## Tuesday: 28 December 2010

The snow is disappearing now, but still remains about 50% coverage. Until today our temperatures haven't broken 40 degF, and only close to that for a couple of hours yesterday. Last night it dropped to 17 deg, the fourth time in December it's dropped below 20 deg.

I measured a total of 3.6 inches, but it compacted down to 2.7" within a day. Actually it was probably more than that since probably 3/4 of what fell in the first round on Christmas night melted, leaving only 0.3" before the second round started. The total snow melt was 0.28" of water, which I'd ordinarily consider as a negligible rainfall.

Measuring snow is a skill that I have to redevelop once a year, or less, although I do a pretty good job of it once I've reconstructed everything.

Glenn was exploring an interesting demo version of a panorama construction software, AutoStitch. It's currently not available for Linux/Mac, but there must be similar software out there.

On Sunday afternoon, at the peak, I took eight photos from the southeast deck corner, spanning 270 degrees (!!) around me, and it transparently pieced together all of those to produce this downsized image. Clicking on the image links to a 400kb 2000 pixel across. This slightly overfills my very large screen, but gives you a good idea of the seamless quality.

At N (north) is the east side of the house, with two of the ponds between N and E, and the top of the driveway invisible just to the left of E. The fairy ring, in the distance, is around South. And if you could see beyond the stuff in the photo then from that point rightward to West the terrain would drop fifty feet to the creek. There have been many, many blog entries arising from explorations in what you can see here.

I didn't really challenge the software, probably. In the past, I've produced panoramas manually, and learned to use the automatic setting on the camera to get the approximate exposure and aperture, and then switched to manual for those settings. That way I don't have superbright and super dim photos as I move along. But there has always been a visible seam, and the lighting has varied across the panorama.

The software was capable of handling my eight photos, each 3-5 MB, with no problem. Glenn had really challenged it, with his own series of 16 unreduced photos, taken on automatic setting, and the result was superb. I couldn't detect any seams.

I think the demo version of AutoStitch will only do a 1-D reconstruction (a series taken in a row). If you want to produce a panorama that has 2-D images (one or more series atop the others), the demo won't do that. Still, it's quite a nice trick.

## Sunday: 26 December 2010

идёт дождь

идёт снег

Well that was fun. Not oodles of fun, and not as much fun as a barrel of monkeys, but definitely more fun than near freezing temperatures on a clear night. There are safety issues here, and four other fire departments were called out last night on two occasions, so I'll go into some detail as of 7am.

UPDATE: OK, it's reached the oodles of fun stage. At 7:30am, it's very pretty and continuing to come down. Snow is so passive-aggressive.

UPDATE2: We're now into the barrel of monkeys level of fun. At 9am, it's still snowing at 1.6" since 4:30am. This started at that time as a 30-mile diameter event, right over us, and it's now expanded to cover much of east Georgia. Atlanta isn't getting much of it at all. It's lovely, but with the prediction of temperatures through Tuesday I'm really skeptical of my competence at driving in what results.

Temperatures since Friday evening haven't been above 40 degF, so the ground is quite cool, especially since Saturday's afternoon rain. That turned to snow around 8pm, directly, without a transition involving mixed rain. It snowed until midnight and then the plume of moisture coming up from the Gulf moved quickly to our east and away. The temperatures never got below 33 degF - the cold wave from the north didn't reach us quickly enough, so when I measured the snow depth at 2AM it was only 0.6". However, the snow and melt in the rain gauge outer cylinder was 0.14", so somewhere between 1" and 1.5" of snow must have actually fallen.

Glenn was out around 4am picking rosemary and oregano for the turkey soup, and we laughed about it being washed pure by snow melt already. It's a good thing that he got his herbs then, because at 4:30am it started snowing again and is falling quite nicely now at 7am. I just measured the new snow at 0.7" and the old+new at 1.3". Best guess is that at this time we've had a little over a couple inches of snow, with a good bit melting away early on.

Temperatures are now below freezing and not expected to get much warmer today and certainly not tonight. We'll probably get high winds after the snow stops around noon, and maybe that will sublimate some of the frozen water from the roads in places, but there will be icy patches for the next day or so, so watch out if you're in the northern half of Georgia.

UPDATE2, continued - roads are going to be MUCH more hazardous around here than it appeared at that time.

My sourdough starter culture was fed for the first time yesterday, and is bubbling away, very happy snuggling next to the computer fan exhaust.

идёт снег

Well that was fun. Not oodles of fun, and not as much fun as a barrel of monkeys, but definitely more fun than near freezing temperatures on a clear night. There are safety issues here, and four other fire departments were called out last night on two occasions, so I'll go into some detail as of 7am.

