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From YouTube: 2020-04-17- Troy Arcomano - A Data-Driven Global Weather Model Using Reservoir Computing
Description
NERSC Data Seminars: https://github.com/NERSC/data-seminars
Title: A Data-Driven Global Weather Model Using Reservoir Computing
Abstract: Data-driven approaches to predict chaotic spatiotemporal dynamical systems have been shown to be successful for a number of high-dimensional, complex systems. One of the most important chaotic systems which impacts our lives is the atmosphere. This, naturally, leads to the question whether a purely data-driven machine learning algorithm can accurately predict the weather. In this talk, we present a prototype machine learning model that can skillfully predict the three dimensional state of the atmosphere for 3-5 days. The training of the machine learning model is computationally efficient and parallelized over thousands of computer cores. Our results suggest that machine learning has the potential to improve the prediction of atmospheric state variables most affected by parameterized processes in numerical models.
References: Arcomano et al. "A Machine-Learning-Based Global Atmospheric Forecast Model." (2020). https://www.essoar.org/doi/pdf/10.1002/essoar.10502527.1
A
He
did
his
bachelor's
in
atmospheric
sciences
and
a
minor
in
physics
at
the
university
of
maryland,
and
he
has
worked
on
several
interesting
projects
related
to
the
atmospheric
sciences
and
weather
and
climate
modeling
at
the
national
center
for
environmental
prediction
and
the
naval
research
laboratory.
He's
gonna
talk
about
his
current
project,
which
is
using
machine
learning
to
improve
weather
forecasting
and
I'll.
Let
him
take
the
screen
from
here.
B
Thank
you
jd
for
that
very
nice
introduction.
First,
I'd
like
to
thank
all
of
you
for
allowing
me
to
speak.
This
is
a
really
exciting
project
that
we've
all
been
working
on
for
the
last
two
to
one
and
a
half
years
and
very
excited
to
present
our
results
before
I
get
started
just
like
to
thank
some
of
our
collaborators,
dr
ishwan,
soon
young
dr
brian
hunt,
dr
ed,
alex
wickner
and
jd
pathak,
which
I'm
sure
you
all
know
for
making
some
of
this
work
possible.
B
Sorry
nope.
There
we
go
okay,
so
just
a
little
introduction.
So,
as
many
of
all
know,
machine
learning
has
a
wide
range
of
applications
from
image
processing
to
playing
complex
human
games
such
as
go
to
language
processing.
Machine
learning
has
been
applied
to
almost
every
field
in
the
science
community
many
times
with
great
results.
B
So
it's
no
surprise
that
previous
work
is
showing
success,
using
machine
learning
to
predict
complex
spatial
temporal
chaotic
systems,
one
of
the
most
important
chaotic
systems
that
affects
every
person's
life
daily,
whether
you're
going
to
want
to
wear
shorts
or
put
a
jacket
on
all
the
way
up
to
billions
and
trillions
of
dollars
in
terms
of
economic
potential
loss
or
economic
potential.
Growth
is
the
weather.
B
So
before
I
get
into
an
actual
pure
machine
learning
weather
prediction
model?
I
want
to
just
talk
about
some
machine
learning.
Applications
that
are
being
used
today
for
numerical
weather
prediction
or
nwp
numerical
weather
prediction
is
using
numerical
modeling
to
predict
the
weather
x
number
of
days
into
the
future.
This
is
how
your
weather
channel
app
or
your
favorite
weather
app,
gets
its
forecasts.
B
B
B
So
parameterization
is
anything
that
a
numerical
model
can't
explicitly
simulate
so,
for
example,
in
a
weather
prediction
model,
there's
no
way
that
you
could
account
for
all
of
the
rain
droplets
in
a
cloud
and
if
you
scale
that
up
all
the
way
to
the
globe,
there's
no
way
that
you
can
keep
track
of
every
single
rain
droplet
in
the
entire
globe.
So
how
they
do
it
is
they
come
up
with
some
parameterization
technique?
B
Many
of
times
these
parameterization
techniques
are
the
most
computationally
complex
part
of
a
numerical
weather
prediction
model
so
being
able
to
train
a
neural
network
to
emulate
these
parameterizations
once
the
training
is
done,
is
actually
much
more
computationally
efficient,
there's
been
many
results,
encouraging
results
and
I
believe
one
of
the
operational
centers
is
actually
replace
some
of
their
parameterization
with
a
trained
neural
network.
Another
important
machine
learning
application
is
post
processing.
B
So
once
these
numerical
weather
prediction
models
run
and
you
have
a
forecast,
there's
inherent
biases
because
of
the
complex
terrain
and
topography
in
some
locations
models
are
unable
to
explicitly
resolve
mountains
to
the
fullest
extent,
so
being
able
to
post
process
and
down
scale.
These
simulations
in
the
forecast
using
machine
learning
has
been
extensively
used
almost
for
the
last
two
decades,
so
those
things
are
used
operationally
as
well,
and
when
we
make
forecasts
for
a
day
two
prediction:
we
don't
just
run
one
simulation.
B
B
This
is
particularly
important
for
those
who
are
at
the
national
weather
service
or
other
agencies
that
are
human
forecasters
and
need
to
express
to
the
public
what
the
weather
is
going
to
be
like.
