Showing posts with label standard deviation. Show all posts
Showing posts with label standard deviation. Show all posts

Saturday, March 13, 2010

Utah Temperatures and Colorado UHI

This is now the fourth in an originally unplanned series looking at the differences between GISS and USHCN average temperatures and some trends in the data that are not necessarily obvious when one only looks at global data. Tracking Westward from Colorado, Utah has the next set of temperature data that I will look at, and I will also comment on Anthony Watts note on Colorado UHI , which he posted since my post on that state.

Utah has a different topography in that while in Colorado as we head West the land rises, in Utah that is no longer the case. So for the hypothesis of the week I will assume that while there will be a correlation with elevation, that there will be none with longitude. Let’s see if I’m correct. And while there was little correlation with latitude in Colorado, because of the strong effect of elevation and the wide range it covered, I am going to hypothesize that we will see a significant effect of latitude again, even though the elevation is considerably higher.

As usual I am writing this as I carry out the tabulation, and so I begin, following the initial procedure, by going to the USHCN web site and, yikes, there are 40 weather stations listed for Utah. OK, there will be a slight pause while I enter all these into the data table . . . . 40 stations, mutter, mutter).


Hmm! And we have the same problem of missing data that showed up in Colorado, but with more stations. For some stations there is no data in specific years before 1900. Well I am going to apply the same procedure as I did for Colorado and calculate an assumed temperature for those sites. First is Blanding, for which there is no temperature for 1896. Blanding is, on average at 51.15 deg, 2.8 deg warmer than the rest of the state. If that year the average temp was 47.5 deg, then Blanding should be at 50.3 degrees. If the average temperature for 1896 was, at 47.5 degrees, 0.8 degrees below the average annual temp, and the annual temp for Blanding is 51.15 deg, then the temp in 1896 would be 50.35 deg. Taking the average of these gives 50.33 deg, which is what I insert.

I follow the same procedure to calculate the temperatures for Bluff in 1895, 1896, 1896, and 1898; Farmington in 1895; Morgan Power in 1895; Snake Creek in 1895; (if you get the table these values are marked in red.)

Again checking on Chiefio’s list of the GISS stations. I find only one station out of the stations in Utah, that has survived the cut is the one in Salt Lake City. So I go to get the GISS data for that station.

Adjusting the tabulation to calculate averages for the different numbers of USHCN and GISS stations reveals that the GISS station reads 4 degrees higher than the state average from the USHCN stations.

Looking for the populations of the different cities and towns, Deseret is now apparently preferably called Delta. Modena, UT is also not on the city-data file, and so I got the population of 35 from Century 21. The population for Snake River Powerhouse also requires a little detective work, and two communities have merged to form Midway, and so I will use that number. And for Zion National Park I used Springdale.

And so all the data is in the table and what do we find? First of all, looking at the primary hypothesis of the day:


There is realistically no correlation here, so the first hypothesis is apparently valid.


As with the Colorado data, this again suggests that the trend that we saw with the Kansas data in regard to longitude was really a reflection of the increasing height above sea level. And at the high elevations, looking at latitude, there is a trend:


Not as strong as elevation, given the widely carrying heights of the stations around the state, but it is still there.

In regard to the population distribution, Utah is a state with a large number of small communities , which also have weather stations, so I shrunk the scale of the plot shown to below 10,000 population:


And the log correlation still shows.

In terms of the standard deviation plot that I have calculated for all the states so far:


There has been a slight increase in scatter over the years, (which would validate Anthony Watts observation on station quality) though it is not at a significant level (which I have set at an r-squared of 0.05).
However Utah is a state that has seen a warming over the years:


But the growth of the small communities, relative to the single GISS station in Utah, and the sensitivity of temperature more to the growth of small communities, means that the difference between the GISS and USHCN averages has declined over the years, due to the makeup of the USHCN average.


Which brings me back to Anthony Watts recent post on Colorado data. What he and Stephen Goddard have done is to look at the relative population growths of Boulder, and Ft Collins in Colorado.

Growth in relative populations of Boulder and Ft Collins in Colorado

Now, taking the data that I had discussed last Saturday, it was fairly easy to pull out the data for Ft Collins and Boulder and find the difference, and plot it against time:



I have taken it back a little further than WUMT, since I had the data, but the two curves are otherwise the same. And it does show the effect of the Urban Heat Island, from the point of view that the most significant change between the two towns has been their relative growth.

And so it continues, perhaps next week we will look at Nevada?


Read more!

Saturday, February 20, 2010

The Precipitation Hypothesis - is it true?

Today we test the “Diane Sawyer” hypothesis. The hypothesis we are testing is that global warming has led to an increase in precipitation. I’d call it rain for short, but Ms Sawyer made the remark at the end of an ABC newscast the other day about snow. Namely she stated that we should not think, because we have more snow that Global Warming is not happening. In fact, she went on to say words to the effect that because the Earth is getting warmer this causes more precipitation, which, at the time was what Washington was seeing, and that this has been predicted.

