VIC Frozen Soils Simulation in Permafrost Regions: Modifications, Improvements, and Testing

VIC Frozen Soils Simulation in

Permafrost Regions Modifications

Improvements and Testing

Jennifer AdamAmanda Tan

May 2 2007

Hydro Group Seminar

Talk Overview1 Motivation 2 Model Description 3 Model Improvements 4 Study Domain 5 Testing of Model Improvements 6 Conclusions

Motivation

1 PrecipitationStreamflow Trend Inconsistency in Permafrost Basins (eg Aldan River)

1940 1960 1980 2000

Adam and Lettenmaier (2007)

Trend mmyear-2

Precipitation

Streamflow

Winter Summer Winter Summer

Permafrost Definition (loose)

Seasonally Frozen Ground Permafrost

Active Layer

Permafrost Layer cm km

cm m

2 Active Layer Depth Simulated Poorly

Snow cover extent lake freeze and break-up dates streamflow climatology ndash satisfactory

Permafrost active layer depth ndash unsatisfactory

Su et al (2005)

3 Historical Streamflow Trends Not Captured in Permafrost Basins

Observed

Simulated

Yenisei

LenaQ

103

m3 s

-1

1940 1960 1980 2000

Obrsquo

Q 1

03 m

3 s-1

1940 1960 1980

Permafrost BasinsNon-Permafrost Basin

Model Description

Frozen Soils Simulation Heat Equation

tL

zT

ztTC i

fis

(Cherkauer et al 1999) With parameterizations for Cs κ and θi

Term 1Heat

Storage(Time)

Term 2Vertical

Heat Conduction

(Space)

Term 3Latent Heat

(Time)

VIC Frozen Soils Algorithm Cherkauer and Lettenmaier

(1999) finite difference algorithm

solving of thermal fluxes through soil column

infiltrationrunoff response adjusted to account for effects of soil ice content

parameterization for spatial distribution of frost

tracks multiple freezethaw layers

can use either ldquozero fluxrdquo or ldquoconstant temperaturerdquo bottom boundary

(Cherkauer et al 1999)

Current Implementation


Spatial Frost Algorithm To produce a

spatial distribution of ice content and subsequently soil moisture drainage


Frozen Soils Optionshellip WOW NODES 18 number of soil thermal nodes FULL_ENERGY TRUE run full energy balance mode GRND_FLUX TRUE solve surface energy balance FROZEN_SOIL TRUE run frozen soils QUICK_FLUX FALSE Liang et al 1999 otherwise

Cherkauer et al 1999 QUICK_SOLVE FALSE Cherkauer et al 1999 for final

step only Liang et al 1999 for rest NOFLUX TRUE zero flux bottom boundary IMPLICIT TRUE uses implicit solver (NEW) EXP_TRANS TRUE exponential grid transform (NEW) QUICK_FS FALSE linear equations for max unfrozen

water content (not tested) QUICK_FS_TEMPS 7

SPATIAL_FROST TRUE sub-grid frost distribution FROST_SUBAREAS 10

Dp 15 damping depth (m) Tave -42 temp at damping depth (degC)

Changes and Improvements

1 Zero Flux Bottom Boundary Parameterization

2 Exponential Grid Transformation3 Implicit Solver4 Patch for the ldquoCold Noserdquo Problem

1 Soil Temperature Sensitivity to Bottom Boundary Specification

Soil

Tem

pera

ture

degC

1930 1931 1932 1930 1931 1932 1930 1931 1932

Constant T BBDp = 4 m

Tbinit = -12 degC10

0

-10

-20

Zero Flux BBDp = 4 m

Tbinit = -12 degC


Tbinit = -3 degC

Soil Surface (Top Boundary)Soil Bottom Boundary

BB Temperature Initialization

Annual Soil Temperature 32 m C

-6 -4 -2 0 2 4 6

A) Frauenfield et al 2004 station data

B) Interpolated station data

2 Exponential Grid Transformation

Linear Distribution

Exponential Distribution

bull Parameters Dp=15m Nnodes=18

z1=soil depth1

z2=2soil depth1

zi=linearly distributed to Dp

Problem discontinuity in

Δz between nodes 2 and 3

zi=exp(bi)+c

Problem discontinuity in Δz between all

nodes

1 m

3 m

5 m

7 m

9 m

11 m

13 m

15 m

i=0

i=Nnodes-1

Exponential Grid Transformation continuedbull Transform spatial derivatives only (temporal

