Ci a ion: G ucho , A.; Zyd o´n, T.;
Wał˛ega, A.; Paˇ ílko á, J.; S anisz, J.
In luence o Rain all E en s and
Su ace Inclina ion on O e land and
Subsu ace Runo Fo ma ion on
Low-Pe meable Soil. Sus ainabili y
2022,14, 4962. h ps://doi.o g/
10.3390/su14094962
Academic Edi o : Li He
Recei ed: 17 Feb ua y 2022
Accep ed: 11 Ap il 2022
Published: 20 Ap il 2022
Publishe ’s No e: MDPI s ays neu al
wi h ega d o ju isdic ional claims in
published maps and ins i u ional a il-
ia ions.
Copy igh : © 2022 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
sus ainabili y
A icle
In luence o Rain all E en s and Su ace Inclina ion on
O e land and Subsu ace Runo Fo ma ion on
Low-Pe meable Soil
And zej G ucho 1,* , Tymo eusz Zyd o´n 1, And zej Wał˛ega 2, Jana Paˇ ílko á3and Jacek S anisz 4
1Depa men o Hyd aulic Enginee ing and Geo echnics, Facul y o En i onmen al Enginee ing and Land
Su eying, Uni e si y o Ag icul u e in K aków, Mickiewicza 24/28, 30-059 C acow, Poland;
[email p o ec ed]
2Depa men o Sani a y Enginee ing and Wa e Managemen , Facul y o En i onmen al Enginee ing and
Land Su eying, Uni e si y o Ag icul u e in K aków, Mickiewicza 24/28, 30-059 C acow, Poland;
[email p o ec ed]
3Ins i u e o Wa e S uc u es, Facul y o Ci il Enginee ing, B no Uni e si y o Technology, Ve eˇ í331/95,
60200 B no, Czech Republic; [email p o ec ed]
4Mine al and Ene gy Economy Resea ch Ins i u e, Polish Academy o Science, Józe a Wybickiego 7 A,
31-261 C acow, Poland; [email p o ec ed].pl
*Co espondence: and zej.g [email p o ec ed]; Tel.: +48-12-622-4136
Abs ac :
This pape p esen s he esul s o labo a o y es s ha allowed us o de e mine he e ec o
he soil su ace inclina ion and i s ini ial mois u e con en on he o ma ion o o e land and subsu ace
uno . The expe imen s we e ca ied ou o he soil ha is commonly p esen in he sou he n pa o
Poland, including he Ou e Ca pa hians. The esul s o hese measu emen s se ed as a e e ence
o o e land uno calcula ions using he Richa ds model, simpli ied G een–Amp model, and he
empi ical model (MSME). The esul s o he measu emen s showed ha , o low-pe meable soil,
o e land uno is he dominan o m. I was shown ha a slope in he ange o 2.5–5.0% does no
ha e a signi ican e ec on he amoun o o e land uno , bu a ec s i s dynamics. The measu emen s
also showed ha he s a ing ime and amoun o o e land uno a e s ic ly associa ed wi h he
ini ial soil mois u e con en . High soil mois u e con en in he pe iod p eceding he onse o ain all
causes as e gene a ion and an inc ease in o e land uno , which is caused by he sa u a ion o
he su ace laye o he soil. This mechanism was con i med by he esul s o calcula ions using he
Richa ds model and measu emen s o he elec ical esis ance o he soil. Theo e ical calcula ions
showed ha he esul s o he uno calcula ions using he Richa ds and G een–Amp models a e
s ongly dependen on he hyd aulic p ope ies o he soil adop ed o he analysis. I was also
demons a ed ha he modi ied MSME model sa is ac o ily es ima es he amoun o o e land and
subsu ace uno , bu equi es pa ame e calib a ion based on exis ing hyd ological da a.
Keywo ds: o e land low; in il a ion; subsu ace low; ponding o su ace; su ace inclina ion
1. In oduc ion
Rain all– uno modeling has been de eloped o e many decades. Despi e he el-
a i ely simple heo e ical basis, he models a e s ill commonly used in hyd ological ap-
plica ions wo ldwide. Values o he model pa ame e s a e es ima ed using eco ded
ain all– uno episodes. In many pa s o he wo ld, ain all and uno da a a e seldom
adequa e o de e mine a uni hyd og aph o a ca chmen o a wa e shed. In he absence o
ain all– uno da a, uni hyd og aphs can be de i ed by syn he ic means [1,2].
One o he c ucial p oblems wi h he p ac ical use o ain all– uno models is he
unce ain y o he ne o excess ain all es ima ion. Many ain all– uno models a e capable
o assessing di ec uno , which can be in e p e ed as Ho onian o e land low o o e land
sa u a ed low and subsu ace low ( h ough low o in e low) [3].
Sus ainabili y 2022,14, 4962. h ps://doi.o g/10.3390/su14094962 h ps://www.mdpi.com/jou nal/sus ainabili y
Sus ainabili y 2022,14, 4962 2 o 27
Examples o ain all– uno models ha can be used o di ec uno assessing include
syn he ic uni hyd og aphs (Snyde , SCS-UH, Cla k-UH) [
4
,
5
] o concep ual models based
on he cascade o Nash linea anks, o double cascade o anks (Wacke mann model) [
6
].
An al e na i e o he ain all– uno models used so a may be he ecen ly de eloped
“E en -based App oach o Small and Ungauged Basins” (EBA4SUB) model. I allows o
es ima ing he magni ude o he peak low along wi h he cha ac e is ics o he design
hyd og aph [
7
–
9
] o new modi ica ion, named COSMO4SUB (“Con inous Simula ion
Model o Small and Ungauged Basins”) o con inuous simula ion o uno [
10
]. All o
he men ioned models a e common ools used in hyd ological s udies o design hyd aulic
s uc u es like cul e s, ese oi s, and lood a eas.
Depending on he ca chmen condi ions, uno can be domina ed by o e land uno
o subsu ace d ainage. In na u al ca chmen s, di ec uno can be domina ed by subsu ace
uno , which may also occu ou side he immedia e icini y o wa e cou ses [
11
]. Many
commonly used empi ical models, like he Soil Conse a ion Se ice Cu e Numbe
(
SSC-CN
) desc ibed by he Na u al Resou ces Conse a ion Se ice [
4
], a e only able o
assess o e land uno . Yuan e al. [
12
] modi ied he SCS-CN me hod o calcula e subsu ace
uno by de ining CN alues o d ainage low o i e poo ly d ained si es in eas -cen al
Illinois, USA. Wał˛ega e al. [
13
] p oposed a modi ica ion o he SCS-CN me hod, named he
MSME model, o p edic o e land and subsu ace uno om a small, o es ed wa e shed
in No h Ca olina, USA. They modi ied he Sahu–Mish a–Eldo (SME) app oach [
14
] by
including a componen o assess he dep h o subsu ace uno . The key ole he e was
played by he “a” pa ame e — ha is, he ac o de e mining he p opo ion o sa u a ed
a ea in he whole ca chmen . The me hod was success ully es ed on a la , coas al o es ed
wa e shed in he Sou h Ca olina A lan ic Coas al Plain, USA. The me hod, howe e , has
no ye been es ed in ca chmen s wi h highe slope inclina ion and less pe meable soils.
Based on he li e a u e e iew, i is clea ha he e is a lack o s udies ha would desc ibe
simple ain all– uno models, including o e land and subsu ace uno . The i s s age o
s udies comp ises expe imen s on uno o ma ion, including in il a ion p ocesses and
soil p ope ies. A no el y o he p esen ed s udies was ha he MSME model was es ed
o i s abili y o es ima e he o e land and subsu ace uno in slopes wi h low-pe meable
soils and a ied uno su ace inclina ions. The MSME model was es ed in labo a o y
condi ions, which allowed us o show he ela ionship be ween he soil pa ame e s and he
model pa ame e s; his me hod can be used o analyze in de ail he o ma ion o o e land
low [15–18].
De e minis ic models o wa e low in unsa u a ed soil can also be used o su ace
and subsu ace uno calcula ions. The mos popula physical in il a ion model is ha o
Richa ds [
19
], which is an ex ension o Da cy’s law o he unsa u a ed medium. The model
equi es in o ma ion on he soil e en ion and hyd aulic conduc i i y unc ions, so i s use in
hyd ology can be imp ac ical o can make hyd ological calcula ions complica ed. The e o e,
simpli ied physical models a e a good al e na i e o Richa ds’. One o he mos popula
physical-based in il a ion models used o calcula ion o e land low is he
G een–Amp
model [
20
]. This model assumes he uni o m dis ibu ion o wa e con en wi h he soil
p o ile, cons an alue o suc ion p essu e in he unsa u a ed zone, and pe meabili y
coe icien o soil. These assump ions ensu e ha he model is no oo sophis ica ed and
does no ha e a signi ican impac on he accu acy o he calcula ion esul s. So, he model
is o en used no only in hyd ology [
21
–
24
] bu also in slope s abili y analysis [
25
–
27
].
