Índice de saturação topográfico

1. Índice de saturação topográfico Walter Collischonn

2. Indicador • wetness index • topographic index • saturation index • índice de saturação • índice de saturação do modelo TopModel

3. Processos de geração de escoamento From http://snobear.colorado.edu/IntroHydro/geog_hydro.html

4. Processos de geração de escoamento P Infiltration excess overland flow aka Horton overland flow f P qo P f Partial area infiltration excess overland flow P P qo P f P Saturation excess overland flow P qo P qr qs

5. 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]

6. Região saturada de acordo com a época do ano: • preto: verão • cinza claro: outono • cinza escuro: inverno • [Dunne and Leopold, 1978]

7. 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

8. Índice de saturação

9. Digital Elevation Model based Hydrologic Modeling Outline • Topography and Physical runoff generation processes (TOPMODEL) • Raster calculation of wetness index • Raster calculation of TOPMODEL runoff • Extendability of ArcGIS using Visual Basic Programming

10. 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.”

11. 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

12. Saturation in zones of convergent topography

15. 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.

16. Outros usos do índice topográfico • relacionar com ndvi • relacionar com evapotranspiração • relacionar com início de um rio

17. Obtenção do índice topográfico • equação • variáveis • passos

18. partindo do mnt filtrado

19. TOPMODEL a = runoff do idrisi teoricamente a = A/c e é dado em metros não parece ser importante

20. declividade em percentual dividindo por 100 chegamos a tg(b)

21. a/tgb

22. ln(a/tgb)

24. Histograma do índice ln(a/tgb)

25. Specific catchment area a is the upslope area per unit contour length [m2/m  m] Stream line Contour line Upslope contributing area a Numerical Evaluation with the D Algorithm Topographic Definition 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)

26. 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

27. 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 • 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]

28. D Dw S Topmodel - Assumptions • The soil profile at each point has a finite capacity to transport water laterally downslope. e.g. or

29. D Dw S Topmodel - Assumptions Specific catchment areaa [m2/m  m] (per unit contour length) • The actual lateral discharge is proportional to specific catchment area. • R is • Proportionality constant • may be interpreted as “steady state” recharge rate, or “steady state” per unit area contribution to baseflow.

30. D Dw S Topmodel - Assumptions Specific catchment areaa [m2/m  m] (per unit coutour length) • Relative wetness at a point and depth to water table is determined by comparing qact and qcap • Saturation when w > 1. i.e.

31. D Dw S Topmodel Specific catchment areaa [m2/m  m] (per unit coutour length) z

32. Slope Specific Catchment Area Wetness Index ln(a/S) from Raster Calculator. Average, l = 6.91

33. Numerical Example • Compute • R=0.0002 m/h • l=6.90 • T=2 m2/hr Given • Ko=10 m/hr • f=5 m-1 • Qb = 0.8 m3/s • A (from GIS) • ne = 0.2 Raster calculator -( [ln(sca/S)] - 6.90)/5+0.46

34. 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

35. Why Programming

36. 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.

37. 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.

38. 4 3 2 5 1 6 7 8 Direction encoding 1 2 3 1 7 6 5 2 7 6 5 3 6 7 7 Distances to outlet Programming the calculation of distance to the outlet 102.4 72.4 30 72.4 42.4 0

40. Visual Basic Programming in ArcMAP References ESRI, (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.

41. AREA 2 3 AREA 1 12 Are there any questions ?

42. Idéia para trabalho • Relacionar índice de saturação com índice de vegetação de imagem de satélite • importante georeferenciamento!

43. 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.