derivatives are unaffected)

bull Expand heat conduction term (chain rule) because κ varies with z

2

2

zT

zT

zzT

z

tL

zT

ztTC i

fis

Exponential Grid Transformation continuedbull Introduce new space variable η (T will vary

exponentially with z but linearly with η)

bull Develop transform function η=f(z)

cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb

Exponential Grid Transformation continued Determine partial derivatives (in η)

Substitute partial derivatives with η into heat conduction terms

1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements

Exponential Grid Transformation continued Determine constants b and c

Boundary condition 1 z(η=Nnodes-1) = Dp Boundary condition 2 z(η=0) = 0 Therefore c = -1

Solve in η-space (because the η-nodes are linearly distributed the finite difference assumptions are not compromised)

Map temperatures in η-space back to z-space Recalculate Cs κ and θi as a function of T for each

z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456

Explicit (forward in time)

Implicit (backward in time)

knownunknown

7 explicit equations solved independently

7 implicit equations solved simultaneously

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456

Stability Issues Stability of convergence

Implicit unconditionally stable Explicit satisfy the Courant-Friedrichs-Lewy Condition

λle14 for no oscillating errorsλ=16 to minimize truncation error

(solution make Δtle1hr or Δzge02m ) Ability to find a solution

Explicit not an issue with physically reasonable values (root_brent is very robust)

Implicit often is unable to find a solution at the initial formation of ice in the soil column

2zt

Cs

=1 to 15 for Δt=3hr Δz=01m

Implicit VIC Frozen Soils Algorithm Newton-Raphson method to solve non-linear

system of simultaneous equations (Ming Pan) New Functions (mainly from Numerical Recipes)

solve_T_profile_implicit (replaces solve_T_profile) fda_heat_eqn (replaces soil_thermal_eqn) newt_raph (replaces root_brent)

fdjac3 (approximation for Jacobian) tridiag (solves tridiagonal linear system)

Modifications from original code Merged to VIC 410 from VIC 403 Added NOFLUX and EXP_TRANS options Nodal updating of Cs κ and θi as a function of T during

iteration Allowed for time-varying Cs When unable to find a solution defers to explicit solver for

that time-step

tTC

tCTTC

t ss

s

4 ldquoCold Noserdquo Problem

Time Step

Tem

pera

ture

degC

Soil Top BoundarySoil Bottom Boundary

Run-away temperatures in near-surface thermal nodes

The coldest node becomes colder and breaks the 2nd law of thermodynamics eg ldquoHeat cannot of itself pass from a colder to a hotter bodyrdquo

VIC crashes ndash error statement is ldquoincrease SOIL_DTrdquo or ldquoincrease SURF_DTrdquo

Occurs for all versions of VIC when using the finite-difference scheme with all modes (implicitexplicit noflux explinear etchellip)

Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule

bull As T decreases κ increases (especially if θi increases)bull Therefore at a ldquocold noserdquo but

bull If |Term1|gt|Term2| heat flows from the cold nodebull T at that node escape towards -infin

