<s>
Taylor	B-Application
diagrams	I-Application
are	O
mathematical	B-Application
diagrams	I-Application
designed	O
to	O
graphically	O
indicate	O
which	O
of	O
several	O
approximate	O
representations	O
(	O
or	O
models	O
)	O
of	O
a	O
system	O
,	O
process	O
,	O
or	O
phenomenon	O
is	O
most	O
realistic	O
.	O
</s>
<s>
It	O
is	O
used	O
to	O
quantify	O
the	O
degree	O
of	O
correspondence	O
between	O
the	O
modeled	O
and	O
observed	O
behavior	O
in	O
terms	O
of	O
three	O
statistics	O
:	O
the	O
Pearson	O
correlation	O
coefficient	O
,	O
the	O
root-mean-square	B-General_Concept
error	I-General_Concept
(	O
RMSE	B-General_Concept
)	O
error	O
,	O
and	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
.	O
</s>
<s>
Although	O
Taylor	B-Application
diagrams	I-Application
have	O
primarily	O
been	O
used	O
to	O
evaluate	O
models	O
designed	O
to	O
study	O
climate	O
and	O
other	O
aspects	O
of	O
Earth	O
's	O
environment	O
,	O
they	O
can	O
be	O
used	O
for	O
purposes	O
unrelated	O
to	O
environmental	O
science	O
(	O
e.g.	O
,	O
to	O
quantify	O
and	O
visually	O
display	O
how	O
well	O
fusion	O
energy	O
models	O
represent	O
reality	O
)	O
.	O
</s>
<s>
Taylor	B-Application
diagrams	I-Application
can	O
be	O
constructed	O
with	O
a	O
number	O
of	O
different	O
open	O
source	O
and	O
commercial	O
software	O
packages	O
,	O
including	O
:	O
GrADS	O
,	O
IDL	O
,	O
MATLAB	O
,	O
NCL	O
,	O
Python	O
,	O
R	O
,	O
and	O
CDAT	O
.	O
</s>
<s>
The	O
sample	O
Taylor	B-Application
diagram	I-Application
shown	O
in	O
Figure	O
1	O
provides	O
a	O
summary	O
of	O
the	O
relative	O
skill	O
with	O
which	O
several	O
global	O
climate	O
models	O
simulate	O
the	O
spatial	O
pattern	O
of	O
annual	O
mean	O
precipitation	O
.	O
</s>
<s>
For	O
each	O
model	O
,	O
three	O
statistics	O
are	O
plotted	O
:	O
the	O
Pearson	O
correlation	O
coefficient	O
(	O
gauging	O
similarity	O
in	O
pattern	O
between	O
the	O
simulated	O
and	O
observed	O
fields	O
)	O
is	O
related	O
to	O
the	O
azimuthal	O
angle	O
(	O
blue	O
contours	O
)	O
;	O
the	O
centered	O
RMS	B-General_Concept
error	I-General_Concept
in	O
the	O
simulated	O
field	O
is	O
proportional	O
to	O
the	O
distance	O
from	O
the	O
point	O
on	O
the	O
x-axis	O
identified	O
as	O
“	O
observed	O
”	O
(	O
green	O
contours	O
)	O
;	O
and	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
simulated	O
pattern	O
is	O
proportional	O
to	O
the	O
radial	O
distance	O
from	O
the	O
origin	O
(	O
black	O
contours	O
)	O
.	O
</s>
<s>
It	O
is	O
evident	O
from	O
this	O
diagram	O
,	O
for	O
example	O
,	O
that	O
for	O
Model	O
F	O
the	O
correlation	O
coefficient	O
is	O
about	O
0.65	O
,	O
the	O
RMS	B-General_Concept
error	I-General_Concept
is	O
about	O
2.6mm/day	O
and	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
is	O
about	O
3.3mm/day	O
.	O
</s>
<s>
Model	O
F	O
's	O
standard	B-General_Concept
deviation	I-General_Concept
is	O
clearly	O
greater	O
than	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
observed	O
field	O
(	O
indicated	O
by	O
the	O
dashed	O
contour	O
at	O
radial	O
distance	O
2.9mm/day	O
)	O
.	O
</s>
<s>
These	O
models	O
have	O
relatively	O
high	O
correlation	O
and	O
low	O
RMS	B-General_Concept
errors	I-General_Concept
.	O
</s>
<s>
Models	O
lying	O
on	O
the	O
dashed	O
arc	O
have	O
the	O
correct	O
standard	B-General_Concept
deviation	I-General_Concept
(	O
which	O
indicates	O
that	O
the	O
pattern	O
variations	O
are	O
of	O
the	O
right	O
amplitude	O
)	O
.	O
</s>
<s>
In	O
Figure	O
1	O
it	O
can	O
be	O
seen	O
that	O
models	O
A	O
and	O
C	O
generally	O
agree	O
best	O
with	O
observations	O
,	O
each	O
with	O
about	O
the	O
same	O
RMS	B-General_Concept
error	I-General_Concept
.	O
</s>
<s>
Model	O
A	O
,	O
however	O
,	O
has	O
a	O
slightly	O
higher	O
correlation	O
with	O
observations	O
and	O
has	O
the	O
same	O
standard	B-General_Concept
deviation	I-General_Concept
as	O
the	O
observed	O
,	O
whereas	O
model	O
C	O
has	O
too	O
little	O
