5 Rainfall Runoff

7/29/2019 5 Rainfall Runoff

http://slidepdf.com/reader/full/5-rainfall-runoff 1/96

BEGINRainfall-Runoff Models



Excess Precipitation or

Runoff Volume Models

May be:

– Physically Based

– Empirical

– Descriptive– Conceptual

– Generally Lumped

– Etc……

– May 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 Methods

Necessary for a

single basin

Focus on

Excess

Precipitation



Goal of Rainfall-Runoff

Models The fate of the falling precipitation

is: …modeled in order to account for

the destiny of the precipitation that

falls and the potential of theprecipitation to affect the therunoff hydrograph.

… losses include interception,evapotranspiration, storage,

infiltration, percolation, and finally- runoff. Let’s 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 asrunoff 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!



Interception…the point

The point of the interception is that theprecipitation is temporarily stored beforethe next process begins.

The intercepted/stored precipitation maynot reach the ground to contribute torunoff.

Interception may be referred to as anabstraction 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 arate 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 point

The vertical percolation of the water intovarious 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 soil

- The 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 T E = -

Channel

Storage

Depression

Storage

Ground Water

Storage

Detention

Storage

Retention

Storage

Vegetation

Storage

Is I > f? yes

no

Surface

runoff

Channel

runoff Is

retention

full?

yes

no

Surface

runoff

B a s e F l o w

S t o r m F

l o

w



Is I > f? Is I > f?

Storage....The thought process.......

Channel

Storage

Depression

Storage

Ground Water

Storage

Detention

Storage

Retention

Storage

Vegetation

Storage

RO P T E - =

yes

Surface

runoff

Channel

runoff

no

yes

no

B a s e F l o w

Is

retention

full?

Surface

runoff

S t o r m F

l o

w

P RO



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 conditionshave?

– These are the issues that a continuousrainfall-runoff model must consider……



The Units

The units are very important…

Storage is a volume (L3) and flow isa volume per time (L3 /T) ….

We often think of these volume unitsin terms of length only!

This implies a uniform depth or valuethroughout the watershed….



Examples of Length Units for

Storage The watershed can infiltrate 75mm of

water – a length…

The lower zone of the soil can hold

60mm... The initial abstraction for the watershed is

10mm

The reservoir can hold 2.5 inches of

runoff… These 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 assumesthat the soil can constantly infiltrate thesame amount of precipitation throughoutthe storm event. The obviousweaknesses are the neglecting of spatialvariability, temporal variability, andrecovery potential.

Other methods include exponentialdecays (the infiltration rate decaysexponentially), empirical methods, andphysically based methods.

… There are also combinations of thesemethods.



Initial Abstractions

Initial Abstraction - It is generally

assumed that the initial abstractions must

be satisfied before any direct storm

runoff may begin. The initial abstractionis 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 Models

Phi-Index

Horton Equation

SCS CurveNumber

SAC-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 theinfiltration rate.

The obvious weakness is the inability to model changes ininfiltration rate.

The phi-index may also be estimated from individual stormevents by looking at the runoff hydrograph.



Hydrograph Breakdown

0.0000

100.0000

200.0000

300.0000

400.0000

500.0000

600.0000

700.0000

0 . 0 0

0 0

0 . 1 6

0 0

0 . 3 2

0 0

0 . 4 8

0 0

0 . 6 4

0 0

0 . 8 0

0 0

0 . 9 6

0 0

1 . 1 2

0 0

1 . 2 8

0 0

1 . 4 4

0 0

1 . 6 0

0 0

1 . 7 6

0 0

1 . 9 2

0 0

2 . 0 8

0 0

2 . 2 4

0 0

2 . 4 0

0 0

2 . 5 6

0 0

2 . 7 2

0 0

2 . 8 8

0 0

3 . 0 4

0 0

3 . 2 0

0 0

3 . 3 6

0 0

3 . 5 2

0 0

3 . 6 8

0 0

Baseflow

Surface

Response



Hydrograph Breakdown

0.0000

100.0000

200.0000

300.0000

400.0000

500.0000

600.0000

700.0000

0.0000 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000

Total

Hydrograph

Surface

Response

Baseflow



Derive phi-index sample watershed = 450 mi2

0

5000

10000

15000

20000

25000

0 8 1 6 2 4 3 2 4 0 4 8 5 6 6 4 7 2 8 0 8 8 9 6 1 0 4

1 1 2

1 2 0

1 2 8

Time (hrs.)

F l o w

( c f s )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

P r e c i p i t a t i o n ( i n c h e s )



Separation of Baseflow

•... generally accepted that the inflection point on therecession limb of a hydrograph is the result of achange in the controlling physical processes of theexcess precipitation flowing to the basin outlet.