0z0

zT

The ldquoCold Noserdquo Patch

Finite Difference ApproxActual

Is calculation being made for the two near-surface nodes

Is the node fall on a ldquocold noserdquo

Is Term1 greater than Term2 in absolute value

THEN Term1 = 0

To allow for some lenience can also check that |TL-TU| gt 5

i=0

i=1

i=2

i=3-10

0

-5 0Temperature degC

Dept

h c

m

10

20

30-15

T

TU

TL

Summary of Changesbull Zero Flux Bottom Boundary Parameterization

bull Change in implementation not in codebull Involves also increasing Dp and Nnodesbull Necessary for climate change studies in permafrost regions

bull Exponential Grid Transformationbull Allows for closer node spacing near surfacebull Solves problem of discontinuity in Δz

bull Implicit Solverbull Should give more accurate solution

bull No convergence instability (no wildly wrong results)bull Nodal updating change of Cs with time

bull Defers to explicit when no solution is foundbull Should give lower simulation time but doesnrsquothellip

bull Patch for the ldquoCold Noserdquo Problembull Inelegant but it works (exists in implicit and explicit modes)bull Does this problem go away if Δz becomes infinitesimally small

Study Area Aldan River Basin

Arctic Ocean

Lena River Basin

ForestShrublandSavannaGrasslandWetlandCroplandUrbanBarrenTundra

Revenga et al 1998

Aldan Tributary 700000

km2

Permafrost DistributionContinuous 90-100Discontinuous 50-90Sporadic 10-50

Seasonally Frozen GroundIsolated lt10

Brown et al 1998

Aldan89 continuous

10 discontinuous1 sporadic

Model Testing

In-Situ Observations

Soil Moisture

Precipitation

Soil TemperatureSnow Depth

Air Temperature

Simulations conductedRun Parameters Simulation Time

1(Base-line)

Optimum parametersDamping depth Dp = 15mNodes = 18Exponential transformationImplicit solutionNo Flux bottom boundary

703132

2 Damping depth Dp = 10m 5524193 Implicit = False 6124244 Exp_Trans = False 2328455 No_Flux = False

No of nodes = 5 Dp = 4m(Su et al 2005 set-upTraditional)

172943

6 Frost subareas = 10 374442

Comparison of simulation time

0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours

Soil Moisture ComparisonRun Parameter

ChangedBias(mm)

Difference from Baseline

(mm)1 Baseline -0732 -2 Damping depth

decreased3292 4024

3 Implicit solution off

-3793 -3007

4 Exponential transform off

2891 3623

5 Su et al (2005) 1973 2705

6 Increasing frost subareas

3427 4159

Soil Moisture Comparison Optimized Run (Run 1)

--- Observed (Liquid) --- Total Soil Moisture--- Liquid Water --- Ice Content

Soil Temperature ComparisonRun

Parameter Changed

Bias Difference from

Baseline1 Baseline 0953 -

2 Damping depth decreased

1756 0803

3 Implicit solution off 7143 5387


3844 2891

5 Su et al (2005) 3748 1208


2348 1395

Soil Temperature Comparison Optimized Run (Run 1)

Streamflow comparison

2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)

Baseline Run 1 Run2 Observed

Streamflow Comparison

2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions

Conclusions Optimum set of parameters

Damping depth = 15m Number of nodes = 18 Implicit solution Exponential distribution of thermal nodes No flux bottom boundary

Traditional setup Constant flux Dp=4m 5 nodes Gives lowest simulation time Not suitable for climate changepermafrost studies

When using the optimized parameters calibration for streamflow is required

VIC Frozen Soils Simulation in Permafrost Regions Modifications Improvements and Testing

Talk Overview

Motivation





Model Description

Slide 9


VIC Frozen Soils Algorithm


Spatial Frost Algorithm

Frozen Soils Optionshellip WOW





Exponential Grid Transformation continued

Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues

Implicit VIC Frozen Soils Algorithm


Explanation


Summary of Changes


Lena River Basin

Permafrost Distribution

Model Testing


Simulations conducted


Soil Moisture Comparison


Soil Temperature Comparison




Conclusions

Slide 44

Talk Overview1 Motivation 2 Model Description 3 Model Improvements 4 Study Domain 5 Testing of Model Improvements 6 Conclusions

