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Q: Ocean evaporation rate calculation ( Answered 5 out of 5 stars,   2 Comments )
Subject: Ocean evaporation rate calculation
Category: Science > Earth Sciences
Asked by: centure7-ga
List Price: $20.05
Posted: 22 Apr 2005 05:28 PDT
Expires: 22 May 2005 05:28 PDT
Question ID: 512638
How would I calculate evaporation rate of ocean water, in terms of
volume per time per area (gallons per minute per acre for example)
given the following:
- Relative humidity
- Wind speed
- Water temperature
- Air temperature

Would air pressure make a significant difference? Would there be a
significant difference from small waves to large waves? Are there
other factors I am not mentioning here that make a big difference?
Subject: Re: Ocean evaporation rate calculation
Answered By: hedgie-ga on 20 May 2005 00:40 PDT
Rated:5 out of 5 stars
             You  have interesting but complex questions.
 It would be helpful (and it may increase the rate at which your questions
 are answered) if you would rate the answers.
 Rating helps researcher to gage how useful was his/her the
contribution to the answer in those situations when full, exhaustive
answer is not possible.
(This is one of those situations ;-)

I will focus on the physical processes which determine the rate of evaporation.
That will provide a handle on, what the units are and will provide a
complement to the empirical study referenced in the comment.

But first, some actual numbers for the ocean:

     "       The average amount of evaporation F.e from the sea
surface is about 120 cm/yr, i.e. the equivalent of the sea surface
sinking by that amount.  Local values range from an annual minimum of
as little as 30 to 40 cm/yr in high latitudes to maxima of 200 cm/yr
in the tropics associated with the trade winds.  This decreases to
about 130 cm/yr at the equator where the mean wind speeds are lower.

How is the evaporation rate Fe determined?  A direct method is to
determine the rate of water loss from a pan of water, but this has
serious practical difficulties.  For large area estimates and for
prediction, a formula using easily measured parameters is desirable. 
Evaporation is basically a diffusive process that depends on how water
vapor concentration changes with height above the sea surface and on
the processes that cause diffusion.  In section 5.1.3, we discussed
"eddy diffusion" which is analogous to molecular diffusion, except
that the turbulence in the air or water is considered to be the
process that diffuses properties, rather than movement of individual
molecules.  The air turbulence is the process that controls the
diffusion that creates evaporation, and this air turbulence depends on
wind speed.   Therefore we expect the evaporation rate to depend on
wind speed.  (This explains why we feel cooler when the wind is
blowing which creates the effect known as 'wind chill'   "

This is quote from section 5.4.6 of excellent text: 
CHAPTER 5  Water, Salt and Heat Budgets of the Oceans
whole book
and books
and projects described on the site , such as

may be of interest for this and the for the related question

I now want to focus on the theoretical aspect of the evaporation:
 What does it mean " Evaporation is basically a diffusive process?" 

The search term for the fundamental mechanism is: Stefan Problem 
named after Slovenian physicist ( J. Stephan)

The quote from his book, given in the  above link:

"There always something will remain,  that we shall not know, why?"

is appropriate comment (sigh) to your question.

One reason 'why' is that even if we would know all the physical
parameters of the phase transition (evaporation, melting, .. ) that is
latent heat of the transition, diffusion rates,heat conductivity, ... 
,we still would need to solve the transport equations, to determine
the rate of transition, speed of the boundary.

OK - let me try to put it more simply:

The (textbook) example of the Stefan problem is an ice cube, melting
in the glass of water.

Melting is phase transition (just like evaporation) and the boundary
between the phases (surface of the cube) is moving (in either
direction, depending on temperatures). The speed of the moving
boundary depends on how quickly the fluid phase can supply the heat
(and in same cases material) needed for the transition. This is how
winds into play. Heat comes by conduction, radiation (sun rays) and
convection and water vapour is carried away by wind (convection) and
diffusion (condiction).
When you look at the 'big' picture:
you will notice that while water evaporates and vapor is carried away
by the wind, some of that water returns to the ocean right away. Only
small part  comes back through rains over land and runoff.
How much? That depends on the local conditions -- it is different near
coast and in the open sea.
For large scale (global) model (cumulative) numbers are known:
  361 Tm^3 evaporates and 324 returns directly (by rain over the
ocean), according  to courses/dc/dcgn101/StreamsRivers.doc

Here Tm^3 means Tera-cubic-meters; T= E12 is SI prefix for million of
millions as defined here

So, at one spot, water may evaporate and be carried away by winds; at
another spot it may rain all the time and that same water is returned
to the ocean.
This distances (from one sot to the other spot) affects the 'net evaporation':
 The scale of the model and the grid (cell size) needs to be specified
before 'net evaporation rate' is well defined.

