Índice de saturação topográfico Walter Collischonn

Índice de saturação topográfico

Walter Collischonn

Indicador

• wetness index

• topographic index

• saturation index

• índice de saturação

• índice de saturação do modelo TopModel

Processos de geração de escoamento

From http://snobear.colorado.edu/IntroHydro/geog_hydro.html

Processos de geração de escoamentoInfiltration excess overland flowaka Horton overland flow

Partial area infiltration excess overland flow

Saturation excess overland flow

PP

P

qrqs

qo

PP

P

qo

f

PP

P

qo

f

f

Mapa de áreas saturadas numa bacia mostrando a expansão da região saturada durante um evento de chuva. A região escura é a região saturada no início da chuva. A região cinza claro está saturada no final da chuva. Nesta região o lençol freático atingiu o nível da superfície do terreno. [Dunne and Leopold, 1978]

Região saturada de acordo com a época do ano:

•preto: verão•cinza claro: outono•cinza escuro: inverno

[Dunne and Leopold, 1978]

Runoff generation at a point depends on

• Rainfall intensity or amount

• Antecedent conditions

• Soils and vegetation

• Depth to water table (topography)

• Time scale of interest

These vary spatially which suggests a spatial geographic approach to runoff estimation

Índice de saturação

Digital Elevation Model based Hydrologic Modeling

• Topography and Physical runoff generation processes (TOPMODEL)

• Raster calculation of wetness index

• Raster calculation of TOPMODEL runoff

• Extendability of ArcGIS using Visual Basic Programming

Outline

TOPMODEL

Beven, K., R. Lamb, P. Quinn, R. Romanowicz and J. Freer, (1995), "TOPMODEL," Chapter 18 in Computer Models of Watershed Hydrology, Edited by V. P. Singh, Water Resources Publications, Highlands Ranch, Colorado, p.627-668.

“TOPMODEL is not a hydrological modeling package. It is rather a set of conceptual tools that can be used to reproduce the hydrological behaviour of catchments in a distributed or semi-distributed way, in particular the dynamics of surface or subsurface contributing areas.”

TOPMODEL and GIS

• Surface saturation and soil moisture deficits based on topography– Slope– Specific Catchment Area– Topographic Convergence

• Partial contributing area concept• Saturation from below (Dunne) runoff

generation mechanism

Saturation in zones of convergent topography

Uso do índice topográfico

• A esperança é que usando o índice de saturação se obtenha melhores resultados de simulação, porque apenas a região saturada contribui efetivamente para a geração de escoamento.

Outros usos do índice topográfico

• relacionar com ndvi

• relacionar com evapotranspiração

• relacionar com início de um rio

Obtenção do índice topográfico

• equação

• variáveis

• passos

partindo do mnt filtrado

TOPMODEL a = runoff do idrisi

teoricamentea = A/ce é dado em metros

não parece ser importante

declividade em percentual

dividindo por100chegamosa tg()

a/tg

ln(a/tg)

Histograma do índice ln(a/tg)

Flowdirection.

Steepest directiondownslope

1

2

1

234

5

67

8

Proportion flowing toneighboring grid cell 3is 2/(1+

2)

Proportionflowing toneighboringgrid cell 4 is

1/(1+2)

Numerical Evaluation with the D Algorithm

Upslope contributing area a

Stream line

Contour line

Topographic Definition

Specific catchment area a is the upslope area per unit contour length [m2/m m]

Tarboton, D. G., (1997), "A New Method for the Determination of Flow Directions and Contributing Areas in Grid Digital Elevation Models," Water Resources Research, 33(2): 309-319.) (http://www.engineering.usu.edu/cee/faculty/dtarb/dinf.pdf)

Hydrological processes within a catchment are complex, involving:

• Macropores

• Heterogeneity

• Fingering flow

• Local pockets of saturation

The general tendency of water to flow downhill is however subject to macroscale conceptualization

TOPMODEL assumptions• The dynamics of the saturated zone can be approximated

by successive steady state representations.

• The hydraulic gradient of the saturated zone can be approximated by the local surface topographic slope, tan.

• The distribution of downslope transmissivity with depth is an exponential function of storage deficit or depth to the water table

m/SoeTT fz

oeTT - To is lateral transmissivity [m2/h]- S is local storage deficit [m]- z is local water table depth [m] (=S/ne)- ne is effective porosity- m is a storage-discharge sensitivity parameter [m]- f =ne/m is an alternative storage-discharge sensitivity

parameter [m-1]

Topmodel - Assumptions

• The soil profile at each point has a finite capacity to transport water laterally downslope.

dzKTwhereSTqcap

f

KdzeKT

KDT

o

0

fzo

e.g.

or

UnitsD mz mK m/hrf m-1

T m2/hrS dimensionlessq m2/hr = m3/hr/m

S

DwD

Topmodel - Assumptions

• The actual lateral discharge is proportional to specific catchment area.

aRqact

Unitsa mR m/hr

qact m2/hr = m3/hr/m

Specific catchment area a [m2/m m] (per unit contour length)

S

DwD

• R is

– Proportionality constant

– may be interpreted as “steady state” recharge rate, or “steady state” per unit area contribution to baseflow.