If
you
know
that
there's
going
to
be
a
tornado
outbreak
in
five
days
and
the
models
are
very
certain
of
this,
then
you
can
use
more
strongly
worded
language
to
inform
the
public.
B
However,
if
these
more
uncertainty
than
usual
for
a
day,
five
prediction,
then
you'd
also
want
to
highlight
that
and
using
these
machine
learning
with
ensembles
offers
another
great
benefit
being
able
to
non-linearly
weight
ensembles
instead
of
the
usual
linear
combination
of
x,
number
of
ensembles
leads
to
much
better
forecasts.
When
you
linearly
weight
a
number
of
ensembles
you
get
much
more
smooth
and
broad
fields.
You
lose
a
lot
of
the
finer
scale
detail
and
being
able
to
non-linearly
weight.
Different
members
for
different
situations
leads
so
much
better
and
more
realistic
forecast.
B
This
is
particularly
useful
for
precipitation
forecasts,
because
when
you
wait
a
linear
combination
of
the
ensembles,
you
lose
things
like
terrain
and
topography,
which
are
quite
important
so
now
that
we've
seen
what
the
applications
are,
none
of
these
applications
really
predict
the
weather.
You
still
need
a
numerical
model
to
predict
what
the
weather
is
going
to
be
like
in
four
days,
so
we
propose
a
criteria
for
what
a
global
machine
learning
forecast
model
is
and
there's
we
came
up
with
three
criteria
or
three
requirements.
B
B
Is
it
going
to
be
computationally
feasible?
These
state-of-the-art
numerical
weather
prediction
models
predict
on
the
order
of
millions
of
variables
at
every
time,
step,
because
these
are
very
high
resolution,
simulations
from
usually
at
with
grid
spacing
of
5
to
20
kilometers
for
the
entire
globe.
We're
talking
about
millions
of
grid
points
in
the
horizontal
and
then
the
vertical
extent
makes
this
even
more
complicated
numerical
weather
prediction
models
start
from
the
surface
and
they
go
all
the
way
up
to
almost
the
mesosphere
so
having
a
computationally,
feasible
machine
learning
architecture
is
the
first
requirement.
B
Again,
it's
weather
does
happen
at
the
surface
and
that's
what
affects
us,
but
whether
it's
just
not
a
two-dimensional
field.
We
need
to
be
able
to
predict
all
all
the
variables
at
each
grid
point
in
the
three
dimensions
and
then
there's
other
applications
like
what's
the
weather
going
to
be
like
for
an
airplane.
So
we
don't
even
care.
B
Not
only
do
we
care
about
what
the
surface
is,
but
we
have
to
go
all
the
way
up
into
the
stratosphere
and
in
some
applications
even
into
the
mesosphere,
so
having
a
machine
learning
algorithm
that
can
be
aware
of
these
three-dimensional
aspects
to
these
fields
instead
of
a
two-dimensional,
makes
the
problem
much
more
complex
and
we're
not
going
to
only
be
predicting
one
variable.
We're
going
to
want
to
predict
multiple
variables.
B
B
Is
it
going
to
produce
realistic
atmospheric
motions
and
phenomena
if
it
can
predict
one
time
step
into
the
future?
That's
great,
but
that
really
limits
the
number
of
applications.
Your
machine
learning
algorithm
has
typical
weather
models
run
from
one
day.
All
the
way
to
two
weeks.
Two
weeks
is
about
the
area
where
we
reach
practical
predictability
limit
so
first,
whether
that
affects
us
from
day
to
day
two
weeks
is
about.
As
far
as
we
can
predict.
B
So
if
we
wanted
to
use
a
machine
learning
climate
model,
we're
going
to
have
to
be
able
to
have
realistic
atmospheric
motions
and
phenomena
for
not
only
a
few
weeks
but
out
to
centuries
and
the
climate
model
situation
becomes
even
more
complex
because
you
have
things
you
have
very
long-term
variability
on
the
scales
of
years,
and
you
also
have
this
increasing
radiation
forcing
from
global
warming
so
being
able
to
predict
something.
That's
much
more
doing
something
that
would
be
a
climate
model.
Application
is
much
more
robust
than
a
weather
prediction
model.
B
B
But
again
this
was
the
first
real
attempt
at
being
able
to
use
machine
learning
to
predict
a
atmospheric
variable
on
the
global
scale.
They
used
re-analysis
data,
so
re-analysis
data
is
our
best
attempt
at
a
state
of
the
atmosphere
at
in
the
past.
We
have
millions
of
observations
for
windows
of
time
in
the
atmosphere,
however,
they're
not
homogeneous
in
the
x
and
y
space,
as
well
as
in
the
vertical
level.
B
So
that
is
one
thing:
is
the
machine
learning
algorithms
that
I'm
going
to
be
describing
and
ours
are
limited
to
using
re-analysis
data?
So
we
still
need
a
numerical
model,
so
there's
still
limitations,
they
use
this
re-analysis
model
and
got
encouraging
results.
This
leads
to
share
at
all
2018
and
2019
b.
They
used
again
a
convolutional
neural
network
to
predict
full
three-dimensional
atmospheric
variables.
