is a link to a video of the surface temperature during the 2008 season. This is more of a test than anything else.
is a link to a video of the surface temperature during the 2008 season. This is more of a test than anything else.
Here's an early model sensitivity result from a series of runs I just did. I tested the model's sensitivity to two parameters:
1. The initial starting temperature: The base case has a uniform initial temperature of 3.8C, and I did two runs where everything else is identical, but I use an initial temperature of 2.8C or 4.8C. These are HUGE swings in initial heat content, but not completely unrealistic, based on observational data.
2. The air temperature. For the base case, I use a forcing field of AT, then I did two runs where I added and subtracted 1C.
I present the results in two different fashions:
1. Heat content, scaled to average temperature
2. Surface temperature at the location of the western NOAA buoy.
here are the results:
The first row shows the case where I start with a different initial condition. What I'm really interested in here is, since they are all being forced identically, they should all eventually approach the same solution. Here we can see that after a year, they are still separated by ~0.1C or so. Most of the difference goes away in the fall cooling period at the end of the year- much of the difference is retained through the winter and much of the summer. It also clearly makes a huge impact on the date of summer overturn.
In the case where I start with an identical initial condition but vary the air temperature by +/- 1C, there is remarkably little difference, but it has just occurred to me that I may not have done these right. For now, ignore the bottom row.
So the ice had cleared off of the lake a few days ago. Yesterday, however, was a remarkably windy (25-30kt) day, with the wind blowing directly down the western arm of the lake towards Duluth/Superior. Around 2:00, I noticed from our house giant sheets of ice WAY out on the lake, towards MI/WI. A few hours later, these giant sheets moved into the tip of the western arm, where as far as I know they remain (it's a very cloudy day). It was very impressive to see these giant sheets of ice move down the lake.
So I ran three model configurations over the weekend.
1. A new "base case" model with the humidity field fixed (NDBC+quikscat winds, monthly cloud averages for shortwave forcing, etc);
2. A run with a 170m-deep flat bottom to assess how important the very shallow regions of the lake are;
3. A run with a small amount of precipitation turned on, constant, as a sensitivity check.
The top plot shows the average and maximum ice thickness (I don't account for open ares of the lake here- I simply divide the total volume by total area of ice.). This is still bad- we're seeing some ice hold on until the end of June, which is unrealistic. I'm still not sure why ice is sticking around so long.
The second plot shows the total areal extend of ice during the run (this is 2008 forcing, BTW). This is actually pretty encouraging. Though it lasts very late, the total area maxes out at around 50% of the total lake area (the solid line on top, about 8x10^10m2). This is in line with observations. I haven't actually seen any ice estimates for 2008 but it's something worth looking for.
The third shows the ice volume. I don't know of any way observationally to verify this or even to see if it is in the ballpark.
The fourth plot shows "heat content" relative to 0C of the entire lake. There are two curves plotted: the change in heat content due to change in water temperature, and that plus the heat change due to the latent heat of fusion needed to freeze ice. The two curves are VERY close to each other- only in March can you really discern a difference. This is really interesting, and I think un- or under-appreciated. The "negative thermal storage" of the ice is essentially trivial compared to the amount of heat that goes into changing the temperature of the water. I guess this makes sense since there's only O(0.1m) of ice but O(100m) of liquid water. Still, very interesting. It implies that ice plays a very minor role in the uptake of heat, but may play a very significant role in the heat balance by shutting down the shortwave flux. I'm going to run an identical model with the ice model turned off and compare the two.
By the way, the heat content shown here is very much in line with observations (both from the Werne/Austin mooring and from the GLENDA data).
My suspicion on the thickness of ice and the lateness of ice is that wind forcing is still nowhere near strong enough. It's clear comparing model results with moored results that we're not mixing cold water down far enough in the winter. It doesn't take much more water column cooling to completely offset the formation of ice (as in the last panel). I'm going to do another model run with the wind cranked up a bit as a sensitivity study.
Oh. Comparisons: The flat bottomed run produced less ice and it went away earlier, though not dramatically so. The maximum heat content in this case in the summer was less than in the base case.
Adding precipitation caused only minor changes in ice area or volume.
Okay, just for fun I've plotted moored data (from the Werne/Austin mooring in Western Superior) and temperature data from the model ,at the nearest equivalent grid point. Remember that we only have mooring data available through the end of September , when we last visited the mooring. Take a look:
A few quick comments:
It's not bad, for a first cut. The model does a good job of producing winter stratification. It fails to mix away stratification in the spring, which occurs at the mooring. The model does a good job of predicting the timing of the onset of summer stratification. The model heats up a little more slowly than the observations, though both predict a maximum surface temperature of around 18C, though the timing is slightly different. there's an intense mixing event in late August which is followed by seiching activity (in general, the model results are a bit more seiche-y than the observations). The deep water in both cases is very close to Tmd.
It will be interesting to recover the mooring this spring and see how the fall data plays out.
Not sure how this will work- I got it to run with Real Player, but didn't work with the Windows media player.
I've completed a run with the new bathymetry and wind forcing which includes Quikscat data. Considerably less ice forms, which is good, but there's still too much, which is bad.
The ice seems to be difficult to blow away from the coast. It may be that having so few grid points in some of the tighter parts of the lake (like the western arm) make it difficult for the ice to get blown out.
I think a large part of the problem is that I'm using the MODIS imagery to estimate clouds, and my algorithm does not distinguish between clouds and ice. Therefore, when there is ice in the imagery, it automatically cuts down on the amount of SHF the surface receives. The model, of course, then applies an albedo to this artificially reduced radiation, and results in even less heat entering the system.
