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Description
2022 CESM Day 1 Atmosphere Modeling I Intro & Dynamics Peter Lauritzen
A
So
welcome
back
everyone.
I
hope
you
had
a
good
coffee
break
and
we're
able
to
get
some
refreshments
and
get
yourself
caffeinated.
One
thing
that
I
have
to
mention
is
the
fact
that
the
doors
on
the
building
lock
and
if
you
go
outside
you're,
not
gonna,
be
able
to
get
back
in
unless
someone
helps
you
in
we'll
have
people
looking
up
the
doors
to
sort
of
keep
track
of
that.
A
But
if
you
go
out
at
some
time
during
the
session
and
there's
no
one
there,
you
can
either
call
me
or
monica
morrison
whose
numbers
are
on
the
door
and
we
can
come
and
get
you
if
you
find
yourself
locked
out,
we're
also
going
to
be
going
to
lunch
and
so
we'll
help
people
go
through
the
logistics
of
lunch
after
the
second
we've
got
two
atmospheric
lectures
coming
up.
We
have
a
short
break
between
them.
The
first
lecture
is
going
to
be
peter
laritzan.
A
B
You
all
caffeinated
remember
to
drink
more
water
than
coffee.
Okay,
it's
high
up
here.
It's
dry,
it's
hot
alrighty,
so
I
have
the
pleasure
to
spend
the
next
45
minutes
with
you
talking
about
the
atmospheric
component
of
the
cesm.
The
atmospheric
component
is
called
the
community
atmosphere
model
and
again
there's
a
big
emphasis
on
community.
Here
we
built
this
model
with
the
community,
we're
here
for
you
to
help
run
the
model
you
can
do,
research
with
us,
etc.
B
If
you
guys
want
to
come
visit,
us
encar
has
various
programs
for
for
graduate
students
or
postdocs
to
come
and
visit
us
and
sometimes
also
bring
your
advisor
with
you.
So
if
you
want
to
explore
that
and
look
that
up
before,
I
start
how
many
of
you
here
think
of
yourself
as
like
doing
more
atmosphere
than
the
other
components.
B
No
ice?
P?
Oh
there's
one
good
great!
So
my
intention
with
this
lecture
is
to
kind
of
reach
all
of
you.
So
I
want
the
people
here
who
have
less
experience
with
atmospheric
modeling.
I
want
you
to
walk
away
with
an
idea
of
what
goes
into
building
this
model
and
then
for
you
for
those
of
you
who
are
in
atmospheric
modeling.
I
have
some
juicy
stuff
for
you
as
well.
B
So
here's
the
outline
of
my
of
my
talk,
so
I'm
gonna
give
an
introduction
suggested
discretization
grids,
which
leads
me
to
defining
results
and
unresolved
scales,
kind
of
a
gray
area
where
we
don't
have
a
good
mathematical
handle
of
what's
going
on
and
then
just
a
brief
introduction
to.
You
know
the
the
nature
of
atmospheric
dynamics
and
non
non-linearities
over
it
and
then
I'll
define
you
know
the
dynamical
core,
which
is
loosely
speaking.
You
know
the
fluid
flow
solver
in
our
system
and
then
you
know
everything
else
which
we
put
into
permanentization.
B
So
I'm
going
to
loosely
define
those
two
terms
after
that,
I'm
going
to
dive
into
our
current
or
I
should
say
past
workhorse
dynamical
call
the
finite
volume
dynamical
core.
That's
the
one
you're
going
to
be
using
in
the
practical
sessions
I'm
going
to
go
into
some
details
there
and
throughout
the
presentation,
I'm
also
going
to
talk
about
what
I
would
call
the
next
generation
dynamical
course
that
we
have
in
the
system
and
we're
trying
to
switch
over
to
them,
because
the
finite
volume
dynamical
core
is
roughly
20
years
old.
B
B
B
We
do
not
know
how
to
solve
the
equations
of
motions
analytically
unless
we
vastly
simplify
it.
So
our
best
tool
is
to
discretize
our
our
system
and
solve
it
on
a
computer.
So
the
first
step
in
discretizing
in
terms
of
global
modeling
is
we
need
a
global
grid.
So
here
I'm
just
throwing
a
regular
lat
long
grid
over
light
overlaid
this
satellite
image.
B
B
B
So
for
those
of
you
who
have
taken
classes
in
numerical
methods,
you
probably
don't
have
a
neumann
stability
analysis
where
you
linearize
the
system
and
then
you
look
at
how
different
waves
are
damped
or
dispersed,
in
other
words
not
represented
accurately,
but
we
can
also
look
at
this
in
full
models
and
we
do
that
by
looking
at
the
total
kinetic
energy
spectra.
