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Monsoon Rainfall Forecasting. Pankaj Jain IIT Kanpur. Introduction. Monsoon prediction is clearly of great importance for India One would like to make long term prediction, i.e. predict total monsoon rainfall a few weeks or months in advance
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Monsoon Rainfall Forecasting Pankaj Jain IIT Kanpur
Introduction • Monsoon prediction is clearly of great importance for India • One would like to make • long term prediction, i.e. predict total monsoon rainfall a few weeks or months in advance • short term prediction, i.e. predict rainfall over different locations a few days in advance
Predicting total monsoon rainfall (June-September) • predicted by using its correlation with observed parameters • The predictors keep changing with time • Several regression and neural network based models are currently available • Indian Met. Dept (IMD) provides statistical forecast in two stages, • March/April • May/June
Model • IMD uses both linear and non-linear regression for their forecast • use ensemble forecast • large number of models are used for all possible combinations of predictors • only a few models with best skill are selected • The forecast is the weighted average of the outcome of these models • The model error • 5% for April forecast • 4% for June forecast
Short term Forecasting • We have been interested in forecasting daily rainfall over a particular location a few days in advance. • The government agency National Center for Medium Range Weather Forecasting (NCMRWF) provides daily forecasts, mainly to assist farmers.
Numerical Weather Prediction (NWP) Models • Numerical Weather Prediction (NWP) models • Used to make short (1-3 days) and medium (4-10) forecast • Navier Stokes equation is written on a spherical grid covering the entire earth • use spherical polar coordinates • need to account for the earth’s rotation, which makes it a non-inertial frame. This introduces fictitious Centrifugal and Coriolis force
The variables are expanded in spherical harmonics, truncated up to a certain multipole, which determines the resolution of the grid. • For example the current model is T254, which implies a grid size of 0.5ox0.5o • 64 vertical levels • 7.5 min time steps
Long wavelength radiation Kinetic Energy unequal Potential Energy Solar Radiation heating Frictional Dissipation Earth-Atmosphere System
The inputs to the model are the initial conditions obtained by observations throughout the earth temperature, pressure, wind velocity, humidity etc as a function of position and height
The output of the model is the desired prediction However the model is severely limited: • The outcome, especially rainfall, is strongly dependent on local factors • This is particularly true in tropics where the circulation is primarily driven by convection • It is unfeasible to take all local factors into consideration in a global model • The prediction may change considerably by very small changes in the input parameters
The input data, especially high altitude balloon data, is severely limited • Also in many regions, especially India, the data quality is often not very good
There may also exist some unknown effects. An interesting possibility is effect of galactic cosmic rays This possibility has been studied by Tripathi et al (CE, IITK)
Variation of low-altitude cloud cover, galactic cosmic rays and total solar irradiance (1984-1994). The cosmic ray intensity data is from Huancayo observatory, Hawaii Carslaw et al., 2002, Science The physical links for the correlation is subject of research.
Two Routes to cloud modification: Charged Species is the Key! Condensational growth Thermodynamically Stable clusters Molecules Ion-induced nucleation Neutral or ion clusters Initial growth step Aerosol particles Particle-particle coagulation Tripathi and Harrison, 2001; Tripathi et al, 2006 CONDUCTING WATERDROP Drop charge D c Image charge I Cloud drop s Charged Aerosol Trajectory Further growth CCN CHARGED AEROSOL Modgil, Kumar, Tripathi et al., 2005, JGR Charged Aerosol Collision Ion Mediated Rote
Statistical Interpretation of NWF output • It may be better to statistically correlate the model output with observations • This is the technique used by NCMWRF to predict daily rainfall a few days in advance at a particular station • The rainfall at a particular station is obtained by a rain gauge • We have been trying to determine if neural network based relationship can improve the predictability. Jain et al 1999, Jain and Jain 2002
Scale invariance in daily rainfall • The predictability of the quantity can often be judged by its distribution function. • If the variable shows a normal distribution then large fluctuations from the mean value are improbable • However a power law distribution f(x) = x implies no characteristic scale (scale invariant) indicates an underlying chaotic behaviour
Distribution of daily rainfall: Kanpur Frequency Precipitation (0.1mm)
Distribution of Daily Rainfall: Lucknow Frequency Precipitation (0.1mm)
Hourly rainfall Distribution SSM/I satellite data Frequency 5S-10S Rainfall rate in mm/hour A power law fits the distribution very well at low latitudes
Hourly rainfall Distribution Frequency 15N-20N Rainfall rate in mm/hour
Frequency 0N-5N Rainfall rate in mm/hour
Frequency 50N-55N Rainfall rate in mm/hour
Frequency Rainfall rate in mm/hour
short term rainfall over a localized region shows a scale invariant power law distribution Jain and Jain 2002 Peters et al (2002) show this for individual events at the Baltic coast
Power law exponent as a function of the latitude f(x) = x Exponent Latitude In tropics =1.130.14 At higher latitudes =1.3-1.6 Jain and Jain, 2002
It is better to define variable which we may have a better chance of predicting. • Rather then using a single rain gauge it may be more appropriate to use the rainfall averaged over many rain gauges. • The NWF has a grid size of order 100x100 Km. Hence its predictions should be interpreted as the average over the grid rather than for a particular location.
Predicting Daily Rainfall • We studied daily rainfall forecast one day in advance • The following stations were considered: Delhi, Pune, Hyderabad, Bangalore,Bhubaneshwar • The output variable (y) is the daily rainfall • 47 input variables (xi), each at 9 grid points surrounding the station. select by quadratic fitting over the 9 grid locations • 6 years data (1994-1999) from June to September for Pune, Hyderabad, Bangalore,Bhubaneshwar For Delhi we consider data from June to August
Neural Networks Neural networks differ from statistical regression techniques since one does not try to fit the output. By fitting we mean minimization of the error Sum runs over the training set yi is the predicted variable and y’i the measured variable. Instead one only tries to learn the behaviour of the predictor.
We terminate the training when the error in the validation becomes minimum • Then the results are checked on an independent set. • While training one has to be careful that the network is not struck in some local minima • genetic algorithms or • simulated anealing
Performance Indices We shall predict (a) the probability of rainfall and (b) the actual rainfall (actually the cube root of rainfall) The skill of the model is tested by suitable performance indices A model is skillful if it performs better than persistence model
Probability of Rainfall Performance Indices: Ratio = number correct / total N(dry) = no. of correctly predicted dry days M(dry) = no. of incorrectly predicted dry days
Amount of RainfallCube root of Precipitation Performance Index: Root Mean Square Error
