SWAT+ Documentation
  • INTRODUCTION
    • Introduction to SWAT+
    • Watershed Configuration
      • Spatial Objects
    • Calibration
  • SWAT+ Input Files
    • Input File Format
    • Master File (file.cio)
    • Simulation Settings
      • object.cnt
      • time.sim
        • day_start
        • yrc_start
        • day_end
        • yrc_end
        • step
      • print.prt
        • nyskip
        • interval
        • aa_int_cnt
        • hydcon
        • object
      • object.prt
        • obj_typ
        • obj_typ_no
        • hyd_typ
    • Climate
      • weather-sta.cli
        • name (weather_sta.cli)
        • wgn
        • pcp
        • tmp
        • slr
        • hmd
        • wnd
        • pet
        • atmo_dep
      • weather-wgn.cli
        • name (weather_wgn.cli)
        • yrs_pcp
        • tmp_max_ave
        • tmp_min_ave
        • tmp_max_sd
        • tmp_min_sd
        • pcp_ave
        • pcp_sd
        • pcp_skew
        • wet_dry
        • wet_wet
        • pcp_days
        • pcp_hhr
        • slr_ave
        • dew_ave
        • wnd_ave
      • pcp.cli and pcp data files
      • tmp.cli and tmp data files
      • hmd.cli and hmd data files
      • slr.cli and slr data files
      • wnd.cli and wnd data files
      • atmo.cli
        • timestep
        • num_aa
    • Basin
      • codes.bsn
        • pet
        • crack
        • swift_out
        • rte_cha
        • nostress
        • carbon
        • lapse
        • uhyd
        • tiledrain
        • wtable
        • soil_p
        • gampt
        • qual2e
        • gwflow
      • parameters.bsn
        • sw_init
        • surq_lag
        • adj_pkrt
        • prf
        • orgn_min
        • n_uptake
        • p_uptake
        • n_perc
        • p_perc
        • p_soil
        • p_avail
        • rsd_decomp
        • pest_perc
        • msk_co1
        • msk_co2
        • msk_x
        • nperco_lchtile
        • evap_adj
        • denit_exp
        • denit_frac
        • adj_uhyd
        • cn_froz
        • dorm_hr
        • plaps
        • tlaps
        • n_fix_max
        • rsd_decay
        • urb_init_abst
        • uhyd_alpha
        • splash
        • rill
        • surq_exp
        • cov_mgt
        • co2
    • Landscape Units
      • ls_unit.def
        • id (ls_unit.def)
        • name (ls_unit.def)
        • elem_tot
        • elements
      • ls_unit.ele
        • id (ls_unit.ele)
        • name (ls_unit.ele)
        • obj_typ
        • obj_typ_no
        • bsn_frac
    • Routing Units
      • rout_unit.rtu
        • id (rout_unit.rtu)
        • name (rout_unit.rtu)
        • define
        • topo
        • field
      • rout_unit.def
        • id (rout_unit.def)
        • name (rout_unit.def)
        • elem_tot
        • elements
      • rout_unit.ele
        • id (rout_unit.ele)
        • name (rout_uni.ele)
        • obj_typ
        • obj_id
    • Hydrologic Response Units
      • hru-data.hru
        • id (hru-data.hru)
        • name (hru-data.hru)
        • topo
        • hydro
        • soil
        • lu_mgt
        • soil_plant_init
        • surf_stor
        • snow
        • field
      • hru-lte.hru
        • id (hru-lte.hru)
        • name (hru-lte.hru)
        • area
        • cn2
        • cn3_swf
        • t_conc
        • soil_dp
        • perco_co
        • slp
        • slp_len
        • et_co
        • aqu_sp_yld
        • alpha_bf
        • revap
        • rchg_dp
        • sw_init
        • aqu_init
        • aqu_sh_flo
        • aqu_dp_flo
        • snow_h2o
        • lat
        • soil_text
        • trop_flag
        • grow_start
        • grow_end
        • plnt_typ
        • stress
        • pet_flag
        • irr_flag
        • irr_src
        • t_drain
        • usle_k
        • usle_c
        • usle_p
        • usle_ls
    • Hydrology
      • topography.hyd
        • name (topography.hyd)
        • slp
        • slp_len
        • lat_len
        • depos
      • hydrology.hyd
        • name (hydrology.hyd)
        • lat_time
        • lat_sed
        • can_max
        • esco
        • epco
        • orgn_enrich
        • orgp_enrich
        • cn3_swf
        • bio_mix
        • perco
        • lat_orgn
        • lat_orgp
        • pet_co
        • latq_co
      • snow.sno
        • name (snow.sno)
        • fall_tmp
        • melt_tmp
        • melt_max
        • melt_min
        • tmp_lag
        • snow_h2o
        • cov50
        • snow_init
      • field.fld
        • name (field.fld)
        • len
        • wd
    • Soils
      • soils.sol
        • name (soils.sol)
        • hyd_grp
        • dp_tot
        • anion_excl
        • perc_crk
        • texture
        • bd
        • awc
        • soil_k
