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

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

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

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

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

- 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 analysesSimEnv (Flechsig et al., 2005)

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

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

Model interface:

Experiments:

- Global sensitivity analysis in T38
- Behavioural analysis in S5
- Monte Carlo analysis in T38 and A5

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

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

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

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

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

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