Hydrology and modelisation a quick outlook

Etienne Leblois Cemagref Lyon

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Basic aspects of hydrology 2

The aim of hydrology • Determine how much water will be in a given location and condition 3

The hydrological cycle • A continuum, broken by the observator into – storages • water bodies • with possible internal evolutionary laws – water fluxes • inside or between water bodies • associated to hydrological processes 4

Main freshwater storages • Ranked here by increasing time constant – atmosphere – soil moisture (non saturated area) – rivers – snowpack – lakes ; reservoirs – groundwater (saturated area) – icepack 5

Main freshwater fluxes • Precipitation • (actual) Evapotranspiration • Infiltration and seepage (= ex filtration) • Runoff (on slopes) • Discharge (in rivers) 6

Hydrological processes • Water fluxes are linked to hydrological processes – not only fluxes between water bodies – also internal evolution of water bodies • A process is an elementary behaviour – that can described as a whole – whose level of formalisation may vary – under control of various factors 7

Sample processes 8

Sample process runoff formation • according to Horton – runoff occurs where and when rain rate exceeds infiltration capacity • according to Capus, Hewlett, Beven, ... – runoff occurs where and when rain falls on saturated areas • importance of the soil structure 9

Sample process runoff collection to discharge • Overland flow (on slopes) – Gullies, connectivity topics – Importance of relative location of land use – Importance of subrogate features of land use (direction of ploughing) 10

Sample process underground flow • The continuous model – unsatured zone : the Richards equation – satured zone : the Darcy equation • local formula • integrated form for alluvial aquifers • integrated form for constrained aquifer – The problem of parameters estimation • importance of K(  , x, y, z) (a tensor) 11

Sample process underground flow • Preferential pathes – biological macropores – pipes – roots • Impervious layers – bottom of ploughing area 12

Catchment 13

An key hydrological object the catchment (= the basin) • An outlet • The river network upstream • Slopes – both side of the rivers – up to the water divides • Includes – surface and subsurface storages in relation to the river 14

Why study catchments ?

• the best possible system to study as far as geophysical fluxes as considered – one input (rain, other atmospheric conditions) – one output (discharge at the outlet) • the best possible unit for effective management – what I do here is my problem 15

The catchment : limits • A fully explicit, exhaustive description is impossible because of – the fractal nature of the river network – the fractal nature of the topography – the partially unreachable description of the under ground – the unsteady character of the topography and soil properties at detailed scale 16

The catchment limits (continued…) • The catchment is – a point (the outlet) – a set of lines (the river network) – an area (interacting with the atmosphere), – a volume (including the underground). • Implementation of such an object in a GIS is not straightforward.

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The catchment limits (continued…) • The definition of a catchment is outlet dependent. • Two gauging stations define either nested or non-nested catchments • Data out of many catchments are part of a data hierarchy that must sometimes be considered explicitly (discharge mapping).

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The catchments limits (continued…) • Some problems seem point oriented...

– « how can I reduced floods here » … but must be handled considering all the processes – upstream (causes) and – downstream (consequencies of options to take). Often we have to « zoom out » to have a grasp at the problem as a whole.

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The catchments limits (continued…) • It is usually not an administrative division • The concept may break down – karstic areas – flat, human dominated areas 20

Hydrological monographies • A balanced description of a catchment (hydrological monography) can be very interesting.

• It will not solve all possible and unexpected questions. 21

A problem oriented description of a catchment • needs a variety of choices to be done – selecting the processes relevant to the problem – the scale of the features to explicitely take into account.

– the time to be considered • the abduction of non-relevant details has to remain in mind. 22

Rain-Discharge transformation within a catchment 23

Production and transfert functions • « Production » – relates the gross precipitation over the catchment to the net precipitation that is to flow through the outlet. – non-flowing water is only considered as a soil moisture controling factor, influencing the soil behaviour under further rains.

• « Transfert » – relates the produced « net precipitation » to the discharge.

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About this scheme • It is common choice to – upload the production function with all the non linearity of the rain-discharge transformation. – consider the transfert function as linear.

• This approximation may be valid for heavy rains 25

Conceptual approaches to the transfert aspects • Unit Hydrograph (Sherman, 1932) – the transfert function is assumed linear. – the structure of the non-linear production function remains author-dependant.

– parameters for both parts are identified from a joint pair of long rainfall/discharge time series. 26

Conceptual approaches to the transfert aspects • Geomorphologic Unit Hydrograph : – an improvement from the previous approach – the shape of the unit hydrograph is related to distances and slopes along the runoff pathways from the catchment to the outlet – this gives clearer constraints to what the production function can be 27

Limits to these approaches • Isotopes evaluations show that most of the water of the flood has been in the soil long before the begin of the rain.

