Macroscale hydrological modeling
Dennis P. LettenmaierDepartment of Civil and Environmental Engineering
University of Washington
IAI La Plata Basin Graduate Summer School
Itaipu, Brazil
November 10, 2009
Outline of this talk
1. Macroscale hydrological modeling strategy
2. Some aspects of model structure – the Variable Infiltration Capacity model as an example
3. Model calibration
4. Model evaluation and testing
1. Macroscale modeling strategy
Use of Models
•Precipitation
•Temperature
•Radiation
•Vegetation
•Atmospheric model output
Land Surface Hydrology Model (VIC)
•Forecasting
•Land Use change assessment
•Climate change assessment
•Wildfire Forecast
Forcings ModelingApplications
Differences between macro-scale land surface hydrology models and traditional hydrology models
Land Surface Scheme
Traditional Hydrology model
Purpose For inclusion in the GCM as a land surface scheme
Flood forecasting, water supply
Fluxes Both water and energy balance
Only water balance
Model More physically based formulation
Mainly conceptual model (i.e. parameters not physically based)
Vegetation Explicitly simulated Implicitly simulated
Run Grid-based Lumped parameter or fully distributed
Function Dynamic coupling with GCM or off-line simulations
Off line simulations
The Variable Infiltration Capacity (VIC) macroscale hydrology model
Liang et al. (JGR, 1994 – standard reference for model)
2-layer soil vegetation model designed to be dynamically coupled to GCMs or weather models (e.g. at 5 degree lat lon resolution)Parameterized infiltration and base flow schemesSingle layer energy balance snow modelPhysically-based vegetation model including canopy effectsPhysically-based evaporation based on the Penman/Monteith approach
Development of the VIC Model
Historic Use of the Model
Despite the original conception of the model, until very recently the vast majority of the hydrologic research using the model has implemented the model in an “off-line” configuration.
That is, driving data is produced (either from observations or simulations) and the model is run as a stand alone tool often as a “black box” used to interpret the hydrologic implications of the variations in the driving data.
Most of the improvements in the model have come about because of the discovery of shortcomings of the model during the course of investigations focused on particular “off line” applications.
In the last several years, as computational constraints have been relaxed somewhat and the importance of the land surface state as an important driver of atmospheric circulation and precipitation variability, more attention has been focused on using the tool in a dynamic setting. Precipitation and temperature bias remain difficult elements of fully coupled models to resolve. (I.e. it is often difficult to realize the benefits of an improved land surface scheme if precipitation or temperature in the coupled application are strongly biased for other reasons.)
Simulation Modes
Water balance:Assumes that surface temperature = surface air temperature, hance ground het flux = 0, and once Lh is computed (given Rnet, surface wind, humidity, and vegetation properties), Ls is by difference (hence balance closes by construct)
Energy balance:Iterates on surface temperature that closes the water balance (Ts is a term in emitted longwave, and latent and sensible heat). This formulation is more physically correct than water balance, however it does come at a much greater (typically order of magnitude) computational requirement.
Reference:http://www.hydro.washington.edu/Lettenmaier/Models/VIC/Technical_Notes/NOTES_model_modes.html
Modelo de Nieve
Land Surface Hydrology Model
PNW
CA CRB
GB
1/8thDeg.
1/8th
Deg.
12 km
12 k
m
Water and Energy balances
Water Balance( )
( )W W K W
D Wt z z z
Wn=Soil MoistureKn(W)=Hydraulic ConductivityDn(W)=DiffusivityZn=Soil Depthn= layer
Qb= BaseflowQd= RunoffP= PrecipitationE= Evapotranspiration
E1= bare soil Ec =Canopy Et=Transpiration
z0z1
z2
K1
K2
Qb
D1
D2
PEc
Qd
E1Et
z3
11)()(. 1
1zz z
DKERPzt
22)()(. 2
2zz z
DKERPzt
bzz Qz
DKzzt
22)()().( 23
3
Runoff (Qd)
Fractional Area (A)As As’ 1
Infi
ltrat
ion
Cap
acity
(i)
io
im
io+P
W1
W1Qd i=Infiltrationim=Maximum Infiltrationbi=Shape parameterA=Fraction of the areaAs=fraction of the saturated areaW1=Soil Moisture in Layer 1io=specific point of I capacity
Baseflow(Qb)
Ds=Fraction of Dm
Dm=Maximum subsurface flowW2
c=Maximum soil moisture content
Ws=Fraction of W2c
W2= Soil moisture in layer 2W2
- Soil moisture in layer 2
Layer 2 Soil Moisture (W2)
b
W2cWsW2
c
Dm
Ds Dm
2
2 22
2 2 2
cs m s m s
b mc c cs s s
D D D D W W WQ W D
W W W W W W
Insaturated
Saturated
0
20
40
60
80
100
120
0 250 500
Lower Soil Layer Content (mm)
Ba
se
flo
w (
mm
)
Three Parameter Non-linear Baseflow Relationship The modeler selects Dmax, Ds, Ws. (Wmax is determined by the soil parameters.) Ws and Ds determine the x and y positions of the linear threshold in the curve. Dmax determines the maximum base flow when the lower layer is fully saturated.