The mos eliable esul s o su ace and subsu ace uno s udies a e p o ided by ield
and labo a o y measu emen s. In mos cases, esea ch on expe imen al plo s ocuses on
de e mining he impac o plo use o dimensions on he uno [
28
–
33
], bu he in il a ion
p ocess is a ely moni o ed on hem [
34
–
36
]. On he o he hand, he bes way o selec soil
condi ions, con ol he in ensi y o ain all, o choose he ins umen a ion o he measu ing
model is based on labo a o y measu emen s. Poesen [
37
] desc ibed a labo a o y expe imen
wi h he aid o simula ed uno , illus a ing ha he su ace slope inclina ion is nega i ely
co ela ed o he Ho onian o e land uno , while he in il a ion a e is dependen no
Sus ainabili y 2022,14, 4962 3 o 27
only on he soil p ope ies bu also on elie pa ame e s such as he su ace slope inclina ion.
Labo a o y es s by Chu e al. [
17
] showed ha su ace mic o elie , soil ype, ini ial soil
mois u e con en , and ain all cha ac e is ics a ec he o e land low gene a ion. Nassi and
Wilson [
38
] show ha , o soils o low pe meabili y, he e is li le e ec o ain all in ensi y
on in il a ion. Simila esul s we e p o ided by Wang e al. [
16
], who e ealed ha an
inc ease in he inclina ion o soil su ace inc eases o e land low and dec eases in il a ion.
The o ma ion o o e land and subsu ace uno signi ican ly a ec s he dynamics o
loods. In Poland and o he coun ies, his p oblem mainly conce ns sealed su aces, i.e.,
u banized a eas [
11
,
39
–
43
], as well as moun ain a eas [
44
–
47
]. The sealing o he a ea
causes an inc ease in he numbe o loods wi h a apid cou se o a lood wa e, bu o
sho du a ion. The o ma ion o such loods is heigh ened by clima e change and o he
human ac i i ies, which causes an imbalance be ween p ecipi a ion and he p ocesses o
uno , in il a ion, and anspi a ion. As a esul o his dis u bance, he olume o wa e
in il a ing he soil dec eases and o e land uno de elops.
In sou he n Poland, including moun ainous a eas o he Ou e Ca pa hians, he na u al
subs a e is ela i ely o en o med by sil y (loesses) and clay soils o medium and low
wa e pe meabili y. These soils a e he p oduc o wea he ing o shales and sands ones ha
we e o med in he Te yda Ocean and li ed du ing Alpine o ogenesis. The p esence o his
ype o o ma ion and he high inclina ion o slopes a o he o ma ion o o e land uno .
Ano he ac o con ibu ing o he inc ease in o e land uno in his egion is human
ac i i y ela ed o changes in land use, i.e., de o es a ion, sealing, and he de elopmen
and econs uc ion o anspo ne wo ks. All kinds o ea hwo ks accompanying human
ac i i ies emo e ege a ion, pe manen ly o empo a ily exposing he soil, which becomes
mo e suscep ible o he o ma ion o o e land uno [48–50].
S ill common in p ac ical calcula ions o uno a e simple empi ical models based on
a hyd ological app oach. In compa ison o physical-based models like he G een–Amp o
Richa ds, he hyd ological app oach uses many simpli ica ion, mainly o he desc ip ion
o uno o ma ion. In his s udy we es ed ollowing hypo hesis: he modi ied SCS-CN
me hod, name MSME model, gi es simila esul s o uno o compa e o he commonly
using G een–Amp and Richa ds models.
The aim o his s udy was o assess he in luence o he slope inclina ion, he ini ial
mois u e con en o he soil on he o ma ion o o e land, and subsu ace uno . In
addi ion, he use ulness o he MSME me hod o es ima ing o e land and subsu ace
uno o med on a slope wi h low-pe meable soils was de e mined. The esul s om he
MSME model we e compa ed o commonly used models o wa e in il a ion in he soil, e.g.,
he one-dimensional G een–Amp model and he wo-dimensional model desc ibed by he
Richa ds equa ion. In he es s, he in il a ion p ocess was moni o ed using he elec ic
impedance spec ome y (EIS) me hod.
2. Ma e ials and Me hods
The es s we e ca ied ou in labo a o y condi ions on a uno simula o o sil y
soil collec ed om he icini y o K aków, Poland. The K aków egion is loca ed on he
bo de o se e al la ge ec onic uni s, which gi es i a complica ed and a ied geological
s uc u e [
51
]. The no he n pa o he ci y and he pa sou h o he Vis ula Ri e a e
loca ed in he Ca pa hian Fo edeep zone. The sou he n pa o he ci y is loca ed in he
Flysch Ca pa hians. The eas e n pa o K aków is loca ed in he Sandomie z Basin, whe e
he i e sedimen s o he Vis ula and i s ibu a ies p edomina e. In u n, he wes e n pa
o K aków is he a ea o he K akowska Ga e, which is made o a limes one amewo k
sepa a ed by na ow ec onic di ches [
52
]. Acco ding o he De ailed Geological Map o
Poland, Pa : K aków [
53
], in he no he n pa o K aków, whe e he soil samples we e
aken, he su ace o ma ions a e ep esen ed by loesses, and hei p esence is also no ed in
he sou he n zone, whe e hey co e lysch o ma ions. Loesses in he icini y o K akow
a e cha ac e ized by a a ied con en o he clay ac ion (5–13%) [
54
], which allows hem
o be classi ied as sil and sil y loams acco ding o geo echnical s anda ds [55].
Sus ainabili y 2022,14, 4962 4 o 27
The o al annual ain all in K aków (Poland) is app oxima ely 700 mm [
56
]. Some o
his ain all is in ense, causing apid inc eases in wa e le els in wa e cou ses and local
looding. The scale o his phenomenon can be p o ed by he da a om he Ins i u e o
Me eo ology and Wa e Managemen –Na ional Resea ch Ins i u e [
57
]. In May–June 2021,
he Hyd ological Fo ecas ing O ice in K aków issued almos 50 hyd ological wa nings
indica ing he occu ence o s o ms, including u banized ca chmen s loca ed in sou heas -
e n Poland.
2.1. Resea ch on Geo echnical P ope ies
The scope o he esea ch included he de e mina ion o he pa icle size dis ibu ion,
bulk densi y, consis ency limi s, compac ion pa ame e s, and he il a ion coe icien . The
g ain size composi ion was de e mined by he combined me hod, i.e., we sie e analysis
o g ains la ge han 0.063 mm and he hyd ome ic me hod o pa icles smalle han
0.063 mm [
55
,
58
]. The liquidi y limi was de e mined by he Casag ande me hod [
59
] as he
mois u e con en a which a ine-g ained soil no longe lows like a liquid. The plas ici y
limi was de e mined by he olling me hod [
59
], as he mois u e con en a which a ine-
g ained soil can no longe be emolded wi hou c acking. The compac ion pa ame e s
(op imum mois u e con en and maximum d y densi y) we e de e mined in he P oc o
appa a us a a compac ion ene gy o 0.59 J
·
cm
−3
[
60
]. The compac ion cha ac e is ics o a
soil can be assessed by means o s anda d labo a o y es s. In he P oc o es , he olume
o he mold is 1 dm
3
and he soil is compac ed by a amme consis ing o a 2.5 kg mass
alling eely h ough 320 mm. The soil is compac ed in h ee equal laye s, wi h each laye
ecei ing 25 blows wi h he amme o a leas i e soil samples. A e compac ion, he
bulk densi y and wa e con en o he soil a e de e mined and he d y densi y calcula ed.
The il a ion coe icien was de e mined in an oedome e on samples o 7 cm in
diame e and 1.9 cm high, o med in he ing o he appa a us a he op imum mois u e
o ob ain a compac ion index o I
S
= 0.88, 0.92, 0.95, o 1.00, which co esponds o a
soil po osi y n= 0.40, 0.38, 0.35, o 0.32, espec i ely. The de e mina ion o he il a ion
coe icien was also ca ied ou wi h he use o a Sa u o in il ome e (dual head) (METER
G oup, Pullman, DC, USA) (Figu e 1). In his case, he es s we e pe o med on samples
o med in he cylinde o a medium-sized P oc o appa a us (Wille Geo echnik, Ge many)
wi h a diame e o 25 cm and a heigh o 20 cm a a mois u e con en o 10% un il a
compac ion index o I
S
= 0.88 (n= 0.40) was ob ained. The il a ion coe icien om he
in il ome e es s was de e mined using a ing wi h a diame e o 14.4 cm s uck in o he
soil sample o a dep h o 5 cm. The es was pe o med in duplica e wi h wo and h ee
measu emen cycles.
