Interesting article in last weekend's NYT Magazine on Freeman Dyson. Dyson is a member of physics "greatest generation" that emerged from WWII. While he didn't invent the vacuum, he did unify several theories, hung out with Richard Feynman, and provided the scientific rationale for a Star Trek episode. The declared purpose of the article was to describe how such an eminent scientists became an outspoken climate change skeptic, but the article was mostly just an interesting biography of a notable scientist. My interpretation, based on the few snippets about Dyson's views on climate change, is that he is not objecting to much of the scientific rationale behind global warming, but rather is uncomfortable with some of the hyperbole from folks like Al Gore. I have to say, I agree. I think that the scientific basis behind climate change is very strong. There is definitely uncertainty over some of the details, for example, how ecosystems will respond and whether certain ecosystems will become sources or sinks, but the basic idea that CO2 in the atmosphere is contributing to general warming is supported by multiple lines of evidence. A much thornier issue is what to do about it? In the article, Dyson is quoted as saying that industrialization in China has been a good thing, lifting millions out of poverty but at the cost of additional CO2. While China is particularly dramatic, both in terms of the CO2 costs and the benefit to their society, you could make similar cases about any country. Many of these decisions come down to rationale considerations, for example, comparing the costs of coping with rising sea level versus the costs of reducing CO2 emissions. Science, for example, improved regional predictions of climate change impacts, could help with these calculations. However, as Dyson points out, many of the decisions are moral: is it fair for the developed world, who became the "developed world" by accessing cheap fossil fuels, to ask underdeveloped countries to sacrifice economic growth? Thornier still, when do you declare a country "developed" and ask it to pay an increased share of CO2 reductions? My point is that most of the climate change debate has little to do with science. It's up to us and the people we elect to figure out how we will respond. Our ability to make rationale and even moral decisions is not helped by unscientific appeals to emotion from the left or pseudoscientific arguments against climate change from the right.
March 2009 Archives
While our crack economic team predicts a recovery in the "future", 2010 looks like a bleak year for stocks. One stock that stands out is the North Atlantic right whale. After taking a beating for the last 300 years, this year's 39 calves suggests that this stock may be poised for a slow recovery. However, Seascape Investments is cautioning our short-term investors from jumping into right whales at this time. While stock prices do have some autocorrelation (explaining why past performance seems like a good indicator), the number of right whale births has a strong tendency for boom and bust cycles. While right whales may become a conservative long-term investment (that is, slow growing), the cyclic nature of this stock suggests taking the long view, especially in the highly speculative calving market. Here's our reasoning:
The number of right whale births depends on the number of reproductively active females, better known as cows, in the population. However, right whales require two, or more likely three or more, years between births. This means that we need to remove the 39 mothers from this year from the available pool of females. We should also remove most of the mothers from last year, which I believe was pretty good, say 25. The wild card in this guess is how many new females will be added to the pool. Since it takes at least 5 years for a female to become sexually mature (average is 11, see Ch. 6 in the Urban Whale), the high birth years from the early part of this decade are only now starting to enter the population. Let's say that we've added 20 new females since 2005, then we have 112 total cows. Subtracting this year's births and my guesstimate of last year's gives us 48 available females. This provides an upper limit on the number of births for next year. How many will actually give birth will depend on a lot of factors, with my favorite being food. If Calanus is abundant this year, then our earlier modeling work suggests that as many as 63% could calve, producing 30 new whales. Realistically, I think 50% is a better guess, giving 24 calves. While Seascape Labs would never condone the practice, opportunities for short selling in 2010 could be lucrative.
Our lab et al. published a series of papers in the latest issue of Marine Ecology Progress Series in which we explored linkages between copepod abundance and the migration patters of right whales. Better knowledge of where and when right whales might show up can help prevent ship strikes and gear entanglements. The full articles can be found here: 1 2 3.
One of our results was a strong correlation between the computed abundance of Calanus finmarchicus and the arrival date of right whales in the Great South Channel critical habitat. Researchers have known for awhile that right whales use this habitat every year, but the factors that influence the timing of that usage are harder to pin down. (Details on our computations, like how we calculate arrival date and C.fin. abundance, can be found in the papers.)
This correlation may have use as a forecasting tool. The correlation spans the years 1998-2006. By computing the C.fin. abundance for ensuing years, we can use a linear fit to produce a forecast for the arrival date in the Great South Channel (see figure). Our prediction this year is for an early arrival date--right around now, in fact. We also predicted an early arrival for 2007, and a late arrival for 2008.