•… In this example, baseflow is considered to be a

straight line connecting that point at which thehydrograph begins to rise rapidly and the inflectionpoint on the recession side of the hydrograph.

•… the inflection point may be found by plotting thehydrograph in semi-log fashion with flow being plotted

on the log scale and noting the time at which therecession side fits a straight line.



Semi-log Plot

1

10

100

1000

10000

100000

2 9 3 4 3 9 4 4 4 9 5 4 5 9 6 4 6 9 7 4 7 9 8 4 8 9 9 4 9 9 1 0 4

1 0 9

1 1 4

1 1 9

1 2 4

1 2 9

1 3 4

Time (hrs.)

F l o w

( c f s )

Recession side of hydrograph

becomes linear at approximately hour

64.



Hydrograph & Baseflow

0

5000

10000

15000

20000

25000

0 7 1 4

2 1

2 8

3 5

4 2

4 9

5 6

6 3

7 0

7 7

8 4

9 1

9 8

1 0 5

1 1 2

1 1 9

1 2 6

1 3 3

Time (hrs.)

F l o w ( c

f s )



Separate Baseflow

0

5000

10000

15000

20000

25000

0 7 1 4 2 1 2 8 3 5 4 2 4 9 5 6 6 3 7 0 7 7 8 4 9 1 9 8 1 0 5

1 1 2

1 1 9

1 2 6

1 3 3

Time (hrs.)

F l o w ( c

f s )



Sample Calculations

In the present example (hourly time step), the flows aresummed and then multiplied by 3600 seconds todetermine the volume of runoff in cubic feet. If desired,this value may then be converted to acre-feet bydividing by 43,560 square feet per acre.

The depth of direct runoff in feet is found by dividing thetotal volume of excess precipitation (now in acre-feet)by the watershed area (450 mi2 converted to 288,000acres).

In this example, the volume of excess precipitation ordirect runoff for storm #1 was determined to be 39,692acre-feet.

The depth of direct runoff is found to be 0.1378 feetafter dividing by the watershed area of 288,000 acres.

Finally, the depth of direct runoff in inches is 0.1378 x12 = 1.65 inches.



Summing Flows

Continuous process

represented with

discrete time steps



Estimating Excess Precip.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Time (hrs.)

P r e c i p i t a t i o n

( i n c h e s )

Uniform loss rate of

0.2 inches per hour.

1.65 inches of

excess

precipitation



Phi-Index Summary

The phi-index for this storm was 0.2inches per hour.

This is a uniform loss rate.

If the precipitation stops for a time period,the infiltration will still be 0.2 inches perhour when the precipitation starts again.

Regardless of this weakness, this is still

very powerful information to haveregarding the response of a watershed.



Exponential Decay - Horton This is purely a mathematical function - of the following form:

kt)ec

f o

(f c

f i

f

f i = infiltration capacity at time, t

f c

= final infiltration capacity

f o = initial infiltration capacity

f o

f c



Effect of f o or f c

Horton



Effect of K

Horton



0

1

2

Horton

Assumes that precipitation supply is

greater than infiltration rate.



There are now 2 parameters to

estimate or calibrate for a watershed!!

f o & k

Horton

H t I ith



Horton – Issues with

Continuous Simulation

Again, if it stops raining how doesthe 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

PRECIPITATION

We can imply that precipitation minus excess

precipitation = infiltration/retention :

P - Pe = F

SCS Curve Number

SCS (NRCS)



SCS (NRCS)

Runoff Curve Number The basic relationships used to develop the curve number

runoff prediction technique are described here asbackground for subsequent discussion. The techniqueoriginates with the assumption that the followingrelationship describes the water balance of a storm event.

where F is the actual retention on the

watershed, Q is the actual direct stormrunoff, S is the potential maximum retention,and P is the potential maximum runoff

P

Q

S

F



Modifications

Pe = P - Ia

Effective precipitation equals total

precipitation minus initial

abstraction…

We will use effective precipitation in

place of precipitation…



More Modifications

At this point in the development, SCSredefines S to be the potential maximumretention

SCS also defines Ia in terms of S as : Ia =0.2S

A little substituting gives the familiar SCSrainfall-runoff equation:

0.8S)+(P

)0.2S -(P =Q

2



Estimating “S”

The difficult part of applying this method to awatershed is the estimation of the watershed’spotential maximum retention, S.

SCS developed the concept of the dimensionlesscurve number, CN, to aid in the estimation of S.

CN is related to S as follows :

10-CN

1000 =S

CN ranges from 1 to 100 (not really!)



Determine CN

The Soil Conservation Service has classified over 8,500 soilseries into four hydrologic groups according to theirinfiltration characteristics, and the proper group isdetermined for the soil series found.

