The Concept of Runoff Elements As a Basis of Scale-Free Approach To Runoff Formation Modelling the...

The Concept of Runoff Elements The Concept of Runoff Elements As a Basis of Scale-Free Approach As a Basis of Scale-Free Approach

To Runoff Formation ModellingTo Runoff Formation Modelling

the experience of “Hydrograph” model the experience of “Hydrograph” model development and implementationdevelopment and implementation

Yu.B. Vinogradov, O. SemenovaYu.B. Vinogradov, O. Semenova

State Hydrological InstituteState Hydrological Institute

St. Petersburg, RussiaSt. Petersburg, Russia

To describe the water dynamics in river basin

- slope and channel transformation

Scientific objectiveScientific objective

Modelling objectiveModelling objective

To estimate the water income to channel system and

finally to the basin outlet

Main tasksMain tasks

1. Infiltration, water movement in the soil layer, formation of classical surface and subsurface flow

2. Slope (surface, subsurface and underground) inflow to channel network3. Channel flow and lag time

Main modelling lawsMain modelling laws

• Adequacy to natural processes

• The parameters of the equations should not

depend on the argument

• Use of only available data (otherwise,

simplification of the model)

The basic equations of water dynamicsThe basic equations of water dynamicsin a “physically-based” models…in a “physically-based” models…

violation of the main modelling rules?violation of the main modelling rules?

• Water dynamics in soil – the Richard’s equation

• Slope and channel flow – the equation of Saint-Venant or kinematic wave

• Underground flow – the Boussinesq equation

The Richard’s equation The Richard’s equation (moisture diffusion/conductivity)(moisture diffusion/conductivity)

z

Kz

D

t

)()(

– volume moistureD() – moisture diffusion coefficient K( ) – hydraulic conductivity t – time, z – soil depth

• Parallel between the “diffusion of soil water” and heat

conductivity – suspended moisture existence is impossible?

• The Hallaire's effect

• Nonlinearly dependence of D and K on

• Change of D in 104 and K in 106 - 107 times corresponds to

the range of natural variation of

t - time, x – distance, H – depth, V – velocity, q – inflow, C – Chezy coefficient,

The equation of Saint-Venant The equation of Saint-Venant (kinematic wave, etc…)(kinematic wave, etc…)

• Water movement is represented by thin continuous water layer

• Disagreement between units of flow depth (mm) and grid sizes

(km)

• Requirement for absent information (morphology, roughness)

• No possibility to evaluate the described process except by runoff

in the outlet

• Need of calibration – different methods – different parameters

• Exaggeration of slope distances and underestimation of slope

inclination in spatial schematization

)(sin||

21 2

x

Hg

H

Vq

HC

VVg

x

VV

t

V

q

x

VH

x

HV

t

H

– coefficients1 2

The Boussinesq equationThe Boussinesq equation

• True structure of the underground aquifers is unknown

• Information on quantity and stratigraphy of impervious beds

and aquifers (capacity, inclinations, connection with

underground and external channel system, filtration and

water yield coefficients) is required and ABSENT

• The fact of great groundwater storage is not taken into

account

xxH

HK

t

H

K, – filtration and water yield coefficients of rock, H – level of ground waters over the surface of impervious bed or piezometric head in the case of heady movement, t – time, x – distance

What fee do we pay for the What fee do we pay for the ““physical base” of such models?physical base” of such models?

•Nonlinearity•Uniqueness•Uncertainty•Equifinality

•Scale [Beven, 2001]

Is not it a time for some other methods? Is not it a time for some other methods?

Should we stop to pretend for Should we stop to pretend for our knowledge of real runoff processes?our knowledge of real runoff processes?

The concept of runoff elementsThe concept of runoff elements

Basin – elementary slopes or watersheds – runoff elements system

Runoff element:Runoff element:• Natural formation

• Part of elementary slope limited by micro-divides directed with its open part to the slope non-channel or underground drainage system

• The size depends on natural conditions but mainly inclination (the underground runoff elements are much larger than surface ones)

qsdt

dw

1)exp( wq

For each runoff element there is a balance ratio (1)

W – water volume (m3), s and q – inflow and outflow (m3s-1); t – time (s).

(2)

, - hydraulic parameters of a runoff element.

a = /n and b = n, where n is a number of runoff elements.

a = a*/F and b = b*F, T = 1/(a* b*), H = ln(q/b*+1)/a*

a* [m-1], b* [ms-1] – standardized hydraulic coefficients, F – area, T – typical outflow time, H – water storage

Q from all runoff elements of the given level to channel system is:

bbStabQQS

bSQ

)](exp[)]()([1 00

(3)

Q - initial value of runoff Q and S is runoff formation intensity (m3s-1); t - computation time interval (sec) during which S is constant.

