Determining The Area Of SF Bay 10/14 Integrated Science 1 Redwood High School Name: Period:

¢ Background

When studying an ecosystem, it is imperative to the ecologist that they clearly identify the boundaries of the study area. If she were studying Bay, it might appear quite obvious to most people which body of water she was studying. However, since the Bay opens into the ocean, to a series of rivers, to the , and up the Delta, she must delineate carefully just where the boundaries of the study area are. For example, is it outside or inside the ? A very careful line must be made so that she can communicate to her audience exactly what she means. We sometimes refer to such definitions as “operational.” For example, one might arbitrarily decide that the shall serve as the westernmost end of the Bay. In addition to setting out the boundaries of a body of water, it is also desirable that she report the surface area and volume of the body of water under study. The purpose of this activity is to learn one method that is commonly used to determine the surface area of a large body of water, similar to the , from maps that are available.

¢ Materials

Map of San Francisco Bay with appropriate kilometer scale, Balance, Sharp scissors

¢ Procedure

A. Gathering data

1. On the San Francisco Bay Region Map there is a square. The square represents 400.0 square kilometers. 2. Accurately cut out the square marked on the map that equals 400.0 square kilometers and find its mass (to the nearest 0.01g) on the Balance. Record the mass in Data Table 1. 3. With extreme precision, cut out all the water within the operational definition of San Francisco Bay (note special border marks); determine its mass to the nearest 0.01g. Record the mass in Data Table 1.

B. Calculating data

If the known surface area of the SF Bay is divided by 400km2 the resulting ratio should equal the value calculated when the mass of the map of the SF Bay surface is divided by the mass of a scaled 400km2 section of the same map. *this assumes the map boundaries match the boundaries used to calculate the actual surface area. § this approach works because the comparison is relative to both mass and area of the same map.

FORMULAS:

Area of SF Bay in km2 Mass of SF Bay Cutout 1. ratio equality = 400.0 km2 Mass of 400.0 km2 Cutout

2 2 (400.0 km ) × (Mass of SF Bay Surface Area Cutout) 2. area calculation Area of SF Bay in km = Mass of 400.0 km2 Cutout Data Table 1

Measured Map Sections Mass (g) 400.0 km2 Scaled Cut Out SF Bay Surface Area Cut-Out

€ ¢ Discussion and Conclusion

1. Finding the surface area of the Bay:

a. Use your data from Data Table 1 to calculate the area of the SF Bay in Km2. Record your answer in Data Table 2

b. Convert all km2 values in Data Table 2 to mi2.

Data Table 2 [1km2 = 0.386mi2] SF Bay Surface Area Sources Area (km2) Area (mi2) California State Water Board 1127 Harold Gilliam, author/scientist 1036 Your Name:

2. What might be some reasons for the differences in reported values for the surface area of the Bay? including your own value (*assume the other reported values were not calculated with your method)

published value - experimental value 3. Calculate your percentage of error. Percent error = × 100 experimental value SHOW WORK (use the Cal. State Water Board Value as the Published Value) - round your answer to the nearest tenth.

4. Describe another method for determining the surface area of a body of water?

5. Why might the surface area of a body of water be a factor in determining the ecological potential (potential for maximum healthiness) for any given estuary? GIVE AN EXAMPLE

€ 2 Determining The Area of the SF Bay