        • carbon
        • clay
        • silt
        • sand
        • rock
        • alb
        • usle_k
        • ec
        • caco3
        • ph
      • nutrients.sol
        • name (nutrients.sol)
        • exp_co
        • lab_p
        • nitrate
        • fr_hum_act
        • hum_c_n
        • hum_c_p
    • Landuse and Management
      • landuse.lum
        • name (landuse.lum)
        • cal_grp
        • plnt_com
        • mgt
        • cn2
        • cons_prac
        • urban
        • urb_ro
        • ov_mann
        • tile
        • sep
        • vfs
        • grww
        • bmp
      • plant.ini
        • name (plant.ini)
        • plnt_cnt
        • rot_yr_ini
        • plnt_name
        • lc_status
        • lai_init
        • bm_init
        • phu_init
        • plnt_pop
        • yrs_init
        • rsd_init
      • management.sch
        • name (management.sch)
        • op_typ
        • op_data1
        • op_data2
        • op_data3
      • cntable.lum
        • name (cntable.lum)
        • cn_a
        • cn_b
        • cn_c
        • cn_d
      • cons_practice.lum
        • name (cons_practice.lum)
        • usle_p
        • slp_len_max
      • ovn_table.lum
        • name (ovn_table.lum)
        • ovn_mean
        • ovn_min
        • ovn_max
    • Decision Tables
      • "name".dtl
        • var
        • obj
        • obj_num
        • lim_var
        • lim_op
        • lim_const
        • alt
        • act_typ
        • obj
        • obj_num
        • name
        • option
        • const
        • const2
        • fp
        • outcome
    • Management Practices
      • harv.ops
        • name (harv.ops)
        • harv_typ
        • harv_idx
        • harv_eff
        • harv_bm_min
      • graze.ops
        • name (graze.ops)
        • fertname
        • bm_eat
        • bm_tramp
        • man_amt
        • grz_bm_min
      • irr.ops
        • name (irr.ops)
        • irr_eff
        • surq_rto
        • irr_amt
        • irr_dep
        • irr_salt
        • irr_no3n
        • irr_po4
      • chem_app.ops
        • name (chem_app.ops)
        • app_eff
        • inject_dp
        • surf_frac
      • fire.ops
        • name (fire.ops)
        • chg_cn2
        • frac_burn
      • sweep.ops
        • name (sweep.ops)
        • swp_eff
        • frac_curb
    • Structural Practices
      • tiledrain.str
        • name (tiledrain.str)
        • dp
        • t_fc
        • lag
        • rad
        • dist
        • drain
        • pump
        • lat_ksat
      • filterstrip.str
        • name (filterstrip.str)
        • fld_vfs
        • con_vfs
        • cha_q
      • grassedww.str
        • name (grassedww.str)
        • mann
        • sed_co
        • dp
        • wd
        • len
        • slp
      • bmpuser.str
        • name (bmpuser.str)
        • sed_eff
        • ptlp_eff
        • solp_eff
        • ptln_eff
        • soln_eff
        • bact_eff
      • septic.str
        • name (septic.str)
        • typ
        • yr
        • operation
        • residents
        • area
        • t_fail
        • dp_bioz
        • thk_bioz
        • cha_dist
        • sep_dens
        • bm_dens
        • bod_decay
        • bod_conv
        • fc_lin
        • fc_exp
        • fecal_decay
        • tds_conv
        • mort
        • resp
        • slough1
        • slough2
        • nit
        • denit
        • p_sorp
        • p_sorp_max
        • solp_slp
        • solp_int
    • Databases
      • plants.plt
        • name (plants.plt)
        • plnt_typ
        • gro_trig
        • nfix_co
        • days_mat
        • bm_e
        • harv_idx
        • lai_pot
        • frac_hu1
        • lai_max1
        • frac_hu2
        • lai_max2
        • hu_lai_decl
        • dlai_rate
        • can_ht_max
        • rt_dp_max
        • tmp_opt
        • tmp_base
        • frac_n_yld
        • frac_p_yld
        • frac_n_em
        • frac_n_50
        • frac_n_mat
        • frac_p_em
        • frac_p_50
        • frac_p_mat
        • harv_idx_ws
        • usle_c_min
        • stcon_max
        • vpd
        • frac_stcon
        • ru_vpd
        • co2_hi
        • bm_e_hi
        • plnt_decomp
        • lai_min
        • bm_tree_acc
        • yrs_mat
        • bm_tree_max
        • ext_co
        • leaf_tov_min
        • leaf_tov_max
        • bm_dieoff
        • rt_st_beg
        • rt_st_end
        • plnt_pop1
        • frac_lai1
        • plnt_pop2
        • frac_lai2
        • frac_sw_gro
        • aeration
        • rsd_pctcov
        • rsd_covfac
      • urban.urb
        • name (urban.urb)
        • frac_imp
        • frac_dc_imp
        • curb_den
        • urb_wash
        • dirt_max
        • t_halfmax
