1 A soil moisture accounting-procedure with a Richards equation-based soil texturedependent parameterization Simon Mathias The Department of Earth Sciences Durham University Co-workers: Todd Skaggs, US Salinity Laboratory Simon Quinn, AMEC S Egan, L Finch, C Oldham, formerly at Durham University James Sorensen, BGS
Outline 2 Introduction to soil moisture accounting. Sensitivity analysis of percolation rates to soil texture according to Richards Equation (RE). Development of a new simple soil moisture accounting procedure (SMAP) to emulate RE for different soil textures. Application of the new SMAP to forecast soil moisture at four instrumented sites in England. Conclusions.
Research objective 3 To design a simple soil moisture accounting procedure that provides close to identical groundwater recharge results as compared to Richards equation for a given soil texture.
Soil moisture accounting procedure 4 PSMD(i)=SMD(i-1)+Ep(i)-qr(i); if PSMD(i)>WP Ea(i)=WP-SMD(i-1)+qr(i); SMD(i)=WP; qvp(i)=0; else Ea(i)=Ep(i); if PSMD(i)<0 SMD(i)=0; end qvp(i)=-psmd(i); else SMD(i)=PSMD(i); qvp(i)=0; end WP SMD Ea qvp qr Notation PSMD Potential soil moisture deficit SMD Soil moisture deficit Ep Potential evaporation Ea Actual evaporation qr Rainfall (following deduction of interception) qvp Vertical percolation WP Wilting point
5 Ep & Ea (mm) q r & q vp (mm) q r q vp Vertical percolation occurs only when SMD = 0 There is no actual evaporation when SMD = WP E p E a Maximum SMD = WP
6 Storage obtained by trapezoidal integration of moisture content measurements Field capacity? Soil Moisture Deficit (SMD) = Field capacity - Storage Wilting point? No return to field capacity in 2006 (Data courtesy of Andrew Ireson, University of Saskatchewan)
7 Comparison of SMAPs Sorensen et al. (2014) compared four different soil moisture accounting procedures (SMAP). This example is for water content (in mm) for a 3m profile at Beche Park Wood. Water content is quite similar for each model but recharge rates are more varying. Only JULES predicts recharge during periods of soil moisture deficit. (mm) (Sorensen et al., 2014, Hydrol. Proc. 28:2091-2012)
Sorensen s models 8 Penman Grindley (PG) FAO56 SPADE 1 1 1 E a / E p E a / E p E a / E p 0 SMD 0 SMD 0 SMD JULES JULES solves the Richards equation, normally using four finite difference nodes. Hydraulic conductivity, pressure head and E a / E p are treated as empirical functions of moisture content at each node.
Soil moisture characteristics 9 (after van Genuchten, 1980, Soil Sci. Soc. America J., 44:892-898)
The van Genuchten functions Moisture content, θ = Hydraulic conductivity, Effective saturation, S ( θ θ ) e s K = = r K S s e S + θ η e ( ) n 1+ αψ r [ ( ) ] 1/ m m 1 1 S m e where m = 1 1/ n 2 10 and ψ [L] is pressure head θs [-] is the saturated moisture content θr [-] is the residual moisture content S [-] is the effective saturation e K s α [L [LT -1-1 ] is the saturated hydraulic conductivity ] is the reciprocal of a reference state pressure head η, n [-] are empirical exponents (after van Genuchten, 1980, Soil Sci. Soc. America J., 44:892-898)
US Salinity Laboratory: ROSETTA Model 11 % Sand % Silt % Clay Artificial neural network based on results of drainage experiments from thousands of different soil samples. θ θ S s r e K α η n s The ROSETTA model is an example of a so-called pedotransfer function, which seeks to transform soil texture information into hydraulic properties that describe how water flows through the associated pore structure. Note that % Sand + % Silt + % Clay = 100%. Therefore a soil can be described by just 2 parameters (e.g. % Sand and % Silt). ROSETTA model allows the 7 van Genuchten parameters to be obtained from just 2. (for more information see Schaap et al., 2001, J. Hydrol. 251:163-176)
USDA soil texture classification system 12 Particle diameters 100 0 Clay: below 2 μm 90 10 Silt: 2 to 50 μm 80 20 Sand: 50 to 2000 μm 70 30 60 CLAY 40 40 50 SANDY CLAY SILTY CLAY 50 60 10 20 30 SANDY CLAY LOAM SANDY LOAM CLAY LOAM LOAM SILTY CLAY LOAM SILT LOAM 70 80 90 0 SAND SILT 100 100 90 80 70 60 50 40 30 20 10 0 PERCENT SAND
UK Soil Observatory http://www.ukso.org/maps.html 13
Research objective 14 To design a simple soil moisture accounting procedure that provides close to identical groundwater recharges results as compared to Richards equation for a given soil texture.
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Outline 16 Introduction to soil moisture accounting. Sensitivity analysis of percolation rates to soil texture according to Richards Equation (RE). Development of a new simple soil moisture accounting procedure (SMAP) to emulate RE for different soil textures. Application of the new SMAP to forecast soil moisture at four instrumented sites in England. Conclusions.
Finite difference model 17 (following deduction of interception) Actual evaporation: E Water currently in storage : where f 1 ( z) [L -1 ] is a function that describes how the plant roots are distrubuted with depth. f a Θ = 2 = E 0 L p 0 L θdz f 1 f 2 dz ( ψ ) [-] is a function that describes plant stress due to reduced water content.