UPDATE: OK, it's reached the oodles of fun stage. At 7:30am, it's very pretty and continuing to come down. Snow is so passive-aggressive.

UPDATE2: We're now into the barrel of monkeys level of fun. At 9am, it's still snowing at 1.6" since 4:30am. This started at that time as a 30-mile diameter event, right over us, and it's now expanded to cover much of east Georgia. Atlanta isn't getting much of it at all. It's lovely, but with the prediction of temperatures through Tuesday I'm really skeptical of my competence at driving in what results.

Temperatures since Friday evening haven't been above 40 degF, so the ground is quite cool, especially since Saturday's afternoon rain. That turned to snow around 8pm, directly, without a transition involving mixed rain. It snowed until midnight and then the plume of moisture coming up from the Gulf moved quickly to our east and away. The temperatures never got below 33 degF - the cold wave from the north didn't reach us quickly enough, so when I measured the snow depth at 2AM it was only 0.6". However, the snow and melt in the rain gauge outer cylinder was 0.14", so somewhere between 1" and 1.5" of snow must have actually fallen.

Glenn was out around 4am picking rosemary and oregano for the turkey soup, and we laughed about it being washed pure by snow melt already. It's a good thing that he got his herbs then, because at 4:30am it started snowing again and is falling quite nicely now at 7am. I just measured the new snow at 0.7" and the old+new at 1.3". Best guess is that at this time we've had a little over a couple inches of snow, with a good bit melting away early on.

Temperatures are now below freezing and not expected to get much warmer today and certainly not tonight. We'll probably get high winds after the snow stops around noon, and maybe that will sublimate some of the frozen water from the roads in places, but there will be icy patches for the next day or so, so watch out if you're in the northern half of Georgia.

UPDATE2, continued - roads are going to be MUCH more hazardous around here than it appeared at that time.

My sourdough starter culture was fed for the first time yesterday, and is bubbling away, very happy snuggling next to the computer fan exhaust.

## Saturday: 25 December 2010

Merry Christmas to everyone, and may none of us have 10-70 or 10-50 calls. If the forecast comes through, and while we've been sitting on a pins and needles not daring to hope it does look now like it's going to make, it will be the first white Christmas that I can remember in a place that I called home. It's starting to rain now, the temperatures are dropping, and 1-2 inches of snow is expected later this afternoon, tonight, and tomorrow. It looks like Mark is already getting a mixture. |

Glenn was in Wisconsin, visiting his father and step mom this past week, where it snows and is cold, though not as cold as you might have thought. He came through with a smashing color contrast here. I'll let the northern taxonomists figure this one out, although I think I know what it is.

## Friday: 24 December 2010

I had been idly following along with Donna Currie's sourdough starter posts, beginning with this one. She has a nice, stripped down approach, complete with photographs, and a respectable flurry of comments on each post.

Her approach tosses out all the pineapple juice, grape, raisin, and other complicated additions, using only flour and water and whatever yeasts and lactobacilli are clinging to the flour, in the water, and in the air. It still takes "9 days" to get it to the point of First Harvest, but that will be true of all sourdough starters from the very beginning.

The reason I like it is the reason any scientist likes a good experimental setup - it reduces the number of variables. And figuring out what's going on is aided by a feel for ecological succession and cellular respiration, believe it or not.

Sourdough starter was the original source for yeast in leavened bread. A substantial glob of starter is fortified with flour and water, and allowed to incubate for a day even before you begin the process of breadmaking. Now you buy a packet of activated freeze-dried yeast, and that shortens the process of rising from a couple days to an hour or two. But there's a purported loss of unique flavor due to the balance of yeast and lactobacilli that can only come from the starter culture.

Now in my case, I'm more interested in the holy grail of pizza. After a number of trials, I've settled on the cold rise approach, in which the pizza dough is left in the fridge for two or three days before the final product is made. Consequently, the time involved in the use of a starter instead of activated yeast does not particularly deter me.

Let's start with ecological succession.

You're probably familiar with the usual example of ecological succession: a disturbed area, annuals and the beginnings of shrubs and pine trees in the next couple of years, a pine forest over the next decade or two. Eventually hardwoods take over and over the next *century* or two, without further disturbance, a climax forest diagnostic for the climate will result.

Except for the times involved, making a sourdough starter is much the same. Instead of a disturbed area, we have at Day 0 a mixture of flour and water. Instead of the dormant annual, shrub, and pine seeds in the disturbed ground, we have the endospores of lactobacilli, yeast, AND a whole lot of other stuff.

