Hidrología PAE 2020
THEME 5: Surface flow
Hydrograph
Graphical representation of the variation of discharges with
time, at a given point in the river (runoff gauge, punto de
aforos)
Annual Hydrograph
Storm Hydrograph
Hidrograma de tormenta
crecida
Recesión
Trinity River, California, USA
Separation of Baseflow from the Total Runoff (=escorrentía)
N refers to the Linsley
method (next slide)
Chow, Applied Hydrology,p.132-135
Separation of Baseflow from the Total Runoff
Method of Linsley (1949)
N…number of days after peak
A…area in km2
Q 3.4d after peakflow= ca. 14m3/s
Example 1200 km2
N= 0.826 x 12000.2 =3.4d
Definitions
-Discharge (=Caudal) Q (L3/T, typically m3/s)
-Runoff Depth (=Índice o Lámina de escorrentía) R= Q/A (typically
mm/a) or Specific Runoff (=Módulo específico de escorrentía) in L/s.km2
-Runoff coefficient (Coef. De Escorrentia)
CE = Runoff/Precipitation R/P(dimensionsless)
Runoff regime in rivers
(régimen de escorrentía)
Regime Pluvial (from rain)
Determined by climate
1. Pluvial
2. Nival (Glacial)
3. Mixed
Mixed regime Pluvial and Nival (rain and snow)
Regime Nival and Glacial (snowmelt and
glacier melt) (=deshielo)
Trinity River, California, USA
Rotmoos River, Switzerland
Presentation of discharge data in Ecuador
1. Hidrograma, Caudal
Rating curve (=Curva de Descarga, Curva de
Gastos)
Discharge in fuction of the gauge height (=cota de nivel del río) at a runoff gauge
(=punto de aforo, punto de salida)
Flow Duration Curve
=Curva de Caudales Clasificados
365 daily discharges ranked from highest to lowest
Shows how many days a discharge was equaled or exceeded during a year
Flow Duration Curve
Example from Spain
Spanish book 5.2, p.1
The Flow Duration Curve can be also constructed from daily discharges of a
series of years
The Flow Duration Curve can be also constructed from daily discharges of a
series of years. Then the discharge axis is referred to a discharge that is
equaled or exceeded in a certain % of time (not in a certain number of days)
Q1 Extremely high discharge, Q1- Q10 High discharge
Q70- C100 Low discharge (hydroenergy)
Ecological Flow, Low Flow
Ecological flow refers to the water considered sufficient for protecting the
structure and function of a water ecosystem and its dependent species.
Sometimes used the term Environmental flow.
Has also use in hydropower, water transport, …….under the
general term Low Flow
Methods
Statistical, for example the lowest daily flow not reached
with return period of 10 years (USA). For longer Tr it may
become 0.
Flow Duration curves, for example Q330d (equaled or
exceeded 330
days in a year)
Percentages (%) of Annual discharges, for example the
Tenant method (1976)
- QE(10%): minimal flow for survival (sobrevivir) of most
aquatic life (vida acuática).
- QE(30%): flow recommended to provide adequate
conditions for the aquatic life
- QE(60%): flow recommended to provide excellent
conditions for the aquatic life
Lowest daily flow each year
Low Flow – continuation from the previous slide
Probabilidad
Statistical, for example the lowest daily flow not reached
with return period of 10 years (USA). For longer Tr it may
become 0.
Determination of discharge
(usually maximal discharge, with a given return period)
1. Statistical methods (when historical data are available) – see
the methods from previous weeks of classes:))
2. Empirical equations
a)
Regional, using the area of the basin and regional empirical coefficients
There are many formulas in the world, but none is universal!!
-Creager formula, regional coefficients exist for USA, Mexico, Peru,…..
-Formula of Sandoval+ Aguilera, regional coefficients developed for Ecuador
b) Universal, using
the area of the basin, precipitation and a type of runoff
coefficient
-Rational Method
-Method of Soil Conservation Service (curve numbers and
triangular unit hydrograph)
3. Discharge simulation software, for example HEC-RAS
(Hydrological Engineering Center – River Analysis System)
Ecological flow for Ecuador
Mean annual
Precip. (mm)
km2
Empirical formula of Creager (1945)
Does NOT use precipitation data!!
m3/s
return period (years)
m, n, C1, C2……regional coefficients
in Ecuador not yet determined
Empirical formula of Creager (1945)
Regional coefficients for Perú
Source---Capítulo de Ing. Civil,
Consejo Departamental Cajamarca,
2011
Empirical formula of Sandoval and Aguilera for Ecuador (2014)
Download via Google!!!!!