        • conc_totn
        • conc_totp
        • conc_no3
        • urb_cn
      • tillage.til
        • name (tillage.til)
        • mix_eff
        • mix_dp
      • fertilizer.frt
        • name (fertilizer.frt)
        • min_n
        • min_p
        • org_n
        • org_p
        • nh3_n
      • pesticide.pes
        • name (pesticide.pes)
        • soil_ads
        • frac_wash
        • hl_foliage
        • hl_soil
        • solub
        • aq_reac
        • aq_volat
        • mol_wt
        • aq_resus
        • aq_settle
        • ben_act_dep
        • ben_bury
        • ben_reac
      • septic.sep
        • name (septic.sep)
        • q_rate
        • bod
        • tss
        • nh4_n
        • no3_n
        • no2_n
        • org_n
        • min_p
        • org_p
        • fcoli
    • Aquifers
      • aquifer.aqu
        • id (aquifer.aqu)
        • name (aquifer.aqu)
        • aqu_init
        • gw_flo
        • dep_bot
        • dep_wt
        • no3_n
        • sol_p
        • carbon
        • flo_dist
        • flo_max
        • alpha_bf
        • revap
        • rchg_dp
        • spec_yld
        • hl_no3n
        • flo_min
        • revap_min
      • initial.aqu
        • name (initial.aqu)
        • org_min
        • pest
        • path
        • hmet
        • salt
    • GWFlow
    • Channels
      • channel-lte.cha
        • id (channel-lte.cha)
        • name (channel-lte.cha)
        • ini
        • hyd
        • nut
      • initial.cha
        • name (initial.cha)
        • org_min
        • pest
        • salt
      • hyd-sed-lte.cha
        • name (hyd-sed-lte.cha)
        • wd
        • dp
        • slp
        • len
        • mann
        • k
        • erod_fact
        • cov_fact
        • sinu
        • eq_slp
        • d50
        • clay
        • carbon
        • dry_bd
        • side_slp
        • bed_load
        • fps
        • fpn
        • n_conc
        • p_conc
        • p_bio
      • nutrients.cha
        • name (nutrients.cha)
        • plt_n
        • plt_p
        • alg_stl
        • ben_disp
        • ben_nh3n
        • ptln_stl
        • ptlp_stl
        • cst_stl
        • ben_cst
        • cbn_bod_co
        • air_rt
        • cbn_bod_stl
        • ben_bod
        • bact_die
        • cst_decay
        • nh3n_no2n
        • no2n_no3n
        • ptln_nh3n
        • ptlp_solp
        • q2e_lt
        • q2e_alg
        • chla_alg
        • alg_n
        • alg_p
        • alg_o2_prod
        • alg_o2_resp
        • o2_nh3n
        • o2_no2n
        • alg_grow
        • alg_resp
        • slr_act
        • lt_co
        • const_n
        • const_p
        • lt_nonalg
        • alg_shd_l
        • alg_shd_nl
        • nh3_pref
    • Reservoirs and Ponds
      • reservoir.res
        • id (reservoir.res)
        • name (reservoir.res)
        • init
        • hyd
        • rel
        • sed
        • nut
      • initial.res
        • name (initial.res)
        • org_min
        • pest
        • salt
      • hydrology.res
        • name (hydrology.res)
        • yr_op
        • mon_op
        • area_ps
        • vol_ps
        • area_es
        • vol_es
        • k
        • evap_co
        • shp_co1
        • shp_co2
      • sediment.res
        • name (sediment.res)
        • nsed
        • d50
        • carbon
        • bd
        • sed_stl
        • stl_vel
      • nutrients.res
        • name (nutrients.res)
        • mid_start
        • mid_end
        • mid_n_stl
        • n_stl
        • mid_p_stl
        • p_stl
        • chla_co
        • secchi_co
        • theta_n
        • theta_p
        • n_min_stl
        • p_min_stl
      • weir.res
        • name (weir.res)
        • linear_c
        • exp_k
        • width
        • height
    • Wetlands
      • wetland.wet
        • id (wetland.wet)
        • name (wetland.wet)
        • init
        • hyd
        • rel
        • sed
        • nut
      • hydrology.wet
        • name (hydrology.wet)
        • hru_ps
        • dp_ps
        • hru_es
        • dp_es
        • k
        • evap
        • vol_area_co
        • vol_dp_a
        • vol_dp_b
        • hru_frac
    • Initialization
      • soil_plant.ini
        • name (soil_plant.ini)
        • sw_frac
        • nutrients
        • pest
        • salt
      • om_water.ini
        • name (om_water.ini)
        • vol
        • sed
        • part_n
        • part_p
        • no3
        • solp
        • chl_a
        • nh3
        • no2
        • cbn_bod
        • dis_ox
        • sand
        • silt
        • clay
        • sm_ag
        • l_ag
        • gvl
        • tmp
      • pest_water.ini
      • pest_hru.ini
      • salt_water.ini
      • salt_hru.ini
    • Constituents