For the first few days we have a mad rush of many organisms, especially bacteria: the ones we want plus a lot we don't want, trying to gain the majority. Folks complain about the early odor of a starter culture: smells of old shoes, baby puke. A microbiologist could probably tell you what temporary populations are waxing and waning just by the smells. But all that disappears after a bit, leaving the characteristic, desirable odor of a sourdough starter.

In the same way, that disturbed ground is going to grow up all sorts of temporary denizens - blackberries will come to mind. But the sun-loving blackberries will go away as soon as the pines begin to tower over them, cutting off the sun.

The pines themselves are a temporary species - they contribute to the acidity of the soil. That, along with the shade they produce, inhibits germination of any pine seeds they drop. Broad-leaved hardwoods will not have this vulnerability, and will ultimately take over.

And so with the sourdough starter, but the process will only take a few days. The culture will produce acid, as do all living cells, and in that environment only the yeasts and lactobacilli, our hardwoods of the culture, will be able to persist. Given the appropriate feeding and attention, our climax culture is stable indefinitely. The shaping of the starter environment by the interacting yeast and lactobacilli will prevent other organisms from gaining a foothold.

Her approach tosses out all the pineapple juice, grape, raisin, and other complicated additions, using only flour and water and whatever yeasts and lactobacilli are clinging to the flour, in the water, and in the air. It still takes "9 days" to get it to the point of First Harvest, but that will be true of all sourdough starters from the very beginning.

The reason I like it is the reason any scientist likes a good experimental setup - it reduces the number of variables. And figuring out what's going on is aided by a feel for ecological succession and cellular respiration, believe it or not.

Sourdough starter was the original source for yeast in leavened bread. A substantial glob of starter is fortified with flour and water, and allowed to incubate for a day even before you begin the process of breadmaking. Now you buy a packet of activated freeze-dried yeast, and that shortens the process of rising from a couple days to an hour or two. But there's a purported loss of unique flavor due to the balance of yeast and lactobacilli that can only come from the starter culture.

Now in my case, I'm more interested in the holy grail of pizza. After a number of trials, I've settled on the cold rise approach, in which the pizza dough is left in the fridge for two or three days before the final product is made. Consequently, the time involved in the use of a starter instead of activated yeast does not particularly deter me.

Let's start with ecological succession.

You're probably familiar with the usual example of ecological succession: a disturbed area, annuals and the beginnings of shrubs and pine trees in the next couple of years, a pine forest over the next decade or two. Eventually hardwoods take over and over the next *century* or two, without further disturbance, a climax forest diagnostic for the climate will result.

Except for the times involved, making a sourdough starter is much the same. Instead of a disturbed area, we have at Day 0 a mixture of flour and water. Instead of the dormant annual, shrub, and pine seeds in the disturbed ground, we have the endospores of lactobacilli, yeast, AND a whole lot of other stuff.

For the first few days we have a mad rush of many organisms, especially bacteria: the ones we want plus a lot we don't want, trying to gain the majority. Folks complain about the early odor of a starter culture: smells of old shoes, baby puke. A microbiologist could probably tell you what temporary populations are waxing and waning just by the smells. But all that disappears after a bit, leaving the characteristic, desirable odor of a sourdough starter.

In the same way, that disturbed ground is going to grow up all sorts of temporary denizens - blackberries will come to mind. But the sun-loving blackberries will go away as soon as the pines begin to tower over them, cutting off the sun.

The pines themselves are a temporary species - they contribute to the acidity of the soil. That, along with the shade they produce, inhibits germination of any pine seeds they drop. Broad-leaved hardwoods will not have this vulnerability, and will ultimately take over.

And so with the sourdough starter, but the process will only take a few days. The culture will produce acid, as do all living cells, and in that environment only the yeasts and lactobacilli, our hardwoods of the culture, will be able to persist. Given the appropriate feeding and attention, our climax culture is stable indefinitely. The shaping of the starter environment by the interacting yeast and lactobacilli will prevent other organisms from gaining a foothold.

## Tuesday: 21 December 2010

A couple days ago I was walking down the creek, noticing odd white droppings on fallen leaves. They looked like large bird droppings. Within a short distance, I came upon the grisly remains of a deer carcass in SBS Creek. I'll just put this teensy little thumbnail that will open up in a new page if you click on it.

The first thought is that it's the result of messy hunters, which is possible but I judge it unlikely. The presence of the head with its rack seems like a reasonable argument against that. If hunter-caused, it could be that the deer was shot poorly at some distance away, and escaped to die at this point. It's also possible that the deer just died.