Motivation


1940 1960 1980 2000


Trend mmyear-2

Precipitation

Streamflow




Active Layer


cm m




Su et al (2005)


Observed

Simulated

Yenisei

LenaQ

103

m3 s

-1

1940 1960 1980 2000

Obrsquo

Q 1

03 m

3 s-1

1940 1960 1980


Model Description


tL

zT

ztTC i

fis


Term 1Heat

Storage(Time)

Term 2Vertical

Heat Conduction

(Space)

Term 3Latent Heat

(Time)
























Soil

Tem

pera

ture

degC

1930 1931 1932 1930 1931 1932 1930 1931 1932


Tbinit = -12 degC10

0

-10

-20


Tbinit = -12 degC


Tbinit = -3 degC




-6 -4 -2 0 2 4 6




Linear Distribution



z1=soil depth1

z2=2soil depth1




zi=exp(bi)+c


nodes

1 m

3 m

5 m

7 m

9 m

11 m

13 m

15 m

i=0

i=Nnodes-1




2

2

zT

zT

zzT

z

tL

zT

ztTC i

fis




cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44

Motivation


1940 1960 1980 2000


Trend mmyear-2

Precipitation

Streamflow




Active Layer


cm m




Su et al (2005)


Observed

Simulated

Yenisei

LenaQ

103

m3 s

-1

1940 1960 1980 2000

Obrsquo

Q 1

03 m

3 s-1

1940 1960 1980


Model Description


tL

zT

ztTC i

fis


Term 1Heat

Storage(Time)

Term 2Vertical

Heat Conduction

(Space)

Term 3Latent Heat

(Time)
























Soil

Tem

pera

ture

degC

1930 1931 1932 1930 1931 1932 1930 1931 1932


Tbinit = -12 degC10

0

-10

-20


Tbinit = -12 degC


Tbinit = -3 degC




-6 -4 -2 0 2 4 6




Linear Distribution



z1=soil depth1

z2=2soil depth1




zi=exp(bi)+c


nodes

1 m

3 m

5 m

7 m

9 m

11 m

13 m

15 m

i=0

i=Nnodes-1




2

2

zT

zT

zzT

z

tL

zT

ztTC i

fis




cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44


1940 1960 1980 2000


Trend mmyear-2

Precipitation

Streamflow




Active Layer


cm m




Su et al (2005)


Observed

Simulated

Yenisei

LenaQ

103

m3 s

-1

1940 1960 1980 2000

Obrsquo

Q 1

03 m

3 s-1

1940 1960 1980


Model Description


tL

zT

ztTC i

fis


Term 1Heat

Storage(Time)

Term 2Vertical

Heat Conduction

(Space)

Term 3Latent Heat

(Time)
























Soil

Tem

pera

ture

degC

1930 1931 1932 1930 1931 1932 1930 1931 1932


Tbinit = -12 degC10

0

-10

-20


Tbinit = -12 degC


Tbinit = -3 degC




-6 -4 -2 0 2 4 6




Linear Distribution



z1=soil depth1

z2=2soil depth1




zi=exp(bi)+c


nodes

1 m

3 m

5 m

7 m

9 m

11 m

13 m

15 m

i=0

i=Nnodes-1




2

2

zT

zT

zzT

z

tL

zT

ztTC i

fis




cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44




Active Layer


cm m




Su et al (2005)


Observed

Simulated

Yenisei

LenaQ

103

m3 s

-1

1940 1960 1980 2000

Obrsquo

Q 1

03 m

3 s-1

1940 1960 1980


Model Description


tL

zT

ztTC i

fis


Term 1Heat

Storage(Time)

Term 2Vertical

Heat Conduction

(Space)

Term 3Latent Heat

(Time)
