Mean annual
precipitation (mm)
Area (km2)
Return period
Concentration time (Tiempo de concentración)
Isochrones (Líneas isocronas) –
determine zones of equal travel
(travesía) time to the runoff gauge
(=punto de aforo)
1h each isochrone
Tc = 8 hours
Concentration time (=Tiempo de concentración) Tc
It is defined as the time needed for water to
flow from the most remote point in a
Spanish book, Unit 5.1, p. 3 to 4
watershed to the watershed outlet. It is a
function of the topography, geology, and land
use within the watershed. Usually some
minutes or hours
Rational Method (Kuichling, 1889)
Based on a simple, but not realistic concept
From hours to seconds
Spanish book, Unit 5.1, p. 3 to 4
English book p. 496 to 502
In the nature, the runoff also depends on the runoff coefficient
If A is in hectars, then
Rational Method – Rainfall Intensity input
The Rational method provides the maximal design flow
(=caudal máximo de diseňo). The usual input is the design rainfall (from the
curves IDF) for various return periods (usually 10, 25, 50,100 years)
Design rainfall (or flow) = theoretical rainfall intensity for a given duration
(or theoretical flow value), associated with a return period
Rational Method – Runoff coefficient (=Coef. de escorrentía)
=R/P, portion of runoff depth on the precipitation depth
Difficult to estimate:
a)
b)
The coefficient substracts infiltrated water, but this water also participates in runoff !!
The coefficient is not constant for a land use type and increases with soil humidity
(this is expressed by increasing coef. with increasing Tr)
Rational Method –
Conditions of use
1. Rainfall instensity I is constant in time, rainfall is uniformly distributed
over the area A
2. Smaller watersheds, approx. max. 20 to 100 km2 (but various books
permit different areas…..)
3. Rainfall duration≥ Concentration time!!
If the rainfall duration is shorter than the concetration time, the maximal
discharge cannot be generated
Concentration Time - Equations
There are many, none of them is universal!!
Problem: most of them developed in small watersheds. Big differences among (=entre)
methods in larger watersheds.
Chow, Applied Hydrology, p.500
Kirpich: frequently
used
Rural
Mountains
Metric units
In Spain
Also larger watersheds
Rational Method – Exercise in class
Determine the maximal discharge in a watershed for Tr 25 years and
duration of rainfall equal to concentration time
Area = 125 Ha
Length of the principal watercourse (= cauce principal) 1350m
Slope (pendiente) of the watercourse = 0.11
Landuse in the following table
years
Curva IDF regional
min
Tc (Kirpich)
How to get C and I ?
Determination of C
Rainfall Intensity from the regional IDF curve for Duration = Tc (Kirpich) and Tr= 25 years
Tc (Kirpich)
=11.6 min
I=
=160.2 mm/h
Method of Soil Conservation Service (SCS) 1964/1972
Concept of Abstractions (=Abstracciones)
Abstraction – does not participate in
direct runoff
Ponding time
Tiempo de
encharcamiento
Excess rainfall, net rainfall (=lluvia neta)
this is the direct runoff
=Begin of the surface
runoff
Chow: Applied Hydrology, 146-155
Spanish book 5.3
Method of Soil Conservation Service (SCS) 1964/1972
Concept of Abstractions (=Abstracciones)
Total Rainfall
Rainfall excess, Net rainfall (=Lluvia neta)
=Runoff
Abstracción = Fa + Ia = P- Pe
Ia= initial abstraction
Abstraccion inicial
S = abstraction total potential, all water below the
infiltration line (from tables). Has similar function to
the Runoff Coefficient (Coef. de escorrentía) in the
Rational method
All units in mm
Method of Soil Conservation Service (SCS) 1964/1972
Tables to characterize the Potential Abstraction
The Potential Abstraction is described in 4 soil groups, (A, B,C,D) characterized
by type and „runoff potential“ and………….more on the next slide
Spanish
English
A….deep soils, low direct runoff (low
runoff coefficient
.
.
D….shallow soils, impervious, high
direct runoff , high runoff coefficient
Method of Soil Conservation Service (SCS) 1964/1972
Tables to characterize the Potential Abstraction
….the Potential Abstraction is also characterized by LAND USE (=uso del suelo)
The abstraction has a value CN (Curve Number„Curvas Numeradas“, adimensional)
Spanish
English
Runoff =
Net
Rainfall
mm
C
C
cm
Method of Soil Conservation Service (SCS) 1964/1972
R
u
n
o
ff
Called Curve Number Method, because of the numbered curves in the Nomographs
Originally developed in INCHES (pulgadas)
Chow, p.168
R
u
n
o
ff
Rainfall
Rainfall
Relation between
the CN and Total
Abstraction S
Runoff = Net
Rainfall
mm
Method of Soil Conservation Service (SCS) 1964/1972
…sometimes we do not need the total abstraction S, but the Initial Abstraction Ia
to determine how much rainfall is abstracted before the begin of the direct runoff
We use this relation…
….and call Po = Ia Umbral de escorrentía
Abstracción Inicial
=Water abstracted (infiltrated) prior to the
begin of the direct runoff Pe
Po is alternative to the CN number and is used in Spain and Europe
(metric units). Available in tables similar to CN tables (next slide)
CN has no unit. Po has unit in mm.!!
