Transcript Spatially Distributed Hydrologic Modeling and Scale Issues

PROCESS-BASED,
DISTRIBUTED
WATERSHED MODELS
•New generation
•Source waters and flowpaths
•Physically based
Objectives
• Use distributed hydrologic modeling to
improve understanding of the
–
–
–
–
Hydrology (flowpaths?)
water balance
streamflow variability
contaminant transport
Objectives, continued
• Test and validate model components and
complete model against internal and
spatially distributed measurements.
– Isotopes are often ideal for cross-validating
model results
Objectives, continued
• Evaluate the level of complexity needed to
provide adequate characterization of
streamflow at various scales.
– Evaluate minimum data requirements
– Evaluate minimum process-level information
Objectives, continued
• Quantify spatial heterogeneity of inputs
(rainfall, topography, soils - where data
exist) and relate this to heterogeneity in
streamflow.
Objectives, continued
• Role of groundwater?
• Fracture flow?
• Back out as residual?
Top Ten Reasons for Modeling
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You don’t need data!
You don’t need to conduct fieldwork!
We’ll model it!
Synthesis
Diagnostic
Prognostic
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
MMS Modular Modeling
System
PRMS on Steroids
•
Conceptually, the framework is an integrated
system of computer software designed to
provide the modeling tools needed to support a
broad range of model applications and model
user skills. The framework supports the
1. application and analysis of existing models,
2. modification and enhancement of existing models for
problem-specific applications,
3. research, devleopment, testing, and application of
new models.
TOP_PRMS
PRMS
National Weather
Service - Hydro17
TOPMODEL
PRECIPITATION-RUNOFF
MODELING SYSTEM
(PRMS)
MODELING OVERVIEW
&
DAILY MODE COMPONENTS
http://wwwbrr.cr.usgs.gov/projects/SW_precip_runoff/
BASIC HYDROLOGIC MODEL
Q
=
P
-
ET

S
Components
Runoff
Precip
Met Vars
Ground Water
Soil Moisture
Reservoirs
Basin Chars
Snow & Ice
Water use
Soil Moisture
3rd HRU DIMENSION
Distributed Parameter
Approach
Hydrologic Response Units - HRUs
HRU Delineation Based on:
- Slope
- Aspect
- Elevation
- Vegetation
- Soil
- Precip Distribution
HRUs
PRMS
Parameters
original
version
Darcy’s Law Applied to Profile
h
i
x
depth
m0
mt
p
Total head = h + x + p
di/dt = K [(h + x + p) / x]
I = x (mt -m0)
[Green & Ampt]
h<<p
PRMS
GROUND-WATER FLOW
Qbase= RCB * Sgw
Equation solved at 15 minute dt and
pro rated to shorter dt as needed
Relation of HRUs and
Subsurface and GW Reservoirs
Surface ( 6 hrus )
Subsurface ( 2 reservoirs )
Ground water (1 reservoir)
PRMS
• HANDLES DISTRIBUTED
PRECIPITATION WELL
• HANDLES INFILTRATION WELL
• DOES NOT DO SO WELL WITH
GROUNDWATER COMPONENT
• SOLUTION: ADD TOPMODEL TO PRMS
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.627668.
“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 semidistributed 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
Topographic index is used to compute the depth to the water
table, which in turn influences runoff generation:
ln(A /tan b )
where ln is the natural logarithm,
A is the area drained
per unit contour or the specific area, and
tan b is the slope
Topographic Index
• 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.
Topographic Definition
Specific catchment area a is the upslope
area per unit contour length [m2/m  m]
Stream line
Numerical Evaluation
with the D Algorithm
Steepest direction
downslope
Proportion flowing to
neighboring grid cell 3
is 2/(1+2)
Proportion
flowing to
neighboring
grid cell 4 is
1/(1+2)
3
Contour line
4
2
1
2
Flow
direction.
5
1
6
8
7
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)
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, tanb.
• The distribution of downslope transmissivity with depth is
an exponential function of storage deficit or depth to the
water table
T  Toe
-
S / m
T  Toe
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]
fz
Topmodel - Assumptions
• The soil profile at each point
has a finite capacity to transport
water laterally downslope.
q cap  T S where T   K dz
e.g. T  KD
or
D
S
Dw