So, while local studies, such as the one cited in the comment are
possible, and constants determined empirically may reflect local
miroclima, and have some temporary and limited validity, true answers
are tied to global circulation models (both water and atmosphere),
which are a topic of an ongoing research,
 are far from completion and very complex.

That is one reason why Stephan's sigh is still valid.
Hope this is useful. Questions welcome, rating appreciated.


Request for Answer Clarification by centure7-ga on 28 May 2005 02:51 PDT
I found that information to be very useful, but am hoping you can
actually clarify someone else's comment. Since hfshaw hasn't responded
to my comment below, I am hoping that you can provide the answer to
the questions I asked hfshaw, which are (in regards to the equation
provided with the comment):

1) What are the units of measurement units expected to be used for
each variable given?

2) What should I plug in for k(v)?

3) Please provide an example equation using specific variables so I
can be sure that I understand.


Clarification of Answer by hedgie-ga on 01 Jun 2005 06:57 PDT
Hello again  centure7-ga,

and thanks for the rating and tip on the other question.

That equation hfshaw  mentioned is explained on page 28 of the reference he gave

E is in units mm/day
K.e in 1/kPa is a complex function of geometry 
conversion constant  is given as 86.4 * E6 

Please do look at the referenced paper,
particularly pages 20-30. 
and if anything is not clear
after that, post another RFC.

Hanon's eq. on page 26 is much more simple -
and more credible then 'Bulk-Aerodynamic' on page 28.
 Please, bear in mind this is students research,
not a peer reviewed article.

centure7-ga rated this answer:5 out of 5 stars and gave an additional tip of: $4.95
Thanks for going out of your way yet again to thoroughly answer my question.

Subject: Re: Ocean evaporation rate calculation
From: hfshaw-ga on 22 Apr 2005 10:39 PDT
There are a number of ways to parameterize the evaporation rate from a
water surface as a function of "observable" variables.  See the
appendix of the  document at
for a good summary of the various approaches.

The set of variables you have chosen correspond to the ones used in
what is called the "bulk aerodynamic" method, the equation for which
can be written as:

   E = a * k(v), * v *(e_sat(T) - e)


E is the evaporation rate

a is a constant that accounts for the units used to express the other variables

v is the wind speed measured at a specified height above the air-water surface

k(v) is an "efficiency factor" that parameterizes the the extent to
which wind eddies near the surface are effect vertical transport of
water vapor away from the water-air interface.  k depends on v, the
densities of the air and water, the atmospheric pressure, and it also
takes into account the surface roughness of the interface due to

e_sat is the saturation water vapor at the water surface, which is a
function of temperature (T)

e is the actual water vapor pressure of the air above the surface. 
Note that 100*e/e_sat is the relative humidity, expressed as a

The URL given above will provide you more detail on the numerical
values for the constants, as well as an expression for k.
Subject: Re: Ocean evaporation rate calculation
From: centure7-ga on 23 Apr 2005 07:14 PDT
hfshaw, I found your link to be very helpful. Could you give an
example of what the math would be for humidity of 80%, wind speed of
15mph, a k(v) of a typical value for the ocean along the coastline
(air pressure of perhaps 1ATM, and water density of maybe 1.03g/cc),
and a water temperature of 30C? The part I don't understand is mostly
just what unit measurements are used. In other words, how you would
calculate with any specified units, and what units must be specified.
I would imagine that the equation requires metric units and a Celcius
temperature. I'm also not sure what to plug in for k(v). Again, thanks
for the information you have provided!

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