Spreadsheet: 52731d1252574157-matrix-formula-problem-uhdev
Sheet: Calcs

Derivation of a Unit Hydrograph from a Multi period Storm |  |  |  |  |  |  |  | k= | 7 |  | "= n - j + 1"
[NAME] |  | Periods | 3 | Time period (hrs) |  | 2 |  | Note: always start the P array in cell D6 and rainfall Excess in B7
Create the range Pe |  | Using Macro E
 |  |  | Matrix array P is |  | 9 | rows | 7 | columns |  |  |  |  |  |  | Excss Runoff Hydrograph Q
Time (hr) | Excess (mm) |  | 9.4 | 0 | 0 | 0 | 0 | 0 | 0 |  |  |  |  |  | Time (hr) | Q (m3/s)
0 | 9.4 |  | 4.6 | 9.4 | 0 | 0 | 0 | 0 | 0 |  |  |  |  |  | 0 | 0
2 | 4.6 |  | 2.7 | 4.6 | 9.4 | 0 | 0 | 0 | 0 |  |  |  |  |  | 2 | 50
4 | 2.7 |  | 0 | 2.7 | 4.6 | 9.4 | 0 | 0 | 0 |  |  |  |  |  | 4 | 183
6 |  |  | 0 | 0 | 2.7 | 4.6 | 9.4 | 0 | 0 |  |  |  |  |  | 6 | 375
8 |  |  | 0 | 0 | 0 | 2.7 | 4.6 | 9.4 | 0 |  |  |  |  |  | 8 | 395
10 |  |  | 0 | 0 | 0 | 0 | 2.7 | 4.6 | 9.4 |  |  |  |  |  | 10 | 322
12 |  |  | 0 | 0 | 0 | 0 | 0 | 2.7 | 4.6 |  |  |  |  |  | 12 | 200
14 |  |  | 0 | 0 | 0 | 0 | 0 | 0 | 2.7 |  |  |  |  |  | 14 | 135
16 |  |  |  |  |  |  |  |  |  |  |  |  |  |  | 16 | 50
 |  |  | Transpose    PT |  | 7 | x | 9 |  |  |  |  |  |  |  | 18 | 15
 |  |  | 9.4 | 4.6 | 2.7 | 0 | 0 | 0 | 0 | 0 | 0 |  |  |  | 20 | 0
 |  |  | 0 | 9.4 | 4.6 | 2.7 | 0 | 0 | 0 | 0 | 0 |  |  |  | 22
 |  |  | 0 | 0 | 9.4 | 4.6 | 2.7 | 0 | 0 | 0 | 0 |  |  |  | 24
 |  |  | 0 | 0 | 0 | 9.4 | 4.6 | 2.7 | 0 | 0 | 0 |  |  |  | 26
 |  |  | 0 | 0 | 0 | 0 | 9.4 | 4.6 | 2.7 | 0 | 0 |  |  |  | 28
 |  |  | 0 | 0 | 0 | 0 | 0 | 9.4 | 4.6 | 2.7 | 0 |  |  |  | 30
 |  |  | 0 | 0 | 0 | 0 | 0 | 0 | 9.4 | 4.6 | 2.7 |  |  |  | 32
 |  |  | Inverse PTP |  |  | 7 | x | 7
 |  |  | 0.01131622258574102 | -0.005535620666053506 | -0.0005411865235567705 | 0.001847019022085688 | -0.0007360978686442896 | -0.0001640106460000095 | 0.0002380874622254308
 |  |  | -0.005535620666053506 | 0.0140191042485063 | -0.005267434691495293 | -0.001429216157086496 | 0.002168239860109417 | -0.0006444815682773252 | -0.0001640106460000092
 |  |  | -0.0005411865235567705 | -0.005267434691495293 | 0.01404260885521254 | -0.005366435014436362 | -0.001367243442764015 | 0.002168239860109417 | -0.0007360978686442894
j = | 3 |  | 0.001847019022085688 | -0.001429216157086496 | -0.00536643501443636 | 0.01429619517113917 | -0.005366435014436362 | -0.001429216157086496 | 0.001847019022085687
 |  |  | -0.0007360978686442893 | 0.002168239860109417 | -0.001367243442764016 | -0.005366435014436359 | 0.01404260885521254 | -0.005267434691495294 | -0.0005411865235567696
