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

1. 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

2. 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

3. 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)

4. 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)

5. 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

6. 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

7. Monsoon Model Uncertainty Analyses Model interface: Experiments: • Global sensitivity analysis in T38 • Behavioural analysis in S5 • Monte Carlo analysis in T38 and A5

8. 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

9. 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

10. 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

11. 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

12. 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

13. Thank you for your Attention SimEnv on the Internet: http://www.pik-potsdam.de/software/simenv