Dmax = 100Ds = 0.2Ws = 0.8
Vegetation (Canopy surface), topography, snow, soil
representations
High Elevation Band
Equal Area Elevation Bands
Medium Elevation Band
Low Elevation Band
The number of bands is determined by the elevation gradient and a specified interval used in pre-processing (e.g. 1500 m/ 500m in the example).
Having determined the number of bands, the bands are forced to have equal area by ranking the pixels in a high resolution DEM and dividing them into groups within the cell boundaries with equal numbers of pixels.
Temperature and precipitation are different in each band, but are keyed to the driving data for each cell.
In current model implementations the mosaic of vegetation types is identical in each elevation band.
Representation of the Canopy and Canopy Storage
Canopy Storage (determined by LAI)
Canopy evap (wet canopy or snow)Transpiration (dry canopy)
Canopy “throughfall” occurs when additional precipitation exceeds the storage capacity of the canopy (rain or snow) in the current time step.
Precipitation
Vegetation Characteristics
The model represents a particular vegetation class primarily by:
•Canopy albedo
•Seasonal Leaf Area Index (LAI)– can be unique for each cell.
•Canopy storage (assumed to be a function of LAI)
•Characteristic vegetation roughness and displacement height
•Stomatal resistance (evaporative resistance associated with transpiration)
•Architectural resistance (evaporative resistance related to humidity gradient within the canopy structure as compared to the free air)
•Rooting depth
•Radiation attenuation factor (used to attenuate incoming solar radiation)
ET
wet canopy evaporation
dry canopy transpiration
bare soil surface evaporation
pEE
)/1(
/)(
as
aapnp rrs
rdcGRsE
Evapotranspiration in VIC model
Evaporation and TranspirationEvaporation from wet vegetation and transpiration from dry vegetation are estimated by the physically-based Penman Monteith approach. The equation has the form:
Evap = (Term1 + Term 2) / (Term 3)
(see e.g. equation 3 in Wigmosta et al. 1994)
Term 1 is net radiation term, which is primarily a function of incoming solar radiation (cloudiness) and the slope of the saturated vapor pressure-temperature curve.
Term 2 is the vapor pressure deficit term which is primarily a function of the humidity and temperature of the air, scaled by an aerodynamic resistance term related primarily to wind speed and surface roughness.
Term 3 is a function of the slope of the saturated vapor pressure and resistance terms associated with canopy resistance and aerodynamic resistance
Bare soil calculations are similar but include a resistance term related to the soil’s ability to deliver moisture to the surface (a function of upper layer moisture content and soil characteristics)
)/1(
/)(
as
aapnp rrs
rdcGRsE
Key drivers such as net radiation budget and wind speed are calculated explicitly for each component of the land surface (canopy, understory, bare soil, and snow surface). Wet or dry vegetation is incorporated by selecting the canopy resistance term (same equation).
Overall Modeling Structure for Evaporation Calculations
Snow
No Snow
Wet Vegetation
Dry Vegetation
Overstory
Understory
Energy Balance Snow Model
http://www.ce.washington.edu/pub/WRS/WRS161.pdf
Partitioning of Rain and Snow
The model currently uses a very simple partitioning method to determine the initial form of the precipitation.
E.g.
RainMin= 0.0 CSnowMax = 2.0 C
If T <= RainMin then 100% snow.
If T >= SnowMax the 100% rain.