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Hydraulically based description of the transfert aspects • Continuity equation • Dynamic equation – Head • potential energy + kinetic energy – Head losses • along the stream (energy loss in turbulence, interactions between the water and the reach) • localised (in hydraulic jumps from torrential to fluvial conditions 29

Various levels of description for hydraulic transfer • in general, PDE equations • 3D equations (Navier Stokes) – small scale studies like geomorphology, flow around a bridge • 2D equations (Barré Saint-Venant) – where overland flow is most relevant : dam breakes, flooding of broader areas with non negligible speed in the flooded part 30

Various levels of description for hydraulic transfer (continued) • 1D+storages (Barré Saint-Venant) : – where the flooded area is broken in independent storages, where speed is negligible • 1D (Barré Saint-Venant) : – where streamflow is concentrated in the minor riverbed (no flooding).

– including dam breaks, working spillways, moving hydraulic jumps, ...

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Various levels of description for hydraulic transfer (continued) • Simplified 1D equations : – Diffusive wave approximation : • flood diffusion in gentle, sub-horizontal rivers – Cinematic wave approximation : • flood propagation in steep rivers or lateral slopes 32

Governing equations for hydraulic transfer (continued) • 1D, steady-state approximation : – if time variations are negligible. Mostly broad, gentle rivers, – a important step for text-books in hydraulics (clear, intuitive relation of results to energetic consideration and limits) • 1D, uniform approximation : – to be considered only in regular, chenalized reaches 33

Hydrology of floods 34

Hydrology of floods • To predict floods, or to assess flood hazard?

– To predict • Given a current stage of water and observed or predicted rain, guess the shape, time of arrival and water stage to occur in the next future at the interest point.

– To assess • Given a observed discharge time-serie, give probability of a given flood characteristic (peak flow, duration, volume,…) to be over-seeded 35

Flood warning systems • who – civil servants ; river authorities ; majors ; meteorologists ; hydrologists • how – real time data collection – quick data processing, mostly empirical models or analogues – 365 days, 24 H communication system to people 36

Flood warning systems (continued) • what – technical choice of a flood index to predict, level of confidence • to who – police, municipality representatives, everybody ?

• what to say – how clear the warning messages ?

– readiness to cooperate ?

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A personal interpretation • some rivers have long time constants – gentle rain, so progressive saturation ; broad basins, so long hydraulic transferts • some rivers have short time constants – steep, small catchments ; convective storms.

• this – enable different kind of human measures – induced an “hydrology of flash floods” to exist • but hydrology is one !

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Flood management approaches • flood – is a natural event – can be characterised as an random event => alea • flooding – can yield damages – this depends on the sensitivity of land use => vulnerability 39

The dammage approach : principle • considers vulnerability as the cost of damages • to minimise by – protective measures (levees), – storing or evacuating waters via various works, • as far as monetary evaluation proves efficient. 40

The dammage approach : drawback • Due to ...

– the probabilistic nature of events, – the short memory of human beings, – teleconnections of local actions and basin-wide effects, • … spontaneous local management exhibits a drift towards heavy works that appears to be unsustainable at the basin scale (spiral of corrective measures).

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The alea / vulnerability approach • vulnerability of each type of landuse is a socially determined, possibly negociated acceptance for flooding • some areas, like marshes, may have a positive demand for flooding.

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The alea / vulnerability approach • This approach induce a description of the basin as a set of areas – the one are in a lack of protection (red) – the other one are “underflooded” (green). • Relevant decision board can decide – to freeze some areas for them not to turn red soon, to modify land use, or to spatially modify the alea pattern with minimal river works, turning areas red to green at the “hydrological expenses” of green 43

The alea / vulnerability approach • This can be done – via administrative measures, or – via local negociations • including payment to insurance companies • according to the cultural habits of each community.

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What is the problem with hydrology ?

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Definitively lacking data • rain known via – rain gauges select 400 cm2 in 100 km2 – weather radar • spatial pattern, but little quantitative consistency • potential evapotranspiration known via – observed meteorological estimation of control factors (temperature, wind, …), at 100 km grid size 46

Definitively lacking data • real evapotranspiration known – only via water balance estimation at the field or basin scale • discharge – known at 15 % in some gaging stations (500 working stations in France). – include non registered man-made perturbations that make the assessment of the intrinsic behaviour of the catchment very difficult 47

The hierarchy of processes is unstable • a process can easily take precedence on an other because of – the quasi-systematic non linearity of processes – their sensitivity to the initial conditions • effect of water contents • effect of soil structure 48

