Hydraulic models in unsatfit

See also this paper and models in SWRC Fit. WRF = water retention function, HCF = hydraulic conductivity function, CH = common H.

Basic unimodal models

Brooks and Corey (BC) model

Brooks and Corey (1964)
Name: bc, BC
WRF parameters: qs, qr, hb, l
get_init() = get_init_bc(): returns hb, l
get_wrf() = get_wrf_bc(): returns full WRF parameters
HCF: General HCF
Parameters which only appears in HCF: Ks, p, q, r
Bound: b_qs, b_qr, b_hb, b_lambda, b_ks, b_p, b_q, b_r

van Genuchten (VG) model

van Genuchten (1980)
Name: vg, VG
WRF parameters: qs, qr, a, m, q
Converted parameter: n = q/(1-m) i.e. m = 1-q/n
Note that in unsatfit, m is used as a variable instead of n, because the bound of m, 0<m<1 is easier to handle than the bound of n, n>q, as unsatfit can make q as a variable.
get_init() = get_init_vg(): returns a, m where q=1
get_wrf() = get_wrf_vg(): returns full WRF parameters where q=1
HCF: General HCF
Parameters which only appears in HCF: Ks, p, r
Bound: b_qs, b_qr, b_a, b_m, b_ks, b_p, b_q, b_r

Modified van Genuchten model

Vogel et al. (2000)
Name: mvg, MVG, Modified VG
WRF parameters: qs, qr, a, m, hs, q
Converted parameter: n = q/(1-m) i.e. m = 1-q/n
hs = 2 cm for 1<n<2 in Vogel et al., (2000)
HCF: General HCF
Parameters which only appears in HCF: Ks, p, r
Bound: b_qs, b_qr, b_a, b_m, b_hs, b_ks, b_p, b_q, b_r

In general, modified model can be made by calling modified_model(hs) after set_model()

Kosugi (KO) model

Kosugi (1996)
Name: ln, KO
WRF parameters: qs, qr, hm, sigma
get_init() = get_init_ln(): returns hm, sigma
get_wrf() = get_wrf_ln(): returns full WRF parameters
HCF: General HCF
Parameters which only appears in HCF: Ks, p, q, r
Bound: b_qs, b_qr, b_hm, b_sigma, b_ks, b_p, b_q, b_r

Fredlund und Xing (FX) model

Fredlund and Xing (1994)
Name: fx, FX
WRF parameters: qs, qr, a, m, n
get_init() = get_init_fx(): returns a, m, n
HCF: not provided
Bound: b_qs, b_qr, b_fxa, b_fxm, b_fxn

Bimodal models

dual-BC model

Seki et al. (2022)
Name: bc2f, DB, dual-BC
WRF parameters: qs, qr, w1, hb1, l1, hb2, l2
get_init() = not provided
get_wrf() = not provided
HCF: General HCF
Parameters which only appears in HCF: Ks, p, q, r
Bound: b_qs, b_qr, b_w1, b_hb, b_lambda1, b_hb2, b_lambda2, b_ks, b_p, b_q, b_r

dual-BC-CH model

Seki et al. (2022)
Name: bc2, DBCH, dual-BC-CH
WRF parameters: qs, qr, hb, hc, l1, l2
Converted parameter: w1 = 1/(1+(hc/hb)^(l2-l1))
get_init() = get_init_bc2(): returns hb, hc, l1, l2
get_wrf() = get_wrf_bc2(): returns full WRF parameters where qr=0
HCF: General HCF
Parameters which only appears in HCF: Ks, p, q, r
Bound: b_qs, b_qr, b_hb, b_hc, b_lambda1, b_lambda2, b_ks, b_p, b_q, b_r

dual-VG model

Priesack and Durner (2006), equation corrected at Seki et al. (2022)
Name: vg2, DV, dual-VG
WRF parameters: qs, qr, w1, a1, m1, a2, m2, q
Converted parameter: n1 = q/(1-m1), n2 = q/(1-m2)
get_init() = get_init_vg2(): returns w1, a1, m1, a2, m2 where q=1
get_wrf() = get_wrf_vg2(): returns full WRF parameters where qr=0, q=1
HCF: General HCF
Parameters which only appears in HCF: Ks, p, r
Bound: b_qs, b_qr, b_w1, b_a1, b_m, b_a2, b_m, b_ks, b_p, b_q, b_r

dual-VG-CH model

Priesack and Durner (2006), equation corrected at Seki et al. (2022)
Name: vg2ch, DVCH, dual-VG-CH
WRF parameters: qs, qr, w1, a1, m1, m2, q
Converted parameter: n1 = q/(1-m1), n2 = q/(1-m2)
get_init() = get_init_vg2ch(): returns w1, a1, m1, m2 where q=1
get_wrf() = get_wrf_vg2ch(): returns full WRF parameters where qr=0, q=1
HCF: General HCF
Parameters which only appears in HCF: Ks, p, r
Bound: b_qs, b_qr, b_w1, b_a1, b_m, b_m, b_ks, b_p, b_q, b_r

dual-KO model

Seki (2007), Seki et al. (2022)
Name: ln2, DK, dual-KO
WRF parameters: qs, qr, w1, hm1, sigma1, hm2, sigma2
get_init() = not provided
get_wrf() = not provided
HCF: General HCF
Parameters which only appears in HCF: Ks, p, q, r
Bound: b_qs, b_qr, b_w1, b_hm1, b_sigma, b_hm2, b_sigma, b_ks, b_p, b_q, b_r

dual-KO-CH model

Seki et al. (2022)
Name: ln2ch, DKCH, dual-KO-CH
WRF parameters: qs, qr, w1, hm1, sigma1, sigma2
get_init() = not provided
get_wrf() = not provided
HCF: General HCF
Parameters which only appears in HCF: Ks, p, q, r
Bound: b_qs, b_qr, b_w1, b_hm1, b_sigma, b_sigma, b_ks, b_p, b_q, b_r

