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BEGIN BEGIN Rainfall-Runoff Models Rainfall-Runoff Models
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BEGINRainfall-Runoff Models
Excess Precipitation or Runoff Volume ModelsMay be:
Physically BasedEmpiricalDescriptiveConceptualGenerally LumpedEtcMay not only estimate excess precipitation hence, we will refer to them as rainfall-runoff models..
The Basic Process.
Excess Precip. Model
Excess Precip.
Excess Precip.
Runoff Hydrograph
Runoff Hydrograph
Stream and/or Reservoir Routing
Downstream Hydrograph
Basin Routing UHG MethodsNecessary for a single basin
Focus on Excess Precipitation
Goal of Rainfall-Runoff ModelsThe fate of the falling precipitation is:modeled in order to account for the destiny of the precipitation that falls and the potential of the precipitation to affect the the runoff hydrograph. losses include interception, evapotranspiration, storage, infiltration, percolation, and finally - runoff. Lets look at the fate of the precipitation..
Interception...........First, the falling precipitation may be intercepted by the vegetation in an area.It is typically either distributed as runoff or evaporated back to the atmosphere.The leafy matter may also be a form of interception.
Canopy(or lack of)
Leafy Matter also intercepts...Very thick ground litter layers can hold as much as 0.5 inches!
Interceptionthe pointThe point of the interception is that the precipitation is temporarily stored before the next process begins.The intercepted/stored precipitation may not reach the ground to contribute to runoff.Interception may be referred to as an abstraction and is accounted for as initial abstraction in some models.This is also true for snowfall which may sublimate and leave the watershed!
Infiltration...........Precipitation reaching the ground may infiltrate.This is the process of moving from the atmosphere into the soil.Infiltration may be regarded as either a rate or a total. For example: the soil can infiltrate 1.2 inches/hour. Alternatively, we could say the soil has a total infiltration capacity of 3 inches.Note that in both cases the units are Length or length per time!
Infiltration, cont...........Infiltration is nearly impossible to measure directly - as we would disturb the sample in doing so. We can infer infiltration in a variety of ways (to be discussed at a later point). The exact point at which the atmosphere ends and the soil beings is very difficult to define and generally we are not concerned with this fine detail!In other words, we mostly want to know how much of the precipitation actually enters the soil.
Percolation.....
Once the water infiltrates into the ground, the downward movement of water through the soil profile may begin.
Percolation.....
The percolating water may move as a saturated front - under the influence of gravity
Percolation.....
Or, it may move as unsaturated flow mostly due to capillary forces.
Percolation.the pointThe vertical percolation of the water into various levels or zones allows for storage in the subsurface these zones will be very important in the SAC-SMA model.This stored subsurface water is held and released as either evaporation, transpiration, or as streamflow eventually reaching the watershed outlet.
Evaporation....Is the movement of water from the liquid state to the vapor state - allowing transport to the atmosphere.Occurs from any wet surface or open body of water.Soil can have water evaporate from within, as can leafy matter, living leaves and plants, etc..The water evaporates from a storage location....
Transpiration....The process of water moving from the soil via the plants internal moisture supply system.This is a type of evaporative process.The water moves through the stomates, tiny openings in the leaves (mostly on the underside), that allow the passage of oxygen, carbon dioxide, water vapor, and other gases.
Evapotranspiration....The terms transpiration and evaporation are often combined in the form :
EVAPOTRANSPIRATION
Storage....Storage occurs at several locations in the hydrologic cycle and varies in both space and time - spatially and temporally.Water can be stored in:The unsaturated portion of the soilThe saturated portion (below the water table)On the soil or surface - snow/snowpack, puddles, ponds, lakes, wetlands.Rivers and stream channels - even though they are generally in motion!
Storage....Water in storage can still be involved in a process.i.e. :Water in a puddle may be evaporating.....
The hydrologic cycle represented as a series of storage units & processes....
RO
P
TE=-Is I > f?yesnoSurface runoffChannel runoffIs retention full?yesnoSurface runoffBase FlowStorm Flow
Storage....The thought process.......
Storage....Things to consider:
We looked at these as independent processes!We looked at the processes as discrete time steps!What were the initial conditions before the storm? What effects would initial conditions have?
These are the issues that a continuous rainfall-runoff model must consider
The Units The units are very importantStorage is a volume (L3) and flow is a volume per time (L3/T) .We often think of these volume units in terms of length only!This implies a uniform depth or value throughout the watershed.
Examples of Length Units for StorageThe watershed can infiltrate 75mm of water a lengthThe lower zone of the soil can hold 60mm...The initial abstraction for the watershed is 10mmThe reservoir can hold 2.5 inches of runoffThese all imply uniformity over the watershed
The Rainfall-Runoff Modeling Process simplistic methods such as a constant loss method may be used. A constant loss approach assumes that the soil can constantly infiltrate the same amount of precipitation throughout the storm event. The obvious weaknesses are the neglecting of spatial variability, temporal variability, and recovery potential.Other methods include exponential decays (the infiltration rate decays exponentially), empirical methods, and physically based methods. There are also combinations of these methods.
Initial AbstractionsInitial Abstraction - It is generally assumed that the initial abstractions must be satisfied before any direct storm runoff may begin. The initial abstraction is often thought of as a lumped sum (depth). Viessman (1968) found that 0.1 inches was reasonable for small urban watersheds.
Would forested & rural watersheds be more or less?
Rural watersheds would probably have a higher initial abstraction.The Soil Conservation Service (SCS) now the NRCS uses a percentage of the ultimate infiltration holding capacity of the soil - i.e. 20% of the maximum soil retention capacity.
Some Rainfall-Runoff ModelsPhi-IndexHorton EquationSCS Curve NumberSAC-SMA
Constant Infiltration RateA constant infiltration rate is the most simple of the methods. It is often referred to as a phi-index or f-index. In some modeling situations it is used in a conservative mode.The saturated soil conductivity may be used for the infiltration rate.The obvious weakness is the inability to model changes in infiltration rate.The phi-index may also be estimated from individual storm events by looking at the runoff hydrograph.