Oedome e es s we e ca ied ou in a labo a o y unde sa u a ed condi ions. The
di ec ion o wa e h ough he soil was om bo om o op o a soil sample and he
hyd aulic g adien du ing he es was a iable. A Sa u o in il ome e was used o measu e
he in il a ion a e o he wa e h ough soil po e spaces unde ield condi ions. The
measu emen ook place wi hin a single ing ha was pushed in o he soil. The es s we e
ca ied ou a he wo alues o ponding head, which enabled us o educe he impac o
la e al low on he measu ed in il a ion a e.
2.2. Su ace and Subsu ace Runo S udies
The physical model was p epa ed in a uno simula o (Figu e 2a), which enables he
simula ion o ain all wi h a p ede e mined in ensi y o any soil o ma e ial used o he
cons uc ion o communica ion pa emen s. The basic elemen s o he simula o include he
wa e ese oi , he main bed in which he soil sample is o med and he ese oi s o eed
wa e , and wa e lowing ou o he bed in he o m o su ace and subsu ace uno . The
ac i e heigh o he main bed o he simula o is 0.216 m, wi h c oss sec ion dimensions o
0.64 m
×
1.54 m. On one side o he bed, he e a e channels collec ing wa e lowing down
he g ound su ace and wa e d aining om he soil (subsu ace uno ) (Figu e 2b). A
0.5 m abo e he main channel, he e is a wa e ank wi h 372 holes (nozzles) om which
Sus ainabili y 2022,14, 4962 5 o 27
wa e alls on o he sample su ace. The hyd aulic low o wa e supplied o he ese oi is
egula ed, and o he pu poses o his esea ch i was ela ed o he bed (soil) su ace and
con e ed in o he in ensi y o p ecipi a ion. Be o e s a ing he es s, he pump dosing he
p ecipi a ion o he soil sample was calib a ed.
Sus ainabili y 2022, 14, x FOR PEER REVIEW 5 o 31
(a) (b)
Figu e 1. Gene al iew o Sa u o in il ome e (dual head) (a) and model o soil pe meabili y es -
ing by he in il a ion me hod (b).
2.2. Su ace and Subsu ace Runo S udies
The physical model was p epa ed in a uno simula o (Figu e 2a), which enables
he simula ion o ain all wi h a p ede e mined in ensi y o any soil o ma e ial used o
he cons uc ion o communica ion pa emen s. The basic elemen s o he simula o in-
clude he wa e ese oi , he main bed in which he soil sample is o med and he ese -
oi s o eed wa e , and wa e lowing ou o he bed in he o m o su ace and subsu ace
uno . The ac i e heigh o he main bed o he simula o is 0.216 m, wi h c oss sec ion
dimensions o 0.64 m × 1.54 m. On one side o he bed, he e a e channels collec ing wa e
lowing down he g ound su ace and wa e d aining om he soil (subsu ace uno )
(Figu e 2b). A 0.5 m abo e he main channel, he e is a wa e ank wi h 372 holes (nozzles)
om which wa e alls on o he sample su ace. The hyd aulic low o wa e supplied o
he ese oi is egula ed, and o he pu poses o his esea ch i was ela ed o he bed
(soil) su ace and con e ed in o he in ensi y o p ecipi a ion. Be o e s a ing he es s, he
pump dosing he p ecipi a ion o he soil sample was calib a ed.
Two se ies o es s we e ca ied ou , in which he inclina ion o he sample (soil) su -
ace was 2.5% and 5.0%. Bo h samples we e o med a he same compac ion, di ec ly in
he simula o ’s main bed, in i e laye s. The soil was compac ed a 10% mois u e o ob ain
a olume ic densi y o 1.75 g·cm−3, which allowed us o ob ain a soil compac ion index o
IS = 0.87. This index co esponds o a soil po osi y o n = 0.40, which alls wi hin he ange
o sil y soil po osi y gi en by Kaczyński [61] o upland and moun ain a eas o sou he n
Poland. Fo each se ies, h ee p ecipi a ion simula ions we e pe o med, du ing which he
simula o ope a ed o 40 min. As pa o he esea ch, 30 mm ain all was gene a ed o
a du a ion o 40 min, which co esponds o a ain all in ensi y o 0.75 mm·min−1.
Figu e 1.
Gene al iew o Sa u o in il ome e (dual head) (
a
) and model o soil pe meabili y es ing
by he in il a ion me hod (b).
Two se ies o es s we e ca ied ou , in which he inclina ion o he sample (soil) su ace
was 2.5% and 5.0%. Bo h samples we e o med a he same compac ion, di ec ly in he
simula o ’s main bed, in i e laye s. The soil was compac ed a 10% mois u e o ob ain a
olume ic densi y o 1.75 g
·
cm
−3
, which allowed us o ob ain a soil compac ion index o
I
S
= 0.87. This index co esponds o a soil po osi y o n= 0.40, which alls wi hin he ange
o sil y soil po osi y gi en by Kaczy´nski [
61
] o upland and moun ain a eas o sou he n
Poland. Fo each se ies, h ee p ecipi a ion simula ions we e pe o med, du ing which
he simula o ope a ed o 40 min. As pa o he esea ch, 30 mm ain all was gene a ed
o a du a ion o 40 min, which co esponds o a ain all in ensi y o 0.75 mm
·
min
−1
.
Acco ding o Lambo [
62
], o an a ea wi h an annual p ecipi a ion o 700 mm, his in ensi y
is cha ac e ized by a p obabili y o abou 5–10%, which co esponds o he p obabili y o
which oad d ainage de ices a e designed [
63
]. Acco ding o he Ins i u e o Me eo ology
and Wa e Managemen –Na ional Resea ch Ins i u e [
64
], ain all o 30 mm is conside ed
c i ical, leading o ising wa e in wa e cou ses and he s a o su ace uno .
Runo measu emen s we e conduc ed du ing each ain all episode e e y 2 min, and
con inued o 10–40 min he ea e , depending on he dynamics o he eco ded uno .
Be o e he esea ch was s a ed and a e he end o each episode, he soil mois u e con en
was con olled by aking soil samples om wo ex eme poin s o he model.

Sus ainabili y 2022,14, 4962 6 o 27
Sus ainabili y 2022, 14, x FOR PEER REVIEW 6 o 31
Acco ding o Lambo [62], o an a ea wi h an annual p ecipi a ion o 700 mm, his in en-
si y is cha ac e ized by a p obabili y o abou 5–10%, which co esponds o he p obabili y
o which oad d ainage de ices a e designed [63]. Acco ding o he Ins i u e o Me eo -
ology and Wa e Managemen –Na ional Resea ch Ins i u e [64], ain all o 30 mm is con-
side ed c i ical, leading o ising wa e in wa e cou ses and he s a o su ace uno .
Runo measu emen s we e conduc ed du ing each ain all episode e e y 2 min, and
con inued o 10–40 min he ea e , depending on he dynamics o he eco ded uno .
Be o e he esea ch was s a ed and a e he end o each episode, he soil mois u e con en
was con olled by aking soil samples om wo ex eme poin s o he model.
(a) (b)
Figu e 2. Gene al iew (a) and scheme (b) o he uno simula o .
2.3. Moni o ing o he In il a ion P ocess Using he EIS Me hod
The EIS me hod used in his s udy was applied o measu e he elec ical cha ac e is-
ics o he soil in a complex o m, i.e., he esis ance Rx (elec ical esis ance) and eac ance
X in he equency ange o he supply signal. Resis ance is he ac ual (ac i e) esis ance
in an elec ical ci cui and is he so-called elec ical esis ance, which depends on he soil
ype and he wa e con en in i s po es. On he o he hand, eac ance is he imagina y pa
o he impedance. A nonze o alue o eac ance causes a phase shi (phase di e ence)
be ween he in ensi y and ol age o he elec ic cu en in he ci cui . Reac ance cha ac-
e izes he changes in he soil caused by a ia ions in i s g ain size o po osi y [65].
The esis ance measu emen s o he soil buil in o he model we e ca ied ou wi h
wo i e-channel EIS measu ing elec odes wi h a o al leng h o 22.5 cm (Figu e 3b) a a
signal equency o 2050 Hz. The elec odes we e placed in he cen al pa o he sample
wi h a spacing o 20 cm. The measu ing elec odes we e pai ed up o a measu ing p obe
wi h i e e ical measu ing segmen s (channels), 2.5 cm high each (cu en -conduc ing
sec ions), spaced e ically e e y 2.5 cm. Due o he heigh o he soil sample, ou meas-
u emen channels we e used in he expe imen . A Z-Me e (GEO es , B no, Czech Repub-
lic) was used o eco d he elec ical esis ance o he soil embedded in he model du ing
wa e in il a ion (Figu e 3a). The de ice uses a measu emen me hod ha consis s o com-
pa ing he measu ed impedance Z wi h no mal esis ance Rx wi h a known alue o elec-
ical esis ance. The measu emen esul s we e eco ded in a Mic oso Excel sp eadshee .
