GISTEMP Rural Station Combination (post 3 of 6 in GISTEMP example)

This post shows how the five adjusting rural stations for NAR’JAN-MAR are combined. The log file shows the adjustment details:

PApars.GHCN.CL.1000.20.log
==========================
urb stnID:222232050004 # rur:   5 ranges: 1927 2009     500.
longest rur range: 1890-2009    98  [wgt: 0.507  246.7 km] 222234050000  [UST'-CIL'MA]
add stn    2 range: 1916-2009    92 [wgt: 0.161  419.4 km] 638221650004  [KANIN NOS]
data added:  92  overlap: 75  years
add stn    3 range: 1913-1989    76 [wgt: 0.217  391.8 km] 638225830000  [KOJNAS]
data added:  76  overlap: 75  years
add stn    4 range: 1932-2001    68 [wgt: 0.441  279.7 km] 222232190004  [HOSEDA-HARD]
data added:  68  overlap: 68  years
add stn    5 range: 1915-1950    34 [wgt: 0.225  387.7 km] 222230220010  [WAIGATZ]
data added:  34  overlap: 34  years
possible range increase 32 63 63

The five stations are combined in order of record length. The sequence of operations can be seen in the table below. Years with missing data for the stations are highlighted using a coloured cell background. The full range from 1890 to 2007 is shown for each stage of the process, but only the rows with marked cell boundaries across the row are considered at each stage. At the final stage, the “head” and “tail” years based on less than three stations which will be dropped before the least squares fit are also indicated using a coloured cell background for the first two columns in the table.
AVG, WT, IWT and DNEW are the array names used in the GISTEMP code. Initially AVG contains the anomaly data for the rural station with the longest record (in this case this is also the nearest station, with the greatest weight, but this need not be the case elsewhere). At the end of each stage in the process AVG contains the combined anomaly record. DNEW contains the anomaly data for the next station to be combined. WT at the start of each stage contains the weight for the anomaly data in the AVG array. Initially this is the weight for the station with the longest record, or zero for years with no data. After combination the weight for a given year will be determined by the stations combined which have data for the given year. At the end of each stage these weights are returned in the WT array. IWT contains the number of stations contributing information to the values in AVG.

Further details of the process follow this table.

