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 processes
Sample 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 discharge
Sample 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 flow
An 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 : limits
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. 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 catchment
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.
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 aspects
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.
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 transfer
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, ... 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 : drawback
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. 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 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. The alea / vulnerability approach
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
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 data
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
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 catchment
Examples of atypical conditions : Zebra bush in sahelian regions Mulch Snow redistribution by the wind Groundwater sustained rivers Man-made linear patterns in landscape