During the Spring of 1998, over 400 California sea lions (Zalophus californianus) were found dead, and many others were seen displaying signs of neurological dsyfunction along the central California coast. A bloom of pseudo-nitzschia australis (a diatom) was observed in the Monterey Bay region during the same period. This bloom was associated
with production of domoic acid (DA), a neurotoxin that was also detected in planktivorous fish, including the northern anchovy (Engraulis mordax), and in sea lion body fluids. These and other concurrent observations demonstrated the trophic transfer of DA resulting in marine mammal mortality (Reference).

The biologists who study these blooms would like to be able to estimate the concentrations of pseudo-nitzschia australis based on measured conditions in Monterey Bay. They have performed experiments to determine the conditions in which pseudo-nitzschia australis grows best; they would like you to produce a computer model of what theconcentration of pseudo-nitzschia australis might be given particular conditions.

Experiments in Monterey Bay and in the laboratory show that the density of pseudo-nitzschia australis (in milligrams/m^3) is dependent on four things: the water temperature (in degrees C); the salinity of the water (in parts per million); the average light (measured as lumens); and the nutrients available. Nutrients are measured from samples that were drawn into seasoned polyethylene scintillation vials and frozen for later processing with an AlpChem autoanalyzer. Pseudo-nitzschia australis is most sensitive to nitrates (NO3 and NO2), which are measured in milligrams per cubic meter (mg/m^3).

Data is available that shows the seasonal average of some of these values for the Monterey Bay. Typical values for each are:

• Lumens: 960 typical day, 1920 bright afternoon, 480 dim day
• Water Temperature: 12 to 15 degrees C depending on time of year
• Salinity: 32 to 37 ppm
• Nutrients: 10 to 25 ppm

• The measured maximum concentration of pseudo-nitzschia australis during a bloom is 2100 mg/m^3.
• The diatom will not grow at all below 10 degrees C. Growth peaks at16 degrees C and falls back to zero at about 22 degrees C, at which point it is too warm for the organism to survive. The increase in growth rate from 10 to 16 degrees does not seem linear, but shows sharp increases as the temperature goes past 10 degrees, though the increases decline as they approach the peak. Similarly, going from 16 degrees upward does not result in dramatic reduction in production of the organism immediately, and production decreases rapidly as the temperature approaches 22 degrees.
• Pseudo-nitzschia australis is very sensitive to water salinity. It will not grow at all in water with a salinity greater than 37 ppm. Production increases linearly as the salinity drops, with maximum productivity occurring when salinity falls below 32 ppm.
• The effect of light is the inverse of salinity. Below 600 lumens, the organism will not grow. Growth increases approximately linearly up to1350 lumens; beyond that more light has no effect.
• Finally, growth of pseudo-nitzschia australis is approximately linear with an increase in nitrate nutrients from 0 to 25 ppm. Beyond 25 ppm, no additional growth is seen.

There are two parts to this project.
 

• First, you will develop a mathematical model of pseudo-nitzschia australis growth. Once you have developed this model, you will develop an algorithm that will allow estimation of its concentration given the factors that determine growth. You can express this algorithm in any way you like, as long as the steps of the algorithm are clear and the names of the variables and the operations performed on them are evident. You also need to develop a plan for testing your final program. For this program, this is mostly determining what values will you use to verify that your model is reasonably accurate according to the results of the experiment above. This first part of the project is due on September 26th, in class.
• Second, you will translate your algorithm into a working, well-documented C++ program. Your program should take as input the water temperature in degrees C, the water salinity in ppm, the amount of light in lumens, and the amount of nitrates in the water. It should output the probable concentration of pseudo-nitzschia australis. A sample run of such a program is shown below. This program is due on October 3rd, by electronic submission. Details on how to perform electronic submission will be posted after the first part of the project is done.

Sample Run:

This program will provide an estimate of the concentration
of pseudo-nitzschia australis in Monterey Bay given:
  the average light (in lumens);
  the average water temperature (in degrees Centigrade);
  the water salinity (in ppm);
  and the concentration of nutrients (in mg/m^3).
Output is in mg/m^3

Please enter the average amount of light in lumens: 1280
Please enter the average water temperature in degrees C: 12.5
Please enter the water salinity in ppm: 33
Please enter the nutrients in mg/m^3: 14

The estimated amount of pseudo-nitzschia australis (in mg/m^3) is: 519.256
 
 

Submission instructions