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description=2 posts published by scienceofdoom during December 2011;

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f latitudinal variations in vertical diffusivity on climate simulations jochum jgr 2009 free mixed layer depth over the global ocean an examination of profile data and a profile based climatology de boyer montegut et al jgr 2004 notes note 1 the 1d version is really t t z α t z due to the fact that α can be a function of z and definitely is in the case of the ocean although this looks tricky and it is tricky to find analytical solutions solving the 1d version numerically is very straightforward and anyone can do it in plain english is looks something like heat flow into cell x temperature difference between cell x and cell x 1 heat flow out of cell x temperature difference between cell x and cell x 1 change in temperature heat flow into cell x heat flow out of cell x x time heat capacity note 2 i am in the process of examining ceres data apart from the challenge of extracting the data from the netcdf format there is a lot to examine a lot of data and a lot of issues surrounding data quality read full post measuring climate sensitivity part two mixed layer depths posted in measurement ocean physics on december 23 2011 26 comments in measuring climate sensitivity part one we saw that there can be potential problems in attempting to measure the parameter called climate sensitivity using a simple model spencer braswell 2008 had demonstrated that even when the value of climate sensitivity is constant and known measurement of it can be obscured for a number of reasons the simple model was a slab model of the ocean with a top of atmosphere imbalance in radiation murphy forster 2010 criticized spencer braswell for a few reasons including the value chosen for the depth of this ocean mixed layer as the mixed layer depth increases the climate sensitivity measurement problems are greatly reduced first we will consider the mixed layer in the context of that simple model then we will consider what it means in real life the simple model of climate sensitivity the simple model used by spencer braswell has a mixed ocean layer of depth 50m figure 1 in the model the mixed layer is where all of the imbalance in top of atmosphere radiation gets absorbed the idea in the simple model is that the energy absorbed from the top of atmosphere gets mixed into the top layer of the ocean very quickly in reality as we will see there isn t such a thing as one layer but it is a handy approximation murphy forster commented for the heat capacity parameter c sb08 use the heat capacity of a 50 m ocean mixed layer this is too shallow to be realistic because heat slowly penetrates deeper into the ocean an appropriate depth for heat capacity depends on the length of the period over which eq 1 is being applied watterson 2000 held et al 2010 for 80 yr global climate model runs gregory 2000 derived an optimum mixed layer depth of 150 m watterson 2000 found an initial global heat capacity equivalent to a mixed layer of 200 m and larger values for longer simulations held et al 2010 found an initial time constant τ c α of about four yr in the geophysical fluid dynamics laboratory global climate model schwartz 2007 used historical data to estimate a globally averaged mixed layer depth of 150 m or 106 m if the earth were only ocean the idea is an attempt to keep the simplicity of one mixed layer for the model but increase the depth of this mixed layer for longer time periods there is always a point where models simplified versions of the real world start to break down this might be the case here the initial model was of a mixed layer of ocean all at the same temperature because the layer is well mixed and with some random movement of heat between this mixed layer and the ocean depths in a more realistic scenario more heat flows into the deeper ocean as the length of time increases what murphy forster are proposing is to keep the simple model and account for the ever increasing heat flow into the deeper ocean by using a depth of the mixed layer that is dependent on the time period if we do this perhaps the model will work perhaps it won t by work we mean provide results that tell us something useful about the real world so i thought i would introduce some more realism complexity into the model and see what happened this involves a bit of a journey real life ocean mixed layer water is a very bad conductor of heat as are plastic and other insulators good conductors of heat include metals however in the ocean and the atmosphere conduction is not the primary heat transfer mechanism it isn t even significant instead in the ocean it is convection the bulk movement of fluids that moves heat think of it like this if you move a parcel of water the heat in that parcel moves with it let s take a look at the temperature profile at the top of the ocean here the first graph shows temperature soloviev lukas 1997 figure 2 note that the successive plots are