Figu e 2. Gene al iew (a) and scheme (b) o he uno simula o .
2.3. Moni o ing o he In il a ion P ocess Using he EIS Me hod
The EIS me hod used in his s udy was applied o measu e he elec ical cha ac e is ics
o he soil in a complex o m, i.e., he esis ance Rx (elec ical esis ance) and eac ance X in
he equency ange o he supply signal. Resis ance is he ac ual (ac i e) esis ance in an
elec ical ci cui and is he so-called elec ical esis ance, which depends on he soil ype
and he wa e con en in i s po es. On he o he hand, eac ance is he imagina y pa o he
impedance. A nonze o alue o eac ance causes a phase shi (phase di e ence) be ween
he in ensi y and ol age o he elec ic cu en in he ci cui . Reac ance cha ac e izes he
changes in he soil caused by a ia ions in i s g ain size o po osi y [65].
The esis ance measu emen s o he soil buil in o he model we e ca ied ou wi h wo
i e-channel EIS measu ing elec odes wi h a o al leng h o 22.5 cm (Figu e 3b) a a signal
equency o 2050 Hz. The elec odes we e placed in he cen al pa o he sample wi h a
spacing o 20 cm. The measu ing elec odes we e pai ed up o a measu ing p obe wi h i e
e ical measu ing segmen s (channels), 2.5 cm high each (cu en -conduc ing sec ions),
spaced e ically e e y 2.5 cm. Due o he heigh o he soil sample, ou measu emen
channels we e used in he expe imen . A Z-Me e (GEO es , B no, Czech Republic) was
used o eco d he elec ical esis ance o he soil embedded in he model du ing wa e
in il a ion (Figu e 3a). The de ice uses a measu emen me hod ha consis s o compa ing
he measu ed impedance Z wi h no mal esis ance Rx wi h a known alue o elec ical
esis ance. The measu emen esul s we e eco ded in a Mic oso Excel sp eadshee .
2.4. Calcula ions o O e land and Subsu ace Runo wi h he Use o Models Taking in o Accoun
he In il a ion P ocess
The ob ained esul s o o e land and subsu ace uno measu emen s we e compa ed
wi h he esul s o calcula ions ca ied ou using he one-dimensional G een–Amp model
and he wo-dimensional soil model de eloped in he GeoS udio 2020 so wa e (Seequen , a
Ben ley Company, B oom ield, CO, USA), in which he Richa ds [
19
] equa ion was adop ed
o calcula e he low o wa e in he soil:
∂θ
∂ =∂
∂xkx∂H
∂x+∂
∂zkz∂H
∂z+Q, (1)
Sus ainabili y 2022,14, 4962 7 o 27
whe e
θ
(-) is he olume ic wa e con en , (s) is ime, k
x
(m
·
s
−1
) is he hyd aulic conduc-
i i y o he soil in he x-di ec ion, k
z
(m
·
s
−1
) is he hyd aulic conduc i i y o he soil in he
z-di ec ion, H(m) is he wa e o al head, and Q(m·s−1) is he bounda y lux.
Sus ainabili y 2022, 14, x FOR PEER REVIEW 7 o 31
(a) (b)
Figu e 3. View o he Z-Me e IV appa a us (a) and measu ing elec odes (b).
2.4. Calcula ions o O e land and Subsu ace Runo wi h he Use o Models Taking in o
Accoun he In il a ion P ocess
The ob ained esul s o o e land and subsu ace uno measu emen s we e com-
pa ed wi h he esul s o calcula ions ca ied ou using he one-dimensional G een–Amp
model and he wo-dimensional soil model de eloped in he GeoS udio 2020 so wa e
(Seequen , a Ben ley Company, B oom ield, CO, USA), in which he Richa ds [19] equa-
ion was adop ed o calcula e he low o wa e in he soil:

=

+

+
, (1)
whe e θ (-) is he olume ic wa e con en , (s) is ime, kx (m·s−1) is he hyd aulic conduc-
i i y o he soil in he x-di ec ion, kz (m·s−1) is he hyd aulic conduc i i y o he soil in he
z-di ec ion, H (m) is he wa e o al head, and Q (m·s−1) is he bounda y lux.
The calcula ion o he in il a ion by he G een–Amp me hod [20] consis s o de e -
mining he soil capaci y a e (po en ial in il a ion a e):
=∙=∙++
[·]
(2)
whe e ks (m·s−1) is he hyd aulic conduc i i y o a soil, gi en as hal o he alue o he soil
coe icien o pe meabili y [66]; i (-) is he hyd aulic g adien ; Hp (m) is he heigh o pond-
ing, o en assumed o be equal o 0, because su ace ponding igge s o e land uno ; z
(m) is he dep h o he we ing on loca ion; and ψ (m) is he weigh o soil suc ion p es-
su e a he base o he we ing on .
The heigh o he soil suc ion p essu e a he base o he we ing on can be de e -
mined in a ious ways [3,67]. In his s udy, he o mula gi en by Maidmend [3] was used,
as shown in Equa ion (3):
Figu e 3. View o he Z-Me e IV appa a us (a) and measu ing elec odes (b).
The calcula ion o he in il a ion by he G een–Amp me hod [
20
] consis s o de e -
mining he soil capaci y a e (po en ial in il a ion a e):
=ks·i=ks·z +ψ +Hp
z hm·s−1i(2)
whe e k
s
(m
·
s
−1
) is he hyd aulic conduc i i y o a soil, gi en as hal o he alue o he
soil coe icien o pe meabili y [
66
]; i(-) is he hyd aulic g adien ; H
p
(m) is he heigh o
ponding, o en assumed o be equal o 0, because su ace ponding igge s o e land uno ;
z
(m) is he dep h o he we ing on loca ion; and
ψ
(m) is he weigh o soil suc ion
p essu e a he base o he we ing on .
The heigh o he soil suc ion p essu e a he base o he we ing on can be de e -
mined in a ious ways [
3
,
67
]. In his s udy, he o mula gi en by Maidmend [
3
] was used,
as shown in Equa ion (3):
ψ =0.01·6.53 −7.326·n+0.00158Cl2+3.809·n2+0.000344·Sa·Cl −0.04989·Sa·n+0.0016
·Sa2·n2+0.0016·Cl2·n2−0.0000136·Sa2·Cl −0.00348·Cl2·n−0.000799·Sa2
·n] [cm]
(3)
whe e n(-) is he soil po osi y, S
a
(%) is he sand ac ion con en , and Cl (%) is he clay
ac ion con en . The equa ion is easy o calcula e and he e is no need o in o ma ion on
he soil wa e cha ac e is ic cu e ( e en ion cu e).
The abo e equa ion assumes ha he alue o he suc ion p essu e a he base o he
we ing on is independen o he soil mois u e con en . The e o e, o he pu poses o he
analyses, Equa ion (3) was modi ied o ake in o accoun he soil mois u e con en :
ψ m =(1−S )·ψ [cm], (4)
whe e S (-) is he deg ee o soil sa u a ion.
In he calcula ions, he in il a ion capaci y is compa ed wi h he in ensi y o p ecipi-
a ion, assuming ha , un il he alues o bo h pa ame e s a e equal, he o al amoun o
Sus ainabili y 2022,14, 4962 8 o 27
ainwa e in il a es he soil p o ile. This is e e ed o as he su ace looding ime (
p
).
A e his, he o e land uno begins, and he amoun o wa e accumula ed (F) in he soil
p o ile can be calcula ed om he ollowing ela ionship:
F=Fp+ks· − p+(θs−θi)·ψ m·ln
(θs−θi)·ψ m +F
(θs−θi)·ψ m +Fp
, (5)
whe e F
p
(mm) is he accumula ion o ainwa e in he soil a he momen o ponding o he
soil su ace,
θs
(-) is he soil mois u e con en a ull sa u a ion, and
θi
(-) is he soil mois u e
con en be o e ain all.
The solu ion o Equa ion (5) was ound by using he i e a i e me hod in Mic oso
Excel. The alues o ini ial soil mois u e be o e he i s ain all episode we e de e mined
on he basis o he soil po osi y and mass mois u e, while o he nex wo episodes he
balance o wa e in il a ing he soil and he amoun o o e land and subsu ace uno
we e aken in o conside a ion.
The second me hod o calcula ing o e land uno was based on nume ical calcula ions
using he physical Richa ds equa ion [
19
] o wa e low in he zone o incomple e sa u a ion.
