1. PRECIPITATION-RUNOFF MODELING SYSTEM (PRMS) MODELING OVERVIEW & DAILY MODE COMPONENTS

2. SUGGESTED REGERENCE ON WATERSHED MODELING - Overview chapters on basic concepts - 25 Models, each a chapter with discussions of model components and assumptions

3. 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

4. Model Selection Criteria Problem objectives Problem objectives Data constraints Data constraints Time and space scales of application Time and space scales of application

5. Lumped Model Approach TANK MODEL

6. TOPMODEL GRID-BASED MODELS - Explicit grid to grid - Statistical distribution ----(topgraphic index) Distributed Approaches

7. TOPMODEL Distributed Process Conceptualization Statistical Distribution of Topographic Index ln(a/tanB)

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

9. SPATIAL CONSIDERATIONS LUMPED MODELS LUMPED MODELS - No account of spatial variability of processes, input, boundary conditions, and system geometry DISTRIBUTED MODELS DISTRIBUTED MODELS - Explicit account of spatial variability of processes, input, boundary conditions, and watershed characteristics QUASI-DISTRIBUTED MODELS QUASI-DISTRIBUTED MODELS - Attempt to account for spatial variability, but use some degree of lumping in one or more of the modeled characteristics.

10. PRMS

11. PRMS Variations PRMS_WET PRMS_ISO PRMS_Yakima PRMS_Jena PRMS- MODFLOW

12. PRMS Parameters original version

13. PRMS Parameters MMS Version

14. PRMS Features Modular Design Modular Design Deterministic Deterministic Distributed Parameter Distributed Parameter Daily and Storm Mode Daily and Storm Mode Variable Time Step Variable Time Step User Modifiable User Modifiable Optimization and Sensitivity Analysis Optimization and Sensitivity Analysis

15. HYDROLOGIC RESPONSE UNITS (HRUs)

16. Distributed Parameter Approach Hydrologic Response Units - HRUs HRU Delineation Based on: - Slope - Aspect - Elevation - Vegetation - Soil - Precip Distribution

17. HRUs

18. HRU DELINEATION AND CHARACTERIZATION Polygon Hydrologic Response Units (HRUs) Grid Cell Hydrologic Response Units (HRUs)

19. Dill Basin, Germany 750 km 750 km 2 Land Use Sub-basins Topography

20. Topographic Pixelated PRMS -- HRU Delineation

21. Grid Complexity

22. 3rd HRU DIMENSION

23. Relation of HRUs and Subsurface and GW Reservoirs Surface ( 6 hrus ) Subsurface ( 2 reservoirs ) Ground water (1 reservoir)

24. PRMS HRU resolution SSR resolution GWR resolution

25. PRMS

26. MODEL DRIVING VARIABLES - TEMPERATURE - PRECIPITATION - max and min daily - lapse rate varied monthly or daily - spatial and elevation adjustment - form estimation

27. MODEL 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

28. Max Temperature-Elevation Relations

29. TEMPERATURE 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

30. Precipitation-Elevation Relations

31. Mean Daily Precipitation Schofield Pass (10,700 ft) vs Crested Butte (9031 ft) MONTH Mean daily precip, in.

32. Precipitation Gage Catch Error vs Wind Speed (Larsen and Peck, 1972) Rain (shield makes little difference) Snow (shielded) Snow (unshielded)

33. Precipitation Gauge Intercomparison Rabbit Ears Pass, Colorado

34. Catch Ratio Equations WMO Study

35. Catch Ratio WMO Study

36. PRECIPITATION - DEPTH hru_precip(hru) = precip(hru_psta) * pcor(mo) pcor(mo) = Rain_correction or Snow_correction For each HRU

37. PRECIPITATION - FORM (rain, snow, mixture of both) For each HRU RAIN tmin(hru) > tmax_allsnow tmax(hru) > tmax_allrain(mo) SNOW tmax(hru) <= tmax_allsnow

38. PRECIPITATION - 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) * []

39. Precipitation Distribution Methods (module) Manual (precip_prms.f) Manual (precip_prms.f) Auto Elevation Lapse Rate (precip_laps_prms.f) Auto Elevation Lapse Rate (precip_laps_prms.f) XYZ (xyz_dist.f) XYZ (xyz_dist.f) PCOR Computation

40. Manual Manual PCOR Computation

41. Auto Elevation Lapse Rate Auto 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

42. PCOR Computation pmn_mo padj_sn or padj_rn elv_plaps Auto Elevation Lapse Rate Parameters

43. adj_p = pmo_rate * Auto Elevation Lapse Rate Auto 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)

44. XYZ Distribution

45. 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.

