{"id":311,"date":"2011-10-14T11:23:20","date_gmt":"2011-10-14T10:23:20","guid":{"rendered":"http:\/\/jeremyshiers.com\/blog\/?p=311"},"modified":"2011-10-15T09:38:12","modified_gmt":"2011-10-15T08:38:12","slug":"a-very-bad-way-to-calculate-sea-level-rise","status":"publish","type":"post","link":"http:\/\/jeremyshiers.com\/blog\/a-very-bad-way-to-calculate-sea-level-rise\/","title":{"rendered":"A Very Bad Way To Calculate Sea Level Rise"},"content":{"rendered":"

I have been intrigued by these graphs of sea level rise<\/p>\n

\"Environment<\/a><\/p>\n

which the UK Environment Agency (EA) used to display on this page of their website, although the page was removed some time around 13 October 2011.<\/p>\n

http:\/\/www.environment-agency.gov.uk\/cy\/ymchwil\/llyfrgell\/data\/34449.aspx<\/a><\/p>\n

It was claimed that these graphs indicate an average sea level rise of between 2.3 and 4mm\/year sea level rise.\u00a0 These graphs are part of the way EA attempts to justify its policy of managed realignment (abandoning or knocking down sea walls and flooding land). The argument seems to be that sea level rise means the we can not afford to maintain sea walls so we might as well get rid of them.<\/p>\n

However EA are spending billions of tax payer pounds on their preferred policy, outlined in the Shoreline Management Plan.\u00a0 So if the claimed rate of sea level rise is too large we should ask why are EA proceeding with this plan.<\/p>\n

Although the scale of these graphs is very small it seemed that these figures are too high. Just looking at the graphs, without a magnifying glass, and doing approximate sums it seemed that.<\/p>\n\n\n\n\n\n\n\n\n
Location<\/th>\nRise in Sea Level<\/th>\nPeriod<\/th>\nRate of Rise<\/th>\n<\/tr>\n<\/thead>\n
North Shields<\/td>\n200 mm<\/td>\n100 years<\/td>\n2 mm\/year<\/td>\n<\/tr>\n
\n
Sheerness<\/div>\n<\/td>\n
200 mm<\/td>\n170 years<\/td>\n1.2 mm\/year<\/td>\n<\/tr>\n
Liverpool<\/td>\n300 mm<\/td>\n150 years<\/td>\n2 mm\/year<\/td>\n<\/tr>\n
Newlyn<\/td>\n100 mm<\/td>\n80 years<\/td>\n1.25 mm\/year<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

So the sea level rise was actually 1 to 2mm\/year, half what was claimed.<\/p>\n

Fortunately the data on sea level rise is publicly available at Permanent Service For Mean Sea Level<\/a><\/p>\n

So I downloaded the data and used the free stats program R to perform linear regression.<\/p>\n

Linear regression is a way of finding a line which best goes through a set of points on a graph, for example observations of sea level on different dates.<\/p>\n\n\n\n\n\n\n\n\n
Location<\/th>\nRate of Rise<\/th>\n<\/tr>\n<\/thead>\n
North Shields<\/td>\n1.95 mm\/year<\/td>\n<\/tr>\n
\n
Sheerness<\/div>\n<\/td>\n
1.67 mm\/year<\/td>\n<\/tr>\n
Liverpool<\/td>\n1.08 mm\/year<\/td>\n<\/tr>\n
Newlyn<\/td>\n1.78 mm\/year<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

So my approximations were a bit off but they’re in the right ball park. And in the interest of disclosure there are 2 datasets for Liverpool. One going from 1858 to 1983. The second from 1992 to 2007 but even so having 3 missing years. I only used the older dataset.<\/p>\n

So I made a Freedom of Information request to the EA to supply the data and calculation they had used, and EA sent me an Excel spreadsheet.<\/p>\n

To my amazement the average sea level rise had been calculated using the average worksheet function.<\/p>\n

Sounds fair enough doesn’t it. You want to find out average sea level rise use the average function.<\/p>\n

But there’s a problem and that problem is missing data.<\/p>\n

To illustrate the problem lets generate some data, ranging from 1000 to 3000 in steps of 100. Linear regression requires to ranges, so we’ll just run a count from 1 to 21. In the spreadsheet below the count is in the column A, labelled x. Column B, labelled y, contains the values 1000 to 3000. In column C the spreadsheet calculates the change in y from the previous row which is, surprise surprise, 100.<\/p>\n

In cell E3 the average change is calculated using the average function and in E4 the slope function (which uses linear regression) calculates the overall rate of change. Both methods give 100. So far so good.<\/p>\n