Estimating Exchange Rates of Water in Embayments using Simple Budget Equations.

Alyn C. Duxbury, University of Washington and Keith Sverdrup, University of Wisconsin-Milwaukee
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In this exercise students will estimate the volume rate of water inflow and outflow for an embayment using simple water and salt budget equations that capitalize on the concept of steady state and conservation principles. The average volume of water in the bay and the total concentration of salt in the bay water are assumed to remain constant. These budget equations can be solved for water inflow and outflow knowing the rate of addition of fresh water to the embayment and the salinities of the inflowing and outflowing waters. Students will then be asked to calculate inflow and outflow rates for Puget Sound, Washington and the Mediterranean Sea given actual values of fresh water input and salinities of inflowing and outflowing water, and compare their calculations to actual measured values.

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Learning Goals

  • Rearrange simple algebraic equations.
  • Use known values of river freshwater input, net precipitation minus evaporation rates, and water salinites to compute inflow and outflow rates for Puget Sound, Washington and the Mediterranean Sea.
  • Do simple unit conversions.
  • Assess the accuracy of this simple model calculation given actual measured values of inflow and outflow for these two embayments.

Context for Use

  • This exercise uses simple algebra.
  • This exercise can be used effectively in a variety of introductory courses including oceanography courses, general earth science courses, and environmental geology courses.

Description and Teaching Materials

The exercise can be downloaded from this file in a form that can be given to the students.

Activity Description/Assignment (Microsoft Word 169kB Jul17 04)

Teaching Notes and Tips

  • Students like working with this exercise because it involves real data and real locations. The locations have been chosen to provide two very different types of circulation, one in which surface water moves out of the embayment and the other in which surface water moves into the embayment.
  • Students may not realize at first the implication of the (precipitation-evaporation) term changing sign from the Puget Sound data to the Mediterranean Sea data. In the Puget Sound case (P-E) is positive indicating that there is a net addition of fresh water to the sound. This will result in outflow of water at the surface and inflow of water at depth. In the case of the Mediterranean Sea (P-E) is negative indicating that there is a net evaporative loss of fresh water that is not balanced by river inflow. This results in an inflow of water at the surface and an outflow at depth.
  • After they have completed the exercise it is good to ask students specifically to discuss the different directions of flow in the two embayments and what is responsible for this difference. This can be a group discussion that is not individually graded.


There are both quantitative and qualitative assessments that can be made with this exercise. Quantitatively there are specific numerical answers that the students should obtain if their manipulation of the equations and subsequent calculations are correct. In addition, there are thought questions at the end of the exercise that require students to think about the validity of the measurements in light of real data.

The following file contains the answers to this exercise.

Activity Answers (Microsoft Word 34kB Jul17 04)