Soil Processes: SVAT, ET, and the Subsurface CIVE 781: Principles of Hydrologic Modelling University of Waterloo Jun 19 24, 2017 Summary The role of soil and vegetation in the water cycle Soil Physics: Richard s Equation and simplified subsurface modelling The approximations The controls on partitioning PET and AET: Penman Monteith and simplified SVAT modelling Energy balances 2 1
This is easily an entire course worth of material The focus here is on Basic physics How we simplify those physics in standard watershed models The important stuff to get right/consider 3 4 2
Prelims: Soil Moisture Critical Soil Moistures: Saturation > (WET) Pore space completely filled with water 1, Field Capacity > (MOIST) Moisture content at which water does not drain via gravity 0.10.3 Wilting point > (PRETTY DRY) Moisture content at which plants cannot extract water 0.020.1 Oven Dry > (BONE DRY) 0 1 0 5 The Physics: Darcy s Law and Richards Equation Water flow in unsaturated and saturated media is controlled by Darcy s Law, adapted to unsaturated conditions: Where is vertical flow [m/d] (positive upward) is the unsaturated hydraulic conductivity [m/d] pressure head [m] is the elevation head [m] is the total head [m] Flow moves from regions of higher to lower pressure (higher saturation to lower saturation) 6 3
Capillary Forces height height Water table S 7 Soil Characteristics Water in any unsaturated soil is at negative pressures (relative to atmospheric) Leads to the first soil characteristic curve drier Negative pressure pressure head Positive pressure http://www.aardappelpagina.nl/explorer/pagina/soilwater.htm http://croptechnology.unl.edu/ 8 4
Soil Characteristics saturation zone drier Negative pressure Positive pressure pressure head Drier soils become less conductive Mostly because pathways to transmit water aren t there 9 Hysteresis Poulovassilis and Kargas, A Note on Calculating Hysteretic Behavior, SSSAJ, Vol. 64 No. 6, p. 1947 1950 Typically ignored in both integrated and simplified physics based watershed models 10 5
Richards Equation Mass balance on water on unit area. Presumes unsaturated flow only: Re express volume and flow lim Δ where is the water saturation, [ ] is porosity, [ ] is the water volume [m3] is the Darcy Buckingham flux [m/d] Sub in Darcy Buckingham flux: V V Δ Solve for, get Δ 11 Richards Equation Governing equation for vertical flow in unsaturated media Special tricks needed to handle switch to saturation In 3D, (integrated models) Specific storage (for saturated case) Lateral flow no gravity term 12 6
The Infiltration Process 1 2 3 4 Initial application (1 3) suction in soil leads to acceptance of all rainfall 5 6 Wetting front Saturation (3) soil pores fill Ponded (4 6) Self sharpening water front water behind front moves faster than in front = time to ponding 1 1 2 3 4 5 6 ~ 13 Infiltration From Shuttleworth (1993) 14 7
Surface Runoff Mechanisms Figure courtesy of the UCAR Comet Program Hortonian (infiltration excess) Flow Dependent upon concept of infiltration capacity, [mm/hr] (soil property) Valid for short duration, intense rainfall; Clayey soils Dunne (saturation excess) Flow Ground becomes saturated due to Rising water table (groundwater ridging) Not spatially uniform Tends to be in lower lying areas, banks of stream 15 Variable Source Contributing Areas (VSA) Recognized that contributing areas are dynamic the variable source areas are typically located in low lying lands immediately adjacent to streams and rivers and are concentrated near basin outlets. the extent of these variable source areas is a function of topography, the antecedent soil moisture conditions meaning initial conditions when rainfall starts soil moisture storage capacity and rainfall intensity. the variable source area model represents a dynamic version of the partial contributing area model. Brooks et al., Fig 4.11 16 8
Interflow Lateral flow in shallow soil Macropores Figures courtesy of the UCAR Comet Program http://calag.ucanr.edu/archiv e/?article=ca.v064n02p78 17 Continuum version 18 9
Streamflow Mechanisms discharge Surface Runoff Channel precipitation Interflow Baseflow Bank storage In practice: Interflow any moderate slowing process Total Stormflow source volumes (example): 100% time Baseflow any significantly slowing process Mechanisms change greatly from wshed to wshed 0% Boundaries fuzzy it is hard to discern between surface runoff and interflow or interflow and baseflow 19 Some Important Concepts: Proper simplification Unsaturated flow is predominantly vertical, gravity drained flow Soil characteristics strongly impact infil and ET, but are less important for deeper processes Infiltration rates depends upon soil saturation, which may vary within a watershed Runoff rates higher in convergence/seepage zones Lateral subsurface flow from soils (interflow) behaves similar to overland flow Baseflow is dictated by head difference between WT and surface water (effectively extra GW storage) AET is restricted to top dynamic layer 20 10