VG₁BC₂ model

Seki et al. (2022)
Name: vgbc, VGBC, VG1BC2, VB
WRF parameters: qs, qr, w1, a1, m1, hb2, l2, q
Converted parameter: n1 = q/(1-m1)
get_init() = not provided
get_wrf() = not provided
HCF: General HCF
Parameters which only appears in HCF: Ks, p, r
Bound: b_qs, b_qr, b_w1, b_a1, b_m, b_hb2, b_lambda2, b_ks, b_p, b_q, b_r

HCF variation: r=1 and independent p

Name: vgbcp2, VGBCIP, VG1BC2-IP, VB-IP
Parameters which only appears in HCF: Ks, p1, p2

VG₁BC₂-CH model

Seki et al. (2022)
Name: vgbcch, VGBCCH, VG1BC2-CH, VBC
WRF parameters: qs, qr, w1, a1, m1, l2, q
Converted parameter: n1 = q/(1-m1)
get_init() = get_init_vgbcch(): returns w1, a1, m1, l2 where qr=0, q=1
get_wrf() = not provided
HCF: General HCF
Parameters which only appears in HCF: Ks, p, r
Bound: b_qs, b_qr, b_w1, b_a1, b_m, b_lambda2, b_ks, b_p, b_q, b_r

HCF variation: r=1 and independent p

Name: vgbcchp2, VGBCCHIP, VG1BC2CH-IP, VBC-IP
Parameters which only appears in HCF: Ks, p1, p2

KO₁BC₂ model

Seki et al. (2022)
Name: kobc, KOBC, KO1BC2, KB
WRF parameters: qs, qr, w1, hm1, sigma1, hb2, l2
get_init() = not provided
get_wrf() = get_wrf_kobc(): returns full WRF parameters with qr=0
HCF: General HCF
Parameters which only appears in HCF: Ks, p, q, r
Bound: b_qs, b_qr, b_w1, b_hm1, b_sigma, b_hb2, b_lambda2, b_ks, b_p, b_q, b_r

HCF variation: r=1 and independent p

Name: kobcp2, KOBCIP, KO1BC2-IP, KB-IP
Parameters which only appears in HCF: Ks, p1, p2, q

KO₁BC₂-CH model

Seki et al. (2022)
Name: kobcch, KOBCCH, KO1BC2-CH, KBC
WRF parameters: qs, qr, w1, hm, sigma1, l2
get_init() = get_init_kobcch(): returns w1, hm, sigma1, l2
get_wrf() = get_wrf_kobcch(): returns full WRF parameters with qr=0
HCF: General HCF
Parameters which only appears in HCF: Ks, p, q, r
Bound: b_qs, b_qr, b_w1, b_hm1, b_sigma, b_lambda2, b_ks, b_p, b_q, b_r

HCF variation: r=1 and independent p

Name: kobcch2, KOBCCHIP, KO1BC2-CH-IP, KBC-IP
Parameters which only appears in HCF: Ks, p1, p2, q

Giving pressure head of zero water content

Peters model (Kosugi type)

Peters (2013)
Name: pk, PK, Peters-KO, PE, Peters
WRF parameters: qs, qr, w1, hm, sigma1, he
qr=0 by definition. θ=0 at h=he.
get_init() = get_init_pk(he): w1, hm, sigma1
get_wrf() = get_wrf_pk(he): returns full WRF parameters with qr=0
HCF: Peters (2013)
Parameters which only appears in HCF: Ks, p, a, omega
Bound: b_qs, b_qr, b_w1, b_hm1, b_sigma, b_he, b_ks, b_p, b_a, b_w1

Fayer and Simmons model (van Genuchten type)

Fayer and Simmons (1995)
Name: vgfs, VGFS, Fayer-VG
WRF parameters: qs, qr, qa, a, m, he, q
qr=0 by definition. θ=0 at h=he.
q = 1 should be provided. Otherwise not calculated.
Converted parameter: n = q/(1-m) i.e. m = 1-q/n
get_init() = not provided
get_wrf() = not provided
HCF: General HCF
Parameters which only appears in HCF: Ks, p, r
Bound: b_qs, b_qr, b_w1, b_a1, b_m, b_he, b_ks, b_p, b_q, b_r

Hydraulic models in unsatfit

Basic unimodal models

Brooks and Corey (BC) model

van Genuchten (VG) model

Kosugi (KO) model

Fredlund und Xing (FX) model

Bimodal models

dual-BC model

dual-BC-CH model

dual-VG model

dual-VG-CH model

dual-KO model

dual-KO-CH model

VG1BC2 model

VG1BC2-CH model

KO1BC2 model

KO1BC2-CH model

Giving pressure head of zero water content

Peters model (Kosugi type)

Fayer and Simmons model (van Genuchten type)

VG₁BC₂ model

VG₁BC₂-CH model

KO₁BC₂ model

KO₁BC₂-CH model