Hydrograph Breakdown
Hydrograph Breakdown
Derive phi-indexsample watershed = 450 mi2
Separation of Baseflow... generally accepted that the inflection point on the recession limb of a hydrograph is the result of a change in the controlling physical processes of the excess precipitation flowing to the basin outlet. In this example, baseflow is considered to be a straight line connecting that point at which the hydrograph begins to rise rapidly and the inflection point on the recession side of the hydrograph. the inflection point may be found by plotting the hydrograph in semi-log fashion with flow being plotted on the log scale and noting the time at which the recession side fits a straight line.
Semi-log Plot
Hydrograph & Baseflow
Chart1
19263
19963
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9759
8966
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2012
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193
184
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167
159
152
144
137
131
125
119
113
108
103
98
93
89
Recession side of hydrograph becomes linear at approximately hour 64.
Time (hrs.)
Flow (cfs)
Chart2
1000.05
950.05
910.15
860.25
820.15
780.2
750.25
750.1
780.45
1050.5
1660.75
3130.4
5410.25
8870.35
13440.2
19160.15
26130.25
34640.15
44610.1
56350.05
696520
842621
998122
1155723
1311924
1461925
1601126
1727027
1836328
1926329
1996330
2046731
2077032
2086333
2076334
2050635
2010836
1958837
1896138
1823339
1739540
1646941
1547642
1445043
1344044
1244845
1150746
1061147
975948
896649
824150
758051
699752
646853
598254
553555
512556
473957
438058
404859
374560
346361
319862
297263
283164
269665
256866
244567
232968
221869
211270
201271
191672
182573
173874
165575
157676
150177
143078
136279
129780
123581
117682
112083
106784
101685
96886
92287
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83689
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72292
68893
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383105
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347107
331108
315109
300110
286111
272112
259113
247114
235115
224116
213117
203118
193119
184120
175121
167122
159123
152124
144125
137126
131127
125128
119129
113130
108131
103132
98133
93134
89
Storm #2 cfs
Prec. #2 inches
Time (hrs.)
Flow (cfs)
Precipitation (inches)
Chart3
100100
9595
9191
8686
8282
7878
7575
7575
7878
105105
166166
313225.4821428571
541274.6428571429
887323.8035714286
1344372.9642857143
1916422.125
2613471.2857142857
3464520.4464285714
4461569.6071428571
5635618.7678571429
6965667.9285714286
8426717.0892857143
9981766.25
11557815.4107142857
13119864.5714285714
14619913.7321428571
16011962.8928571429
172701012.0535714286
183631061.2142857143
192631110.375
199631159.5357142857
204671208.6964285714
207701257.8571428571
208631307.0178571429
207631356.1785714286
205061405.3392857143
201081454.5
195881503.6607142857
189611552.8214285714
182331601.9821428571
173951651.1428571429
164691700.3035714286
154761749.4642857143
144501798.625
134401847.7857142857
124481896.9464285714
115071946.1071428571
106111995.2678571429
97592044.4285714286
89662093.5892857143
82412142.75
75802191.9107142857
69972241.0714285714
64682290.2321428571
59822339.3928571429
55352388.5535714286
51252437.7142857143
47392486.875
43802536.0357142857
40482585.1964285714
37452634.3571428571
34632683.5178571429
31982732.6785714286
29722781.8392857143
28312831
26962696
25682568
24452445
23292329
22182218
21122112
20122012
19161916
18251825
17381738
16551655
15761576
15011501
14301430
13621362
12971297
12351235
11761176
11201120
10671067
10161016
968968
922922
878878
836836
796796
758758
722722
688688
655655
624624
594594
566566
539539
513513
489489
466466
443443
422422
402402
383383
365365
347347
331331
315315
300300
286286
272272
259259
247247
235235
224224
213213
203203
193193
184184
175175
167167
159159
152152
144144
137137
131131
125125
119119
113113
108108
103103
9898
9393
8989
Storm #2 cfs
Base #2 cfs
Time (hrs.)
Flow (cfs)
Chart4
1001000
95950
91910
86860
82820
78780
75750
75750
78780
1051050
1661660
313225.482142857187.5178571429
541274.6428571429266.3571428571
887323.8035714286563.1964285714
1344372.9642857143971.0357142857
1916422.1251493.875
2613471.28571428572141.7142857143
3464520.44642857142943.5535714286
4461569.60714285713891.3928571429
5635618.76785714295016.2321428571
6965667.92857142866297.0714285714
8426717.08928571437708.9107142857
9981766.259214.75
11557815.410714285710741.5892857143
13119864.571428571412254.4285714286
14619913.732142857113705.2678571429
16011962.892857142915048.1071428571
172701012.053571428616257.9464285714
183631061.214285714317301.7857142857
192631110.37518152.625
199631159.535714285718803.4642857143
204671208.696428571419258.3035714286
207701257.857142857119512.1428571429
208631307.017857142919555.9821428571
207631356.178571428619406.8214285714
205061405.339285714319100.6607142857
201081454.518653.5
195881503.660714285718084.3392857143
189611552.821428571417408.1785714286
182331601.982142857116631.0178571429
173951651.142857142915743.8571428571
164691700.303571428614768.6964285714
154761749.464285714313726.5357142857
144501798.62512651.375
134401847.785714285711592.2142857143
124481896.946428571410551.0535714286
115071946.10714285719560.8928571429
106111995.26785714298615.7321428571
97592044.42857142867714.5714285714
89662093.58928571436872.4107142857
82412142.756098.25
75802191.91071428575388.0892857143
69972241.07142857144755.9285714286
64682290.23214285714177.7678571429
59822339.39285714293642.6071428571
55352388.55357142863146.4464285714
51252437.71428571432687.2857142857
47392486.8752252.125
43802536.03571428571843.9642857143
40482585.19642857141462.8035714286
37452634.35714285711110.6428571429
34632683.5178571429779.4821428571
31982732.6785714286465.3214285714
29722781.8392857143190.1607142857
283128310
269626960
256825680
244524450
232923290
221822180
211221120
201220120
191619160
182518250
173817380
165516550
157615760
150115010
143014300
136213620
129712970
123512350
117611760
112011200
106710670
101610160
9689680
9229220
8788780
8368360
7967960
7587580
7227220
6886880
6556550
6246240
5945940
5665660
5395390
5135130
4894890
4664660
4434430
4224220
4024020
3833830
3653650
3473470
3313310
3153150
3003000
2862860
2722720
2592590
2472470
2352350
2242240
2132130
2032030
1931930
1841840
1751750
1671670
1591590
1521520
1441440
1371370
1311310
1251250
1191190
1131130
1081080
1031030
98980
93930
89890
Storm #2 cfs
Base #2 cfs
Excess #2 cfs
Time (hrs.)