not at higher and higher temperatures they are just artificially separated to make the results easier to see during the afternoon the sun heats the top of the ocean as a result we get a temperature gradient where the surface is hotter than a few meters down at night and early morning the temperature gradient disappears no temperature gradient means that the water is all at the same temperature why is this once the sun sets the ocean surface cools rapidly via radiation and convection to the atmosphere the result is colder water which is heavier heavier water sinks so the ocean gets mixed this same effect takes place on a larger scale for seasonal changes in temperature and the top of the ocean is also well mixed due to being stirred by the wind a comment from de boyer montegut and his coauthors 2004 a striking and nearly universal feature of the open ocean is the surface mixed layer within which salinity temperature and density are almost vertically uniform this oceanic mixed layer is the manifestation of the vigorous turbulent mixing processes which are active in the upper ocean here is a summary graphic from the excellent marshall plumb from marshall plumb 2008 figure 3 there s more on this subject in does back radiation heat the ocean part three how deep is the ocean mixed layer this is not a simple question partly it is a measurement problem and partly there isn t a sharp demarcation between the ocean mixed layer and the deeper ocean various researchers have made an effort to map it out here is a global overview again from marshall plumb figure 4 you can see that the deeper mixed layers occur in the higher latitudes comment from de boyer montegut the main temporal variabilities of the mld mixed layer depth are directly linked to the many processes occurring in the mixed layer surface forcing lateral advection internal waves etc ranging from diurnal brainerd and gregg 1995 to interannual variability including seasonal and intraseasonal variability e g kara et al 2003a mccreary et al 2001 the spatial variability of the mld is also very large the mld can be less than 20 m in the summer hemisphere while reaching more than 500 m in the winter hemisphere in subpolar latitudes monterey and levitus 1997 here is a more complete map by month readers probably have many questions about methodology and i recommend reading the free paper from de boyer montegut et al 2004 figure 5 click for a larger image seeing this map definitely had me wondering about the challenge of measuring climate sensitivity spencer braswell had used 50m mld to identify some climate sensitivity measurement problems murphy forster had reproduced their results with a much deeper mld to demonstrate that the problems went away but what happens if instead we retest the basic model using the actual mld which varies significantly by month and by latitude so instead of one slab of ocean at mld choose your value we break up the globe into regions have different values in each region each month and see what happens to climate sensitivity problems by the way i also attempted to calculate the global annual area weighted average of mld from the maps above by eye i also emailed the author of the paper to get some measurement details but no response my estimate of the data in this paper was a global annual area weighted average of 62 meters trying simple models with varying mld i updated the matlab program from measuring climate sensitivity part one the globe is now broken up into 30º latitude bands with the potential for a different value of mixed layer depth for each month of the year i created a number of different profiles depth type 0 constant with month and latitude as in the original article type 1 using the values from de boyer s paper as best as can be estimated from looking at the monthly maps type 2 no change each month with scaling of 60ºn 90ºn 100x the value for 0ºn 30ºn and 30ºn 60ºn 10x the value for 0ºn 30ºn similarly for the southern hemisphere type 3 alternating each month between type 2 and its inverse i e scaling of 0ºn 30ºn 100x the value for 60ºn 90ºn and 30ºn 60ºn 10x the value for 60ºn 90ºn type 4 no variation by latitude but month 1 1000x month 4 month 2 100x month 4 month 3 10x month 4 repeating 3 times per year in each case the global annual area weighted average 62m essentially types 2 4 are aimed at creating extreme situations here are some results review the original article for some of the notation recalling that the actual climate sensitivity λ 3 0 figure 6 figure 7 as figure 6 without 30 day averaging figure 8 figure 9 figure 10 figure 11 figure 12 what s the message from these results in essence type 0 the original and type 1 using actual mlds vs latitude and month from de boyer s paper are quite similar but not exactly the same however if we start varying the mld by latitude and month in a more extreme way the results come out very differently even though the global average mld is the same in each case this demonstrates that the temporal and area variation of mld can have a significant