UST’-CIL’MA KANIN NOS Combined(2 stations)
Year i AVG WT IWT DNEW AVG WT IWT
1890 11 -3.6 0.5065 1
1891 12 -13.3 0.5065 1
1892 13 9999 0 0
1893 14 9999 0 0
1894 15 9999 0 0
1895 16 9999 0 0
1896 17 1.7 0.5065 1
1897 18 -5.8 0.5065 1
1898 19 -3.7 0.5065 1
1899 20 -10.2 0.5065 1
1900 21 1.8 0.5065 1
1901 22 2.4 0.5065 1
1902 23 -41.2 0.5065 1
1903 24 -5.2 0.5065 1
1904 25 13.5 0.5065 1
1905 26 9.4 0.5065 1
1906 27 10.6 0.5065 1
1907 28 8.7 0.5065 1
1908 29 -13.7 0.5065 1
1909 30 -0.3 0.5065 1
1910 31 6.6 0.5065 1
1911 32 -11.4 0.5065 1
1912 33 -17.2 0.5065 1
1913 34 -5.1 0.5065 1
1914 35 -12.2 0.5065 1
1915 36 8.8 0.5065 1 BIAS: 1.5707
1916 37 -10.2 0.5065 1 -18.7 -11.8740 0.6679 2
1917 38 -23.3 0.5065 1 -20.8 -22.3166 0.6679 2
1918 39 -19.7 0.5065 1 -24.1 -20.3835 0.6679 2
1919 40 9999 0 0 9999 9999 0 0
1920 41 13.3 0.5065 1 12.8 13.5586 0.6679 2
1921 42 16.2 0.5065 1 17.1 16.7969 0.6679 2
1922 43 11.9 0.5065 1 4.1 10.3951 0.6679 2
1923 44 8.1 0.5065 1 4.0 7.4890 0.6679 2
1924 45 9.6 0.5065 1 -2.7 7.0080 0.6679 2
1925 46 -0.3 0.5065 1 -1.7 -0.2588 0.6679 2
1926 47 -2.8 0.5065 1 -8.1 -3.7009 0.6679 2
1927 48 -3.7 0.5065 1 -7.2 -4.1661 0.6679 2
1928 49 -5.2 0.5065 1 -3.9 -4.5065 0.6679 2
1929 50 -5.8 0.5065 1 -10.2 -6.4835 0.6679 2
1930 51 -6.0 0.5065 1 -1.9 -4.6301 0.6679 2
1931 52 9.4 0.5065 1 6.6 9.1030 0.6679 2
1932 53 5.6 0.5065 1 3.5 5.4721 0.6679 2
1933 54 -8.5 0.5065 1 -7.8 -7.9515 0.6679 2
1934 55 8.6 0.5065 1 6.6 8.4963 0.6679 2
1935 56 11.5 0.5065 1 5.4 10.4058 0.6679 2
1936 57 11.9 0.5065 1 4.9 10.5884 0.6679 2
1937 58 24.4 0.5065 1 23.2 24.4895 0.6679 2
1938 59 13.8 0.5065 1 14.8 14.4210 0.6679 2
1939 60 -5.0 0.5065 1 3.7 -2.5188 0.6679 2
1940 61 -4.2 0.5065 1 -5.9 -4.2312 0.6679 2
1941 62 -24.7 0.5065 1 -23.2 -23.9582 0.6679 2
1942 63 -19.5 0.5065 1 -18.1 -18.7824 0.6679 2
1943 64 21.4 0.5065 1 17.4 20.8131 0.6679 2
1944 65 18.8 0.5065 1 13.9 17.9957 0.6679 2
1945 66 -1.4 0.5065 1 0.0 -0.6824 0.6679 2
1946 67 -9.6 0.5065 1 -9.5 -9.1964 0.6679 2
1947 68 0.9 0.5065 1 -2.4 0.4822 0.6679 2
1948 69 12.3 0.5065 1 9999 12.3 0.5065 1
1949 70 -0.8 0.5065 1 2.4 0.3525 0.6679 2
1950 71 6.3 0.5065 1 7.8 7.0418 0.6679 2
1951 72 -2.1 0.5065 1 5.7 0.1637 0.6679 2
1952 73 0.6 0.5065 1 2.2 1.3660 0.6679 2
1953 74 -1.3 0.5065 1 -2.6 -1.2346 0.6679 2
1954 75 17.3 0.5065 1 21.9 18.7907 0.6679 2
1955 76 2.4 0.5065 1 -3.3 1.4024 0.6679 2
1956 77 -18.2 0.5065 1 -18.0 -17.7722 0.6679 2
1957 78 8.9 0.5065 1 3.9 8.0715 0.6679 2
1958 79 -7.7 0.5065 1 -14.1 -8.8667 0.6679 2
1959 80 -1.9 0.5065 1 6.8 0.5812 0.6679 2
1960 81 -11.8 0.5065 1 3.3 -7.7727 0.6679 2
1961 82 18.4 0.5065 1 13.4 17.5715 0.6679 2
1962 83 20.5 0.5065 1 6.0 17.3766 0.6679 2
1963 84 -8.7 0.5065 1 -8.0 -8.1515 0.6679 2
1964 85 -14.7 0.5065 1 -9.1 -12.9677 0.6679 2
1965 86 -10.0 0.5065 1 -7.9 -9.1132 0.6679 2
1966 87 -15.7 0.5065 1 -27.6 -18.1953 0.6679 2
1967 88 20.8 0.5065 1 13.7 19.4642 0.6679 2
1968 89 -19.6 0.5065 1 -15.6 -18.2543 0.6679 2
1969 90 -30.4 0.5065 1 -25.1 -28.7402 0.6679 2
1970 91 0.8 0.5065 1 4.3 2.0250 0.6679 2
1971 92 -12.5 0.5065 1 -11.5 -11.8790 0.6679 2
1972 93 -4.1 0.5065 1 7.9 -0.8216 0.6679 2
1973 94 7.3 0.5065 1 5.7 7.2929 0.6679 2
1974 95 7.9 0.5065 1 9.0 8.5452 0.6679 2
1975 96 13.9 0.5065 1 15.9 14.7626 0.6679 2
1976 97 2.8 0.5065 1 -1.0 2.2614 0.6679 2
1977 98 8.6 0.5065 1 -1.6 6.5153 0.6679 2
1978 99 -9.6 0.5065 1 -11.9 -9.7762 0.6679 2
1979 100 -19.7 0.5065 1 -23.4 -20.2144 0.6679 2
1980 101 -4.7 0.5065 1 -5.4 -4.4897 0.6679 2
1981 102 20.8 0.5065 1 -1.2 15.8647 0.6679 2
1982 103 1.2 0.5065 1 -15.9 -2.5515 0.6679 2
