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The catchment: mechanistic model

NRM L09. The catchment: mechanistic model. Andrea Castelletti. Politecnico di Milano. Schema fisico (bacini). Irrigation district (CBN). CAMPOTOSTO. PROVVIDENZA (P). Fucino. PROVVIDENZA. PIAGANINI. SAN GIACOMO (SG). MONTORIO (M). VILLA VOMANO. S. LUCIA (SL). Adriatic Sea.

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The catchment: mechanistic model

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  1. NRM L09 The catchment: mechanistic model Andrea Castelletti Politecnico di Milano

  2. Schema fisico (bacini) Irrigation district (CBN) CAMPOTOSTO PROVVIDENZA (P) Fucino PROVVIDENZA PIAGANINI SAN GIACOMO (SG) MONTORIO (M) VILLA VOMANO S. LUCIA (SL) Adriatic Sea

  3. Identifying the Model • Definining the components and the system scheme • Identifying the models of the components • Aggregated model

  4. Schema fisico (bacini) Irrigation district (CBN) CAMPOTOSTO PROVVIDENZA (P) Fucino PROVVIDENZA PIAGANINI SAN GIACOMO (SG) MONTORIO (M) VILLA VOMANO S. LUCIA (SL) Adriatic Sea

  5. Reference section The catchment

  6. Reference section Which output? • Outflow from the catchment

  7. Reference section ... and the input? • Outflow from the catchment

  8. Meteorological variables: ... and the input? • Precipitation • Sunshine duration • Temperature • Air relative umidity • Atmospheric pressure • Wind velocity volume in the time interval [t, t+1) average temperature in the interval [t, t+1) Describe and modulate energy and water exchanges between atmosphere and the earth. How to proceed then?

  9. The catchment: block diagram When the model is particularly complex even the simple identification of the causal network might be too difficult. The system is first decomposed into sub-components, then a causal network is constructed for each component. BLOCK DIAGRAM Like causal networks, block diagrams describe cause-effect relationships between relevant variables. However, at a higher conceptual level, at which some complex processes and variables are not yet considered.

  10. Block diagram 1° step precipitation (solid and liquid) air temperature catchment outflow from the catchment

  11. Hydrograph

  12. rainfall The water cycle snowfall snow evaporation intercepted rainfall surface flow infiltration evapotranspiration evaporation capillary flux total flow hypodermic flow percolation deep flow

  13. ground Block diagram2° step: functional components snow pack inflow to the ground outflow from the ground drainage net outfllow from the catchment

  14. band 1 band 2 band m + snow pack Block diagram 3° step: orography flow to the ground

  15. The lake Como catchment

  16. (a) (a) (b) (b) + (a) (a) (c) (b) (b) + (c) + Block diagram4° step: sub-catchments The model of each sub-catchment is first identified, then combined with the other to form the aggregated model of the catchment.

  17. Didactic scheme

  18. Didactic scheme 18

  19. Mechanistic model 1. Model structure

  20. ground Typical structure of rainfall/runoff models Usually rainfall/runoff model have the following structure. precipitation (solid and liquid) air temperature snow pack inflow to the ground outflow from the ground drainge net outfllow from the catchment

  21. Mechanistic model 1. model structure • model structure 1a. snow pack

  22. Solid phase (water equivalent) Liquid phase Snow pack: the state How is the state of the snow-pack made? • snow-pack depth • density • snow temperature • water content of the snow • color of the snow surface • snow-pack depth • density • water content of the snow

  23. Solid phase of the snow-pack (water equivalent) Liquid phase of the snow-pack average air temperature = solid phase of precipitation = liquid phase of precipitation flow to the ground Snowpack: variables State variables snow pack Inputs: Outputs:

  24. Net daily snow-melt - Assumption: snow-melt grows linearly with T. a = mm of snow melt per °C and per day. M always non-negative saturation to Tt+1 This approach is usually known as “degree-day”. Snowpacksolid phase dynamics melting melting Tt+1 max { 0, min [ ] }

  25. Net daily snow melt - For the sake of simplicity let’s assume the same a for melting and re-freezing. Tt+1 - M the frozen volume is always non-negative Tt+1 saturation to Snowpacksolid phase dynamics melting - freezing - freezing melting ( max [ 0, ] } )

  26. Net daily snow melt snow melt - - freezing M Tt+1 Snowpacksolid phase dynamics snow melt snow melt - freezing - freezing

  27. Snowpackliquid phase dynamics min{ , } flow to the ground 45°

  28. Snowpackflow to the ground max{ 0, } 45°

  29. - min{ , } max{ 0, } Consistency check:it’s raining without snow-pack It’s raining ... without snow-pack System equations:

  30. Consistency check:it’s raining without snow-pack - min{ , } max{ 0, } It’s raining ... without snow-pack System equations: The flow to the ground is the very rainfall. 30

  31. Mechanistic model 1. model structure • model structure • 1a. snow pack 1b. ground

  32. Ground snow pack Flow to the ground Evaporation ground Surface flow Soil Infiltration Root zone Total runoff Hypodermic flow Percolation Deep flow Water table

  33. Flow to the ground % of inflow retained by the ground Degree of saturation Surface flow Groundthe soil Evaporation Surface flow Infiltration

  34. % of inflow retained by the soil Degree of saturation Inflow retained by the ground 100%- γ < 1 γ = 1 γ>1 |1

  35. Percolation RM KP rt Groundroot zone Infiltration Hypodermic flow Percolation

  36. Groundwater table Percolation Deep flow

  37. Surface flow Total flow Hypodermic flow Deep flow Storing coeff. Ground- drainage network The total flow from the ground qst+1 is subject to a storing process in the drainage network.

  38. Mechanistic model • model structure • 1a. snow pack • 1b. ground 2. Analysis of the model properties

  39. Soil Roots Water table Total flow affectsdt+1 Outflow from the catchment Raining without snow pack The model is a improper one. It can not be used for managing or forecasting. It is uselles!

  40. Flow to the ground Evaporation Surface flow Soil Infiltration Root zone + Percolation Total flow Water table The model is an improper one

  41. Soil Roots Water table rt+1does not affectqst+1 Total flow does not affectdt+1 Outlfow from the catchment Proper model

  42. Soil Roots Water Table Total flow Outflow from the catchment Rainining without snowpack (ground – proper model) Rainfall is affecting only the outflowdt+2 The new model can be used in managemen and forecasting, however ....

  43. observed simulated Typical model performance A one-day delay due to the model properties. 1250 1000 Inflow ( m³/s ) 750 500 250 0 1 Aug 10 Aug 20 Aug 30 Aug 10 Sep 20 Sep 30 Sep

  44. Solution to reduce the delay • There are two possible solutions: • Reducing the time step to a value smaller than the concentration time in the sub-catchment considered (right solution) • Manipulating and transformin the model into a proper model. (wrong solution) This latter solution is quite common in hydrology, but it precludes the use of the model in prediction.

  45. Readings IPWRM.Theory Ch. 5 + Ap. 5

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