Time scale to get an initial steady state

[feroda]

In ocean modeling, one key issue is how to get the initial steady state.
Take initial steady state for January as an example, modelers usually do it through two ways:

1. initialized with climatological January Temperature and Salinity, the model is keep on running with
constant climatological January forcing(both for surface and open boundaries) until the steady state.
This process is so called spin-up.

2. January conditions from OGCM with several decades integration are averaged as the initial January
steady state.

Though the choice of 2 is theoretically reasonable, it's quite hard to get such a longterm model result.

As to the first choice, I am quite not sure about the time scale to get the steady state. Namely, what is the benchmark of the steady state and when?
Even the model energy shows steady periodical variability, is that the real steady state for January?
(to approach the steady sate, usually, ONE month is not enough. It means January surface forcing(e.g. wind) lasts more than one month which is not true in reality)

Any explanation is greatly appreciated.

[kate]

The classic spin-up problem for a rotating stratified fluid doesn't have winds at all, but the timescale depends on the size of the basin in question. For deep ocean basins, the timescale is in years, though we usually consider one year to be "good enough" for looking at the wind-driven coastal ocean processes. For instance, do a multi-year wind-driven run and consider the first year as "spin-up". I suppose as always, it depends on what you are trying to do. Our winds have variability on many timescales, including decadal.

[feroda]

Thank you, Kate. I really appreciate your precious comment.
According to your comment, I'd like to look into this topic more thoroughly.

Firstly, I don't quite follow:

For instance, do a multi-year wind-driven run and consider the first year as "spin-up".

Does it have wind forcing for the first year?
This question is raised from:

The classic spin-up problem for a rotating stratified fluid doesn't have winds at all,

If yes,
Does the wind forcing vary during the first year which is for "spin-up"?
How about temperature, salinity and open boundary forcing?

Specifically, let's take my application on South China Sea as an example.

but the timescale depends on the size of the basin in question.

The size of the basin is about 30(zonally) by 25(meridionally).It takes about 3 months for the low frequent Rossby wave to travel across the SCS basin.

My ROMS cases for this basin are in two category, one is for climatology and the other is for multi-years.

For the climatology case, I get the initial steady state as follows,
Initialized with climatological January T and S, the model is keep on running for 3 years with
constant wind forcing and lateral open boundaries forcing for climatological January.
I take the last record from ROMS history output file as the steady state for climatological January condition.
Thereafter, the model is going on for another 330 days with monthly climatology forcing accordingly, which are for climatology condition from February to December.

What's your comment on the above strategy? Is it reasonable? If not, what's your opinion?

For the muti-year case(say,1980-2008),
Initialized withe the January condition from the above climatology case, the model is keep on going driven by monthly wind forcing(for each year from 1980-2008) and climatological lateral open boundary forcing(same cycle of open boundary forcing for each year). So, I get the wind-driven dynamic condition for the South China Sea from 1980 to 2008.

Once more, What's your comment on the above strategy? Is it reasonable? If not, what's your opinion?

[kate]

Does it have wind forcing for the first year?

yes

Does the wind forcing vary during the first year which is for "spin-up"?
How about temperature, salinity and open boundary forcing?

yes and yes. Our winds are six-hourly and our boundary conditions change every five days.

The size of the basin is about 30(zonally) by 25(meridionally).It takes about 3 months for the low frequent Rossby wave to travel across the SCS basin.

Your timescales are therefore much shorter than ours. Three years of spin-up may be overkill.

I take the last record from ROMS history output file as the steady state for climatological January condition.

Have you looked to see if you do get a steady state? Some model configurations have a built-in instability in which case it will never be at true steady state.

What's your comment on the above strategy? Is it reasonable? If not, what's your opinion?

What is the point of the climatological run? A better climatology might be gotten from running the multi-year case with higher-frequency winds, then finding the monthly means from that, then averaging all the January means to get a January climatology. Are you using monthly winds for convenience? We have gone to six-hourly winds because they are available globally - and they are available globally because that gives a better response to storms as they move through your region (and my region). "Better" is defined here as higher energy, generating more mixing, and ideally a more faithful representation of the vertical stratification, which in turn is important to the biology. So, as always, what are your goals? Mine are to not have the biologists being terribly upset with us.

[feroda]

Hey Kate,
sorry for my late response. Many thanks for your comments and explanation that I really benefit much from.

firstly,

What is the point of the climatological run?

The point of "climatology" here is a multi-year averaged condition. Specifically, climatological January does NOT refer to a certain year(say 2009), but the month with common condition for Januaries of different years(say the Januaries from 1900 to 2000). As a results, the goal of climatological run is to get the transition among climatological Jan, Feb, Mar, .... Dec.

secondly,

Are you using monthly winds for convenience?

Exactly! My wind forcing file contains 12 time records for Jan, Feb, Mar, ....Dec, accordingly. When the model time goes to the beginning of second year, the wind stress will turn back to Jan once more.

thirdly,

Our winds are six-hourly and our boundary conditions change every five days.

What the data set you used for the five days boundary conditions?
Is it for multi-years?

fourthly,

Your timescales are therefore much shorter than ours. Three years of spin-up may be overkill.
Have you looked to see if you do get a steady state? Some model configurations have a built-in instability in which case it will never be at true steady state.

right! It is really hard to tell if the model is in the steady state. Indeed, from the evolution of the model results I found the spin-up seems to be overkilled after 200 days.
Would you please address some explanation on the "built-in instability"?

We have gone to six-hourly winds because they are available globally - and they are available globally because that gives a better response to storms as they move through your region (and my region). "Better" is defined here as higher energy, generating more mixing, and ideally a more faithful representation of the vertical stratification, which in turn is important to the biology. So, as always, what are your goals? Mine are to not have the biologists being terribly upset with us.

Thank for your advice form the view of biology. I am also greatly interested in marine ecosystem and take biology factor into my consideration while I am doing the physical model.
My goals are:
1. get the monsoon winds-driven transitions of circulation dynamics of the South China Sea(SCS) in the
time scale of climatology months.
2. get the monsoon winds-driven transition of marine ecosystem of the SCS in the time
scale of climatology months.
3. get the inter-annual transition of the upper layer circulation dynamics of the SCS
in the time scale of couple decades.
4. get the inter-annual transition of the upper layer marine ecosystem of the SCS
in the time scale of couple decades.

Looking forward to your precious comment and advice.

[kate]

We are using boundary conditions from SODA from Jim Carton's lab. It is for multiple years.

I was referring to baroclinic and barotropic instabilities. A web search on them will find you much more authoritative sources than I could be.

It might be that a monsoon climatology captures the important features you want. Where I live, the climatology is derived from averaging over one storm after another, so we assume we'd do better by simulating all those storms and averaging over the response to them rather than finding the response to the average atmospheric state.