PRECIPITATION-RUNOFF PRECIPITATION-RUNOFF MODELING SYSTEMMODELING SYSTEM

(PRMS)(PRMS)

MODELING OVERVIEW MODELING OVERVIEW

&&

DAILY MODE COMPONENTSDAILY MODE COMPONENTS

SUGGESTED REGERENCE ON WATERSHED MODELING

- Overview chapters on basic concepts

- 25 Models, each a chapter with discussions of model components and assumptions

BASIC HYDROLOGIC MODELBASIC HYDROLOGIC MODEL

Q = P - ET ± S

Runoff Precip Met Vars Ground Water

Soil Moisture Reservoirs

Basin Chars Snow & Ice

Water use Soil Moisture

Components

Model Selection CriteriaModel Selection Criteria

Problem objectivesProblem objectivesData constraintsData constraintsTime and space Time and space

scales of applicationscales of application

Lumped Model ApproachTANK MODEL

TOPMODETOPMODELL

GRID-BASED MODELS

- Explicit grid to grid

- Statistical distribution ----(topgraphic index)

Distributed Approaches

TOPMODEL Distributed Process Conceptualization

Statistical Distribution of Topographic Index ln(a/tanB)

Fully Coupled 1-D unsat and 3-D sat flow model

SPATIAL SPATIAL CONSIDERATIONSCONSIDERATIONS

LUMPED MODELSLUMPED MODELS - No account of spatial variability of processes, input, boundary conditions, and system geometry

DISTRIBUTED MODELSDISTRIBUTED MODELS - Explicit account of spatial variability of processes, input, boundary conditions, and watershed characteristics

QUASI-DISTRIBUTED MODELSQUASI-DISTRIBUTED MODELS - Attempt to account for spatial variability, but use some degree of lumping in one or more of the modeled characteristics.

PRMS

PRMS VariationsPRMS_WET

PRMS_ISO

PRMS_Yakima

PRMS_Jena

PRMS-MODFLOW

PRMS PRMS ParametersParameters

original original versionversion

PRMSPRMSParametersParameters

MMS Version

PRMS FeaturesPRMS Features

Modular DesignModular Design DeterministicDeterministic Distributed ParameterDistributed Parameter Daily and Storm ModeDaily and Storm Mode Variable Time StepVariable Time Step User ModifiableUser Modifiable Optimization and Sensitivity Optimization and Sensitivity

AnalysisAnalysis

HYDROLOGIC RESPONSE HYDROLOGIC RESPONSE UNITS (HRUs)UNITS (HRUs)

Distributed Parameter Distributed Parameter ApproachApproach

Hydrologic Response Units - HRUs

HRU Delineation Based on:

- Slope - Aspect

- Elevation - Vegetation

- Soil - Precip Distribution

HRUs

HRU DELINEATION AND CHARACTERIZATION

Polygon Hydrologic Response Units (HRUs)

Grid Cell Hydrologic Response Units (HRUs)

Dill Basin, Dill Basin, GermanyGermany

750 km750 km2

Land UseLand Use

Sub-basinsSub-basins

TopograpTopographyhy

TopographicTopographic PixelatedPixelated

PRMS -- HRU DelineationPRMS -- HRU Delineation

Grid ComplexityGrid Complexity

3rd HRU DIMENSION

Relation of HRUs and Relation of HRUs and Subsurface and GW ReservoirsSubsurface and GW Reservoirs

Surface ( 6 hrus )

Subsurface ( 2 reservoirs )

Ground water (1 reservoir)

PRMSPRMS

HRUresolution

SSRresolution

GWRresolution

PRMS

MODEL DRIVING VARIABLESMODEL DRIVING VARIABLES

- TEMPERATURE

- PRECIPITATION

- max and min daily

- lapse rate varied monthly or daily

- spatial and elevation adjustment

- form estimation

MODEL DRIVING VARIABLESMODEL DRIVING VARIABLES

- SOLAR RADIATION

- measured data extrapolated to slope-aspect of each HRU

- when no measured data, then estimated using temperature, precip, and potential solar radiation

- max daily temperature procedure

- daily temperature range procedure

Max Temperature-Elevation Max Temperature-Elevation RelationsRelations

TEMPERATURETEMPERATURE

tmax(hru) = obs_tmax(hru_tsta) - tcrx(mo)

tmin(hru) = obs_tmin(hru_tsta) - tcrx(mo)

tcrx(mo) = [ tmax_lapse(mo) * elfac(hru)] - -----------------------------tmax_adj(hru)

elfac(hru) = [hru_elev - tsta_elev(hru_tsta)] / 1000.

