1. Primer on hydrologic models
Dennis P. Lettenmaier
Department of Civil and Environmental Engineering
University of Washington
for presentation at
Dividing the waters: Science for Judges Workshop IV
Workshop on Climate Change Modeling:
General Circulation Models and Hydrometeorologic Models
Hotel Boulderado
Boulder, Colorado
May 13 – 15, 2007

2. Some caveats
All models are wrong, but some are useful G.E.P. Box, 1979
With poor assumptions, a man can make more mistakes in a millisecond than he could with common sense in a lifetime … unknown
Beware those who believe their models D.P. Lettenmaier, 2007

3. Source: Aqua Terra Consultants, HSPF training course

4. Some background on runoff generation mechanisms
Saturation excess (also “Dunne Mechanism”) – runoff is generated only from areas for which the surface is hydraulically connected to the channel system, meaning saturated areas (which are dynamic at both seasonal and storm time scales). Most common locations: humid and semi-humid environments, especially forested.
Infiltration mechanism (also Horton overland flow) – occurs when rainfall intensity exceeds infiltration rate, causing (at least local) overland flow. Most common locations: urban areas; arid areas with e.g. crusted soils and high precipitation intensities; some agricultural areas (especially in summer).

6. Infiltration excess flow (source: Dunne and Leopold)

8. Saturated area (source: Dunne and Leopold)

10. Seasonal contraction of saturated area at Sleepers River, VT following snowmelt (source: Dunne and Leopold)

11. Expansion of saturated area during a storm (source: Dunne and Leopold)

12. Seasonal contraction of pre-storm saturated areas, Sleepers River VT (source: Dunne and Leopold)

13. The hydrologic modeling problem: Predict Q (streamflow) given P (precipitation), and perhaps other land surface meteorological variables (temperature, downward solar and longwave radiation, etc)
Approaches:
“Black box” models: given sequence of Q and P, “train” a relationship
Examples: unit hydrograph (applicable to storm runoff prediction), regression (applicable to longer periods, e.g., seasonal or annual)
Shortcomings:
No physical causality
Most such models are linear, but nonlinearities govern hydrologic response under many conditions
Extrapolation beyond observed ranges of forcing and response data (extreme droughts, floods)

14. Example: Application of linear regression to seasonal runoff forecasting in the western U.S. (Apr-Aug runoff as a function of Apr 1 observed snow water content)

15. Classification of Hydrological Models
Deterministic
Stochastic
Physically
Based
Conceptual
Empirical
Probabilistic
Time series
Distributed
Lumped
Grid based
Subwatershed
No distribution
Source: USDA/ARS, Tucson, AZ

16. Modeling approaches (cont.)
Rainfall-runoff modeling (aka “conceptual hydrologic modeling”, “physically based modeling”
Essentially all models in this class are temporally distributed (typically meaning time steps hours to a day)
Subcategories:
Event (primarily storm)
Continuous (e.g., multi-years)*
Spatially lumped
Spatially distributed (or semi-distributed)*

17. Model characteristics
“Engineering” models – typically prescribe P and potential evapotranspiration (PET or Ep), which usually implies that vegetation is not represented explicitly. Engineering models generally are not concerned with causality, but rather in producing the most accurate predictions
Physically based models – typically represent vegetation explicitly, and often energy, as well as water cycle. Models that represent both water and energy fluxes often are designed for, or adapted from, land schemes in coupled land-atmosphere models (used for weather and climate prediction).

18. Some questions to ask:
What is the model’s conceptual basis (black box, physically based)?
If physically based, what mechanisms are represented (e.g., saturation vs infiltration excess runoff generation, or both)?
How is vegetation represented (explicitly, or in terms of PET)?
How was the model calibrated (calibration and verification periods, NSE, time series examples, mass balance, correlation with obs, etc)?
What is the basis for assuming applicability beyond the range of observations?