Flow (cfs)
Chart5
10010000
959500
919100
868600
828200
787800
757500
757500
787800
10510500
16616600
313225.482142857187.517857142952.9128519606
541274.6428571429266.3571428571161.0381758508
887323.8035714286563.1964285714340.5057004664
1344372.9642857143971.0357142857587.0832613577
1916422.1251493.875903.1892382104
2613471.28571428572141.71428571431294.8695802384
3464520.44642857142943.55357142861779.6575401624
4461569.60714285713891.39285714292352.7163586112
5635618.76785714295016.23214285713032.7884781482
6965667.92857142866297.07142857143807.1774054241
8426717.08928571437708.91071428574660.7682674037
9981766.259214.755571.1910519952
11557815.410714285710741.58928571436494.3103299361
13119864.571428571412254.42857142867408.9652789774
14619913.732142857113705.26785714298286.1353428917
16011962.892857142915048.10714285719098.0091552945
172701012.053571428616257.94642857149829.4718431508
183631061.214285714317301.785714285710460.5717740542
192631110.37518152.62510974.984885127
199631159.535714285718803.464285714311368.4790119192
204671208.696428571419258.303571428611643.4725341164
207701257.857142857119512.142857142911796.9424771118
208631307.017857142919555.982142857111823.4474866125
207631356.178571428619406.821428571411733.2656762826
205061405.339285714319100.660714285711548.1624632925
201081454.518653.511277.8113663845
195881503.660714285718084.339285714310933.6996890655
189611552.821428571417408.178571428610524.8963551563
182331601.982142857116631.017857142910055.0289341855
173951651.142857142915743.85714285719518.6560718604
164691700.303571428614768.69642857148929.0788564519
154761749.464285714313726.53571428578298.9937813094
144501798.62512651.3757648.9570737606
134401847.785714285711592.21428571437008.5938849542
124481896.946428571410551.05357142866379.1134047331
115071946.10714285719560.89285714295780.4672655035
106111995.26785714298615.73214285715209.0278977371
97592044.42857142867714.57142857144664.1907065123
89662093.58928571436872.41071428574155.0246156504
82412142.756098.253686.9709794438
75802191.91071428575388.08928571433257.6114182069
69972241.07142857144755.92857142862875.4102608395
64682290.23214285714177.76785714292525.8572292278
59822339.39285714293642.60714285712202.3017792365
55352388.55357142863146.44642857141902.3255311798
51252437.71428571432687.28571428571624.7192952151
47392486.8752252.1251361.623337364
43802536.03571428571843.96428571431114.8514423907
40482585.19642857141462.8035714286884.4036102954
37452634.35714285711110.6428571429671.4890309207
34632683.5178571429779.4821428571471.2709448955
31982732.6785714286465.3214285714281.3309725341
29722781.8392857143190.1607142857114.9702021074
2831283100
2696269600
2568256800
2445244500
2329232900
2218221800
2112211200
2012201200
1916191600
1825182500
1738173800
1655165500
1576157600
1501150100
1430143000
1362136200
1297129700
1235123500
1176117600
1120112000
1067106700
1016101600
96896800
92292200
87887800
83683600
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75875800
72272200
68868800
65565500
62462400
59459400
56656600
53953900
51351300
48948900
46646600
44344300
42242200
40240200
38338300
36536500
34734700
33133100
31531500
30030000
28628600
27227200
25925900
24724700
23523500
22422400
21321300
20320300
19319300
18418400
17517500
16716700
15915900
15215200
14414400
13713700
13113100
12512500
11911900
11311300
10810800
10310300
989800
939300
898900
Storm #2 cfs
Base #2 cfs
Excess #2 cfs
Unit graph #2 cfs/inch
Time (hrs.)
Flow (cfs)
Chart7
0.051
0.05
0.15
0.25
0.15
0.2
0.25
0.1
0.45
0.5
0.75
0.4
0.25
0.35
0.2
0.15
0.25
0.15
0.1
0.05
Uniform loss rate of 0.2 inches per hour
Prec. #2 inches
#REF!
Time (hrs.)
Precipitation (inches)
Chart11
0
0
0
0.05
0
0
0.05
0
0.25
0.3
0.55
0.2
0.05
0.15
0
0
0.05
0
0
0
Periods of low excess precipitation at the beginning and end of the storm may be ommitted.
Derived unit hydrograph is the result of 6 hours of excess preciptation.
Excess Prec. #1 inches
Time (hrs.)