B
However,
they
found
that
the
reanalysis
dataset,
which
only
goes
back
to
1979,
was
not
robust
enough
to
train
these
neural
networks.
So
how
so?
They
came
up
with
a
an
experiment
where
they
used
a
simplified
climate
model
to
run
for
centuries.
They
used
this
centuries
worth
of
data,
to
train
their
convolutional
neural
network
and
were
able
to
predict
the
full
three-dimensional
atmospheric
variables.
B
However,
upon
applying
this
using
transfer
learning
to
the
real
atmosphere,
they
got
mixed
results
many
times
the
model
their
model
would
blow
up
and
really
and
predict
very
unrealistic
things
such
as
negative
temperatures
or
pressure
that
was
below
the
surface,
so
they
were
able
to
get
three-dimensional.
Atmospheric
vectors
predict
variables
predicted,
but
they
were
limited
to
a
simplified
climate
simulation
which
finally
leads
us
to
the
wayne
at
all
2019
and
2020
papers.
B
B
They
had
selected
these
four
variables
to
be
some
of
the
most
important
to
a
meteorologist
who
wants
to
predict
the
weather,
such
as
two
meter
temperature,
so
the
temperature
at
two
meters
above
the
surface,
which
is
quite
important
for
everybody
for
day-to-day
decisions.
They
also
predicted
surface
pressure
and
two
other
variables,
and
they
found
that
they
were
able
to
use
reanalysis
data
from
1979
to
2018
and
predict
realistic
and
stable
results.
B
So
before
I
get
into
a
little
more
of
our
model
and
talk
about
how
we
were
able
to
achieve
three-dimensional
global
predictions,
I
just
want
to
go
into
a
little
detail
about
our
machine
learning
algorithm.
So
we
chose
to
use
reservoir
computing
because
of
our
computing
is
one
of
the
many
different
machine
learning
algorithms.
B
I
should
note
that
the
reason
we
chose
this
is
a
bit
arbitrary.
The
way
our
architecture
is
set
up
is
it
could
be
used
for
any
all
machine
learning
algorithm,
a
convolutional
neural
network
or
a
different
flavor
of
a
recurrent
neural
network
would
suffice,
but
we
found
because
reservoirs
computing
is
not
deep
learning.
B
So
we
have
an
input
signal
which
is
a
spatial
spatial
temporal
chaotic
system?
U
of
t
this
is
our
training
data
at
time
t
and
then
we
have
this
input,
layer
or
rwn.
This
couples
our
input
signal
to
our
much
higher
dimensional
reservoir
again,
because
this
is
not
deep
learning.
This
is
just
a
random
fixed
uniformly
distributed
matrix
that
just
maps
our?
U
of
t
to
our
reservoir,
which
is
much
more
high
dimensional,
and
then
we
have
our
reservoir
layer.
B
B
B
We
use
the
activation
function,
tan
of
h
or
a
hyperbolic
tangent,
but
you
could
use
in
theory
any
of
the
many
different
activation
functions
you
have
out
there
and
then
we
take
this
reservoir
state
and
we
now
want
to
minimize
this
matrix
w
out
so
that
we
can
make
the
reservoir
system
predict
one
time
step
into
the
future
I'll
let
that
digest.
I
know
there's
a
lot
on
this
one
and
feel
free.
B
C
C
I
just
don't
understand
like
what's
this,
like
the
direct
benefit
of
having
a
sort
of
you
know
like
an
end-to-end
training
in
this
part
versus
compared
to
breaking
it
down
in
three
or
four
different.
Smaller
parts
to
train
so
like
it
looks
like
it
has
lots
of
information
which
could
be
maybe
used
in
a
more
rigorous
manner
in
step-wise
training,
for
example,.
B
Okay,
so
the
way
we
actually
so,
this
is
just
one
implementation.
So
the
way
we
actually
do
this
is
as
I'm
going
to
allude
to
in
a
second
is
we
actually
break
this?
U
of
t
signal
up
into
many
different
parts
and
make
this
very
large.
You
know
u
of
t
vector
that
could
be
on
the
order
of
hundreds
of
thousands
of
millions
and
then
we're
going
to
break
this
up
into
much
smaller
sections
using
many
different
parallel
reservoirs.
C
B
Yes,
yes,
so,
yes,
the
when
we
presented
this
problem,
the
and
as
the
previous
people
have
looked
at,
the
idea
is
using
a
convolutional
neural
network
with
like
some
auto
and
kerner,
or
something
with
down
sampling
and
then
up
sampling
type
system.
There's
many
different
things
like
u-net,
that's
out
there
and
that's
what
they've
actually
used
most
of
them.
B
B
Oh
no
problem.
Thank
you
for
that
good
question.
Oh
no,
I
can't
move
my
sides.
Oh
there
we
go
so
just
to
get
a
little
more
understanding
of
why
I
said
that
this
machine
learning
algorithm
of
using
a
reservoir
computing
in
this
system
is
kind
of
arbitrary,
so
we
have
a
training
and
predict
two
phases:
a
training
and
prediction
phase.
So
we
have
a
signal?
U
of
t?
