Transcript Slide 1

Forecasting Weather and Climate
Forecasting Methods
1. Local Weather Signs – On-Site
2. Extrapolation Forecasts – The Telegraph
3. Advection Forecasts
4. Storm Model and Analog Forecasts
5. Statistical Forecasts
5. Numerical Forecasts by Computer
Local Weather Signs – On-site Forecasts
For most of history the only way to forecast the weather was to look to the sky for signs
of change. Most on-site forecasts are based on the fact that weather systems move.
In the tropics weather systems usually move from east to west.
Outside the tropics weather systems usually move from west to east.
There are many local weather signs that have entered popular lore and have merit.
Red sky in morning, sailor take warning
Red sky at night, sailor delight.
Consider the rationale of this saying for dawn. The zenith sky turns red near dawn or
sunset only when clouds are overhead and the horizon sky is clear. Since the sun rises
in the east and weather outside the tropics moves from the west, the clouds overhead
suggest a coming storm to the west.
In the evening, a red sky from the setting sun in the west suggests clearing on the way.
There are many short-term weather forecasts you can make by looking at the sky.
1: You can see the anvil of approaching thunderstorms long before they strike. As the
thunderstorm nears, mammatus may appear under the anvil. Sometimes an arc cloud
with a very dark sky below it appears. This shows that heavy rain is only minutes away.
2: As extratropical cyclones approach you see the classical sequence of clouds in the
sky above, Ci  Cs As Ns. This typically takes 12 to 24 hours. Since Cirrostratus
often produce halos, the halo has long been recognized as a sign of a coming storm.
Henry Wadsworth Longfellow
The Wreck of the Hesperus (1840)
Then up and spake an old Sailòr,
Had sailed to the Spanish Main,
"I pray thee, put into yonder port,
For I fear a hurricane.
"Last night, the moon had a golden ring,
And to-night no moon we see!"
The skipper, he blew a whiff from his pipe,
And a scornful laugh laughed he.
Colder and louder blew the wind,
A gale from the Northeast,
The snow fell hissing in the brine,
And the billows frothed like yeast.
Extrapolation Forecasts
Extrapolation forecasts predict weather by continuing a weather system’s
past motion into the future. When you walk across the street and a truck is
coming in the distance you are making an extrapolation forecast. This can fail if
the truck suddenly accelerates.
Extrapolation forecasts are accurate for short lead times but degrade rapidly as
the time span increases because storms change shape, intensity, speed, and
direction. The useful time span of extrapolation forecasts is roughly equal to the
lifespan of the system - an hour for small systems such as thunderstorms, and
up to 24 hours for larger storms such as hurricanes and winter lows.
A simple and still useful example of extrapolation forecast is the hurricane
tracking chart. The position of the hurricane’s center is plotted on a map every 6
hours, and future positions are predicted by continuing the track. You should do
this for Hurricane Katrina on the next page using data from the table. The
solution is on the following slide. The position of highs, lows, and fronts can be
forecast the same way.
Click to illustrate Extrapolation
and its Shortcomings
???
Exercise: Predict the Track of Hurricane Katrina (2005) 24 hours in advance by plotting the hurricane
positions in the table below and then extrapolating by 6 hour steps. (Try to predict the maximum wind also.)
The observed positions and intensities are listed on the next page
24.80
25.10
25.70
26.50
27.20
-85.90
-86.80
-87.70
-88.60
-89.10
08/28/00Z
08/28/06Z
08/28/12Z
08/28/18Z
08/29/00Z
100
125
140
150
140
944
935
908
906
904
HURRICANE-3
HURRICANE-4
HURRICANE-5
HURRICANE-5
HURRICANE-5
90 W
30 N
25 N
Advection Forecasts
An advection forecast is an extrapolation forecast that assumes quantities
such as temperature, potential temperature, or mixing ratio are conserved as
they move with the wind. As an example, advection forecasts of temperature
are made on constant pressure charts by determining where the air at the
forecast point and time will have come from.
