6bf51e0a-6b43-476b-bfeb-38a3b9e363a8 120 3 5 false true 0 7 decimal

&[DATE] &[TIME] - &[FILENAME]

Optimal distribution of interpolation points

Thermodynamic Formulae

saturation steam pressure above water or ice

hPa 100 Pa * :

T E.w e 6096.9385 - T / 16.635794 + 2.711193 102 -^* T * - 1.673952 105 -^* T 2^* + 2.433502 T ln * +^:

T E.i e 6024.5282 - T / 24.7219 + 1.0613868 102 -^* T * + 1.3198825 105 -^* T 2^* - 0.49382577 T ln * -^:

ϑ E ϑ K / E.w hPa * ϑ 0.01 °C * ≥ (ϑ 100 °C * ≤ (& ϑ K / E.i hPa * ϑ 100 - (°C * ≥ (ϑ 0.01 °C * < (& not defined cases :

put together
for water and ice

t f 1.0047 t 50 - (°C * ≥ (t 60 °C * ≤ (& not defined cases :

Enhancement factor

Formula to be interpolated:
Saturation steam pressure in humid air

ϑ E.l ϑ E ϑ f * :

Test

20 °C * E hPa 23

20 °C * E.l 2350 Pa *

20 °C * - E.l not defined 2^

Temperature range from

T.min 25 - (°C * :

T.max 60 °C * :

number of points

n 120 :

wanted: list of temperature points that produce the best fit for

E.l

Parameters of the method

Sampling point of the reference curvature in the first interval

f 0.15 :

Exponent in the step scaling formula

p 0.45 :

Centering shift

s 0.6 - :

Initial step

h.0 14 :

Number of points

n 20 :

Start point

x.0 0 :

Function to interpolate

x f x 273.15 + E.w :

Curvature

x κ x 273.15 + E.w x 2 diff :

X 1 el x.0 :

X 2 el X 1 el h.0 + :

1 κ h.0 * 0.423

κ.0 X 1 el f h.0 * + κ : 0.0321

j 2 n 1 - (range X j 1 + el X j el h.0 κ.0 X j el κ / (p^* + : for

X n el 102

Adjust initial step and number of points such that the range is covered

F X f vectorize eval :

X F s + x linterp x f - X 0 + augment 2 1 sys

Martin Kraska