Lectures-1-2.pdf

Prof. S. K. Dash, IIT Delhi

Basics of Numerical Weather Prediction The horizontal momentum equation, r r r dV ∂ σ φ + fkˆ ×V = − ∇φ + ∇p s + F dt p s ∂σ Continuity equation,

r ∂p s ∂ ∇. ( ps V ) + ( p s σ& ) + =0 ∂σ ∂t Thermodynamic energy equation, 1 d ⎡ ∂φ ⎤ RT [ p s σ& + σ p& s ] = − Q σ + ⎢ ⎥ R dt ⎣ ∂σ ⎦ C p p

Prof. S. K. Dash, IIT Delhi

Hydrostatic equation,

∂φ RT =− σ ∂σ Surface pressure tendency equation,

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1 r ∂p s = − ∫ ∇. p s V d σ ∂t 0

and the moisture equation,

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r ∂ [ p s q ] + ∇. p s q V + ∂ [ p s q σ& ] = p s S ∂t ∂σ The above set of six equations can be solved in principle to get r the values of six unknowns viz., horizontal wind velocity V , surface pressure p s , temperature T , moisture q , geopotential r φ and sigma velocity σ& . The meteorological parameters V , p s , T and q are time dependent while σ& and φ are called the diagnostic fields.

Prof. S. K. Dash, IIT Delhi

These equations constitute a closed system, which can be solved at all future times ™ From a given initial state ™ With the prescribed boundary conditions The governing equations can be written as

∂X = D( X ) + P( X ) ∂t Here, X (x, y, z, t) : any model variable e.g. wind, Temperature, Humidity, Surface pressure etc. D

: Dynamics e.g. advection, pressure forces etc.

P

: Physics e.g. evaporation and Condensation of water, solar heating, infra-red cooling, Frictional drag at the surface of the earth etc.

Prof. S. K. Dash, IIT Delhi

Richardson Factory (1922) Picture Credit

:

A. Lannerback

Prof. S. K. Dash, IIT Delhi

Classification of Forecasts Usually a weather forecast is for a given region and has a definite period of validity. According to the period of validity one can classify as: – – – –

Nowcasting Short range Medium range Long/Extended range

-- Climate

: 0-6hrs : up to 3 days : 3-10 days : more than 10 days Monthly and seasonal means : 30yrs or more

Prof. S. K. Dash, IIT Delhi

Important Surface Boundary Conditions

¾ Sea Surface Temperature ¾ Snow Cover and Snow Depth ¾ Soil Moisture ¾ Vegetation Cover Influence of initial and surface boundary conditions at different time scales of model integrations: Now-casting and Short-range (1-3 days):

Primarily initial values of atmospheric parameters

Medium-range (3-10 days):

Both the initial values and surface conditions

Monthly and more :

Mostly surface boundary conditions

Climate:

Chemical composition of atmosphere

Prof. S. K. Dash, IIT Delhi

Weather observations and Forecasting Values of meteorological parameters and weather conditions at a future time constitute weather forecasting: • Values of Temperature, Wind, Humidity, amounts of Rainfall and Snowfall • Cyclones, Clouds, Sunshine hours, Fog • Heat & cold wave conditions, Extremes

Prof. S. K. Dash, IIT Delhi

Important sources of weather/climate data a) Surface Surface observatories Automatic Weather Stations Ships b) Upper air Balloons Aircrafts Radars c) Satellite derived fields

Prof. S. K. Dash, IIT Delhi

Some landmarks in Weather Forecasting:

–Invention of barometer (1643) Torricelli –Invention of telegraph (1845) Synoptic map displayed in London in 1851 –1850-1920 National Weather Organisations grew. Primary tool of forecast was the surface pressure map and the forecasts were done by empirical means.

Prof. S. K. Dash, IIT Delhi

- V. Bjerknes (1904) recognised forecasting as an initial value problem. He realised that the basic set of equations are very complicated with highly nonlinear terms and these partial differential equations do not possess closed solutions. However, there were inadequate data to define initial conditions at that time.

- L.F. Richardson (1922) sought to solve the system of equations by desk calculator A failure – forecasted pressure changes were found one order of magnitude greater than the actual. - 1930s invention of radiosonde for upper air data and further empirical improvements in forecasting.

Prof. S. K. Dash, IIT Delhi

Synoptic conditions (mean sea level )

Prof. S. K. Dash, IIT Delhi

Synoptic conditions (850 hPa analysis)

Prof. S. K. Dash, IIT Delhi

Different Methods of Forecasting Synoptic, Numerical Weather Prediction (NWP) and Statistical Methods Synoptic method is based on examination of synoptic charts and close watch of weather systems. NWP is based on basic equations and physical principles: Initial conditions and boundary conditions are important. Forecasting techniques for medium range are basically different from short range, because the extrapolation technique decreases in accuracy as the period of extrapolation increases. For 10 days forecast one needs data from all over the globe. For longer days of forecasts, slowly varying boundary conditions and their variations become more important – Sea Surface Temperature (SST) anomalies, variations in surface albedo, snow cover and depth, soil moisture etc. In the climate time scale, atmospheric chemistry plays a dominant role.

Prof. S. K. Dash, IIT Delhi

• Statistical : Regression equation Simple y = a + bx y : predictant x : predictor Multiple linear regression equation y = a + b1x1+ b2x2 +….+ bnxn

Prof. S. K. Dash, IIT Delhi

Growth of NWP due to the factors: 1. Theoretical research by Rossby, Petterssen, Bjerkness, Charney, Eady, Eliassen etc. led to some direct application to practical problems: Radical departure from pure empiricism. 2. Large data collected by satellites, balloons and rockets. 3. High Performance Computers (HPC)

Prof. S. K. Dash, IIT Delhi

Accuracy of weather prediction by NWP limited by errors due to: 1) Truncations associated with the replacement of the fundamental atmospheric (partial differential) equations by numerical schemes. 2) Errors in the initial conditions of the atmospheric variables in terms of their measurements. 3) Approximations in physical processes in the parameterization schemes in numerical models..

Prof. S. K. Dash, IIT Delhi

Necessity of Global Models • For short range forecasting Limited Area Models (LAM) can be used. It usually takes a couple of days for influences from the distant parts to reach the area. • For medium and long-range forecasts: Impact of snow, sea surface temperature (SST), deserts and other surface conditions are important. – The reflection of sun’s energy back to space from clouds. – Influence of large mountain ranges must also be included.

These forcings are of global scale and their effects are cumulative. Hence, for medium and long/extended range forecasts global models are necessary.