Maptime permits users to explore temporal data associated with sixed point location using three major approaches: animation, small multiples, and change maps. Stephen Yoder(1996), the developer of mapTime, argued that animation is a logical solution for showing change over time because “...the cartographic presentation [is not only] a scale model of space, but of time as well”(30). Animation of point data are easiest to interpret when data change relatively gradually over time. For example, an animation of the change in population of U.S. cities from 1790 to 1990 (distributed with MapTime) is easy to follow because city populations gradually increase and decrease. In contrast, an animation of the change in water quality at point location along streams and river would exhibit much sharper increases and decreases, and thus be harder to interpret. Animations in Maptime are constructed using a series of key frames (i.e., frames associated with collected data) and intermediate frames (i.e., frames associated with interpolated data). A distinct advantage of Maptime is that the number of intermediate frames can be varied thus, if one has data for every year from 1900 to 1940, but only for every other year between 1940 and 1980. Intermediate frames might be used just for the 1940-1980 data In the context of temporal data, a small multiple consists of a set of maps, one for maps, one for each time element for which data have been collected. As an example. Figure 22.5 portrays a small multiple of stream discharge for seven collection stations within a hypothetical drainage basin at 12-hour intervals over a four-day period (the data are distributed with Maptime). It is presumed that the streams flow from west, that circle size is proportional to stream discharge (in cubic feet per second), and that heavy rainfall occurs between 6 PM Monday and 3 AM Tuesday throughout the region. The small multiple reveals an initial increase in discharge for upstream stations, followed by a later increase for downstream stations; essentially, a pulse of water move through the system. The pulse of water seen in the small multiple is also detectable in an animation of the stream discharge data, but it is not easy to discern. Thus, small multiples are often a necessary complement to animations. Small multiples can also assist in contrasting two arbitrary point in time. For example, one might examine the beginning and ending multiples for stream discharge and note approximately how much change has taken place over the period at each location. Change map explicitly show the change that takes place between two point in time: in Maptime, change can be computed in terms of the raw data (magnitude change), percent form, or as a rate of change. The U.S. city population data from 1790 to 1990 provide a good illustration of the need for change maps. When these raw data are animated, one sees a major growth in city populations in the Northeast beginning in 1790, with an apparent drop in population for some of the largest northeastern cities from about 1950 to the present. In contrast, a map showing the percent of population change between 1950 and 1990 reveals a distinctive pattern of population decrease throughout most of the Northeast, as show in Color Plate 1.3 An interesting possibility is to create a small multiple of a series of change maps (an example of this for the U.S population data from 1790 to 1990 is shown in Figure 22.6). In an evaluation of Maptime by users, Slocum and his colleagues (2004) found that a small multiple of change maps was favored was favored over both animation and a simple raw small multiple for showing change over time. Animation, however, was deemed useful for examining general trends and providing a sense of change over time, whereas the raw small multiple was useful for comparing arbitrary time periods. As with other exploration software. Maptime can determine precise values associated with a particular location or highlight a subset of the data. Additionally, a zoom feature enables users to enlarge a portion of the map. These feature can be used to explore a single moment in time, or be implemented throughout an animation. Those who wish to experiment with different circle-scaling methods (as described in Chapter 17) also will find that circle-scaling exponents can easily be changed in Maptime.