19. Some examples of physically based or conceptual hydrologic models:
HSPF/BASINS (EPA) – derivative of Stanford model of 1960s, the first time-continuous conceptual simulation model, generalized but still no explicit vegetation representation
NWSRFS (Sacramento) – another derivative of Stanford model; time continuous, used primarily for flood forecasting. No explicit representation of vegetation.
SWAT (USDA) – a quasi-conceptual time-continuous model built around SCS curve number variation of unit hydrograph method; vegetation/land cover links to PET and curve number represented
KINEROS (USDA) – a physically based, event model (physics mostly pertain to infiltration excess overland flow prediction; no representation of vegetation due to event nature)
Variable Infiltration Capacity (VIC) model – designed for coupled and uncoupled land-atmosphere and hydrologic prediction for large river basins. Represents both the water and energy cycles. Includes SVAT (soil-vegetation-atmosphere transfer scheme) representation of vegetation. It is spatially semi-distributed.

20. Source: Aqua Terra consultants, HSPF training course

21. Hydrologic simulation modeling – the Stanford Watershed model (per Steve Gorelik and Keith Loague, Stanford University)

22. USDA Soil Water Assessment Tool (SWAT)
Source: USDA/ARS, Tucson, AZ

23. (KINEROS) Kinematic Runoff & Erosion Model
Event-based (< minute time steps)
Distributed: physically-based model with dynamic routing
Hydrology, erosion, sediment transport
Smaller watersheds (< 100 km2)
Not applicable for snow
Primary Parameters
Area
Slope
Manning’s n
Percent Cover
Interception
Saturated Hydraulic Conductivity
Soil texture (% sand, silt, clay)
Pavement 71 72 73 74
Source: USDA/ARS, Tucson, AZ

24. Excess Runoff From a Planei x Q t h - = +
rainfall intensity (i)
- KINEROS
flow depth (h)
Finite difference
step length (dx)
infiltration (f) q
Other Factors
interception
channel element
hydraulic roughness
rain splash erosion
soil cohesion (erodibility)
Source: USDA/ARS, Tucson, AZ Q

25. Automated Watershed Characterization
1 km
10% = 78.6 ha
5% = 39.3 ha
1.5% = CSA of 11.8 ha
2.5% = 19.6 ha
area is removed due to presence of pond
that never spilled during simulation period
Automated Watershed Characterization
the influence of CSA on watershed complexity
watershed 11, Walnut Gulch Experimental Watershed
Note channel initiation
Point changing with CSA
Source: USDA/ARS, Tucson, AZ

26. Macroscale modeling: A strategy for hydrologic modeling of large (e. g
Macroscale modeling: A strategy for hydrologic modeling of large (e.g. continental) river basins
ref. e.g. B. Nijssen et al, Streamflow Simulation for Continental-Scale Watersheds, Water Resources Research, 1997.
Traditional “bottom up” hydrologic modeling approach (subbasin by subbasin)

27. Macroscale modeling approach (“top down”)
1 Northwest 5 Rio Grande 10 Upper Mississippi
2 California 6 Missouri 11 Lower Mississippi
3 Great Basin 7 Arkansas-Red 12 Ohio
4 Colorado 8 Gulf 13 East Coast
9 Great Lakes

30. VIC/DHSVM Snow Accumulation and Melt Model

31. Macroscale hydrologic modeling – the physical basis

32. 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

33. 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)

34. Summer 1994 - Mean Diurnal Cycle
Point Evaluation of a Surface Hydrology Model for BOREAS
SSA Mature Black Spruce
NSA Mature Black Spruce
SSA Mature Jack Pine
-100
100
300
Rnet
-50 50
150
250 H 60
120 LE 3 6 9 12 15 18 21 24
Rnet H LE 3 6 9 12 15 18 21 24
Rnet H LE 3 6 9 12 15 18 21 24
Flux (W/m2)
Local time (hours)
Observed Fluxes
Simulated Fluxes
Rnet
Net Radiation H
Sensible Heat Flux LE
Latent Heat Flux

35. Range in Snow Cover Extent
Observed and Simulated
Eurasia
North America J F M A S O N D
Month
Observed
Simulated 4 8 12 16 20
snow cover extent (10 6 km 2 ) 10

36. UPPER LAYER SOIL MOISTURE
June 18th-July 20th, 1997
UPPER LAYER SOIL MOISTURE
0.40
0.10
0.20
0.30
SOIL MOISTURE (%) X
TOPLATS regional
ESTAR distributed
TOPLATS distributed
11:00 CST JULY
ESTAR
TOPLATS 50 10
11:00 CST JUNE 20, 1997
Illinois soil moisture comparison