Excess Precipitation (inches)
Sheet1
TimeStorm #2Base #2Excess #2Unit graph #2Prec. #2Excess Prec. #1
hourscfscfscfscfs/inchinchesinches
010010000.000.050
1959500.000.050
2919100.000.150
3868600.000.250.05
4828200.000.150
5787800.000.20
6757500.000.250.05
7757500.000.10
8787800.000.450.25
910510500.000.50.3
1016616600.000.750.55
11313225.48214285718852.910.40.2
12541274.6428571429266161.040.250.05
13887323.8035714286563340.510.350.15
141344372.9642857143971587.080.20
151916422.1251494903.190.150
162613471.285714285721421294.870.250.05
173464520.446428571429441779.660.150
184461569.607142857138912352.720.10
195635618.767857142950163032.790.050
206965667.928571428662973807.18
218426717.089285714377094660.77
229981766.2592155571.19
2311557815.4107142857107426494.31
2413119864.5714285714122547408.97
2514619913.7321428571137058286.14
2616011962.8928571429150489098.01
27172701012.0535714286162589829.47
28183631061.21428571431730210460.57
29192631110.3751815310974.98
30199631159.53571428571880311368.48
31204671208.69642857141925811643.47
32207701257.85714285711951211796.94
33208631307.01785714291955611823.45
34207631356.17857142861940711733.27
35205061405.33928571431910111548.16
36201081454.51865411277.81
37195881503.66071428571808410933.70
38189611552.82142857141740810524.90
39182331601.98214285711663110055.03
40173951651.1428571429157449518.66
41164691700.3035714286147698929.08
42154761749.4642857143137278298.99
43144501798.625126517648.96
44134401847.7857142857115927008.59
45124481896.9464285714105516379.11
46115071946.107142857195615780.47
47106111995.267857142986165209.03
4897592044.428571428677154664.19
4989662093.589285714368724155.02
5082412142.7560983686.97
5175802191.910714285753883257.61
5269972241.071428571447562875.41
5364682290.232142857141782525.86
5459822339.392857142936432202.30
5555352388.553571428631461902.33
5651252437.714285714326871624.72
5747392486.87522521361.62
5843802536.035714285718441114.85
5940482585.19642857141463884.40
6037452634.35714285711111671.49
6134632683.5178571429779471.27
6231982732.6785714286465281.33
6329722781.8392857143190114.97
642831283100.00
652696269600.00
662568256800.00
672445244500.00
682329232900.00
692218221800.00
702112211200.00
712012201200.00
721916191600.00
731825182500.00
741738173800.00
751655165500.00
761576157600.00
771501150100.00
781430143000.00
791362136200.00
801297129700.00
811235123500.00
821176117600.00
831120112000.00
841067106700.00
851016101600.00
8696896800.00
8792292200.00
8887887800.00
8983683600.00
9079679600.00
9175875800.00
9272272200.00
9368868800.00
9465565500.00
9562462400.00
9659459400.00
9756656600.00
9853953900.00
9951351300.00
10048948900.00
10146646600.00
10244344300.00
10342242200.00
10440240200.00
10538338300.00
10636536500.00
10734734700.00
10833133100.00
10931531500.00
11030030000.00
11128628600.00
11227227200.00
11325925900.00
11424724700.00
11523523500.00
11622422400.00
11721321300.00
11820320300.00
11919319300.00
12018418400.00
12117517500.00
12216716700.00
12315915900.00
12415215200.00
12514414400.00
12613713700.00
12713113100.00
12812512500.00
12911911900.00
13011311300.00
13110810800.00
13210310300.00
133989800.00
134939300.00
135898900.00
480270sum cfs
1728971936cubic feet
39692acre-feet
0.13782feet runoff
1.65382inches runoff
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Sheet5
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Sheet6
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Sheet7
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Sheet9
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Sheet10
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Separate Baseflow
Chart1
19263
19963
20467
20770
20863
20763
20506
20108
19588
18961
18233
17395
16469
15476
14450
13440
12448
11507
10611
9759
8966
8241
7580
6997
6468
5982
5535
5125
4739
4380
4048
3745
3463
3198
2972
2831
2696
2568
2445
2329
2218
2112
2012
1916
1825
1738
1655
1576
1501
1430
1362
1297
1235
1176
1120
1067
1016
968
922
878
836
796
758
722
688
655
624
594
566
539
513
489
466
443
422
402
383
365
347
331
315
300
286
272
259
247
235
224
213
203
193
184
175
167
159
152
144
137
131
125
119
113
108
103
98
93
89
Recession side of hydrograph becomes linear at approximately hour 64.
Time (hrs.)
Flow (cfs)
Chart2
1000.05
950.05
910.15
860.25
820.15
780.2
750.25
750.1
780.45
1050.5
1660.75
3130.4
5410.25
8870.35
13440.2
19160.15
26130.25
34640.15
44610.1
56350.05
696520
842621
998122
1155723
1311924
1461925
1601126
1727027
1836328
1926329
1996330
2046731
2077032
2086333
2076334
2050635
2010836
1958837
1896138
1823339
1739540
1646941
1547642
1445043
1344044
1244845
1150746
1061147
975948
896649
824150
758051
699752
646853
598254
553555
512556
473957
438058
404859
374560
346361
319862
297263
283164
269665
256866
244567
232968
221869
211270
201271
191672
182573
173874
165575
157676
150177
143078
136279
129780
123581
117682
112083
106784
101685
96886
92287
87888
83689
79690
75891
72292
68893
65594
62495
59496
56697
53998
51399
489100
466101
443102
422103
402104
383105
365106
347107
331108
315109
300110
286111
272112
259113
247114
235115
224116
213117
203118
193119
184120
175121
167122
159123
152124
144125
137126
131127
125128
119129
113130
108131
103132
98133
93134
89
Storm #2 cfs
Prec. #2 inches
Time (hrs.)
Flow (cfs)
Precipitation (inches)
Chart3
100100
9595
9191
8686
8282
7878
7575
7575
7878
105105
166166
313225.4821428571
541274.6428571429
887323.8035714286
1344372.9642857143
1916422.125
2613471.2857142857
3464520.4464285714
4461569.6071428571
5635618.7678571429
6965667.9285714286
8426717.0892857143
9981766.25
11557815.4107142857
13119864.5714285714
14619913.7321428571
16011962.8928571429
172701012.0535714286
183631061.2142857143
192631110.375
199631159.5357142857
204671208.6964285714
207701257.8571428571
208631307.0178571429
207631356.1785714286
205061405.3392857143
201081454.5
195881503.6607142857
189611552.8214285714
182331601.9821428571
173951651.1428571429
164691700.3035714286
154761749.4642857143
144501798.625
134401847.7857142857
124481896.9464285714
115071946.1071428571
106111995.2678571429
97592044.4285714286
89662093.5892857143
82412142.75
75802191.9107142857
69972241.0714285714
64682290.2321428571
59822339.3928571429
55352388.5535714286
51252437.7142857143
47392486.875
43802536.0357142857
40482585.1964285714
37452634.3571428571
34632683.5178571429
31982732.6785714286
29722781.8392857143
28312831
26962696
25682568
24452445
23292329
22182218
21122112
20122012
19161916
18251825
17381738
16551655
15761576
15011501
14301430
13621362
12971297
12351235
11761176
11201120
10671067
10161016
968968
922922
878878
836836
796796
758758
722722
688688
655655
624624
594594
566566
539539
513513
489489
466466
443443
422422
402402
383383
365365
347347
331331
315315
300300
286286
272272
259259
247247
235235
224224
213213
203203
193193
184184
175175
167167
159159
152152
144144
137137
131131
125125
119119
113113
108108
103103
9898
9393
8989
Storm #2 cfs
Base #2 cfs
Time (hrs.)