Lousy wind forcing I think is in part responsible for the copious ice formation in the previous version of the forcing/model. I have taken QuikScat (satellite-derived) winds for Lake Superior and included it in the production of the wind forcing. this should dramatically increase wind speeds over the open lake, especially in seasons when we don't have open water wind estimates from the buoys.
The buoy data and the QuikScat data compare remarkably well. I've always thought of QS winds as only a step or two removed from magic, and am always amazed that the technology works at all, much less works well.
I've developed a new grid for the model, very slightly larger than the original one. I used a much more highly resolved bathymetry file provided by Steve Colman, which represents a compilation of just about every bathymetric measurement ever made in lake Superior.
About 50% of the grid is masked out, which is a bummer but that's what we get for working in an oddly shaped domain.
I also capped the bottom depth at 20m; I think part of the large ice formation in the previous runs was due to the fact that large swathes of the coastal zone were ~5m deep. In 5m of water, it's easy to generate huge amounts of ice, which is then transported into deeper water, where it is difficult to melt.
One thing to think about: Shallow reaches of the lake as "ice factories"- creating and transporting ice to warmer, deeper parts of the lake.
Here is a comparison of the development of the temperature field at station 1 for two different runs: One using the original ROMS Equation of state (EOS) and one using Chen and Millero. The bottom panel is the difference between the two. These effects are subtle but I am a lot more comfortable with the development of the temperature field wit h the C&M EOS.
In an attempt to figure out what's going on around Tmd in the model, especially after the onset of summer stratification, I've recoded the nonlinear equation of state in rho_eos.F (and added constants to mod_eoscoef.F).
I've used the formulation of Chen and Millero (1986) which is a set of formulae derived specifically for fresh water (i.e. S<0.6). So far the model seems to be behaving just fine- I'll know more in a few hours once it's past the stage where it undergoes the spring/summer overturn.
In SeaIce/ice_mk.h, the salinity of sea ice is set to be 5.00 (not zero, as you might expect in a freshwater lake). Hopefully we've all got SALINITY turned off so that this doesn't affect the density field, but I don't know what else it might affect. I strongly recommend setting sice=0.00 in ice_mk.h.
Here is an analysis of gridded wind speed versus observed open-lake wind speed.
One issue that we face is the lack of open-lake observations of wind speed/velocity during the winter, since the buoys are pulled from November-April. To get a sense of what sort of error I might be incurring by simply using the objective analysis of coastal stations to infer open lake wind speeds, I used the summer NOAA data, MINUS the open lake buoys, and gridded wind velocity. I then compared it to the observed, in-situ wind speeds from the three buoys, using just 2008 data.
In this figure, I compare the EW component, the NS component, and the speed at all three NOAA sites. It's very clear from this that in all cases we dramatically underestimate the open lake speeds by just using the coastal stations. Not just by 10 or 20%, but by 50 or 100%. This is going to have very significant implications for mixed-layer formation.
The transfer function between coastal and open lake measurements is also a strong function of AT-WT, which I am not considering here. This makes it difficult to use these summer relationships to predict what the relationship might be like in the winter.
All of this begs the question: what do we do about it? I think one very well defined, non-trivial goal at this stage is to come up with some method of creating a reasonably realistic open-lake wind velocity field. I am beginning to look at whether Quikscat data might be useful.
I ran a case with wind speeds increased 10% over the base case (2008 forcing). Less ice forms, as predicted (about 10-15% less integrated over the lake) but it's still a lot of ice. It remains to be seen how much stronger the open lake winds really are. In the high wind case, more heat is lost from the lake even though less ice forms. The surface cold layer is thicker in this case.
I find it strange that in none of these cases are we seeing any mixing below about 80m, even thoug hthe density differences are vanishingly small. These big wind events should be mixing down to the bottom, cooling off the lower layer, but this is not happening. This along with the bizarre behavior around 4C makes me think it might be worth considering a different mixing scheme.
I'm not sure who to discuss this with- I don't think the GLERL guys spend a lot of time thinking about this sort of thing. Wuest or Carmack, those sort of guys might have some insights.
Here's what I think the problem (with my current model configuration) may be:
I think that for some combination of reasons (to be discussed) the wind being applied to the model is too weak. THis causes the loss of heat in the winter to be confined to the upper 50m or so. If the wind was stronger, the cooling would extend further down into the water column and the cooling would occur much more slowly. This would prevent the large buildup of ice that I am currently getting. I am currently running a model with winds increased by 10% across the board, just as a sensitivity test and a proof of concept.
Why might the winds I'm using be too weak? Two possibilities, and I think both are true to some extent:
1. I am using 3-hour average winds right now, which does not capture any of the high-frequency variability. Mixing processes are very non-linear, and there are lots of threshold-like rules governing whether a mixed layer deepens, so it may be that using an average gives us, for instance, the right amount of momentum transfer, but does a lousy job at capturing the mixing potential of the wind field.
2. In the winter, we are not using any open water measurements (except, in a sense, STDM). open-lake winds tend to be stronger, in general (Schwab comments on all of this in Schwab and Morton JGLR 10(1) 68-72). Since we're using coastal winds to determine open-lake conditions, I may be underestimating the open-lake winds, at least in the winter. I am going to do some comparisons between STDM and coastal stations ,as well as between the buoys and coastal stations in the spring, to see whether there might be some way of imposing a higer wind speed in the open parts of the lake.
It should be noted that I am using a standard power-law relationship to adjust all winds to 5m. I should poke around inside of ROMS to see what height ROMS assumes winds are measured at. That's not set anywhere.