      • constituents.cs
    • Point Sources and Inlets
      • recall.rec
        • id (recall.rec)
        • rec_typ
        • file
      • 'filename'.rec
    • Connectivity
      • 'object'.con
        • id
        • name
        • gis_id
        • area
        • lat
        • lon
        • elev
        • 'obj'
        • wst
        • cst
        • ovfl
        • rule
        • out_tot
        • obj_typ
        • obj_id
        • hyd_typ
        • frac
      • aqu_cha.lin
      • chan_surf.lin
    • Water Allocation
      • water_allocation.wro
        • rule_typ
        • cha_ob
        • ob_typ (source)
        • limit_mon
        • ob_typ (demand)
        • withdr
        • amount
        • right
        • rcv_ob
        • rcv_num
        • srcs
        • src
        • frac
        • comp
    • Calibration
      • codes.sft
      • wb_parms.sft
      • water_balance.sft
      • cal_parms.cal
      • calibration.cal
  • SWAT+ Output Files
    • Output File Format
    • Debugging Outputs
    • Soil
    • Management
    • Flow Duration Curve
    • Water Balance
    • Nutrient Balance
    • Losses
    • Plant and Weather
    • Channel
    • Aquifer
    • Reservoir
    • Recall
    • Hydrographs
    • Routing Unit
    • Pesticides
    • Object Outputs
  • Theoretical Documentation
    • ☁️Section 1: Climate
      • 🟰Chapter 1:1 Equations: Energy
        • ☀️1:1.1 Sun-Earth Relationships
          • 1:1.1.1 Distance between Earth and Sun
          • 1:1.1.2 Solar Declination
          • 🌄1:1.1.3 Solar Noon, Sunrise, Sunset, and Daylength
        • 1:1.2 Solar Radiation
          • 👽1:1.2.1 Extraterrestrial Radiation
          • 1:1.2.2 Solar Radiation under Cloudless Skies
          • 1:1.2.3 Daily Solar Radiation
          • 1:1.2.4 Hourly Solar Radiation
          • 1:1.2.5 Daily Net Radiation
        • 1:1.3 Temperature
          • 1:1.3.1 Daily Air Temperature
          • 1:1.3.2 Hourly Air Temperature
          • 1:1.3.3 Soil Temperature
          • 1:1.3.4 Water Temperature
        • 1:1:4 Wind Speed
      • Chapter 1:2 Atmospheric Water
        • 1:2.1 Precipitation
        • 1:2.2 Maximum Half-Hour Rainfall
        • 1:2.3 Water Vapor
        • 1:2.4 Snow Cover
        • 1:2.5 Snow Melt
          • 1:2.5.1 Snow Pack Temperature
            • Snow Melt Equation
      • Chapter 1:3 Weather Generator
        • 1:3.1 Precipitation
          • 1:3.1.1 Occurrence of Wet or Dry Day
          • 1:3.1.2 Amount of Precipitation
        • 1:3.2 Maximum Half-Hour Rainfall
          • 1:3.2.1 Monthly Maximum Half-Hour Rain
          • 1:3.2.2 Daily Maximum Half-Hour Rain Value
        • 1:3.3 Distribution of Rainfall Within Day
          • 1:3.3.1 Normalized Intensity Distribution
          • 1:3.3.2 Generated Time to Peak Intensity
          • 1:3.3.3 Total Rainfall and Duration
        • 1:3.4 Solar Radiation & Temperature
          • 1:3.4.1 Daily Residuals
          • 1:3.4.2 Generated Values
          • 1:3.4.3 Adjustment for Clear/Overcast Conditions
            • Maximum Temperature
            • Solar Radiation
        • 1:3.5 Relative Humidity
          • 1:3.5.1 Mean Monthly Relative Humidity
          • 1:3.5.2 Generated Daily Value
          • 1:3.5.3 Adjustment for Clear/Overcast Conditions
        • 1:3.6 Wind Speed
      • Chapter 1:4 Climate Customization
        • 1:4.1 Elevation Bands
        • 1:4.2 Climate Change
    • Section 2: Hydrology
      • Surface Runoff
        • Runoff Volume: SCS Curve Number Procedure
        • SCS Curve Number
        • Soil Hydrologic Groups
        • Antecedent Soil Moisture Condition
        • Retention Parameter
        • Slope Adjustments
        • Runoff Volume: Green & Ampt Infiltration Method
        • Peak Runoff Rate
        • Time of Concentration
          • Overland Flow Time of Concentration
          • Channel Flow Time of Concentration
        • Runoff Coefficient
        • Rainfall Intensity
        • Modified Rational Formula
        • Surface Runoff Lag
        • Transmission Losses
      • Chapter 2:2 Evapotranspiration
        • 2:2.1 Canopy Storage
        • 2:2.2 Potential Evapotranspiration
          • 2:2.2.1 Penman-Monteith Method
            • Soil Heat Flux
            • Aerodynamic Resistance
            • Canopy Resistance
            • Combined Term
          • 2:2.2.2 Priestley-Taylor Method
          • 2:2.2.3 Hargreaves Method
          • 2:2.2.4 Reading Measured or Estimated PET
        • 2:2.3 Actual Evapotranspiration
          • 2:2.3.1 Evaporation of Intercepted Rainfall
          • 2:2.3.2 Transpiration
          • 2:2.3.3 Sublimation and Evaporation from the Soil
            • Sublimation
            • Soil Water Evaporation
