Transcript Monsoon Rainfall Forecasting

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
No. Predictor (Period)
Used for the
forecasts in
1.
North Atlantic Sea Surface April and June
Temperature (Dec. + Jan.)
2.
Equatorial SE Indian
Ocean Sea Surface Temp.
(Feb. + March)
East Asia Mean Sea Level
Pressure (Feb. + March)
April and June
NW Europe Land Surface
Air Temperatures (Jan.)
April
3.
4.
April and June
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)
North Atlantic Mean Sea
Level Pressure (May)
June
7.
8.
June
North Central Pacific Wind June
at 1.5 Km above sea level
(May)
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
Atmosphere
Long wavelength
radiation
Solar
Radiation
unequal
heating
Potential
Energy
Kinetic
Energy
Frictional Dissipation
Earth-Atmosphere System
General Circulation
• 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!
Condensationa
l growth
Molecules
Tripathi and Harrison,
2001; Tripathi et al, 2006
Thermodynamically
Ion-induced Stable clusters
nucleation
Neutral or
ion clusters
Initial
growth
step
CONDUCTING
WATERDROP
Drop charge D
c
Image charge I
Cloud drop
s
CCN
Further growth
Aerosol particles
Particle-particle
coagulation
Modgil, Kumar, Tripathi et al., 2005,
JGR
Ion Mediated Rote
Charged
Aerosol
Trajectory
CHARGED
AEROSOL
Charged Aerosol Collision
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
Number
Variable
Level (hPa)
1-4
Geopotential
1000,850,700,500
5-8
Temperature
1000,850,700,500
9-12
Zonal wind comp.
1000,850,700,500
13-16
Meridional wind comp.
1000,850,700,500
17-20
Vertical velocity
1000,850,700,500
21-24
Relative humidity
1000,850,700,500
25
Saturation deficit
1000-500
26
Precipitable water
1000-500
27
MSLP
Number
Variable
Level (hPa)
28-29
Temperature gradient
850-700,700-500
30-31
Advection of TG
850-700,700-500
32-35
Advection of temp
1000,850,700,500
36-39
vorticity
1000,850,700,500
40-43
Advection of vorticity
1000,850,700,500
44-45
thickness
1000-500
45
Horizontal water vapor
flux divergence
Mean relative humidity
1000-500
46
47
1000-500
Rate of change of moist 1000-500
static energy
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
Frequency
Distribution of daily rainfall: Kanpur
Precipitation (0.1mm)
Frequency
Distribution of Daily Rainfall: Lucknow
Precipitation (0.1mm)
Hourly rainfall Distribution
Frequency
SSM/I satellite data
5S-10S
Rainfall rate in mm/hour
A power law fits the distribution very well at
low latitudes
Frequency
Hourly rainfall Distribution
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
Exponent 
Power law exponent as a function of the latitude
f(x) = x
Latitude
In tropics
=1.130.14
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
( y
i
y)
' 2
i
Sum runs over the training set
i
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) N ( wet )  M (dry) M ( wet )
H .K . 
[ N (dry)  M (dry)][N ( wet )  M ( wet )]
N(dry) = no. of correctly predicted dry days
M(dry) = no. of incorrectly predicted dry days
1
B.S . 
N
' 2
(
y

y
 i i)
i
Amount of Rainfall
Cube root of Precipitation
Performance Index: Root Mean Square Error
RMSE 
1
' 2
( yi  yi )

N i
Results (Pune)
Model Network Training B.S.
error
LR
41.81
Ratio
H.K.
0.164 0.769 0.485
NN
CG
42-3-1-1 42.3
0.154 0.806 0.584
NN
BP
42-4-3-1 43.0
0.151 0.785 0.532
Results (Hyderabad)
Model Network Training B.S.
error
Ratio
H.K.
LR
56.9
0.233 0.620 0.195
NN
CG
42-4-4-1 50.8
0.227 0.694 0.360
NN
BP
42-3-1
0.217 0.661 0.277
57.5
Results (Bangalore)
Model Network Training B.S.
error
LR
62.88
Ratio
H.K.
0.228 0.636 0.176
NN
CG
42-4-4-1 53.2
0.225 0.678 0.318
NN
BP
42-4-4-1 62.2
0.230 0.686 0.332
Results (Bhubaneshwar)
Model Network Training B.S.
error
Ratio
H.K.
LR
53.9
0.219 0.644 0.240
NN
CG
42-4-4-1 54.4
0.211 0.652 0.332
NN
BP
42-4-4-1 53.8
0.209 0.669 0.344
Results (Delhi)
Model Network Training B.S.
error
LR
Ratio
H.K.
36.9
0.191 0.723 0.377
NN
CG
42-1
35.2
0.198 0.723 0.382
NN
BP
42-1
42.2
0.167 0.750 0.436
Results with Average Rainfall over 3
rain gauges in Delhi
Results with Average Rainfall over 3
rain gauges in Delhi
Results with Average Rainfall over 3
rain gauges in Delhi
Results with Average Rainfall over 3
rain gauges in Delhi
Conclusions
• We find that in tropics the short term rainfall
distribution follows a universal power law
with exponent 1.130.14
• Predicting daily rainfall at a particular rain
gauge appears to be difficult
• Neural Networks give a modest improvement
over linear regression results
• We recommend that instead of a single rain
gauge one should use a spatial average over
many rain gauges, which gives significantly
better results
Ion induced nucleation mechanism
Ion-induced nucleation mechanism. In this example, the neutral nucleation pathway is inhibited due
to a barrier on the Gibbs free energy surface. Clusters smaller than the critical cluster preferentially
evaporate whereas clusters larger than the critical cluster grow. The ion cluster growth is
spontaneous and competes with recombination (vertical arrows). Recombination that produces a
neutral particle larger than the critical cluster leads to nucleation. This process is indicated by the
large arrows.
Modgil, Kumar, Tripathi et al., 2005, JGR
More ice formation through contact ice nucleation in cold clouds
Tripathi and Harrison, , 2002

N 20  N 20
plotted
Z
as a function of ion asymmetry
factor x for various aerosol radii a.N20 and N-20
are number concentrationsof aerosols carrying
-20 and +20 charges respectively and Z(103 cm-3 )
is the total number concentration. Horizontal
line indicates the regionabove which 1 particle
per cm will be present.(b) Same as (a) except for
N10
and N-10 .
Freezing
probability
from
electrical
Enhancement of aerosol collection rate P,
calculated as a function of particle elementry
charges J. Neutral (supercooled) droplets of
radii 52, 40, 32, 26 and 18 µ m are considered
to collect aerosol particles of radii 0.4, 0.4, 0.5,
0.6and 0.4 µ m Respectively.