So
we
we
plot
how
much
energy
back
in
point
here
yeah
we
compute
how
much
energy
on
the
y-axis
here
there
is
at
each
wavelength.
B
So
one
can
then
define
say:
okay,
we're
not
representing
these
scales
in
terms
of
having
enough
energy
at
these
scales,
so
we
can
define
the
point
at
which
we
at
which
we
depart
from
this
straight
line,
so
it
will
be
right
around
here.
We
can
define
that
as
our
effect
of
resolution.
So
we
know
when
we
go
beyond
that
resolution.
We
don't
have
as
much
energy
as
in
observation.
That
typically
happens.
You
know
at
the
4
to
10.
Well,
10
is
pretty
bad,
but
typically
at
the
4
to
6
delta,
x,
wavelength.
B
So
that's
400
kilometers
5
500
kilometers,
so
that's
a
lot
longer
than
the
100
kilometer
scale.
So
I
just
want
you
guys
to
be
aware
of
that.
If
you
look
at
the
extremes
in
the
model
that
typically
happen
at
the
grid
scale,
you
should
probably
also
thinking
think
about
this.
The
count
argument
for
this
is
the
parameterizations
actually
work
at
the
grid
scale,
but
from
a
dynamicist
point
of
view,
we
don't
really
trust
the
smaller
scales
of
the
model.
B
B
All
right
in
order
to
build
a
credible
atmospheric
model
we
need
to
represent.
You
know
the
phenomena
in
the
system
that
we
that
are
important
to
have
there
in
order
to
do
credible,
weather
climate
simulations-
and
I
like
to
show
this
figure
here
by
professor
john
fuburn,
who
has
a
space
time
diagram
of
different
important
phenomena
in
the
atmospheres
and
the
x-axis.
Here
you
have
time
scales
from
you
know
less
than
a
second
all
the
way
up
to
the
seasonal
time
scale
and
the
y-axis.
B
So
I'm
just
going
to
walk
down
this
dashed
line
here
you
know
on
the
largest
scales
we
have
you
know
circulations
associated
with
the
asian
summer,
monsoon
on
the
seasonal
time
scale
and
the
planetary
time
space
scale.
So
that's
planetary
means
it's
the
sizes
of
the
size
of
the
earth.
So
it's
about
10
to
the
fourth
kilometers
and
we
walk
down
here.
We
have
undulations
in
the
jet
stream.
I
don't
know
if
you
guys
have
looked
at
weather
maps
looked
at
jet
stream.
B
B
So
you
have
the
you
know,
big
intersectional
oscillations
and
in
the
tropics
down
to
the
supercells
down
to
individual
score
lines.
Now
they
all
go
in
sizes,
from
thousands
of
kilometers
all
the
way
down
to
to
a
few
kilometers
and
then
on
the
smaller
scales.
You
have
these
small
cumulate
clouds
that
form
from
turbulent
eddies
and
the
boundary
they
lift
the
air
high
enough
up
that
you
have
condensation
occurring.
B
So
that's
down
at
the
millimeter
scale,
so
it's
kind
of
just
to
give
an
idea
of
the
different
phenomena
we
need
to
represent
in
one
way
or
another,
and
one
thing
that's
very
important
to
notice
here
that
everything
happens
on
this
continuum
of
scales.
There's
no
clear
scale:
separation
in
this
system
here,
which
makes
it
very
very
challenging
to
model.
B
There
also
some
other
curves
on
this
plot
here.
Those
are
gravity
waves
and
internal
acoustic
waves
in
gravity
waves.
There
can
be
several
sources:
they
can
come
from
the
orography
that
can
be
triggered
by
convection
there's
a
lot
of
release
of
latent
energy
that
sets
up
these.
These
gravity
waves
that
propagate
really
fast.
B
Some
equations
of
motion
also
the
support
acoustic
waves
of
sound
waves,
and
these
waves
here
are
not
energetically
that
significant.
The
reason
why
I
mentioned
them
to
you
is
from
a
numerical
methods,
point
of
view.
These
can
limit
the
maximum
time
step.
We
can
take
in
the
model
to
make
sure
it
doesn't
blow
up.
So,
even
though
we
might
not
care
about
acoustic
waves,
they're,
not
really
that
important,
they
they're
kind
of
a
headache
when
you
do
miracle
discretizations.
B
So
if
I
mark
here
the
resolutions
that
global
models
will
typically
run
at
so
the
gray
area
here
it
would
be
like
the
one
kilometer
scale
or
sorry.
One
degree
scale
on
a
kilometer
scale
in
space
and
time
is
about
30
minutes.
