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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
Recommended