          • 2:2.3.4 Evaporation from Ponded Water
      • Soil Water
        • Soil Structure
        • Percolation
        • Bypass Flow
        • Perched Water Table
        • Lateral Flow
          • Lateral Flow Lag
      • Groundwater
        • Groundwater Systems
        • Shallow Aquifer
          • Recharge
          • Partitioning of Recharge Between Shallow and Deep Aquifer
          • Groundwater/Base Flow
          • Revap
          • Pumping
          • Groundwater Height
        • Deep Aquifer
    • Section 3: Nutrients/Pesticides
      • Nitrogen
        • Nitrogen Cycle in the Soil
          • Initialization of Soil Nitrogen Levels
        • Mineralization & Decomposition / Immobilization
          • Humus Mineralization
          • Residue Decomposition & Mineralization
        • Nitrification & Ammonia Volatilization
        • Denitrification
        • Atmospheric Deposition
          • Nitrogen in Rainfall
          • Nitrogen Dry Deposition
        • Fixation
        • Upward Movement of Nitrate in Water
        • Leaching
        • Nitrate in the Shallow Aquifer
      • Phosphorus
        • Phosphorus Cycle
          • Initialization of Soil Phosphorus Levels
        • Mineralization & Decomposition / Immobilization
          • Humus Mineralization
          • Residue Decomposition & Mineralization
        • Sorption of Inorganic P
        • Leaching
        • Phosphorus in the Shallow Aquifer
      • Pesticides
        • Wash-off
        • Degradation
        • Leaching
      • Bacteria
        • Wash-off
        • Bacteria Die-off/Re-growth
        • Leaching
      • Carbon
        • Sub-model Description
        • Changes from previous version
        • Analytical Solutions
    • Section 4: Erosion
      • Sediment
        • MUSLE
          • Soil Erodibility Factor
          • Cover and Management Factor
          • Support Practice Factor
          • Topographic Factor
          • Coarse Fragment Factor
        • USLE
          • Rainfall Erodibility Index
        • Snow Cover Effects
        • Sediment Lag in Surface Runoff
        • Sediment in Lateral & Groundwater Flow
      • Nutrient Transport
        • Nitrate Movement
        • Organic N in Surface Runoff
          • Enrichment Ratio
        • Soluble Phosphorus Movement
        • Organic & Mineral P Attached to Sediment in Surface Runoff
          • Enrichment Ratio
        • Nutrient Lag in Surface Runoff and Lateral Flow
      • Pesticide Transport
        • Phase Distribution of Pesticide
        • Movement of Soluble Pesticide
        • Transport of Sorbed Pesticide
          • Enrichment Ratio
        • Pesticide Lag in Surface Runoff and Lateral Flow
      • Bacteria Transport
        • Bacteria in Surface Runoff
        • Bacteria Attached to Sediment in Surface Runoff
          • Enrichment Ratio
        • Bacteria Lag in Surface Runoff
      • Water Quality Parameters
        • Algae
        • Carbonaceous Biological Oxygen Demand
          • Enrichment Ratio
        • Dissolved Oxygen
          • Oxygen Saturation Concentration
    • Section 5: Land Cover/Plant
      • Growth Cycle
        • Heat Units
          • Heat Unit Scheduling
        • Dormancy
        • Plant Types
      • Optimal Growth
        • Potential Growth
          • Biomass Production
            • Impact of Climate on Radiation-Use Efficiency
            • Modification of Biomass Calculation for Trees
          • Canopy Cover and Height
          • Root Development
          • Maturity
        • Water Uptake by Plants
          • Impact of Low Soil Water Content
          • Actual Water Uptake
        • Nutrient Uptake by Plants
          • Nitrogen Uptake
            • Nitrogen Fixation
          • Phosphorus Uptake
        • Crop Yield
      • Actual Growth
        • Growth Constraints
          • Water Stress
          • Temperature Stress
          • Nitrogen Stress
          • Phosphorus Stress
        • Actual Growth
          • Biomass Override
        • Actual Yield
          • Harvest Index Override
          • Harvest Efficiency
    • Section 6: Management Practices
      • General Management
        • Planting/Beginning of Growing Season
        • Harvest Operation
        • Grazing Operation
        • Harvest & Kill Operation
        • Kill/End of Growing Season
        • Tillage
          • Biological Mixing
        • Fertilizer Application
        • Auto-Application of Fertilizer
        • Continuous Application of Fertilizer
        • Pesticide Application
      • Water Management
        • Irrigation
          • Manual Application of Irrigation
          • Auto-Application of Irrigation
        • Tile Drainage
        • Impounded/Depressional Areas