The calcula ions we e conduc ed in he SEEP/W module (Seequen , a Ben ley Company,
B oom ield, CO, USA) o he wo-dimensional model o he plo (Figu e 4), assuming ha
he ou low o wa e om he g ound occu s in he lowe pa o one o he walls. On he
o he hand, he amoun o ain all, i s du a ion, and he pe iods be ween indi idual ain all
episodes we e he same as in he ac ual s udies. As a esul o he calcula ions, he olume
o wa e s o ed and d ained om he soil was ob ained, and he amoun o o e land uno
was calcula ed as he di e ence be ween he ain all and he amoun o wa e in il a ing
he soil:
OF =R−S, (6)
whe e OF (mm) is he o e land uno , R(mm) is he ain all, and S(mm) is he heigh o
he wa e column s o ed in he g ound.
Sus ainabili y 2022, 14, x FOR PEER REVIEW 9 o 31
Figu e 4. C oss sec ion o he calcula ion model scheme (5.0% soil su ace inclina ion).
Fo he pu pose o calcula ing he coe icien o pe meabili y o soil, alues o (2 ÷ 5)
× 10−6 m·s−1 we e adop ed om he Sa u o in il ome e es s, and he e en ion cha ac e -
is ics we e de e mined using he e en ion pa ame e s p oposed by he SEEP/W p og am
o sil y soils.
2.5. Es ima ion o O e land and Subsu ace Runo Using he MSME Model
The concep o he model was in oduced by Wałęga and Ama ya [68] o a la
coas al wa e shed. The me hod is based on a common SCS-CN me hod used o calcula e
di ec uno . In he p esen s udy, he concep was sligh ly modi ied. In he MSME model,
he di ec uno was es ima ed o e e y e en using he ollowing equa ions:
=()∙()
 >
; (7)
Supposing =0 hen:
=∙(−)
, (8)
whe e S is he maximum e en ion capaci y, and P (mm) is he sum o he p ecipi a ion
du ing he e en .
In Equa ion (7), he highe he an eceden mois u e (M), he lowe he ini ial abs ac-
ion (Ia), and ice e sa. The an eceden mois u e con en is gi en as ollows:
=(5−)
(5−)+5>
(9)
=05<
, (10)
whe e β (-) and λ (-) a e pa ame e s ha a e op imized, and P5 is he amoun o wa e ha
in il a ed du ing he p e ious i e-day pe iod.
Subsu ace uno (MSMEQsubs) was calcula ed using he ollowing equa ions:
 =(−)∙(−+)
(−+)>
(11)
1=∙5+(−)
(12)
 =0<
(13)
Figu e 4. C oss sec ion o he calcula ion model scheme (5.0% soil su ace inclina ion).
Fo he pu pose o calcula ing he coe icien o pe meabili y o soil, alues o
(2 ÷5) ×10−6m·s−1
we e adop ed om he Sa u o in il ome e es s, and he e en ion
cha ac e is ics we e de e mined using he e en ion pa ame e s p oposed by he SEEP/W
p og am o sil y soils.
2.5. Es ima ion o O e land and Subsu ace Runo Using he MSME Model
The concep o he model was in oduced by Wał˛ega and Ama ya [
68
] o a la coas al
wa e shed. The me hod is based on a common SCS-CN me hod used o calcula e di ec
uno . In he p esen s udy, he concep was sligh ly modi ied. In he MSME model, he
di ec uno was es ima ed o e e y e en using he ollowing equa ions:
Q=(P−Ia)·(P−Ia+M)
P−Ia+Si P >Ia; (7)
Sus ainabili y 2022,14, 4962 9 o 27
Supposing Q=0 hen:
Ia=λ·(S−M), (8)
whe e Sis he maximum e en ion capaci y, and P(mm) is he sum o he p ecipi a ion
du ing he e en .
In Equa ion (7), he highe he an eceden mois u e (M), he lowe he ini ial abs ac ion
(Ia), and ice e sa. The an eceden mois u e con en is gi en as ollows:
M=β(P5−λS)λS
(P5−λS)+S o P5>S(9)
M=0 o P5<S, (10)
whe e
β
(-) and
λ
(-) a e pa ame e s ha a e op imized, and P5 is he amoun o wa e ha
in il a ed du ing he p e ious i e-day pe iod.
Subsu ace uno (MSMEQsubs) was calcula ed using he ollowing equa ions:
MSMEQsubs =(P−Ia1)·(P−Ia1+M)
(P−Ia1+Sa)i P >Ia1(11)
Ia1=a·(PET5+(Sa−M)) (12)
MSMEQsubs =0i P <Ia1(13)
M=β·(P5−PET5)·Sa
(P5−PET5)+Sa(14)
Sa=a25400
CN −254, (15)
whe e I
a1
(mm) is he ini ial abs ac ion o subsu ace uno , PET5 (mm) is he sum o
i e days’ po en ial e apo anspi a ion compu ed using he Penman–Mon ei h me hod,
S
a
(mm) is he maximum po en ial e en ion o he a ea whe e subsu ace uno occu s,
and a(-) is he coe icien o he p opo ion o a ea wi h sa u a ed soil.
O e land uno (MSMEQsu ) was calcula ed using he ollowing equa ions:
MSMEQsu =(P−Ia2)·(P−Ia2)
P−Ia2+Sb
i P >Ia2(16)
Ia2=(1−a)·(PET5+Sb)(17)
MSMEQsu =0i P <Ia2(18)
Sb=(1−a)·25400
100 −CN −254, (19)
whe e I
a2
(mm) is he ini ial abs ac ion o o e land uno , S
b
(mm) is he maximum
po en ial e en ion o he a ea whe e o e land uno occu s, and CN (-) is he cu e
numbe (CN) pa ame e .
To al uno was calcula ed as he sum o o e land and subsu ace uno :
MSME o =MSMEQsu +MSMEQsubs. (20)
In he ini ial phase o ain all, when he soil is d y wi h a la ge soil wa e de ici
(s o age), i is assumed ha uno does no occu . In he case o highly impe meable soil,
a e he i s soil sa u a ion h eshold is exceeded, o e land uno begins. The ac o
de e mining he p opo ion o sa u a ed a ea is pa ame e “a”, which is calib a ed based
on he obse ed ain all and uno om he labo a o y model. I he soil is almos ully
sa u a ed (
S ∼
=
1.0), subsu ace uno may occu a e o e land uno because he we ing
on is mo ing in he soil p o ile and sa u a ion inc eases. I he ain all con inues, he soil
will con inue o be sa u a ed, achie ing he second h eshold and esul ing in subsu ace
Sus ainabili y 2022,14, 4962 16 o 27
we e ca ied ou using wo calcula ion me hods, aking in o accoun he physical p ope ies
o he soil (Table 2). The esul s o he calcula ions show a signi ican in luence o he
coe icien o pe meabili y on he esul s o he o e land and subsu ace uno calcula ions.
Gene ally, o lowe alues o he coe icien o pe meabili y, highe alues o o e land
uno and lowe alues o subsu ace uno we e ob ained. The exempla y esul s o
o e land uno calcula ions using he G een–Amp me hod (Figu e 12) indica e ha he
g ea es disc epancies be ween he calcula ion and obse a ion esul s we e ob ained in he
i s ain all episode, whe e he calcula ed o e land uno alue was signi ican ly g ea e
han he calcula ed alue. The oo mean squa e e o and he Nash–Su cli e coe icien
showed ha , in he case o o e land uno calcula ions, he mos accu a e alues o bo h
pa ame e s we e ob ained wi h a pe meabili y coe icien o 2.10
×
10
−6
m
·
s
−1
. The alue
o he EF pa ame e (Table 3) o he model wi h a 2.5% inclina ion was 0.77–0.80 in he
G een–Amp and Richa ds me hod, espec i ely, and 0.95–0.96 o he model wi h a 5.0%
inclina ion o he g ound su ace. On he o he hand, accep able EF alues (0.64–0.79) we e
ob ained o he model wi h a su ace inclina ion o 5% o he wo highes alues o he
coe icien o pe meabili y. This is aking in o accoun ha , in he analyzed cases, o e land
uno domina ed, so he esul s o he calcula ions we e used o u he analyses, wi h a
coe icien o pe meabili y o 2.10 ×10−6m·s−1.
Sus ainabili y 2022, 14, x FOR PEER REVIEW 17 o 31
Figu e 10. Changes in soil esis ance du ing h ee ain all episodes a a 2.5% inclina ion o he soil
su ace.
Figu e 11. Changes in soil esis ance du ing h ee ain all episodes a a 5.0% inclina ion o he soil
su ace.
3.4. Ve i ica ion o Calcula ion Models
3.4.1. G een–Amp and Richa ds models
The esea ch esul s con i med he e ec o indi idual ain all episodes on he
amoun o o e land uno gene a ed. Fo compa ison, heo e ical calcula ions o wa e
in il a ion we e ca ied ou using wo calcula ion me hods, aking in o accoun he
physical p ope ies o he soil (Table 2). The esul s o he calcula ions show a signi ican
Figu e 11.