A catchment • can have a behaviour that is completely dominated by some usually neglected process • as a behaviour that is not uniquely determine by the contents, but also by their spatial organisation • comparison with a recepie – we know the taste of each ingedient. – we can NOT predict the taste of the meal 49

Examples of atypical conditions : • Zebra bush in sahelian regions • Mulch • Snow redistribution by the wind • Groundwater sustained rivers • Man-made linear patterns in landscape 50

A built-in link with other specialities • Soil physics and plant physiology • Water quality, hydrobiology • River geomorphology • Human and social sciences • Management and economy, law, politics 51

Hydrological modelisation 52

Scientific reasons to build models • Blackboard tool – formalisation of concepts – possible formal checking – knowledge and concepts • Data interpretation • Behavioural simulation – explicitation of non-obvious structure effects 53

Operationnal reasons to build models • answering specialized questions – assessing impacts of land-use change • testing general management strategies 54

Scope of the model ?

• which area ?

• which level of detail ?

– are the details useful ?

– will we be able to gather the details ?

• which time scope – season ? – duration ? – climate and social scenarios ?

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Scope of the model (continued…) ?

• which hydrologically related features do we need ?

– floods ; water quantity ; water quality ; hydrobiology ; river geomorphology ; water uses ; land use • choice of independant and dependant features ?

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Some critical points in hydrological modelisation • Assessing the dominant processes – Is there a link to what I am interested to ?

• Choosing time and space scales • Choosing a topology • Is an object oriented approach usefull ?

– How to separate objects ?

– How to specify the relation between objects ?

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Models relationship to causality • Deterministic models : deductive models • Statistical models : inductive models – probabilistic models • directly on distributions – stochastic models • yielding time-series as output 58

Lumped models • boxes flowing the ones into the others through pipes...

• need for calibration • useful as reference catchments in applications involving reference catchments – detection of changes 59

Steps in elaborating a lumped, conceptual hydrologic model • identification (which structure ?) • calibration (value of parameters) • validation (check) • documentation of limits – physical limits – numerical limits 60

Distributed models • according to a regular grid – an old-fashioned, quite efficient way • according to a dominant process-based grid – slopes and contours • according to an homogeneous area concept – valid only in man-made landscape – terrific topology • a general tool would need the tree forms to be easily mixed !

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Adressing sub-grid variability • mostly for regular grid distributed models • physical parameters unknown and spatially variable at the sub-grid resolution • effective parameters approach : – equations are kept same as in the detailed scale, but with (possibly other) numerical values that account for macroscopic scale behaviour 62

Adressing sub-grid variability • parametrization approach – given a scheme of what the subgrid variability is, a stochastic approach derives a set of macroscopically suitable equations that have a form that is not the same as the one of the small scale 63

Adressing sub-grid variability • inverse approach – parameters are estimated backward from overall behaviour of the catchment • integrated measurement – remote sensors are supposedly able to evaluate some characteristic parameters of the surface (moisture, rugosity, slope…) directly at a scale that is suitable for distributed modeling 64

Explicit physics and parametrisation • part of explicit physics quite modest.

• unresolved part – accounted for via behavioural routines – tend to be the core of models (not just in well localized “parametrisation boxes”). • models who clame to be deterministic (for they are distributed) may be completely behavioural when one consider the scheme implemented at the cell size.

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Examples of hydrological models • square grid, physically based – SHE • contour and slope grid, physically based – TOPOG 66

Examples of hydrological models • square grid, conceptual – Stanford IV, Cequeau, ModCou • lumped, conceptual – CREC, GR4J, Gardenia • semi-lumped, specialised to saturation runoff : Topmodel 67

What could be a typical problem for FIRMA modelling ?

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The chesnut valley • Background – Privas, Ardèche dept, France – Key industry : chesnut processing (Christmas, etc.) – On the Ouvèze river, a tributary to the Rhône – Some agricultural opportunities in the valley, downstream from Privas 69

The chesnut valley • Today state – two tributaries of the Ouveze are used for providing water to the chesnut industry.

– Water shortages in Privas – Ouveze dry off in summer in Privas – Ouveze is merely chesnut waste donwstream from Privas ; biology near to 0 down to the Rhône.

– Agriculture does not really start, because lacking water 70

The chesnut valley • Spontaneous sectorial remediation projects – for problems in Privas • building dams on the tributaries for an enhancement of water availability in Privas ; maybe, to sustain summer discharge of the Ouveze – for agriculture • building a irrigation pipe from the Rhône 71

The chesnut valley • An idea for integrated management • irrigation pipe to go up to Privas • chesnut waste to be diverted to the agricultural areas • Expected benefits • abundant water to the industry and inhabitants • dam project can be forgotten • river will biologically recover • A need • evaluate this and others scheme quickly 72