B
U
n
of
t
coming
into
our
black
box
machine
learning,
we've
trained
it
to
be
able
to
predict
one
time
step
into
the
future.
However,
one
time
step
into
the
future
for
weather
applications
is
really
kind
of
useless.
I
can
probably
you
know
with
my
brain,
be
able
to
tell
you
what
the
weather's
going
to
be
in
an
hour.
B
B
And
the
part
why
we
used
of
a
current
neural
network
instead
of
a
convolutional
neural
network
which
won't
have
memory,
is
because
we're
going
to
end
up
feeding
this
signal
once
the
machine
learning
is
trained
back
in
so
we
make
so
we
train
our
machine
learning.
We
have
a
the
last
observation,
which
is:
u
of
n
of
t.
B
We
put
it
through
the
machine
learning
algorithm,
and
now
we
have
one
prediction
into
the
future
one
time
step
into
the
future,
and
because
this
thing
has
memory
and
it's
already
trained
to
predict
another
time
step.
We
take
this
one
time
step
into
the
future
prediction
and
feed
it
back
into
the
machine
learning
algorithm.
B
But
if
everything
worked
well
in
your
machine
learning,
algorithm
learn
the
dynamics
of
your
complex
system,
you're,
able
to
understand
you're
able
to
capture
the
climate
of
this
complex
system,
even
if
you
aren't
able
to
have
any
predictive
skill.
So
that's
the
really
great
part
about
this
is
the
machine
learning
our
machine
learning
network.
The
reservoir
computers
are
going
to
have
some
sort
of
memory
in
this.
B
It's
going
to
be
able
to
take
that
signal
from
two
times
ago
and
remember
that
there's
some
correlation
in
terms
of
time
with
these
variables
in
the
atmospheric
atmospheric
field
and
be
able
to
use
that
to
correctly
make
another
time
step
into
the
future.
So
now
we
have
a
machine
learning
algorithm
that
can
predict
as
far
into
the
future
as
you
want.
B
However,
as
this
was
alluded
to
with
that
question,
before
is
our?
U
of
t
in
this
case
is
massive,
even
at
very
low
resolution,
horizontal
resolution
and
low
vertical
resolution,
the
atmosphere
and
the
globe
itself
is,
as
you
can
imagine,
massive
we're
going
to
have
to
be
predicting
more
than
one
variable.
As
I
mentioned,
we're
going
to
have
to
predict
at
least
one
high
level,
but
because
we
want
to
do
because
of
the
requirements
that
we
made,
that
we
want
to
do
three
dimensional
fields
we're
going
to
have
to
predict
multiple
vertical
levels.
B
B
And
because
of
the
principle
of
locality,
so
the
weather
in
taiwan
is
not
going
to
be
affecting
the
weather
in
new
york
city
on
the
scale
of
an
hour.
Eventually,
there
will
be
effects
if
we
made
our
time
step
too
large
say
we
made
a
time
step
of
10
days
or
something
because
we
wanted
to
do
climate
simulations.
B
So
we
chose
an
hour
time
step,
which
is
the
highest
temporal
resolution
that
the
reanalysis
data
sets
are
sampled
in
and
we
broke
the
globe
up
into
a
1152
sections
and
when
you
plot
this
into
a
mercator
projection,
we
see
that
each
blue
line
here
represents
the
area
that
a
machine
learning
algorithm
has
to
predict
so
each
time.
So
if
we
go
back
each
one
of
those
blue
boxes
here
represents
one
independent
blue
box
on
this
figure.
So
we
have
many
m
many
reservoirs
that
are
being
trained
to
predict
a
small
geographical
region.
B
B
We
can
train
each
one
of
these
blue
boxes
on
a
different
gpu
or
a
different
cpu,
and
because
these
weather
assist
these
high
performance
clusters,
where
the
large
numerical
weather
prediction
models
are
run,
have
hundreds
of
thousands
of
cpus,
we
can
really
scale
this
up,
which
is
great,
so
we
break
the
domain
into
these
small
little
boxes,
and
so
each
reservoir
only
has
to
predict
a
much
smaller
subset
of
the
data
in
this
case
that
each
reservoir
has
to
predict
four
grid
points.
So
a
two
by
two
box.
B
However,
if
the
reservoirs
are
completely
independent,
there's
no
way
to
resolve
features
larger
than
a
two
by
two
box.
So
in
this
case
we
would
be
able
to
resolve
one
wave
kind
of
you
really
need
more
than
two
grid
points
to
resolve
a
wave,
so
we
would
never
be
able
to
resolve
a
wave.
The
way
we
get
around
this
is
we
take
information
from
the
surrounding
neighbors.
B
B
So
we
so
for
training,
so
we
now
have
a
parallel
machine
learning
architecture
that,
in
theory,
is
able
to
predict
an
entire
globe,
but
we
can
be
trained
in
parallel,
so
we
can
it's
massively
parallel.
So
as
long
as
computational
hours
and
memory
is
not
an
issue
in
theory,
we
can
predict
the
globe
now.
So
how
we
get
the
training
data.
Is
we
take
the
error,
5
reanalysis
data
set?
This
is
the
most
sophisticated
analysis
data
set
available.
B
It
really
only
just
came
out
within
the
last
two
years.