Figure. Top: correlation between computed C.fin. abundance and right
whale arrival day in the Great South Channel (R^2=0.7, p=0.01). Red dots
show predicted values for 2009, with the most current prediction indicated
by text. Bottom: our predictions for the 2009 arrival date. As the year
progresses, we assimilate more data, and our prediction changes (see point
2 below). The abrupt drop in late February is due to a modification in our
calculation (see point 4 below).
Caveats
There are a few caveats to this forecast. I'll outline them here.
1) A linear regression is a simplification of the dynamics at play, and there is variability about the line. Therefore, even though we give a specific arrival date, our forecasts should be taken as approximate. It's better to think of them as "early", "average", or "late", rather than as occurring on a specific date.
2) Our models rely on satellite data, which is updated as the year progresses. Therefore, our forecast changes as the year marches on (bottom plot in figure). It's similar to how the weather forecast gets better as next week gets closer. This limits us somewhat, but our previous work has shown that satellite data from January and February generally provide enough data to get a significant correlation.
3) We check our forecasts against a whale arrival date that is calculated from survey data. That is, real people looking for whales from boats and planes. It takes a long time for that information to be processed and passed to us, so we haven't yet been able to check our 2007 and 2008 forecasts. So, unlike the weather forecaster, we don't have the advantage of knowing what "today's weather" is. Even though our 2009 forecasts tell us that right whales are arriving in the Great South Channel right around now, or possibly have arrived already, we may not be able to check that for awhile.
4) The nature of satellite data changes with technology. For example, resolution has improved. We've developed a new interpolation method that helps the satellite data to be consistent over many years. The down side is that we had to re-run our experiment with all of the satellite data in this new format. The good news is that the correlations persisted, though altered a little.
One of our results was a strong correlation between the computed abundance of Calanus finmarchicus and the arrival date of right whales in the Great South Channel critical habitat. Researchers have known for awhile that right whales use this habitat every year, but the factors that influence the timing of that usage are harder to pin down. (Details on our computations, like how we calculate arrival date and C.fin. abundance, can be found in the papers.)
This correlation may have use as a forecasting tool. The correlation spans the years 1998-2006. By computing the C.fin. abundance for ensuing years, we can use a linear fit to produce a forecast for the arrival date in the Great South Channel (see figure). Our prediction this year is for an early arrival date--right around now, in fact. We also predicted an early arrival for 2007, and a late arrival for 2008.
Figure. Top: correlation between computed C.fin. abundance and right
whale arrival day in the Great South Channel (R^2=0.7, p=0.01). Red dots
show predicted values for 2009, with the most current prediction indicated
by text. Bottom: our predictions for the 2009 arrival date. As the year
progresses, we assimilate more data, and our prediction changes (see point
2 below). The abrupt drop in late February is due to a modification in our
calculation (see point 4 below).
Caveats
There are a few caveats to this forecast. I'll outline them here.
1) A linear regression is a simplification of the dynamics at play, and there is variability about the line. Therefore, even though we give a specific arrival date, our forecasts should be taken as approximate. It's better to think of them as "early", "average", or "late", rather than as occurring on a specific date.
2) Our models rely on satellite data, which is updated as the year progresses. Therefore, our forecast changes as the year marches on (bottom plot in figure). It's similar to how the weather forecast gets better as next week gets closer. This limits us somewhat, but our previous work has shown that satellite data from January and February generally provide enough data to get a significant correlation.
3) We check our forecasts against a whale arrival date that is calculated from survey data. That is, real people looking for whales from boats and planes. It takes a long time for that information to be processed and passed to us, so we haven't yet been able to check our 2007 and 2008 forecasts. So, unlike the weather forecaster, we don't have the advantage of knowing what "today's weather" is. Even though our 2009 forecasts tell us that right whales are arriving in the Great South Channel right around now, or possibly have arrived already, we may not be able to check that for awhile.
4) The nature of satellite data changes with technology. For example, resolution has improved. We've developed a new interpolation method that helps the satellite data to be consistent over many years. The down side is that we had to re-run our experiment with all of the satellite data in this new format. The good news is that the correlations persisted, though altered a little.
Today the New York Times reported that a record number of right whales have been born this year - 39 so far! That's about 10% of the total population size. The last record was set in 2001 when 31 calves were born. The NYT article lays out the challenges posed by shipping and fishing to the North Atlantic right whale population. Check it out, and be sure to watch the videos (included below).
The question of determining what is and what is not suitable habitat can be tackled from many angles. My tool of choice is an empirical "species distribution model" (SDM), also known as an "ecological niche model", "environmental niche model", "habitat model", and by several other phrases. The name of the game is to gather environmental data from the location (and in my case time) of known species occurrence. By associating environmental data with species occurrence, one can build a characterization of the response of the species to its environment. By applying this characterization to spatial environmental datasets, environmental "suitability" can be estimated over a broader area or in a different time than that of the species occurrences.
