Applicability of literature values for green–ampt parameters to account for infiltration in hydrodynamic rainfall–runoff simulations in ungauged basins [original]

Vol.:(0123456789)

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https://doi.org/10.1007/s10666-021-09788-0

Applicability ofLiterature Values forGreen–Ampt Parameters

toAccount forInfiltration inHydrodynamic Rainfall–Runoff

Simulations inUngauged Basins

FranziskaTügel1 · AzizHassan1· JingmingHou2· ReinhardHinkelmann1

Received: 14 January 2021 / Accepted: 10 July 2021

Abstract

This study aimed to evaluate the suitability of literature parameter values for the Green–Ampt infiltration model to be used

in hydrodynamic rainfall–runoff simulations. The outcome of this study supports to decide which literature values should

be taken if observed data for model calibration is not available. Different laboratory experiments, a plot-scale experiment

in the Thiès catchment in Senegal, and a flash flood in the region of El Gouna in Egypt, have been simulated with the 2D

shallow water model Hydroinformatics Modeling System (hms) incorporating the Green–Ampt model. For four test cases

with available runoff data, the results of the calibrated models were compared to those obtained from average values after

Rawls etal. (Journal of Hydraulic Engineering 1:62–70, 1) and Innovyze (Help documentation of XPSWMM and XPStorm,

2). The results showed a clear underestimation of infiltration in two of three considered laboratory experiments, while for a

field experiment in Senegal, average values after Rawls etal. (Journal of Hydraulic Engineering 1:62–70, 1) led to a strong

overestimation and the ones after Innovyze (Help documentation of XPSWMM and XPStorm, 2) to an underestimation of

infiltration. In a case study on flash floods in an ungauged region in Egypt, the values of both sources led to a strong over-

estimation of infiltration, when the simulation results are compared to observed flooding areas. It can be concluded, that

the values after Innovyze (Help documentation of XPSWMM and XPStorm, 2) lead to overall better results than the ones

after Rawls etal. (Journal of Hydraulic Engineering 1:62–70, 1). According to the results, the hydraulic conductivity in

ungauged areas with bare sandy soil should be reduced by about 90–100 % compared to the value after Rawls etal. (Journal

of Hydraulic Engineering 1:62–70, 1).

Keywords Robust 2D shallow water model· Hydroinformatics Modeling System· Sensitivity analysis· Ungauged

catchments· Automatic calibration

1 Introduction

Hydrodynamic models are more and more used to simulate

not only the flow and flooding areas of surface waters but also

rainfall-induced overland flow in small catchments [3–7], the

propagation of flash floods [8–11], and flood inundation in

urban areas [12–15]. Additionally, to the calculation of the flow

field, appropriate methods to represent the runoff generation are

needed to establish an integrated hydrological-hydrodynamic

model. As 2D shallow water models are typically used for the

simulation of relatively short flooding events of some hours up

to a few days rather than long-term rainfall–runoff simulations,

infiltration represents the most important water loss [16], while

evapotranspiration can be neglected in many cases or taken into

account in a very simplified way. Infiltration describes the pro-

cess when rainwater or ponding water is absorbed by the soil.

The infiltrated water can either flow further downstream rela-

tively close and parallel to the surface (interflow), be stored in

the unsaturated soil zone, or percolate into deeper soil layers and

finally contribute to groundwater recharge. For flood modeling

it is specifically interesting how much water of the rainfall will

lead to overland runoff and how much is “lost” by infiltration.

Especially for rural areas and green urban infrastructure, the

* Franziska Tügel

franziska.tuegel@wahyd.tu-berlin.de

1 Chair ofWater Resources Management andModeling

ofHydrosystems, Technische Universität Berlin, Straße des

17. Juni 135, 10623Berlin, Germany

2 School ofWater Resources andHydro-Power Engineering,

Xi’an University ofTechnology, Xi’an, China

Environmental Modeling & Assessment (2022) 27:205–231

/ Published online: 16 August 2021

F.Tügel et al.