The
temporal
evolution
of
that
data
set
is
on
hours
on
an
hourly
time
scale.
So
really
this
architecture
wouldn't
have
been
possible
without
this
data
set,
because
with
a
three
hour
time,
step
we're
really
starting
to
you're,
going
to
start
losing
fast
features
in
the
atmosphere.
So
this
is
really
key
is
having
a
higher
resolution,
a
higher
temporal
resolution
data
set,
and
this
part's
a
little
confusing.
B
The
end
goal
is
to
take
your
climate
model
and
your
trained
machine
learning
network
and
be
able
to
leverage
those
two
that
into
information
in
a
hybrid
type
system
correctly,
thus
improving
upon
your
machine
learning
network
and
your
numerical
network
or
your
numerical
model,
which
I'll
talk
a
little
bit
at
the
end
of
this.
If
I
have
time
we
chose
to
use
five
prognostic
variables,
so
at
each
grid
point
in
this
fig
sorry
can't
go
backwards.
B
Okay
in
each
one
of
these
grid
points,
there's
five
variables
that
need
to
be
predicted
and
there's
eight
vertical
layers.
So
if
we
imagine,
if
you
could
somehow
extend
this
plot
into
the
three
dimensions,
we're
going
to
have.
Eight
of
these
grid
points
lining
on
top
of
each
other,
as
you
go
up
in
the
atmosphere,
each
at
each
grid
point
you're
going
to
have
to
predict
five
prognostic
variables,
your
two
components
to
the
wind,
which
is
called?
U
and
v?
B
U
is
your
east-west
direction
of
your
wind,
your
zonal,
wind
and
your
v
component
of
your
wind
is
your
north-south
direction
of
your
wind
and
those
are
one
of
the
most
important
types
of
variables.
The
next
one
is
your
temperature
again.
If
we
want
to
know
if
we
need
shorts
or
a
jacket
today,
we're
going
to
want
to
know
temperature
and
then
our
last
three
dimensional
variable
is
specific
humidity.
So
this
is
our
moisture
variable.
B
There's
many
different
variables
of
choice
for
moisture,
specific
humidities,
probably
the
most
popular
in
numerical
weather
prediction,
because
it
encompasses
a
lot
of
information
and
the
way
you
formulate
your
equations
that
you
solve
or
make
it
more
simple
with
specific
humidity.
But
there
are
other
ones
out
there.
B
So
we
have
four
three-dimensional
variables,
and
now
we
have
a
special
variable,
which
I
call
surface
pressure.
So
this
is
the
pressure
defined
at
the
interface
between
the
land
and
the
atmosphere.
So
this
is
a
terrain
following
two-dimensional
variable.
This
is
quite
an
important
variable
for
our
machine
learning
architecture,
because
without
surface
pressure,
the
machine
learning
would
have
no
idea
about
orography.
So
we're
not
input.
B
So
one
of
the
inputs
that
we're
not
putting
in
is
terrain
hydrography,
so
the
surface
pressure
is
a
proxy
for
the
orography,
but
a
surface
pressure
has
a
many
other
different
applications.
It's
the
entire
weight
of
the
atmosphere,
so
it
really
encompasses
a
lot
of
information.
It's
what
you
see
on
weather
maps
with
the
nice
red,
low
pressure
systems
and
the
blue
high
pressure
systems.
It
tells
you,
when
your
weather
man's
telling
you
oh
the
low
pressure
systems
moving
off
the
coast
onto
the
coast.
You
probably
want
to
get
your
rain
jacket
and
stuff.
B
And
we
require
we
acquired
20
years
of
this
data
spanning
from
1981
to
2000..
We
partitioned
this
data
such
that
19
years
was
for
training,
and
one
year
was
validating
our
predictions.
We
really
didn't
do
too
much
hyper
parameter
tuning
with
something
as
large
as
this.
Each
geographical
region
is
going
to
need
slightly
different,
hyper
parameters
and
stuff,
so
we
really
just
did
some
hand
tuning,
but
as
far
as
we
were
aware,
there
was
no
systematic
way
of
training.
B
This
using
like
numerics,
are
using
a
computational
software,
so
most
of
the
tuning
was
done
by
hand
and
we
didn't
need
to
partition
the
data
into
a
you
know
another
year
worth
of
validation
and
verification.
So
all
of
that's
done
in
that
one
year,
so
we
did
a
so.
We
trained
the
neural
network,
our
parallel
neural
network,
we
inputted
19
years
of
data,
and
we
now
want
to
make
a
prediction.
B
So
what
I'm
going
to
show
here
is
a
movie.
So
this
is
a
simulated
forecast,
starting
on
january
27,
2000
at
eight
universal
at
eight
a.m.
Universal
time,
what's
plotted
here
in
the
colored
contours,
are
temperature
at
the
near
surface.
So
this
is
the
temperature.
This
is
the
closest
temperature
to
the
surface
that
we
have
in
this
model
and
the
vectors
that
are
plotted
here
are
wind
vectors
again
at
the
closest
level
to
the
surface.
B
So
this
would
be
the
variable
that
you
would
most
likely
be
able
to
feel
you
would
feel
that
you'd
be.
