Post on 22-Apr-2015
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.