• Relative wetness at a point and depth to water table is determined by comparing qact and qcap

STaR

q

qw

cap

act

Specific catchment area a [m2/m m] (per unit coutour length)

S

DwD

• Saturation when w > 1.

i.e. R1

STa

Topmodel - Assumptions

a / T S o r a / S o r l n ( a / S ) o r l n ( a / t a n )[ t a n = S ] i s a w e t n e s s i n d e x t h a t d e t e r m i n e st h e l o c a t i o n s o f s a t u r a t i o n f r o m b e l o w a n ds o i l m o i s t u r e d e f i c i t .

W i t h u n i f o r m K a n d f i n i t e D a s s u m p t i o n

'S/a

wSTaR

w

w h e r e dAS/aA1

'

)w1(Dz

W i t h e x p o n e n t i a l K a s s u m p t i o n

Sa

lnf1

zTSaR

lnf1

z w h e r e

dAS/alnA1

a n d )TR

ln(f1

z

S o i l m o i s t u r e d e f i c i t = z t i m e s p o r o s i t y

Topmodel

Specific catchment area a [m2/m m] (per unit coutour length)

S

DwD

z

Slope

Specific Catchment Area

Wetness Index ln(a/S)

from Raster Calculator.

Average, = 6.91

Numerical ExampleGiven • Ko=10 m/hr• f=5 m-1

• Qb = 0.8 m3/s• A (from GIS)• ne = 0.2

m46.0z

Sa

lnf1

zz

Raster calculator -( [ln(sca/S)] - 6.90)/5+0.46

-3 - 0 (7.8%)0 - 0.1 (2.5%)0.1 - 0.2 (4.0%)0.2 - 0.5 (29%)0.5 - 1 (56%)1 - 1.5 (0.2%)

Flat (0.5%)Depth to saturation z

Compute• R=0.0002 m/h• =6.90• T=2 m2/hr

Calculating Runoff from 25 mm Rainstorm• Flat area’s and z <= 0

– Area fraction (81 + 1246)/15893=8.3%– All rainfall ( 25 mm) is runoff

• 0 < z rainfall/effective porosity = 0.025/0.2 = 0.125 m– Area fraction 546/15893 = 3.4%– Runoff is P-z*0.2 – (1 / [Sat_during_rain ]) * (0.025 - (0.2 * [z]))– Mean runoff 0.0113 m =11.3 mm

• z > 0.125 m – Area fraction 14020/15893 = 88.2 %– All rainfall infiltrates

• Area Average runoff– 11.3 * 0.025 + 25 * 0.083 = 2.47 mm– Volume = 0.00247 * 15893 * 30 * 30 = 35410 m3

Why Programming

GIS estimation of hydrologic response function

• Amount of runoff generated

• Travel time to outlet

• Distance from each grid cell to outlet along flow path (write program to do this)

• Distance from each point on contributing area– overlay grid to outlet distances with

contributing area.

Steps for distance to outlet program

• Read the outlet coordinates• Read the DEM flow direction grid. This is a set of

integer values 1 to 8 indicating flow direction• Initialize a distance to outlet grid with a no data

value• Convert outlet to row and column references• Start from the outlet point. Set the distance to 0. • Examine each neighboring grid cell and if it drains

to the current cell set its distance to the outlet as the distance from it to the current cell plus the distance from the current cell to the outlet.

1

2

3

1 2 3

Distances to outlet

Programming the calculation of distance to

the outlet

5 1

8 7 6

3 2

4

5 6

5 6

7 7 6

7

7

Direction encoding

42.4

72.4

0

30 72.4

102.4

Recursive Procedure DISTANCE(i,j) do for each neighbor (location in, jn)

If neighbor (in, jn) drains to cell (i,j) Distance from (in, jn) is distance from (i,j) +

distance between cells (accounting for possible diagonals)

Call recursive procedure on the neighbor, DISTANCE(in, jn)

endif end do

Visual Basic Programming in ArcMAP

ReferencesESRI, (1999), ArcObjects Developers Guide:

ArcInfo 8, ESRI Press, Redlands, California.

Zeiler, M., (2001), Exploring ArcObjects. Vol 1. Applications and Cartography. Vol 2. Geographic Data Management, ESRI, Redlands, CA.

Are there any questions ?

AREA 1AREA 1

AREA 2AREA 2

3

12

Idéia para trabalho

Relacionar índice de saturação com índice de vegetação de imagem de satélite

importante georeferenciamento!

Exercício

O modelo hidrológico TOPMODEL utiliza como base a distribuição estatística do índice de saturação em uma bacia hidrográfica. O índice de saturação do TOPMODEL é calculado pela equação abaixo.

Calcule Isat.