        • Water Transfer
        • Consumptive Water Use
        • Point Source Loadings
      • Urban Areas
        • Characteristics of Urban Areas
        • Surface Runoff from Urban Areas
        • USGS Regression Equations
        • Build Up/Wash Off
          • Street Cleaning
      • Septic Systems
        • Biozone Algorithm
          • Buildup of Live Bacterial Biomass
          • Fate and Transport of Bacterial Biomass
          • Field Capacity
          • Clogging Effect on Hydraulic Conductivity
          • Soil Moisture and Percolation
          • Nitrogen, BOD, Fecal Coliform
          • Phosphorus Removal
          • Model Assumptions
        • Integration of Biozone Algorithm
          • Simulating Active and Failing Systems
      • Filter Strips and Grassed Waterways
        • Filter Strips
          • Empirical Model Development
          • Sediment Reduction Model
          • Nutrient Reduction Models
            • Total Nitrogen
            • Nitrate Nitrogen
            • Total Phosphorus
            • Soluble Phosphorus
          • VFS SWAT+ Model Structure
        • Grassed Waterways
    • Section 7: Main Channel Processes
      • Water Routing
        • Channel Characteristics
        • Flow Rate and Velocity
        • Variable Storage Routing Method
        • Muskingum Routing Method
        • Transmission Losses
        • Evaporation Losses
        • Bank Storage
        • Channel Water Balance
      • Sediment Routing
        • Landscape Contribution to Subbasin Routing Reach
        • Sediment Routing In Stream Channels
          • Simplified Bagnold Equation (Default method)
          • Physics Based Approach for Channel Erosion
        • Channel Erodibility Factor
        • Channel Cover Factor
        • Channel Downcutting and Widening
      • In-Stream Nutrient Processes
        • Algae
          • Chlorophyll a
          • Algal Growth
            • Local Specific Growth Rate of Algae
            • Local Respiration Rate of Algae
            • Local Settling Rate of Algae
        • Nitrogen Cycle
          • Organic Nitrogen
          • Ammonium
          • Nitrite
          • Nitrate
        • Phosphorus Cycle
          • Organic Phosphorus
          • Inorganic/Soluble Phosphorus
        • Carbonaceous Biological Oxygen Demand
        • Oxygen
          • Oxygen Saturation Concentration
          • Reaeration
            • Reaeration By Fickian Diffusion
            • Reaeration By Turbulent Flow Over A Dam
      • In-Stream Pesticide Transformations
        • Pesticide In The Water
          • Solid-Liquid Partitioning
          • Degradation
          • Volatilization
          • Settling
          • Outflow
        • Pesticide In The Sediment
          • Solid-Liquid Partitioning
          • Degradation
          • Resuspension
          • Diffusion
          • Burial
        • Mass Balance
      • Bacteria Routing
        • Bacteria Decay
        • Bacteria Sediment
      • Heavy Metal Routing
    • Section 8: Water Bodies
      • Impoundment Water Routing
        • Reservoirs
          • Surface Area
          • Precipitation
          • Evaporation
          • Seepage
          • Outflow
            • Measured Daily Outflow
            • Measured Monthly Outflow
            • Average Annual Release Rate For Uncontrolled Reservoir
            • Target Release For Controlled Reservoir
        • Ponds/Wetlands
          • Surface Area
          • Precipitation
          • Inflow
          • Evaporation
          • Seepage
          • Outflow
            • Pond Outflow
            • Wetland Outflow
        • Depressions/Potholes
          • Surface Area
          • Precipitation
          • Inflow
          • Evaporation
          • Seepage
          • Outflow
            • Overflow
            • Release Operation
            • Tile Flow
      • Sediment In Water Bodies
        • Mass Balance
        • Settling
        • Sediment Outflow
      • Nutrients In Water Bodies
        • Nutrient Transformations
        • Total Balance
        • Eutrophication
          • Phosphorus/Chlorophyll a Correlations
      • Pesticides In Water Bodies
        • Pesticide In The Water
          • Solid-Liquid Partitioning
          • Degradation
          • Volatilization
          • Settling
          • Outflow
        • Pesticide In The Sediment
          • Solid-Liquid Partitioning
          • Degradation
          • Resuspension
          • Diffusion
          • Burial
        • Mass Balance
      • Bacteria In Water Bodies
        • Bacteria Decay
    • References
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  1. Theoretical Documentation
  2. Section 3: Nutrients/Pesticides
  3. Carbon