If
I
put
the
highest
resolution,
we
typically
run
at
so
goku
talked
about
the
ihas
project
that
would
be
run
at
25
kilometers.
B
B
Kind
of
the
big
thing
that's
going
on
in
the
global
modeling
community
is
now
that
we
can
get
down
to
roughly
three
kilometer
resolution.
We
can
actually
explicitly
resolve
some
of
the
deeper
convections
if
you're
interested
in
that
you
know,
look
up
these
diamond
simulations
that
is
taking
up
a
lot
of
attention
in
our
community.
B
Alrighty
in
terms
of
model
code,
we
we
artificially
or
somewhere
artificially
separate
things
into
two
modules.
So
we
have
the
dynamical
core
that,
roughly
speaking,
solves
the
equations
of
motion
associated
with
thermodynamics
and
on
resolved
scales,
and
then
everything
else
is
taken
care
of
by
the
primarization,
so
that
will
be
radiation
turbulence,
etc.
Everything
we
can't
do
in
the
dynamical
core.
B
There
are
several
approaches
here:
one
is
called
process
split,
so
that
means
that
each
of
the
parameterizations,
the
gravity,
waves,
convection
and
so
on.
They
all
given
the
same
resolved
scale
state
of
the
atmosphere
and
then
they
compute
their
tendencies.
Based
on
that,
the
other
approach
is
called
time
split.
This
was
used
in
the
finite
volume
chord
that
you
guys
would
be
going
to
be
using
and
that's
where
each
parameterization
updates
the
state
and
then
that
updated
state
is
given
to
the
next
personalization.
B
This
topic
here
didn't
use
to
get
a
lot
of
attention
in
our
community,
but
it's
there's
some
renewed
interest
in
it.
So
there's
a
conference
series
called
physics
dynamics,
coupling
of
focus
and
on
these
kinds
of
issues,
and
it's
it's
my
favorite
conference
every
18
months,
it's
a
pretty
small
nerdy
community,
but
it's
taking
on
some
some
pretty
interesting
problems
and
global
modeling.
B
B
Finite
volume
down
paul
uses
a
lat,
regular
latitude
longitude
grid,
which
is
shown
on
the
on
the
figure
here
and
here's
the
command
we
use
to
to
set
up
the
model
to
run
with
that
grid.
So
this
rest
dash
res
option.
Here
you
set
it
to
f09
f49
mg17,
then
you,
the
atmosphere,
will
run
on
this
one
degree
grid.
B
We
also
have
other
dynamical
cores,
I'm
just
quickly.
Gonna
gonna
show
you
how
you
could
specify
the
grids
for
those.
So
one
of
our
newer
dynamical
cores
that
I'll
talk
about
more
a
little
bit
later
is
called
the
spectral
element,
dynamical
core,
with
a
variant
called
sec,
slam
that
uses
a
a
different
transport
scheme
and
then
spectral
elements
and
again
it's
set
up
with
these
commands
here
and
we're
not
the
way
we
specify
resolution
is
kind
of
relates
to
how
the
discretization
grid
is
is
defined.
B
B
B
B
We
also
have
a
newer
dynamical
core
in
here.
It's
called
model
for
prediction
across
scales.
It's
defined
on
this
virani
tessellation
of
the
spheres
shown
down
here
here.
The
resolution
is
specified
in
terms
of
kilometers,
so
it's
about
120,
kilometer
resolution
mesh
I'll
provide
some
more
details
about
that.
Dicor
later
then,
we
also
have
the
fv3
dynamical
core
in
here.
It's
loosely
speaking
a
cube
sphere
version
of
the
finite
volume
dynamical
core,
that's
what
the
national
weather
service
is
used
for
its
global
weather
forecast.
So
we
have
a
version
of
that
within
cesm.
B
B
B
There's
also
a
lot
of
performance
comparison
happening
in
in
in
the
community
and
when
I
mean
performance
is
computational
performance
and
again
you
can
do
an
apples
to
apples
comparison
here,
running
everything
within
cesm,
it's
hard
to
compare
computational
performance
across
modeling
systems
and
on
different
platforms,
and
then
last
but
not
least,
you
know
this
facilitates
or
enables
numerical
methods
research,
if
you're
interested
in
that
we've.
Actually
one
example
where
we
ported
numerical
methods
from
one
dicor
to
to
the
other.
B
That
means
we
define
our
vertical
levels
in
terms
of
these
hybrid
coefficient,
the
a's
and
b's
here,
then
we
have
a
p0
here
which
is
constant
and
then
the
surface
pressure
here
so
near
the
surface.