1983 104 11.8 0.5065 1 6.4 10.8749 0.6679 2
1984 105 9.8 0.5065 1 8.4 9.8412 0.6679 2
1985 106 -11.1 0.5065 1 -12.0 -10.9380 0.6679 2
1986 107 -5.8 0.5065 1 -6.6 -5.6138 0.6679 2
1987 108 -15.7 0.5065 1 -14.2 -14.9582 0.6679 2
1988 109 7.7 0.5065 1 0.9 6.4367 0.6679 2
1989 110 19.4 0.5065 1 20.1 19.9485 0.6679 2
1990 111 9999 0 0 4.9 6.4707 0.1613 1
1991 112 9999 0 0 6.1 7.6707 0.1613 1
1992 113 9999 0 0 -2.7 -1.1293 0.1613 1
1993 114 9999 0 0 9.4 10.9707 0.1613 1
1994 115 9999 0 0 -4.0 -2.4293 0.1613 1
1995 116 9999 0 0 8.0 9.5707 0.1613 1
1996 117 9999 0 0 13.7 15.2707 0.1613 1
1997 118 9999 0 0 -8.9 -7.3293 0.1613 1
1998 119 9999 0 0 -26.0 -24.4293 0.1613 1
1999 120 9999 0 0 -13.6 -12.0293 0.1613 1
2000 121 9999 0 0 13.9 15.4707 0.1613 1
2001 122 9999 0 0 -1.3 0.2707 0.1613 1
2002 123 9999 0 0 -3.3 -1.7293 0.1613 1
2003 124 9999 0 0 7.6 9.1707 0.1613 1
2004 125 9999 0 0 14.4 15.9707 0.1613 1
2005 126 9999 0 0 13.9 15.4707 0.1613 1
2006 127 1.3 0.5065 1 5.7 2.7424 0.6679 2
2007 128 24.3 0.5065 1 20.0 23.6407 0.6679 2
2008 129 9999 0 0 13.2 14.7707 0.1613 1
2009 130 13.3 0.5065 1 10.5 13.0030 0.6679 2
NSM: 92 NCOM: 75
Combined(2 stations) KOJNAS Combined(3 stations)
Year i AVG WT IWT DNEW AVG WT IWT
1890 11 -3.6 0.5065 1
1891 12 -13.3 0.5065 1
1892 13 9999 0 0
1893 14 9999 0 0
1894 15 9999 0 0
1895 16 9999 0 0
1896 17 1.7 0.5065 1
1897 18 -5.8 0.5065 1
1898 19 -3.7 0.5065 1
1899 20 -10.2 0.5065 1
1900 21 1.8 0.5065 1
1901 22 2.4 0.5065 1
1902 23 -41.2 0.5065 1
1903 24 -5.2 0.5065 1
1904 25 13.5 0.5065 1
1905 26 9.4 0.5065 1
1906 27 10.6 0.5065 1
1907 28 8.7 0.5065 1
1908 29 -13.7 0.5065 1
1909 30 -0.3 0.5065 1
1910 31 6.6 0.5065 1
1911 32 -11.4 0.5065 1
1912 33 -17.2 0.5065 1 BIAS: -0.0118
1913 34 -5.1 0.5065 1 -5.0 -5.0736 0.7232 2
1914 35 -12.2 0.5065 1 -7.8 -10.8855 0.7232 2
1915 36 8.8 0.5065 1 -0.5 6.0107 0.7232 2
1916 37 -11.8740 0.6679 2 -10.8 -11.6138 0.8845 3
1917 38 -22.3166 0.6679 2 -18.5 -21.3848 0.8845 3
1918 39 -20.3835 0.6679 2 -10.9 -18.0639 0.8845 3
1919 40 9999 0 0 -16.7 -16.7118 0.2166 1
1920 41 13.5586 0.6679 2 16.1 14.1781 0.8845 3
1921 42 16.7969 0.6679 2 9999 16.7969 0.6679 2
1922 43 10.3951 0.6679 2 18.6 12.4016 0.8845 3
1923 44 7.4890 0.6679 2 5.9 7.0969 0.8845 3
1924 45 7.0080 0.6679 2 5.8 6.7093 0.8845 3
1925 46 -0.2588 0.6679 2 5.7 1.1977 0.8845 3
1926 47 -3.7009 0.6679 2 -5.5 -4.1444 0.8845 3
1927 48 -4.1661 0.6679 2 -6.6 -4.7650 0.8845 3
1928 49 -4.5065 0.6679 2 -6.5 -4.9976 0.8845 3
1929 50 -6.4835 0.6679 2 -9.3 -7.1761 0.8845 3
1930 51 -4.6301 0.6679 2 1.4 -3.1562 0.8845 3
1931 52 9.1030 0.6679 2 5.1 8.1198 0.8845 3
1932 53 5.4721 0.6679 2 10.3 6.6516 0.8845 3
1933 54 -7.9515 0.6679 2 8.7 -3.8764 0.8845 3
1934 55 8.4963 0.6679 2 8.3 8.4453 0.8845 3
1935 56 10.4058 0.6679 2 12.2 10.8423 0.8845 3
1936 57 10.5884 0.6679 2 14.2 11.4700 0.8845 3
1937 58 24.4895 0.6679 2 24.7 24.5382 0.8845 3
1938 59 14.4210 0.6679 2 12.8 14.0211 0.8845 3
1939 60 -2.5188 0.6679 2 -5.0 -3.1294 0.8845 3
1940 61 -4.2312 0.6679 2 -8.3 -5.2306 0.8845 3
1941 62 -23.9582 0.6679 2 -24.5 -24.0938 0.8845 3
1942 63 -18.7824 0.6679 2 -21.8 -19.5243 0.8845 3
1943 64 20.8131 0.6679 2 19.6 20.5131 0.8845 3
1944 65 17.9957 0.6679 2 16.7 17.6755 0.8845 3
1945 66 -0.6824 0.6679 2 1.1 -0.2487 0.8845 3
1946 67 -9.1964 0.6679 2 -10.6 -9.5430 0.8845 3
1947 68 0.4822 0.6679 2 -1.3 0.0429 0.8845 3
1948 69 12.3000 0.5065 1 10.4 11.7273 0.7232 2
1949 70 0.3525 0.6679 2 2.0 0.7531 0.8845 3
1950 71 7.0418 0.6679 2 5.3 6.6124 0.8845 3
1951 72 0.1637 0.6679 2 4.4 1.1983 0.8845 3
1952 73 1.3660 0.6679 2 1.9 1.4939 0.8845 3