This
is
close
to
sensible
temperature
and
sensible
wind.
Well,
you
can
feel,
and
the
direction
of
the
vector
of
the
wind
vector
is
the
direction
of
the
wind
and
the
magnitude
of
the
wind
vector
is
the
size
of
the
arrow.
So
this
is
the
first
hour
prediction.
After
we
trained
our
neural
network,
we
see
that
the
you
know,
machine
learning,
algorithm
is
able
to
for
at
least
one
hour
produce
realistic
results.
B
We
see
that
it's
warmer
in
the
equatorial
regions
and
colder
in
the
polls,
as
you
would
expect,
there's
a
large
scale,
phenomena
much
larger,
so
each
one
of
these
wind
vectors
represents
a
grid
point.
So
if
you
remember
two
figures
ago,
each
machine
learning
algorithm
is
only
able
to
predict
four
of
these,
but
we
see
features
that
are
much
larger
resolve.
We
see
a
large
low
pressure
system,
that's
spinning
in
the
correct
direction
in
the
southern
hemisphere
somewhere
in
the
southern
pacific.
That's
much
large!
That's
a
much
larger
feature
than
a
two
by
two
box.
B
We
see
the
trade
winds
over
the
equatorial
region
and
we
see
a
very
large
low
pressure
system
over
alaska.
So
at
least
for
one
hour,
the
machine
learning
algorithm
is
able
to
work.
But
let's
see,
if
our
third
criteria
being
able
to
produce
realistic
weather
phenomena
for
at
least
two
weeks
is
correct.
B
We
also
see
some
large
systems
over
the
in
between
russia
and
alaska
coming
off
the
coast
of
japan.
So
this
is
where
the
movie
ends.
So
this
is
15
days
after
the
simulation
starch
again
still
warmer
in
the
equatorial
region,
colder
in
the
polar
regions.
We
see
low
pressure
systems,
so
we
are
at
least
able
to
get
realistic
for
simulated
forecasts
out
to
day
15
and
if
we
can
even
extend
this
to
day
20.,
so
we're
able
to
have
stable,
realistic
weather
phenomena
out
to
day
20,
at
least
after
day
20.
B
We
start
running
into
some
problems
with
the
way
we
implemented
our
parallel
architecture,
but
we're
quite
confident
that
we're
going
to
be
able
to
continue
these
simulations
even
further
than
20.
so
for
our
climate
application
for
this
15
day
forecast,
there's
just
a
couple
of
more
interesting
phenomena
that
I'd
love
like
to
point
out.
B
B
This
is
because
there's
a
large
sea
surface
temperature
gradient,
corresponding
with
the
kuroshimo
current
right
off
the
gulf
of
alaska.
Sorry,
not
the
last
right
off
the
japan
coast
without
being
explicitly
told
the
machine
learning,
because
there's
no
sea
surface
temperatures
being
inputted.
The
machine
learning
algorithm
is
able
to
understand
that
they're
supposed
to
be
during
this
time
of
year,
storms
here
and
we
see
that
it
does
develop
quite
a
large
system
at
apparently
day
15..
B
We
see
a
couple
of
other
features
that
quickly
catch
the
eye
of
a
meteorologist,
so
we
see
that
the
machine
learning
algorithm
is
not
only
able
to
resolve
features
that
would
be
present
in
the
field,
but
it
also
understands
the
correlation
between
each
variable,
so
the
wind
is
usually
a
really
important
variable.
If
you
want
to
know
what
the
temperature
is
going
to
be
because
it's
warmer
in
the
equator
and
the
gradient
goes,
and
we
have
a
temperature
gradient
going
towards
the
poles
where
it's
colder.
B
When
you
have
southerly
winds,
you
expect
there
to
be
warmer
temperatures
associated
with
this.
So
we
see
with
this
very
large
low
pressure
system
off
the
coast
of
alaska.
We
have
warm
air
getting
invected
north
towards
the
poles
by
the
southerly
winds.
We
see
what
looks
like
a
cold
front
situated
here
where
there's
these
change
in
wind
direction.
So
now
you
have
air
coming
from
the
poles
moving
down
and
we
see
colder
at
temperatures
again.
None
of
this
was
explicitly
told
in
the
reservoir.
B
B
The
easiest
metric
to
beat
is
called
persistence,
so
this
means
that
the
state
of
the
atmosphere
at
time
t
when
you
start
your
prediction-
is
going
to
be
the
state
of
the
atmosphere
for
the
entire
length
of
the
prediction.
So
that
means
it's
just
assuming
that
the
atmosphere
is
static.
If
you
can't
be
persistent,
that
means
whatever
your
model
is
doing
is
doing
worse
than
nothing.
So
you
really
don't
want
to
be
doing
worse
than
persistence.
B
The
other
important
benchmark
for
predictability
is,
are
you
beating
climatology
climatology
actually
is
in
the
long
term,
always
the
winner?
No
matter
how
good
your
numerical
model
is,
if
you
let
your
simulations
run
long
enough,
they're,
never
going
to
be
able
to
beat
climatology
climatology
is
defined
as
a
30-year
average
of
the
atmospheric
variable
that
you
want
to
predict
at
that
time.