For each HRU

where

Precipitation-Elevation Precipitation-Elevation RelationsRelations

Schofield Pass and Crested Butte (1975-97)

0

0.05

0.1

0.15

0.2

0.25

0.3

1 2 3 4 5 6 7 8 9 10 11 12

M onth

Av

era

ge

da

ily

pre

cip

ita

tio

n,

in i

nc

he

s

Schofield Pass

Crested Butte

Mean Daily PrecipitationSchofield Pass (10,700 ft) vs Crested Butte (9031 ft)

MONTH

Mea

n da

ily

prec

ip, i

n.

Precipitation Gage Catch Error vs Precipitation Gage Catch Error vs Wind Speed Wind Speed (Larsen and Peck, 1972)(Larsen and Peck, 1972)

Rain (shield makes little difference)

Snow (shielded)

Snow (unshielded)

Precipitation Gauge Intercomparison Precipitation Gauge Intercomparison Rabbit Ears Pass, ColoradoRabbit Ears Pass, Colorado

Catch Ratio Equations Catch Ratio Equations WMO Study WMO Study

Catch Ratio Catch Ratio WMO StudyWMO Study

PRECIPITATIONPRECIPITATION

- DEPTH

hru_precip(hru) = precip(hru_psta) * pcor(mo)

pcor(mo) = Rain_correction or Snow_correction

For each HRU

PRECIPITATIONPRECIPITATION

- FORM (rain, snow, mixture of both)

For each HRU

RAIN

tmin(hru) > tmax_allsnow

tmax(hru) > tmax_allrain(mo)

SNOW

tmax(hru) <= tmax_allsnow

PRECIPITATIONPRECIPITATION

- FORM (rain, snow, mixture of both)

For each HRU

Precipitation Form Variable

Snowpack Adjustment

MIXTURE

OTHER

prmx = adjmix_rain(mo)tmax(hru) - tmax_allsnow

(tmax(hru) - tmin(hru)*[ ]

Precipitation Distribution MethodsPrecipitation Distribution Methods(module)(module)

Manual Manual (precip_prms.f)(precip_prms.f)Auto Elevation Lapse Rate Auto Elevation Lapse Rate

(precip_laps_prms.f)(precip_laps_prms.f)XYZ XYZ (xyz_dist.f)(xyz_dist.f)

PCOR Computation

ManualManual

PCOR Computation

Auto Elevation Lapse RateAuto Elevation Lapse Rate

PCOR Computation

For each HRU

hru_psta = precip station used to compute hru_precip

[ hru_precip = precip(hru_psta) * pcor ]

hru_plaps = precip station used with hru_psta to compute ------ -------precip lapse rate by month [pmo_rate(mo)]

hru_psta

hru_plaps

PCOR Computation

pmn_mo

padj_sn or padj_rn

elv_plaps

Auto Elevation Lapse Rate Parameters

adj_p = pmo_rate *

Auto Elevation Lapse RateAuto Elevation Lapse Rate

PCOR Computation

For each HRU

snow_adj(mo) = 1. + (padj_sn(mo) * adj_p)

if padj_sn(mo) < 0. then snow_adj(mo) = - padj_sn(mo)

pmo_rate(mo) =pmn_mo(hru_plaps) - pmn_mo(hru_psta)

elv_plaps(hru_plaps) - elv_plaps(hru_psta)

hru_elev - elv_plaps(hru_psta)

pmn_mo(hru_psta)

XYZ Distribution

San Juan Basin

Observation Stations 37

XYZ Spatial Redistribution of Precip and Temperature

1. Develop Multiple Linear Regression (MLR) equations (in XYZ) for PRCP, TMAX, and TMIN by month using all appropriate regional observation stations.