1953 74 -1.2346 0.6679 2 -1.7 -1.3515 0.8845 3
1954 75 18.7907 0.6679 2 14.7 17.7860 0.8845 3
1955 76 1.4024 0.6679 2 -1.4 0.7132 0.8845 3
1956 77 -17.7722 0.6679 2 -24.9 -19.5207 0.8845 3
1957 78 8.0715 0.6679 2 11.2 8.8348 0.8845 3
1958 79 -8.8667 0.6679 2 -5.8 -8.1185 0.8845 3
1959 80 0.5812 0.6679 2 -2.2 -0.1028 0.8845 3
1960 81 -7.7727 0.6679 2 -8.8 -8.0272 0.8845 3
1961 82 17.5715 0.6679 2 18.5 17.7960 0.8845 3
1962 83 17.3766 0.6679 2 14.2 16.5957 0.8845 3
1963 84 -8.1515 0.6679 2 -8.6 -8.2642 0.8845 3
1964 85 -12.9677 0.6679 2 -7.6 -11.6561 0.8845 3
1965 86 -9.1132 0.6679 2 -13.4 -10.1660 0.8845 3
1966 87 -18.1953 0.6679 2 -14.2 -17.2198 0.8845 3
1967 88 19.4642 0.6679 2 15.9 18.5885 0.8845 3
1968 89 -18.2543 0.6679 2 -22.2 -19.2235 0.8845 3
1969 90 -28.7402 0.6679 2 -31.8 -29.4924 0.8845 3
1970 91 2.0250 0.6679 2 0.9 1.7466 0.8845 3
1971 92 -11.8790 0.6679 2 -15.3 -12.7197 0.8845 3
1972 93 -0.8216 0.6679 2 -2.9 -1.3335 0.8845 3
1973 94 7.2929 0.6679 2 7.4 7.3163 0.8845 3
1974 95 8.5452 0.6679 2 11.6 9.2904 0.8845 3
1975 96 14.7626 0.6679 2 15.4 14.9158 0.8845 3
1976 97 2.2614 0.6679 2 -1.8 1.2639 0.8845 3
1977 98 6.5153 0.6679 2 10.1 7.3903 0.8845 3
1978 99 -9.7762 0.6679 2 -8.8 -9.5400 0.8845 3
1979 100 -20.2144 0.6679 2 -20.4 -20.2627 0.8845 3
1980 101 -4.4897 0.6679 2 -4.8 -4.5686 0.8845 3
1981 102 15.8647 0.6679 2 20.2 16.9236 0.8845 3
1982 103 -2.5515 0.6679 2 0.9 -1.7091 0.8845 3
1983 104 10.8749 0.6679 2 12.0 11.1476 0.8845 3
1984 105 9.8412 0.6679 2 10.7 10.0487 0.8845 3
1985 106 -10.9380 0.6679 2 -17.7 -12.5969 0.8845 3
1986 107 -5.6138 0.6679 2 -5.8 -5.6623 0.8845 3
1987 108 -14.9582 0.6679 2 -18.8 -15.9019 0.8845 3
1988 109 6.4367 0.6679 2 3.2 5.6412 0.8845 3
1989 110 19.9485 0.6679 2 17.7 19.3950 0.8845 3
1990 111 6.4707 0.1613 1
1991 112 7.6707 0.1613 1
1992 113 -1.1293 0.1613 1
1993 114 10.9707 0.1613 1
1994 115 -2.4293 0.1613 1
1995 116 9.5707 0.1613 1
1996 117 15.2707 0.1613 1
1997 118 -7.3293 0.1613 1
1998 119 -24.4293 0.1613 1
1999 120 -12.0293 0.1613 1
2000 121 15.4707 0.1613 1
2001 122 0.2707 0.1613 1
2002 123 -1.7293 0.1613 1
2003 124 9.1707 0.1613 1
2004 125 15.9707 0.1613 1
2005 126 15.4707 0.1613 1
2006 127 2.7424 0.6679 2
2007 128 23.6407 0.6679 2
2008 129 14.7707 0.1613 1
2009 130 13.0030 0.6679 2
NSM: 76 NCOM: 75
Combined(3 stations) HOSEDA-HARD Combined(4 stations)
Year i AVG WT IWT DNEW AVG WT IWT
1890 11 -3.6 0.5065 1
1891 12 -13.3 0.5065 1
1892 13 9999 0 0
1893 14 9999 0 0
1894 15 9999 0 0
1895 16 9999 0 0
1896 17 1.7 0.5065 1
1897 18 -5.8 0.5065 1
1898 19 -3.7 0.5065 1
1899 20 -10.2 0.5065 1
1900 21 1.8 0.5065 1
1901 22 2.4 0.5065 1
1902 23 -41.2 0.5065 1
1903 24 -5.2 0.5065 1
1904 25 13.5 0.5065 1
1905 26 9.4 0.5065 1
1906 27 10.6 0.5065 1
1907 28 8.7 0.5065 1
1908 29 -13.7 0.5065 1
1909 30 -0.3 0.5065 1
1910 31 6.6 0.5065 1
1911 32 -11.4 0.5065 1
1912 33 -17.2 0.5065 1
1913 34 -5.0736 0.7232 2
1914 35 -10.8855 0.7232 2
1915 36 6.0107 0.7232 2
1916 37 -11.6138 0.8845 3
1917 38 -21.3848 0.8845 3
1918 39 -18.0639 0.8845 3
1919 40 -16.7118 0.2166 1
1920 41 14.1781 0.8845 3
1921 42 16.7969 0.6679 2
1922 43 12.4016 0.8845 3
1923 44 7.0969 0.8845 3
1924 45 6.7093 0.8845 3
1925 46 1.1977 0.8845 3
1926 47 -4.1444 0.8845 3
1927 48 -4.7650 0.8845 3
1928 49 -4.9976 0.8845 3
1929 50 -7.1761 0.8845 3
1930 51 -3.1562 0.8845 3
1931 52 8.1198 0.8845 3 BIAS: 0.7360
1932 53 6.6516 0.8845 3 1.2 5.0835 1.3252 4
1933 54 -3.8764 0.8845 3 9999 -3.8764 0.8845 3
1934 55 8.4453 0.8845 3 6.4 8.0099 1.3252 4
1935 56 10.8423 0.8845 3 12.1 11.5053 1.3252 4
1936 57 11.4700 0.8845 3 10.6 11.4254 1.3252 4