It's not the first time I've found a dead deer (or other animal) in one of the two creeks that run through or along the border of the property. I have an immediate impulse to remove the carcass, but so far have just let such things remain. If we or others used the water in the creek, it would be objectionable to have a rotting carcass foul the creek, but we don't. And in any event, the worst of the damage, if damage it is, is already done. The words "foul" and "damage" are only relevant from the human point of view. Nonhuman organisms would quickly outvote us in this matter, if they were enfranchised.

These things disappear surprisingly fast. Oh, the hair and bones will remain for years, but they'll quickly be dispersed as animals drag parts away - it's already happening. I'm guessing all manner of scavengers, including vultures and crows, have been at it, and that that explained the droppings on the fallen leaves. Raccoons, opossums, coyotes - all have probably benefited from this bounty. Of course it would be nice if it were bounty somewhere else, but no one but me will come upon it or be affected by it.

And unseen has been the downstream influx of energy rich organic material, including valuable reduced nitrogen. This has surely been appreciated by the tiny things that operate 24/7, as well as the larger things that consume the smaller.

The first thought is that it's the result of messy hunters, which is possible but I judge it unlikely. The presence of the head with its rack seems like a reasonable argument against that. If hunter-caused, it could be that the deer was shot poorly at some distance away, and escaped to die at this point. It's also possible that the deer just died.

It's not the first time I've found a dead deer (or other animal) in one of the two creeks that run through or along the border of the property. I have an immediate impulse to remove the carcass, but so far have just let such things remain. If we or others used the water in the creek, it would be objectionable to have a rotting carcass foul the creek, but we don't. And in any event, the worst of the damage, if damage it is, is already done. The words "foul" and "damage" are only relevant from the human point of view. Nonhuman organisms would quickly outvote us in this matter, if they were enfranchised.

These things disappear surprisingly fast. Oh, the hair and bones will remain for years, but they'll quickly be dispersed as animals drag parts away - it's already happening. I'm guessing all manner of scavengers, including vultures and crows, have been at it, and that that explained the droppings on the fallen leaves. Raccoons, opossums, coyotes - all have probably benefited from this bounty. Of course it would be nice if it were bounty somewhere else, but no one but me will come upon it or be affected by it.

And unseen has been the downstream influx of energy rich organic material, including valuable reduced nitrogen. This has surely been appreciated by the tiny things that operate 24/7, as well as the larger things that consume the smaller.

## Sunday: 19 December 2010

On the west coast - looks like some ones in the northern California area are having an interesting day.

Today I'm going to blow everyone out of the water by demonstrating that rainfalls in Tucson AZ, St Louis MO, and Oglethorpe County GA are different. Furthermore I'm going to show that rainfalls in Wolfskin and Lexington, 10 miles away, are not significantly different.

We're going to do this two ways. First, visually: I took rainfall data from 2009 and 2010 from four reliable CoCoRaHS observers. It wasn't that easy to find suitable observers - they had to have made observations just about every one of the 714 days with as few multi-day entries as possible. I used myself (of course) for Wolfskin, my reliable fellow Oglethorpian Al, GA-OG-1, in Lexington GA ten miles away, MO-FSA-189 in St Louis MO (purported to have a climate and rainfall similar to ours), and AZ-PM-46 in Tucson, AZ (purported to have a very different climate). These are also as close as I could get to Bisbee and Kansas City!

Here is the plot for Wolfskin vs Lexington, with rainfall in Wolfskin plotted vs that in Lexington ten miles away. By pure coincidence, it rained on 239 days out of 714 for both locations. There is a 0.335 probability of rain on any given day in both locations.

There are a few times when it rained in one place and not the other, but very few - you'd otherwise see those points sitting on the X or Y axis instead of in the middle. There are differences in the amounts that it rained, otherwise all the data points would lie on the diagonal. The points roughly cluster about the diagonal, with a similar number above and below it.

Notice that there isn't any particular pattern to the colors of the data points, indicating that the time of year isn't likely to be important.

Now here is the plot of Wolfskin vs St Louis MO. This observer measured rainfall on 166 days out of 714, a little lower than Wolfskin, giving a 0.232 probability of rain on any given day.

Suddenly there are lots of points on the X and Y axes, indicating that it frequently rained in one location, but not the other. There are fewer points within the area of the plot where it rained in both locations on the same day. There isn't much suggestion of any clustering about the diagonal.

Finally, we plot Wolfskin vs Tucson AZ. It only rained on 86 days for this observer in Tucson, out of 714 days total. Tucson has only a 0.120 probability of rain on any given day.