T   K oe
0
Units
D m
z m
K m/hr
f m-1
T
S
q
fz
Ko
dz 
f
m2/hr
dimensionless
m2/hr = m3/hr/m
Topmodel
Specific catchment area a [m2/m  m]
(per unit coutour length)
a/TS or a/S or ln(a/S) or ln(a/tanb)
[tanb=S] is a wetness index that determines
the locations of saturation from below and
soil moisture deficit.
With uniform K and finite D assumption
Ra
a /S
1
w
w
where  '   a / S dA
TS
'
A
z  D (1  w )
z
D
S
Dw
With exponential K assumption
1  aR 
1 a

z   ln   z   ln    where
f  TS 
f S

1
1
R
   lna / S dA and z   (  ln )
A
f
T
Soil moisture deficit = z times porosity
Hydraulic conductivity (K) decreases with depth
K  K oe
f z
where z is local water table depth (m)
f is a scaling parameter (m-1):
shape of the decrease in K with depth
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
12
• Measured
discharge
• Measured
solar radiation
Precipitation (cm)
8
6
4
2
Temperature (oC)
20
10
0
-10
-20
-30
Minimum Daily Temperature at GL4
-40
o
• Measured
temperature
Daily Precipitation at D1
0
Temperature ( C)
• Measured
precipitation
10
30
20
10
0
-10
-20
-30
-40
136
Maximum Daily Temperature at GL4
256
1996
11
131
1997
251
6
126
Calendar Days
246
1998
1
121
241
1999
361
116
236
2000
Calibration
• Calibrate model with discharge in 1996
• Model calibrates internal processes and
parameters to match discharge
• Run model with climate parameters from
modeling years
• Calibration is key
SIMULATED SNOWMELT VS. RUNOFF
Martinelli
Snowmelt (cm)
5
Martinelli Daily Modeled Snowmelt
4
3
2
1
Runoff (cm)
0
7
6
5
4
3
2
1
0
Observed
Modeled
136
256
1996
11
131
251
1997
6
126
246
1998
Calendar Days
1
121
241
1999
361
116
236
2000
Model Verification
• Discharge is almost always used
• Good idea or bad idea? Why?
SENSITIVITY ANALYSIS AND
PARAMETER CALIBRATION
Sensitivity Analysis
• Sensitivity controlled by
optimization function of
observed and modeled runoff
• Sensitive parameters in snow
module: snowmelt factor and
sublimation rate
• Sensitive parameters in
topographic module: scaling
factor and transmissivity
Parameter Calibration
• Rosenbrock optimization
• Same optimization function as
sensitivity analysis
• Parameters in snow module
control magnitude of modeled
runoff
• Parameters in topographic
module control shape of rising
and receding limbs
• Improvement evaluated by
modeling efficiency
SENSITIVITY ANALYSIS AND
PARAMETER CALIBRATION
Martinelli
Parameter
Module
Description
Unit
Range
o
Green Lake 4
Initial
Optimized
Initial
Optimized
MFMAX
snow
maximum non-rain melt factor
mm/(6hrs. C)
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
o
NMF
snow
maximum value of negative melt factor
mm/(6hrs. C)
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
o
C (or F)
-10-10
*
*
*
*
C (or F)
-10-10
*
*
*
*
monthly maximum temperature lapse rate
Tmin_lap
temp
monthly minimum temperature lapse rate
o
Tmax_adj
temp
MRU maximum temperature adjustment
o
C (or F)
-10-10
0
0.0782
0/0/0
1/1/-1
C (or F)
-10-10
0
0.484
0/0/0
1/1/-1
0.04-0.008
0.0055
0.00486
0.0055
0.0055
0.01-5
0.02
0.02
0.02/0.02/0.02
0.02/0.02/0.02
0-10
0.04
0.0539
0.04/0.05/0.05
