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BEGIN. Rainfall-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….

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BEGIN

Rainfall-Runoff Models

excess precipitation or runoff volume 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
The Basic Process….

Necessary for a single basin

Focus on Excess Precipitation

Excess Precip. Model

Excess Precip.

Basin “Routing” UHG Methods

Runoff Hydrograph

Excess Precip.

Stream and/or Reservoir “Routing”

Downstream Hydrograph

Runoff Hydrograph

goal of rainfall runoff models
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 the precipitation to affect the the runoff hydrograph.
  • … losses include interception, evapotranspiration, storage, infiltration, percolation, and finally - runoff.
  • Let’s look at the fate of the precipitation…..
interception
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.

leafy matter also intercepts
Leafy Matter also intercepts...

Very thick ground litter layers can hold as much as 0.5 inches!

interception the point
Interception…the point
  • The 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
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, 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
Percolation.....

Once the water infiltrates into the ground, the downward movement of water through the soil profile may begin.

percolation12
Percolation.....

The percolating water may move as a saturated front - under the influence of gravity…

percolation13
Percolation.....

Or, it may move as unsaturated flow mostly due to capillary forces.

percolation the point
Percolation….the point
  • The 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
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
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
Evapotranspiration....

The terms transpiration and evaporation are often combined in the form :

EVAPOTRANSPIRATION

storage
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!
storage19
Storage....

Water in storage can still be involved in a process.

i.e. :

Water in a puddle may be evaporating.....

slide20

Depression Storage

Channel Storage

Detention Storage

Ground Water Storage

Retention Storage

Vegetation Storage

The hydrologic cycle represented as a series of storage units & processes....

-

RO

=

E

P

T

Surface runoff

Is I > f?

Storm Flow

yes

Base Flow

no

Channel runoff

Is retention full?

yes

Surface runoff

no

storage21

-

RO

RO

=

E

P

P

T

Depression Storage

Surface runoff

Channel Storage

Is I > f?

Is I > f?

Storm Flow

yes

Base Flow

no

Detention Storage

Channel runoff

Is retention full?

yes

Ground Water Storage

Surface runoff

no

Retention Storage

Vegetation Storage

Storage....

The thought process.......

storage22
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
  • The units are very important…
  • Storage 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 storage
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
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 abstractions
Initial Abstractions

Initial 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?

slide27

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
Some Rainfall-Runoff Models
  • Phi-Index
  • Horton Equation
  • SCS Curve Number
  • SAC-SMA
constant infiltration rate
Constant Infiltration Rate

A 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.

separation of baseflow
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.
sample calculations
Sample Calculations
  • In 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
Summing Flows

Continuous process represented with discrete time steps

estimating excess precip
Estimating Excess Precip.

0.8

1.65 inches of excess precipitation

0.7

0.6

0.5

Uniform loss rate of

0.2 inches per hour.

Precipitation (inches)

0.4

0.3

0.2

0.1

0

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

Time (hrs.)

phi index summary
Phi-Index Summary
  • The 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
Exponential Decay - Horton

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

fo

fi = infiltration capacity at time, t

fc = final infiltration capacity

fo = initial infiltration capacity

fc

horton
Horton

Effect of fo or fc

horton43
Horton

Effect of K

horton44
Horton

Assumes that precipitation supply is greater than infiltration rate.

2

1

0

horton45
Horton

There are now 2 parameters to estimate or calibrate for a watershed!!

fo & k

horton issues with continuous simulation
Horton – Issues with Continuous Simulation
  • Again, 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?

scs curve number
SCS Curve Number

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 nrcs runoff curve number
SCS (NRCS) Runoff Curve Number
  • The 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
modifications
Modifications

Pe = P - Ia

Effective precipitation equals total precipitation minus initial abstraction…

We will use effective precipitation in place of precipitation…

more modifications
More Modifications
  • At this point in the development, SCS redefines S to be the potential maximum retention
  • SCS also defines Ia in terms of S as : Ia = 0.2S
  • A little substituting gives the familiar SCS rainfall-runoff equation:
estimating s
Estimating “S”
  • The difficult part of applying this method to a watershed is the estimation of the watershed’s 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 cn
Determine CN
  • The 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
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 condition A B C D

Fallow

Straight 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
Initial Conditions

5-day antecedent rainfall, inches

Antecedent 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

sample application
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.

problems
Problems
  • The 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.
slide59

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
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 model structure

E T Demand

Precipitation Input

Px

Impervious

Area

E T

Direct Runoff

PCTIM

ADIMP

Pervious Area

Impervious Area

Upper Zone

Surface Runoff

EXCESS

Tension Water

UZTW Free Water

UZFW

E T

UZK

Interflow

E T

Percolation

Zperc. Rexp

Total Channel Inflow

Distribution Function

E T

RIVA

Streamflow

1-PFREE

PFREE

Lower Zone

Free Water

Tension Water P S

LZTWLZFP LZFS

RSERV

Supplemental

Base flow

LZSK

E T

LZPK

Total Baseflow

Primary

Baseflow

Side

Subsurface Discharge

Sacramento Model Structure
hydrograph decomposition

Impervious and Direct Runoff

Surface Runoff

Interflow

Discharge

Supplemental Baseflow

Primary Baseflow

Time

Hydrograph Decomposition
sacramento soil moisture components

SAC-SMA Model

Precipitation

Impervious and Direct Runoff

Pervious

Impervious

Surface Runoff

Evaporation

Upper

Zone

Interflow

Supplemental Baseflow

Lower

Zone

Primary Baseflow

Sacramento Soil Moisture Components
initial soil moisture parameter estimates by hydrograph analysis continued
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

slide96

END

Rainfall-Runoff Models