The
b
here
is
one
a
is
0,
so
that
means
our
lowest
layer.
Here
will
just
follow
surface
pressure,
meaning
it
will
just
follow
whatever
the
orography
looks
like
as
we
go
higher
up
in
the
atmosphere,
the
bees
get
smaller
and
smaller
towards
zero
and
then
a
become
a
move
towards
one.
So
you
have
pressure
levels
aloft.
C
B
Floating
lagrangian
vertical
coordinate,
so
that
means
that
the
vertical
coordinate
are
material
surfaces.
So
if
you
think
of
two
coordinate
surfaces
sitting
like
this
and
you
have
convergence
of
air
coming
in
these
are
material
surfaces,
they
all
just
expand.
You
have
divergence,
they
will
contract,
as
shown
on
the
figure
right
here.
So
you
see
they
start
deforming.
B
The
advantage
of
doing
this
is
that
you
only
need
2d
numerical
methods,
because
the
vertical
coordinate
just
moves
up
and
down
according
to
the
flow
there's
no
flow
across
the
boundaries.
So
you
only
need
2d
methods,
that's
what
makes
this
very
attractive,
but
the
problem
is
with
lagrangian
methods.
B
B
In
terms
of
vertical
levels,
we've
kind
of
been
a
little
behind
the
curves.
We
only
had
26
levels
in
our
cam
4
configuration,
cam,
5,
32
and
cam
6,
or
I
think
it
was
only
30
in
cam,
5
and
cam
6,
which
is
the
latest
generation.
We
have
32
levels
and
the
latest
cutting
edge
model.
We're
working
on
right
now
has
about
80
or
90
levels
and
a
much
higher
lid
than
we
currently
have
again.
You
can
change
this
with
these.
These
commands
we'll
learn
more
about
later,
just
a
little
warning.
B
If
you
do
change
either
horizontal
or
the
vertical
resolution,
you
need
to
provide
a
new
initial
condition
file
and
our
physics
package
is
very
sensitive,
especially
to
vertical
resolution,
so
you
might
have
to
re-tune
the
model
which
is
a
non-trivial
exercise,
but
functionally
everything
is
there
for
you.
If
you
want
to
change
these
things,.
B
Alrighty
the
story
so
far,
I've
talked
about
defining
grid
scale
and
subgrid
scale
resolved
from
hundred
skulls
waves.
We've
looked
at
the
of
the
space-time
overview
of
different
phenomena
in
the
atmosphere
as
an
important
I've
defined
horizontal
vertical
grids
for
you
now
it's
time
to
look
at
the
dynamical
core
in
terms
of
equations
and
it's
helpful
to
take
a
step
back
and
and
and
look
at
like
what
equations
are
we
using?
What
is
the
thermodynamics
we're
using
and
what
approximations
and
assumptions
are
we
making.
B
So,
in
terms
of
of
a
single
component
fluid
the
most
advanced
equations
that
we
have
is
the
compressible
euler
equations.
I
won't
show
them
here,
but
we
make
a
series
of
assumptions
to
simplify
this
equation,
set
for
global
models,
we're
actually
in
the
process
of
undoing
these
assumptions
now,
but
these
are
the
ones
that
are
used
in
in
the
finite
volume
and
spectral
element
that
have
the
course.
So,
first
of
all,
we
make
the
spherical
geoid
approximation,
which
basically
is
saying
that
gravity
only
acts
radially,
and
that
also
means
you're.
B
Assuming
that
earth
is
a
sphere
which
we
know
it's
not
but
close
to
being
a
sphere,
then
we
make
what's
called
the
quasar
hydrostatic
assumption.
That
means
we
replace
the
vertical
momentum
equation
with
a
diagnostic
balance.
That's
the
balance
shown
here.
It's
rho
is
density,
g
is
gravity
and
we
have
the
partial
derivative
with
respect
to
off
pressure
with
respect
to
z,
that's
called
the
hydrostatic
approximation,
it's
pretty
good
approximation
down
to
10
kilometers,
and
then
it
starts
breaking
down.
B
That
means,
basically,
if
you
think,
of
the
grid
cells
coming
out
of
a
sphere
that
would
come
out
like
this
straight
out.
We
basically
assume
that
the
area
of
each
of
the
cells
as
you
go
up
just
have
the
same
area
so
they're,
basically
a
column
like
this.
Instead
of
columns
like
this
that
get
much
bigger
as
you
go
higher
up,
it's
a
good
approximation
for
for
low
top
modeling,
but
when
we
go
to
the
geospace
model,
this
is
not
a
great
approximation
to
make
several
dicors
are
moving
away
from
these
approximations.
