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