single column modeling: sensitivity analysis, parameter estimation, and land-atmosphere interactions...

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



Real World

Model ({})

Measured Inputs

Measured Outputs

Computed Outputs

t

Yt

Error

Parameter

Tuning

Parameter Optimization

{}: Parameters

Parameter Sensitivity Analysis



Context

TOA Radiation

Land Surface Model

(www.arm.gov)A Single Column Model

Single Column Model


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. ….


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


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


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


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


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


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


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)


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)



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)



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)


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


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


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


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


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


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


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


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


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


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


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


Future work: combine parameter optimization & state estimation

Outer loop: parameter calibration

Inner loop: ensemble state assimilation

M

single column modeling: sensitivity analysis, parameter estimation, and land-atmosphere interactions...

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