B
So
the
m
pass
model
that
we
have
does
not
have.
The
the
hydrostatic
assumption
is
a
fully
non-hydrostatic
compressible
euler
equation
model,
and
there
is
a
lot
of
work
by
several
group
in
including
here
at
encar
to
get
rid
of
this
shallow
atmosphere
approximation,
but
it
makes
a
lot
of
things
very
complicated
to
get
rid
of
that.
One.
B
That's
in
terms
of
kind
of
the
the
dynamics
of
the
system.
A
very
very
important
component
of
system
is
the
thermodynamics
of
the
system.
So
we
don't
just
transport
around
or
solve
the
equation
of
motion
for
dry
air.
We
we
have
to
include
water,
vapor
and
all
the
other
forms
of
water
in
the
system.
So
let's
define
what
I
mean
when
I
say
a
moist
air
paracel,
so
it
has
water
vapor
in
it.
That's
a
gaseous
phase
of
of
water
as
the
most
abundant
form
of
water
in
the
atmosphere.
B
Then
we
have
liquid
water.
It
can
exist
in
many
forms,
so
we
have
them
as
cloud
liquid.
For
example,
then
we
have
frozen
forms
of
water,
so
different
forms
of
ice.
It
can
be
in
the
form
of
rubble
or
snow
or
something
like
that.
So
everything
on
the
items
two
and
three
here
they
all
condensate,
they're,
not
gases,
they're,
very
different,
thermodynamic
properties,.
B
Associated
with
with
this
is
stepping
back
and
asking
what
what
approximations
are
we
making
in
the
thermal
and
thermodynamics
here
so
first
of
all,
we're
assuming
that
a
specific
volume
and
condensate
is
zero.
They
don't
occupy
any
any
area
or
any
volume
of
the
cell.
It's
a
pretty
good
approximation,
we're
also
really
lucky
in
the
atmosphere.
The
the
for
the
most
part,
air
obeys
the
ideal
gas
law.
So
it
means
that
pressure
is
related
to
density
and
temperature.
With
this
equation
free
here,
oceanographers
do
not
have
this
privilege.
B
B
B
B
B
Typically,
modeling
groups
make
approximations
to
some
thermodynamic
quantities.
Take
equation
four
here
where
people
simplify
that
equation
somewhat,
but
one
thing
that
can
happen
is
you
can
actually
violate
basic
thermodynamic
law
such
as
the
first
and
second
law
of
thermodynamics.
When
doing
so
so
there
is
a
movement
now
in
our
community,
like
the
cutting
edge
movement,
now
is
looking
into
using
what's
called
thermodynamic
potentials
and
the
cool
thing
about
those
and
oceanographers
use.
These
is
that
you
can
derive
all
thermodynamical
variables
from
there
and
you
make
sure
everything
is
consistent.
B
If
we
don't
have
that
and
we
run
climate
simulation,
we
can
just
get
runaway
effects
in
the
system
and,
if
you're,
if
you're
interested
in
that,
we
just
submitted
an
article,
I'm
really
excited
about
I'm
sorry,
it's
a
hundred
pages,
but
it's
written
in
a
quite
a
pedagogical
form
introduction
to
introducing
the
concept
of
energy
and
energy
budgets
and
in
the
climate
system.
So
if
you're
interested
have
a
look
talk
to
me
all
right,
so
we're
making
all
of
these
assumptions
so
all
the
dynamic
assumptions.
B
B
B
So
if
you
have
divergence,
you
know
this
will
reduce
in
size.
If
you
have
convergence,
it
will
increase
similarly
for
the
tracers
here
and
then
we
have
a
momentum
equation.
I
won't
go
too
much
into
detail
with
then
the
finite
volume
core
casts
the
thermodynamic
equation
in
terms
of
potential
temperature
and
the
beauty
of
doing
that
is.
It
takes
exactly
the
same
form
as
your
continued
equation,
so
you
solve
it
with
the
same
numerical
method,.
B
So
the
finite
volume
dynamical
course
solves
this
system
using,
what's
called
an
eulerian
finite
volume
method.
Just
to
give
you
an
idea
of
what
that's
about,
let's
illustrate
on
the
next
couple
of
slides
here.
So
what
we
do
is
we
we
take
the
equation
of
motion,
and
this
creates
the
continuous
equation
for
air
finite
volume
means
we
integrate
over
a
control
volume
over
a
finite
volume,
as
shown
up
here.
Has
the
area
delta
a
pressure
level
thickness
dp.
B
B
Then
we
also
discretize
in
time,
so
this
was
just
in
space.