Method of Soil Conservation Service (SCS) 1964/1972
Direct Runoff
Rainfall
Class exercise – Determine the abstraction
and the direct runoff using the formula SCS
Data to determine Po – soil type C, very dense forest (=bosque muy espeso)
1. We determine the Po (table on previous slide)
=43mm
t (hour) P total (mm) S P total (mm) S excess (mm) excess (mm)
1
11
2
8
3
40
4
34
5
13
6
27
7
3
8
6
Abstrac
tion
(mm)
2. We determine the accumulated Ptotal and accumulated Excess (=Pnet, =direct runoff)
3. We determine the hourly excess (= runoff) and hourly abstraction
1
11
11
0.0
0.0
2
8
19
0.0
0.0
8.0
3
40
59
1.1
1.1
38.9
4
34
93
9.4
8.3
25.7
5
13
106
14.3
4.8
8.2
6
27
133
26.6
12.3
14.7
7
3
136
28.1
1.5
1.5
8
6
142
31.2
3.1
2.9
11.0
Corrections of the parameter CN for the antecendent
moisture AMC (=humedad antecendente)
AMC = „Antecendent
Moisture Conditions“
(AMC II) Condiciones normales
(AMC I) Condiciones secas
(AMC III) Condiciones húmedas
Corrections of the parameter CN for the antecendent
moisture AMC (=humedad antecendente)
We do not need to calculate the corrected number CN….
…we can just use the multiplication coefficients
In wet conditions the CN number is always higher than in normal conditions –
the soil infiltration capacity is full and the direct runoff therefore increases
Corrections of the parameter Po (initial abstraction) for
the antecendent moisture AMC (=humedad antecendente)
In wet conditions the Po is always lower than in
normal conditions – the soil infiltration
capacity is full and the direct runoff therefore
increases
Exercise in class:
Area 22 km2
Length (longitud)= 14 km, slope(pendiente) = 0.004
Antecendent Wetness (Humedad)= more than 6 cm
Forest (bosque) with good cover =80%, cultivated land with
conservation =10%, parking lots and roofs
(parqueaderos,techos) = 10% ; geology = sand and loam
(arenas y limos), shallow soils (suelos poco profundos) of
group B
Total rainfall= 10 cm
Determine the direct runoff (=rainfall excess, net rainfall,
Pneta), using the SCS method
%
CN1 = 55
80
CN2 = 71
10
CN3 =98
10
CN average=(4400+710+980)/100 = 61
Correction of the CN number
CN corr = 61 x 1.3 = 79
Proof (comproba) !!
C
C
50
100
=Q
(cm)
Correction of the CN number using the Po (Umbral de escorrentía)
=5080/79 – 50.8 mm = 13.5 mm
Runoff coefficient?
=0.5
Attention! Is not
equal to CN or
Po!!
Proof!!
The method SCS delivers Direct Runoff Depth (Lámina de lluvia neta) as a
response to a precipitation event.
=Duration
Peak
But what is the
flow in m3/s?
=Concentration time
=Time of Rise
= Base time
Triangular Unit hydrograph
Victor Mockus, SCS, 1975
Converts the rainfall excess
(Precipitación neta) = Direct runoff
(in mm) to a simple triangular
hydrograph (m3/s), using the
watershed geometry and the
concentration time
Spanish book 5.1, p.5
Chow, p. 228
This is the direct rainfall depth, as determined by the CN or Po nomogram
Triangular Unit hydrograph
Exercise
Using the method of the Mockus triangular hydrograph, calculate
the peakflow in the watershed from the previous exercise for a
rainfall of 1 mm with duration equal to concentration time.
Area 22 km2
Length (longitud)= 14 km, slope(pendiente) = 0.004
=4.2h
Qp = 1 m3/s/mm. This is also called Unit Hydrograph – a watershed
discharge response for UNIT of rainfall input.
What is the peakflow for the rainfall excess (=runoff) of 50mm
calculated in the previous exercise?
50 m3/s
Triangular Unit hydrograph
Dimensionsless form „hidrograma suavizado“
Spanish book, 5.1, p.6, Chow p.229
Why „Unit“ Hydrograph? (Hidrograma Unitario)
(Sherman, 1932)
Unit Hydrograph = The direct runoff response to a UNIT
rainfall excess input (typically 1mm) of a UNIT duration
(typically 1hour).