Errors in advection forecasts occur if the wind changes speed or direction, or if
vertical motions are not included. For example, when the lapse rate is stable,
sinking motion increases temperature and rising motion decreases temperature
on a constant pressure surface.
The next slide illustrates advection and the slides after that show a sequence of
850 mb charts with cold air advancing over the Eastern United States while
warm air moves from southwest to northeast over the Atlantic Ocean. The
length of the wind arrows in each of the charts is roughly equal to the distance
the wind covers in 12 hours. Try advancing the air by a distance equal to the
length of the arrows to see how well the advection forecast performs.
Forecasting Temperature by Advection (Wind)
Temperature changes over time when the air upwind is colder or warmer. This
is seen on constant pressure charts when Isotherms (typically solid lines) cross
Contours (typically dashed lines).
Directions for making a 12 hour Temperature Forecast
1. Estimate average wind speed and direction upwind from forecast city.
3. Calculate distance air travels (each 5 knots = 1° latitude per 12 hours).
4. Pinpoint upwind source of air arriving at forecast city.
5. Future T at forecast city is current T at upwind source.
Assumptions: No heating or cooling, no vertical motions, no change of wind.
Problems: 1: When the atmosphere is stable, rising air causes cooling. 2: Weather
systems also tend to move from west to east and change shape so that wind changes
both speed and direction.
In the drawing to the right, cold
air in the Northwest (NW)
moves to the SE while warm air
in the SE moves toward the N.
The next slides shows how an
advection forecast is made
and also show any errors.
WARM
Here winds at two points
were extrapolated 12 hrs
into the future. If the wind
does not change in speed
or direction and if there is
no vertical motion and
heating or cooling then
the temperature at point A
on the next map, now 15C should be -17C
and the temperature at
point B, now 2C should
be 5.5C.
Now, turn to the next
slide
A
B
Verifying the Forecast
At point A, temperature did
not fall as expected even
though neither the wind
speed nor direction
changed much. The
forecast failed because
the cold, stable air was
sinking. In much of the
nearby area the cold air
did, however advance so
that the advection forecast
was not a total failure.
At point B, T rose more
than expected, namely to
7C. The extra warming
occurred because the
nearby winds accelerated.
Now, you pick a few
points, forecast T for the
next map and then
diagnose your errors.
A
B
Storm Model Forecasts and Analogs
Storm Model Forecasts assume a certain structure and evolution to storms and then
moves them. Thus, the forecast technique using the change of cloud forms as an
extratropical cyclone approaches is an example of using the frontal model of cyclones.
This technique that we still use today gave a tremendous boost to weather forecasting
accuracy after World War I, and came to dominate the field for almost half a century. It
had its most notable success on D-Day. In early June, 1944, rough weather plagued the
English Channel and more storms were on the way from the Atlantic. The Germans,
sure that an Allied landing could not come in such rough seas, kept only 1 of 10 panzer
divisions available for an unlikely emergency. Allied meteorologists, using the cyclone
wave model, noticed a small gap of gentler weather between successive cyclone waves
and gave General Eisenhower the go-ahead for the invasion. The forecast proved to be
accurate and the invasion was a success.
Another popular and useful forecasting technique is to use analogs, or past weather
situations that resemble the current situation. The assumption is that storms which look
similar tend to have similar evolutions and sequences. Forecasters often searched for or
recalled analogs. The analog method is both simple and reasonably successful, and is
still used as an aid by meteorologists today. Its problem is that weather systems are so
varied in their structure that close analogs simply do not exist. There are no twin weather
maps.
Statistical Forecasts
Whenever an event is too difficult to forecast, gamblers place odds on it. Similarly,
meteorologists make statistical weather and climate forecasts when the situation is too
complex or too far in the future to forecast precisely. Since violent tornadoes cannot yet
be predicted directly by computer before the parent thunderstorm forms, statistical
forecasts have been developed. One of the simplest techniques is to make graphs
called contingency diagrams that display the conditions under which tornadoes are apt
to occur. Since tornadoes occur in unstable air
with large values of CAPE and vertical shear,
every time a tornado occurs, CAPE and shear
are calculated from the sounding and plotted
as a point on a graph. After plotting many
cases, the criteria for forecasting tornadoes
are established.
