Components of the "climate system"

How much air and water are on the earth, and where?

(This page is not finished. It will be revised after the lecture.)

Physical variables and SI units

Dimension of space, dimension of physical quantities ... different concept.

We live in 3-dimensional space, or 4-dimensional space-time.

3-dimensional space: position of a point can be expressed in 3 real numbers.



Unit of spatial dimensions

Unit of time

Concepts of "weight" and "mass"

Primitive concept "weight", "heavy"

differentiated scientific concepts "gravity", "mass", "density"

Basic roles of mass in physical sciences

SI unit of mass and force

Conservation of mass

"Conservation" in physics is a different concept from the term in "conservation of cultural heritage" or "nature conservation".

No spontaneous generation, no spontaneous decay.

Formulation of conservation of X in isolated systems and open systems


This concept of conservation is useful for "budget analysis", by which we can evaluate quantities which are not directly measurable.

Also, this concept of conservation is used for "prognostic" (i.e. forcasting-type) computations.

The atmosphere

atmosphere vs. air

Vertical temperature profile


thermosphere (ionosphere) ... ionized, not well mixed

troposphere, stratosphere, mesosphere ... electrically neutral, well mixed

Constituents of air

expression of concentration (fraction)

2-component approximation of the atmosphere: "dry air" and water vapor

Atmospheric pressure

Unit: Pa = N/m2, hPa = 100 Pa

Sea level pressure : around 1000 hPa

(Approximate) hydrostatic balance

Approximate vertical distribution of pressure (also density)


What proportion (in terms of mass) of the atmosphere is below 11 km (approx. in the troposphere)?

Density at 1000 hPa ... approx. 1.2 kg/m3 (Note: not g/m3)

Range of "specific humidity" (mass fraction of water vapor) at 1000 hPa ... 0 to 50 g/kg

Vertically integrated mass of water vapor per unit mass (global average)... 25 kg/m2

The Ocean

Ocean vs. seawater ... similar to atmosphere vs. air

Ocean covers 70 % of earth's surface

Maximum depth 11 km, average depth 4 km


2-component approximation "water and salt"

"Salinity": mass of salt / mass of seawater. Typically 35 g/kg

Density of seawater

Density of water 1.0 g/cm3, 1000 kg/m3

At first approximation, density is constant.

For discussion of dynamics, variation of density due to tempearture and salinity is relevant.

Temperature dependence: higher temperature, lower density (thermal expansion).

Note: freshwater (salinity near zero) has abnormal characteristics "higher temperature, higher density" below 4 deg. C. Seawater (salinity near 35 g/kg) does not have this characteristics.

Salinity dependence: higher salinity, higher density.

Inhomogeneity of salinity is mainly caused by input/output of water (rather than input/output of salt).

Vertical divisions and time scales of the ocean

(To be discussed after the energy balance of the climate system)

Snow and ice ... the cryosphere

Water on the earth, hydrological cycle

[Figure from Oki (1999)]

2019-Apr-25 (before lecture)
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