<s>
The	O
Semi-Lagrangian	B-Application
scheme	I-Application
(	O
SLS	O
)	O
is	O
a	O
numerical	B-Algorithm
method	I-Algorithm
that	O
is	O
widely	O
used	O
in	O
numerical	B-General_Concept
weather	I-General_Concept
prediction	I-General_Concept
models	O
for	O
the	O
integration	O
of	O
the	O
equations	O
governing	O
atmospheric	O
motion	O
.	O
</s>
<s>
A	O
Lagrangian	O
description	O
of	O
a	O
system	O
(	O
such	O
as	O
the	O
atmosphere	O
)	O
focuses	O
on	O
following	O
individual	O
air	O
parcels	O
along	O
their	O
trajectories	B-Application
as	O
opposed	O
to	O
the	O
Eulerian	O
description	O
,	O
which	O
considers	O
the	O
rate	O
of	O
change	O
of	O
system	O
variables	O
fixed	O
at	O
a	O
particular	O
point	O
in	O
space	O
.	O
</s>
<s>
A	O
semi-Lagrangian	B-Application
scheme	I-Application
uses	O
Eulerian	O
framework	O
but	O
the	O
discrete	O
equations	O
come	O
from	O
the	O
Lagrangian	O
perspective	O
.	O
</s>
<s>
There	O
are	O
ways	O
round	O
this	O
,	O
such	O
as	O
the	O
technique	O
known	O
as	O
Smoothed	B-Application
Particle	I-Application
Hydrodynamics	I-Application
,	O
where	O
a	O
dependent	O
variable	O
is	O
expressed	O
in	O
non-local	O
form	O
,	O
i.e.	O
</s>
<s>
Semi-Lagrangian	B-Application
schemes	I-Application
avoid	O
the	O
problem	O
of	O
having	O
regions	O
of	O
space	O
essentially	O
free	O
of	O
parcels	O
.	O
</s>
<s>
Semi-Lagrangian	B-Application
schemes	I-Application
use	O
a	O
regular	O
(	O
Eulerian	O
)	O
grid	O
,	O
just	O
like	O
finite	O
difference	O
methods	O
.	O
</s>
<s>
The	O
references	O
listed	O
contain	O
more	O
details	O
on	O
how	O
the	O
Semi-Lagrangian	B-Application
scheme	I-Application
is	O
applied	O
.	O
</s>
