Role & Effect of Numerics in the simulation of Indian Monsoon

Saroj Kanta Mishra saroj@caos.iisc.ernet.in Center for Atmospheric & Oceanic Sciences,IISc Role & Effect of Numericsin the simulation of Indian Monsoon

About the problem Resources used A brief discussion about climate modelling Model physics Model numerics Analysis LAYOUT PREREQUISITE FOR THE PROBLEM

Motivation behind the problem: Monsoon is a complex phenomena and no GCM captures all thre features of the Indian Monsoon. The physics behind the monsoon is not yet known clearly,many of its mechanism are parameterized where as numerics is done regourously. Unlike the pure fluidmechanics , the simulation of the atmospheric flows depends on the numerical technique used. To know the degree of effectiveness of numerics on the simulation of monsoon.

RESOURCES USED : • MODEL USED : CAM 3.0 (Community Atmospheric Model). It is the latest in a series of global atmosphere models developed by the National Center for Atmospheric Research(NCAR). • DATA SET USEDFOR MODEL: The initial and boundary condition datasets are available with the source code. • DYNAMICS PACKAGE USED IN THE MODEL: The model was run for all the three supported dynamics (FV,EUL,SLD) package. • ARKIN DATA : A 17 year monthly analysis based on gauge observations , satellite estimates and numerical model output • NCEP DATA : National Center for Environmental Prediction • ERA DATA : ECMRWF datasets

MODEL SELECTION : A very few model has the option to run with 3 different dynamics. Finite Volume technique is available as one of its dynamical core. NCAR,CAM 3.0 is the 5th generation of the NCAR atmospheric GCM. ==>Many correction has been done and it is latest of its version recently launched(23rd-june-2004).

Indian summer monsoon It rains over India during June to September with an average rate 8 to 12 mm/day, • The figure shown is the observed rainfall over Indian region during 2003,July. • Highest rainfall occurs over Cherapunji. • At the west coast of India, high rainfall occurs. • It rains over the whole of BOB. • Central and east coast of India has comparatively less rainfall.

ATMOSPHERIC GENERAL CIRCULATION MODEL (AGCM): A computer based climate model that produces future forecast of climate and weather for regions of earth or the whole A MAIN OBJECTIVE OF CLIMATE MODELLING : To predict the response of the climate to external forcing (i.e. What will happen if % of carbondioxide will become double?). SS SCHEMATIC OF AN AGCM : A set of equations Boundary conditions Initial conditions Model output Some known physical constants Parameterization of subgrid scale phenomena AGCM

Initial conditions The condition at time, t=0 is fed from observation (ground,satellite,ships and radio-sonde ). Ex: Surface pressure cloud coverage U,V,T,Q... Boundary conditions Conditions specified for the solution of a set of differential equations is called boundary conditions. Here : Surface geopotential Sea surface temperature A flag at each point to specify it as land/ocean/sea-ice

GOVERNING EQUATIONS : Momentum equations:  Du/Dt -2v sin Ф +2  cos Ф +uw /a -uvtan Ф/a = -(1/ )p/x +Fx Dv/Dt -2usin Ф +vw /a + tan Ф/a = -(1/ )p/y +Fy Dw/Dt -2ucosФ +( + )/a = -(1/ )p/z -g +Fy Conservation of moisture: Dq/Dt = -∇ ( Vq ) + E – C  Conservation of Energy : CP * dln/dt = ds/dt + Q F,E,C,Q : Physics (Governing equations) – (physics) = (Adiabatic,inviscid flow with no phase change) Model dynamics : The discretization of the adiabatic inviscid equations .

NUMERICS The adiabatic-inviscid sets of coupled non-linear partial differential equations are solved numerically in three different ways.. Eulerian approach Semi-Lagrangian approach Finite Volume approach Grid point method Spectral method Good at Sharply varying function Smoothly varying function Number of gridpoints required in finite difference is more Number of terms required in spectral expression is lesser. For comparable solution accuracy Gibbs oscillation causes spectral/-ve rain There is no gibbs oscillation Harmful effect

MODEL & OBSERVATION :1. Overestimation of rainfall over Indian region. 2. Underestimation of rainfall over western pacific. 3. Difference in pattern . Rainfall (10 yrs. July average) SEMI-LAGRANGIAN OBSERVATION EULERIAN FINITE VOLUME

Difference Between Numerics:1. Highest over Indian region 2. Difference between SLD & FV is highest EUL – SLD FV - EUL SLD – FV

COMPARASION OVER INDIAN REGION:1. There is a difference in pattern as well as in magnitude of rainfall between thethree numerics. 2. SLD and EUL have almost same magnitude . 3.Arabian Sea has higher rainfall as compared to Bay Of Bengal (against observation). 4.East and head of Bay Of Bengal has very poor rainfall (against observation). RAINFALL SEMI LAGRANGIAN OBSERVATION EULERIAN FINITE VOLUME