So,
in
this
case,
if
we
go
back
to
the
previous
movie,
we
start
at
january
27
2000
at
eight
o'clock
in
the
morning.
B
We
do
some
averaging
with
climatology
to
remove
things
like
the
diurnal
cycle,
but
basically
that
climatology
and
persistence
are
the
two
for
tr
forecast
metrics
that
you
need
to
beat
so
I'm
going
to
just
show
some
global
root
mean
squared
error,
plots
for
temperature
at
day,
one
day
two
and
day
three,
the
red
curve
is
persistence.
So
that's
the
state
of
the
atmosphere
is
going
to
be
the
same
throughout
this
entire
length
of
the
forecast.
B
Then
we
have
blue,
which
is
our
machine
learning
algorithm
the
that's
fully
trained
on
19
years
of
data,
then
we
have
green.
This
is
called
speedy.
This
is
a
climate
model,
so
this
is
our
numerical
model
that
we
want
to
see
if
we
can
beat
and
then
finally,
black
is
climatology,
and
we
see
that
for
the
day
one
forecast
for
temperature.
We
have
root,
mean
squared
error
as
a
function
on
the
x
and
we
have
pressure
at
the
y.
B
So,
at
each
pressure
level
of
the
model
we're
going
to
average
our
mean
squared
error,
and
we
plot
that
as
a
vertical
line.
So
these
are
vertical
profiles
of
root
mean
squared
error.
We
see
that
almost
everywhere
in
the
vertical
profile,
our
machine
learning
is
doing
on
par
or
better
than
our
numerical
model,
and
again
we
use
the
same
initial
conditions
for
our
numerical
model
on
the
same
grid.
So
it
is
a
completely
fair
comparison
to
that.
B
The
stratosphere
has
quite
complex
dynamics
that
require
you
getting
the
troposphere,
which
is
the
lowest
level
of
the
atmosphere,
forecast
correct.
So,
if
we're
not
going
to,
if
your
numerical
model
is
not
able
to
understand
the
relationship
between
the
stratosphere
and
the
troposphere
you're
going
to
get
bad
results
and
speedy,
because
the
interactions
are
quite
complex
and
are
very
driven
by
convection
speedy,
our
numerical
model
actually
does
very
badly
for
temperature
in
the
stratosphere.
B
Our
numeric.
Our
machine
learning
model,
though,
seems
to
have
no
problem.
We
don't
see
any
real
large
inflection,
like
we
do
here
with
our
error
curve,
it's
basically
straight
from
the
upper
troposphere
into
the
stratosphere.
This
means
that
the
machine
learning
algorithm
is
able
to
understand
these
relationships
in
the
vertical
direction.
It's
understanding
that
there's
convection
the
stratosphere
is
going
to
warm
there's
things
like
tropospheric,
folding
and
stuff
that
drive
that
really
drives
these
temperatures
at
this
scale
by
day.
Two
again,
it's
a
very
similar
story.
We,
which
is
48
hours.
B
We
are
still
beating
persistence,
we're
definitely
still
beating
climatology
or
red
and
black
curves.
Our
numerical
model
again
is
still
struggling
to
now,
not
only
doing
worse
than
persistence,
but
it's
doing
worse
than
climatology
or
on
par
and
with
climatology
in
the
stratosphere,
especially
at
the
highest
level,
or
the
numerical
model
was
never
designed
to
be
a
stratospheric
model.
B
But
in
order
to
get
these
relationships
between
the
stratosphere
and
troposphere,
it
does
need
to
forecast
those
because
without
a
stratospheric
forecast,
your
troposphere
and
your
weather
at
the
surface
is
eventually
going
to
fail.
So
it's
good
to
it's
important
that
we
have
forecast
of
these
atmospheric
fields,
all
the
way
up
to
25,
millibars
or
25
hectopascal,
but
the
machine
learning
and
the
numerical
model
are
basically
doing
on
par.
B
This
is
where
we
start
seeing
the
machine
learning
model
start
to
rapidly
increase
in
terms
of
error
in
the
lower
troposphere
from
400
hectopascal
to
a
thousand
hectopascal.
The
machine
learning
algorithm
is
doing
much
worse
than
that
of
the
numerical
model.
We
are
not
going
to
be
beating
climatology
for
too
much
longer,
but
we're
still
being
able
to
have
skill
both
compared
to
climatology
and
persistence
in
the
stratosphere.
With
this
variable.
B
B
This
is
probably
the
most
difficult
there's
it's
hard
to
quantify
difficulty
in
terms
of
prediction,
but
I
would
say
this
is
the
most
difficult
for
the
machine
learning.
This
involves
things
like
bear:
barotropic
and
baroclinic
instabilities
to
generate
raspy
waves,
there's
dispersion
with
group
and
phase
velocities
in
this
variable,
so
it's
quite
complex
and
it's
a
little
different
than
temperature,
where
there's
really
just
you're
advecting
or
moving
around
temperature
here,
there's
sources
and
sinks.
B
You
know,
there's
troughs
that,
come
into
existence
out
of
nowhere
and
then
these
troughs
decay
and
there's
multiple
wave
numbers
on
top
of
each
other,
so
it's
kind
of
like
a
wave
packet.