A quick check and there are sites that state, for example:
Numerous empirical observations and models of the global climate confirm the hypothesis that global warming enhances the global hydrologic cycle. For instance, a global warming by 4°C (7.2°F) is expected to increase global precipitation by about 10 percent. Models suggest that the increase is more likely to come as heavier rainfall, rather than as more frequent rainfalls or falls of longer duration.
Well that is pretty definitive, and so let us, using the same procedure as last week, see if in fact this hypothesis is true.


And, to make my life (and yours if you are following along) easier I am going to use the structure of the spreadsheet that I created last week, and merely, where possible, replace the temperature data with annual precipitation data from the same set of weather stations. To get the precipitation information I step through the same sequence from the United States Historical Climatology Network to get to the station sites for Missouri, which if you will remember, gets me to this map.


As before I will step down through the list of weather stations that are given for the state to get the data that I need. After clicking on the name of the station (and again I will use Appleton City as the example) I already have the station data entered from last time, so all I need to do is click on the “Get Monthly Data” phrase.

Now, when I get to the Monthly data page I now scroll down to the bottom of the page, where I can see the following selection:


As before this will take you to a screen that gives you the file name that has been created,


And when you click the blue line, then a file is downloaded to your computer. As before if you open the file, then you get the list of annual precipitation for the site since 1895.


Returning to the spreadsheet with all the stations on it, I now paste that column of data into the table, starting in square C13. As before I continue doing this, until I have all the precipitation data from the USHCN weather stations (all 26).

In contrast with the temperature data I don’t know where to go to get the precipitation data for Missouri from GISS – a visit to their site notes that they get their information from the Climate Research Unit at the University of East Anglia – and given the current kerfuffle over there, I am going to give trying to get info from them a pass. Still we have the information from the last 114 years for Missouri, based on 26 stations.

I already have the average for those stations set up from when I created the original spreadsheet (though I have to change the data ranges for the plots). And now I can check the hypothesis that we started with. Given the reported increase in global temperature, has there been an increase in precipitation in Missouri?


Well if one looks there has been a very small, and statistically insignificant, increase in precipitation over the last 114 years, so it appears that the Diane Sawyer hypothesis is incorrect.

To explain the “statistically insignificant” remark, I am going to give a relatively simple explanation that I found here of the meaning of the r-squared values that I put on every graph, to show how significant the trend is
The main result of a correlation is called the correlation coefficient (or "r"). It ranges from -1.0 to +1.0. The closer r is to +1 or -1, the more closely the two variables are related.

If r is close to 0, it means there is no relationship between the variables. If r is positive, it means that as one variable gets larger the other gets larger. If r is negative it means that as one gets larger, the other gets smaller (often called an "inverse" correlation).

While correlation coefficients are normally reported as r = (a value between -1 and +1), squaring them makes then easier to understand. The square of the coefficient (or r square) is equal to the percent of the variation in one variable that is related to the variation in the other. After squaring r, ignore the decimal point. An r of .5 means 25% of the variation is related (.5 squared =.25). An r value of .7 means 49% of the variance is related (.7 squared = .49).
To show where the significant variable is for the state data, lets look at the change in precipitation with latitude (r-squared is 0.82):


Still nothing significant with longitude, but it is interesting to revisit (since the plots were already set up) the questions I posed last time on data scatter, and population. I had hypothesized that (based on Anthony Watts evaluation of weather stations) the scatter in the measure of the data (as identified by the standard deviation) would get worse over time. It did not for temperatures in Missouri – possibly because it might be tied to rates of temperature change, and Missouri hasn't seen one - but also that could have been because of the change in thermometers. Here is the plot for precipitation:


Well there is a trend, if not a very significant one, which gives a little scientific credence to Anthony Watts for the state of Missouri. And does population size have an impact?


I was going to leave that without comment, but I suspect that the apparent correlation has more to do with where folk live in regard to latitude, than the actual size of the population, but to validate the relationship would require a lot more data than I have input to date.

Now you may say that what I have posted today really has little relevance, since Missouri has had an insignificant amount of warming over the past 114 years but the moisture that Missouri sees (and feels in the rain and snow) is largely generated elsewhere, and so if there is a correlation, given the relatively large amount of precipitation the state gets, then it should show up, or should it?

The reason I ask the last question is that if you go to GISS you will find this plot:


Now (I checked) there is no real correlation between Missouri precipitation and that which is global, but the conclusions regarding changing rates are the same. I quote NOAA :
Globally-averaged land-based precipitation shows a statistically insignificant upward trend with most of the increase occurring in the first half of the 20th century.

So I am afraid it is not just Missouri data but also global data that falsifies the “Sawyer” hypothesis.

Read more!