Plant stress function 18 Feddes et al.(1976) proposed commonly used function for this purpose f2( ψ ) = where ψ ψ ψ a d w 0, 1, ψ ψ d 1 ψ w ψ 0, = 0.05 m = 4.0 m = 150.0 m d, ψ ψ ψ ψ a d ψ > ψ a > ψ > ψ ψ ψ w d w Ratio of actual to potential evapotranspiration 1 0 Plant is stressed and unable to transpire at the potential rate. ψ w The water content is so low that the plant has wilted and is therefore not transpiring. Optimal conditions: Plant is transpiring at the potential rate. ψ d Pressure head ψ a Anaerobiosis: The soil is so wet that the roots are unable to access oxygen and the plant is unable to transpire.
Rainfall (mm/d) Silty soil (Mathias et al., 2015, WRR) 19 Evaporation (mm/d) Ep Ea Storage (mm) Percolation (mm/d) Smooth & attenuated percolation. Depth to ZFP (m) Persistent summer zero flux plane (ZFP).
Vertical flow patterns over a year 20 Soil surface Time months J F M A M J J A S O N D First stage of wetting Depth Winter drainage through whole profile Upward flux to satisfy evapotranspiration demand Profile wetted: drainage through whole profile Slow residual drainage Beneath ZFP Water table (Diagram kindly provided by Andrew Ireson, after Wellings and Bell, 1980, Journal of Hydrology)
Rainfall (mm/d) Clay soil (Mathias et al., 2015, WRR) Triangles are where surface runoff occurred 21 Evaporation (mm/d) Ep Ea Depth to ZFP (m) Percolation (mm/d) Storage (mm) Higher winter peak flow events.
Rainfall (mm/d) Sandy soil (Mathias et al., 2015, WRR) 22 Evaporation (mm/d) Ep Ea Transpiration is frequently limited due to water stress. Percolation (mm/d) Storage (mm) Rapidly changing percolation. Depth to ZFP (m) Episodic zero flux plane generation.
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Outline 24 Introduction to soil moisture accounting. Sensitivity analysis of percolation rates to soil texture according to Richards Equation (RE). Development of a new simple soil moisture accounting procedure (SMAP) to emulate RE for different soil textures. Application of the new SMAP to forecast soil moisture at four instrumented sites in England. Conclusions.
Model structure for proposed SMAP 25 E a q r q ro Θ q d q vp
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Obtaining the other parameters 27 In addition to the parameters that can be obtained from ROSETTA, the new SMAP also requires the following additional parameters for a given soil texture: Infiltration capacity, q ic Storage capacity available for plant uptake, Θ pu Depth of water at which plant wilting occurs, Θ w Residence of the lower water store, T r These four parameters were determined by calibrating the new SMAP to percolation data from the Richards equation (RE) model for 231 different soil textures. The RE model was simulated using weather data from 1961 to 1998. The SMAP was calibrated using data from 1964 to 1984. The SMAP was then validated using data from 1984 to 1998.
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Model performance during validation 29 In terms of vertical percolation In terms of soil moisture storage
Rainfall (mm/d) Silty soil q r RE SMAP (Mathias et al., 2015, WRR) 30 Evaporation (mm/d) E p RE SMAP Storage (mm) RE SMAP Percolation (mm/d) RE SMAP Smooth & attenuated percolation. Depth to ZFP (m)
Rainfall (mm/d) Clay soil q r RE SMAP (Mathias et al., 2015, WRR) Triangles are where surface runoff occurred. 31 Evaporation (mm/d) E p RE SMAP Storage (mm) RE SMAP Percolation (mm/d) RE SMAP Higher winter peak flow events. Depth to ZFP (m)
Rainfall (mm/d) Sandy soil q r RE SMAP (Mathias et al., 2015, WRR) 32 Evaporation (mm/d) E p RE SMAP Transpiration is frequently limited due to water stress. Storage (mm) RE SMAP Percolation (mm/d) RE SMAP Rapidly changing percolation. Depth to ZFP (m)
Outline 33 Introduction to soil moisture accounting. Sensitivity analysis of percolation rates to soil texture according to Richards Equation (RE). Development of a new simple soil moisture accounting procedure (SMAP) to emulate RE for different soil textures. Application of the new SMAP to forecast soil moisture at four instrumented sites in England. Conclusions.
Revisiting Sorensen s recharge data 34 (Sorensen et al., 2014, Hydrol. Proc. 28:2091-2012)
Warren Farm
Warren Farm 36 (Observed data and JULES output courtesy of James Sorensen, BGS)
Highfield Farm
Highfield Farm 38 (Observed data and JULES output courtesy of James Sorensen, BGS)
Beche Park Wood
Beche Park Wood 40 (Observed data and JULES output courtesy of James Sorensen, BGS)
Grimsbury Wood
Grimsbury Wood 42 (Observed data and JULES output courtesy of James Sorensen, BGS)
Conclusions The soil textural triangle is an interesting medium to study vertical percolation behaviour of different soil types. Homogenous Richards equation recharge models can be effectively emulated by simple store models in conjunction with pressure head and hydraulic conductivity relationships with water saturation. A proposed new soil moisture accounting procedure (SMAP) resulting from this work, parameterised only in terms of soil texture, has been shown to efficiently forecast observed soil moisture data from four field sites. Percolation rates are less well constrained than water content. The new SMAP is more simple than RE type approaches such as JULES but more realistic than other simple approaches such as FAO56. The new SMAP is advocated for use in future groundwater recharge studies. 43