monsoon rainfall forecasting pankaj jain iit kanpur

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  • Slide 1
  • Monsoon Rainfall Forecasting Pankaj Jain IIT Kanpur
  • Slide 2
  • 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
  • Slide 3
  • 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
  • Slide 4
  • No.Predictor (Period)Used for the forecasts in 1.North Atlantic Sea Surface Temperature (Dec. + Jan.) April and June 2.Equatorial SE Indian Ocean Sea Surface Temp. (Feb. + March) April and June 3.East Asia Mean Sea Level Pressure (Feb. + March) April and June 4.NW Europe Land Surface Air Temperatures (Jan.) April
  • Slide 5
  • No.Predictor (Period)Used for the forecasts in 5.Equatorial Pacific Warm Water Vol. (Feb.+March) April 6.Central Pacific (Nino 3.4) Sea Surface Temperature Tendency (MAM-DJF) June 7.North Atlantic Mean Sea Level Pressure (May) June 8.North Central Pacific Wind at 1.5 Km above sea level (May) June
  • Slide 6
  • 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
  • Slide 7
  • 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.
  • Slide 8
  • 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 earths rotation, which makes it a non-inertial frame. This introduces fictitious Centrifugal and Coriolis force
  • Slide 9
  • 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 0.5 o x0.5 o 64 vertical levels 7.5 min time steps
  • Slide 10
  • Atmosphere
  • Slide 11
  • Earth-Atmosphere System Potential Energy Kinetic Energy Frictional Dissipation Solar Radiation unequal heating Long wavelength radiation
  • Slide 12
  • General Circulation
  • Slide 13
  • 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
  • Slide 14
  • 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 output of the model is the desired prediction
  • Slide 15
  • 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
  • Slide 16
  • 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)
  • Slide 17
  • 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.
  • Slide 18
  • Ion Mediated Rote Cloud drop Further growth CCN Neutral or ion clusters Molecules Ion-induced nucleation Thermodynamically Stable clusters Initial growth step Aerosol particles Condensationa l growth Particle-particle coagulation Tripathi and Harrison, 2001; Tripathi et al, 2006 s Charged Aerosol Collision Two Routes to cloud modification: Charged Species is the Key! Drop charge D Image charge I CONDUCTING WATERDROP c CHARGED AEROSOL Charged Aerosol Trajectory Modgil, Kumar, Tripathi et al., 2005, JGR
  • Slide 19
  • 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
  • Slide 20
  • NumberVariableLevel (hPa) 1-4Geopotential1000,850,700,500 5-8Temperature1000,850,700,500 9-12Zonal wind comp.1000,850,700,500 13-16Meridional wind comp.1000,850,700,500 17-20Vertical velocity1000,850,700,500 21-24Relative humidity1000,850,700,500 25Saturation deficit1000-500 26Precipitable water1000-500 27MSLP
  • Slide 21
  • NumberVariableLevel (hPa) 28-29Temperature gradient850-700,700-500 30-31Advection of TG850-700,700-500 32-35Advection of temp1000,850,700,500 36-39vorticity1000,850,700,500 40-43Advection of vorticity1000,850,700,500 44-45thickness1000-500 45Horizontal water vapor flux divergence 1000-500 46Mean relative humidity1000-500 47Rate of change of moist static energy 1000-500
  • Slide 22
  • Slide 23
  • 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
  • Slide 24
  • Distribution of daily rainfall: Kanpur Frequency Precipitation (0.1mm)
  • Slide 25
  • Distribution of Daily Rainfall: Lucknow Frequency Precipitation (0.1mm)
  • Slide 26
  • SSM/I satellite data A power law fits the distribution very well at low latitudes Hourly rainfall Distribution 5S-10S Rainfall rate in mm/hour Frequency
  • Slide 27
  • Hourly rainfall Distribution 15N-20N Rainfall rate in mm/hour Frequency
  • Slide 28
  • Rainfall rate in mm/hour Frequency 0N-5N
  • Slide 29
  • 50N-55N Rainfall rate in mm/hour Frequency
  • Slide 30
  • Rainfall rate in mm/hour Frequency
  • Slide 31
  • 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
  • Slide 32
  • Power law exponent as a function of the latitude f(x) = x In tropics =1.13 0.14 At higher latitudes =1.3-1.6 Jain and Jain, 2002 Latitude Exponent
  • Slide 33
  • 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.
  • Slide 34
  • 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 (x i ), 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
  • Slide 35
  • 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 y i is the predicted variable and y i the measured variable. Instead one only tries to learn the behaviour of the predictor. Sum runs over the training set
  • Slide 36
  • 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
  • Slide 37
  • 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
  • Slide 38