October 2011

TERRA Watershed Model 

Hydrologic, Sediment Tran

Chemical Transport Model F

Mark Velleux, Paul Paqu

Aaron Redman, and Robert S
Tool for Antimicrobial Ass

z Screening process for agricultural 

well-established, but not for antim

z Antimicrobials differ from agricult

“[D]etermining human and ecologicaexposure to antimicrobial pesticides types of measurements and models tneeded for pesticides largely applied other plants.” (http://www.epa.gov/op

z TERRA is a tool that can address t

distributed nature of antimicrobial 
Basis for TERRA Develo

z Surface water is often derived from waterz Many water-borne chemical have their so

point of impact: upland source, downstre

z Degree of Interaction between land and re

controlled by the surface component of th

z Need to understand link between rainfall, 

and chemical delivery to receiving waters

z Example: Total Maximum Daily Load (TMD

pesticide exposure concentrations, etc.

z It all starts with rainfall and the hydrologic 
Infiltration

The Hydrologic Cy

Infiltration

Our focus is rinfluence on c
Spatial and Temporal Scales 

z Different processes predominate 

at different space and time scales

z Our focus: watershed scale...

z Land surface and stream channelsz Space scale: ~1 to ~10,000 km

2

z Time scale: storm events, annual+

z Grid scale vs. model performance

z Lumped Parameter: entire watershed 

(Blue Line)

z Semi-Distributed: sub-watershed 

within watershed (Orange Lines)

z Distributed: many cells within 

watershed (Purple Boxes)

z Grid scale: < 1,000 m, often 30-90 m

Condiare reeveryt
Grid Size Alters Computed Sed

30-m 90-m 150-m 210-m 270-m 

1

10

10

10 10

1 10 10 

Drainage area 

A (mi )

S DR

t

2

-1

-2

-2 -1 

SDR = 0.31 A 

(A in mi ) tt-0.3

2

SDR = 0.41 A 

(A in km ) tt-0.3

2

Drainage area 

A (km ) t

2

10

1 10 10 

-1 2
TERRA Watershed Mode

z TERRA: Two-dimensional Exposure Rainz Publication and peer-review history unde

Two-dimensional Runoff Erosion and Exp

z Derived from the CASC2D family of water

developed at Colorado State University (U

z Chemical transport capability derived fro

family of exposure models: IPX (EPA/600

z Fully distributed (grid-based), physically-z Uses GIS to pre/post-process model inpuz Event hydrology, sediment transport, che
Erosion of Upland 

Sources...

Why Was TERRA Deve

z Needed a tool to link upland so

downstream effects at the wate
TERRA Watershed model: Two

Exposure Rainfall-Runoff 

http://www.engr.colostate.edu/%7Epierre/ce_old/Projects/TREX%20W
Model Implementat

z Hydrology:

z Rainfall (Uniform, Distributed, more optiz Infiltration and Transmission Loss (Greez Overland (2-D) and Channel (1-D) Flow (

z Sediment Transport:

z Advection (and Dispersion)z Erosion and Deposition

z Chemical Transport:

z Phase Distribution (Equilibrium Partitionz Transport by Phase: Dissolved, Bound, z Infiltration of Dissolved and Bound (Mob
Some TERRA-Related Model 

Site Area (km

2) Study Purpose 

Macks Creek, ID 32 hydrology Taylor Arroyo, CO 120 effects of military maneuveHickahala/Senatobia, MS 560 hydrology, grid scale Belize River, Belize 1,493 hydrology, extreme floods 

Hassayampa Creek, AZ 1,111 flash flood forecasting Cave Creek, AZ 349 flash flood forecasting 

Spring Creek, CO 25 flash flood modeling Little Washita, OK 536 initial soil moisture, infiltration 
Some TERRA-Related Model 

Site Area (km

2) Study Purpose 

Quebrada Estero, Costa Rica 2.5 hydrology, flooding, urbanization Goodwin Creek, MS 20.7 hydrology, sediment, grid scale effects 