46. XYZ Spatial Redistribution 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

47. Z PRCP 2. PRCP mru = slope*Z mru + intercept where PRCP mru is PRCP for your modeling response unit Z mru 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 = PRCP sta - slope*Z sta where PRCP sta is mean station PRCP and Z sta 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 Methodology

48. 2-D Example XYZ and Rain Day Frequency Elevation Mean Station Precipitation 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

49. 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

50. 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

51. Precipitation Distribution Methods (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

52. Precipitation Distribution Methods (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

53. SOLAR 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)

54. Degree-Day Solar Radiation Estimation Procedure (non precip day) For days with precip, daily value is multiplied by a seasonal adjustment factor

55. DRIVING VARIABLE INPUT SOURCES Point measurement data Point measurement data Radar data Radar data Satellite data Satellite data Atmospheric model data Atmospheric model data

57. RADAR DATA NEXRAD vs S-POL, Buffalo Creek, CO

59. Satellite Image for Snow-Covered Area Computation

69. Statistical Downscaling Atmospheric Models Multiple linear regression equations developed for selected climate stations Multiple linear regression equations developed for selected climate stations Predictors chosen from over 300 NCEP variables (< 8 chosen for given equation) Predictors chosen from over 300 NCEP variables (< 8 chosen for given equation) Predictands are maximum and minimum temperature, precipitation occurrence, and precipitation amounts Predictands are maximum and minimum temperature, precipitation occurrence, and precipitation amounts Stochastic modeling of the residuals in the regression equations to provide ensemble time series Stochastic modeling of the residuals in the regression equations to provide ensemble time series 11,000 Climate Station Locations NCEP Model Nodes Collaboratively with U. of Colorado

70. Dynamical Downscaling RegCM2 (Giorgi et al., 1993, 1996)  Period: 1979-1988  Boundary conditions: NCEP Reanalysis  52 km grid (Lambert conformal projection)

71. Representative Elevation of Atmospheric Model Output based on Regional Station Observations

72. Nash-Sutcliff Coefficient of Efficiency Scores Simulated vs Observed Daily Streamflow

73. Performance Measures Coefficient of Efficiency E Nash and Sutcliffe, 1970, J. of Hydrology Widely used in hydrology Range – infinity to +1.0 Overly sensitive to extreme values

74. Animas River, CO Simulated Q with station data (S_3) and downscaled data (N_ds) from NCEP reanalysis

75. PRMS

76. INTERCEPTION 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)]

77. PRMS

78. Transpiration vs Soil Moisture Content and Weather Conditions

79. Potential Evapotranspiration (potet) - Pan Evaporation - Hamon - Jensen - Haise potet(hru) = epan_coef(mo) * pan_evap potet(hru) = hamon_coef(mo) * dyl 2 * vdsat potet(hru) = jh_coef(mo) * --------------- (tavf(hru) - jh_coef_hru) * rin

80. Various Concepts of ET vs Soil Moisture

81. Computed ET (AET) as function of PET and Soil Texture PRMS to PRMS/MMS SMAV = soil_moist SMAX = soil_moist_max RECHR = soil_rechr REMX = soil_rechr_max

82. 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

83. Point Evapotranspiration Comparison Eddy correlation Jensen-Haise Aspen Park, CO ET, inches

84. WORKSHOP ON REGIONAL CLIMATE PREDICTION AND DOWNSCALING TECHNIQUES FOR SOUTH AMERICA Basin Evapotranspiration Comparison Jensen-Haise RegCM2 Animas River Basin, Colarado