Soil

Tem

pera

ture

degC

1930 1931 1932 1930 1931 1932 1930 1931 1932


Tbinit = -12 degC10

0

-10

-20


Tbinit = -12 degC


Tbinit = -3 degC




-6 -4 -2 0 2 4 6




Linear Distribution



z1=soil depth1

z2=2soil depth1




zi=exp(bi)+c


nodes

1 m

3 m

5 m

7 m

9 m

11 m

13 m

15 m

i=0

i=Nnodes-1




2

2

zT

zT

zzT

z

tL

zT

ztTC i

fis




cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44




Su et al (2005)


Observed

Simulated

Yenisei

LenaQ

103

m3 s

-1

1940 1960 1980 2000

Obrsquo

Q 1

03 m

3 s-1

1940 1960 1980


Model Description


tL

zT

ztTC i

fis


Term 1Heat

Storage(Time)

Term 2Vertical

Heat Conduction

(Space)

Term 3Latent Heat

(Time)
























Soil

Tem

pera

ture

degC

1930 1931 1932 1930 1931 1932 1930 1931 1932


Tbinit = -12 degC10

0

-10

-20


Tbinit = -12 degC


Tbinit = -3 degC




-6 -4 -2 0 2 4 6




Linear Distribution



z1=soil depth1

z2=2soil depth1




zi=exp(bi)+c


nodes

1 m

3 m

5 m

7 m

9 m

11 m

13 m

15 m

i=0

i=Nnodes-1




2

2

zT

zT

zzT

z

tL

zT

ztTC i

fis




cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44


Observed

Simulated

Yenisei

LenaQ

103

m3 s

-1

1940 1960 1980 2000

Obrsquo

Q 1

03 m

3 s-1

1940 1960 1980


Model Description


tL

zT

ztTC i

fis


Term 1Heat

Storage(Time)

Term 2Vertical

Heat Conduction

(Space)

Term 3Latent Heat

(Time)
























Soil

Tem

pera

ture

degC

1930 1931 1932 1930 1931 1932 1930 1931 1932


Tbinit = -12 degC10

0

-10

-20


Tbinit = -12 degC


Tbinit = -3 degC




-6 -4 -2 0 2 4 6




Linear Distribution



z1=soil depth1

z2=2soil depth1




zi=exp(bi)+c


nodes

1 m

3 m

5 m

7 m

9 m

11 m

13 m

15 m

i=0

i=Nnodes-1




2

2

zT

zT

zzT

z

tL

zT

ztTC i

fis




cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44

Model Description


tL

zT

ztTC i

fis


Term 1Heat

Storage(Time)

Term 2Vertical

Heat Conduction

(Space)

Term 3Latent Heat

(Time)
























Soil

Tem

pera

ture

degC

1930 1931 1932 1930 1931 1932 1930 1931 1932


Tbinit = -12 degC10

0

-10

-20


Tbinit = -12 degC


Tbinit = -3 degC




-6 -4 -2 0 2 4 6




Linear Distribution



z1=soil depth1

z2=2soil depth1




zi=exp(bi)+c


nodes

1 m

3 m

5 m

7 m

9 m

11 m

13 m

15 m

i=0

i=Nnodes-1




2

2

zT

zT

zzT

z

tL

zT

ztTC i

fis




cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44


tL

zT

ztTC i

fis


Term 1Heat

Storage(Time)

Term 2Vertical

Heat Conduction

(Space)

Term 3Latent Heat

(Time)
