 |  |  | -0.0001640106460000095 | -0.0006444815682773254 | 0.002168239860109417 | -0.001429216157086496 | -0.005267434691495295 | 0.0140191042485063 | -0.005535620666053506 |  |  |  |  |  | n = | 9
 |  |  | 0.0002380874622254309 | -0.0001640106460000092 | -0.0007360978686442894 | 0.001847019022085688 | -0.0005411865235567694 | -0.005535620666053507 | 0.01131622258574102 |  |  |  |  |  | Time | U m3/s |  | Using a nested function |  | in one formula
 |  |  | MMULT | INVERSExPT |  |  |  |  |  |  |  |  |  |  | 0 | 0
 |  |  | 0.1063724923059656 | 1.978963350574015e-05 | 2.792596220992441e-06 | -7.365499910014575e-05 | 0.0001157639227345603 | 5.920109146753606e-05 | -0.0005038910720205755 | 0.0006523735820369562 | 0.0006428361480086633 |  |  |  | 2 | 5.317551745181381 |  | 5.317551745181381
 |  |  | -0.05203483426090295 | 0.1063157248721131 | 2.781764472876286e-05 | 0.0001867500134756124 | -0.0004150133046066477 | 5.689299056292358e-05 | 0.001347932335819646 | -0.00249454920594882 | -0.0004428287442000249 |  |  |  | 4 | 16.86657909855216 |  | 16.86657909855216
 |  |  | -0.005087153321433642 | -0.0520033441084169 | 0.1063091200445163 | -7.056206876140947e-05 | 0.0003773544806848651 | -0.0003972396906641203 | -0.0006369739042158418 | 0.002468197426531697 | -0.001987464245339582 |  |  |  | 6 | 30.11674499684593 |  | 30.11674499684593
 |  |  | 0.01736197880760547 | -0.004938344375018899 | -0.05203193209866831 | 0.1058397499181674 | 0.0008286341125601851 | 0.0004794940190554278 | -0.003701790053970595 | 0.004637403877460621 | 0.004986951359631356 |  |  |  | 8 | 22.42876039546424 |  | 22.42876039546424
 |  |  | -0.006919319965256319 | 0.01699540448926479 | -0.004865649250818008 | -0.05087956135012082 | 0.1036233648771278 | 0.0005927400949437694 | 0.00859769100676189 | -0.01671153167539843 | -0.001461203613603278 |  |  |  | 10 | 14.63061297828096 |  | 14.63061297828096
 |  |  | -0.001541700072400089 | -0.006812575713406903 | 0.0169740107267528 | -0.005200828754458526 | -0.05023403280035822 | 0.1036904967309474 | -0.001769028384811272 | 0.0123877264071209 | -0.01494617579834447 |  |  |  | 12 | 7.706255941253194 |  | 7.706255941253194
 |  |  | 0.002238022144919051 | -0.0004464977461631045 | -0.0070309327888477 | 0.0135330998676417 | 0.001421669934820948 | -0.04953734090963275 | 0.07944743362851621 | 0.03710844809606423 | 0.03055380098150076 |  |  |  | 14 | 6.328609168059897 |  | 6.328609168059897
 |  |  |  |  |  |  |  |  |  |  |  |  |  |  | 16 | 0
Notes: | Direct runoff volume |  | 12420000 | m3 |  |  |  |  |  |  |  |  | Total UHG Volume |  |  | 744444.8231301918 | m3
 | Total excess rainfall |  | 16.7 | [NAME] |  |  |  |  |  |  |  |  | Multiply by total excess |  |  | 12432228.5462742