Changes in soil esis ance du ing h ee ain all episodes a a 5.0% inclina ion o he soil su ace.
Figu es 13a and 14a compa e he esul s o nume ical calcula ions o o e land and
subsu ace uno om he Richa ds model wi h he esul s o labo a o y es s. The calcula-
ions we e ca ied ou as a single ime se ies, which s a ed a leas en minu es be o e he
beginning o he i s ain all episode and ended se e al dozen minu es a e he end o
he las ain all episode. The ime in e als be ween he indi idual ain all episodes we e
iden ical o hose used in he labo a o y expe imen s.
The calcula ion esul s o bo h inclina ions o he uno soil su ace showed ha he
o al alues o o e land and subsu ace uno we e sligh ly lowe han hose ob ained
om he es s. I could be no iced ha he o e land uno alues calcula ed o he i s
ain all episode we e o e es ima ed compa ed o hose measu ed in labo a o y condi ions.
On he o he hand, he alues calcula ed o he second ain all episode we e simila , while
hose o he hi d episode we e unde es ima ed compa ed o he esul s ob ained om he
measu emen s. In he case o he las ain all episode, he measu ed o e land uno was
27 mm, ep esen ing almos 90% o he p ecipi a ion.

Sus ainabili y 2022,14, 4962 17 o 27
Table 2. Summa y o measu emen and calcula ion esul s o o e land and subsu ace uno .
Numbe o
he Rain all
Episode
Type o
Runo
Soil Coe icien o
Pe meabili y Used
in he Calcula ions
(m·s−1)
Inclina ion o Soil Su ace
2.5% 5.0%
Obse a ions
Model
Obse a ions
Model
G een–
Amp Richa ds G een–
Amp Richa ds
Runo Value (mm)
1o e land
4.0 ×10−6
2.0 ×10−6
1.0 ×10−6
5.0 ×10−7
0.61
0.00
3.02
9.76
15.49
0.96
1.32
6.85
12.96
2.03
0.00
3.02
9.76
15.49
0.20
0.88
6.76
12.91
subsu ace
4.0 ×10−6
2.0 ×10−6
1.0 ×10−6
5.0 ×10-7
0.00 -
0.00
0.00
0.00
0.00
0.0 -
0.00
0.00
0.00
0.00
2o e land
4.0 ×10−6
2.0 ×10−6
1.0 ×10−6
5.0 ×10−7
16.11
6.83
14.24
19.37
22.78
7.38
8.33
14.46
19.32
14.15
6.10
13.59
18.87
22.41
8.25
8.95
15.27
19.91
subsu ace
4.0 ×10−6
2.0 ×10−6
1.0 ×10−6
5.0 ×10−7
0.39 -
0.19
0.00
0.00
0.00
0.0 -
0.56
0.19
0.00
0.00
3o e land
4.0 ×10−6
2.0 ×10−6
1.0 ×10−6
5.0 ×10−7
25.17
11.23
17.94
22.14
24.78
28.25
28.36
18.14
18.01
26.78
14.61
20.60
24.10
26.20
28.11
28.31
17.88
18.00
subsu ace
4.0 ×10−6
2.0 ×10−6
1.0 ×10−6
5.0 ×10−7
0.75 -
0.90
0.77
0.00
0.00
1.53 -
1.42
0.77
0.00
0.00
To al o e land
4.0 ×10−6
2.0 ×10−6
1.0 ×10−6
5.0 ×10−7
43.72
18.1
35.2
51.3
63.1
36.59
38.00
39.46
50.29
42.96
20.71
37.21
52.73
64.10
36.56
38.14
39.91
50.82
subsu ace
4.0 ×10−6
2.0 ×10−6
1.0 ×10−6
5.0 ×10−7
5.20 -
1.49
0.91
0.00
0.00
2.66 -
2.42
0.78
0.00
0.00
3.4.2. MSME Model (Ve i ica ion o Sui abili y o he To al Runo Es ima ion)
Table 4shows he mean alues o he o e land and subsu ace uno ob ained based
on he esul s o labo a o y es s and calcula ions using he MSME model. The es esul s
showed ha he subsu ace uno in he es ed soil was small and cons i u ed jus o e
3.3% and 3.7% o he o al uno o he 2.5% and 5.0% soil su ace inclina ion, espec i ely.
The amoun o o e land and subsu ace uno om bo h he obse a ion and he MSME
model inc eased wi h he inclina ion o he uno su ace, which is consis en wi h he
s udy o Chen e al. [
26
]. The esul s ob ained om he MSME model we e simila o he
obse a ions, ega dless o he slope o he uno su ace. The RMSE e o alue was
0.52 and 0.05 mm o he 2.5% and 5.0% slope, espec i ely, while he EF coe icien was
0.99 in bo h cases. The e o e, i can be concluded ha he MSME model allowed o a e y
good es ima ion o he o al uno , which p o es he co ec concep o uno o ma ion
desc ibed by his model. The inclina ion o he uno su ace a ec s he soil deg ee o
sa u a ion, exp essed by he pa ame e “a”, which o he 2.5% inclina ion o he uno
su ace was 0.84, while o 5.0% i was 0.90. Thus, in he case o a su ace wi h highe
inclina ion, he subsu ace uno may be o med a a highe soil sa u a ion. Howe e , he
di e ences in soil mois u e con en a e small due o he ac ha , du ing hea y ain all,
Sus ainabili y 2022,14, 4962 18 o 27
he in il a ion a e depends on he uno su ace slope unde condi ions whe e i exceeds
10
◦
[
26
]. The alue o he CN pa ame e , unde s ood as he ca chmen ’s po en ial o uno
o ma ion, is as high as 89.7 o a 2.5% su ace slope and 93.0 o a 5% slope, which is
unde s andable as he in es iga ed land is cha ac e ized by a low in il a ion capaci y. A
he same ime, i should be no ed ha he inclina ion o he uno su ace a ec s he alue
o he CN pa ame e . The alue o he M pa ame e ela ed o he ini ial wa e con en
in he soil p o ile, coming om he in il a ion o ainwa e be o e he uno occu ed, is
0.00 o bo h a ian s o he uno su ace slope. This is caused by he me hodology used
o p epa e he soil o es ing, which is cha ac e ized by a ela i ely low mois u e con en .
The alues o S
a
and S
b
e en ion pa ame e s we e signi ican ly lowe o soil wi h a 5.0%
slope in compa ison o a 2.5% slope. I is ela ed, as in he case o he CN pa ame e , o a
lowe wa e e en ion capaci y in soils wi h a highe slope o he uno su ace, which was
con i med in his s udy. As a consequence, he ini ial losses o I
a1
pa ame e o subsu ace
uno and Ia2pa ame e o o e land uno we e also educed.
Sus ainabili y 2022, 14, x FOR PEER REVIEW 19 o 31
Figu e 12. Dependence o o e land uno on he du a ion o a ain all episode: compa ison o he
esul s o measu emen s and calcula ions using he G een–Amp me hod.
Figu e 12.
Dependence o o e land uno on he du a ion o a ain all episode: compa ison o he
esul s o measu emen s and calcula ions using he G een–Amp me hod.
Sus ainabili y 2022,14, 4962 19 o 27
Table 3. Values o me ics—RMSE and Nash–Su cli e EF [70].
Type o Runo
Soil Coe icien o
Pe meabili y Used in he
Calcula ions (m.s−1)
Inclina ion o Soil Su ace
2.5% 5.0%
Model Model
G een–Amp Richa ds G een–Amp Richa ds
Roo Mean Squa e E o , RMSE (mm) (Equa ion (21))
o e land
4.0 ×10−6
2.0 ×10−6
1.0 ×10−6
5.0 ×10−7
162.15
35.38
59.77
153.62
49.50
41.10
52.57
123.60
125.29
22.79
51.50
144.27
23.07
17.70
59.35
132.08
subsu ace
4.0 ×10−6
2.0 ×10−6
1.0 ×10−6
5.0 ×10−7
-
0.25
0.30
0.63
0.63
-
0.19
0.33
1.35
1.35
Modeling e iciency, EF [-] (Equa ion (22))
o e land
4.0 ×10−6
2.0 ×10−6
1.0 ×10−6
5.0 ×10−7
0.09
0.80
0.66
0.14
0.72
0.77
0.70
0.31
0.74
0.95
0.89
0.70
0.95
0.96
0.87
0.72
subsu ace
4.0 ×10−6
2.0 ×10−6
1.0 ×10−6
5.0 ×10−7
-
−0.54
−0.86
−2.86
−2.86
-
0.79
0.64
−0.50
−0.50
3.5. Discussion
When analyzing he in luence o he su ace inclina ion on he measu ed alues o
o e land uno , i can be concluded ha i was no e y signi ican . These esul s a e
consis en wi h he esul s o he analyses by Chen and Young [
26
], who showed ha ,
a soil inclina ions smalle han 10
◦
, he di e ences in he amoun o wa e in il a ing
he soil a e small, so he alues o o e land uno will be simila . Simila esul s we e
gene a ed in he ield es s conduc ed by Smolska [
32
]. Labo a o y es s ca ied ou by
Wang e al. [
16
] p o ide sligh ly di e en ela ionships, as hey indica e ha he e a e
di e ences be ween he measu ed alues o e ec i e p ecipi a ion and he amoun o wa e
in il a ing he soil o su ace inclina ions o 3
◦
and 5
◦
. In gene al, he amoun o o e land
uno inc eases wi h inc easing su ace inclina ion, while he amoun o wa e in il a ing
he soil dec eases. Un o una ely, Wang e al. [
16
] do no p o ide he physical p ope ies o
he soil hey examined.