Analytical Solutions

Last updated 3 years ago

The balanced equation for SCS_CSC​ in a single layer (Eq. [3:5.1.2a]) can be combined with Eq. [3:5.1.3a] and Eq. [3:5.1.7] and with a few assumptions allow for an analytical solution to the differential equation. The soil clay content and the C input rate were assumed to be constant and the powers α\alphaα and β\betaβ set to 1, so that the balance equation can be solved explicitly for SCS_CSC​. The time step was considered to be a year and we assumed that residues and manure fully decompose in that time frame so that kR=kM=1k_R=k_M=1kR​=kM​=1. Since the influence of residues and manure on the SCS_CSC​ balance is similar we assumed that C inputs are only through residues. With these substitutions Eq. [3:5.1.2a] becomes:

dSCdt=hxRC−hxRCSxSC−kSxSC2\frac{dS_C}{dt}=h_xR_C-\frac{h_xR_C}{S_x}S_C-\frac{k}{S_x}S^2_CdtdSC​​=hx​RC​−Sx​hx​RC​​SC​−Sx​k​SC2​ 3:5.3.1

The constant k substitutes for kxfEftoolk_xf_Ef_{tool}kx​fE​ftool​. This differential equation can be solved analytically, with integration rendering the following solution:

SC(t)=hxRC2k[(ϕeγtSx−1ϕeγtSx+1)1+4kSxhxRC−1]S_C(t)=\frac{h_xR_C}{2k}[(\frac{\phi e^{\frac{\gamma_t}{S_x}}-1}{\phi e^{\frac{\gamma _t}{S_x}}+1})\sqrt{1+\frac{4kS_x}{h_xR_C}}-1]SC​(t)=2khx​RC​​[(ϕeSx​γt​​+1ϕeSx​γt​​−1​)1+hx​RC​4kSx​​​−1] 3:5.3.2

γ=hxRC1+4kSxhxRC,\gamma=h_xR_C\sqrt{1+\frac{4kS_x}{h_xR_C}},γ=hx​RC​1+hx​RC​4kSx​​​,

ϕ=−2kSC(t=0)+hxRC+γ2kSC(t=0)+hxRC−γ\phi=-\frac{2kS_C(t=0)+h_xR_C+\gamma}{2kS_C(t=0)+h_xR_C-\gamma}ϕ=−2kSC​(t=0)+hx​RC​−γ2kSC​(t=0)+hx​RC​+γ​

The integration constant ϕ\phiϕ depends on the initial SCS_CSC​. The steady state solution for Eq. 3:5.3.2 is:

SC=hxRC2k1+4kSxhxRC−1]S_C=\frac{h_xR_C}{2k}\sqrt{1+\frac{4kS_x}{h_xR_C}}-1]SC​=2khx​RC​​1+hx​RC​4kSx​​​−1] 3:5.3.3

