Ice Modeling of Lake Superior

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.

jay-

Posted by Jay Austin at 11:44 AM | Permalink | Comments (0)

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.

jay-

Posted by Jay Austin at 12:21 PM | Permalink | Comments (0)

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.

jay-

Posted by Jay Austin at 12:53 PM | Permalink | Comments (0)

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.

jay-

Posted by Jay Austin at 10:32 AM | Permalink | Comments (0)

THere are a handful of other fields that need to be determined to provide al lthe data needed for the turbulent fluxes.

1. Barometric pressure: I use a constant value of 1014mb for this, due to a problem wit hthe NOAA NDBC files. In the future, this will be corrected. this is not important but not too hard to get right.

2. Relative Humidity. I use a constant value of 80% at all times, all locations. This is important for the latent flux. A model run with a time varying RH (taken from STDM) resulted in almost exactly the same heat fluxes. It would be nice to improve this but I don't see any easy way.

3. Precipitation. I set rain=0 at all times. This is probably a real problem, especially when there is ice and the precip would be forming snow.

Posted by Jay Austin at 1:43 PM | Permalink | Comments (0)

The downward longwave field is determined in much the same way- using ground-truth data from the 2008 buoy deployment, and then developing a relationship between observed cloud cover, air temperature, and observed longwave. The higher the cloud cover, the higher the longwave signal. The higher the AT the higher the downward longwave.

Posted by Jay Austin at 1:32 PM | Permalink | Comments (0)

Shortwave radiation (0.3-3um) is the main source of heat to the lake. It depends on two things:

1. The position of the sun in the sky;
2. Latitude and longitude
3. Cloud cover.

#1 and #2 can be determined for the model grid as a function of time pretty precisely. #3 is a bit more difficult.

I have taken MODIS imagery for 2008 and compared the image intensity at a set of pixels located roughly around the location of my surface buoy in 2008. I then compare this image intensity to the fraction of the clear-sky shortwave that is reaching the buoy. The fit, while noisy, suggests the expected relationship:

when the image intensity is high (i.e. R, G, and B values are large) the image is very white, indicating the presence of clouds, and the resulting observed shortwave fraction is small. And vice versa. I'm currently using the quadratic fit shown, though I'm tempted to switch back to the linear fit, because it does a good job of going to 1 as the image intensity goes to zero.

Given this relationship, I can take a MODIS image from a given day and combine it with the astronomical prediction of clear-sky radiation to make an estimate of how much radiation should be reaching the surface at every point.

One big drawback: I'm using MODIS imagery since it is easy to access right now (through NOAA GLERL's CoastWatch program). Ice also appears white, so I am biasing the forcing towards the low side in the winter, since I count ice as clouds. In the long run, I'm going to identify a satellite product that tells us about atmospheric moisture instead of using color.

Posted by Jay Austin at 1:19 PM | Permalink | Comments (0)

An objectively interpolated field will of course have uncertainty. The further away you get from the original data, the worse that uncertainty gets. I've made maps of uncertainty for the NOAA stations (assuming all are reporting data, which is almost never true) for two cases: One, the summer case, where we have three open-water buoys available, and two, a winter case, where there is no data from the buoys. Here are those fields:

Things to notice: In the summer field, we do a great job in the western arm of the lake. This is good since that's where we're putting some of our more interesting instrumentation- we'll have better model results in this region because we have better forcing. There are some spots along the NE coast where the uncertainty is very high. Keep in mind that in this case, the interpolation relaxes to the mean of the available data, not to zero or some other un-useful point. So it's not as it there isn't forcing data up ther, it's just that it probably is not particularly representative of any regional variability.

In the winter, without the Central and Eastern buoys, the NE part of the lake is even more poorly covered. The Western Arm, however, still has very good coverage, even without the western buoy.

If we used a longer decorrelation scale, the coverage up north would be better. But the fields would be a lot smoother.

The apparently open-lake site to the E of the Keweenaw is Stannard Rock, a lighthouse, and operable all year round.

Posted by Jay Austin at 1:02 PM | Permalink | Comments (0)

In order to do an objective analysis of the NOAA data onto a regular grid, we need some idea of what the decorrelation lengthscale of the particular value is. The two fields I'm most interested in are wind speed and air temperature. I've taken all of the 2008 data and done correlations between each pair of stations, and plotted those correlations as a function of station separation:

With the wind speed, it appears that stations separated by 100km have a correlation of about 0.5, and stations are essentially uncorrelated once their separation reaches about 500km. I choose a decorrelation lengthscale of 100km from this. This is not a precision operation, as you can see- the point here is that the decorrelation lengthscale for wind speed is neither 10km or 1000km.

The air temperature is a different beast- The correlations remain extremely high regardless of the separation distance. This is because the vast majority of the variability in air temperature is at the annual scale, which is highly coherent across the lake. All the same, I'm going to use a decorrelation scale of 100km for air temperature as well. This will act as a decent interpolator of the AT.

Posted by Jay Austin at 12:36 PM | Permalink | Comments (0)

For reference, here is a simple lake Superior map with the names of all of the NOAA NDBC stations. Not all are active all of the time, and many (most) only have historical data as far back as 2007. One thing that should be very clear from this is that coverage in the North of the lake is poor- Canadian data is hard to come by, but may be worth looking into.

Posted by Jay Austin at 12:27 PM | Permalink | Comments (0)