Problem Set 1
Global Environmental Interactions
ERS 60 Winter 2003
PROBLEM 1
The solar radiation incident upon Earth’s surface plays a vital role in a number of global
environmental interactions and processes, including, for example, climate, evaporation and
condensation, freezing and thawing of soils, and photosynthesis. These processes depend to a
large degree on the intensity of solar radiation, which is a function of latitude, time of year and
time of day. The rate of energy transfer from the Sun is called the solar flux. The solar flux
incident on a unit surface area can be approximated by
S=S0 cosθs
where,
S = solar flux per unit area
S0 = solar constant = 1372 Watts per meter squared (W/m2)
θs = solar zenith angle
a) Show with a diagram and calculate the solar zenith angle, which, recall, is defined as the
angular displacement of the sun from the vertical, at summer solstice and the solar flux for the
following two locations: (1) Jokkmokk, Sweden and (2) Recife, Brazil.
b) At what latitude(s) is the solar flux zero at winter solstice?
c) Repeat your calculations of solar zenith angle and solar flux at the two locations at the fall
equinox.
PROBLEM 2
Heat capacity is the amount of heat energy required to increase the temperature of one gram of a
substance by one degree Centigrade. Because water has a much higher heat capacity than land,
the oceans have a strong moderating influence on both regional and global climate (See, for
example, Fig. 5-7 and Fig. 5-13 in Geosystems). This influence is clearly evident over the
continental United States, where, on average, winter temperatures are colder and summer time
temperatures warmer in the Midwest than on the coasts. For example, Omaha and San Francisco
are at about the same latitude, yet temperatures in Omaha average 10°C lower in January, and
100C higher in July than in San Francisco.
The importance of heat capacity is illustrated by the following example. Consider two adjacent,
but isolated boxes each having the dimensions (30 cm)×(40 cm)×(3 cm). One box is filled with
water of density 1.00 grams per cm3, and the other box is filled with dry soil of density 1.20 grams
per cm3. The heat capacity of the water is four times that of the soil. Both boxes are heated by
the sun. Initially the water and soil are at 200C, and each have uniform temperatures throughout
their respective volumes. Calculate the temperature of the soil if after 4 hours the