Standard Vertical Conceptual Model Topsoil UZ zone Saturated GW 21 Role of Compartments: Topsoil ~100cm 200cm Only zone impacted by AET Most dynamic greatest seasonal fluctuation Reflects measured soil moisture Only layer typically characterized by agricultural soil maps In mountainous regions, often the only zone Often broken into multiple subcompartments in SVAT models AET Deep ET Topsoil percolation runoff Subsurface stormflow 22 11
Role of Compartments: Unsat Zone Above water table Below/includes zero flux plane Typically a throughflow zone Typically a mystery Least monitored part of the landscape Measurements are rare Saturation hovers near field capacity Lensing and perched aquifers problematic Interflow characterizes slower flow paths, likely preferential flow Very difficult to differentiate source of interflow vs. baseflow Deep ET UZ zone Capillary/ WT rise Percolation Recharge From Ameli et al., 2013, Adv. Water Res. Interflow 23 Role of Compartments: Groundwater Below water table Typically, we only represent the active groundwater above surface water elevations GW treated a source, not sink In practice, the Unsat and GW zones usually just moderate different rates of baseflow GW in the model can be confounded with other slow drainage processes Wetlands/lakes/glaciers also generate baseflow If not explicitly modeled, handled via GW Important: in arid regions, GW acts as a sink! Capillary/ WT rise Losing Streams Saturated GW Inactive GW Negative baseflow Recharge Baseflow 24 12
Notes Vertical fluxes often OK in physical conceptual models Conceptual representation::physical point process Lateral fluxes often involve some hand waving Implicitly trying to address Hillslope convergence/divergence Topographic controls Water table geometry Focused landscape saturation Neither conceptual models or integrated models are necessarily getting this right at large scales fundamental research issue Key goal when modelling with multiple soil compartments is to partition precipitation into AET Runoff/interflow (quickflow) Baseflow (slow flow) This partitioning is a balancing act The real story is subtle and complicated, which is why we try to simplify into compartments 25 Commonly Ignored Processes Bank Storage Soil Hysteresis Lateral unsaturated flow Soil heterogeneity Depression storage? Wetland storage? 26 13
Simplifications Infiltration,,, Function of Topsoil saturation, Rainfall/snowmelt intensity, Saturated area fraction, Soil/landscape parameters, Details vary from algorithm to algorithm, but fundamental differences are minor R/P S 27 Percolation Simplifications Commonly handled by just draining to field capacity Technically should be governed by a pressure gradient, but representative gradient at interface of block zones difficult to characterise Integrated average pressure head would grossly underestimate flowthru We are aided in that most water is going downward unless topsoil is really dry Gravity simplifes 28 14
Simplifications Interflow Generally a mystery, typically treated as a calibration parameter, especially at watershed scale Mechanistically poorly understood Mix of fast groundwater drainage, preferential unsaturated flow paths, delayed subsurface overland flow, tile drains, and other things we don t characterize well Often use simple linear/power law flux storage relation as surrogate for not knowing really what is happening Still needed to fit the hydrograph 29 Baseflow Simplfications Surprisingly, a linear storage flux model is reasonably well justified in many cases Groundwater is fairly linear The literature has not done a good job of demonstrating why 30 15
Groundwater Discharge Scaling From Snowdon and Craig, Effective groundwater surface water exchange at watershed scales, Hydrol. Process. 30, 1849 1861 (2016) 31 The Linear Reservoir The linear reservoir model treats the groundwater as a bucket Storage, Inflow, Outflow, Stream Mass balance: For I = constant, solution is 1 Or, in terms of 1 Ignoring inflow (in dry periods) 32 16
The Linear Reservoir: Groundwater Analogy Δ Δ upstream stream length into page Δ Δ Δ Δh Δ Δ For prismatic storage, ΔhLΔ 2 2 Δ i.e., S and k in the linear groundwater reservoir are proxies for other things 33 ET modelling 35 17
