process-based, distributed watershed models

PROCESS-BASED,DISTRIBUTED

WATERSHED MODELS

•New generation•Source waters and flowpaths•Physically based

Objectives• Use distributed hydrologic modeling to improve

understanding of the hydrology, water balance and streamflow variability.

– Test and validate model components and complete model against internal and spatially distributed measurements.

– Evaluate the level of complexity needed to provide adequate characterization of streamflow at various scales.

– Quantify spatial heterogeneity of inputs (rainfall, topography, soils - where data exist) and relate this to heterogeneity in streamflow.

– Role of groundwater? Fracture flow?

Distributed models incorporate the effects of topography through direct used of the digital elevation data during computation, along with process-level knowledge.

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

TOP_PRMS

PRMS

National Weather Service - Hydro17

TOPMODEL

Terrain Based Runoff Generation Using 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

Topographic index is used to compute the depth to the water table, which in turn influences runoff generation: ln(A /tan )where ln is the natural logarithm, A is the area drained per unit contour or the specific area, and tan is the slope

Regions of the landscape that drain large upstream areas or that are very flat give rise to high values of the index; thus areas with the highest values are most likely to become saturated during a rain or snowmelt event and thus are most likely to be areas that contribute surface runoff to the stream.

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 DefinitionSpecific 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)

zfoeKK

Hydraulic conductivity (K) decreases with depth

where z is local water table depth (m) f is a scaling parameter (m-1):

shape of the decrease in K with depth

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 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.

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.

Topmodel - Assumptions

• 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

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

ALGORITHM FOR OVERLAND AND SUBSURFACE FLOW

Subsurface Flow (Darcy Law)qi = T0 tan exp(-Si/m)

Si = S0 + m[ - ln(ai/T0 tan)]

where is the mean value of wetness index over the basin

Overland Flow (Green-Ampt Procedure)qi = f(p, K0)

where p is precipitation (snowmelt) intensity and K0 is saturated hydraulic conductivity

GL4 CASE STUDY: OBJECTIVES

• to test the applicability of the TOP_PRMS model for runoff simulation in seasonally snow-covered alpine catchments

• to understand flowpaths determined by the TOP_PRMS model

• to validate the flowpaths by comparing them with the flowpaths determined by tracer-mixing model

RESAERCH SITE

GIS WEASEL

• Simplify the treatment of spatial information in modeling by providing tools (a set of ArcInfo 8 commands) to:

(1) Delineate the basin from GRID DEM

(2) Characterize stream flow direction, stream channels, and modeling response unit (MRU)

(3) Parameterize input parameters for spatially distributed models such as TOPMODEL and TOP_PRMS model

PROCEDURES FOR DELINEATION AND PARAMETERIZATION

• DEM (10 m) was converted from TIN to GRID format using ArcInfo 8 commands

• a pour-point coverage was generated using location information of gauging stations

• DEM and the pour-point coverage were overlaid to delineate the basin

• DEM slope and direction were re-classified to extract the drainage network

• a base input parameter file and re-classified DEM were used to derive parameters needed for TOP_PRMS model

DELINEATION FOR GREEN LAKE 4

• Delineated basin area: 220ha

• Matches the real basin

• Three HRU (MRU) delineated (one stream tributary one MRU)

INPUT DATA

• Measured discharge

• Measured precipitation

• Measured temperature

• Measured solar radiation

Maximum Daily Temperature at GL4-40-30-20-10

0102030

136 256 11 131 251 6 126 246 1 121 241 361 116 236

Calendar Days

Tem

pera

ture

(o C

)

1997 1998 1999 20001996

Daily Precipitation at D1

0

2

4

6

8

10

12

Prec

ipita

tion

(cm

)

Minimum Daily Temperature at GL4

-40

-30

-20

-10

0

10

20T

empe

ratu

re (

o C)

SIMULATED SNOWMELT VS. RUNOFFGreen Lake 4

0

1

2

3

4

134 254 9 129 249 4 124 244 364 119 239 359 114 234

Calendar Day

Ru

no

ff (

cm) Observed

Modeled

1997 1998 1999 20001996

Modeled Daily Snowmelt at GL4

0

1

2

3

4

5

SN

ow

mel

t (c

m)

MONTHLY WATER BUDGET

-20

-10

0

10

20

30

40

50

60

70

5 8 1 2 5 8 1 2 5 8 1 2 5 8 1 2 5 8

Wa

ter B

ala

nce C

om

po

nen

ts (

cm

)