XYZ XYZ Spatial Spatial

RedistributionRedistribution

2. Daily mean PRCP, TMAX, and TMIN computed for a subset of stations (3) determined by the Exhaustive Search analysis to be best stations

3. Daily station means from (2) used with monthly MLR xyz relations to estimate daily PRCP, TMAX, and TMIN on each HRU according to the XYZ of each HRU

Precip and temp stations

Z

PR

CP

2. PRCPmru = slope*Zmru + intercept

where PRCPmru is PRCP for your modeling response unit

Zmru is mean elevation of your modeling response unit

x

One predictor (Z) example for distributing daily PRCP from a set of stations:

1. For each day solve for y-intercept

intercept = PRCPsta - slope*Zsta

where PRCPsta is mean station PRCP and

Zsta is mean station elevation

slope is monthly value from MLRs Plot mean station elevation (Z)

vs. mean station PRCP

Slope from monthly MLR used to find the

y-intercept

XYZ MethodologyXYZ Methodology

2-D Example XYZ and Rain 2-D Example XYZ and Rain Day FrequencyDay Frequency

Elevation

Mea

n S

tati

on P

reci

pita

tion

P1

P2

P3

Precipitation in the frequency station set but not the mean station set

Precipitation in the mean station set

Mean station set elevation

Slope from MLR

Application of XYZ Methodology

Chesapeake Bay

Subdivide the monthly MLRs by Sea Level

Pressure (SLP) patterns using a map-pattern

classification procedure Sea Level Pressure Patterns

Low SLP High SLP

Application of XYZ Methodology

Chesapeake Bay

PRCP subdivided by SLP

Low SLP High SLP

Sea Level Pressure Patterns

Mean Daily PRCP (mm/day)

Mean Daily Precipitation

0 1 2 3 4 5 6 7

Precipitation Distribution MethodsPrecipitation Distribution Methods(module)(module)

precip_dist2_prms - weights measured precipitation from two or more stations by the inverse of the square of the distance between the centroid of an HRU and each station location

PCOR Computation

Precipitation Distribution MethodsPrecipitation Distribution Methods(module)(module)

ide_prms - Combines XYZ_prms and an inverse distance squared approach but allows you to select which months to apply each approach. You can also limit the number of stations used for the inverse distance computation to the nearest X stations.

PCOR Computation

SOLAR RADIATIONSOLAR RADIATION

- drad and horad computed from table of 13 values for each HRU and a horizontal surface

- Table generated from hru slope, aspect, & latitude

- Missing data computed by

obs_tmax - SolarRad relation

[obs_tmax - obs_tmin] --> sky cover --> SolarRad relation

For each HRU

daily_potsw(hru) = ( drad(hru) / horad ) * ------------------orad /cos_slp(hru)

Degree-Day Solar Radiation Estimation Degree-Day Solar Radiation Estimation Procedure (non precip day)Procedure (non precip day)

For days with precip, daily value is multiplied by a seasonal adjustment factor

DRIVING VARIABLE INPUT DRIVING VARIABLE INPUT SOURCESSOURCES

Point measurement dataPoint measurement data Radar dataRadar data Satellite dataSatellite data Atmospheric model dataAtmospheric model data

RADAR DATA

NEXRAD vs S-POL, Buffalo Creek, CO

Satellite Image for Snow-Covered Area Computation

Statistical Downscaling AtmosphericStatistical Downscaling Atmospheric ModelsModels

Multiple linear regression Multiple linear regression equations developed for equations developed for selected climate stations selected climate stations

Predictors chosen from Predictors chosen from over 300 NCEP variables over 300 NCEP variables (< 8 chosen for given (< 8 chosen for given equation) equation)

Predictands are maximum Predictands are maximum and minimum temperature, and minimum temperature, precipitation occurrence, precipitation occurrence, and precipitation amountsand precipitation amounts

Stochastic modeling of the Stochastic modeling of the residuals in the regression residuals in the regression equations to provide equations to provide ensemble time seriesensemble time series

11,000 Climate Station Locations

NCEP Model Nodes

Collaboratively with U. of Colorado

Dynamical DownscalingDynamical DownscalingRegCM2RegCM2 (Giorgi et al., 1993, 1996) (Giorgi et al., 1993, 1996)

Period: 1979-1988Period: 1979-1988 Boundary conditions: NCEP ReanalysisBoundary conditions: NCEP Reanalysis 52 km grid (Lambert conformal projection)52 km grid (Lambert conformal projection)