Unit input=Unit response
Spanish book 5.1, p.7 to 12
Multiple input=Multiple response
Discharge Measurements in Watersheds
Spanish book Part 5.4
Chow: Applied Hydrology p. 33 to 36 and 184 to 191
1.
2.
3.
4.
5.
Direct (volume, velocity)
a)
Volume (aforo directo)
b)
Velocity - Float (Flotador), Current meter
(Molinete)
c)
Instrument Doppler
Indirect (level of river) - Rating curve
Tracers
Hydraulic methods - weirs (vertederos)
Empirical equations (of Manning)
A.Volumetic method
B. Measurement by velocity
Q
Variation of velocities in a river
Vmax = approx. in 20% of the
depth
=
A
x
v
B1Velocity measurement by float
(flotador)
- Make repetitions
- Select a symetric and direct reach (=tramo) of a river
area
Q = v x area
vfloat = L/ (t1-t0)
vaverage = vfloat x 0.75, because of
inhomogeneous velocities
B2 Velocity measurement by current meter
=molinete
2 options
Number of turns (recorded digitally)
flow velocity
Velocity measurement by current meter
Qtot = sum Qi (=Ai x Vi) in all sectors Ai (=di x ∆wi)
Sector Ai
Advantages (=ventajas) of the current meter in comparison to the float
= velocities in various depths can be measured
= velocities in various sectors can be measured
C. Acoustic Doppler Current Profiler
(=Perfilador de corriente acústico Doppler)
Measures velocity and flow direction in
various depths (= change
of the emitted acoustic signal)
Rapid development of this method for
big and small rivers (approx. 0.8 to12m
of river depth)
USGS
2 Measurements by water levels
Limnimetric sonde (Head gauge, Stage ruler, Escala limnimétrica)
Continuous Water Stage Recording
Float or Pressure Recorder
2 Measurements by water levels
Ultrasonic sensor (Sensor ultrasónico), now very common
Rating curve (=Curva de Descarga, Curva de
Gastos)
Discharge in fuction of the gauge height (=cota de nivel del río) at a runoff gauge
(=punto de aforo, punto de salida)
- Every stream gauge station (=punto de aforo) has its own rating curve
- Needs to be regularly calibrated
3.
Tracers (=trazadores) (salt, colors,…)
A.Vertido constante
Read in the Spanish book, Part 5.4, p. 2-3
Vertido constante - ejemplo
3.
Tracers (=trazadores) (salt, colors,…)
B. Peso vertido
3.
Tracers (=trazadores) (salt, colors,…)
Ejemplo: Aforo con sal, peso vertido de 1000mg de sal
Quebrada Antón, Panamá
Segundos
=1000g / (5s x 23225mg/L) =
9.1 L/s
Medidor continuo de sales disueltos
Concentracion mg/l
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
0
0
0
6
76
198
1210
2480
1940
1828
1374
1343
1176
1052
958
839
380
385
390
395
400
5
5
4
3
3
23225
4. Measurement by Weirs (=vertederos)
Hydraulic constructions to measure discharge
-vertical narrow wall (=pared delgada) with a horizontal crest (=cresta)
-perpendicular to the flow
A.
Trapezoidal Weir (Vertedero trapecial), called Cipoletti Weir
Example: H=15 cm, B= 60cm
B. V-notch weir (=Vertedero triangular)
5. Empirical calculations
Equation of Manning (1889)
v…flow velocity
R…hydraulic radius = Area/Wetted perimeter
S…slope of the canal stretch (=tramo)
n…Manning coefficient of rugosity (=rugosidad), for
rivers approx. 0.03
Chow: Applied Hydrology, p.35
Equation of Manning (1889)
Wetted Perimeter
Valid for uniform turbulent flow
Equation of Manning (1889)
For V in m/s and R in m
For V in feet/s and R in feet
Chow: Applied Hydrology, p.35
Flow Routing (=Tránsito de caudales)
Determine the hydrograph C from the
hydrograph A
Chow: Applied Hydrology p 256 to 260
Spanish book Part 5.5
Flow Routing
delay (retardo)
attenuation
Flow Routing -Muskingum Method (USA, 1938)
= concept of two storages (almacenamientos)
Prism
Wedge
Two storages
Muskingum Method
X = b/K
X….adimensional constant of importance of the wedge and prism storage
X = 0 if there is no wedge. Xmax = 0.5. X in natural rivers approx 0.1-0.3
Storage at precedent time step
Storage at actual time step
Muskingum Method – Input and Output
Flow
Input flow Output flow Storage
Output flow at actual time
Problem: how to get K and X
Modification of Cunge (1969)
To get K and X of the Muskingum method from the
hydraulic parameters
Length
Celerity
Slope
Discharge
Width
Once we have K and X, we can calculate Co, C1 and C2 of Muskingum……
….and calculate the flow delay and attenuation from the Muskingum formula
I
(m3/s)
O