1937 58 24.5382 0.8845 3 20.0 23.2738 1.3252 4
1938 59 14.0211 0.8845 3 11.5 13.4275 1.3252 4
1939 60 -3.1294 0.8845 3 -3.9 -3.1409 1.3252 4
1940 61 -5.2306 0.8845 3 1.1 -2.8806 1.3252 4
1941 62 -24.0938 0.8845 3 -24.2 -23.8843 1.3252 4
1942 63 -19.5243 0.8845 3 -14.9 -17.7417 1.3252 4
1943 64 20.5131 0.8845 3 29.2 23.6466 1.3252 4
1944 65 17.6755 0.8845 3 21.4 19.1588 1.3252 4
1945 66 -0.2487 0.8845 3 4.8 1.6749 1.3252 4
1946 67 -9.5430 0.8845 3 -16.6 -11.6450 1.3252 4
1947 68 0.0429 0.8845 3 4.7 1.8363 1.3252 4
1948 69 11.7273 0.7232 2 14.0 12.8666 1.1639 3
1949 70 0.7531 0.8845 3 -3.1 -0.2835 1.3252 4
1950 71 6.6124 0.8845 3 9.5 7.8174 1.3252 4
1951 72 1.1983 0.8845 3 12.3 5.1348 1.3252 4
1952 73 1.4939 0.8845 3 0.4 1.3749 1.3252 4
1953 74 -1.3515 0.8845 3 0.0 -0.6573 1.3252 4
1954 75 17.7860 0.8845 3 22.4 19.5651 1.3252 4
1955 76 0.7132 0.8845 3 7.0 3.0486 1.3252 4
1956 77 -19.5207 0.8845 3 -9.8 -16.0434 1.3252 4
1957 78 8.8348 0.8845 3 1.3 6.5739 1.3252 4
1958 79 -8.1185 0.8845 3 -16.6 -10.6942 1.3252 4
1959 80 -0.1028 0.8845 3 0.0 0.1761 1.3252 4
1960 81 -8.0272 0.8845 3 -19.4 -11.5644 1.3252 4
1961 82 17.7960 0.8845 3 18.9 18.4079 1.3252 4
1962 83 16.5957 0.8845 3 25.0 19.6353 1.3252 4
1963 84 -8.2642 0.8845 3 -9.0 -8.2641 1.3252 4
1964 85 -11.6561 0.8845 3 -28.8 -17.1124 1.3252 4
1965 86 -10.1660 0.8845 3 -9.2 -9.6000 1.3252 4
1966 87 -17.2198 0.8845 3 -17.6 -17.1014 1.3252 4
1967 88 18.5885 0.8845 3 23.4 20.4333 1.3252 4
1968 89 -19.2235 0.8845 3 -15.8 -17.8403 1.3252 4
1969 90 -29.4924 0.8845 3 -31.6 -29.9485 1.3252 4
1970 91 1.7466 0.8845 3 -9.1 -1.6156 1.3252 4
1971 92 -12.7197 0.8845 3 -14.6 -13.1002 1.3252 4
1972 93 -1.3335 0.8845 3 -11.7 -4.5360 1.3252 4
1973 94 7.3163 0.8845 3 2.0 5.7931 1.3252 4
1974 95 9.2904 0.8845 3 -5.8 4.5170 1.3252 4
1975 96 14.9158 0.8845 3 5.3 11.9629 1.3252 4
1976 97 1.2639 0.8845 3 8.1 3.7820 1.3252 4
1977 98 7.3903 0.8845 3 4.6 6.7072 1.3252 4
1978 99 -9.5400 0.8845 3 -12.9 -10.4126 1.3252 4
1979 100 -20.2627 0.8845 3 -24.6 -21.4603 1.3252 4
1980 101 -4.5686 0.8845 3 -3.7 -4.0350 1.3252 4
1981 102 16.9236 0.8845 3 21.5 18.6902 1.3252 4
1982 103 -1.7091 0.8845 3 -0.2 -0.9625 1.3252 4
1983 104 11.1476 0.8845 3 9.1 10.7114 1.3252 4
1984 105 10.0487 0.8845 3 8.0 9.6122 1.3252 4
1985 106 -12.5969 0.8845 3 -15.1 -13.1845 1.3252 4
1986 107 -5.6623 0.8845 3 -5.3 -5.2971 1.3252 4
1987 108 -15.9019 0.8845 3 -17.1 -16.0556 1.3252 4
1988 109 5.6412 0.8845 3 0.6 4.2095 1.3252 4
1989 110 19.3950 0.8845 3 16.4 18.6438 1.3252 4
1990 111 6.4707 0.1613 1 1.3 3.2245 0.6020 2
1991 112 7.6707 0.1613 1 17.7 15.5508 0.6020 2
1992 113 -1.1293 0.1613 1 -30.8 -22.3093 0.6020 2
1993 114 10.9707 0.1613 1 22.8 20.1684 0.6020 2
1994 115 -2.4293 0.1613 1 9999 -2.4293 0.1613 1
1995 116 9.5707 0.1613 1 40.6 32.8227 0.6020 2
1996 117 15.2707 0.1613 1 11.3 12.9029 0.6020 2
1997 118 -7.3293 0.1613 1 -7.6 -6.9887 0.6020 2
1998 119 -24.4293 0.1613 1 -33.6 -30.6034 0.6020 2
1999 120 -12.0293 0.1613 1 -24.1 -20.3262 0.6020 2
2000 121 15.4707 0.1613 1 22.7 21.3012 0.6020 2
2001 122 0.2707 0.1613 1 0.4 0.9041 0.6020 2
2002 123 -1.7293 0.1613 1
2003 124 9.1707 0.1613 1
2004 125 15.9707 0.1613 1
2005 126 15.4707 0.1613 1
2006 127 2.7424 0.6679 2
2007 128 23.6407 0.6679 2
2008 129 14.7707 0.1613 1
2009 130 13.0030 0.6679 2
NSM: 68 NCOM: 68
Combined(4 stations) WAIGATZ Combined(5 stations)
Year ij AVG WT IWT DNEW AVG WT IWT
1890 11 -3.6 0.5065 1
1891 12 -13.3 0.5065 1
1892 13 9999 0 0
1893 14 9999 0 0
1894 15 9999 0 0
1895 16 9999 0 0
1896 17 1.7 0.5065 1
1897 18 -5.8 0.5065 1
1898 19 -3.7 0.5065 1