Now, almost all the points lie on the axes, with most of them below the diagonal. That's not surprising - we in Wolfskin get rain more frequently than our friends in Tucson. Still, there are a few points within the area of the plot, indicating that there were days when it rained in both Wolfskin and Tucson.

Visually, you can see the differences between the plots, and they make sense. But how can we actually look at the first plot above, of Wolfskin and nearby Lexington, and rigorously say that those rainfall patterns are the same, or that the other patterns are not?

We have to do it statistically, I'm afraid. That's what cold wet winter days will do to you - some people mop floors and clean toilets. I concoct silly experiments and do statistics.

I'm attracted to it, at least on cold wet winter days, because there is something - three things, really - that are intellectually and logically very satisfying:

First, there is the idea of the Null Hypothesis. Students tend not to come up with this one when they're asked to form a hypothesis, but it's really the best one when it comes to performing statistical tests. The null hypothesis simply says that there is NO difference between two sets of data.

The second neat thing is figuring out what aspect of the data can be tested, and how it can be done. Here we have a lot of numbers, and in this simplest form of the test we won't worry about the amount that it rained on any given day. For our two locations, we'll just count the number of times it rained on the same day (YY), the number of times it rained in one place but not the other (YN), the other but not the one (NY), and the number of days it rained in neither place (NN). These numbers are going to be the Observations.

The third thing that all good card players intuitively know, and that we're going to get to play with here, is figuring out what we'd expect on the basis of probability. When we've done this, we'll have a parallel set of numbers that will be our Expectations.

We finally will want to compare the Expected to the Observed. It turns out there is a very good test, the chi-square test, that will tell us whether two distributions of data are the same or not. This will in fact be our hypothesis, the Null Hypothesis, that there is no difference between the rainfall data for two locations.

For instance, Wolfskin has a rain probability of 0.335 (Y), which also means there is a 1-0.335 or 0.665 chance that it will Not rain on a given day (N). Tucson has a similar set of numbers, Y and N = 0.121 and 0.879. The probability that it will rain in both places, YY, is 0.335 x 0.121, or 0.0405. Over 714 days, we'd Expect that it rains in both place 0.0405 x 714, or on 29 days.

We expect 29, and in fact we see that it rained 23 days in both Wolfskin and Tucson. We're off by a difference of 6 days between what we Expect and what we Observe. Here's the whole table of expected and observed events, for all three pairs of locations (rows), in all four categories (columns).

You calculate a chi-square value for each row by squaring the difference between the Observed and Expected, dividing the result by the Expected, and then summing the results across each row. Those numbers appear in the chi-square column.

Now we go to a handy table of probability (p) values for the chi-square distribution. Despite that we have four sets of data each consisting of 714 measurements, we're only looking at n=4 aspects of it (YY, YN, NY, and NN). For reasons we don't have to get into, we have only n-1=3 degrees of freedom in our data. So from the table we read off the p value for 3 degrees of freedom (4-1) and a given chi-square.

For Wolfskin vs Lexington, we get a very large chi-square value of 554. That's because our Expected values, calculated from random probability, were so different from the Observed values. The probability value from the table (<<0.0001) tells us that there is only a 0.01% chance that rainfall patterns in Wolfskin and in Lexington are different, that is, a 99.99% chance that they are the same.

The p value for Wolfskin and Tucson, on the other hand, is 0.7. This says there is only a 30% chance that the two rainfall patterns are related.

Where do we draw the line? For most scientific tests, the cutoff is p=0.05. Anything less than that is not significant, and we accept the null hypothesis that there is no difference. So for the comparison with Wolfskin and St Louis MO, with its p value of 0.17, we'll have to reject the null hypothesis: there is a significant difference between rainfall patterns.

Although this was a totally silly thing to do, it would be kind of neat to test a few more locations at greater distances than Lexington, but much less, say, than Tucson or St Louis. At ten miles distance, there's no significant difference in the rainfall patterns. What about 20 miles? 70? 200? At what distance does this treatment indicate that rainfall patterns are significantly different?

Such interesting questions will have to wait until the next cold wet winter day, because today is supposed to be rather pleasant.

We're going to do this two ways. First, visually: I took rainfall data from 2009 and 2010 from four reliable CoCoRaHS observers. It wasn't that easy to find suitable observers - they had to have made observations just about every one of the 714 days with as few multi-day entries as possible. I used myself (of course) for Wolfskin, my reliable fellow Oglethorpian Al, GA-OG-1, in Lexington GA ten miles away, MO-FSA-189 in St Louis MO (purported to have a climate and rainfall similar to ours), and AZ-PM-46 in Tucson, AZ (purported to have a very different climate). These are also as close as I could get to Bisbee and Kansas City!