20 1 3

infiltration losses have to be taken into account. A good under-

standing of infiltration and its representation in models is crucial

not only for the appropriate risk management of heavy rainfalls

and flash floods but also for successful solutions of water har-

vesting and groundwater recharge [17]. Concerning the global

trends of ongoing urbanization and climate change coming along

with more frequent and more intense hydro-meteorological

extremes in terms of floods and droughts, damages from inunda-

tions on the one hand and lowered groundwater tables and water

stress, on the other hand, will increase and get more severe in

future [4, 10, 18, 19]. To mitigate these effects, so-called water-

sensitive or climate-adapted urban planning and water resources

management strategies considering sustainable urban drainage

systems (SUDS) [20, 21] and low impact developments (LIDs)

[22–24] are gaining increasing importance. Measures such as

infiltration basins, swales, raingardens, or permeable pavement

should lead back to a more natural water cycle to mitigate flood

risks, store water, enhance evapotranspiration, and stabilize

groundwater tables. To investigate the effectiveness of such

sustainable stormwater management measures with regard to

flood mitigation, an appropriate representation of infiltration in

2D hydrodynamic rainfall–runoff models is also needed.

The infiltration process is influenced by many factors,

such as soil texture class, soil moisture, soil surface condi-

tion, soil bulk density, content of organic matters and litter

in the soil, land cover, land use, topography, rainfall charac-

teristics as well as spatial variability of soil properties [17,

25–28]. It has been, for example, observed that infiltration

capacities are usually higher on vegetated than on bare soil

surfaces, which is caused among other things by the protec-

tion of the surface against the kinetic energy of raindrops

preventing the rearrangement of soil particles and thus sur-

face sealing or crust formation. Observations of Ribolzi etal.

[29] confirmed the hypothesis that higher effective rainfall

intensity was responsible for the formation of less permeable

erosion crusts on a 30 % slope than the structural crusts that

developed on a 75 % slope. Mohammadzadeh-Habili and

Heidarpour [30] carried out column experiments and numer-

ical simulations to study various effects of infiltration into

layered soils. If, for example, water infiltrates through an

upper layer of finer and less permeable soil than the coarser

sublayer, the wetting front, which is usually considered to be

stable, becomes unstable forming narrow wetting columns

or fingers. Deng and Zhu [31] stated—that similar to satu-

rated flow—the harmonic average of hydraulic conductivi-

ties is the best approach to calculate infiltration in layered

soils. In their study, they showed that this is true for both,

coarse-over-fine and fine-over-coarse layer formations [31].

Assouline and Mualem [17] concluded from their study on

heterogeneous small bare catchments, that the impact of sur-

face sealing is much more important than the one of spatial

soil variability. Another important factor that can influence

infiltration processes is the microtopography, which was,

for example, investigated by Esteves etal. [32], Fiedler and

Ramirez [33], Mallari etal. [34], Thompson etal. [35], and

Xiang etal. [36]. Also, friction can influence infiltration,

as higher friction leads to lower flow velocities and more

water can infiltrate during the decelerated propagation of

the flood wave. Ries etal. [28] conducted 120 experiments

with a rainfall simulator on different land covers and soil

types with different initial water contents, rain intensities

and durations. Based on their observations they stated, that

simplified approaches, which are still often applied in mod-

els used for the risk management of flash floods—up to the

strongest simplification of completely neglecting the run-

off reduction during heavy rainfalls—are not suitable. This

is shown among others by the fact, that in their conducted

experiments even saturated soils still showed significant

infiltration rates [28].

There exist many different approaches to model the water

losses caused by infiltration, starting from simplified empiri-

cal approaches such as the well-known runoff-coefficient,

loss-rate, and SCS-CN (Soil Conservation Service Curve

Number) methods as well as the Horton equation, more

physically-based methods like the Philip infiltration model

and the Green–Ampt model, up to the Richards equation. In

investigations of Caviedes-Voullième etal. [3], the SCS-CN

method was found to be inadequate to be coupled with a

distributed model for runoff computations, and as the Rich-

ards equation is very complex and the solution needs a lot

of computational effort as well as many measured data [37,

38], simplified equations are often used in rainfall–runoff

models, where the Green–Ampt model is one of the most

popular ones [4, 16, 39, 40]. Developed by Green and Ampt

already in 1911 [41], many different applications, modifica-

tions, and extensions have been carried out in the last more

than 100 years, and in many test cases, it was proven that this

model is generally able to appropriately represent infiltration

processes [16, 42–44].