AssumptionsAssumptions

with the depth…with the depth…

• The infiltration capacity of water-holding rocks naturally decreases

• The outflow rate decreases

• The water storage increases

System of runoff elementsSystem of runoff elements

LevelType

of runoffa* τ Water

storage, mm

Outflow intensity, mm/min

- Surface 1000 17 min 4.6 6.0

- Soil 100 2.8 hours 24 0.6

1-3 Rapid ground

10 – 11.2–11.6

days69.3–195

(1 – 0.22)*6*10-2

4-6Ground 0.32 – 0.032

1.2months – 1 year

301–674

(1 – 0.22)*6*10-3

7-9 Upper underground

0.01 – 10-3 3.2–32 years

995–2152

(1 – 0.22)*6*10-4

10-12 Deep underground

3.2*10-4–3.2*10-5

100–1000 years

3161– 6812

(1 – 0.22)*6*10-5

13-15Historical underground

10-5 – 10-6

3200–32000 years

10000– 21450

(1 – 0.22)*6*10-6

parameter b* is constant

• It is a schematization in the conditions of full

uncertainty.• It doesn’t contradict the known hydro-geological

items (structure and water storage).• It corresponds to observed curves of runoff

depletion for the basins of various sizes.• It corresponds to the materials of isotope

hydrology on residence time.• It works for different scales and conditions…!

The concept of runoff elements – The concept of runoff elements – what is that?what is that?

Some results…Some results…

Observed (black)Observed (black)

againstagainst simulated (red)simulated (red)

hydrograpshydrograps

7 Viluy

136000

9 Vitim

186000

6 Uchur

108000

5 Amga

65000

1 Katyryk

40

3 Ebetiem

1000

14 Lena

2430000

L a p t e vS e a

C H I N A

2 Timpton

613

8 Lena (Zmeinovo)

140000

12 Kolyma

526000

11 Indigirka

305000

13 Aldan

696000

10 Yana

216000

4 Suntar

7680

SMALL

MIDDLE

LARGE

1

2

3

4

5

6

7

8 9

10

11

12

13

14

Study areaStudy area

LARGE-SCALE BASINSLARGE-SCALE BASINS

Lena at KusurLena at Kusur basin area basin area 2,4 2,4 millionmillion km km22

Рассчитанный Наблюденный

1E5

5E4

XIIXIXIXVIIIVIIVIVIVIIIIII

2E5

1E5

5E4


1E5

5E4


1E5

5E4


Q

Т

1977 1978

1979 1980

Aldan at Verkhoyansky Aldan at Verkhoyansky PerevozPerevoz

basin area basin area 696000696000 km km22

40000

30000

20000

10000


30000

20000

10000


30000

20000

10000


40000

30000

20000

10000


Q

T

1978 1979

1980 1981

1978 1979

1980 1981

Kolyma at KolymskoyeKolyma at Kolymskoye, , basin area basin area 526000526000 km km22

30000

20000

10000

0XIIXIXIXVIIIVIIVIVIVIIIIII

25000

20000

15000

10000

5000


20000

15000

10000

5000


20000

15000

10000

5000


Q

T

1977 1978

1979 1980

1977 1978

1979 1980

Indigirka at VorontsovoIndigirka at Vorontsovo basin area basin area 315000315000 km km22

8000

6000

4000

2000


8000

6000

4000

2000


6000

4000

2000


15000

10000

5000


Q

T

1981 1982

1983 1984

1981 1982

1983 1984

Yana at Dgangky, Yana at Dgangky, basin area basin area 216000216000 kmkm22

8000

6000

4000

2000


6000

4000

2000


6000

4000

2000


6000

4000

2000


Q

T

1970 1971

1972 1973

1970 1971

1972 1973

MIDDLE-SCALE BASINSMIDDLE-SCALE BASINS

Vitim at BodayboVitim at Bodaybo, , basin area basin area 186000186000 km km22

10000

5000


10000

8000

6000

4000

2000


10000

5000


15000

10000

5000


Q

T

1980 1981

1982 1983

1980 1981

1982 1983

Uchur at Chyul’buUchur at Chyul’bu,,basin area basin area 108000108000 km km22

15000

10000

5000


15000

10000

5000


10000

5000


15000

10000

5000


Q

T

1981 1982

1983 1984

1981 1982

1983 1984

SMALL-SCALE BASINSSMALL-SCALE BASINSSuntar at Sakharynia Suntar at Sakharynia

river mouthriver mouth, , basin area basin area 76807680 km km22

1000

800

600

400

200


1000

800

600

400

200


400

300

200

100


1500

1000

500


Q

T

1959 1960

1961 1962

1959 1960

1961 1962

Timpton at Nagorny, Timpton at Nagorny, basin area basin area 613613 km km22

100

50


100

50


250

200

150

100

50


200

150

100

50


Q

T

1977 1978

1979 1980

1977 1978

1979 1980

Katyryk at TokoKatyryk at Toko, , basin area basin area 40.240.2 km km22

Рассчитанный Наблюденный

10

5

0 XIIXIXIXVIIIVIIVIVIVIIIIII

5


10

5


10

5


Q

Т

1981 1982

1983 1984

Statistics on observed vs simulated flow Statistics on observed vs simulated flow (averaged for all basins in Eastern Siberia)(averaged for all basins in Eastern Siberia)

Daily Year

Nash-Sutcliffe 0.78 0.93

Relative error (in absolute value)

36 % 10 %

• to state the fact of specific complexity and

unsolveness of the problem• to state the weakness of traditional “physically-

based” approaches

• to arise the critique and following to arise the critique and following

discussion on the problemdiscussion on the problem

We aimed:We aimed:

And finally, we are looking for:And finally, we are looking for:

serious cooperation in order to test our approach on

isotope data

Thank you for your attention!Thank you for your attention!

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