1899 20 -10.2 0.5065 1
1900 21 1.8 0.5065 1
1901 22 2.4 0.5065 1
1902 23 -41.2 0.5065 1
1903 24 -5.2 0.5065 1
1904 25 13.5 0.5065 1
1905 26 9.4 0.5065 1
1906 27 10.6 0.5065 1
1907 28 8.7 0.5065 1
1908 29 -13.7 0.5065 1
1909 30 -0.3 0.5065 1
1910 31 6.6 0.5065 1
1911 32 -11.4 0.5065 1
1912 33 -17.2 0.5065 1
1913 34 -5.0736 0.7232 2
1914 35 -10.8855 0.7232 2 BIAS: 1.8073
1915 36 6.0107 0.7232 2 -0.4 4.9190 0.9480 3
1916 37 -11.6138 0.8845 3 -36.3 -16.2504 1.1093 4
1917 38 -21.3848 0.8845 3 -47.4 -26.2907 1.1093 4
1918 39 -18.0639 0.8845 3 9999 -18.0639 0.8845 3
1919 40 -16.7118 0.2166 1 9999 -16.7118 0.2166 1
1920 41 14.1781 0.8845 3 12.6 14.2246 1.1093 4
1921 42 16.7969 0.6679 2 4.3 14.1049 0.8927 3
1922 43 12.4016 0.8845 3 9.0 12.0785 1.1093 4
1923 44 7.0969 0.8845 3 5.6 7.1598 1.1093 4
1924 45 6.7093 0.8845 3 15.3 8.8165 1.1093 4
1925 46 1.1977 0.8845 3 -3.4 0.6322 1.1093 4
1926 47 -4.1444 0.8845 3 -15.3 -6.0389 1.1093 4
1927 48 -4.7650 0.8845 3 -4.7 -4.3856 1.1093 4
1928 49 -4.9976 0.8845 3 -9.8 -5.6046 1.1093 4
1929 50 -7.1761 0.8845 3 -11.3 -7.6456 1.1093 4
1930 51 -3.1562 0.8845 3 -7.9 -3.7513 1.1093 4
1931 52 8.1198 0.8845 3 10.1 8.8873 1.1093 4
1932 53 5.0835 1.3252 4 1.3 4.7968 1.5500 5
1933 54 -3.8764 0.8845 3 -19.8 -6.7371 1.1093 4
1934 55 8.0099 1.3252 4 7.8 8.2416 1.5500 5
1935 56 11.5053 1.3252 4 7.0 11.1140 1.5500 5
1936 57 11.4254 1.3252 4 8.7 11.2923 1.5500 5
1937 58 23.2738 1.3252 4 31.6 24.7436 1.5500 5
1938 59 13.4275 1.3252 4 21.1 14.8024 1.5500 5
1939 60 -3.1409 1.3252 4 1.4 -2.2202 1.5500 5
1940 61 -2.8806 1.3252 4 7.2 -1.1564 1.5500 5
1941 62 -23.8843 1.3252 4 -20.4 -23.1169 1.5500 5
1942 63 -17.7417 1.3252 4 -12.9 -16.7774 1.5500 5
1943 64 23.6466 1.3252 4 25.1 24.1196 1.5500 5
1944 65 19.1588 1.3252 4 24.8 20.2391 1.5500 5
1945 66 1.6749 1.3252 4 36.8 7.0315 1.5500 5
1946 67 -11.6450 1.3252 4 -15.0 -11.8695 1.5500 5
1947 68 1.8363 1.3252 4 4.3 2.4558 1.5500 5
1948 69 12.8666 1.1639 3 2.4 11.4647 1.3887 4
1949 70 -0.2835 1.3252 4 -6.6 -0.9375 1.5500 5
1950 71 7.8174 1.3252 4 4.9 7.6564 1.5500 5
1951 72 5.1348 1.3252 4
1952 73 1.3749 1.3252 4
1953 74 -0.6573 1.3252 4
1954 75 19.5651 1.3252 4
1955 76 3.0486 1.3252 4
1956 77 -16.0434 1.3252 4
1957 78 6.5739 1.3252 4
1958 79 -10.6942 1.3252 4
1959 80 0.1761 1.3252 4
1960 81 -11.5644 1.3252 4
1961 82 18.4079 1.3252 4
1962 83 19.6353 1.3252 4
1963 84 -8.2641 1.3252 4
1964 85 -17.1124 1.3252 4
1965 86 -9.6000 1.3252 4
1966 87 -17.1014 1.3252 4
1967 88 20.4333 1.3252 4
1968 89 -17.8403 1.3252 4
1969 90 -29.9485 1.3252 4
1970 91 -1.6156 1.3252 4
1971 92 -13.1002 1.3252 4
1972 93 -4.5360 1.3252 4
1973 94 5.7931 1.3252 4
1974 95 4.5170 1.3252 4
1975 96 11.9629 1.3252 4
1976 97 3.7820 1.3252 4
1977 98 6.7072 1.3252 4
1978 99 -10.4126 1.3252 4
1979 100 -21.4603 1.3252 4
1980 101 -4.0350 1.3252 4
1981 102 18.6902 1.3252 4
1982 103 -0.9625 1.3252 4
1983 104 10.7114 1.3252 4
1984 105 9.6122 1.3252 4
1985 106 -13.1845 1.3252 4
1986 107 -5.2971 1.3252 4
1987 108 -16.0556 1.3252 4
1988 109 4.2095 1.3252 4
1989 110 18.6438 1.3252 4
1990 111 3.2245 0.6020 2
1991 112 15.5508 0.6020 2
1992 113 -22.3093 0.6020 2
1993 114 20.1684 0.6020 2
1994 115 -2.4293 0.1613 1
1995 116 32.8227 0.6020 2
1996 117 12.9029 0.6020 2
1997 118 -6.9887 0.6020 2
1998 119 -30.6034 0.6020 2
1999 120 -20.3262 0.6020 2
2000 121 21.3012 0.6020 2
2001 122 0.9041 0.6020 2
2002 123 -1.7293 0.1613 1
2003 124 9.1707 0.1613 1
2004 125 15.9707 0.1613 1
2005 126 15.4707 0.1613 1
2006 127 2.7424 0.6679 2
2007 128 23.6407 0.6679 2
2008 129 14.7707 0.1613 1
2009 130 13.0030 0.6679 2
NSM: 34 NCOM: 34