85. Mirror Lake, NH GW - ET Relations

86. PRMS

87. Distribution, Flow, and Interaction of Water

88. SOIL ZONE ( Original Version) Recharge Zone (soil_rechr_max) Lower Zone excs (soil_moist > soil zone field capacity) sroff soil_moist_max (rooting depth) soil2gw_max excs - soil_to_gw to subsurface reservoir to ground-water reservoir

89. Original and Revised Soil Zone

90. Original PRMS Conceptualization SRO

91. Revised PRMS Conceptualization

92. Soil Zone Structure and Flow Computation Sequence

93. wp fc sat soil_moist_max = fc -wp sat_threshold = sat -fc Capillary Reservoir Gravity Reservoir Preferential-Flow Reservoir pref_flow_stor slow_stor pref_flow_thresh = sat_threshold * (1.0 – pref_flow_den) pref_flow_max = sat_threshold – pref_flow_thresh soil_moist soil_rechr soil_zone_max = sat_threshold + soil_moist_max ssres_stor = slow_stor + pref_flow_stor

94. Soil Zone Water Flux

95. Soil Zone Module

96. HYDROLOGIC RESPONSE UNITS (HRUs)

97. Cascading Flow

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

99. OVERLAND FLOW PLANES channel Overland Flow Plane 1.0 } } ∆x Pervious Precipitation excess Unit overland flow % Impervious % Pervious Impervious Precipitation excess

100. CASCADING FLOW PLANES 3 Overland Flow Path Channel Segment Overland Flow Plane 2 1 3 2 7 4 5 6 8 9 10 1112 Grass/Agriculture Bare Ground/Rock Trees Shrubs length width 1 3 1 2 4 Channel Junction

101. Soil Texture vs Available Water-Holding Capacity

102. Infiltration - 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_precip 2 / fr ) net_precip < fr qrp = net_precip - (.5 * fr) Otherwise fin = net_precip - qrp

103. PRMS

104. STREAMFLOW Integration of a variety of runoff generation processes Surface Runoff Subsurface Flow (Interflow) Baseflow

105. ANIMAS RIVER, CO SURFACE GW SUBSURFACE PREDICTED MEASURED

106. EAST FORK CARSON RIVER, CA SUBSURFACE GW SURFACE

107. PRMS

108. SURFACE RUNOFF GENERATION MECHANISMS

109. Variable-Source Area Concept

110. Contributing Area vs Basin Moisture Index

111. 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)

112. Surface Runoff Contributing Area vs Soil Moisture Index (nonlinear approach)

113. Surface Runoff Contributing Area vs Soil Moisture Index (nonlinear)

114. STARKWEATHER COULEE, ND Depression Storage Prairie Pothole Region

115. DEPRESSION STORAGE ESTIMATION (BY HRU) USING THE GIS WEASEL (AREA & VOLUME)

116. Depression Store Hydrology DEPRESSION STORES (flowing and closed) HRU 1 HRU 2 STORAGE HRU FLOW S GW PET FLOW

117. PRMS

118. SUBSURFACE FLOW = IN - (ssrcoef_lin * S) - -----(ssrcoef_sq * S 2 ) dS dt IN Subsurface Reservoir ssr_to_gw = ssr2gw_rate * S ssrmax_coef () ssr2gw_exp

119. PRMS

120. GROUND-WATER FLOW gwres_flow= gwflow_coeff * ------------------gwres_stor soil_to_gw + ssr_to_gw Ground-water Reservoir gwres_sink = gwsink_coef * gwres_stor

121. Qbase = gwflow_coef x gwres_stor Q0Q0 QtQt Q t = Q 0 e -kt gwflow_coef = k Estimating GW Reservoir Parameters Daily recharge SEP fits interannual variation in Q base outflow inflow

122. 3rd HRU DIMENSION

123. Relation of HRUs and Subsurface and GW Reservoirs Surface ( 6 hrus ) Subsurface ( 2 reservoirs ) Ground water (1 reservoir) Assumes No Cascade Flow