.
Some numbers are too large or too small to express conveniently by writing them out in full. Any number can be written in terms of powers of ten for convenience. For example, a million (1,000,000) can be written as 1x10[6] and three billion (3,000,000,000) can be written as 3x10[9]. In other words, the power of ten appropriate for any number greater than one is one less than the total number of its digits. Fractions can also be written in terms of powers of ten. A thousandth (.001) can be written as 1x10[-3] (that is, 1/10[3]) while a billionth (.000000001) is 1x10[-9].
In this notebook, we approximate most numbers for convenience; it's much easier to focus on the concepts by using, for example, 10 rather than 9.9. We also will avoid using numbers when possible by relying on terms that have specific meanings to us, even though their everyday usage is often more vague. For example, roughly means the number lies within a range of 10% about that number. When we say that there are roughly 10 items, then there could be 9 or maybe 11; the key point is that for our purposes, the actual number is relatively unimportant. Negligible also has a specific meaning. It indicates that one number differs from another by several powers of ten. For example, carbon dioxide gas in the atmosphere constitutes only a tiny fraction of all of the gas in the atmosphere (roughly 3x10[-4] of the total). So, we can say that carbon dioxide constitutes a negligible fraction of the atmosphere as a whole. However, as you shall see, carbon dioxide gas has a profound effect on the behavior of the climate system, even if its concentration is negligible compared to other gases.
The convention in all scientific disciplines is to use the SI (Systeme Internationale) units. Units are necessary in order to quantify distance, mass, time, etc. as shown in the following table:
Quantity Unit Symbol
distance meter m
mass kilogram kg
time second s
temperature kelvin K
energy joule J
power watt W
Because of the large span of numbers that we will use, it is convenient to use prefixes to the units to make the numbers more manageable. You are already familiar with some of these prefixes, such as kilo and milli. Kilometer (a thousand meters) and milligram (a thousandth of a gram) are common measures of distance and mass respectively. The following table lists prefixes that we will use to express the size of things:
Prefix Size Power of Ten
nano billionth 10-9
micro millionth 10-6
milli thousandth 10-3
kilo thousand 103
mega million 106
giga billion 109
We will have an occasional need to convert these quantities to the conventional English system of units (miles, pounds, degrees Farhenheit, etc.) so that you are able to more readily grasp the size of some quantity. For convenience, here are a few rough conversions that will be used in the text:
* 10 kilometers is roughly 6 miles.
* 100 pounds is roughly 50 kilograms.
Temperature in Kelvin can be expressed in degrees Celsius by adding 273. For reference, the melting temperature of ice is 273 K (0[o]C) while its boiling temperature is 373 K (100[o]C). To convert from degrees Celsius to degrees Farhenheit, the following equation is used:
.
The melting point of ice is 32[o]F while the boiling point of water at sea level is 212[o]F.
We will show a number of figures in this text that convey how one quantity varies as a function of another. Consider Fig A.1, one of the central figures of this text. It shows how the globally averaged surface temperature varies as a function of time from 1861 through 1989.
Figure A.1. Globally averaged surface temperature as a function of time. The values are plotted relative to the 1951-80 climate state (see Section 1.2 for a definition of climate state).
The temperature scale on the left varies from -.5[o]C to
.3[o]C. Now look at Fig. A.2, which has exactly the same
information, but the aspect ratio of the graph has been changed: the time axis
(right-to-left direction) is compressed while the temperature axis (up-down
direction) is expanded.
Figure A.2. Globally averaged surface temperature as a function of time. The values are plotted relative to the 1951-80 climate state (see Section 1.2 for a definition of climate state). The aspect ratio of this figure has changed relative to that in Fig. A.1.
Notice that by changing the aspect ratio of this figure, the temperature rise has become more dramatic. The temperature change observed over the past 130 years isn't any different in Fig. A.2 compared to Fig. A.1, but the impact of this figure is quite different. It lends itself to a more alarming view of climate change, even though the information content is exactly the same in the two figures. You need to pay attention to the magnitude of the quantities displayed in each figure of this text rather than the figure's appearance.