So
this
is
quite
more.
This
is
a
quite
more
complex
variable
and
we
see
that
you
know
the
machine.
Learning
algorithm
for
the
first
day
does
on
par,
but
quickly
starts
losing
skill
by
day
three
and
lastly,
we
have
our
moisture
variable.
This
is
where
the
numerical
model
struggles,
the
most
this
is
heavily
parameterized
and
by
the
numerical
model.
B
B
The
one
of
the
most
important
things,
though,
is
the
horizontal
resolution
for
this
that
I
showed
is
considerably
lower
than
that
of
a
state-of-the-art
numerical
weather
prediction
models
on
the
order
of
at
least
a
magnitude.
So
the
resolutions
that
we
were
resolving
here
on
the
scale
300
kilometers,
the
state-of-the-art
global
numerical
weather
prediction
models
are
on
the
order
of
5
to
15
miles,
and
then,
lastly,
though,
the
climate
of
our
model,
actually
once
we
go
out
to
day,
20
is
just
too
high.
B
There's
too
much
variability
in
the
long
wave
dynamics
of
the
atmosphere,
so
wave
numbers
around
the.
If
you
imagine
the
around
a
longitudinal
band
wave
numbers,
one
through
three
really
don't
vary
on
the
time
scales
of
one
to
two
days.
They
really
vary
on
the
scales
of
seven
to
ten
to
fifteen
days,
but
our
machine
learning
algorithm
puts
too
much
variability
in
these
long
wave
dynamics
which
ends
up
causing
us
to
saturate
at
a
much
higher
our
errors
to
saturate
at
a
considerably
higher
level
than
that
of
where
you'd
expect
in
a
perfect
model.
B
We
would
expect
that
our
blue
or
machine
learning,
algorithm
saturates
at
the
red
curve
and
then
our
see
our
numerical
model,
which
is
very
finely
tuned
to
saturate
at
climatology
or
saturated
persistence,
forecast,
hasn't
even
reached
that
level.
So
our
so
in
that
respect,
our
numerical
model
or
our
machine
learning
model
actually
fails.
B
But
there
is
a
next
step
and
I'm
going
to
go
through
this
very
quickly,
because
I
think
I'm
running
out
of
time
here
we
want
to
incorporate
our
machine
learning
algorithm
into
something
we
call
a
hybrid
weather
prediction
model.
So
previous
work
has
shown
success
in
combining
a
numerical
model
algorithm
with
a
machine
learning
algorithm
for
spatial
temporal
chaotic
systems
which
this
hybrid
type
system
improved,
forecast,
skill
compared
to
that
of
a
numerical
model
and
a
machine
learning
only
predictions.
B
So
it's
our
eventual
goal
to
develop
a
system
that
leverages
both
a
general
circulation
model,
which
I
showed
earlier
for
our
climate
model,
which
is
speedy
and
our
machine
learning
algorithm,
which
I've
been
showing
for
our
entire
talk
and
we're
going
to
improve
the
both
of
these
predictions
by
training.
The
machine
learning
algorithm
to
correct
correctly
leverage
our
climate
model,
our
gcm,
and
be
able
to
make
predictions
by
training
it
on
re-analysis
data
set.
B
B
I
won't
go
too
much
into
our
parallel
hybrid
architecture,
but
basically
we
take
our
knowledge
base
model
which
is
denoted
by
m,
and
we
put
our
signal
through
that
knowledge
base
model
and
we
put
the
signal
of
the
our
your
uot
into
our
reservoirs.
So
we
then
have
a
hybrid
type
system.
That's
able
to
make
prediction
the
hybrid.
The
numerical
model
that
we
use
in
our
hybrid
is
speedy,
which
again
I
won't
go
into
too
much
detail
for
lack
of
time.
But
speedy
stands
for
simplified
parameterization,
primitive
equation,
dynamics
model.
B
So
again
we
have.
This
is
a
time
series
of
the
global
root
mean
squared
error
for
near
surface
temperature.
We
have
our
purple
curve,
which
is
our
parallel
or
machine
learning
only
model.
This
is
what
I've
been
talking
about
for
the
entire
talk.
We
have
speedy
our
numerical
model,
which
I've
been
talking
about
for
our
talk,
and
then
we
have
persistence,
which
again
is
defined
as
the
forecast
at
time.
B
The
start
of
the
forecast
is
going
to
be
the
state
of
the
atmosphere
at
any
time
during
the
forecast,
and
we
see
that
for
very
short
term
forecasts.
The
hybrid
system
is
actually
able
to
be
not
only
the
numerical
model,
but
our
machine
learning
only
algorithm
too
for
the
first
nine
hours
of
our
forecast.
B
The
really
big
problem,
though,
is
the
stability
of
our
hybrid
system.
As
we
see
the
error,
curves
really
quickly,
steepen
much
higher
than
that
of
the
numerical
model
speedy
and
our
machine
learning
only
which
is
the
purple
so
there's.
Obviously,
these
non-linear
feedbacks
that
are
occurring
between
our
climate
model
and
our
machine
learning
only
which
we
are
trying
to
fix
and
with
a
minute
or
two
left.
I
believe
I'm
just
going
to
draw
some
conclusions.