The ratio hxRCk\frac{h_xR_C}{k}khx​RC​​ is the equilibrium SCS_CSC​ that would be obtained if neither hCh_ChC​ nor kSk_SkS​ had a dependence on SCS_CSC​. As RCR_CRC​ increases, the value of the fraction 4kSxhxRC\frac{4kS_x}{h_xR_C}hx​RC​4kSx​​ will get smaller. Therefore, the squared root term in Eq. 3:5.3.3 can be approximated as 1+124kSxhxRC1+\frac{1}{2}\frac{4kS_x}{h_xR_C}1+21​hx​RC​4kSx​​ by preserving just the first two terms of the binomial expansion, from which Eq. 3:5.3.4 can be re-written as:

SC=hxRC2k(1+(12)4kSxhxRC−1)=SxS_C=\frac{h_xR_C}{2k}(1+(\frac{1}{2})\frac{4kS_x}{h_xR_C}-1)=S_xSC​=2khx​RC​​(1+(21​)hx​RC​4kSx​​−1)=Sx​ 3:5.3.4

Therefore, as RCR_CRC​ increases SCS_CSC​ approaches SxS_xSx​ asymptotically (Figure 1). Taking as a reference a soil layer with SxS_xSx​ = 25 Mg C ha−1^{-1}−1, hxh_xhx​ = 0.2, and k=0.01k=0.01k=0.01 y−1y^{-1}y−1, it can be seen in Figure 1 that doubling hxh_xhx​ and kkk have a similar effect but of opposite sign such that the equilibrium SCS_CSC​ increases with increasing hxh_xhx​ and decreases with increasing kkk. In both cases the increase and the decrease in SCS_CSC​ are less than proportional to the increase in these two parameters. The equilibrium SCS_CSC​, however, is very sensitive to changes in SxS_xSx​, which makes this variable critical for a correct representation of SCS_CSC​ dynamics. This formulation is a mathematical representation of the concept of SCS_CSC​ saturation (Hassink and Whitmore, 1997; Six et al., 2002), enhanced with a control of the decomposition rate by SCS_CSC​.

The transient trajectory of SCS_CSC​ is controlled by the quotient of the two exponential terms in Eq. [3:5.3.5].

d=1−∑i=1N(Oi−Si)2∑i=1N(∣Si−O‾∣+∣Oi−O‾∣)2d=1-\frac{\sum^N_{i=1}(O_i-S_i)^2}{\sum^N_{i=1}(|S_i-\overline O|+|O_i-\overline O|)^2}d=1−∑i=1N​(∣Si​−O∣+∣Oi​−O∣)2∑i=1N​(Oi​−Si​)2​ [3.5.3.5]

For a given SxS_xSx​ and initial SCS_CSC​, increasing the inputs (RCR_CRC​) changes the steady state SCS_CSC​ with decreasing marginal increments as SCS_CSC​ approaches SxS_xSx​, yet the steady state condition is approached faster with higher inputs (Figure 3:5-1). For a given RCR_CRC​, changing SxS_xSx​ has a substantial impact on the rate of change of SCS_CSC​ when the inputs are medium to high (Figure 3:5-1) but a minor effect if inputs are too low. This formulation strongly suggests that soils with higher carbon storage capacity (higher SxS_xSx​) that are currently depleted of SCS_CSC​ should be the primary targets for storing SCS_CSC​, or that soils with low SxS_xSx​ may store carbon quickly for a few years but the rate of gains will decrease earlier than in soils with higher SxS_xSx​.

The conditions for which the SCS_CSC​ can be modeled analytically as shown here are very restrictive. The numerical solution implemented in the model is more flexible as the constants α\alphaα and β\betaβ are allowed to differ from 1. The model can be expanded to accommodate saturation of different SOM pools, instead of just one uniform pool, as strongly suggested by the results and analysis of Stewart et al. (2008). Yet, this will require a level of parameterization for which we consider there is simply not sufficient information for a realistic implementation in numerical models.

Figure 3:5-1. Equilibrium soil organic carbon (SC, Mg C ha−1^{-1}−1) for the steady state condition (Eq. [3:5.3.3]) with different values for humification (hxh_xhx​, kg kg−1^{-1}−1), SOM apparent turnover rate (kkk, yr−1^{-1}−1), and saturation soil organic carbon (SCCS_{CC}SCC​, Mg C ha−1^{-1}−1). The line without a symbol in both panels was arbitrarily chosen as a reference. The linear, no asymptotic line in Panel A shows the equilibrium for the case in which hxh_xhx​ and kkk do not depend on SCS_CSC​ so that SCS_CSC​ at equilibrium = hxRC/kh_xR_C/khx​RC​/k, where RCR_CRC​ is the residue carbon input rate (Mg C ha−1^{-1}−1 yr−1^{-1}−1). Panel A shows the equilibrium when SCCS_{CC}SCC​ is doubled and Panel B shows the equilibrium SCS_CSC​ when hxh_xhx​ or kkk is doubled.