Flow (cfs)
Chart4
1001000
95950
91910
86860
82820
78780
75750
75750
78780
1051050
1661660
313225.482142857187.5178571429
541274.6428571429266.3571428571
887323.8035714286563.1964285714
1344372.9642857143971.0357142857
1916422.1251493.875
2613471.28571428572141.7142857143
3464520.44642857142943.5535714286
4461569.60714285713891.3928571429
5635618.76785714295016.2321428571
6965667.92857142866297.0714285714
8426717.08928571437708.9107142857
9981766.259214.75
11557815.410714285710741.5892857143
13119864.571428571412254.4285714286
14619913.732142857113705.2678571429
16011962.892857142915048.1071428571
172701012.053571428616257.9464285714
183631061.214285714317301.7857142857
192631110.37518152.625
199631159.535714285718803.4642857143
204671208.696428571419258.3035714286
207701257.857142857119512.1428571429
208631307.017857142919555.9821428571
207631356.178571428619406.8214285714
205061405.339285714319100.6607142857
201081454.518653.5
195881503.660714285718084.3392857143
189611552.821428571417408.1785714286
182331601.982142857116631.0178571429
173951651.142857142915743.8571428571
164691700.303571428614768.6964285714
154761749.464285714313726.5357142857
144501798.62512651.375
134401847.785714285711592.2142857143
124481896.946428571410551.0535714286
115071946.10714285719560.8928571429
106111995.26785714298615.7321428571
97592044.42857142867714.5714285714
89662093.58928571436872.4107142857
82412142.756098.25
75802191.91071428575388.0892857143
69972241.07142857144755.9285714286
64682290.23214285714177.7678571429
59822339.39285714293642.6071428571
55352388.55357142863146.4464285714
51252437.71428571432687.2857142857
47392486.8752252.125
43802536.03571428571843.9642857143
40482585.19642857141462.8035714286
37452634.35714285711110.6428571429
34632683.5178571429779.4821428571
31982732.6785714286465.3214285714
29722781.8392857143190.1607142857
283128310
269626960
256825680
244524450
232923290
221822180
211221120
201220120
191619160
182518250
173817380
165516550
157615760
150115010
143014300
136213620
129712970
123512350
117611760
112011200
106710670
101610160
9689680
9229220
8788780
8368360
7967960
7587580
7227220
6886880
6556550
6246240
5945940
5665660
5395390
5135130
4894890
4664660
4434430
4224220
4024020
3833830
3653650
3473470
3313310
3153150
3003000
2862860
2722720
2592590
2472470
2352350
2242240
2132130
2032030
1931930
1841840
1751750
1671670
1591590
1521520
1441440
1371370
1311310
1251250
1191190
1131130
1081080
1031030
98980
93930
89890
Storm #2 cfs
Base #2 cfs
Excess #2 cfs
Time (hrs.)
Flow (cfs)
Chart5
10010000
959500
919100
868600
828200
787800
757500
757500
787800
10510500
16616600
313225.482142857187.517857142952.9128519606
541274.6428571429266.3571428571161.0381758508
887323.8035714286563.1964285714340.5057004664
1344372.9642857143971.0357142857587.0832613577
1916422.1251493.875903.1892382104
2613471.28571428572141.71428571431294.8695802384
3464520.44642857142943.55357142861779.6575401624
4461569.60714285713891.39285714292352.7163586112
5635618.76785714295016.23214285713032.7884781482
6965667.92857142866297.07142857143807.1774054241
8426717.08928571437708.91071428574660.7682674037
9981766.259214.755571.1910519952
11557815.410714285710741.58928571436494.3103299361
13119864.571428571412254.42857142867408.9652789774
14619913.732142857113705.26785714298286.1353428917
16011962.892857142915048.10714285719098.0091552945
172701012.053571428616257.94642857149829.4718431508
183631061.214285714317301.785714285710460.5717740542
192631110.37518152.62510974.984885127
199631159.535714285718803.464285714311368.4790119192
204671208.696428571419258.303571428611643.4725341164
207701257.857142857119512.142857142911796.9424771118
208631307.017857142919555.982142857111823.4474866125
207631356.178571428619406.821428571411733.2656762826
205061405.339285714319100.660714285711548.1624632925
201081454.518653.511277.8113663845
195881503.660714285718084.339285714310933.6996890655
189611552.821428571417408.178571428610524.8963551563
182331601.982142857116631.017857142910055.0289341855
173951651.142857142915743.85714285719518.6560718604
164691700.303571428614768.69642857148929.0788564519
154761749.464285714313726.53571428578298.9937813094
144501798.62512651.3757648.9570737606
134401847.785714285711592.21428571437008.5938849542
124481896.946428571410551.05357142866379.1134047331
115071946.10714285719560.89285714295780.4672655035
106111995.26785714298615.73214285715209.0278977371
97592044.42857142867714.57142857144664.1907065123
89662093.58928571436872.41071428574155.0246156504
82412142.756098.253686.9709794438
75802191.91071428575388.08928571433257.6114182069
69972241.07142857144755.92857142862875.4102608395
64682290.23214285714177.76785714292525.8572292278
59822339.39285714293642.60714285712202.3017792365
55352388.55357142863146.44642857141902.3255311798
51252437.71428571432687.28571428571624.7192952151
47392486.8752252.1251361.623337364
43802536.03571428571843.96428571431114.8514423907
40482585.19642857141462.8035714286884.4036102954
37452634.35714285711110.6428571429671.4890309207
34632683.5178571429779.4821428571471.2709448955
31982732.6785714286465.3214285714281.3309725341
29722781.8392857143190.1607142857114.9702021074
2831283100
2696269600
2568256800
2445244500
2329232900
2218221800
2112211200
2012201200
1916191600
1825182500
1738173800
1655165500
1576157600
1501150100
1430143000
1362136200
1297129700
1235123500
1176117600
1120112000
1067106700
1016101600
96896800
92292200
87887800
83683600
79679600
75875800
72272200
68868800
65565500
62462400
59459400
56656600
53953900
51351300
48948900
46646600
44344300
42242200
40240200
38338300
36536500
34734700
33133100
31531500
30030000
28628600
27227200
25925900
24724700
23523500
22422400
21321300
20320300
19319300
18418400
17517500
16716700
15915900
15215200
14414400
13713700
13113100
12512500
11911900
11311300
10810800
10310300
989800
939300
898900
Storm #2 cfs
Base #2 cfs
Excess #2 cfs
Unit graph #2 cfs/inch
Time (hrs.)
