A NOVEL TOPOGRAPHY BASED LIMITED AREA MODEL FOR MAURITIUS

Mr. R. VirasamiPr. S.D.D.V. Rughooputh Dr. B. Pathack

RESEARCH OBJECTIVES The main aim behind this study is to adapt a high resolution limited area

model for Mauritius. The model should have sufficient number of grid points so as to compare the different meteorological parameters with the actual observations over the island.

This work is targeted towards developing a regional model for the island taking into the consideration the elevation and the size.

To apply novel information technology techniques and, at the same time, assuring the soundness of the physics and mathematics for running such a model..

To make use of model output statistics so as to increase the precision of the dynamic outputs of the regional model.

To study the climate of the island with respect to those small scale events especially which are topography related

BACKGROUND Weather plays a very important role in everyday life and knowledge about

its future state is crucial for our economy and daily life. Numerical weather prediction is a model, (in this context a computer)

program, that produces meteorological information (the weather) for future times at given positions and altitudes.

For the model, nonlinear mathematical equations for the physics and dynamics of the atmosphere are solved but since no exact solution can be derived numerical methods are used to obtain approximate solutions, the forecast.

The aim behind Regional Numerical Weather Prediction (NWP) models is to produce more detailed forecasts of the weather than those available from global models. A finer computational grid on a specific area, more detailed specification of terrain, and more sophisticated prescription of physical processes are the other crucial elements which make up a regional model

INTRODUCTION TO NWP (A BRIEF HISTORY)

•In 1904, the Norwegian hydrodynamist V. Bjerknes suggested that the weather could be quantitatively predicted by applying the complete set of hydrodynamic and thermodynamic equations to carefully analysed initial atmospheric states. •A British mathematician named Lewis Fry Richardson spent three years developing Bjerkness techniques and procedures to solve these equations but lack the computational facilities . He envisaged that some time in future there would a forecast factory with 26,000 accountants doing the calculation to determine the weather patterns around the world •In 1948, a young meteorological theoretician, Jule Charney, succeeded to derive simplified mathematical models of the atmospheric motions, based on the quasi-geostrophic approximations. These equations would be able to forecast the large scale flow in spite of minor inaccuracies in the initial analyses•After several decades, meteorological observation, research, and technology struggled to reach the level necessary to make the computations envisioned by Richardson .•. In April 1950, the first one-day, nonlinear weather prediction was made but required the round-the-clock services of the modelers and, because of several ENIAC breakdowns, more than 24 hours to execute. However, this first forecast was successful in proving to the meteorological community that numerical weather prediction was feasible. Since then development of improved and new NWP followed rapidly as computer technology improved

THE ATMOSPHERE

The object of numerical weather prediction models is to assist in the prediction of the weather.

However, the atmosphere is unstable and small perturbations in the flow are able to grow exponentially in time by means of the mechanisms of baroclinic and barotropic instability

The property of the atmosphere, instability, is related mathematically to the non linearity of the primitive equations.

Chaos theory is also applicable to the atmosphere and thus the future state of the atmosphere is extremely sensitive to its initial state.

COMPONENTS OF ATMOSPHERIC MODELS

SCHEME OF NWP

PRIMITIVE EQUATIONS

The foundation of any model is a set of conservation principles, and for atmospheric models are:

- (i) conservation of mass -the continuity equation - (ii) conservation of heat -first law of thermodynamic - (iii) conservation of motion -Newton‘s second law - (iv) conservation of water - (v) conservation of other gaseous and aerosol materials -

equation of state for ideal gas These principles are coupled into a set of relations which must

be solved simultaneously.

GLOBAL MODELS

A model is run by applying the basic equations to a 3-dimensional grid of the earth and evaluating the results.

The aim of atmospheric models is to predict the future state of the atmosphere especially parameters like winds, heat transfer, radiation, relative humidity, and surface hydrology at each grid point and to evaluate interactions with neighboring points.

LIMITED AREA MODELS

Despite the use of global models, the need for more detailed outputs of meteorological parameters has lead to the development of Limited Area Models also known as Regional models.

Another factor which contributed to this development was the computing power available nowadays as compared to some years back.

Limited Area Models used a finer computational grid on a specific area which is more representative of the actual topography and more detailed computation for dynamic processes.