Difference between numerics over Indian region: 1. The difference between semi-Lagrangian and Finite Volume is highest. EUL – FV EUL -SLD SLD - FV

Comparision of Relative Humidity :Relative Humidity of some portion of Bay Of Bengal is very low (F.V has 40 %,against observation). Among the numerics Finite Volume has minimum relative humidity. RELATIVE HUMIDITY ( 850 mb. ) SEMI LAGRANGIAN OBSERVATION ( NCEP ) FINITE VOLUME EULERIAN

Difference between numerics :Among the numerics,the difference between semi Lagrangian and Finite Volume is highest. DIFFERENCE BETWEEN NUMERICS ( 850 mb.) EUL – SLD EUL – FV SLD – FV

Area Analysed : It comes within the monsoon region + Difference between numerics is highest REGION “1” ( 60 ==> 70 , 10 ==> 20 ) REGION “2” ( 80 ==> 90 , 7 ==> 17 ) 1 2

WHAT MAY BE THE REASON ? 1. All the numerics overestimate the rainfall over Indian region,and underestimate over east and head of BOB ,and some portion of western pacific.It indicates that the parameterisation scheme used may be one of the reasons. 2. For all the three simulations physics and parameterization are same,only difference is numerics .The difference of simulated rainfall over Indian region between the numerics are as large as 60% to 100% .Hence numerics have crucial role in the simulation of atmospheric flows ,and it may be one of the reasons.

Lesser Precipitable water & higher Rainfall : Bay Of Bengal ,Arabian Sea : SLD > EUL > FV( rainfall as well as pwat.)PWAT: Arabian Sea > Bay Of BengalRAINFALL : Bay Of Bengal > Arabian Sea(Why B.O.B has more rainfall as compared toA.S ?) PRECIPITABLE WATER & RAINFALL IN JULY FOR 10 yrs. BAY OF BENGAL ARABIAN SEA R.FALL PWAT. PWAT. R.FALL

MODEL & OBSERVATION , 10 yrs. CLIMATOLOGY : ARABIAN SEA : CONSISTENTLY MODEL > OBS. & IN MODEL SLD > FVBAY OF BENGAL : EXCEPT SEPTEMBER( Why is this abnormality in sept. over BOB.) ARABIAN SEA BAY OF BENGAL Rainfall Pwat Pwat Rainfall

Rainfall vs. Precipitablewater ( july of 10 yrs. ):Widespread variation . RAINFALL VS PRECIPITABLE WATER BAY OF BENGAL ARABIAN SEA Rainfall Precipitable water

Phase relationship between different numerics: All the three numerics are in phase with each other . Model is lagging behind the observation during Monsoon period.

Deviation between numerics with time (Bay Of Bengal): At time t = 0 , precipitable water as well as rainfall is same in all the three. Difference between numerics is higher in Monsoon period. BAY OF BENGAL Rainfall pwat

Deviation between numerics with time (Arabian Sea) :At time t = 0, Precipitable water as well as rainfall are same in all the three numerics. The difference is higher in Monsoon period . ARABIAN SEA Rainfall pwat

Profile of specific humidity : At all levels : EUL > SLD > FVThough the sp. Humidity at all levels is higher in EUL than in SLD, why is the rainfall estimated by them is reverse ? It might be due to stability. BAY OF BENGAL ARABIAN SEA

PROFILEOFl (= Ln(q0/q)/ Ln(p0/p) ) :  : FV > EUL > SLD ; BOB FV > SLD >EUL ; AS ==> FV IS MOST STABLE AND HENCE RAINS LEAST BAY OF BENGAL ARABIAN SEA

VERTICAL PROFILE OF Relative humidity,vertical velocity,zonal velocity: 1.At all levels, FV has lowest relative humidity. 2.At all levels,FV has lowest zonal velocity. 3.At all levels ,FV has lowest vertical velocity. This indicates :numerics => moisture advection => parameterization => precipitation=> pressure gradient => moisture advection...... effect in a loop and triggers the difference. BAY OF BENGAL ARABIAN SEA

CONCLUSION • A complete explanation (physics) for Monsoon is not yet known,also it involves various phenomena of various spatial scales, of which, everything cannot be resolved by a single model and help of parameterization schemes are taken for its analysis. • All the equations (solved by the model) are highly nonlinear partial differential equations,which needs numerical integration for its solution, and all numerical methods necessarily involve some type of discrete approximations to the continuous differential equations. • Western Ghats have an important role for Indian summer monsoon and the spatial resolution of working model is unable to capture it. • All the numerical techniques have some positive quality(for same physical resolution spectral offers higher order of accuracy) and its own limitations (poles are points of singularity and computation of vector(V) in such region is difficult) • For a better simulation of Monsoon,the above mentioned points need investigations and necessary corrections. • The intercomparision of dynamical cores proved that,Indian region is very much sensitive to numerics during summer Monsoon.

Thank you

Role & Effect of Numerics in the simulation of Indian Monsoon