Soil

Tem

pera

ture

degC

1930 1931 1932 1930 1931 1932 1930 1931 1932


Tbinit = -12 degC10

0

-10

-20


Tbinit = -12 degC


Tbinit = -3 degC




-6 -4 -2 0 2 4 6




Linear Distribution



z1=soil depth1

z2=2soil depth1




zi=exp(bi)+c


nodes

1 m

3 m

5 m

7 m

9 m

11 m

13 m

15 m

i=0

i=Nnodes-1




2

2

zT

zT

zzT

z

tL

zT

ztTC i

fis




cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44
























Soil

Tem

pera

ture

degC

1930 1931 1932 1930 1931 1932 1930 1931 1932


Tbinit = -12 degC10

0

-10

-20


Tbinit = -12 degC


Tbinit = -3 degC




-6 -4 -2 0 2 4 6




Linear Distribution



z1=soil depth1

z2=2soil depth1




zi=exp(bi)+c


nodes

1 m

3 m

5 m

7 m

9 m

11 m

13 m

15 m

i=0

i=Nnodes-1




2

2

zT

zT

zzT

z

tL

zT

ztTC i

fis




cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44



-6 -4 -2 0 2 4 6




Linear Distribution



z1=soil depth1

z2=2soil depth1




zi=exp(bi)+c


nodes

1 m

3 m

5 m

7 m

9 m

11 m

13 m

15 m

i=0

i=Nnodes-1




2

2

zT

zT

zzT

z

tL

zT

ztTC i

fis




cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44


Linear Distribution



z1=soil depth1

z2=2soil depth1




zi=exp(bi)+c


nodes

1 m

3 m

5 m

7 m

9 m

11 m

13 m

15 m

i=0

i=Nnodes-1




2

2

zT

zT

zzT

z

tL

zT

ztTC i

fis




cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44




2

2

zT

zT

zzT

z

tL

zT

ztTC i

fis




cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44




cbz )exp(

T

zzT

T

zT

zzT

2

2

2

2

2

2

zz

(chain rule)

)ln(1 czb



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44



1)ln(1 cz

bz 2

2

2

)ln(1 cz

bz

2

2

zT

zT

z

z

Tczbz

Tczbz

Tzczb 22

2

22 )ln(1

)ln(1

)ln(1

new elements





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44





z-node

)1()1ln(

NnodesDpb

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44

3 Implicit Solvers

Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456



knownunknown



Time

Spac

e

(The

rmal

Nod

es)

t-1 t

0123456







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44







2zt

Cs








that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44







that time-step

tTC

tCTTC

t ss

s


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44


Time Step

Tem

pera

ture

degC






Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44

Explanation

tL

zT

ztTC i

fis

Heat Equation

Term1

Conduction 2

2

zT

zT

zzT

z

Term2

chain rule



0z0

zT






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44






THEN Term1 = 0


i=0

i=1

i=2

i=3-10

0


Dept

h c

m

10

20

30-15

T

TU

TL









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44









Arctic Ocean

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44

Lena River Basin


Revenga et al 1998


km2



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44



Brown et al 1998

Aldan89 continuous


Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44

Model Testing


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44


Soil Moisture

Precipitation


Air Temperature


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44


1(Base-line)


703132



172943



0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44


0 10 20 30 40 50 60 70 80

Run1

Run 2

Run 3

Run 4

Run 5

Run 6

Time in hours


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44


ChangedBias(mm)



decreased3292 4024


-3793 -3007


2891 3623

5 Su et al (2005) 1973 2705


3427 4159




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44




Parameter Changed




1756 0803



3844 2891

5 Su et al (2005) 3748 1208


2348 1395



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)



2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44


2500

3500

4500

5500

6500

7500

8500

1940

1950

1960

1970

1980

1990

2000

Year

Stre

amflo

w (1

0sup3 m

sup3s)


Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44

Conclusions






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44






Talk Overview

Motivation





Model Description

Slide 9











Slide 20

Slide 21

Slide 22

3 Implicit Solvers

Stability Issues



Explanation


Summary of Changes


Lena River Basin


Model Testing










Conclusions

Slide 44

VIC Frozen Soils Simulation in Permafrost Regions: Modifications, Improvements, and Testing

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Transcript of VIC Frozen Soils Simulation in Permafrost Regions: Modifications, Improvements, and Testing