0.19/0.23/0.23
Tmin_adj
temp
MRU minimum temperature adjustment
o
hamon_adj
potet
monthly temperature coefficient-Hamon
none
xko
topc
surface vertical hydraulic conductivity
mh
szm
topc
value of M in recession equation
m
-1
2 -1
to
topc
mean MRU value of ln(To)
ln(m h )
-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
Mean Value of ln(To)
MRU1
0.15
MRU2
0.1
2 -1
0.2
to (ln(m h ))
SZM (m)
0.25
MRU3
0.05
0
LV
MART
0
-1
-2
-3
-4
-5
-6
-7
MRU2
MRU3
LV
GL4
Available Water Capacity of Root Zone
MART
GL4
Initial Root Zone Deficit
0.06
2.5
2
1.5
MRU1
0.05
MRU1
MRU2
0.04
MRU2
0.03
0.02
MRU3
sro
srmax (m)
MRU1
MRU3
1
0.5
0.01
0
0
LV
MART
GL4
LV
MART
GL4
SIMULATED SNOWMELT VS. RUNOFF
Green Lake 4
SNowmelt (cm)
5
Modeled Daily Snowmelt at GL4
4
3
2
1
0
Runoff (cm)
4
Observed
Modeled
3
2
1
0
134
254
1996
9
129
249
1997
4
124
244
364
1998
Calendar Day
119
239
1999
359
114
2000
234
Water Balance Components (cm)
MONTHLY WATER BUDGET
70
60
50
40
30
20
10
0
-10
-20
Martinelli
5
8
1
2
5
Runoff
Storage
8
1
2
5
8
ET
Snowmelt
1
2
5
8
1
2
5
8
Water Balance Components (cm)
70
60
Green Lake 4
Runoff
Storage
ET
Snowmelt
50
40
30
20
10
0
-10
5
8
1
2
5
-20
1996
1997
8
1
2
5
8
1
1998
Year/Month
2
5
1999
8
1
2
5
2000
8
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.
MODFLOW
• THE IDEAL SITUATION FOR
GROUNDWATER TYPES WOULD BE
TO COMBINE PRMS WITH MODFLOW
• MODFLOW-PRMS CONNECTION IS
BEING DONE TODAY
• BETA VERSIONS NOT YET
AVAILABLE, BUT SOON
Are there any questions ?
AREA 2
3
AREA 1
12
WARNING: TAKE ALL
MODELS WITH A GRAIN OF SALT!
DON’T HAVE TOO MUCH
CONFIDENCE IN MODELS!
REFERENCES
• Leavesley, G.H., Lichty, R.W., Troutman, B.M., and Saindon, L.G.,
1983, Precipitation-runoff modeling system--Users manual: U.S.
Geological Survey Water-Resources Investigations Report 83-4238,
207 p.
• Leavesley, G.H., Restrepo, P.J., Markstrom, S.L., Dixon, M., and
Stannard, L.G., 1996, The modular modeling system (MMS)--User's
manual: U.S. Geological Survey Open-File Report 96-151, 142 p.
• Mastin, M.C., and Vaccaro, J.J., in press, Watershed models for
decision support in the Yakima River Basin, Washington: U.S.
Geological Survey Open-File Report..
• Ryan, Thomas, 1996, Global climate change response program-Development and application of a physically based distributed
parameter rainfall runoff model in the Gunnison river basin: United
States Department of Interior, Bureau of Reclamation, 64 p.
Topmodel - Assumptions
Specific catchment area a [m2/m  m]
(per unit contour length)
• The actual lateral discharge is
proportional to specific
catchment area.
q act  R a
• R is
– Proportionality constant
– may be interpreted as “steady state”
recharge rate, or “steady state” per
unit area contribution to baseflow.
D
S
Dw
Units
a m
R m/hr
qact m2/hr = m3/hr/m
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
q
Ra
w  act 
q cap T S
D
S
• Saturation when w > 1.
a
1
i.e.

TS R
Dw
ALGORITHM FOR OVERLAND AND
SUBSURFACE FLOW
Subsurface Flow (Darcy Law)
qi = T0 tanb exp(-Si/m)
Si = S0 + m[ - ln(ai/T0 tanb)]
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