Statistical techniques are even used in
numerical weather forecasting models. After
the computer completes a forecast, a
statistical routine corrects any biases by
analyzing the model’s previous errors. For
example, if a model predicts temperature
1.5C too high on average when it predicts
NW wind, the statistical routine will lower the
forecast temperature by 1.5C.
Prediction by Calculation of Change
Input
Rate
SYSTEM
The Fundamental
Equation of Systems
Change = Input – Output
(Rate) (Rate) (Rate)
Output Rate
Often, Input for one System or Reservoir is Output for another.
Cycles may occur when there are both Inputs and Outputs
Fundamental
Equation
The Derivative
Finite
Difference
in Ratio
Calculus of Change
liminterval0
[
New Value - Old Value
Interval
]
=

Rate of change
+

The Equation of Change is a finite difference prediction equation. It is only accurate
when the interval or step is small. For example, when you put money in the bank (the
principal), it earns interest. But since the interest adds to the principal, the earnings
compound. If you want to know how much money you will have after, say, 3 years, if you
solve the equation of change in a single 3-year interval or step, it will underestimate your
final total because it did not include the effect of compounding.
The prediction technique using the Equation
of Change is then to take many small steps
and recalculate or update the new principle at
each step. This technique, illustrated to the
right and calculated on the next Slide, is
called ITERATION, and it is the approach
taken for computer forecasting of weather,
climate, economics, etc., as we will soon see.
Forecasting by Iteration
Example: At year 0, you put P(0) = $100 in the bank. The interest rate, IR = 50% = 0.50.
Using the Equation of Change, calculate how much money you will have in the bank 3
years later A: by taking a single 3-year step, B: by taking three 1-year steps.
Single 3-year Step
P(3) = P(0) + P(0)  IR  Dt = $100 + $100  0.50  3 = $250
Three 1-year Steps
P(1) = P(0) + P(0)  IR  Dt = $100 + $100  0.50  1 = $150
P(2) = P(1) + P(1)  IR  Dt = $150 + $150  0.50  1 = $225
P(3) = P(1) + P(2)  IR  Dt = $225 + $225  0.50  1 = $337.50
Clearly, neglecting compounding will cost you. In impartial terms it does not
provide an accurate forecast.
Numerical Weather Forecasts by Computer
Ever since Isaac Newton used his laws to describe the motions of all objects, scientists
have dreamed of predicting the future by solving the equations of motion. But weather
seemed so erratic that no one suggested it could be predicted mathematically until 1901,
when the American meteorologist, Cleveland Abbe wrote down the seven equations that
govern the atmosphere and insisted that there must be some way to solve them,
1-3. Newton’s 2nd law of motion in three directions.
4. Conservation of energy (First Law).
5. The ideal gas equation.
6. Conservation of mass of dry air.
7. Conservation of mass of water.
An ocean away, Vilhelm Bjerknes had the same vision in 1903. Abbe and Bjerknes both
recognized that the problem was formidable but saw no way to solve the equations.
Lewis Fry Richardson did see a way. A pacifist and psychologist as well as a physicist,
he established the mathematical basis for computerized weather forecasts during World
War I, long before the computer was invented. Because the equations are too difficult to
solve using calculus, Richardson transformed them to simple arithmetic equations via
the Equation of Change. But every simplification has its price. In order to predict the
weather 24 hours in advance, each of the 7 equations must be solved hundreds of times
at thousands of points.
Richardson envisioned a peaceful army of 64,000 human computers to "race the
weather" mathematically and produce forecasts before the weather actually occurred.
He then formed his own one-man army and spent six weeks making all the
computations to forecast the weather for a single point, one time step (six hours) ahead.
His forecast called for a pressure change of 145 mb, which he realized was a "glaring
error," but one he was not able to explain. (It was not a careless error.) Disillusioned,
Richardson never attempted another calculation and sadly remarked, “Perhaps some
day in the dim future it will be possible to advance the computations faster than the
weather advances....But that is a dream.”
The dream has become reality.
