Digital Elevation Model based Hydrologic Modeling Outline Physical runoff generation processes Modeling infiltration excess Modeling saturation excess (TOPMODEL) Semi-distributed hydrologic modeling with TOPNET

Physical Processes involved in Runoff Generation From http://snobear.colorado.edu/IntroHydro/geog_hydro.html

Runoff generation processes Infiltration excess overland flow aka Horton overland flow P P f P qo f Partial area infiltration excess overland flow P P P qo f P Saturation excess overland flow P P qo qr qs

Runoff generation processes contd. Subsurface stormflow P P P qs Perched subsurface stormflow P Horizon 1 Horizon 2 P qs P

Seasonal variation in saturated area

Dominant processes of hillslope response to rainfall (Dunne 1978) Thin soils; gentle concave footslopes; wide valley bottoms; soils of high to low permeability Direct precipitation and return flow dominate hydrograph; subsurface stormflow less important Horton overland flow dominates hydrograph; contributions from subsurface stormflow are less important Variable source concept Subsurface stormflow dominates hydrograph volumetrically; peaks produced by return flow and direct precipitation Topography and soils Steep, straight hillslopes; deep,very permeable soils; narrow valley bottoms Arid to sub-humid climate; thin vegetation or disturbed by humans Humid climate; dense vegetation Climate, vegetation and land use

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

Modeling infiltration excess Rigorous – Richards equation w r=w-f z f t1 t2 t3  Generally requires numerical solution

Modeling infiltration excess Conceptual, e.g. Green and Ampt, Horton, Philip w r=w-f z fc(t) or fc(F) if w > fc then f=fc, r=w-f else f=w, r=0 f fc  t or F

Modeling infiltration excess Empirical, e.g. SCS Curve Number method CN=100 90 80 70 60 50 40 30 20

SCS Curve Number, CN Relates storm rainfall and runoff (0<CN<100) Computed as a function of soil and land use using a lookup table All soils of the US grouped into four Hydrologic Soil Groups (A, B, C, D) where A is freely draining sand and D is poorly draining clay Hydrologic Soil Group is a component property in Statsgo

SCS Curve Number Grid

Cell based discharge mapping using weight grid in flow accumulation Radar Precipitation grid Soil and land use grid Runoff grid from raster calculator operations implementing runoff generation formula’s Flow accumulation using runoff grid as weights from hydrology toolbar

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

Numerical Evaluation with the D Algorithm Specific catchment area a is the upslope area per unit contour length [m2/m  m] Numerical Evaluation with the D Algorithm Topographic Definition Upslope contributing area a Stream line Contour line 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 To lateral transmissivity [m2/h] S local storage deficit [m] z local water table depth [m] m a parameter [m] f a scaling parameter [m-1]

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

Topmodel - Assumptions Specific catchment area a [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. S Dw D

Topmodel - Assumptions Specific catchment area a [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. S Dw D

Topmodel z D Dw S Specific catchment area a [m2/m  m] (per unit coutour length) S Dw D z

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

Numerical Example Given Compute Ko=10 m/hr R=0.0002 m/h f=5 m-1 l=6.91 Qb = 0.8 m3/s A (from GIS) Compute R=0.0002 m/h l=6.91 T=2 m2/hr Raster calculator -( [ln(sca/S)] - 6.91)/5+0.46

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 = 0.025/0.25 = 0.1 m Area fraction 410/15893 = 2.5% Runoff is P-z*0.25 (1 / [Calculation3 ]) * (0.025 - (0.25 * [depthtosat])) Mean runoff 0.0117 m =11.7 mm z > 0.1 m Area fraction 14156/15893 = 89.1 % All rainfall infiltrates Average runoff 11.7 * 0.025 + 25 * 0.083 = 2.37 mm Volume = 0.00237 * 15893 * 30 * 30 = 33900 m3