Flow (cfs)
Chart7
0.051
0.05
0.15
0.25
0.15
0.2
0.25
0.1
0.45
0.5
0.75
0.4
0.25
0.35
0.2
0.15
0.25
0.15
0.1
0.05
Uniform loss rate of 0.2 inches per hour
Prec. #2 inches
#REF!
Time (hrs.)
Precipitation (inches)
Chart11
0
0
0
0.05
0
0
0.05
0
0.25
0.3
0.55
0.2
0.05
0.15
0
0
0.05
0
0
0
Periods of low excess precipitation at the beginning and end of the storm may be ommitted.
Derived unit hydrograph is the result of 6 hours of excess preciptation.
Excess Prec. #1 inches
Time (hrs.)
Excess Precipitation (inches)
Sheet1
TimeStorm #2Base #2Excess #2Unit graph #2Prec. #2Excess Prec. #1
hourscfscfscfscfs/inchinchesinches
010010000.000.050
1959500.000.050
2919100.000.150
3868600.000.250.05
4828200.000.150
5787800.000.20
6757500.000.250.05
7757500.000.10
8787800.000.450.25
910510500.000.50.3
1016616600.000.750.55
11313225.48214285718852.910.40.2
12541274.6428571429266161.040.250.05
13887323.8035714286563340.510.350.15
141344372.9642857143971587.080.20
151916422.1251494903.190.150
162613471.285714285721421294.870.250.05
173464520.446428571429441779.660.150
184461569.607142857138912352.720.10
195635618.767857142950163032.790.050
206965667.928571428662973807.18
218426717.089285714377094660.77
229981766.2592155571.19
2311557815.4107142857107426494.31
2413119864.5714285714122547408.97
2514619913.7321428571137058286.14
2616011962.8928571429150489098.01
27172701012.0535714286162589829.47
28183631061.21428571431730210460.57
29192631110.3751815310974.98
30199631159.53571428571880311368.48
31204671208.69642857141925811643.47
32207701257.85714285711951211796.94
33208631307.01785714291955611823.45
34207631356.17857142861940711733.27
35205061405.33928571431910111548.16
36201081454.51865411277.81
37195881503.66071428571808410933.70
38189611552.82142857141740810524.90
39182331601.98214285711663110055.03
40173951651.1428571429157449518.66
41164691700.3035714286147698929.08
42154761749.4642857143137278298.99
43144501798.625126517648.96
44134401847.7857142857115927008.59
45124481896.9464285714105516379.11
46115071946.107142857195615780.47
47106111995.267857142986165209.03
4897592044.428571428677154664.19
4989662093.589285714368724155.02
5082412142.7560983686.97
5175802191.910714285753883257.61
5269972241.071428571447562875.41
5364682290.232142857141782525.86
5459822339.392857142936432202.30
5555352388.553571428631461902.33
5651252437.714285714326871624.72
5747392486.87522521361.62
5843802536.035714285718441114.85
5940482585.19642857141463884.40
6037452634.35714285711111671.49
6134632683.5178571429779471.27
6231982732.6785714286465281.33
6329722781.8392857143190114.97
642831283100.00
652696269600.00
662568256800.00
672445244500.00
682329232900.00
692218221800.00
702112211200.00
712012201200.00
721916191600.00
731825182500.00
741738173800.00
751655165500.00
761576157600.00
771501150100.00
781430143000.00
791362136200.00
801297129700.00
811235123500.00
821176117600.00
831120112000.00
841067106700.00
851016101600.00
8696896800.00
8792292200.00
8887887800.00
8983683600.00
9079679600.00
9175875800.00
9272272200.00
9368868800.00
9465565500.00
9562462400.00
9659459400.00
9756656600.00
9853953900.00
9951351300.00
10048948900.00
10146646600.00
10244344300.00
10342242200.00
10440240200.00
10538338300.00
10636536500.00
10734734700.00
10833133100.00
10931531500.00
11030030000.00
11128628600.00
11227227200.00
11325925900.00
11424724700.00
11523523500.00
11622422400.00
11721321300.00
11820320300.00
11919319300.00
12018418400.00
12117517500.00
12216716700.00
12315915900.00
12415215200.00
12514414400.00
12613713700.00
12713113100.00
12812512500.00
12911911900.00
13011311300.00
13110810800.00
13210310300.00
133989800.00
134939300.00
135898900.00
480270sum cfs
1728971936cubic feet
39692acre-feet
0.13782feet runoff
1.65382inches runoff
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Sample CalculationsIn the present example (hourly time step), the flows are summed and then multiplied by 3600 seconds to determine the volume of runoff in cubic feet. If desired, this value may then be converted to acre-feet by dividing by 43,560 square feet per acre.The depth of direct runoff in feet is found by dividing the total volume of excess precipitation (now in acre-feet) by the watershed area (450 mi2 converted to 288,000 acres). In this example, the volume of excess precipitation or direct runoff for storm #1 was determined to be 39,692 acre-feet. The depth of direct runoff is found to be 0.1378 feet after dividing by the watershed area of 288,000 acres. Finally, the depth of direct runoff in inches is 0.1378 x 12 = 1.65 inches.
Summing Flows
Continuous process represented with discrete time steps
Estimating Excess Precip.
00.10.20.30.40.50.60.70.8012345678910111213141516171819Time (hrs.)Precipitation (inches)
Uniform loss rate of 0.2 inches per hour.1.65 inches of excess precipitation
Phi-Index SummaryThe phi-index for this storm was 0.2 inches per hour.This is a uniform loss rate.If the precipitation stops for a time period, the infiltration will still be 0.2 inches per hour when the precipitation starts again.Regardless of this weakness, this is still very powerful information to have regarding the response of a watershed.
Exponential Decay - Horton This is purely a mathematical function - of the following form:fi = infiltration capacity at time, tfc = final infiltration capacityfo = initial infiltration capacityfofc
Effect of fo or fcHorton
Effect of KHorton
012HortonAssumes that precipitation supply is greater than infiltration rate.
There are now 2 parameters to estimate or calibrate for a watershed!!fo & kHorton
Horton Issues with Continuous SimulationAgain, if it stops raining how does the soil recover in a Horton model?i.e.
Stopped raining for a short period how does the soil recover?