The hydrologic groups have been designated as A, B, C, andD.

Group A is composed of soils considered to have a lowrunoff potential. These soils have a high infiltration rateeven when thoroughly wetted.

Group B soils have a moderate infiltration rate whenthoroughly 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 slowinfiltration 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 thesoil group - SAMPLE

Land use and treatment Hydrologic soil group

or Hydrologic

practice condition A B C D

FallowStraight row ---- 77 86 91 94

Row Crops

Straight row Poor 72 81 88 91

Straight row Good 67 78 85 89

Contoured Poor 70 79 84 88



Initial Conditions

5-day antecedent rainfall, inchesAntecedent moisture

Dormant Season Growing Season

I Less than 0.5 Less than 1.4

II 0.5 to 1.1 1.4 to 2.1

III Over 1.1 Over 2.1



Adjust CN’s

CN for AMC II Corresponding CN’s

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 Application

The 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

Precipitatio

n

(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



Problems

The initial abstraction (Ia) consists of interception,depression storage, and infiltration that occurs priorto runoff.

It is not easy to estimate the initial abstraction for aparticular storm event.

SCS felt that there should be a connection between Ia versus S, and they attempted to develop therelationship by plotting Ia versus S for a largenumber 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 MoistureAccounting Model (SAC-SMA) is aconceptual model of soil moistureaccounting that uses empiricism andlumped coefficients to attempt tomimic the physical constraints of watermovement in a natural system.

Sacramento Soil Moisture




Accounting Model



Sacramento Model Structure

E T Demand

Impervious

Area

E T

E T

E T

E T

Precipitation Input

Px

Pervious Area

E T

Impervious Area

Tension Water

UZTW Free Water

UZFW

Percolation

Zperc. Rexp

1-PFREE PFREE

Free Water

Tension Water P S

LZTW LZFP LZFS

RSERV

Primary

Baseflow

Direct Runoff

Surface

Runoff

Interflow

Supplemental

Base flow

Side Subsurface

Discharge

LZSK

LZPK

Upper Zone

Lower Zone

EXCESS

UZK

RIVA

PCTIM

ADIMP

Total

Channel

Inflow

Distribution

Function Streamflow

Total

Baseflow



Hydrograph Decomposition

Supplemental Baseflow

Primary Baseflow

Interflow

Surface Runoff

Impervious and

Direct Runoff

D i s c h a r g e

Time





Components

Impervious and Direct Runoff

Surface Runoff

Interflow

Supplemental Baseflow

Primary Baseflow

SAC-SMA Model

Evaporation

Precipitation

Upper Zone

Lower

Zone

Pervious Impervious

Initial Soil moisture Parameter



Initial Soil-moisture Parameter

Estimates By Hydrograph AnalysisParameters for which good estimates generally can be obtained

LZPK - minimum baseflow recession

recession rate Kr =t/1

1

2

Q

Q

LZPK = 1.0 - Kr

Things to consider

Ground melt in winter

Riparian vegetation ET in summer

Extended supplemental recessions

Reservoirs - diversions

Variable primary recession

-E ti t B H d h A l i



Estimates By Hydrograph Analysis(continued)

LZSK - Supplemental baseflow recession (always >LZPK)

Flow that typically persists anywhere from 15 days to 3 or4 months

recession rate Kr =t/1

1

2

Q

Q

LZSK = 1.0 - Kr

Things to consider

Combination of supplemental and primary is not a straight line on semi-logplot

Better (but not necessary) to replot with primary subtracted

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



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 (SQ KM) = 2826.5 WATER YEARS 1965 TO 1972

Monthly Simulatedmean (cmsd)

Observedmean (cmsd)

Percentbias

Monthly bias(SIM-OBS)

(mm)

Maximum error (SIM-OBS)(cmsd)

Percentaverageabsolute error

Percentdailyrms error

Max monthlyvolume error (mm)

Percent avgabs monthlyvol error

Percent monthlyvol 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 23.87May 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 averageabs error (cmsd)

Average abs monthlyvol error (mm)

Monthly volumerms error (mm)

CorrelationCoefficientdaily flows

Line of best fitObs = a + b*sim

a b

7.962 2.626 1.494 2.757 0.7801 .5786 .8632

Flow interval

Number of cases

Simulatedmean (cmsd)

Observedmean (cmsd)

Percent bias Bias(sim-obs) (mm)

Maximumerror (cmsd)

Percentavg abs error

Percentrms 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



Multiyear Statistical Output(continued)

25 Largest Daily Error Values in CMSD

Month Day Year Observed Simulated Error (sim-obs) Percent error Percent totalsq deviation Percentreduction 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 2 018.95 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 0.67February 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





















































END

Rainfall-Runoff Models

Documents

5 Rainfall Runoff