The comments in the GISS GISTEMP FORTRAN code describe the rural station combination:

C**** Combining of rural stations
C**** ===========================
C**** Stations within Rngbr km of the urban center U contribute
C**** to the mean at U with weight  1.- d/Rngbr  (d = distance
C**** between rural and urban station in  km). To remove the station
C**** bias, station data are shifted before combining them with the
C**** current mean. The shift is such that the means over the time
C**** period they have in common remains unchanged. If that common
C**** period is less than 20(NCRIT) years, the station is disregarded.
C**** To decrease that chance, stations are combined successively in
C**** order of the length of their time record.

C**** The homogeneity adjustment parameters
C**** =====================================
C**** To minimize the impact of the natural local variability, only
C**** that part of the combined rural record is actually used that is
C**** supported by at least 3 stations, i.e. heads and tails of the
C**** record that are based on only 1 or 2 stations are dropped. The
C**** difference between that truncated combination and the non-rural
C**** record is found and the best linear fit and best fit by a broken
C**** line (with a variable "knee") to that difference series are found.
C**** The parameters defining those 2 approximations are tabulated.

The BIAS value for each stage is the difference in means for the two records, calculated taking only years in which both records have data. The variables NSM and NCOM at the end of each stage give the number of years added, and the number of years overlap. Two data values and their weights are combined using the code:

C**** Update period of valid data, averages and weights
 DO 20 N=NF1,NL1
 IF(DNEW(N).GE.XBAD) GO TO 20
 WTNEW=WT(N)+WT1
 AVG(N)=(WT(N)*AVG(N)+WT1*(DNEW(N)+BIAS))/WTNEW
 WT(N)=WTNEW
 IWT(N)=IWT(N)+1
 NSM=NSM+1
 20 CONTINUE

Taking for example the combination of 1916 values for UST’-CIL’MA (-10.2 with weight 0.5065) and KANIN NOS (-18.7 with weight 0.1613):

  1. The new weight is calculated, 0.5065 + 0.1613 = 0.6679 (using the full precision values and rounding)
  2. The combined value is calculated, (0.5065 * -10.2 + 0.1613 * (-18.7 + 1.5707)) / 0.6679 = -11.8740 (1.5707 is the BIAS value)

The log lines detailing the combination and adjustment:

urb stnID:222232050004 # rur:   5 ranges: 1927 2009     500.
  • NAR’JAN-MAR (222 23205000) has anomaly data available from 1927 to 2009, and has 5 rural stations within 500 km
 longest rur range: 1890-2009    98  [wgt: 0.507  246.7 km] 222234050000  [UST'-CIL'MA]
  • UST’-CIL’MA (222 23405000) is the rural station with the longest record, 1890-2009, has 98 years with data (there are 22 years with missing data), and is 246.7 km away, giving a weight of 0.507.
 add stn    2 range: 1916-2009    92 [wgt: 0.161  419.4 km] 638221650004  [KANIN NOS]
  • KANIN NOS (638 22165000) is the rural station with the next longest record, 1916-2009, has 92 years with data (there are two years with missing data), and is 419.4 km away, giving a weight of 0.161.
 data added:  92  overlap: 75  years
  • KANIN NOS is combined with UST’-CIL’MA, using data for the 92 years with data (there are two years with missing data). 75 years overlap, with data for both stations.
 add stn    3 range: 1913-1989    76 [wgt: 0.217  391.8 km] 638225830000  [KOJNAS]
  • KOJNAS (638 22583000) is the rural station with the next longest record, 1913-1989,has 76 years with data (there is one year with missing data), and is 391.8 km away, giving a weight of 0.217.
 data added:  76  overlap: 75  years
  • KOJNAS is combined with the combined result of UST’-CIL’MA and KANIN NOS, using data for the 76 years with data (there is one year with missing data). 75 years overlap, with data for both KOJNAS and the combined stations.
 add stn    4 range: 1932-2001    68 [wgt: 0.441  279.7 km] 222232190004  [HOSEDA-HARD]
  • HOSEDA-HARD (222 23219000) is the rural station with the next longest record, 1932-2001, has 68 years with data (there are two years with missing data), and is 279.7 km away, giving a weight of 0.441.
 data added:  68  overlap: 68  years
  • HOSEDA-HARD is combined with the combined result of UST’-CIL’MA KANIN NOS and KOJNAS, using data for the 68 years with data (there are two years with missing data). 68 years overlap, with data for both HOSEDA-HARD and the combined stations.
 add stn    5 range: 1915-1950    34 [wgt: 0.225  387.7 km] 222230220010  [WAIGATZ]
  • WAIGATZ (222 23022001) is the last rural station used, 1915-1950, has 34 years with data (there are two years with missing data), and is 387.7 km away, giving a weight of 0.225.
 data added:  34  overlap: 34  years
  • WAIGATZ is combined with the combined result of UST’-CIL’MA, KANIN NOS, KOJNAS and HOSEDA-HARD, using data for the 34 years with data (there are two years with missing data). 34 years overlap, with data for both WAIGATZ and the combined stations.
 possible range increase 32 63 63
  • (this log line is generated after the least squares fit, and will be described in the next post)

In this example sufficient rural stations were found within 500 km. Where sufficient stations are not found, a search for stations within 1000 km follows. All rural stations found were included in the combined rural record. In other cases some rural stations may be dropped when there is less than 20 years overlap with the stations combined up to that point. Stations are combined successively in order of the length of their time record to decrease the probability of dropping stations in this way. A future post will examine the alternative strategy of combining the rural stations in order of increasing distance from the urban station.

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One Response to GISTEMP Rural Station Combination (post 3 of 6 in GISTEMP example)

  1. Pingback: Roman’s Anomaly Regression and GISTEMP « Peter O'Neill's Blog

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