Here is the plot for Wolfskin vs Lexington, with rainfall in Wolfskin plotted vs that in Lexington ten miles away. By pure coincidence, it rained on 239 days out of 714 for both locations. There is a 0.335 probability of rain on any given day in both locations.

There are a few times when it rained in one place and not the other, but very few - you'd otherwise see those points sitting on the X or Y axis instead of in the middle. There are differences in the amounts that it rained, otherwise all the data points would lie on the diagonal. The points roughly cluster about the diagonal, with a similar number above and below it.

Notice that there isn't any particular pattern to the colors of the data points, indicating that the time of year isn't likely to be important.

Now here is the plot of Wolfskin vs St Louis MO. This observer measured rainfall on 166 days out of 714, a little lower than Wolfskin, giving a 0.232 probability of rain on any given day.

Suddenly there are lots of points on the X and Y axes, indicating that it frequently rained in one location, but not the other. There are fewer points within the area of the plot where it rained in both locations on the same day. There isn't much suggestion of any clustering about the diagonal.

Finally, we plot Wolfskin vs Tucson AZ. It only rained on 86 days for this observer in Tucson, out of 714 days total. Tucson has only a 0.120 probability of rain on any given day.

Now, almost all the points lie on the axes, with most of them below the diagonal. That's not surprising - we in Wolfskin get rain more frequently than our friends in Tucson. Still, there are a few points within the area of the plot, indicating that there were days when it rained in both Wolfskin and Tucson.

Visually, you can see the differences between the plots, and they make sense. But how can we actually look at the first plot above, of Wolfskin and nearby Lexington, and rigorously say that those rainfall patterns are the same, or that the other patterns are not?

We have to do it statistically, I'm afraid. That's what cold wet winter days will do to you - some people mop floors and clean toilets. I concoct silly experiments and do statistics.

I'm attracted to it, at least on cold wet winter days, because there is something - three things, really - that are intellectually and logically very satisfying:

First, there is the idea of the Null Hypothesis. Students tend not to come up with this one when they're asked to form a hypothesis, but it's really the best one when it comes to performing statistical tests. The null hypothesis simply says that there is NO difference between two sets of data.

The second neat thing is figuring out what aspect of the data can be tested, and how it can be done. Here we have a lot of numbers, and in this simplest form of the test we won't worry about the amount that it rained on any given day. For our two locations, we'll just count the number of times it rained on the same day (YY), the number of times it rained in one place but not the other (YN), the other but not the one (NY), and the number of days it rained in neither place (NN). These numbers are going to be the Observations.

The third thing that all good card players intuitively know, and that we're going to get to play with here, is figuring out what we'd expect on the basis of probability. When we've done this, we'll have a parallel set of numbers that will be our Expectations.

We finally will want to compare the Expected to the Observed. It turns out there is a very good test, the chi-square test, that will tell us whether two distributions of data are the same or not. This will in fact be our hypothesis, the Null Hypothesis, that there is no difference between the rainfall data for two locations.

Here is how we calculate the Expected number of events. We calculate these according to probabilities, starting with the rain probabilities we already figured out for each location, shown in the table, left. |

For instance, Wolfskin has a rain probability of 0.335 (Y), which also means there is a 1-0.335 or 0.665 chance that it will Not rain on a given day (N). Tucson has a similar set of numbers, Y and N = 0.121 and 0.879. The probability that it will rain in both places, YY, is 0.335 x 0.121, or 0.0405. Over 714 days, we'd Expect that it rains in both place 0.0405 x 714, or on 29 days.

We expect 29, and in fact we see that it rained 23 days in both Wolfskin and Tucson. We're off by a difference of 6 days between what we Expect and what we Observe. Here's the whole table of expected and observed events, for all three pairs of locations (rows), in all four categories (columns).

You calculate a chi-square value for each row by squaring the difference between the Observed and Expected, dividing the result by the Expected, and then summing the results across each row. Those numbers appear in the chi-square column.

Now we go to a handy table of probability (p) values for the chi-square distribution. Despite that we have four sets of data each consisting of 714 measurements, we're only looking at n=4 aspects of it (YY, YN, NY, and NN). For reasons we don't have to get into, we have only n-1=3 degrees of freedom in our data. So from the table we read off the p value for 3 degrees of freedom (4-1) and a given chi-square.

For Wolfskin vs Lexington, we get a very large chi-square value of 554. That's because our Expected values, calculated from random probability, were so different from the Observed values. The probability value from the table (<<0.0001) tells us that there is only a 0.01% chance that rainfall patterns in Wolfskin and in Lexington are different, that is, a 99.99% chance that they are the same.