effect and modeling the ocean as one slab for the purposes of this enterprise may be risky non linearity we haven t considered the effect of non linearity in these simple models that is what about interactions between different regions and months if we created a yet more complex model where heat flowed between regions dependent on the relative depths of the mixed layers what would we find losing the plot now in case anyone has lost the plot by this stage and it s possible that i have don t get confused into thinking that we are evaluating gcm s and gosh aren t they simplistic no gcm s have very sophisticated modeling what we have been doing is tracing a path that started with a paper by spencer braswell this paper used a very simple model to show that with some random daily fluctuations in top of atmosphere radiative flux perhaps due to clouds the measurement of climate sensitivity doesn t match the actual climate sensitivity we can do this in a model prescribe a value and then test whether we can measure it this is where this simple model came in it isn t a gcm however murphy forster came along and said if you use a deeper mixed ocean layer which they claim is justified then the measurement of climate sensitivity does more or less match the actual climate sensitivity they also had comment on the values chosen for radiative flux anomalies a subject for another day what struck me was that the test model needs some significant improvement to be able to assess whether or not climate sensitivity can be measured and this is with the caveat if climate sensitivity is a constant the next phase more realistic ocean model as murphy forster have pointed out the longer the time period the more heat is injected into the deeper ocean from the mixed layer so a better model would capture this better than just creating a deeper mixed layer for a longer time modeling true global ocean convection is an impossible task as a recap conducted heat flow q k δt d where q heat flow per unit area k conductivity δt temperature difference and d depth of layer take a look at heat transfer basics part zero for more on these basics for water k 0 6 w m² k so as an example if we have a 10ºc temperature difference across 1 km depth of water q 0 006 w m² this is tiny heat flow via conduction is insignificant convection is what moves heat in the ocean many researchers have measured and estimated vertical heat flow in the ocean to come up with a value for vertical eddy diffusivity this allows us to make some rough estimates of vertical heat flow via convection in the next version of the matlab program in press the ocean is modeled with different eddy diffusivities below the mixed ocean layer to see what happens to the measurement of climate sensitivity so far the model comes up with wildly varying results when the eddy diffusivity is low i e heat cannot easily move into the ocean depths and it comes up with normal results when the eddy diffusivity is high i e heat moves relatively quickly into the ocean depths due to shortness of time this problem has not yet been resolved more in due course this article is already long enough so the next part will cover the estimated values for eddy diffusivity because it s an interesting subject conclusion regular readers of this blog understand that navigating to any kind of conclusion takes some time on my part and that s when the subject is well understood i m finding that the signposts on the journey to measuring climate sensitivity are confusing and hard to read and that said this article hasn t shed any more light on the measurement of climate sensitivity instead we have reviewed more ways in which measurements of it might be wrong but not conclusively next up we will take a detour into eddy diffusivity hoping in the meantime that the matlab model problems can be resolved finally a more accurate model incorporating eddy diffusivity to model vertical heat flow in the ocean will show us whether or not climate sensitivity can be accurately measured possibly articles in this series measuring climate sensitivity part one measuring climate sensitivity part three eddy diffusivity references potential biases in feedback diagnosis from observational data a simple model demonstration spencer braswell journal of climate 2008 on the accuracy of deriving climate feedback parameters from correlations between surface temperature and outgoing radiation murphy forster journal of climate 2010 observation of large diurnal warming events in the near surface layer of the western equatorial pacific warm pool soloviev lukas deep sea research part i oceanographic research papers 1997 atmosphere ocean and climate dynamics an introductory text marshall plumb elsevier academic press 2008 mixed layer depth over the global ocean an examination of profile data and a profile based climatology de boyer montegut et al jgr 2004 read full post pages about this blog comments moderation etiquette roadmap atmospheric circulation atmospheric radiation and the greenhouse effect back radiation c...