Representative Representative Elevation of Elevation of Atmospheric Atmospheric

ModelModelOutput based on Output based on Regional StationRegional Station

ObservationsObservations

Nash-Sutcliff Coefficient of Efficiency Nash-Sutcliff Coefficient of Efficiency Scores Simulated vs Observed Daily Scores Simulated vs Observed Daily

StreamflowStreamflow

Performance MeasuresPerformance Measures

Coefficient of Efficiency ECoefficient of Efficiency E

Nash and Sutcliffe, 1970, J. of Hydrology

Widely used in hydrology Range – infinity to +1.0 Overly sensitive to extreme values

Animas River, CO

Simulated Q with station data (S_3) and downscaled data (N_ds) from NCEP reanalysis

PRMS

INTERCEPTIONINTERCEPTION

net_precip = [ hru_precip * (1. - covden)] + (PTF * covden)

PTF = hru_precip - (max_stor - intcp_stor) -----

Throughfall

Losses from intcp_stor

Rain - Free water surface evaporation rate

Snow - % of potet rate for sublimation

Net precipitation

PTF = 0. if [hru_precip <= (max_stor - intcp_stor)]

if [hru_precip > (max_stor - intcp_stor)]

PRMS

Transpiration vs Soil Transpiration vs Soil Moisture Content and Moisture Content and Weather ConditionsWeather Conditions

Potential Evapotranspiration (potet)Potential Evapotranspiration (potet)

- Pan Evaporation

- Hamon

- Jensen - Haise

potet(hru) = epan_coef(mo) * pan_evap

potet(hru) = hamon_coef(mo) * dyl2 * vdsat

potet(hru) = jh_coef(mo) * ---------------

(tavf(hru) - jh_coef_hru) * rin

Various Concepts of ET vs Various Concepts of ET vs Soil MoistureSoil Moisture

Computed ET (AET) as function Computed ET (AET) as function of PET and Soil Textureof PET and Soil Texture

PRMS to PRMS/MMS

SMAV = soil_moist

SMAX = soil_moist_max

RECHR = soil_rechr

REMX = soil_rechr_max

Actual Evapotranspiration (actet)Actual Evapotranspiration (actet)

- f ( antecedent conditions, soil type)

- Taken first from Recharge Zone & then Lower Zone

- actet period ( months transp_beg to transp_end)

transp_beg - start actet on HRU when S tmax_sum(hru) > transp_tmax(hru)

transp_end - end actet

Point Evapotranspiration Comparison

Eddy correlation

Jensen-Haise

Aspen Park, COE

T, i

nche

s

0

1

2

3

4

5

1980 1982 1984 1986 1988

PRSM vs. ReGCM2 Evapotranspiration

PRSM [SM]

RegCM2 [SM]

[mm

/day

]

Year

WORKSHOP ON REGIONAL CLIMATE PREDICTION AND DOWNSCALING TECHNIQUES FOR SOUTH AMERICA

Basin Evapotranspiration Comparison

Jensen-Haise RegCM2

Animas River Basin, Colarado

Mirror Lake, NH

GW - ET Relations

PRMS

Distribution, Flow, and Distribution, Flow, and Interaction of WaterInteraction of Water

SOIL ZONESOIL ZONE((Original Version)Original Version)

Recharge Zone (soil_rechr_max)

Lower Zone

excs (soil_moist > soil zone field capacity)

sroff

soil_moist_max (rooting depth)

soil2gw_maxexcs - soil_to_gw

to subsurface reservoir

to ground-water reservoir

Original and Revised Soil Original and Revised Soil ZoneZone

Original PRMS Original PRMS ConceptualizationConceptualization

SRO

Revised PRMS Revised PRMS ConceptualizationConceptualization

Soil Zone Soil Zone Structure Structure and Flow and Flow ComputatComputat

ion ion SequenceSequence

wpwp

fcfc

satsat

soil_moist_max = soil_moist_max = fc -wpfc -wp

sat_threshold = sat -fc

Capillary Capillary ReservoirReservoir

Gravity Gravity Reservoir Reservoir

Preferential-Preferential-Flow Flow

Reservoir Reservoir pref_flow_stopref_flow_storr

slow_storslow_stor

pref_flow_threshpref_flow_thresh = = sat_threshold sat_threshold * (* (1.01.0 – – pref_flow_den)pref_flow_den)pref_flow_max = sat_threshold – pref_flow_thresh

soil_moistsoil_moistsoil_rechrsoil_rechr soil_zone_max =

sat_threshold + soil_moist_max

ssres_stor = slow_stor + pref_flow_stor

Soil Zone Water FluxSoil Zone Water Flux

Soil Zone Module

Capillary (CR)

