Question

b. The Table below provides the annual rainfall records at gages A, B, C, D and X. The records of A, B, C and D are consistent. Gage X was temporarily relocated in January 2012 and was returned to the original station in January 2016. Adjust the 2012 to 2015 records of X, and determine the adjusted average annual rainfall at the X gage for the period 2006-2015. YEAR PRECIPITATION, cm A B с D X 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 210 270 290 250 190 210 230 170 180 220 190 240 280 230 220 200 200 160 160 190 200 270 270 230 170 180 220 180 180 200 230 290 290 260 230 220 250 200 200 250 170 240 250 220 160 200 240 200 220 250 Markis: 11+9

Answer 1

The concept of double mass curve will be used for checking the consistency and adjusting of precipitation data. The data given in the question is tabulated below: year Station a b с d х 2006 210 190 200 230 170 2007 240 270 290 240 280 230 270 270 290 290 250 230 260 220 250 190 220 170 230 160 200 180 220 200 2008 2009 2010 2011 2012 2013 2014 2015 200 220 240 210 230 170 180 220 160 160 190 180 180 200 250 200 200 250 200 220 250 where the precipitation is in cm. Steps for adjusting the inconsistencies are given below: 1) The data has to be cumulated first Cumulative Reading of current year = Sum of readings of all the previous years and the current year. a b с d х year 2006 210 190 230 170 200 470 2007 480 430 520 410 770 740 660 970 710 940 1160 1360 2008 2009 2010 2011 2012 2013 2014 810 1070 1300 1520 880 1040 1140 1320 1240 1020 1210 1420 1650 1820 2000 2220 1540 1770 1480 1680 1720 1970 1560 1720 1880 2070 2170 1900 2100 1900 2150 2015 2420

2) The mean cumulative precipitation for each year is calculated. a b с d mean year 2006 210 190 200 230 200 170 410 2007 480 430 470 520 462 2008 660 738 710 940 740 970 810 1070 2009 880 976 2010 1160 1140 1300 1040 1240 1170 1372 2011 1320 770 1020 1210 1420 1650 1820 2000 2220 1540 1480 1360 1560 1720 1880 2070 2012 2013 2014 2015 1680 1520 1770 1970 2170 2420 1720 1900 2100 1600 1782 1970 2192 1900 2150 3) The cumulative precipitation of each station is plotted against the mean. Assuming the data of A (or B, C or D) to be consistent for they were not relocated, data of Station A and Station X has been taken for convenience in calculation. 2500 y = 1.0094x + 22.113 2000 1500 x 1000 Linear (a) Linear (x) 500 y = 0.9074x - 10.43 ******** 0 0 500 1000 1500 2000 2500 The double mass curve of station A is unbroken straight line with slope a=1.0094 The double mass curve of station X has been plotted upto year 2011, because of relocation in year 2012. The slope of line is b=0.9074

4) To adjust the data of station X from year 2012, following formula is used Padj = Pobs* [a/b] Where Padj is adjusted precipitation Pobs is observed precipitation a is the slope of graph to which records are adjusted b is slope of graph at time Pobs was observed 5) The adjusted values of Station X for relocated years (2012-2015) are tabulated below year 2012 2013 2014 2015 Xobserved Xadjusted 240 266.9782 200 222.4818 220 244.73 250 278.1023 6) The precipitation values of station X from 2006-2015 are tabulated below year Xadjusted 2006 170 2007 240 2008 250 2009 220 2010 160 2011 200 2012 266.9782 2013 222.4818 2014 244.73 2015 | 278.1023 Hope that completes your question.