To make a numerical forecast, data is substituted into the finite difference equations at
some initial time. The equations are then solved one time step at a time as far into the
future as desired. After each step, the new values of all quantities are substituted into
the equations. This updating or iteration procedure forms the backbone of all numerical
forecasts.
On the next slide. we solve the logistic difference equation, the simplest equation that
exhibits erratic behavior like the atmosphere and weather, CHAOS. It demonstrates the
extreme difficulty of making accurate long range weather forecasts. The procedure is:
1. Choose a value for R ( 0 < R < 4).
2. Choose an initial value for xold.
new
old
old
3. Solve the equation for xnew.
4. Update and repeat the process. Replace the value of xold with xnew and solve again.
x
CHAOS PREDICTION
BUTTERFLY DIAGRAM
 Rx 1  x

A now classic illustration of chaotic
behavior is
Ed Lorenz’s so-called
butterfly diagram. Chaos occurs for
Instability  23.
Iteration
We now solve an example of the logistic difference equation by the magic process of
iteration, or as Yogi Berra said, “iteration all over again”. The procedure starts by using
the present value of variables to solve for the future values. Time is then advanced and
the variables are updated by replacing Xnow with Xfut so that the future becomes now!!!
Then the entire process is repeated as often as needed.
Initial data:
Xnow = .7
R = 2.5
First forecast:
Xfut = (2.5)(.7)[1 - .7] = .525
Update:
Xnow = .525
Second forecast:
Xfut = (2.5)(.525)[1 - .525] = .623
Update:
Xnow = .623
Third Forecast:
Xfut = (2.5)(.623)[1 - .623] = .587
Etc., etc., etc., (and so forth).
But for the computer to predict the weather the atmosphere is not a single point but must
be divided into millions of tiny cells. The numerical world is a world of grid boxes or cells.
The Grid Box World of Cells
For the computer to predict
the weather the atmosphere
cannot be treated as a single
entity but must be divided into
millions of tiny cells. The
numerical world is a world of
grid boxes or cells. Just as we
are made of cells, so is this
picture of George Bush. When
the cells are small enough we
cannot tell what they are
made of, cannot see them,
and may not even suspect
that they exist unless we take
a magnified view and look
through a microscope.
The next slide shows that
George Bush’s face actually
consists of hundreds of tiny
cells, each of which contains
its own face.
The Grid Box World of Models
Numerical models divide the atmosphere into a 3-D grid of boxes and predict at least 8
quantities – p, T, RH, water, ice, and 3 directions of wind a short time step (1 minute)
ahead in each box. Since boxes are linked by inputs and outputs (convection, radiation,
precipitation, etc.) and since the large models have  50 million boxes (3 km wide and
0.5 km high), at each time step some 400 million equations must be solved and the
process repeated 6024 = 1440 times in 24 hours. The number of steps, grid boxes and
calculations constantly increase as computer power increases.
IR Radiation
Solar Radiation
Convection
Cold Advection
Precipitation
Warm Advection
The figure shows 1-box and 2box models of climate. Both
models have sunlight as input
and radiation as output. The 2box model has 1 extra feature
– heat transport by the winds
or ocean currents. Since the
tropical box is warmer than the
polar box, winds and currents
transport heat from the tropical
box to the polar box. Thus the
tropics never gets too hot and
the polar regions never get too
cold.
To include seasons, there must
be at least 3 boxes since there
are two polar regions.
The more cells, the more
accurate the model but the
more calculations are needed.
The next slides show that
models with more and smaller
cells are increasingly accurate.
Height above Sea Level (meters)
When cells are large we cannot
see the forest – just the trees
0
1
10 20 50 100 150 200
Height above Sea Level (meters)
0
1
10 20 50 100 150 200
Height above Sea Level (meters)
0
1
10 20 50 100 150 200
Height above Sea Level (meters)
When cells are tiny we cannot see
the trees – just the forest.
