◆ insolation()

static double pism::surface::details::insolation	(	double	solar_constant,
		double	distance_factor,
		double	hour_angle,
		double	latitude,
		double	declination
	)

static

Average top of atmosphere insolation (rate) during the daily melt period, in W/m^2.

This should be equation 5 in Zeitz et al or equation 12 in Krebs-Kanzow et al, but both of these miss a factor of Delta_t (day length in seconds) in the numerator.

To confirm this, see the derivation of equation 2.2.21 in Liou and note that

omega = 2 * pi (radian/day)

or

omega = (2 * pi / 86400) (radian/second).

The correct equation should say

S_Phi = A * B^2 * (h_phi * sin(phi) * sin(delta) + cos(phi) * cos(delta) * sin(h_phi)),

where

A = (S0 * Delta_t) / (Delta_t_Phi * pi), B = d_bar / d.

Note that we do not know Delta_t_phi but we can use equation 2 in Zeitz et al (or equation 11 in Krebs-Kanzow et al) to get

Delta_t_phi = h_phi * Delta_t / pi.

This gives

S_Phi = C * B^2 * (h_phi * sin(phi) * sin(delta) + cos(phi) * cos(delta) * sin(h_phi))

with

C = (S0 * Delta_t * pi) / (h_phi * Delta_t * pi)

or

C = S0 / h_phi.

Parameters

[in]	solar	constant solar constant, W/m^2
[in]	distance_factor	square of the ratio of the mean sun-earth distance to the current sun-earth distance (no units)
[in]	hour_angle	hour angle (radians) when the sun reaches the critical angle Phi
[in]	latitude	latitude (radians)
[in]	declination	declination (radians)

Definition at line 266 of file DEBMSimplePointwise.cc.

References hour_angle().

Referenced by pism::surface::DEBMSimplePointwise::insolation(), and pism::surface::DEBMSimplePointwise::melt().