Soil Conservation Service is an empirical method of estimating EXCESS PRECIPITATIONWe can imply that precipitation minus excess precipitation = infiltration/retention :P - Pe = FSCS Curve Number
SCS (NRCS) Runoff Curve NumberThe basic relationships used to develop the curve number runoff prediction technique are described here as background for subsequent discussion. The technique originates with the assumption that the following relationship describes the water balance of a storm event.
where F is the actual retention on the watershed, Q is the actual direct storm runoff, S is the potential maximum retention, and P is the potential maximum runoff
ModificationsPe = P - IaEffective precipitation equals total precipitation minus initial abstraction We will use effective precipitation in place of precipitation
More ModificationsAt this point in the development, SCS redefines S to be the potential maximum retentionSCS also defines Ia in terms of S as : Ia = 0.2SA little substituting gives the familiar SCS rainfall-runoff equation:
Estimating SThe difficult part of applying this method to a watershed is the estimation of the watersheds potential maximum retention, S.SCS developed the concept of the dimensionless curve number, CN, to aid in the estimation of S.CN is related to S as follows :
CN ranges from 1 to 100 (not really!)
Determine CNThe Soil Conservation Service has classified over 8,500 soil series into four hydrologic groups according to their infiltration characteristics, and the proper group is determined for the soil series found. The hydrologic groups have been designated as A, B, C, and D. Group A is composed of soils considered to have a low runoff potential. These soils have a high infiltration rate even when thoroughly wetted. Group B soils have a moderate infiltration rate when thoroughly wetted, while group C soils are those which have slow infiltration rates when thoroughly wetted. Group D soils are those which are considered to have a high potential for runoff, since they have very slow infiltration rates when thoroughly wetted (SCS, 1972).
Determine CN, cont.Once the hydrologic soil group has been determined, the curve number of the site is determined by cross-referencing land use and hydrologic condition to the soil group - SAMPLE
Land use and treatment Hydrologic soil group or Hydrologic practice conditionABCD
FallowStraight row----77869194Row CropsStraight rowPoor72818891Straight rowGood67788589ContouredPoor70798488
Initial Conditions
5-day antecedent rainfall, inches Antecedent moisture
Dormant SeasonGrowing Season
ILess than 0.5Less than 1.4
II0.5 to 1.11.4 to 2.1
IIIOver 1.1Over 2.1
Adjust CNs
CN for AMC II
Corresponding CNs
AMC I
AMC III
100
100
100
95
87
98
90
78
96
85
70
94
80
63
91
75
57
88
70
51
85
65
45
82
60
40
78
55
35
74
50
31
70
Sample ApplicationThe curve number is assumed to be 70. The cumulative runoff (c) is calculated from the cumulative precipitation (b), using equation (4). The potential maximum storage, S, is calculated to be S = (1000/70) - 10 = 4.286 inches. Using 20% as the initial abstraction percentage yields 0.2 x 4.286 = 0.8572 inches and will require that at least 0.8572 inches of precipitation must accrue before runoff may begin.
Computations
Time (hours)
(a)
Cumulative Precipitation (inches)
(b)
Cumulative
Runoff
(inches)
(c)
Incremental Precipitation
(inches)
(d)
Incremental Runoff
(inches)
(e)
Infltration (inches)
(f)
0
0
0
1
0.005
0.995
1
1
0.005
2
0.709
1.291
2
3
0.714
2
1.326
0.674
3
5
2.04
2
1.58
0.42
4
7
3.62
ProblemsThe initial abstraction (Ia) consists of interception, depression storage, and infiltration that occurs prior to runoff. It is not easy to estimate the initial abstraction for a particular storm event. SCS felt that there should be a connection between Ia versus S, and they attempted to develop the relationship by plotting Ia versus S for a large number of events on small experimental watersheds. - Quite a SCATTER - not very successful.
These rainfall-runoff models have varied in complexity but would have difficulty in modeling a continuous event, as they all lack the ability to allow the soil zones to recover when the precipitation stops.. This leads us to model systems that are intended for continuous simulation with updating abilities.
SAC-SMA The Sacramento Soil Moisture Accounting Model (SAC-SMA) is a conceptual model of soil moisture accounting that uses empiricism and lumped coefficients to attempt to mimic the physical constraints of water movement in a natural system.
Sacramento Soil Moisture Accounting Model
Sacramento Model Structure
Hydrograph Decomposition
Sacramento Soil Moisture Components
Initial Soil-moisture ParameterEstimates By Hydrograph Analysis
Parameters for which good estimates generally can be obtained
LZPK - minimum baseflow recession
recession rate Kr =
LZPK = 1.0 - Kr
Things to consider
Ground melt in winter
Riparian vegetation ET in summer
Extended supplemental recessions
Reservoirs - diversions
Variable primary recession
_971268764.unknown
Initial Soil-moisture Parameter Estimates By Hydrograph Analysis (continued) LZSK - Supplemental baseflow recession (always > LZPK) Flow that typically persists anywhere from 15 days to 3 or 4 months
recession rate Kr =
LZSK = 1.0 - Kr
Things to consider
Combination of supplemental and primary is not a straight line on semi-log plot
Better (but not necessary) to replot with primary subtracted
_971268764.unknown
Initial Soil Moisture Parameters Estimates by Hydrograph Analysis (continued)
PCTIM - minimum impervious area
Only storm runoff that occurs when UZTWC not full
Use small rise in summer following a week or more of dry weather
PCTIM = Runoff Volume/(Rain + Melt)
Things to consider
Use a number of events, take average of ones with the smallest PCTIM
Be aware of approximate magnitude of ET-demand
Derive in conjunction with UZTWM
Initial Soil Moisture Estimates by Hydrograph Analysis (continued)
Methods
Extension of recession
Examination of semi-log plot (Search through semi-log plot and try to approximate
the highest level of primary baseflow runoff that occurs. This is Qx.)
LZFPM = Qx/LZPK
Things to consider
This is a minimal estimate because LZFPC probably never equals LZFPM. Fills to 60 to 90+ percent capacity. Lowest percentage usually associated with most permeable soils.
Further recharge normally occurs after Qx.