Runoff ETStorage Snowmelt

Martinelli

-20

-10

0

10

20

30

40

50

60

70

5 8 1 2 5 8 1 2 5 8 1 2 5 8 1 2 5 8

Year/Month

Wa

ter B

ala

nce C

om

po

nen

ts (

cm

)

Runoff ETStorage Snowmelt

1996 1997 1998 1999 2000

Green Lake 4

SENSITIVITY ANALYSIS AND PARAMETER CALIBRATION

Martinelli Green Lake 4Parameter Module Description Unit Range

Initial Optimized Initial Optimized

MFMAX snow maximum non-rain melt factor mm/(6hrs. oC) 0.5-2.0 1.2 0.8 1.2/1.2/1.2 1.2/1.2/1.2

MFMIN snow minimum non-rain melt factor mm/(6hrs.oC) 0.2-1.0 0.1 0.1 0.1/0.1/0.1 0.1/0.1/0.1

NMF snow maximum value of negative melt factor mm/(6hrs.oC) 0.05-0.5 0.15 0.05 0.15/0.15/0.15 0.15/0.15/0.15

PLWHC snow snow liquid water holding capacity none 0.01-0.3 0.05 0.05 0.05/0.05/0.05 0.05/0.05/0.05

SUBRATE snow average daily snowpack sublimation rate In/day 0-0.2 0.01 0.00065 0.01/0.01/0.01 0.01/0.01/0.01

TIPM snow antecedent temperature index none 0.2-0.6 0.3 0.3 0.3/0.3/0.3 0.3/0.3/0.3

WEI snow initial snow water equivalent in 0-1000 65 97 5/20/20 25/25/25

Tmax_lap temp monthly maximum temperature lapse rate oC (or F) -10-10 * * * *

Tmin_lap temp monthly minimum temperature lapse rate oC (or F) -10-10 * * * *

Tmax_adj temp MRU maximum temperature adjustment oC (or F) -10-10 0 0.0782 0/0/0 1/1/-1

Tmin_adj temp MRU minimum temperature adjustment oC (or F) -10-10 0 0.484 0/0/0 1/1/-1

hamon_adj potet monthly temperature coefficient-Hamon none 0.04-0.008 0.0055 0.00486 0.0055 0.0055

xko topc surface vertical hydraulic conductivity mh-1 0.01-5 0.02 0.02 0.02/0.02/0.02 0.02/0.02/0.02

szm topc value of M in recession equation m 0-10 0.04 0.0539 0.04/0.05/0.05 0.19/0.23/0.23

to topc mean MRU value of ln(To) ln(m2h-1) -6-4 -2 -2.44 -2/-2/-4 -3/-3/-6

srmax topc available water capacity of root zone m 0-5.0 1.0 0.0051 1/1/2 0.56/0.56/1.12

sro topc initial value of root zone deficit m 0-1.0 0.05 0.0 0.05/0.05/0.05 0.05/0.05/0.05

COMPARISON OF TOPOGRAPHIC PARAMETERS IN GLV WITH LOCH VALE

M in Recession Equation

0

0.05

0.1

0.15

0.2

0.25

LV MART GL4

SZM

(m) MRU1

MRU2

MRU3

Mean Value of ln(To)

-7-6-5-4-3-2-10

LV MART GL4

t o (

ln(m

2 h-1))

MRU1

MRU2

MRU3

Available Water Capacity of Root Zone

0

0.5

1

1.5

2

2.5

LV MART GL4

srm

ax (

m) MRU1

MRU2

MRU3

Initial Root Zone Deficit

0

0.01

0.02

0.03

0.04

0.05

0.06

LV MART GL4

sro

MRU1

MRU2

MRU3

PROBLEM ON RUNOFF SIMULATION

• Runoff peaks in May and June failed to be captured by the model

• The modeled runoff tells us that a large amount of snowmelt was infiltrated into soil to increase soil water storage

• However, the reality is that there were runoff peaks in May and June as observed

• It is hypothesized that a large amount of the snowmelt produced in May and June may contribute to the stream flow via overland and topsoil flowpaths due to impermeable barrier of frozen soils and basal ice

Summary and Conclusions

• Modeling system centered on TOPMODEL for representation of spatially distributed water balance based upon topography and GIS data (vegetation and soils).

• Capability to automatically set up and run at different model element scales.

• Encouraged by small scale calibration, though physical interpretation of calibrated parameters is problematic.

• Large scale water balance problem due to difficulty relating precipitation to topography had to be resolved using rather empirical adjustment method.

• Results provide hourly simulations of streamflow over the entire watershed.

DON’T HAVE TOO MUCHCONFIDENCE IN MODELS!

WARNING: TAKE ALLMODELS WITH A GRAIN OF SALT!