Deriving Historical TSI Variations from Lunar Borehole Profiles
Guoyong Wen1,2, Hiroko Miyahara3, and Robert F. Cahalan1
1
NASA/Goddard Space Flight Center
2
GEST/University of Maryland, Baltimore Co., 3Nagoya University, Japan
Theoretical Basis for Recovering Historical TSI
Introduction
Satellite observations revealed total solar irradiance (TSI) varies due to solar
activity. Variations in TSI are evident in 11-year cycle of solar activity as well
as sunspot passage. Accurate observations of both TSI and spectral solar
irradiance (SSI) from SORCE satellite are useful for sun-earth climate study.
The sun had experienced a very low inactive time period - Maunder Minimum,
and may have caused a change in Earth’s climate. To reconstruct TSI
variations in centennial time scale is very important in understanding the solar
variation and its impact on Earth’s climate.
The Moon, a coevolving natural satellite of the Earth, without atmosphere,
biosphere, hydrosphere, and human activities is an ideal place for
reconstructing TSI variations in centennial time scale. The Moon is covered by
regolith layer with very lower thermal conductivity and diffusivity. With
undisturbed lunar surface albedo, changes in solar input lead to changes in
lunar surface temperature which diffuse downward to be recorded in the
temperature profile.
Here we present a feasibility study of recovering TSI from lunar borehole
temperature profiles back to Galileo's time.
Apollo Heat Flow Experiments
∂T ∂ 
∂T 
ρ c(T )
=
 k (T )  (1)
∂t ∂z
∂z 
∂T
∂ 2T
= K 2 ( 2)
∂t
∂z
∂T
k (T )
= ε σ T 4 − h (t )(3)
∂ z z= 0
h0
T ( z, t ) = T ( z,0) +
k
d=
z
 2π
KP − d
e cos
t−
2π
 P
KP
penetrationdepth
π
Deriving Historical TSI from Lunar Borehole Profiles
Where ρ is density, c thermal capacity, and k
the thermal conductivity. For temperature
independent thermodynamic properties Eq. (1)
becomes to Eq. (2) with thermal diffusivity of K.
Equation (3) describes boundary condition.
Figure 3. A reference TSI (black)
and a scenario of variation of TSI
in centennial scale (blue).
π
π 
z −  ( 4)
KP
4
For an ideal periodic forcing with amplitude of h0
and period of P, the solution of Eq. (2) can be
expressed as Eq. (4). And penetration depth of
the forcing is proportional to the square root of
the product of diffusivity and the period of the
forcing as show above
Conductivity (W/m/K)
Earth Crust
1.0-1.5
Lunar Regolith
0.01-0.013
(a)
(b)
Diffusivity (10-6m2/s)
0.8-1.2
0.002-0.01
Two heat flow experiments (HFEs) were conducted during Apollo 15 and
17 missions.
Fig. 4(a) Temperature profiles
from current reference TSI at
different latitudes (black: 0o; red
40oS; blue: 80oS).
10000
30day with amplitude of 140(K)
Fig. 4(b) Differences in profiles
computed for the 2 scenarios of Fig 3, at
the same latitudes as in Fig 4(a).
10yr with amplitude of 0.24(K)
1000
500yr with amplitude of 0.14(K)
100
Summary
10
Depth for 0.01K amplitude (m)
1
Lunar soil
10X
100X
Thermal Diffusivity
Figure 1. The left diagram showing emplacement of lunar heat-flow probes at
the Apollo 15 landing site (from Langseth et al., 1972). The results show that
lunar regolith has very low thermal conductivity and diffusivity. The right image
show the Apollo landing sites.
Figure 2. Penetration depth as a function of time for 1X (lower line), 10X
middle line) and 100X (upper line) of lunar regolith diffusivity (left panel)).
The depth for a change of temperature of 0.01K as a function of thermal
diffusivity (right panel)
The Earth’s Moon is an unique place for reconstructing TSI variations
back to Galileo's time. This study shows that the TSI variations over
400 years has a strong signature in borehole temperature profiles.
The solar activity-induced variations of borehole temperature profiles
depend on latitude. For a given latitude, the depth where the
maximum difference occurs determines the time scale of the solar
variation, the amplitude of the the difference gives the strength of
historical change of TSI. Thus borehole temperature profiles can be
used to derive historical TSI variations.