1. Looking for universality...
The deadlock of “physically-based” modelling or what limits the hydrological predictability in ungauged basins – alternative approaches to the description of catchment processes
Yu.B. Vinogradov,
Olga Semenova
State Hydrological Institute
St. Petersburg, Russia

2. What we would like our models to be?
Looking for universality...
Be useful in life
applications Be
transferable
Describe real
processes
Use of only
available data
Adequacy
The parameters of the equations
must not depend on the arguments
State Hydrological Institute, St. Petersburg, Russia

3. The Richard’s equation (moisture diffusion/conductivity)
Looking for universality... ?
 – volume moisture
D() – 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
Nonlinearly dependence of D and K on 
Change of D in 104 and K in times corresponds to the range of natural variation of 
[J. McDonnell lectures]
State Hydrological Institute, St. Petersburg, Russia

4. The equation of Saint-Venant (kinematic wave, etc…)
Looking for universality...
The equation of Saint-Venant (kinematic wave, etc…) ?
t - time, x – distance, H – depth, V – velocity, q – inflow, C – Chezy coefficient,
– coefficients
Water movement is represented by thin continuous water layer
Disagreement between units of flow depth (mm) and grid sizes (km)
Requirement for NOT AVAILABLE information (morphology, roughness)
No possibility to evaluate the described process except by runoff in the outlet
[from
gpu/visualwave.html by Knut-Andreas Lie]
Exaggeration of slope distances and underestimation of slope inclination in spatial schematization
Need of calibration – different methods – different parameters
State Hydrological Institute, St. Petersburg, Russia

5. The Boussinesq equation
Looking for universality...
The Boussinesq equation ?
K,  – filtration and water yield coefficients of rock, H – of ground waters over the surface of impervious bed or piezometric head in the case of water movement due to differential head, t – time, x – distance
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 NOT AVAILABLE
It does not account for the great groundwater storage
It does not describe the fact of different water ages
State Hydrological Institute, St. Petersburg, Russia

6. The basin schematization
Looking for universality...
To ignore the existence of elementary slopes and to make calculations for integrated areas X
To conduct calculations selectively for
the chosen elementary slopes X
State Hydrological Institute, St. Petersburg, Russia

7. Looking for universality...
The model flowchart
State Hydrological Institute, St. Petersburg, Russia

8. The concept of runoff elements
Looking for universality...
The concept of runoff elements
Watershed – elementary slope –
runoff elements system
Runoff element: a part of elementary slope limited by micro-divides directed with its open part to the slope non-channel or underground drainage system
Surface, soil,
underground
The size depends on inclination and natural conditions
State Hydrological Institute, St. Petersburg, Russia

9. Looking for universality...
W – water volume (m3), q – outflow (m3s-1)
a* [m-1], b* [ms-1] – standardized hydraulic coefficients,
F – basin area
Typical outflow time
T = 1/(a* b*)
Water storage
H = ln(q/b*+1)/a*
State Hydrological Institute, St. Petersburg, Russia

10. Looking for universality...
The main assumptions
Looking for universality...
The infiltration capacity of water-holding rocks naturally decreases with the depth
The outflow rate decreases with the depth
The water storage increases with the depth
State Hydrological Institute, St. Petersburg, Russia

11. Looking for universality...
System of runoff elements
Looking for universality...
Type
of runoff a* T
H [mm]
Outflow intensity, [liter s-1 km2] -
Surface
1000
17 min
4.6
105
Soil
100
2.8 hours 24
104
1-3
Rapid
ground
10 – 1
1.2–11.6 days
69.3–
195
103 – 215
4-6
Ground
0.32 – 0.032
1.2months – 1 year
301–
674
100 – 21.5
7-9
Upper underground
0.01 – 10-3
3.2–32 years
995–
2152
10 – 2.15
10-12
Deep underground
3.2*10-4–3.2*10-5
100–1000 years
3161– 6812
1 – 0.215
13-15
Historical underground
10-5 – 10-6
3200–32000 years
10000– 21450
0.1 –
= 67256
parameter b* = 10-6
[different sources: – 70000]
State Hydrological Institute, St. Petersburg, Russia

12. Runoff element system: parameters
Lena, Kusur
km2
Vitim, Bodaybo
km2
Katyryk, Toko
40.2 km2 1
0.30 2
0.20
0.25
0.70 3
0.15 4
0.12
0.10 5
0.08
0.05 6
0.07
0.03 7
0.02 8
0.022 9
0.007 10
0.004 11
0.003 12
0.002 13
0.001 14
0.0005 15
0.0001
parameter a*
parameter b*
ratio of the distribution of incoming water content among modelling groundwater layers