GENERAL STRUCTURE OF A REGIONAL NWP SYSTEM

GraphicsVisualization

MOSKalman

Applications Wave model,Trajectories

VerificationDiagnostics

provided for HRM by DWD

Topographical data

Initial data (analysis)

Lateral boundary data

Direct modeloutput (DMO)

RegionalNWPModel

SHORT DESCRIPTION OF THE HIGH-RESOLUTION REGIONAL MODEL (HRM)

HYDROSTATIC LIMITED-AREA MESO- AND MESO- SCALE NUMERICAL WEATHER PREDICTION MODEL

Prognostic variables

Surface pressure ps

Temperature T

Water vapour qv

Cloud water qc

Cloud ice qi

Horizontal wind u, vSeveral surface/soil parameters

Diagnostic variablesVertical velocity Geopotential Cloud cover clcDiffusion coefficients tkvm/h

NUMERICS OF THE HRM

Regular or rotated latitude/longitude grid Mesh sizes between 0.25° and 0.05° (~ 28 to 6 km) Arakawa C-grid, second order centered differencing Hybrid vertical coordinate, 25 to 50 layers Split semi-implicit time stepping; t = 150s at = 0.25° Lateral boundary formulation due to Davies Radiative upper boundary condition as an option Fourth-order horizontal diffusion, slope correction Adiabatic implicit nonlinear normal mode initialization

or diabatic digital filter initialization (Lynch, 1997)

HARDWARE AND SOFTWARE SPECIFICATION

Hardware : High Performance Server, FUJITSU SIEMENS - TX 300

Operating system: Scientific Linux ( based on RedHat Enterprise Linux)Compiler : Intel Fortran Suite

Paralell processing : MPICH

Visualization : Grads

CASE STUDY: TROPICAL CYCLONE DANIELLA (DECEMBER 1996)

GUSTS AND RAINFALL ASSOCIATED WITH PASSAGE OF DANIELLA

Source : Martin Seul (1999) Source :MMS cyclone report

Highest gusts recorded

HRM : COMPUTATIONAL ASPECTS

HRM: TRACK OF T.C. DANIELLA

HRM: ACCUMULATED RAINFALL

HRM: SURFACE WINDS

HRM: GUSTS

UPPER LEVELS

RESULTS & DISCUSSIONS It has been found that the model performed well on the synoptic scale and for

the case study of tropical cyclone Daniella, its track as well as its intensity was quite realistic when compared to the actual scenario.

Over the island, the HRM output of precipitation and wind captured the microscale signals but, however, lacked the precision in magnitude. It is must be noted that it is the first time that a study of the effect of a tropical cyclone at this resolution over the island of Mauritius is being carried out using a hydrostatic model.

Moreover, a lot of effort was also made for setting up the server with the appropriate software and running this model as the server at the University was provided in the beginning of year 2009 without any operating system or software. All work were carried out initially on laptop and then started from scratch again using the server.

The concept of parallel processing using MPICH is a first at the University and was successfully implemented on the server, thus optimizing the time for the running the model at 5-7 km.

FUTURE WORKS (I) Mauritius is affected by different weather systems which is at times small

scale. These weather events will be studied separately using input data from DWD global systems in an attempt to find the model strengths and weaknesses when dealing with small islands.

Additionally, the large scale interaction between the planetary systems and thesmall scale phenomena over Mauritius will also be studied.

The same weather events will be studied using a non-hydrostatic model and the results between these two models will be compared.

Additionally, model output statistics will be applied to enable the study of the localized effects of meteorological parameters like ,excessive rainfall, associated to these events.

FUTURE WORKS (II) The topography plays an important role in atmospheric variables such as pressure,

temperature, humidity and wind speed and directions, precipitation distribution over the island. The high resolution dynamic modelling approach along with model output statistics can help to study these different parameters with respect to small to microscale phenomena. The precipitation distribution over the island will be extracted from a local statistical precipitation model which is related to the topography and a correlation will be carried between the dynamic and statistical results.

The correlation will be used to incorporate elevation and also other atmospheric variables and to develop models which will be implemented which will be using artificial neural networks.

Given the importance of the effects of tropical cyclones in SouthWest Indian Ocean, the studies will put more emphasis on the predictability (development and tracking) of such systems. Data and information from ECMWF, Era-Interim, and HRM will also be utilized in this endeavour.