Values in between are a linear interpolation between the two values. E.g. simulated precipitation at 0.5 degrees C would produce 75% snow, 25% rain.
Source: Storck, P., 2000, Trees, Snow and Flooding: An Investigation of Forest Canopy Effects on Snow Accumulation and Melt at the Plot and Watershed Scales in the Pacific Northwest, Water Resources Series Technical Report No. 161, Dept of CEE, University of Washington. http://www.ce.washington.edu/pub/WRS/WRS161.pdf
Effects of Forest Canopy on Snow Accumulation
Loss of canopy increases the snow water equivalent and increases the rate of melt.
Representation of Soil Column
~10cm
~20cm
~1.5 m
Infiltration and surface runoff
Interflow processes
Baseflow processes
True depth and composition of the soil column is usually imperfectly known.
Porosity, Ksat, field capacity, wilting threshold, residual capacity and other soil characteristics are determined from estimates of soil composition
Storage capacity of eachlayer is depth times porosity.
Rooting distribution is specified in the vegetation file as the fraction of the roots occurring in each depth range. The model then calculates the fraction of roots in each soil layer. Thus the rooting depths and soil layers can be varied independently.
Model Combinatorial AlgorithmEach cell is completely independent of the others. The model solves the water and energy balance independently for each elevation band and vegetation type within the cell (plus bare soil).
Band 1
Band 2
.
.
.
Band N
Then in each time step the model creates a linear combination of each variable according to the fraction of the cell area that is associated with each band and veg type.
Veg 1..Veg M
Veg 1..Veg M
Veg 1..Veg M
Area fraction weightingby variable
FinalModel Output
Value
Energy Balance
Rn= Absorbed Radiation f(Ts,Albedo, Sw, Lw)H=Sensible Heat Flux f(rw,Ta, Ts, a ,Cp)wLeE=Latent Heat Flux f(ro, W,Ts)G=Ground Heat Flux f(Ts, T1, thermal conductivity, Z1)Hs=Change Energy Storage f(a,Cp, Ts)
Iteratively solved for Ts
n w e sR H L E G H
Sub-daily air temperature (°C) Surface albedo (fraction) Atmospheric density (kg/m3) Precipitation (mm) Atmospheric pressure (kPa) Shortwave radiation (W/m2) Daily maximum temperature (°C) Daily minimum temperature (°C) Atmospheric vapor pressure (kPa) Wind speed (m/s)
Below is an example of a 4 column daily forcing file:
Pcp Tmax Tmin Wind6.000 22.560 6.440 3.320 1.775 20.800 4.480 1.260 0.000 25.870 4.360 0.970 0.000 28.470 4.610 1.400 0.000 26.130 8.680 0.880 0.500 25.280 6.860 1.770 ...
Model Forcing Data
Forcing Data PreprocessorThe driving data for the model can be explicitly given as a time series, or the model will construct a set of complete forcings from a set of limited daily observations (usually daily precip, tmax, tmin, wind speed) following methods developed by Thornton and Running (1997).
Hourly temperature data (needed for the hourly snow model simulations) are reconstructed based on empirical relationships to Tmax and Tmin.
Cloudiness and solar radiation attenuation and incoming long wave radiation are estimated via the diurnal temperature range.
Dew point temperature is related to daily minimum temperature with a long wave radiation correction.
How to get the Forcings and Parameters
长江流域
黄河流域
淮河流域
2604 60km×60km grid cell
Distribution of meteorological station in China
------ Station
Preprocessing Regridding
Lapse Temperatures
Correction to RemoveTemporal
Inhomogeneities
HCN/HCCDMonthly Data
Topographic Correction forPrecipitation
Coop Daily Data
PRISM MonthlyPrecipitation
Maps
Schematic Diagram for Data Processing of VIC Meteorological Driving Data
Preprocessing Regridding
Lapse Temperatures
Correction to RemoveTemporal
Inhomogeneities
HCN/HCCDMonthly Data
Topographic Correction forPrecipitation
Coop Daily Data
PRISM MonthlyPrecipitation
Maps
Preprocessing Regridding
Lapse Temperatures
Correction to RemoveTemporal
Inhomogeneities
HCN/HCCDMonthly Data
Topographic Correction forPrecipitation
Coop Daily Data
PRISM MonthlyPrecipitation
Maps
Schematic Diagram for Data Processing of VIC Meteorological Driving Data
Result:Daily Precipitation, Tmax, Tmin
1915-2003
Overview of Data Processing Steps•Collect observed station data and preprocess wind data
•Reformat station data to an irregularly spaced gridded file.