spatial	O
variability	O
(	O
with	O
a	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
2.3mm/day	O
compared	O
to	O
the	O
observed	O
value	O
of	O
2.9mm/day	O
)	O
.	O
</s>
<s>
Of	O
the	O
poorer	O
performing	O
models	O
,	O
model	O
E	O
has	O
a	O
low	O
pattern	O
correlation	O
,	O
while	O
model	O
D	O
has	O
variations	O
that	O
are	O
much	O
larger	O
than	O
observed	O
,	O
in	O
both	O
cases	O
resulting	O
in	O
a	O
relatively	O
large	O
(	O
~	O
3mm/day	O
)	O
centered	O
RMS	B-General_Concept
error	I-General_Concept
in	O
the	O
precipitation	O
fields	O
.	O
</s>
<s>
Although	O
models	O
D	O
and	O
B	O
have	O
about	O
the	O
same	O
correlation	O
with	O
observations	O
,	O
model	O
B	O
simulates	O
the	O
amplitude	O
of	O
the	O
variations	O
(	O
i.e.	O
,	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
)	O
much	O
better	O
than	O
model	O
D	O
,	O
resulting	O
in	O
a	O
smaller	O
RMS	B-General_Concept
error	I-General_Concept
.	O
</s>
<s>
Taylor	B-Application
diagrams	I-Application
display	O
statistics	O
useful	O
for	O
assessing	O
the	O
similarity	O
of	O
a	O
variable	O
simulated	O
by	O
a	O
model	O
(	O
more	O
generally	O
,	O
the	O
“	O
test	O
”	O
field	O
)	O
to	O
its	O
observed	O
counterpart	O
(	O
more	O
generally	O
,	O
the	O
“	O
reference	O
”	O
field	O
)	O
.	O
</s>
<s>
Mathematically	O
,	O
the	O
three	O
statistics	O
displayed	O
on	O
a	O
Taylor	B-Application
diagram	I-Application
are	O
related	O
by	O
the	O
error	B-General_Concept
propagation	I-General_Concept
formula	O
(	O
which	O
can	O
be	O
derived	O
directly	O
from	O
the	O
definition	O
of	O
the	O
statistics	O
appearing	O
in	O
it	O
)	O
:	O
</s>
<s>
where	O
ρ	O
is	O
the	O
correlation	O
coefficient	O
between	O
the	O
test	O
and	O
reference	O
fields	O
,	O
E′	O
is	O
the	O
centered	O
RMS	B-General_Concept
difference	I-General_Concept
between	O
the	O
fields	O
(	O
with	O
any	O
difference	O
in	O
the	O
means	O
first	O
removed	O
)	O
,	O
and	O
and	O
are	O
the	O
standard	B-General_Concept
deviations	I-General_Concept
of	O
the	O
reference	O
and	O
test	O
fields	O
,	O
respectively	O
.	O
</s>
<s>
(	O
where	O
a	O
,	O
b	O
,	O
and	O
c	O
are	O
the	O
length	O
of	O
the	O
sides	O
of	O
the	O
triangle	O
,	O
and	O
is	O
the	O
angle	O
between	O
sides	O
a	O
and	O
b	O
)	O
provides	O
the	O
key	O
to	O
forming	O
the	O
geometrical	O
relationship	O
between	O
the	O
four	O
quantities	O
that	O
underlie	O
the	O
Taylor	B-Application
diagram	I-Application
(	O
shown	O
in	O
Figure	O
2	O
)	O
.	O
</s>
<s>
The	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
observed	O
field	O
is	O
side	O
a	O
,	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
test	O
field	O
is	O
side	O
b	O
,	O
the	O
centered	O
RMS	B-General_Concept
difference	I-General_Concept
between	O
the	O
two	O
fields	O
(	O
E′	O
)	O
is	O
side	O
c	O
,	O
and	O
the	O
cosine	O
of	O
the	O
angle	O
between	O
sides	O
a	O
and	O
b	O
is	O
the	O
correlation	O
coefficient	O
( ρ	O
)	O
.	O
</s>
<s>
normalization	O
of	O
dimensional	O
quantities	O
(	O
dividing	O
both	O
the	O
RMS	B-General_Concept
difference	I-General_Concept
and	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
"	O
test	O
"	O
field	O
by	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
observations	O
)	O
so	O
that	O
the	O
"	O
observed	O
"	O
point	O
is	O
plotted	O
at	O
unit	O
distance	O
from	O
the	O
origin	O
along	O
the	O
x-axis	O
,	O
and	O
statistics	O
for	O
different	O
fields	O
(	O
with	O
different	O
units	O
)	O
can	O
be	O
shown	O
in	O
a	O
single	O
plot	O
;	O
</s>
<s>
One	O
of	O
the	O
main	O
limitation	O
of	O
the	O
Taylor	B-Application
diagram	I-Application
is	O
the	O
absence	O
of	O
explicit	O
information	O
about	O
the	O
prediction	O
bias	O
.	O
</s>
<s>
A	O
variant	O
of	O
the	O
Taylor	B-Application
diagram	I-Application
that	O
accounts	O
for	O
the	O
prediction	O
bias	O
is	O
provided	O
by	O
the	O
solar	O
diagram	O
(	O
see	O
,	O
Wadoux	O
et	O
al.	O
,	O
2022	O
)	O
.	O
</s>
