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Uncertainty Analyses of an Indian Summer Monsoon Model: Methods and Results

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Outline Phenomenon, model, aims Methodical approach Monsoon stability under uncertainty Conclusions PIK - Potsdam Institute for Climate Impact Research, Germany http://www.pik-potsdam.de Michael Flechsig & Brigitte Knopf

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outline phenomenon model aims methodical approach monsoon stability under uncertainty conclusions
Outline

Phenomenon, model, aims

Methodical approach

Monsoon stability under uncertainty

Conclusions

PIK - Potsdam Institute for Climate Impact Research, Germany http://www.pik-potsdam.de

Michael Flechsig & Brigitte Knopf

Uncertainty Analyses of an Indian Summer Monsoon Model: Methods and Results

the indian monsoon

ITCZ N-Summer

Equator

ITCZ N-Winter

© Paul R. Baumann State University of New York

The Indian Monsoon
  • Semi-annual shift of the intertropical convergence zone ITCZ in conjunction with Temperature gradients in the atmosphere between land surface and ocean lead toIndian Monsoon: wet summers and relatively dry winters over the Indian sub-continent
  • Economic implications of the monsoon stability for India:
    • Agriculture accounts for 25% of the GDP
    • Agriculture employs 70% of the population
the model zickfeld et al grl 32 2005

Stratosphere

Tibetan Plateau

stable states instable states

Indian Ocean

Indian Ocean

(20N , 75W)

LandSurface

2 Soil Layers

instable

stable

stable

present value

The Model(Zickfeld et al., GRL 32, 2005)
  • One-dimensional (idealised) box model of the tropical atmosphere over India with about 60 parameters for qualitative studies
  • Prognostic state variables
    • Air temperature
    • Specific air humidity
    • Moisture in two soil layers
  • Drivers: boundary conditions for
    • Air temperature
    • Air humidity
    • Cloudiness
  • For the summer monsoon the model shows a saddle node bifurcationagainst parameters that govern the heat budget
    • Atmospheric CO2 concentration
    • Solar insolation
    • Albedo As of the land surface(AS for broad-leafed trees = 0.12, for desert = 0.30)
aims and applied methods
Aims and Applied Methods
  • Study the stability of the Indian summer monsoon under potential land use and climate change
  • Determine robustness of the bifurcation at SN1against the surface albedo AS under parameter uncertainty
  • Consider three parameter / initial value spaces (all without parameter As)
    • T38 the total space of all 38 uncertain parameters:determine most important parameters
    • S5 a 5-dimensional subspace of the most influential parameters: study parameter sensitivity
    • A5 a 5-dimensional subspace of anthropogenically influenceable parameters: get implications of potential climate change
  • Applied methods and used tools:
    • Combine a qualitative analysis (QA) of a model (“bifurcation analysis”)AUTO (Doedel, 1981)
    • with multi-run model sensitivity and uncertainty analysesSimEnv (Flechsig et al., 2005)
multi run simenv approach

ExperimentPerformance

ExperimentPostprocess.

OriginalModel

InterfacedModel

ExperimentPreparation

ResultEvaluation

Multi-Run SimEnv Approach
  • Consider Y = F(X) SN1 = QA ( model ( [ T38 | S5 | A5 ] ) )
    • X factor space: model parameters, initial values, boundary values, drivers
    • Y model output (multi-dimensional, large volume)
  • Apply deterministic and random sampling techniques in the multi-factor space Xto study model sensitivity and uncertainty of model output Y multi-run experiments
  • Simple model interface to SimEnv for factors X and model output Y

“Include for each factor and for each model output field one SimEnv function call into the model source code”

    • at programming language level: C/C++ Fortran Python
    • at modelling language level: MatLab Mathematica GAMS
    • at shell script level
simenv experiment types

x2

x1

assessment

strategy

SimEnv Experiment Types
  • SimEnv provides generic multi-run simulation experiment typesthat differ in their sampling strategies
  • To generate a sample in the factor space under study a selected experiment type has to be equipped with numerical information

o = default value

x = 1 single run

x = 2nd sample

monsoon model uncertainty analyses
Monsoon Model Uncertainty Analyses

Model interface:

Experiments:

  • Global sensitivity analysis in T38
  • Behavioural analysis in S5
  • Monte Carlo analysis in T38 and A5
morris design 1991 model free

k=2 factors p=5 levelsNTraject=4 trajectoriestrajectory

σ

nonlinear effect on model output 

μabs

sensitivity w.r.t. model output 

Morris’ Design (1991)model free
  • Modified by Campolongo et al. (2005)
  • Grid factor space x = (x1 ,…, xk) with p levels for each factor and constant grid widths Δi (i=1,…,k)
  • Define a local elementary effect di of xifrom two grid points in xthat differ only in one factor xi by Δi bydi := Y(x+eiΔi) - Y(x)
  • Select randomly NTraject trajectories of length k (from k+1 points) where exactly one elementary effect dij (j=1,…,NTraject) can be derived from two consecutive points
  • Consider distributions Fiabs = { |dij| } and compute μiabs = mean of Fiabs Fi = { dij } and compute σi = standard deviation of Fi

Interpretation:

  • high μiabs :factor xi has an important overall influence on model output Y
  • high σi:factor xi is involved in interactions with other factors w.r.t. Yoreffect of factor xi on Y is nonlinear
global sensitivity analysis

σ -nonlinear effects with respect to SN1

μabs - sensitivity with respect to SN1

Global Sensitivity Analysis
  • Morris’ design for all 38 parameters T38
    • p = 7-level grid for the variation rangesof the 38 parameters
    • NTraject = 1,000 trajectories
    • Resulting in 39,000 single model runs
  • 93.1% of all runs show a bifurcation
  • Some outstanding parameters and one cluster

S5most influential parameters

A5anthropogenically influenceable parameters

behavioural analysis

Maximum value Asat the bifurcation pointover the 5*5 single runs of the two dimensions that are not shown

rank 1

rank 5

Behavioural Analysis
  • Deterministic screening exercise for the 5 most sensitive parameters S5
    • for deep insight into the model
    • 5 equidistant values per parameterin its variation range result in 55 single model runs
  • All runs show a bifurcation
  • Most sensitive parameters show largest variation
monte carlo analyses

T38

A5

value without uncertainty

present value

Monte Carlo Analyses
  • For all 38 parameters T38 and the 5 anthropogenic parameters A5
    • Uniform marginal distributions on their variation ranges
    • Latin hypercube sampling
    • 20,000 single model runs
  • 94.4% of all runs in T38,all runs in A5show a bifurcation
  • According to the model it is not likelythat the system reaches the bifurcation point under influence of human activity
  • Variation of As for T38 at the bifurcation point SN1 is the same as variation of As for current vegetation
conclusions
Conclusions

Methods:

  • Combination of a bifurcation analysis with multi-parameter uncertainty studies enabled qualitative considerations for the whole parameter space
  • SimEnv as a multi-run simulation environment with the focus on model sensitivity and uncertainty studies

Model results:

  • Bifurcation for surface albedo in the model is robust under parameter uncertainty though the value of the bifurcation point varies
  • The present state of the system is far away from the variability range of the bifurcation point
  • More detailed studies are necessaryExample:
    • System: air pollutants  aerosols  optical thickness of stratum clouds
    • Model: parameter τst bifurcation point for surface albedo
thank you for your attention
Thank you for your Attention

SimEnv on the Internet:

http://www.pik-potsdam.de/software/simenv