The p value for Wolfskin and Tucson, on the other hand, is 0.7. This says there is only a 30% chance that the two rainfall patterns are related.

Where do we draw the line? For most scientific tests, the cutoff is p=0.05. Anything less than that is not significant, and we accept the null hypothesis that there is no difference. So for the comparison with Wolfskin and St Louis MO, with its p value of 0.17, we'll have to reject the null hypothesis: there is a significant difference between rainfall patterns.

Although this was a totally silly thing to do, it would be kind of neat to test a few more locations at greater distances than Lexington, but much less, say, than Tucson or St Louis. At ten miles distance, there's no significant difference in the rainfall patterns. What about 20 miles? 70? 200? At what distance does this treatment indicate that rainfall patterns are significantly different?

Such interesting questions will have to wait until the next cold wet winter day, because today is supposed to be rather pleasant.

## Saturday: 18 December 2010

## Thursday: 16 December 2010

Finals and fall semester are finally, fully finished. We thought there might be a crisis over the weather toward the end of the weekend. We did get some snow flurries on Sunday night, but they were insufficient to prompt panic.

It looks like the Arctic Oscillation is acting up again, like it did last December and January when it go so cold. (Indeed, it has been going negative over the last few weeks). We've just about duplicated the lows of the first two weeks in January, with our lowest temperature this winter so far, 15.0F yesterday morning.

Now just about everyone in the eastern US north of us is seeing more dramatic winter weather, so I won't usurp their experience. How about a data presentation instead?

This is a plot of the temperatures I took during the course of 2010, so far, usually 4 or 5 to 8 or 10 per day. The X-axis is here at Wolfskin, vs the KAHN temperatures displayed at the UGA Climatology Research Lab in Athens. My temperatures are taken on the north side of the house, and the sensor never sees the sun. Their temperatures are measured at Ben Epps Airport, about ten miles west northwest of us.

It was rendered colorful by accident, by the way. Excel won't plot more than 255 paired points as a scatter plot. I have over 2400 points for 2010, so far. So I got around that by entering the couple hundred points for each month under a different series. It just turned out that I was able to color each series according to a tasteful preference of my own. I naturally chose blues for winter and reds and oranges for warm months. Spring and autumn got various shades of green and brown.

I've long noticed that the KAHN temperatures often don't correspond closely to my own measurements, and it seemed to me that a good visualization of this would be to plot my temperature measurements versus theirs over the course of a year.

The two features that stand out to me are the spread, and the asymmetry above and below the diagonal line.

The spread: If all things were perfect, and there was no variation in actual temperatures between Wolfskin and Athens ten miles away, all the points would lie on the diagonal. The spread indicates how different the temperatures are. Generally the spread is fairly uniform over the temperature range, except at the extremes, where the data points are sparser anyway.

The asymmetry: You might notice is that the diagonal line doesn't run through the center of the cloud of data points. Most of them are above the line, indicating that most (but not all) of the time the corresponding KAHN airport temperatures are higher than mine.

I can think of a couple explanations for this. First, our thermometers (if you can still call them that) may not be calibrated the same - this would be a determinate instrumental error. I can't dismiss that possibility, but I will say that a comparison of temperatures with several personal weather stations located close by (usually closer than the airport) are almost always in close correspondence with my measurements.

The second explanation might be that there really is a temperature difference between our two locations. Athens isn't a large city, and the airport is more or less on the outskirts, but the urban heat island effect might be contributing to this. It is certainly the case that many times, especially at night in the summer, I'll notice a large temperature difference downward as I leave campus and drive home.

Outiers: Besides the spread and placement of the bulk of the points, there are the outliers, especially during the warm months.

I traced back to my written observations a dozen of these outliers, most of which are on the top side of the diagonal. In all cases these were data taken at a time when we were having storms. During the summer, we occasionally get pulse storms when our temperature can drop ten or twenty degrees. If these are sufficiently localized, then there will be an outlier point well above or below the line. The outliers above the line indicate pulse storms that formed over Wolfskin, or moved over us, presumably cooling us in the short term without affecting Athens farther away. Apparently this happened more frequently over Wolfskin than it did over Athens.

You'll notice that the coldest bluest points tend to lie closer to the diagonal, and there are fewer outliers until you get above 45-50 degF, or so. We just don't tend to have many storms in the winter, and if we do, they'll form at higher temperatures. It looks like there's just less difference between Athens and Wolfskin in the winter months (dark blue points).

