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

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

The Indian MonsoonThe 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

ITCZ N-Summer

ITCZ N-Winter

Equator

© Paul R. Baumann State University of New York

The ModelThe Model (Zickfeld (Zickfeld et al.et al., GRL , GRL 3232, 2005), 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)

present value

stable states instable states

Tibetan Plateau

Indian Ocean

LandSurface

Indian Ocean

2 Soil Layers

Stratosphere

(20N , 75W)

stable stable

instable

Aims and Applied MethodsAims 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 ApproachMulti-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

Interfaced Model

ExperimentPreparation

ExperimentPerformance

ExperimentPostprocess.

ResultEvaluation

OriginalModel

SimEnv Experiment TypesSimEnv 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

Experiment Type Task Computat. Costs (k factors)

global sensitivity analysis identify sensitive factors globally by qualitative methods (Morris, 1991)

NTraject*(k+1)+1

behavioural analysis

screen factor spaces deterministically dependent on screening

local sensitivity analysis compute local sensitivity measures (quantitative method)

2*NIncr*k+1

Monte Carlo analysis derive statistical measures on Y based on pdf’s of factors

NMc+1

uncertainty analysis (in prep.)

variance decomposition of Y to all factors (linear and total effects, Saltelli et. al, 2004)

NMc*(k+1)+1

optimization (simulated annealing)

to minimize a cost function cf(Y) over a factor space (Ingber, 1989)

unpredictable

asse

ssm

ent

stra

teg

y

o = default value x = 1 single run

x2

x1

x = 2nd sample

Monsoon Model Uncertainty Monsoon Model Uncertainty AnalysesAnalyses Model interface:

Experiments: Global sensitivity analysis in T38

Behavioural analysis in S5

Monte Carlo analysis in T38 and A5

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 xi

from two grid points in x that 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 μi

abs = mean of Fiabs

Fi = { dij } and compute σi = standard deviation of Fi

Interpretation: high μi

abs :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

Morris’ Design (1991)Morris’ Design (1991) model free

no

nlin

ear

effe

ct o

n m

od

el o

utp

ut

sensitivity w.r.t. model output μabs

σ

k=2 factors p=5 levelsNTraject=4 trajectories trajectory

Global Sensitivity Global Sensitivity AnalysisAnalysis 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

Parameter UnitDefault value

Variation range Rank Meaning

Pcs 1 0.8 0.72 – 0.86 1 transmission parameter of clear sky

B00 W/m2/K 2.1 1.6 – 2.3 2 parameter of reflected solar radiation

Ck 1 7.5 5 – 15 4 parameter of eddy diffusivities

τst 1 7.5 5 – 15 5 optical thickness of stratum clouds

Γ0 10-3K/m 6.0 4.8 – 7.2 6 lapse rate coefficient

τst 1 7.5 5 – 15 5 optical thickness of stratum clouds

Toc K 300 298 – 303 10 ocean temperature of model boundary condition

pCO2 ppm 360 300 – 440 13 atmospheric CO2 concentration

z0 m 0.06 0.01 – 0.80 14 surface roughness length for vegetation

bcs 1 0.05 0.02 – 0.07 28 albedo of clear sky

A5

anthropogenically influenceable

parameters

S5

most influential parameters

σ

- n

on

linea

r ef

fect

s w

ith

res

pec

t to

SN

1

μabs - sensitivity with respect to SN1

Behavioural AnalysisBehavioural Analysis

Deterministic screening exercise for the 5 most sensitive parameters S5

for deep insight into the model 5 equidistant values per parameter

in its variation range result in 55 single model runs

All runs show a bifurcation Most sensitive parameters show

largest variation

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

rank 1

rank 5

Monte Carlo AnalysesMonte 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 A5 show 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

A5

T38

present value

value without uncertainty

ConclusionsConclusions

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 necessary

Example: 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