Arkansas River, CO 12,000 hydrology, extreme floods 

California Gulch, CO 30.6 hydrology, sediments, metals (Cd, Cu, Zn) 

Black Earth Creek, WI 0.08 hydrology, flooding Naesung Stream, Korea 1,825 hydrology, sediments 

Experimental Test Plots bench- scale chemicals (RDX, TNT) 
Hydrologic Model Form
TERRA Watershed M

Hydrology Model Form

http://www.engr.colostate.edu/%7Epierre/ce_old/Projects/TREX%20W
Surface Hydrology Processe

z Hortonian (precipitation excess) Ruz Rainfall: gages (points) or radar (arz Interception, Surface Depression Sz Green and Ampt Infiltration/Transmz 2-D Diffusive Wave Overland Flow Rz 1-D Diffusive Wave Channel Routin
Land Surface and Stream 

z Two separate domains (and state v

z Overland Planez Channel Network (nested in overland p

z Overland and channel areas interacz Channel Geometry: general trapezo

Trapezoidal Rectangular Triangular (

z Channel top width (T) 

≤ 80% of grid 

hbank

TB

1

Z

W
Gross Rainfall

z Two Options: (1) point values, (2) gz Point values (gage data):

z Spatial interpolation by Inverse Distan

with user-defined exponent and radius 

z Gages linearly interpolated in time bef

z Gridded values (radar data):

z Pre-processed to match model grid scz Values constant over time interval betw

= ∑( ) ∑( 

n

n

P

nn gross yxi di 1 d ,
Interception and Net R

z Interception is the retention of gros

vegetated (and constructed) surfacrainfall reaches the ground

z Physically, controlled by surface tensiz Typically amounts to ~ 1-2 mm (more oz Represented as rainfall depth retained 

z Net rainfall is gross rainfall minus i

fo

intercepti on fo

,

, x,

y

,

−

=

gross yxgross yx

net yx

ii

i
Infiltration and Transmiss

z Green and Ampt (1-D, vertical):z Single eventsz No soil moisture redistribution (limz For infiltration: neglect 

H

w

( )( 

e

r

cw 

h

F

SHH Kf

θφθ

−=

⎢⎣⎡ −+ +=

1

1
Hydrology: Overland Flo

z Continuity and Momentum, Diffusiv

z Flow depth must exceed depression st

SS

x

h SS

n

S

hq

fi

y

q

x

q

t

h

oxf oyf

yxf

yxyx yx

x

y

−=

∂

∂

−=

=

=

−=

∂

∂

+

∂

∂

+

∂

∂

5.0

,

,,

αα , 

β
Hydrology: Channel Flo

z Continuity and Momentum, Diffusiv

z Flow depth must exceed dead storage 

x

h SS

SR

nA

Q

v

q

t

A

x

Q

oxf

x xfh

L

∂

∂

−=

==

=

∂

∂

+

∂

∂

5.0

1 667.0
Floodplain Couplin

z Controls: water surface elevation a

To Channel To Over
Data Needed To Run The Hyd

z Digital elevation model (DEM) data: z Soil and Sediment characteristics: z Land use characteristics: interceptz Precipitation data (time series): 

igros

z Channel characteristics: topology, z Initial conditions: water depths ove

channel (

hch), and depth of wetting 
Main Hydrology Model Pa

z Infiltration:

z saturated (effective) hydraulic conduct

z Overland and Channel Flow

z Manning 

n

z However, these constants are not r

z Soil characteristics vary with depth an

layer may control hydraulic conductivi

z Manning 

n varies with flow depth, subm

This is why ca
Sediment Transport Model F
Overland Erosion and Dep

Hillslope Erosion...