Now
we
discretize
this
guy
on
the
left
hand,
side,
and
it
basically
says
you
know
the
new
value
of
pressure
level
thickness
minus
the
old
one
has
to
equal
the
time
integral
of
these
instantaneous
fluxes
over
the
time
step,
I
always
like
to
show
things
in
a
graphical
way.
This
is
the
way
I
like
to
view
things
and
again
I
have
done
a
lot
of
research
on
lagrangian
methods.
B
B
The
continuous
equations
say
mass
over
this
area
should
equal
mass
over
this
area
and
you're
done.
When
you
do
an
eulerian
flux
form.
Discretization
of
this,
you
can
visualize
the
fluxes
like
this.
This
gray
area
here
is
exactly
the
same
that
I
showed
on
the
right
hand,
side
here
and
this
yellow
area
here
after
one
time
steps
get
pushed
through
this
cell
wall
over
here
in
one
time
step.
B
B
The
lin
root
scheme
is
a
dimensionally
split
scheme,
so
it
makes
use
of
one-dimensional
operators
if
you're
interested.
There
are
some
extra
slides
here
showing
the
details
of
this
that
I
won't
go
through.
You
can
ask
me
about
them
later,
if
you
want
to
so
I'll
just
flip
through
them
here
about
those
details.
B
C
B
Hydrostatic
system
and
a
low
top
or
stability
criteria
is
gravity
waves
that
moves
about
342
meters
per
second,
so
we're
limited
in
time
step
for
this
equation
by
that
the
continued
equation
for
tracers
only
depends
on
the
fastest
winds
in
your
system.
So
if
you
have
a
relatively
low
top,
that's
not
that's
slower
than
342
meters
per
second.
So
that
means
that
this
equation
here
we
can
solve
with
a
longer
time
step.
That's
a
really
big
deal
in
our
system
because
we
have
lots
of
tracers.
B
B
And
again,
I've
I
used
to
go
through
the
details
of
all
of
that.
I
don't
have
time
for
that
that
I
put
those
slides
in
the
appendix,
because
you
have
to
be
careful
that
you
know
don't
violate
important
criteria.
For
example,
you
need
to
make
sure
that
you
preserve
a
constant,
for
example,
meaning
that
if
q
is
one
this
equation
here
has
to
numerically
reduce
to
this
equation
here.
B
So
there's
stuff,
you
need
to
consider
when
you
run
things
on
different
time,
steps
momentum
equation.
I
won't
go
into
the
details,
but
just
think
of
it
that
we
we
solve
that
equation
with
these
gamma
operators.
That,
at
the
end
of
the
day,
again,
is
a
combination
of
these
1d
operators
that
we
use
for
advection
as
well,
and,
as
I
mentioned,
the
phone
dynamic
equation,
we're
lucky.
B
It
looks
like
the
continuity
equation,
so
same
numerical
method
there
as
well,
so
this
equation
set
here
has
no
at
this
point
no
explicit
diffusion
operators
to
control
our
model
at
the
grid
scale
and
the
way
this
model
is
formulated.
We
have
control
over
vorticity
at
the
grid
scale
through
implicit
diffusion
in
our
operators,
but
we
don't
have
control
over
divergence
and
I'm
going
to
show
that
on
this
plot
here
this
is
an
total
kinetic
energy
spectra.
So
that's
what
I
showed
on
a
schematic,
the
schematic
on
the
right
hand.
B
B
If
we
do
that-
and
we
get
the
blue
lines
here,
we
see
we
tail
off
and
quote-unquote
in
a
good
way
like
we
don't
have
spurious
accumulation
of
the
grid
scale
again,
you
can
go
in
here
and
then
you
can
estimate
what
the
effective
resolution
to
finite
volume
dynamical
core-
and
you
see
it
actually
starts
to
deviate
from
this
minus
three
curve.
Quite
early
on
or
at
quite
large
scales.
B
C
B
B
B
That
does
not
lend
itself
very
well
for
like
two
day
2d
domain
decomposition
of
this
domain
here
and
it's
a
similar
story
for
spherical
moniks.
That
used
to
be
very,
very
popular,
they've
dominated
for
a
very
long
time,
but
you
have
to
do
these
led
hundreds
transforms
that
are
very
hard
to
scale
out.
That
said,
you
know
when
I
was
taking.
My
phd
people
were
talking
about
the
eminent
depth
of
the
spherical
transform
method.
Here
I
am
many
years
later,
these
and
wf
are
still
using
them.
So
it's
a
very
hard
meth
to
kill.
B
So
what
we
have
done
in
in
as
a
community
as
a
whole
as
we
move
to
more
isotropic
grids,
that
means
that
the
grid
cell
sizes
are
more
or
less
the
same
size
again
as
whether
you
like
rice
or
pasta.
