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### Hydrology and modelisation a quick outlook

Etienne LebloisCemagref Lyon

The aim of hydrology

Determine how much water will be in a given location and condition

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

Main freshwater storages

Ranked here by increasing time constant

atmosphere

soil moisture (non saturated area)

rivers

snowpack

lakes ; reservoirs

groundwater (saturated area)

icepack

Main freshwater fluxes

Precipitation

(actual) Evapotranspiration

Infiltration and seepage (= ex filtration)

Runoff (on slopes)

Discharge (in rivers)

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

Hydrological processesSample processrunoff 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

Overland flow (on slopes)

Gullies, connectivity topics

Importance of relative location of land use

Importance of subrogate features of land use (direction of ploughing)

Sample process runoff collection to dischargeSample processunderground 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)

Preferential pathes

biological macropores

pipes

roots

Impervious layers

bottom of ploughing area

Sample processunderground flowAn key hydrological objectthe catchment (= the basin)

An outlet

The river network upstream

Slopes

both side of the rivers

up to the water divides

Includes

surface and subsurface storagesin relation to the river

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

Why study catchments ?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

The catchment : limitsThe 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.

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).

The catchmentlimits (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.

The catchmentslimits (continued…)It is usually not an administrative division

The concept may break down

karstic areas

flat, human dominated areas

The catchmentslimits (continued…)Hydrological monographies

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

It will not solve all possible and unexpected questions.

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.

A problem oriented description of a catchmentProduction 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.

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

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.

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

Conceptual approaches to the transfert aspectsLimits 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.

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

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

Various levels of description for hydraulic transfer1D+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, ...

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

Various levels of description 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

Governing equations for hydraulic transfer (continued)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

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

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 ?

Flood warning systems (continued)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 !

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

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.

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).

The dammage approach : drawbackvulnerability 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.

The alea / vulnerability approachThis 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

The alea / vulnerability approachThis can be done

via administrative measures, or

via local negociations

including payment to insurance companies

according to the cultural habits of each community.

The alea / vulnerability approachDefinitively 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

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

Definitively lacking dataThe 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

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

A catchmentExamples of atypical conditions :

Zebra bush in sahelian regions

Mulch

Snow redistribution by the wind

Groundwater sustained rivers

Man-made linear patterns in landscape

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

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

Operationnal reasons to build models

answering specialized questions

assessing impacts of land-use change

testing general management strategies

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 ?

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 ?

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 ?

Models relationship to causality

Deterministic models : deductive models

Statistical models : inductive models

probabilistic models

directly on distributions

stochastic models

yielding time-series as output

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

Steps in elaborating a lumped, conceptual hydrologic model

identification (which structure ?)

calibration (value of parameters)

validation (check)

documentation of limits

physical limits

numerical limits

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 !

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

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

Adressing sub-grid variabilityinverse 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

Adressing sub-grid variabilityExplicit 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.

Examples of hydrological models

square grid, physically based

SHE

contour and slope grid, physically based

TOPOG

Examples of hydrological models

square grid, conceptual

Stanford IV, Cequeau, ModCou

lumped, conceptual

CREC, GR4J, Gardenia

semi-lumped, specialised to saturation runoff : Topmodel

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

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

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

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

The chesnut valley
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