There's more interesting stuff. For instance, the green of April and May, and even the light blue of March, intrude quite a way into the region occupied by red and orange summer months. We had quite a hot spring, with temperatures well above average, from mid March on.

We have two dependent variables here - measurements of temperatures in Athens and in Wolfskin. The independent variable is, of course, time.

Normally you plot an independent variable vs a dependent variable, and these tend to be the easiest for people to interpret. They're the ones I usually make, temperatures in Wolfskin during the course of the month, or year, for instance.

It's a step up, though, to plot one dependent variable against another dependent variable, although it's an intellectual exercise that stretches the mind a bit. These kinds of plots are esthetically very satisfactory, because such plots produce clustering effects, and clustering is often very interesting. Adding the dimension of color, which I hadn't planned to do, roughly tracked time as well.

## Tuesday: 14 December 2010

OK, who peed in the hallway?

(Not my image and I wasn't able to find an attribution. Clever, though.)

## Thursday: 2 December 2010

It's The Month of November, Number 58 in a series. What were your weather extremes in November?

This time, they're hiding the usual temperature anomalies product here, at the National Weather Service Climate Prediction Center.

This time around the western US experienced cooler than average mean temperatures (except for that tongue of warmer temperatures in the southwest). Warmer than normal temperatures persisted in must of the rest of the US eastward, again with the exception of Florida and the south Atlantic states.

For much of the eastern half of the country, these warmer mean temperatures continue the trend for the eighth month in a row, since April. Much of the north and middle eastern states continued sharply warmer temperatures for the second month in a row.

We find the National Weather Service Climate Prediction Center's precipitation plots here these days.

Dry or just-normal precipitation conditions prevailed through most of the US in November, with patches of green excess appearing in the Rockies north and a little swath through the central US.

For Athens:

For Athens, we continued for the eighth month in a row with warmer than usual average temperatures, but just barely. Our high temperatures averaged 0.3 degF higher than normal, however our highs and lows were a degree or two above and below normal, respectively. We had some extremes in both directions, almost breaking a high temperature record around Nov 23, and then hit freezing three times.

Here is my plot of high temperatures for the month of November in Athens. As usual, the black dots are for the years 1990-2009 (black dots), 2010 (green line), and 2009 (red line).

We broke no low or high temperature records in November.

We only had 6 days in November that were more than one standard deviation above the mean high (5.5 days is normal). We only had 4nights in November that were more than 1 SD below the mean low (4.9 nights normal). Nothing particularly abnormal there.

The figure below shows the Athens rainfall data which are official for our area. As usual the green line shows our actual rainfall, the red shows the average accumulation expected. The black dots are rainfall over the last 20 years, the vast river of peach shows the standard deviation.

In November, Athens received lower than normal rainfall until the last day of the month, when our area got 2-3 inches of rain before midnight. That lifted us from a deficit into a surplus. That rainfall, and a couple others during the month, was variable across our two-county area: Woflskin had just above the average of 3.71" wiwth 3.84". Other parts of Clarke and Oglethorpe Counties had anywhere from 2.51" to 5.12" during the month, so the official Athens rainfall is a little high.

November is the beginning of our water recharge season, when deciduous trees are not photosynthesizing and pulling water out of the ground, and evaporation rates are fairly low. Here is where we are as we try to repair the damage from the 2007-2009 drought:

After three years of drought, we had six months of considerable excess rainfall, and since the beginning of 2010 have been largely holding steady without appreciable gains.

Our descent into winter continues, with the cloud of this year's blue dots, out here at Wolfskin, dropping ten degrees per month since the weird summer and September. The 25-point (4-5 day) running average shows that our rough mean has been above and below the smooth area mean for the last two months.

And we went over 40 inches total rainfall on Nov 30. Unless December is very wet (and there is to be no rain for the next ten days) we'll end up with about 80-90% normal rainfall for the year.

Checking back at this neat prognosticator I see that we'll have dry and cool temperatures for most of the rest of December. But our three month prediction is now for considerably warmer temperatures, with somewhat drier conditions.

Again, this is the typical La Niña influence in the southeast, and so far in the last three months it has been fulfilled.

ENSO stuff:

La Niña holds steady with large negative anomalies since June: NOAA's weekly ENSO update tells us that we're continuing to experience La Niña conditions, and we're expected to continue these into Spring 2011. Scroll down to the bottom of that update for temperature and precipitation map forecasts through the winter.

NOAA's Monthly State of the Climate product for October is now up - November should be appearing soon. Detailed explanations for weather events occurring during October(or whatever month is current) can be found for the several sections of the US under the National Overview. There are many interesting weather- and climate-related items to be found here.