I
guess
some
people
have
really
gone
off
the
cube
sphere
grid.
Some
people
really
like
the
boronia
grid,
they're
groups
in
japan
that
are
using
this
lat
long
grid.
Where
you
take
two
lat
long,
grits
chop
up,
the
poles
rotate
one
glue
them
together,
like
a
baseball.
B
B
B
The
finite
volume
core
here
the
quarter
degree
is
it
does
really
well
in
the
beginning
and
then
there's
not
enough
work
to
do
our
masses.
Passing
takes
over
the
computational
overall
computational
cost
of
the
model,
but
then,
if
we
use
a
cube
sphere
model
like
the
spectral
element
model
here,
you
see
the
thing
just
keeps
scaling,
so
it
means
the
more
you
throw
at
it
in
terms
of
computational
resources,
the
faster
you
get
your
solution,
however,
do
note
that
you
know
if
you
don't
only
have
a
small
cluster
available,
you
get
way
more
throughput.
B
Okay,
I
mentioned
all
these
different
cores
here
before
here's
just
some
more
details
and
and
references
if,
if
you're
interested,
as
I
said
in
cam
right
now,
all
eyes
are
a
lot
of
eyes
on
the
spectral
element:
dynamical
core:
that's
the
next
generation
dicor
we
have
the
most
experienced
with
it
was
developed
as
a
collaboration
between
doe
and
ncar.
Before
I
joined
ncar,
it
has
some
nice
properties.
It's
mass
conservative,
as
are
the
other
dynamical
cores,
but
also
has
really
good.
Energetics
conserves
angular
momentum
really
well
important
for
super
rotating
planets.
B
We
don't
know
how
important
it
is
for
for
earth.
We've
been
using
it
for
a
long
time
for
high
resolution
climate
now
we're
trying
to
make
it
the
one
degree
default
and
then,
as
I
alluded
to
earlier,
we
also
have
this
option
for
a
more
accurate
and
faster
transport
scheme
that
we're
using
the
mpas
model.
It's
developed
here
at
end
car
in
the
m
cubed
lab
again.
This
was
developed
at
the
weather
scale.
B
So,
if
you're
going
beyond
you
say
down
to
three
kilometers,
you
definitely
you
need
to
use
a
dicor
like
this
one
and
then,
as
I
mentioned,
we
also
have
impasse
in
here.
Unfortunately,
we
didn't
have
funding
to
do
the
non-hydrostatic
version,
so
we're
only
supporting
the
hydrostatic
version
of
fv3
in
our
system.
B
That
means
you
can
increase
the
horizontal
resolution
over
your
area
of
interest
and
with
the
csm2
we
have
functional
support
for
free
grids.
That
means
they
run
out
of
the
box.
You
don't
need
to
make
your
own
boundary
data
sets
and
whatnot
here's
the
conus
that
the
gokan
mentioned.
Here's
the
arctic
grip,
25
kilometers
over
the
arctic
and
then
here
one
that
refines
down
to
about
10
kilometers
over
greenland.
B
Just
a
little
word
of
warning,
please
don't
use
the
2
2
release
with
spectral
elements.
Please
use
cam
development
because
we
found
several
bugs
in
that
release
related
to
the
numerix
all
due
to
me.
Actually,
so,
please
use
newer
code
bases
if
you
want
to
run
this
dynamical
core,
just
a
little
short
success
story
of
variable
resolution,
so
I
didn't
mention
this,
but
it's
really
really
hard
to
make
or
to
have
our
physics
permittizations
at
least
some
of
them
to
be
well
behaved
across
this
scale.
B
Some
of
the
permanentizations
were
developed,
making
assumptions
statistical
assumptions,
for
example
with
mass
flux,
convection
schemes.
You
want
the
updrafts
to
only
be
a
very
small
part
of
your
your
grid
cell.
When
you
go
down
to
really
high
resolution,
some
of
these
assumptions
may
start
breaking
down
and
we
go
into
what's
called
the
gray
zone,
we're
kind
of
resolving
convection
but
kind
of
not
called
the
gray
zone,
and
this
will
happen
if
you
go
down
to
high
enough
resolution.
B
Also,
we
tune
a
lot
of
our
parametrizations
at
one
degree
and
that
tuning
might
not
work
well
for
high
resolution.
So
in
terms
of
variable
resolution,
I
think
the
dynamical
core
problem
has
been
solved.
We
have
whale
behave,
solutions
across
scales
in
terms
of
physics,
that's
where
a
lot
of
emphasis
is
right
now
and
that's
a
really
really
challenging
problem.