V
TERRA Watershed M

Sediment Transport Model F

http://www.engr.colostate.edu/%7Epierre/ce_old/Projects/TREX%20W
Surface Sediment Transport 

z Overland: Sheet and rill soil erosionz Channels: bed erosion (degradationz Advection: total load (transport capz Deposition: gravity sedimentation m

probability of deposition

z Surface elevation change over time z Lots of (not fully tested) for cohesiv

cohesive transport...
Point of Departure: Soil Erosi

z Universal Soil Loss Equation: USLE 

→ M

z Implied incipient motion threshold is zeroz Best Use: Long-term annual average eros

CKSLRJ Erosion

= 

****

DEM Hydrau

Climate (Rainfall)

Land Use

Soils 
Overland Erosion (Applie

z Modified Kilinc-Richardson equation for s

erosion (total load 

→ bed load):

v

W

Q t smtonsq

S

f

25500)//(

66.1

⎜⎝⎛

=

−

DEM (and Hydraulics)

Added Incipient Motion Threshold

Hydraulics
Generalized Overland Transp

z Erosion is a function of overland flow and z

k is a function of soil type and erodibilitysize, etc.

z Parameters: 

β = 1.4 (1.0 – 1.8), 

λ = 1.4 (0.9 

z Can express incipient motion threshold a

[

] λβ SqkTLMqt //

=
z Modified Engelund and Hansen equation

[ ] ( ) 

5.0 1 1 

05.0 

⎠⎞ ⎜⎜⎝⎛ − − ⎟⎠⎞ ⎜⎝⎛ − = 

s fcf w 

gdG SVVS GG C

Channel Erosion (1

Hydraulics

Particle Characteristics

Added Incipient Motion Threshold
Data Needed To Run The Sed

z Everything for the hydrologic modez Particle types: 

ds, 

ws, optional: 

τcd, 

z Soil and Sediment characteristics: z Land use characteristics: 

C, 

P

z Soil and Sediment stacks: areal and 

distribution of soil and sediment ch

z Initial conditions: concentrations in 
Main Calibration Param

z Erosion:

z Soil erodibility (

K), erosion threshold a

(

vc) or shear stress for erosion (

τce

)

z Deposition:

z Particle fall velocity (

ws), shear stress 

z Other parameters (but usually less 

z Land cover and management practice z Effective diameter of fine, cohesive so
Grid Scale Matters for E

z Goodwin Creek, MS Case Study: Roz Model grid, soils, and land use resa

upscaled resolutions: 90, 150, 210, 

z Cell aggregation alters land surface 

channel network (drainage density)

z This affects surface hydrology and 

calculations: infiltration, flow volumtime to peak, gross erosion, deposi

z Scale effects for other model param
Effect of Grid Size on 

Nearly complete loss of resolution as grid size increa
Grid Scale Maximum and Av

Decrease While Minimum Slo

MDMDMM

• Flow and sediment transport depend on slo
Erosion and Deposition O

*Net difference between erosion and d
Alteration of Sediment Trans

30 m (0.22 acres)

90 m(2 acres)

150 m(5.5 ac

210 m(11 acres)

270 m(18 acres)

330 m(27 acres)

From which locations do soils really erode?
As Grid Size Increases SDR I

30-m 90-m 150-m 210-m 270-m 

1

10

10

10 10

1 10 10 

Drainage area 

A (mi )

S DR

t

2

-1

-2

-2 -1 

SDR = 0.31 A 

(A in mi ) tt-0.3

2

SDR = 0.41 A 

(A in km ) tt-0.3

2

Drainage area 

A (km ) t

2

10

1 10 10 

-1 2
Chemical Transport Model F
TERRA Watershed M

Chemical Transport Model F

http://www.engr.colostate.edu/%7Epierre/ce_old/Projects/TREX%20W

Surface Elevation Change Over Time

t

z

∂

∂ Soil & 

Sediment ,

t

c

∂

∂

z

c

∂

∂
Model Implementat

z Hydrology:

z Rainfall (Uniform, Distributed, more optiz Infiltration and Transmission Loss (Greez Overland (2-D) and Channel (1-D) Flow (

z Sediment Transport:

z Advection (and Dispersion)z Erosion and Deposition

z Chemical Transport:

z Phase Distribution (Equilibrium Partitionz Transport by Phase: Dissolved, Bound, z Infiltration of Dissolved and Bound (Mob