0
1
10 20 50 100 150 200
Example of a Computer Weather Forecast
the Monster Snowstorm of 05-06 Feb 2010
The monstrous snowstorm of 05-06 February 2010 that buried the Mid Atlantic from
Virginia to Washington DC to Baltimore to Philadelphia and just barely reached the
southern fringe of NYC (see next slide) was forecast at least 8 days in advance,
although with errors. Two series of slides follow.
The first series shows the actual evolution of weather from 29 January to 06 February. At
least 6 low pressure areas crossed the United States from west to east. The snow storm
resulted when Low #5 and Low #6 merged along the Eastern Seaboard.
The second series shows the forecasts for 00 UTC of 06 February starting 180 hours in
advance. The 180 hour forecast (7.5 days in advance) predicted that the low pressure
area would be about 200 miles SSE of New York City and that it would be snowing in
NYC. This forecast moved the storm too fast and too far north. But all the subsequent
forecasts from as long as 156 hours ahead (6.5 days) placed the storm center right
around South Carolina, and indicated that there would be a second storm center around
Tennessee. They also showed that the area around Washington, DC would get a major
snowstorm on the 6th and that the furthest north the snow would extend was NYC. No
one could have forecast the storm’s existence, let alone its position, strength and form
so accurately, without the immense power of the computer. Note also the pretty accurate
computer forecast of the high pressure area west of Hudson Bay that extended through
NYC and that supplied the storm with enough cold air to produce the snow.
07 Feb 2010 1750 UTC (Terra)
http://rapidfire.sci.gsfc.nasa.gov/realtime/2010038/
Low #1
Low #3
Low #2
http://archive.atmos.colostate.edu/
Low #1
Low #3
Low #2
Low #3
Low #2
Low #3
Low #3
Low #4
Low #3
Low #5
Low #4
Low #5
Low #6
Low #5
Low #6
Low #5
Low #6
http://archive.atmos.colostate.edu/
Note that it was snowing over NYC but the snow did not reach the ground.
Surface Weather
Map 1243 UTC 06
February 2010
Decrease of Forecast Accuracy with Increasing Lead Time
The next 3 slides show how forecast accuracy decreases with increasing lead time.
Forecasts of heights of the 500 mb chart are much more accurate than forecasts of
weather features we consider important such as temperature and precipitation. But the
extreme high accuracy of 500 mb height forecasts even at 48 hours testifies to the
enormous progress we have made with the help of the computer, satellites and radar.
Before the computer the 48 hour accuracy was only about 35%, now it is 98%.
Hurricane forecasts also decrease in accuracy with increasing lead time but have
improved tremendously over the past several years because of improvements in the
computer models and measurements. This is particularly true for forecasts of the
hurricane track, so that now, with the help of the computer, we can forecast the track of
the hurricane’s eye within about 100 nautical miles (115 miles) some 48 hours in
advance. The forecast for landfall for Hurricane Katrina, for example, was highly
accurate, and should have convinced FEMA to evacuate New Orleans. But forecasts of
hurricane intensity or maximum wind speed are still woefully inadequate, and some
massive evacuations have not been necessary.
Climate Forecasts
The models that produce weather forecasts can be modified to predict climate. These
models are not designed to give accurate weather forecasts 20 or 200 years in advance
but do show how average conditions are likely to change. The 4th slide shows a climate
forecast when CO2 is double the pre-industrial content. They make it clear that we are in
for a warmer world, particularly near the Poles. Much ice will melt and raise sea level.
Decrease of 500 mb Forecast Accuracy with Increasing Lead Time
Correlation of Forecast with Observation (%)
June 08 – September 09
100
90
80
70
60
50
40
30
20
2
4
6
8
10
Forecast Lead Time (Days)
12
http://www.emc.ncep.noaa.gov/annualreviews/2009Review/index.html
14
GFS Atlantic Hurricane Track Error
2008 Hurricane Season
GSI/GFS Bundle – Red
Operational GFS - Green
GFS Atlantic Hurricane Intensity Error
2008 Hurricane Season
GSI/GFS Bundle – Red
Operational GFS - Green
Not so far in the Future: Predicted Temperature Changes
NASA GISS Climate Model Simulation for 2xCO2.
http://data.giss.nasa.gov/efficacy/#table1