At a spot in the ocean , the surface irradiance is 7.8*10^16 photons cm^-2 s^-1, and k=0.14 m^-1. At what depth does the euphotic zone end? (Find definition for euphotic zone and solve for z)

Question

At a spot in the ocean , the surface irradiance is 7.8*10^16 photons cm^-2 s^-1, and k=0.14 m^-1. At what depth does the euphotic zone end? (Find definition for euphotic zone and solve for z)

Answer 1

Same idea as the last question but e^-(.14 z)

and Io = 7.8*10^16
and you have to look up the irradiance for light to die out enough.
Once you do that, take the ln of both sides to solve it.

Answer 2

From wikipedia:

"It extends from the atmosphere-water interface downwards to a depth where light intensity falls to 1 percent of that at the surface (also called euphotic depth), "
so where I = .01 Io

or
I/Io = .01 = e^-.14z
ln .01 = -.14 z
-4.6 = -.14 z
solve for z

Answer 3

The euphotic zone is the depth in a body of water where there is enough sunlight for photosynthesis to occur. To find the depth at which the euphotic zone ends, we need to use the given values of surface irradiance (I) and the coefficient of attenuation (k), and solve for the depth (z).

The equation that describes the attenuation of light with depth is given by Beer-Lambert's Law: I = I0 * e^(-kz), where I0 is the initial surface irradiance.

To find the depth (z) at which the euphotic zone ends, we need to find the value of z when I becomes negligible. In this case, we can assume that I becomes negligible when it is less than 1% of I0.

Let's calculate the depth (z):

I = I0 * e^(-kz)

Rearranging the equation to solve for z:

ln(I/I0) = -kz

z = -ln(I/I0) / k

Now we can substitute the given values into the equation:

I = 7.8 * 10^16 photons cm^-2 s^-1
k = 0.14 m^-1

Convert the units of I to m^-2 s^-1:
I = 7.8 * 10^16 * (10^4 cm^2 / m^2) * (1 s)

Now we have:

I = 7.8 * 10^20 m^-2 s^-1

Substituting the values into the equation:

z = -ln(I/I0) / k
z = -ln(7.8 * 10^20 / I0) / 0.14

Note: We need the value of I0, which is the initial surface irradiance. Unfortunately, it is not provided in the given information. Without I0, it is not possible to determine the exact depth at which the euphotic zone ends.

However, if we assume I0 to be the same as I (surface irradiance), we can calculate the approximate depth (z). Assuming I0 = I:

z ≈ -ln(1/0.01) / 0.14
z ≈ -ln(100) / 0.14
z ≈ -4.605 / 0.14
z ≈ -32.893

Since depth cannot be negative, we can approximate the depth (z) at which the euphotic zone ends to be around 33 meters.