LZFPM - lower zone free water capacity
Multiyear Statistical Output
MULTIYEAR STATISTICAL SUMMARY
STAT-QME
AREA (SQKM) = 2826.5
WATER YEARS 1965 TO 1972
Monthly
Simulated
mean (cmsd)
Observed
mean (cmsd)
Percent
bias
Monthly bias
(SIM-OBS)
(mm)
Maximum error
(SIM-OBS)
(cmsd)
Percent
average
absolute error
Percent
daily
rms error
Max monthly
volume error
(mm)
Percent avg
abs monthly
vol error
Percent monthly
vol rms vol
RMS error
October
2.058
2.883
-28.61
-0.782
-86.957
44.09
238.04
-4.315
34.72
64.47
November
1.521
1.853
-17.92
-0.305
-30.655
45.6
138.3
-1.564
19.33
34.1
December
4.763
3.906
21.95
0.812
-122.272
69.81
254.32
7.349
49.21
80.93
January
1.501
0.78
92.34
0.683
26.376
118.49
433.66
3.162
99.92
183.88
February
5.416
3.672
47.51
1.493
85.814
75.87
271.45
4.519
48.36
76.41
March
4.021
2.856
40.8
1.104
55.495
51.71
210.83
6.953
42.72
97.84
April
0.485
0.57
-14.95
-0.078
2.349
28.32
59.54
-0.238
18.76
23.87
May
0.411
0.445
-7.64
-0.032
1.431
31.11
44.53
-0.228
21.25
28.06
June
1.184
0.804
47.27
0.349
-25.129
101.07
349.7
2.303
70.03
123.04
July
11.926
10.463
13.98
1.386
88.298
69.64
128.66
7.116
29.62
39.7
August
12.941
18.146
-28.68
-4.932
-59.106
48.29
73.02
-10.723
28.68
33.49
September
5.769
5.371
7.41
0.365
-72.167
82.52
184.48
-6.814
59.86
79.77
YEAR AVG
4.32
4.307
0.29
0.063
-122.272
60.97
184.85
-10.723
37.28
68.78
Daily rms error
(cmsd)
Daily average
abs error (cmsd)
Average abs monthly
vol error (mm)
Monthly volume
rms error (mm)
Correlation
Coefficient
daily flows
Line of best fit
Obs = a + b*sim
a b
7.962
2.626
1.494
2.757
0.7801
.5786 .8632
Flow interval
Number
of cases
Simulated
mean (cmsd)
Observed
mean (cmsd)
Percent bias
Bias
(sim-obs) (mm)
Maximum
error (cmsd)
Percent
avg abs error
Percent
rms error
.00 - 1.05
1769
0.715
0.541
32.23
0.0053
18.388
61.3
169.65
1.05 - 3.27
306
3.989
1.889
111.12
0.0642
48.455
152.89
356.34
3.27 - 10.47
281
7.971
5.953
33.91
0.0617
85.814
85.97
164.95
10.47 - 32.71
182
17.549
18.621
-5.76
-0.0328
88.298
58.77
80.97
32.71 - 104.68
75
39.368
52.609
-25.17
-0.4048
-72.167
42.46
51.8
104.68 - 327.14
4
108.221
182.5
-40.7
-2.2705
-122.272
40.7
44.5
327.14 and above
No Cases
Multiyear Statistical Output (continued)
25 Largest Daily Error Values in CMSD
Month
Day
Year
Observed
Simulated
Error
(sim-obs)
Percent error
Percent total sq deviation
Percent reduction of daily rms if error equal zero
December
16
1967
235
112.728
-122.272
-52.03
9.01
4.61
July
9
1968
31.2
119.498
88.298
283.01
4.7
2.38
October
29
1971
212
125.043
-86.957
-41.02
4.56
2.31
February
13
1968
7.15
92.964
85.814
1200.2
4.44
2.24
September
3
1965
89.4
17.233
-72.167
-80.72
3.14
1.58
August
2
1968
100
40.894
-59.106
-59.11
2.11
1.06
July
10
1968
36.9
94.346
57.446
155.68
1.99
1
March
3
1968
48.5
103.995
55.495
114.42
1.86
0.93
August
18
1966
75.2
23.887
-51.313
-68.24
1.59
0.8
December
31
1965
2.4
50.855
48.455
2018.95
1.42
0.71
July
29
1971
57.9
9.707
-48.193
-83.23
1.4
0.7
September
12
1969
7.5
55.563
48.063
640.83
1.39
0.7
July
28
1971
54.4
6.91
-47.49
-87.3
1.36
0.68
February
11
1968
1.92
49.141
47.221
2459.42
1.34
0.67
February
15
1968
148
101.437
-46.563
-31.46
1.31
0.66
August
4
1967
13
57.378
44.378
341.37
1.19
0.6
July
19
1968
58.6
14.454
-44.146
-75.33
1.17
0.59
September
6
1970
8.65
51.856
43.206
499.49
1.13
0.56
August
24
1967
45.7
2.933
-42.767
-93.58
1.1
0.55
August
12
1966
43.2
85.601
42.401
98.15
1.08
0.54
September
13
1969
10.2
51.597
41.397
405.85
1.03
0.52
February
14
1968
135
93.678
-41.322
-30.61
1.03
0.52
December
15
1967
21.9
62.726
40.826
186.42
1
0.5
July
16
1968
50.7
10.025
-40.675
-80.23
1
0.5
July
22
1971
58.8
19.387
-39.413
-67.03
0.94
0.47
12 Largest Monthly Volume Errors in mm
Month
Year
Observed
Simulated
Error
(sim-obs)
Percent error
Percent total sq deviation
Percent reduction of monthly rms if error equal zero
August
1966
33.065
22.342
-10.723
-32.43
17.6
9.23
August
1971
19.947
12.537
-7.41
-37.15
8.4
4.29
December
1965
6.42
13.769
7.349
114.48
8.27
4.22
July
1969
2.814
9.93
7.116
252.9
7.75
3.95
March
1968
16.044
22.997
6.953
43.34
7.4
3.77
September
1965
10.579
3.764
-6.814
-64.42
7.11
3.62
September
1970
5.504
11.959
6.455
117.29
6.38
3.24
July
1971
10.31
4.882
-5.427
-52.64
4.51
2.28
August
1970
14.02
8.596
-5.424
-38.69
4.5
2.28
July
1967
10.182
15.148
4.966
48.78
3.78
1.91
February
1968
15.468
19.987
4.519
29.21
3.13
1.57
October
1971
13.153
8.838
-4.315
-32.81
2.85
1.44
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ENDRainfall-Runoff Models