Preferential (PR)

Gravity (GR)Inflow/outflow—Arrow indicates direction

Internal flow—Arrow indicates direction

12

1

13

11

6

2

8

7

4

3

5

9

Direction of increasing water content

ReservoirsEXPLANATION

Computational sequence listed in table 6

Flow to unsaturated zone or to ground water

Ground-water discharge to GR

Upslope Dunnianrunoff and interflow

Water above field capacity to GR

Replenish CR when

below field

capacity

Fraction of water to PR when water content

exceeds thresholdDown-slopeslow interflow

Transfer water between zones

Transpiration from

lower zone

Evaporation and transpiration

from upper zone

Down-slopeFast interflow

Down-slope runoff when soil zone filled

Immobile water (not included in soil-zone storage)

Infiltration with fraction to PR

Field-capacity threshold

Preferential threshold

Saturation threshold

Wilt threshold

10

8

Evaporation threshold

Surface depression

storage

Capillary (CR)

Preferential (PR)

Gravity (GR)Inflow/outflow—Arrow indicates direction

Internal flow—Arrow indicates direction

1212

11

1313

1111

66

22

88

77

44

33

55

99

Direction of increasing water content

ReservoirsEXPLANATION

Computational sequence listed in table 6

Flow to unsaturated zone or to ground water

Ground-water discharge to GR

Upslope Dunnianrunoff and interflow

Water above field capacity to GR

Replenish CR when

below field

capacity

Fraction of water to PR when water content

exceeds thresholdDown-slopeslow interflow

Transfer water between zones

Transpiration from

lower zone

Evaporation and transpiration

from upper zone

Down-slopeFast interflow

Down-slope runoff when soil zone filled

Immobile water (not included in soil-zone storage)

Infiltration with fraction to PR

Field-capacity threshold

Preferential threshold

Saturation threshold

Wilt threshold

1010

88

Evaporation threshold

Surface depression

storage

HYDROLOGIC HYDROLOGIC RESPONSE RESPONSE

UNITS (HRUs)UNITS (HRUs)

1

2

3 4

5

6

Watershed boundary

EXPLANATION

Stream

1 65432Hydrologic response unit

Streamflow gage at basin outlet

Direction of streamflow

1

2

3 4

5

6

Watershed boundary

EXPLANATION

Stream

1 65432Hydrologic response unit

Streamflow gage at basin outlet

Direction of streamflow

CascadingCascading Flow Flow 1

234

5

Watershed boundary

EXPLANATION

Stream

1 21Hydrologic response unit and numerical

identification

Streamflow gage at basin outlet

Direction of streamflow

678

9

10

11

12

13

14

15

1617

18

1920

21

…

Direction of runoff and interflow among hydrologic response units

A

1

234

5

Watershed boundary

EXPLANATION

Stream

1 21Hydrologic response unit and numerical

identification

Streamflow gage at basin outlet

Direction of streamflow

678

9

10

11

12

13

14

15

1617

18

1920

21

…

Direction of runoff and interflow among hydrologic response units

1

234

5

Watershed boundary

EXPLANATION

Stream

1 21Hydrologic response unit and numerical

identification

Streamflow gage at basin outlet

Direction of streamflow

678

9

10

11

12

13

14

15

1617

18

1920

21

…

Direction of runoff and interflow among hydrologic response units

A

HRUs AS FLOW PLANES & HRUs AS FLOW PLANES & CHANNELS (Storm Mode)CHANNELS (Storm Mode)