In e es ing da a we e gene a ed by nume ical calcula ion. The esul s o soil deg ee o
sa u a ion calcula ions (Figu es 13b and 14b) indica e ha , du ing he i s ain all episode,
he e we e signi ican changes in he su ace pa o he soil sample, ega dless o he soil
slope. In he lowe pa o he sample, a a dep h o 15.5 cm, hese changes we e e y small
and appea ed a he end o he p ecipi a ion e en . This seems o be consis en wi h he
esul s o measu emen s o he elec ical esis ance o he soil (Figu es 10 and 11). The
esul s o calcula ions o soil mois u e con en in he uppe pa o he soil sample indica e
ha , in he inal phase o he i s episode, he soil becomes sa u a ed, which coincides wi h
he beginning o he o e land uno . This ela ionship indica es ha he wa e low in he
soil is consis en wi h he assump ions o in il a ion calcula ions using pis on models, in
which he we ing on o med in he uppe pa o he p o ile mo es downwa ds wi h he
exis ing wa e supply (p ecipi a ion) o he soil.
In he second ain all episode, he sa u a ion o he su ace laye o soil occu ed in he
ini ial pe iod o he ain all, simila o when he o e land uno began. On he o he hand,
he soil mois u e con en in he lowe pa o he soil sample sys ema ically inc eases un il
Sus ainabili y 2022,14, 4962 20 o 27
soil sa u a ion was achie ed, a he end o he ain all episode. The calcula ions show ha ,
a e he episode ends, he subsu ace uno s a s, which is consis en wi h he es esul s
ob ained o he model wi h a uno slope o 2.5%. The alues esul ing om he elec ical
esis ance measu emen s in he lowe pa o he sample wi h a slope o 2.5% dec eased
no iceably a he end o his episode, o a alue ha was main ained un il he end o he
s udy. This dependence may indica e he sa u a ion o he lowe pa o he sample. In he
case o he soil sample wi h a 5.0% slope, he esis ance alue sys ema ically dec eased, bu
he minimum alue was achie ed only du ing he las ain all episode.
Sus ainabili y 2022, 14, x FOR PEER REVIEW 22 o 31
Figu e 13. The esul s o o e land and subsu ace uno calcula ions o he model wi h a soil su -
ace inclina ion o 2.5%.
Figu e 13.
The esul s o o e land and subsu ace uno calcula ions o he model wi h a soil su ace
inclina ion o 2.5%.
The nume ical calcula ions indica e ha , a e he second ain all episode, he soil was
ully o nea ly sa u a ed in i ually he en i e sample p o ile. The e o e, du ing he hi d
episode, mos o he ain all was ans o med in o o e land uno . When analyzing he
esul s o he nume ical calcula ions, i can be no iced ha , be o e he beginning o he
ain all, he lowe pa o he sample was cha ac e ized by a highe mois u e con en han
i s uppe pa . This obse a ion seems o be consis en wi h he esul s o soil esis ance
measu emen s, in which highe esis ance alues as well as lowe soil mois u e con en
we e eco ded close o he su ace. The nume ical calcula ions indica e ha , in he hi d
Sus ainabili y 2022,14, 4962 21 o 27
ain all episode, he in il a ion o ainwa e does no ha e he na u e o a pis on mo emen ,
bu causes he supply o wa e o he lowe , sa u a ed zone o he soil.
Sus ainabili y 2022, 14, x FOR PEER REVIEW 23 o 31
Figu e 14. The esul s o o e land and subsu ace uno calcula ions o he model wi h soil su -
ace inclina ion o 5.0%.
The calcula ion esul s o bo h inclina ions o he uno soil su ace showed ha he
o al alues o o e land and subsu ace uno we e sligh ly lowe han hose ob ained
om he es s. I could be no iced ha he o e land uno alues calcula ed o he i s
ain all episode we e o e es ima ed compa ed o hose measu ed in labo a o y condi-
ions. On he o he hand, he alues calcula ed o he second ain all episode we e simila ,
while hose o he hi d episode we e unde es ima ed compa ed o he esul s ob ained
om he measu emen s. In he case o he las ain all episode, he measu ed o e land
uno was 27 mm, ep esen ing almos 90% o he p ecipi a ion.
3.4.2. MSME model ( e i ica ion o sui abili y o he o al uno es ima ion)
Table 4 shows he mean alues o he o e land and subsu ace uno ob ained based
on he esul s o labo a o y es s and calcula ions using he MSME model. The es esul s
showed ha he subsu ace uno in he es ed soil was small and cons i u ed jus o e
3.3% and 3.7% o he o al uno o he 2.5% and 5.0% soil su ace inclina ion, espec-
i ely. The amoun o o e land and subsu ace uno om bo h he obse a ion and he
MSME model inc eased wi h he inclina ion o he uno su ace, which is consis en wi h
he s udy o Chen e al. [26]. The esul s ob ained om he MSME model we e simila o
he obse a ions, ega dless o he slope o he uno su ace. The RMSE e o alue was
0.52 and 0.05 mm o he 2.5% and 5.0% slope, espec i ely, while he EF coe icien was
0.99 in bo h cases. The e o e, i can be concluded ha he MSME model allowed o a e y
Figu e 14.
The esul s o o e land and subsu ace uno calcula ions o he model wi h soil su ace
inclina ion o 5.0%.
Table 4. A e age uno cha ac e is ics om he expe imen al labo a o y model and MSME model.
Slope
Inclina ion Qsu obs Qsubsu obs Q o obs Qsu calc Qsubsu calc Q o calc CN M SaSbIa1Ia2
- mm - mm
2.5 10.8 0.40 11.16 11.19 0.21 11.40 89.7 0.00 27.1 787.1 22.9 122.6
5.0 12.1 0.47 12.53 11.91 0.59 12.51 93.0 0.00 18.2 654.7 16.5 62.2
No es: Q
su obs
is he obse ed o e land uno , Q
subsu obs
is he obse ed subsu ace uno , Q
o obs
is he obse ed
o al uno (sum o o e land and subsu ace uno ), Q
su calc
is he calcula ed obse ed o e land uno , Q
subsu cal
is he calcula ed obse ed subsu ace uno , Q
o calc
is he calcula ed o al uno (sum o o e land and subsu ace
uno ), I
a1
is he ini ial abs ac ion o subsu ace uno , Mis he an eceden mois u e con en , S
a
is he maximum
po en ial e en ion o he a ea whe e subsu ace uno occu s, I
a2
is he ini ial abs ac ion o o e land uno
(in mm), S
b
is he maximum po en ial e en ion o he a ea whe e o e land uno occu s (mm), and CN is he
calcula ed cu e numbe .
I should also be no ed ha , in he hi d episode, bo h he measu ed and calcula ed
alues o he subsu ace uno we e highe han in p e ious episodes. On he o he
hand, he calcula ed alues o subsu ace uno we e clea ly smalle han he measu ed
esul s. I seems ha he di e ences may be signi ican ly in luenced by he accu acy o he
p epa a ion o he soil sample in he c i ical places, i.e., whe e he soil is exposed by he
g oo es cap u ing he wa e lowing ou o he soil.

Sus ainabili y 2022,14, 4962 22 o 27
The nume ical calcula ion o in il a ion and o e land uno , which we e simula ed
o labo a o y uno appa a us, was p esen ed by Mendes e al. [
34
]. Analysis esul s
indica e ha he ini ia ion o uno gene a ion is signi ican ly ela ed o he sa u a ion o
he soil sample in i s uppe pa . They also s a ed ha he simula ed uno esul s a e
insensi i e o he leng h o he sample leng h, which di e s om some si e measu emen
esul s (e.g., [
29
,
30
,
82
]), which ound ha highe uno coe icien s we e ound on small
plo s han on la ge plo s.
The esul s o he expe imen s conduc ed indica e ha , du ing he ain all, he amoun
o o e land uno o he model wi h a soil su ace inclina ion o 5.0% was sligh ly highe .