B
B
Longer
story
short
when
we
go
down
to
the
higher
resolution
25
or
10k
these
curves
down.
Here
we
match
this
high
resolution
regional
model
of
the
green
line,
whereas
the
one
degree
solutions
are
off
by
quite
a
bit.
So
it's
a
cool
thing
we're
resolving
what
needs
to
be
resolved
over
greenland
to
get
this
part
of
the
problem
right.
B
If
you
want
to
use
or
make
your
own
variable
resolution
grid,
we
put
a
lot
of
effort
in
to
make
this
easier
note
easier.
It's
not
easy
doesn't
really
run
out
of
the
box,
but
we
can
help
you
there's
a
github
repo
repository
repository,
send
up
by
patrick
callahan
here
at
ncar,
and
this
pdf
here
is
basically
a
cookbook
of
how
to
set
things
up,
and
it
has
like
this
gui
here
where
you
you
manually,
show
you
know
what
area
do
I
want
to
refine
so
there's
an
example
of
the
atlantic.
B
B
So
look
at
that
website
if
you're
interested
in
making
your
own
grids
and
remember
you
have
to
also
then
make
other
data
that
goes
into
the
model
needs
to
be
mapped
to
this
grid
and
so
on,
there's
a
lot
of
work
on
making
this
a
lot
easier.
I
just
want
to
make
the
point
that
you
know
you
won't
be
up
and
running
in
one
day:
it'll
take
a
little
longer.
B
That's
the
one
I
used
when
I
went
to
I
went
to
grad
school.
However,
it
doesn't
really
go
into
some
of
the
complexities
we
have
with
with
global
models.
So
I
have
another
book:
apologies
for
the
self-promotion!
I
don't
get
any
money
out
of
this,
but
we
had
a
colloquium
here
back
in
2006,
where
all
the
lectures
were
written
written
up
as
chapters
and
that
book
goes
more
into
a
lot
of
the
details
of
of
what
goes
into
designing
a
global
model.
C
C
Yeah
I
had
a
question
about
the
non-hydrostatic
dynamical
cores
that
you
showed
so
at
that
point
when
you're
resolving
the
compression
of
like
the
air
or
water,
whatever
fluid
and
now
you're
having
sound
acoustic
waves.
Does
that
sort
of
impose
a
barrier
of
the
time
step?
But
you
have
to
like
make
them
so
small
now,
because
you
have
to
resolve
these
very
fast
waves.
B
Yeah,
so
in
the
case
of
the
mpas
dynamical
core,
most
people
use
an
implicit
solver
in
the
vertical.
So
implicit
means
you
can.
You
can
run
longer
time
steps
in
the
vertical
than
with
explicit
representation
and
then
in
the
horizontal,
there's
sub
stepping
solving
for
the
the
faster
terms
and
equation
of
motion.
So
the
dynamic
record
is
like
a
hierarchy
of
time
step
but
over
the
acoustic
modes
to
take
very
short
time,
steps
to
make
sure
that
the
model
is
stable.
B
That's
that's
a
really
good
point
that
I
didn't
mention
the
way
we
currently
run.
These
variable
resolution
model
is
we
we
run
them
as
if
we
had
the
high
resolution
everywhere.
So
that
means
we
set
the
time
step
to
whatever
is
stable
in
the
high
resolution
area,
but
that
means
you
run
the
low
resolution
area
with
very,
very
small
time
steps.
B
But
if
you
look
at
it
from
a
computational
cost
point
of
view,
unless
your
refinement
area
is
super
super
small,
it's
still
like
ninety
percent
of
the
computational
cost
is
in
the
high-res
area.
So
you
get
the
global
solution
basically
for
free,
but
the
tough
thing
that
to
put
some
work
into
is
that
we
also
run
physics
at
a
time
step.
We
we
would
run
it
at
as
if
we
are
running
at
the
highest
resolution
everywhere,
and
that
means
we
are
running
physics
in
the
low
resolution
area.
At
that
time
step.
B
A
Thanks
peter,
that
was
excellent.
I
guess
introduction
and
understanding
of
the
framework
on
which
the
atmospheric
dynamics
are
working.
You
know
looking
looking
at
fluid
mechanics
and
thermodynamics
and
understanding
the
perspective
after
the
break,
we're
going
to
be
going
into
what's
called
the
physics
of
the
model,
looking
convection
and
other
components
by
rich
neal.
It's
now,
I'm
going
to
say
15
minutes
break.
So
what
we'll
do
is
come
back
at
20.
I
think
it's
10
at
10
40.,
so
get
her
get
some
more
coffee.