sound and light in seawater radiation balance september 3

Sound and Light in SeawaterSound and Light in SeawaterRadiation BalanceRadiation Balance

September 3September 3

T-S DiagramT-S Diagram

Density (Density (σσtt) is less for warmer, fresher water) is less for warmer, fresher water Various water masses can be distinguished by Various water masses can be distinguished by

its temperature and salinity characteristics, its temperature and salinity characteristics, which helps trace the origin of water masseswhich helps trace the origin of water masses

σσθθ and and σσtt vary rapidly with temp. at high temp. at vary rapidly with temp. at high temp. at all salinitiesall salinities

σσt t varies more slowly with temp. at low temp. and varies more slowly with temp. at low temp. and low salinitieslow salinities

Identifying water massesIdentifying water masses

Temperature and Salinity are conservative Temperature and Salinity are conservative propertiesproperties

θθ ( (potential temperature) is conservativepotential temperature) is conservative T (in situ) is not, it changes with pressureT (in situ) is not, it changes with pressure

Water massWater mass Temperature rangeTemperature range Salinity rangeSalinity range

AABWAABW -0.5-0.5°C - 0°C°C - 0°C 34.6 – 34.734.6 – 34.7

NADWNADW 22°C - 4°C°C - 4°C 34.9 - 35.034.9 - 35.0

AAIWAAIW 33°C - 4°C°C - 4°C 34.2 - 34.334.2 - 34.3

Figure from http://www.es.flinders.edu.au/~mattom/ShelfCoast/notes/figures/fig10a1.html

Sound in SeawaterSound in Seawater

Sound travels as pressure wave – Sound travels as pressure wave – compression waves: compression waves:

)( ctxikAep

)](sin)([cos ctxkictxkAp

2

21

k

Tf

kTfC

Sound spreads equally in all directions in homogeneous water

Sound decays due to:Sound decays due to:- spreading loss- spreading loss- attenuation – absorption and scattering; absorption - attenuation – absorption and scattering; absorption depends on frequencydepends on frequency

Phase Speed C

Frequency f

Angular frequency

Wave Number k

Wave Length

1

C

- β: adiabatic compressibility

- C de/increases because ρ and β de/increase

- C de/increases by:

3 m s-1 /K temperature de/increase (ρ decreases)

1.4 m s-1 / 1‰ salinity increase

17 m s-1 / 1000m depth de/increase

p

x

1

1 Specific Volume

α: Volume/unit mass

α = α(S,T,P)

- If ρ increases, α decreases

- in upper ocean, C is determined primarily by Temperature (and salinity to a lesser degree)

- in deeper ocean, C is determined by pressure

Speed does not depend on frequencySpeed does not depend on frequency

1

fC

f =10 KHz → λ = 0.14 m

f =100 KHz → λ = 0.014 m = 14 mm

- Sonars and echo sounders operate in this range

- Spreading loss in sound channel is proportional to distance traveled

Sound absorption is due primarily to viscosity:Sound absorption is due primarily to viscosity:

Idr

dI

2

1

I: sound intensity r: distance along ray path

Beer’s Law – Loss proportional to energy present

reII 0

higher frequencies → shorter wavelength → stronger absorption

SO, low frequency sound can travel very far in sound channel

Exponential Decay – you will see this again!

C = C0 e –kx - solution to dC/dx = -kC(x) – rate of change depends on concentration

1/k : e-folding scale – scale at which concentration is 1/e of it’s initial value

see http://en.wikipedia.org/wiki/Exponential_decay

Figure 3.15 in Stewart

Figure 3.15 in Stewart

Sound refracted Downward

Sound refracted Upward

Sound Channel

Figure 3.16 (Stewart): Sound emitted near axis of sound channel is focused along axis – low frequencies can travel many thousands of kilometers

Sound Channelaka SOFAR Channel

The ATOC prototype array was an acoustic source located just north of Kauai, Hawaii, and transmissions were made to receivers of opportunity in the North Pacific Basin. (from http://en.wikipedia.org/wiki/Acoustic_thermometry)

Acoustic Thermometry of Ocean Climate (ATOC) is a program began by Walter Munk to observe the state of the world's ocean climate using long-range acoustic transmissions

Figure 4.2 (Stewart): Map of mean annual sea-level pressure calculated from the ECMWF 40-year reanalysis. From From Kallberg et al 2005. Wind blows along contours of pressure (except near Equator) – closer contours mean stronger wind – Geostrophic Balance

Winds over the Ocean

Figure 4.3(a) (Stewart): Simplified schematic of Earth's atmospheric circulation driven by solar heating in the tropics and cooling at high latitudes. The meridional cells in the atmosphere and the influence of Earth's rotation on the winds. From The Open University (1989a).

Figure 4.3(b) (Stewart): Simplified schematic of Earth's atmospheric circulation driven by solar heating in the tropics and cooling at high latitudes. Cross-section through the atmosphere showing the two major cells of meridional circulation. From The Open University (1989a).