13. Nyzhnaya Tunguska, km2
High plain, permafrost

14. Looking for universality...
The concept of runoff elements –
what is that?
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 should correspond to the materials of tracers experiment on residence time (if not, should be changed!!!)
It works for different scales and conditions…!
It states the weakness of traditional “physically-based” approaches
State Hydrological Institute, St. Petersburg, Russia

15. Looking for universality...
The routing approach
State Hydrological Institute, St. Petersburg, Russia

16. Looking for universality...
The main assumptions
The transit velocity is equal to the flow velocity in the river
The lag time is constant for each calculating point
Direct observations of measured mean flow velocities are used
The averaged minimum value of lag time (corresponding to 10-% range of the maximum velocities) is taken as the calculating value.
The underestimated shift of hydrograph shape during the period of low flow can not affect the resulting runoff significantly.
– distance between gauges
– maximum (10-%) velocity
State Hydrological Institute, St. Petersburg, Russia

17. Looking for universality...
“Hydrograph” model
Distributed
Universal
Calculating interval – 24-hour or less (?)
Apriori estimation of the most parameters
Forcing data – precipitation, temperature and humidity
Output – runoff hydrograph, water balance elements, state variables of soil and snow cover
State Hydrological Institute, St. Petersburg, Russia

18. Some results… Observed (black) against simulated (red) hydrograps
Looking for universality...
Some results… Observed (black) against simulated (red) hydrograps
State Hydrological Institute, St. Petersburg, Russia

19. Looking for universality...
The model application
Looking for universality... 5 3 4 6 1 2 8 7
State Hydrological Institute, St. Petersburg, Russia

20. Looking for universality...
LARGE-SCALE BASINS
Lena at Kusur basin area 2,4 million km2
State Hydrological Institute, St. Petersburg, Russia

21. Yenisey Nizhnyaa Tunguska at Bolshoy Porog, basin area 418000 km2
State Hydrological Institute, St. Petersburg, Russia

22. Looking for universality...
MIDDLE-SCALE BASINS Vitim at Bodaybo, basin area km2
Vitim
State Hydrological Institute, St. Petersburg, Russia

23. Looking for universality...
SMALL-SCALE BASINS Suntar at Sakharynia river mouth, basin area 7680 km2
Suntar
State Hydrological Institute, St. Petersburg, Russia

24. Looking for universality...
Timpton at Nagorny, basin area 613 km2
Timpton
State Hydrological Institute, St. Petersburg, Russia

25. Looking for universality...
SLOPE SCALE Yuzhny stream, area 0.27 km2
Slope
State Hydrological Institute, St. Petersburg, Russia

26. Snow height, meteorological station Zilair, 2004 – 2005
Looking for universality...
State variables of soil and snow
Snow height, meteorological station Zilair, 2004 – 2005
State Hydrological Institute, St. Petersburg, Russia

27. SWE, snow survey near the meteorological station Zilair, 2001 – 2003
State Hydrological Institute, St. Petersburg, Russia

28. Soil temperature at 0.2 m, meteorological station Zilair, 2004 – 2005
Looking for universality...
State Hydrological Institute, St. Petersburg, Russia

29. Soil temperature at 0.8 m, meteorological station Zilair, 2004 – 2005
Looking for universality...
Soil temperature at 0.8 m, meteorological station Zilair, 2004 – 2005
State Hydrological Institute, St. Petersburg, Russia

30. averaged content of moisture in 1-m layer
SOIL MOISTURE
Stream Dolgy, area 2.51 km2,
averaged content of moisture in 1-m layer
State Hydrological Institute, St. Petersburg, Russia

31. State Hydrological Institute, St. Petersburg, Russia

32. Looking for universality...
Rio Nare, Colombia, basin area 1250 km2: Preliminary results
State Hydrological Institute, St. Petersburg, Russia

33. Looking for universality...
Conclusion
WHY TO OPPOSE THE OBJECTIVITY OF NATURE TO OUR PRETENTIOUS SELF-CONFIDENCE?
IT’S TIME TO MOVE FORWARD TOWARDS NEW PARADIGMS!
State Hydrological Institute, St. Petersburg, Russia