On he o he hand, he o al amoun o ain all was simila (Table 2). These esul s may
p o e he in luence o he soil su ace inclina ion on he delay in he ou low o wa e om
he ca chmen , as con i med by Wang e al. [16].
The ob ained esul s also p o e he signi ican in luence o he soil mois u e con en
on he condi ions o o ma ion and he amoun o o e land and subsu ace uno . The
occu ence o a se ies o sho - e m and in ense ain all episodes a o s an inc ease in he
soil mois u e con en and a educ ion in i s e en ion capaci y. Simila ela ionships a e
obse ed in na u al condi ions (e.g., [
36
,
48
]) and when aking in o accoun he clima e
change obse ed o e many yea s, e.g., sho and in ense ain all in Cen al Eu ope [
83
]
and o he egions [
84
,
85
]. They gene a e o e land uno , o en causing looding, usually
o a local na u e. The conduc ed expe imen s showed ha in ex eme cases mo e han
wo- hi ds o ain all is ans o med in o o e land uno . Simila dependencies in na u al
condi ions a e p esen ed, among o he s, by Kijowska-S ugała and Kiska [
79
], Sche e
e al. [
36
], and Zyd o´n e al. [
86
]. I should be emphasized ha he o ma ion o his p ocess
is g ea ly in luenced by he soil pe meabili y coe icien , and, in buil -up a eas, by he
deg ee o su ace sealing. In he p esen ed s udies, he p ecipi a ion in ensi y was, on
a e age, 0.75 mm
·
min
−1
, and he alue o he coe icien o pe meabili y was es ima ed
a 0.12 mm
·
min
−1
. In he case o less pe meable soil, one should expec a highe alue o
o e land uno .
I should be no ed ha he esul s o labo a o y es s conce ned soil wi hou ege-
a ion co e , which may co espond o a eas co e ed by cons uc ion wo k o g ound
communica ion ou es. Simila condi ions may also apply o ba e soil. Measu emen s on
ba e soil [
31
,
32
] indica e ha o e land uno on his kind o su ace is highe han ha
on cul i a ed land o soil wi h ege a ion co e . The esea ch ca ied ou by Mouni ou
e al. [
43
] showed he e ec o land use and land co e changes on he wa e cycle in a
small Sahelian wa e shed. Simula ion esul s p o ided an explana ion o he Sahelian a ea
pa adox. The au ho s p o ed ha a change in he sealing o he ca chmen a ea could lead
o an inc ease in su ace uno despi e he d op in ain all.
Resul s o uno om he G een–Amp and Richa ds equa ions we e compa ed wi h
he hyd ological model MSME. The quali y o he MSME model, despi e i s conside able
simplici y compa ed o he physical models, was be e han ha o he Richa ds and
G een–Amp models. The e o e, he MSME model co ec ly desc ibes he o al uno and
i s indi idual pa s in he case o low-pe meable soils. In he MSME model, he soil deg ee
o sa u a ion pa ame e “a” plays an essen ial ole in sepa a ing subsu ace and o e land
uno . The alue o he “a” pa ame e depends on he soil inclina ion. The alues o he
“a” pa ame e ob ained in his s udy we e much lowe compa ed o in o es ca chmen s
wi h gen le slopes, as desc ibed by Wał˛ega e al. [
13
]. Howe e , i should be aken in o
conside a ion ha , in he case o a o es ca chmen , midsoil uno is p edominan , while
o e land uno is o med only a e e y in ense ain all.
In he o iginal me hodology [
4
], he uno su ace slope is no aken in o accoun in he
calcula ion o he CN pa ame e ; howe e , as he slope o he uno su ace inc eases, he
uno a e inc eases, and he e o e he in il a ion capaci y dec eases. A simila endency
was obse ed in he p esen s udy, i.e., ha he wa e in il a ion capaci y was educed
wi h an inc ease in he uno su ace inclina ion. This was mani es ed by an inc ease in he
alue o he CN pa ame e . The impac o an inc ease in he inclina ion o he uno su ace
Sus ainabili y 2022,14, 4962 23 o 27
on he alue o he CN pa ame e has been he subjec o many s udies. Fo example,
Mły´nski [
87
] showed ha aking in o accoun he slope o a ca chmen a ea imp o es he
quali y o adjus ing he CN o he obse ed alues.
The ob ained esul s may be a good indica o o a eas subjec o high human p essu e.
The ob ained esul s indica e ha high-in ensi y o e land uno is accompanied by soil
denuda ion p ocesses, and he e o e, in o de o educe he in ensi y o hese p ocesses, i
seems easonable o use app op ia e biogeo echnical ea men s.
4. Conclusions
Based on he esul s o es s conduc ed on he coa se clay sil , i can be concluded
ha o e land uno is he dominan ype o uno in he analyzed soil. The impac o
subsu ace uno on he wa e balance will be small due o he low wa e pe meabili y o
he examined soil. This may ha e a signi ican impac on he o ma ion o a lood wa e
in a wa e cou se in a eas whe e he e a e soils wi h simila geo echnical cha ac e is ics,
in pa icula in e ms o il a ion. Ou es s p o ed ha an inc ease in he soil su ace
inclina ion om 2.5% o 5.0% did no cause a signi ican change in he amoun o o e land
uno . Howe e , inc eased dynamics o i s o ma ion was ound, which was ce ainly
in luenced by he lack o a ege a ion co e ha would educe and delay i s o ma ion.
The ob ained esul s indica e ha , a a low ini ial soil mois u e con en , he uno is o
Ho on o e land low cha ac e , in which he subsu ace laye o soil is mos ly sa u a ed,
and in he case o high mois u e con en i is caused by he sa u a ion o he en i e soil
p o ile. This is con i med by he esul s o elec ical esis ance measu emen s and nume ical
calcula ions. I was demons a ed ha in ensi e ain all epea ing in sho in e als will
con ibu e o he gene a ion o signi ican o e land uno , and in ex eme cases mo e han
wo- hi ds o ain all can be ansposed in o o e land uno .
I was also demons a ed ha he G een–Amp and Richa ds models co ec ly desc ibe
he cou se o he in il a ion p ocess and o e land uno o ma ion. The Richa ds model,
howe e , ended o unde es ima e he amoun o subsu ace uno . The il a ion coe icien
adop ed o he calcula ions has a e y signi ican in luence on he esul s o he calcula ions,
especially in he case o he G een–Amp model.
The MSME model can be used o es ima e he o e land uno (Qsu ) and subsu ace
uno (Q
subs
) o impe meable soils, and i s quali y is compa able o ha o he G een–
Amp and Richa ds models. The G een–Amp and Richa ds me hod a e based on physical
assump ions and soil p ope ies, bu he simple empi ical model MSME has pa ame e s
ha a e op imized based on obse ed ain all– uno e en s. This may be he main eason
why he esul s o he MSME model a e sligh ly be e han hose achie ed by physical
app oaches. A limi a ion o he MMSE model in ela ion o he physical models is he
inabili y o de e mine he cou se o in il a ion o e ime and he need o calib a e he
pa ame e s based on he obse ed ain all– uno episodes. Howe e , since i is a simple
empi ical model, i can be used by hyd ologis s o es ima e he uno in ca chmen s. So, i
is necessa y o conduc u he esea ch on he applica ion o his model on a eal scale in
a ious ca chmen s o p o e i s use ulness in enginee ing calcula ions. Also, he au ho s
will conside pe o ming a s udy on he in luence o a i icial d ainage on uno o ma ion
and would include hese esul s in he analyzed models. In a eal ca chmen , he use
o mode n echnique, like sa elli e imagines will be conside ed o indi ec ly assess soil
mois u e and link hem wi h he pa ame e s o he MSME model.
Au ho Con ibu ions:
Concep ualiza ion, A.G., T.Z. and A.W.; me hodology, A.G., T.Z. and A.W.;
so wa e, A.G., T.Z., A.W. and J.P.; alida ion, A.G., T.Z., A.W. and J.S.; o mal analysis, A.G., T.Z.,
A.W. and J.P.; in es iga ion, A.G., T.Z., A.W. and J.P.; esou ces, A.G., T.Z. and A.W.; da a cu a ion,
A.G., T.Z. and J.P.; w i ing—o iginal d a p epa a ion, A.G., T.Z. and A.W.; w i ing— e iew and
edi ing, A.G., T.Z. and A.W.; isualiza ion, T.Z.; supe ision, T.Z. and J.S. All au ho s ha e ead and
ag eed o he published e sion o he manusc ip .
Funding: This esea ch ecei ed no ex e nal unding.
Sus ainabili y 2022,14, 4962 24 o 27
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : No applicable.
Acknowledgmen s:
The au ho s would like o hank Adam Kapała o his help ca ying ou he
labo a o y es s p esen ed in his pape . The au ho s would like o hank he anonymous e iewe s
o hei e o s owa ds imp o ing he manusc ip .
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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