Standard ET Rates Three standard ET rates are commonly used in hydrology: Potential Evaporation the quantity of water evaporated per unit area from an idealized, extensive free water surface under existing atmospheric conditions i.e., lake evaporation rates = PE Potential Evapotranspiration rate of ET from an area planted with a specific vegetation, where water availability is not a limiting factor Factors in boundary layer effects, vegetation resistance Actual ET (AET) or Crop ET The ET that occurs under actual conditions Often AET is calculated under standard conditions (i.e. wet soils) for a given crop and then adjusted further for actual conditions (i.e. dry soils) Important : A 36 Actual ET Actual ET controlled by: Water availability/accessibility Is there water to be evaporated/transpired? Is it connected to the atmosphere? (e.g., snow cover) Energy availability Transformation of water to water vapor requires energy Internal (deficit driven) External (radiation driven) Water saturation of atmosphere Relative humidity/vapour pressure Wind velocity Boundary layer effects (vegetation, wind speed) which slow diffusion 37 18
Relative & Absolute Humidity Psychrometric chart Δ Dry bulb (regular ol ) temperature Absolute Humidity (gmwater/gmair) Total amount of water in air limited by temperature Key: equilibrium means air is at saturation Equilibrium impeded by Resistance to diffusion of water through vegetation and into air column Availability of water Energy available for phase change 38 Seasonal Trends Summer (May 1 Sep 1) Summer (May 1 Sep 1) > Reduced water availability in soil over course of summer 39 19
Transpiration gis.ess.washington.edu/grg/courses/ess326 40 Estimating ET: Penman Monteith Preferred method if data is available Relatively accurate and consistent Driven by radiation: Uses external energy Driven by vapour deficit: converts internal energy 1 Δ Δ Δ Fraction of total energy going to evaporation Total energy supplied [MJ/m 2 /d] Converts deficit to energy Converts latent heat flux density to mm/d evaporation 1 Δ Vapour deficit atmospheric resistance 41 20
Penman Monteith: In Detail 1 Δ Δ Δ Latent heat of vaporization [J/kg], air/water density [kg/m 3 ] saturation vapour pressure [kpa] is psychrometric constant [kpa C 1 ] (~0.065 kpa/ C) Δ slope of vapour pressure curve [kpa C 1 ], specific heat of air [MJ/kg] (~0.001) air temperature [ C] net radiation at the crop surface [MJ m 2 day 1 ] soil heat flux density [MJ m 2 day 1 ], Can assume 0 for 24 hr timestep actual vapour pressure [kpa] is psychrometric constant corrected for resistance to sensible heat transfer 1 atmospheric resistance to vapor transfer [s/m] 42 Penman Monteith Psychrometric chart: Evaporation moves air mass from state A (drier) to B (wetter) or Absolute humidity Energy added to saturated system heating and evaporating (driven by radiation) Lines of constant energy (enthalpy) in system Evaporative cooling: no energy change, water added using energy of air (driven by vapour deficit) 43 21
Open Water Evap: Priestley Taylor Assumes conditions of minimum advection (moisture deficit non influential) Often used for open water evaporation in depressions, lakes Δ Δ Where =1.26 (empirically determined, often a fitting coefficient) 44 ET Estimation Controlled by Proper water balance of soil soil saturation controls availability Proper net radiation estimation/provision Proper vapour deficit calculation Proper estimation of resistance to sensible heat flux The latter three suggest a flux tower is mandatory. It probably is. You won t typically have one Many simplifications available for penman monteith with more easily accessible parameters A laundry list of methods exist for estimating net radiation to the landscape. We won t go through these here. 45 22
Hargreaves (FAO) Approach Simpler and less data intensive than Penman Monteith Fully empirical Same reference crop and conditions as Penman Monteith 0.0023 17.8 where T in Celsius is in mm/day is extraterrestrial radiation Cloud cover/atmospheric effects 46 Partitioning Issues Errors readily propagate through model Overestimate infiltrationoveresti mate ET, percolation, baseflow Underestimate ETOverestimate runoff, recharge Topsoil UZ zone Saturated GW 47 23
Take Home The subsurface plays a signficant role in the water balance Data sparse Subsurface structure controls response Often have poor characterization of this Sloping vs. flat landscape differ greatly in character Similar representations used for both in most modelling schemes Proper partitioning of AET Baseflow Interflow critical Tough to justify either 1D richards equation or 3D richards equation given the available data 48 24