectives
Land fluxes/variables (E, H, Tg)
FL
cases
Atmospheric forcing variables (Pcp, Rnet, Ta)
FA
Both (E, H, Tg) and (Pcp, Rnet, Ta)
FLA
ParametersLand parameters (L, 23)
L
cases
Atmo. parameters (A,
8)
A
Both land and atmo parameters (LA, 31)
LA
FLL
FLA
FLLA
FLL, FLA, FLLA, FLLAS, FLLA
P
FAL, FAA, FALA, FALAS, FALA
P
FLAL, FLAA, FLALA, FLALAS, FLALA
P
15 cases in total:
Opt. L offline first,then opt. A in the SCCM
SStep-wise
Decouple Pcp and Rnet, opt. LA
PPartially decoupled
GABLS/GLASS Workshop 19De Bilt, The Netherlands Sept. 19-21, 2005
Calibration – Land surface parameters
Default FL only FA only FL & FA
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
0
0.2
0.4
0.6
0.8
1a) Optimize Land Parameters Only
No
rmali
zed
P
ara
mete
r V
alu
es
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
0
0.2
0.4
0.6
0.8
1
Z0
MV
T
ZP
DV
T
RH
OL
2
TA
UL
2
XL
CH
2O
P
HV
T
AV
CM
X
CO
VE
R
RL
SO
I
WA
TS
AT
HK
SA
T
SM
PS
AT
BC
H
WA
TD
RY
WA
TO
PT
TK
DR
Y
CS
OL
AL
BS
AT
1
AL
BS
AT
2
DZ
SO
I1
H2
OS
OI1
H2
OS
OI2
b) Optimize Both Land and Atmo Parameters
Vegetation Parameters Soil Parameters/Initial Conditions
No
rmali
zed
P
ara
mete
r V
alu
es
GABLS/GLASS Workshop 20De Bilt, The Netherlands Sept. 19-21, 2005
Calibration – atmospheric parameters
Default FL only FA only FL & FA
24 25 26 27 28 29 30 31
0
0.2
0.4
0.6
0.8
1
CA
PE
LM
T
TA
U
FM
AX
AL
FA
RH
MIN
L
RH
MIN
H
CC
ON
V
RH
CC
N
a) Optimize Atmospheric Parameters Only
No
rma
lize
d
P
ara
me
ter
Va
lue
s
24 25 26 27 28 29 30 31
0
0.2
0.4
0.6
0.8
1
CA
PE
LM
T
TA
U
FM
AX
AL
FA
RH
MIN
L
RH
MIN
H
CC
ON
V
RH
CC
N
b) Optimize Both Land and Atmo Parameters
GABLS/GLASS Workshop 21De Bilt, The Netherlands Sept. 19-21, 2005
c) Ground Temperature (3.87 K)
0.00
0.50
1.00
A B C
1
2
3
4
5
Calibration – Objective Function Values
b) Sensible Heat (48 W/m2)
0.00
0.50
1.00
A B C
1
2
3
4
5
e) Net Radiation ( 187 W/m2)
0.00
0.50
1.00
A B C
1
2
3
4
5
a) Latent Heat (105 W/m2)
0.00
0.50
1.00
A B C
1
2
3
4
5
d) Precipitation (2.93 mm/6hr)
0.00
0.50
1.00
A B C
1
2
3
4
5
f) Air Temperature ( 5.1 K)
0.00
0.50
1.00
A B C
1
2
3
4
5
Normalized by default (a priori) RSM errors
L
A
LA
LAS
LAPFL FA FLA
FL FA FLA
FL FA FLA
FL FA FLA
FL FA FLA
FL FA FLA
GABLS/GLASS Workshop 22De Bilt, The Netherlands Sept. 19-21, 2005
Latent Heat (W/m2
)
Sensible Heat (W/m2)
Ground Temp (K)
0
200
400
600
0
100
200 DefaultObservationOptimized
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17295
300
305
310
Time in days
Calibration – Time series, land surface
GABLS/GLASS Workshop 23De Bilt, The Netherlands Sept. 19-21, 2005
Precip. (mm/day)
Net Radiation (W/m2)
Air Temp (K)
0
50
100
0
500
1000
DefaultObservationOptimized
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17290
295
300
305
310
Time in days
Calibration – Time series, atmosphere
GABLS/GLASS Workshop 24De Bilt, The Netherlands Sept. 19-21, 2005
Part II Summary
Parameter Optimization
Including atmospheric parameters can greatly reduce the errors
Including atmospheric variables can help make the parameter sets better converged
Calibration results are best for ground temperature, worst for sensible heat
Step-wise calibration scheme works well
Decoupling Precipitation and net radiation greatly improves the calibration results
GABLS/GLASS Workshop 25De Bilt, The Netherlands Sept. 19-21, 2005
Other parameter estimation method
Using ensemble-based data assimilation methods by recasting parameters as state variables:
Potential concerns: Constant parameters are adjusted instantly/frequently Lead to unstable model simulations Difficult to apply to complex, dynamical models Not suitable to real-time applications
sXX
GABLS/GLASS Workshop 26De Bilt, The Netherlands Sept. 19-21, 2005
Model calibration for parameter estimation – Pros & Cons
Parameters are time-invariant properties (i.e., constants) of the physical system …
Traditional Model Calibration methods long-term systematic errors properly corrected Parameter uncertainties considered State uncertainties ignored Estimated parameters could be biased if substantial
state and observational errors
GABLS/GLASS Workshop 27De Bilt, The Netherlands Sept. 19-21, 2005
Future work: combine parameter optimization & state estimation
Outer loop: parameter calibration
Inner loop: ensemble state assimilation
M