1

2

3 4

5

6

Watershed boundary

EXPLANATION

Stream

1 65432Hydrologic response unit

Streamflow gage at basin outlet

Direction of streamflow

1

2

3 4

5

6

Watershed boundary

EXPLANATION

Stream

1 65432Hydrologic response unit

Streamflow gage at basin outlet

Direction of streamflow

OVERLAND FLOW PLANESOVERLAND FLOW PLANES

channel

Overla

nd F

low P

lane

1.0} } ∆x

Pervious Precipitation excess

Unit overland flow

% Impervious

% Pervious

Impervious Precipitation excess

CASCADING FLOW CASCADING FLOW PLANESPLANES

3

Overland Flow Path

Channel Segment

Overland Flow Plane2

1

3

2

7

4

5

6

8

9 10

1112

Grass/Agriculture

Bare Ground/Rock

Trees

Shrubslength

width

1

3

1

2

4 Channel Junction

Soil Texture vs Available Soil Texture vs Available Water-Holding CapacityWater-Holding Capacity

InfiltrationInfiltration

- DAILY MODE

- STORM MODE

infil(hru) = net_precip(hru) - sroff(hru)

Point Infil (fr)

fr = dI/dt = ksat * [1. + (ps / S fr)]

Areal Infil (fin)

qrp = ( .5 * net_precip2 / fr ) net_precip < fr

qrp = net_precip - (.5 * fr) Otherwise

fin = net_precip - qrp

PRMS

STREAMFLOWSTREAMFLOW Integration of a variety of Integration of a variety of

runoff generation runoff generation processesprocesses

Surface Runoff

Subsurface Flow(Interflow)

Baseflow

ANIMAS RIVER, CO

SURFACE GW

SUBSURFACE

PREDICTED

MEASURED

EAST FORK CARSON RIVER, CA

SUBSURFACE

GW

SURFACE

PRMS

SURFACE RUNOFF

GENERATION MECHANISMS

Variable-Source Area ConceptVariable-Source Area Concept

Contributing Area vs Basin Contributing Area vs Basin Moisture IndexMoisture Index

SURFACE RUNOFF (SRO)SURFACE RUNOFF (SRO)Contributing-Area Concept

- Linear Scheme (by HRU)

- Non-linear Scheme (by HRU)

ca_percent = carea_min + [(carea_max - carea_min) ---------------* (soil_rechr/soil_rechr_max)]

ca_percent = smidx_coef * 10.(smidx_exp * smidx)

where smidx = soil_moist(hru) + (net_precip(hru) / 2.)

sroff(hru) = ca_percent * net_precip(hru)

Surface Runoff Contributing Area vs Soil Surface Runoff Contributing Area vs Soil Moisture Index (nonlinear Moisture Index (nonlinear

approach)approach)

Surface Surface Runoff Runoff

Contributing Contributing Area vs Soil Area vs Soil

Moisture Moisture IndexIndex

(nonlinear)(nonlinear)

STARKWEATHER COULEE, STARKWEATHER COULEE, NDND

Depression Depression StorageStorage

Prairie Prairie Pothole Pothole RegionRegion

DEPRESSION DEPRESSION STORAGE STORAGE

ESTIMATION ESTIMATION (BY HRU)(BY HRU)

USING THE USING THE GIS WEASELGIS WEASEL

(AREA & (AREA & VOLUME)VOLUME)

Depression Store Depression Store HydrologyHydrology

DEPRESSION STORES (flowing and closed)

HRU 1

HRU 2

STORAGE HRU

FL

OW

S

GW

P ET

FLOW

PRMS

SUBSURFACE FLOWSUBSURFACE FLOW

= IN - (ssrcoef_lin * S) - -----(ssrcoef_sq * S2)

dSdt

IN

Subsurface Reservoir

ssr_to_gw = ssr2gw_rate * S

ssrmax_coef( )

ssr2gw_exp

PRMS

GROUND-WATER FLOWGROUND-WATER FLOW

gwres_flow= gwflow_coeff * ------------------gwres_stor

soil_to_gw + ssr_to_gw

Ground-water Reservoir

gwres_sink = gwsink_coef * gwres_stor

Qbase = gwflow_coef x gwres_stor

Q0 Qt

Qt = Q0 e-kt

gwflow_coef = k

Estimating GW Reservoir Parameters

Daily recharge SEP fits interannual variation in Qbase

outflow

inflow

3rd HRU DIMENSION

Relation of HRUs and Relation of HRUs and Subsurface and GW ReservoirsSubsurface and GW Reservoirs

Surface ( 6 hrus )

Subsurface ( 2 reservoirs )

Ground water (1 reservoir)

Assumes No Cascade Assumes No Cascade FlowFlow