I'm using several years of right whale sightings, along with satellite- and model-derived physical and biotic environmental data (e.g. previously posted copepod model output), to produce weekly estimates of right whale habitat suitability. I'm in the model validating phase, in which I build a model with data from years 1,2,...,n-1, and test it with data from year n. I refer to this as an "out of sample" test. A common alternative to this method of model validation is to randomly select and remove a subset of occurrences from all n years, and test the model using these occurrence locations. The former method is a considerably harder task for a model, but I think it is a better for my purposes because it measures the model's performance in the face of inter-annually varying response of a species to its environment.
For certain years I can (using Maxent) build good models the springtime distribution of right whales in the Cape Cod Bay and Great South Channel critical habitats. Pictured is a plot of the receiver operator characteristic curve, and the area underneath that curve (AUC). AUC=0.5 indicates that the model is no better than random, AUC=1.0 indicates that the model is perfect (always placing species occurrences in "good" habitat). An AUC score greater than about 0.75 is generally considered to be the cut-off for a useful model. I built this model with springtime data from 2002, 2003, 2004, 2006, and I tested it with data from 2005. AUC=0.846. Not bad.
We received data from PCCS for four additional cruises. According to Stormy, Pseudocalanus is still running the show in the Bay. Here's the model's take on Pseudocalanus abundance on 2/25, the day of the last survey:
The images are no assimilation (left), assimilating just the January cruises (middle), and assimilating all of the cruises (right). Our model dynamics have Pseudocalanus declining during this time of year, which explains the decrease from left to right in the images. Basically, since Pseudocalanus is higher than normal this year, when we assimilate a cruise, we bump up the abundance. The model dynamics then operate, and the population goes down. So, when we run the model through today, the abundances decrease further:
Interestingly, the image on the right has lower abundance than the one in the middle--something we'll have to look into.
One more comment on the forecasts. We're still waiting on the 2009 circulation fields. So, each ensemble member in the assimilation chooses a flow field from a previous year. This effectively accounts for our uncertainty in the circulation field, assuming that this year is not too far from normal. For the forward run (images above), I ran the model with each of the prior year fields and averaged the results.
As Pete just described, specifying the initial conditions for a model is difficult. In forecasting, whether weather or copepods, a major problem is estimating the initial conditions from the data. Ideally, you would send a few thousand undergrads to the locations of your model grid and have them simultaneously sample whatever you're trying to model. You could then use this data to initialize your model. In the real world, where undergrads are expensive and unreliable, we have to make do with samples collected from only a few locations. We need a way to estimate the state of the system from this sparse array of data.
Data assimilation is a grab-bag of techniques for merging observations and models, and state estimation is the most common application. The idea is to find an initial condition, such that, when the model is started from this condition, it comes close to hitting the observation points. There are lots of procedures that can do this, with cool names like "4D-Var" or "representers", and each has its advantages, disadvantages, and acolytes. For our system, I'm using the ensemble Kalman filter (EnKF), mainly because it is an ensemble method, and I like ensemble methods. At the moment, I'm using a 10 day update cycle. This means that every sample collected between day j and j+10 is used to adjust the model state at day j.
I made three runs of the system for Massachusetts Bay. The first is a control run. I started from the climatological (long-term average) initial conditions and let 'er rip. The second used the EnKF to assimilate the PCCS cruise on January 13, 2009, producing a new initial condition for January 11 (remember the 10 day update cycle). The third assimilated the cruise from January 30, producing a new initial conditions for January 21. Here's how the three runs compare on January 30 for Pseudocalanus:
| No assimilation | First cruise | Second cruise |
|---|---|---|
 |
 |
 |
| Model estimates of Pseudocalanus on January 30 | ||
Assimilating the first cruise increased the concentrations on 1/13 a little bit. This led to increased concentrations on 1/30. Assimilating the second cruised increased the values even more. I continued to run all three versions until today (March 3):
| No assimilation | First cruise | Second cruise |
|---|---|---|
 |
 |
 |
| Model estimates of Pseudocalanus on March 3 | ||
The model predicts that all three should decline (this is the model dynamics--Pseudocalanus usually declines this time of year), but the large values in model three allow some persistence.
In case you get the idea that assimilation always increases the values, here are the plots for Centropages on 1/30:
| No assimilation | First cruise | Second cruise |
|---|---|---|
 |
 |
 |
| Model estimates of Centropages on January 30 | ||
The first cruise encountered some very high Centropages concentrations, but the levels had declined by the second cruise.