37. Mean Normalized Observed and Simulated Soil Moisture
Central Eurasia,
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
50°N
60°N A B C D E F G H
100
200
Soil Moisture (mm) J M S O N
Normalized
Observed
Simulated

38. Cold Season Parameterization -- Frozen Soils
Key
Observed
Simulated
5-100 cm layer
0-5 cm layer

39. Macroscale hydrology models – implementation for large continental river basins

40. Shasta Reservoir inflows

41. Model calibration (parameter estimation)
Applicable to conceptual/physically based models (parameter estimation for e.g. statistical models has stronger theoretical basis)
Most model parameters have some physical basis, typically used to place bounds on feasible range
Some model parameters are often constrained to literature values, in some cases based on sensitivity analysis that shows limited sensitivities
Other parameters subject to search – usually manual, sometimes via automated search procedures
Split sample approach of calibration vs verification periods is the norm, to avoid model overfitting
Simplifications are often made to reduce dimensionality of search problem, especially for distributed or semi-distributed models (where some parameters may be made identical spatially)
Objective function for search is usually (although doesn’t have to be) single valued, related to difference between predicted and observed runoff

42. Calibration criteria
Correlation obs – simulated (problem: linear multiples yield perfect correlation; lags can greatly reduce correlation)
Bias (necessary for water balance, but not sufficient)
Nash-Sutcliffe efficiency [1 – sum(sim – obs)2/variance(obs)] – most commonly used
Various multivariate measures

43. Source: EPA BASINS training course

44. Source: EPA BASINS training course

45. Source: EPA BASINS training course

46. Source: EPA BASINS training course

47. Source: EPA BASINS training course

48. Source: EPA BASINS training course

49. VIC model -- Typical Calibration Parameters
Infiltration: bi (more identifiable in dry climates)
Baseflow: Ds Ws Dsmax
Other: Soil Depths (particularly the baseflow layer) Ks
expt (exponent n in Brooks –Corey eqn – describes
variation of Ksat with soil moisture
‘global precip multiplier’
Alternative Parameter Formulation
Nijssen parameters (select
model converts from D1, D2, D3 and D4 back to Ds, Ws, Dsmax and c
Ds = D1*D3 / D2
Dsmax = D2*(1/(max moisture-D3))^D4 + D1*D3
Ws = D3/(max layer moisture)
c = D4 (exponent in infiltration curve, usually set to 2)
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)

50. Automatic Calibration (Optimization)
“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]
loop until done
Mocom-UA: - evaluates stats from runs, generates new params
calls shell script to run VIC … etc.

51. Automatic Calibration Routine

52. Automatic Calibration Routine

53. VIC model calibrated to observations (monthly), Green River, Utah
NSE = 0.88
ρ = 0.95

54. West Walker River, Nevada
NSE = 0.72
ρ = 0.88

55. What Could Possibly Go Wrong??
SYSTEMIC ERRORS
These are “hidden” & include:
Poor conceptual model
Poor process representation
Forcing data errors
Errors in land cover data
Programming errors
PROCESSING ERRORS
These are “visible” & include:
Errors in GIS data orocessing
DEM – e.g., watershed area
delineation, channel connectivity
Lack of input data
Rainfall especially
Source: USDA/ARS, Tucson, AZ

56. Spatial Distribution of Rain Gauges# #
High Density Watershed
Walnut Gulch Exp. WS
148 km2
89 rain gauges
Typical Distribution
Upper San Pedro Basin
6100 km2
15 rain gauges
Source: USDA/ARS, Tucson, AZ

57. Reconstructed (VIC) CO discharge,
real-time forcings

58. Reconstructed (VIC) CO discharge, retrospective forcings

59. Sacramento River at Shasta, 1950-99

60. Tolumne River at New Don Pedro, CA 1950-99

61. Summary
Hydrologic modeling has its shortcomings (as do all predictive models of natural systems) – but it is our primary means of providing insight into the hydrologic future
Increasingly water planning will have to rely on models to construct a range of future conditions, as contrasted with a single observational record
The tools for using ensemble methods already exist (and date to the Harvard Water Program of the 1960s). The problems of implementation largely have to do with difficulties at the intersection of water science and engineering, and legal/institutional