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 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

BASIC HYDROLOGIC MODEL Q = P - ET  S Runoff Precip Met Vars Ground Water Soil Moisture Reservoirs Basin Chars Snow & Ice Water use Soil Moisture Components

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 depth h x p Total head = h + x + p di/dt = K [(h + x + p) / x] i I = x (m t -m 0 ) h<<p mtmt m0m0 [Green & Ampt]

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 “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 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

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.

Numerical Evaluation with the D  Algorithm Upslope contributing area a Stream line Contour line Topographic Definition Specific catchment area a is the upslope area per unit contour length [m 2 /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): ) (

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 -T o lateral transmissivity [m 2 /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. e.g. or S DwDw D

Topmodel Specific catchment area a [m 2 /m  m] (per unit coutour length) S DwDw D z

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

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

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

Model Verification Discharge is almost always used Good idea or bad idea? Why?

SENSITIVITY ANALYSIS AND PARAMETER CALIBRATION 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 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 AnalysisParameter Calibration

SENSITIVITY ANALYSIS AND PARAMETER CALIBRATION

COMPARISON OF TOPOGRAPHIC PARAMETERS IN GLV WITH LOCH VALE

SIMULATED SNOWMELT VS. RUNOFF Green Lake 4

MONTHLY WATER BUDGET

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 1 AREA

DON’T HAVE TOO MUCH CONFIDENCE IN MODELS! WARNING: TAKE ALL MODELS WITH A GRAIN OF SALT!

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 , 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 , 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 The actual lateral discharge is proportional to specific catchment area. Specific catchment area a [m 2 /m  m] (per unit contour length) S DwDw D 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 q act and q cap Specific catchment area a [m 2 /m  m] (per unit coutour length) S DwDw D Saturation when w > 1. i.e.