The catchment: mechanistic model Andrea Castelletti Politecnico di Milano NRML09

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

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

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

5 The catchment Reference section

6 Which output? Reference section  Outflow from the catchment

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

8... and the input?  Precipitation  Sunshine duration  Temperature  Air relative umidity  Atmospheric pressure  Wind velocity Meteorological variables: Describe and modulate energy and water exchanges between atmosphere and the earth. volume in the time interval [t, t+1) average temperature in the interval [t, t+1) 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 catchment air temperature precipitation (solid and liquid) outflow from the catchment

11 Hydrograph

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

13 Block diagram 2° step: functional components snow pack ground drainage net inflow to the ground outflow from the ground outfllow from the catchment

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

15 The lake Como catchment

16 Block diagram 4° step: sub-catchments + (c) + + (a) (b) (a) 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 COMPONENTReservoirCatchment Other components TYPES of MODELS  BBNs  Mechanistic DETAILS  Mechanistic Campotosto

18 Didactic scheme COMPONENTReservoirCatchment Other components TYPES of MODELS  BBNs  Mechanistic DETAILS  Mechanistic Campotosto  Mechanistic intercept.1350

19 Mechanistic model 1. Model structure

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

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

22 Snow pack: the state 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 Solid phase (water equivalent) Liquid phase How is the state of the snow-pack made?

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

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

25 M T t+1 the frozen volume is always non- negative Snowpack solid phase dynamics melting- freezing T t+1 - max [ 0,]} () - freezing For the sake of simplicity let’s assume the same  for melting and re-freezing. melting saturation to - Net daily snow melt

26 M T t+1 Snowpack solid phase dynamics snow melt- freezing snow melt - freezing Net daily snow melt -

27 Snowpack liquid phase dynamics 45° min{, } flow to the ground

28 Snowpack flow to the ground 45° max{ 0, }

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

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

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

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

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

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

35 Ground root zone Infiltration Percolation Hypodermic flow Percolation rtrt RMRM KPKP

36 Ground water table Percolation Deep flow

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

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

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

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

41 Outlfow from the catchment Total flow Water table Roots Soil Proper model r t+1 does not affect q s t+1 does not affect d t+1

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

43 Typical model performance 1 Aug 10 Aug 20 Aug 30 Aug 10 Sep 20 Sep 30 Sep Inflow ( m³/s ) simulatedobserved A one-day delay due to the model properties.

44 Solution to reduce the delay There are two possible solutions: 1)Reducing the time step to a value smaller than the concentration time in the sub-catchment considered (right solution) 2)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