•Regrid the raw station information to the VIC lat lon grid.
•Quality control to remove implausible values
•Adjust gridded raw station data to remove station inhomogeneities using HCN or HCDN data sets as a standard (optional)
•Topographic adjustment of precipitation data (using PRISM data as a standard).
•Reformatting to final file format needed by VIC.
Regridding Details
Symap regridding algorithm accounts for station proximity via an inverse square weighting, but also accounts for the independence of the stations from one another.
The interpolation scheme ensures that collectively these two nearly coincident stations are assigned about the same weight as each of the other two stations.
Hydro1k (all continents)
http://edc.usgs.gov/products/elevation/gtopo30/hydro/index.html
Digital Elevation Models• Hydro1k: equal area projection, 1 km res.• Gtopo30 or SRTM30: geographic projection, 30
arc-secondshttp://edc.usgs.gov/products/elevation/gtopo30/gtopo30.htmlhttp://topex.ucsd.edu/WWW_html/srtm30_plus.html
Land Cover Classification
• U. Maryland AVHRR, 1 km global product– http://glcf.umiacs.umd.edu/data/landcover/
• IGBP, 3 arc-minute global product– http://landcover.usgs.gov/globallandcover.php
Soil Information• UNESCO/FAO global soil maps
– http://www.lib.berkeley.edu/EART/fao.html
Example:
Basin Delineation
Method 1:
• Use Hydro1k Basin Delineations
• Best for larger basins faster process
Method 2:• Use ArcInfo Functions to Delineate a Basin• Any size basin – all small watersheds• Uses a high-resolution DEM to delineate
Why process VIC output?
What we typically want:• Hydrograph at various points in stream network• Monthly average water and/or energy budget of a basin
What VIC (currently) gives us:• Moisture and energy fluxes and states for individual grid cells• Output interval = model time step
We generally must process VIC’s output before we can use it
VIC assumptions & routing
• Most other models run in “image” mode– For each time step, they compute fluxes and state
for all grid cells
• VIC currently runs in “vector” mode– For each grid cell, it runs the entire simulation
period (all time steps)– This means each grid cell’s water and energy
balance is independent of its neighbors
Why can VIC get away with this behavior?
Assumptions:– The vast majority of grid cell runoff goes into the
grid cell’s local channel network– Very little runoff goes from one grid cell’s soil to its
neighbor’s soil– Water from the channel does not recharge into
the soil (water transport is one-way)
Why can VIC get away with this behavior?
These assumptions are valid if:– Grid cells are large (typically we have 1/8 degree;
12.5 km on a side)– Groundwater flow is small relative to surface and
near-surface flow– Lakes/wetlands do not have significant channel
inflows– Flooding (over banks) is insignificant
These conditions hold most of the time
Consequences
• VIC gives us a separate set of output files for each grid cell
• VIC does not (currently) perform channel routing of runoff
• VIC does not give us a hydrograph• Routing is performed by a stand-alone program
(“rout”)• A benefit: VIC uses very little memory
– system only needs to store state and fluxes of one grid cell at a time
How to get a hydrograph
Routing program: “rout”• Takes VIC fluxes files for all cells in basin• Reads daily runoff and baseflow totals• Convolves local (runoff+baseflow) with unit hydrograph
response function• Adds local hydrograph response to flow from upstream• Propagates flow downstream
Runoff + baseflow
Runoff + baseflowRunoff + baseflow
Runoff + baseflow
3. Model calibration (“the Achilles heel of hydrological modeling”)
Typical Calibration ParametersInfiltration: bi (more identifiable in dry climates)Baseflow: Ds Ws DsmaxOther: Soil Depths (particularly the baseflow layer)
Ks expt (exponent n in Brooks –Corey eqn – describes
variation of Ksat with soil moisture‘global precip multiplier’
“Nijssen parameters”
model converts from D1, D2, D3 and D4 back to Ds, Ws, Dsmax and cDs = D1*D3 / D2Dsmax = D2*(1/(max moisture-D3))^D4 + D1*D3Ws = D3/(max layer moisture)c = D4 (exponent in infiltration curve, usually set to 2)
Alternative Parameter Formulation
D1 linear reservoir coeff; D2 nonlinear res coeff; D3 threshold for switch
See: Demaria et al., 2007, Monte Carlo Sensitivity Analysis of land surface parameters using the VIC model, JGR (in review)
Automatic Calibration (Optimization)www.hydro.washington.edu/Lettenmaier/Models/VIC/Documentation/Optimization.html
• “Mocom-UA”
• very general structure for routine, although this makes code structure confusing
shell script runs optimization
calls C-program Mocom-UA
Mocom-UA: - generates initial parameter samples
calls shell script to:- run VIC- calculate statistics- [etc – anything else you want, e.g., plot]
Mocom-UA: - evaluates stats from runs, generates new params
calls shell script to run VIC … etc.