Plus

reac
Chemical Transport Pro

z Equilibrium partitioning and phase distribz Non-equilibrium reactive particle phase:

z A particle state variable that reacts with the en

being a chemical state variable

z Useful for simulating granular “pure phase” c

weathering, metals release from granules, DU 

z Deposition: gravity sedimentation with op

probability of deposition (Gessler, Krone

z Soil and sediment chemical concentratioz Chemical reactions, products and pathwa

z Chemical state variables and react and intercoz Can be used to simulate non-equilibrium parti
z Chemicals can start transport in one phas

delivered downstream in a different phas

z Phase distribution controlled by partition 

solids concentration (m), DOC binding co

and DOC concentration (CDOC):

Cd = freely dissolved chemical concentration (

rn = chemical concentration sorbed to particle 

chemical concentration (on a pore volume bas

Chemical Partitioning and 

d

n

n p C

r ¶ = ∑

=

+

=

N

n

n px

m

1

1

¶ ¶
z The mass fraction of chemical associated 

(fd), bound (fb), and particulate phase (for 

Multi-Phase Chemical Dis

∑

=

++

=

N

n

n DOC b n px

d

C m

f

1

¶¶1

1

+

=

D

b

C 

f

1

∑

=

++

=

N

n

n DOC b n px

n n px

n p

C m

m

f

1

¶¶1

¶

+

bd 

ff

The total chemical is the sum of all pha
Aspects of Implement

z User-defined number of chemical tyz Two separate domains (and state v

z Overland Plane and soil stackz Channel Network and sediment stack

z Overland and channel areas interacz Soil and sediment stacks allow 3-D 

of chemical distributions

z Granular non-equilibrium phase no

reported chemical concentration (p
Data Needed To Run The Che

z Everything for the hydrologic modez Everything for the sediment model z Chemical characteristics: 

KPOC, KDO

rates, yields, products, and pathwa

z Initial chemical concentrations in s

(overland and channels), soils, and 

z Environmental characteristics: 

CDO

particle type), temperature, pH, win
Chemical Transport Para

z Partitioning and Binding:

z

K

p (KPOC), K

b (KDOC

)

z Process Rates and Mass Transfer C

z Parameters depend on processes simu

z Environmental parameters and con

z POC, DOC, pH, temperature lapse ratez Depend on processes simulated...
TERRA Summary
Summary

z TERRA:

z Grid-based, fully-distributed, physically-based

z Three Components:

z Hydrology (rainfall, surface runoff, and infiltraz Sediment Transport (any number of solids typz Chemical Transport and Fate (any number of c

z GIS-based model set-up using GIS softwa

z input pre-processing (delineate watershed, chz output post-processing (animate model result
What TERRA Can Sim

z Single Rainfall Events and Pseudo-Continz Overland and Channel Flow:

z Bi-directional floodplain water (sediment and c

z Sediment Transport:

z Any number of grain sizes (particle types)z Erosion and deposition overland and in chann

z Chemical Transport and Fate:

z Any number of chemicalsz Equilibrium partitioning (other reactions...)

Å Includes 
More Features Can Be Added 

z Some things TERRA doesn’t simula

z Evapotranspiration, lateral groundwatez Gully erosion, channel initiationz Bank erosion/accretion, meandering, bz Storm sewers (closed conduits)

z However, TERRA is modular in des

can be added as needed over time

z For example, features were added t

allow simulation of distributed poinantimicrobial copper simulations...
Accounting for Sub-Grid Sca

z Landscape features can occur at spatial s

smaller than the model grid scale

z Examples include buildings, sidewalks, r

cover), individual lawns, etc.

z Spatial averages are used to account for 

features within each cell (e.g. 

Kh, Manning 

(

urbanh naturalh imperv

= KK

1

−

f , ,

=

(

1

−

)

+

(1

−

urban lawn lawn impervious 

nfnn

f
Looking Beyond Model Fo

z Model formulation means:

z Processes represented in TERRA com

z To use TERRA as an evaluation too

model application are defined base

z Chemical usesz Physical setting corresponding to usez Landscape specific to setting and uses

z These three factors (uses, setting, a

define the scenario for exposure as
October 2011

Any Questions?