Wind Stress

The force of the wind, or the work done by the wind on the sea surface: called the wind stress - the vertical transfer of horizontal momentum from the atmosphere to the ocean

Wind stress is calculated from:

= ρ CD U210

where ρ= 1.3 kg/m3 is the density of air, U10 is wind speed at 10 meters, and CD is the drag coefficient

CD is approximately 1 x 10-3 to 3 x 10-3 and varies with wind speed (see text)

Bulk Aerodynamic Formulation

What Do We Get From the Sun?

Keep in mind that this is the ultimate energy source for nearly all of the variability that we have in the ocean and atmosphere.

First let’s look at some numbers :

Solar constant, S = 1376 W/m2 3.5% (max in Jan)

Total energy rec’d = R2 S = 1.75 x 1017 W

Average energy / unit area = total / surface area = S/4 (area of a sphere = 4R2) = 344 W/m2

Albedo (amount reflected or scattered) averages about 0.3 (range 0.1 – 0.6, tropics – Antarctica), soaverage energy / unit area received = 240 W/m2

from Gary Mitchum 2006

Figure 5.2 (Stewart): Insolation (spectral irradiance) of sunlight at top of the atmosphere and at the sea surface on a clear day. The dashed line is the best-fitting curve of blackbody radiation the size and distance of the sun. The number of standard atmospheric masses is designated by m. Thus m = 2 is applicable for sunlight when the sun is 30° above the horizon. From Stewart (1985).

Figure 5.3 (Stewart): Monthly average of clear-sky, downward flux of sunlight through the sea surface in W/m2 during 1989 calculated by the Satellite Data Analysis Center at the NASA Langley Research Center (Darnell et al., 1992) using data from the International Satellite Cloud Climatology Project.

from Gary Mitchum 2006

from Gary Mitchum 2006

from Gary Mitchum 2006

from Gary Mitchum 2006

Physics of Radiation (Stefan’s Law)

from Gary Mitchum 2006

Physics of Radiation (Wien’s Law)

from Gary Mitchum 2006

Wien’s Law and Energy Spectra

T = 6000 K (The Sun)

from Gary Mitchum 2006

The Simplest Balance

Suppose we have a solid planet (no atmosphere) that receives 300 W/m2 at its equator. What should the temperature be based on the physics

we’ve introduced thus far?

If we’ve reached steady state, then the planet must be radiating as much energy as it receives; i.e., it must radiate 300 W/m2 . And if it radiates as

a blackbody, then we can compute the temperature from

T4 = 300 W/m2

which gives T = 270 K = -3 C COLD!!

If we do this at the poles, T is less than –100 C !

Well, clearly we’re missing something. Let’s put on an atmosphere.

from Gary Mitchum 2006

The Greenhouse Effect – Basic Idea

We think of the atmosphere as a sheet of glass that lets all of the Sun’s short wave energy go through.

But our glass atmosphere absorbs a fraction (call it e) of the long wave radiation.

Also, our model atmosphere emits long wave radiation in all directions at a rate proportional to its temperature.

Let’s sketch this situation and see what the predicted temperature of the Earth would be.

from Gary Mitchum 2006

The Greenhouse Effect – Calculating the Temperature

I = (1 - e) U + B

I + B = U

I and e are known, which means we can solve for U and B,

which means we can solve for the ground temperature from U.

For e = 1, T = 50 C at equator too hotFor e = ½ , T = 19 C at equator

too cold, but closer.from Gary Mitchum 2006

The Greenhouse Effect – The Real World

Note all the ways clouds enter in. Cloud physics is one of the biggest challenges in predicting future climate change.

from Gary Mitchum 2006

Radiation at the Sea Surface – Incoming Short Wave

from Gary Mitchum 2006

Radiation at the Sea Surface – Outgoing Long Wave

from Gary Mitchum 2006

from Gary Mitchum 2006

from Gary Mitchum 2006

from Gary Mitchum 2006

from Gary Mitchum 2006

Solar Radiation in the SeaSolar Radiation in the Sea

Short-wave – incomingShort-wave – incoming

kzoeIzI )(

k = Vertical attenuation coefficient

k = k(λ) : depends on wavelength – smallest for blue light

- Reds are longer absorbed in upper meter or less – gives up heat to water

Figure 6.17 (Stewart): Absorption coefficient for pure water as a function of wavelength λ of the radiation. Redrawn from Morel (1974: 18, 19).

Figure 6.18 (Stewart): Left: Attenuation of daylight in the ocean in % per meter as a function of wavelength. I: extremely pure ocean water; II: turbid tropical-subtropical water; III: mid-latitude water; 1-9: coastal waters of increasing turbidity. Incidence angle is 90° for the first three cases, 45° for the other cases. Right: Percentage of 465nm light reaching indicated depths for the same types of water. From Jerlov (1976).

Figure 6.19 (Stewart): Spectral reflectance of sea water observed from an aircraft flying at 305m over waters of different colors in the Northwest Atlantic. The numerical values are the average chlorophyll concentration in the euphotic (sunlit) zone in units of mg/m3. The reflectance is for vertically polarized light observed at Brewster’s angle of 53°. This angle minimizes reflected skylight and emphasizes the light from below the sea surface. From Clarke, Ewing, and Lorenzen (1970).

Can compute Chl by looking at ratio of different wavelengths

Average ocean chlorophyll concentration measured by SeaWiFS since launch

from http://earthobservatory.nasa.gov/Newsroom/NewImages/