loop until done
Automatic Calibration Routine
Automatic Calibration Routine
4. Model testing and evaluation
Investigation of forest canopy effects on snow accumulation and melt
Measurement of Canopy Processes via two 25 m2 weighing lysimeters (shown here) and additional lysimeters in an adjacent clear-cut.
Direct measurement of snow interception
0
50
100
150
200
250
300
350
11/1/96 12/1/96 1/1/97 2/1/97 3/1/97 4/1/97 5/1/97
SW
E (
mm
)ObservedPredicted
Below-canopy
Shelterwood
Tmin = 0.4 C Zo shelterwood = 7 mmTmax = 0.5 C Zo below-canopy = 20 cm
Albedo based onexponential decaywith age; fitted tospot observationsof albedo
Calibration of an energy balance model of canopy effects on snow accumulation and melt to the weighing lysimeter data. (Model was tested against two additional years of data)
Summer 1994 - Mean Diurnal Cycle
Point Evaluation of a Surface Hydrology Model for BOREAS
Flu
x (W
/m2)
-100
100
300 Rnet
-50
50
150
250
H
0
60
120LE
0 3 6 9 12 15 18 21 24
SSA Mature Black Spruce
Rnet
H
LE
0 3 6 9 12 15 18 21 24
SSA Mature Jack Pine
Rnet
H
LE
0 3 6 9 12 15 18 21 24
Local time (hours)
NSA Mature Black Spruce
Observed Fluxes
Simulated Fluxes
Rnet Net Radiation
H Sensible Heat Flux
LE Latent Heat Flux
Range in Snow Cover ExtentObserved and Simulated
Eurasia North America
J F M A M J J A S O N D JMonth
Observed Simulated
0
4
8
12
16
20
sno
w c
ove
r ex
ten
t (1
06 km
2 )
J F M A M J J A S O N D JMonth
0
2
4
6
8
10
June 18th-July 20th, 1997
UPPER LAYER SOIL MOISTURE
0.40
0.10
0.20
0.30
SO
IL M
OIS
TU
RE
(%
)
XX
X
X
XX
X
XX
X
XX
XX X
X
TOPLATS regionalESTAR distributed
TOPLATS distributed
11:00 CST JULY 12 1997
ESTAR TOPLATS
50
10
ESTAR TOPLATS
10
50
11:00 CST JUNE 20, 1997
Illinois soil moisture comparison
Mean Normalized Observed and Simulated Soil MoistureCentral Eurasia, 1980-1985
20°E 30°E 40°E 50°E 60°E 70°E 80°E 90°E 100°E 110°E 120°E 130°E 140°E
40°N 40°N
50°N 50°N
60°N 60°N
A
BC
D
E
F
G
H
0
100
200 S
oil M
oist
ure
(mm
)A
J F MA M J J A S O N D J
Nor
mal
ized
B
J F MA M J J A S O N D J
C
J F MA M J J A S O N D J
D
J F MA M J J A S O N D J
0
100
200
Soi
l Moi
stur
e (m
m)
E
J F MA M J J A S O N D J
Nor
mal
ized
F
J F MA M J J A S O N D J
G
J F MA M J J A S O N D J
H
J F MA M J J A S O N D J
Observed Simulated
Cold Season Parameterization -- Frozen Soils
Key
Observed
Simulated
5-100 cm layer
0-5 cm layer
Shasta Reservoir inflows