The main problem for real-world applications consists

in estimating the Green–Ampt parameters, namely the

hydraulic conductivity, capillary suction head at the wetted

front, and effective porosity (representing the saturated soil

water content), additionally to the initial soil water content

of the soil. The capillary suction in the fine pores of a soil

dominates the infiltration process in dry soils, especially at

the beginning of a rainfall event, if there is an initial soil

moisture deficit which is expressed as difference between

saturated and initial soil water content. With increasing

water saturation of the soil, the capillary suction reduces

and drops to zero, if the soil is completely saturated with

water. Then the infiltration depends only on gravity and the

infiltration rate is usually assumed to be equal to the satu-

rated hydraulic conductivity [45]. For simple test cases or

laboratory experiments, the Green–Ampt parameters might

be measured directly, but due to the high effort and costs,

206

Applicability ofLiterature Values forGreen–Ampt Parameters toAccount forInfiltration in…

1 3

it is usually not feasible to directly measure the needed soil

properties at enough locations within large areas as it would

be needed for real-world applications [46, 47]. If available

runoff and sometimes even infiltration time series exist, the

Green–Ampt parameters can be considered as calibration

parameters [6, 16, 43]. As also observed runoff data is often

not available for real-world applications, e.g., consider-

ing flash floods or ungauged catchments, the Green–Ampt

parameters have to be estimated based on relations to more

easily available soil properties such as the soil texture

class. Many different of such methods have been developed

over the past decades. The probably best known and most

cited contribution is the study of Rawls etal. [1], where

they developed a table of parameter sets in dependence on

soil texture class and soil horizon. These average param-

eter values are the result of analyzing 5000 soil horizons

in the USA, for which the Green–Ampt parameters were

derived from the Brooks and Corey parameters that were

fitted before to the available water retention data. For a more

accurate estimation than taking those average values for the

given soil texture class and if more detailed soil information

is available, they recommend to predict the water retention

matrix potential curve by a regression equation based on par-

ticle size distribution, organic matter, bulk density, and 0.33

bar and 15 bar moisture retention values. The best option, of

course, would be to determine the Green–Ampt parameters

based on measured water retention matrix potential data

[1], but as mentioned before this is usually too costly and

too much effort for large areas in real-world applications.

Other typical values for the Green–Ampt parameters are, for

example, presented in the manual of the modeling software

company Innovyze [2], referring to different sources, where

the hydraulic conductivity is based on minimum infiltration

rates observed from measured rainfall, runoff and infiltrom-

eter data, and the initial soil moisture deficit is given for dry

conditions as typical moisture deficit at the wilting point,

which should be decreased for moist or very wet anteced-

ent conditions [2]. Furthermore, there have been several

studies on finding suitable regression equations, where the

Green–Ampt parameters can be derived from more easily

measured parameters such as percentages of clay, sand,

gravel, and the bulk density [36], or from the percentage

of surface cover and crusting or initial soil moisture and

antecedent rainfall [48].

Especially, on bare soils with no vegetation, the kinetic

energy of raindrops can disturb and rearrange soil aggre-

gates resulting in the formation of a surface crust or sealing

[49–51]. Such layers can lead to a significant decrease in

the infiltration capacity by 20 to 2000 times [52, 53]. The

thickness of such layer has been reported to vary from 1 to 5

mm [53, 54]. Different adaptions and extensions of infiltra-

tion models to account for the effects of a surface crust have

been developed [17, 55]. A very simple one is a modified

Green–Ampt model, where the hydraulic conductivity is cal-

culated as effective hydraulic conductivity of the crust and

subcrust soil [17,32, 51, 56].

For practical applications, tabulated standard parameters

depending on the soil texture class as represented by Rawls

etal. [1] or Innovyze [2] are very interesting and might

sometimes be assumed without further knowledge about

the actual infiltration behavior, especially when investigat-

ing ungauged areas. As these tabulated parameter values

are derived from a limited number of field and lab experi-

ments with soils from limited areas, and as it is not clear

whether these literature values represent a good assump-

tion of the actual infiltration in larger-scale rainfall–runoff

simulations, further analysis is desirable. This study aims

to analyze the applicability of tabulated values from two

different literature sources to consider infiltration with the

Green–Ampt model in 2D shallow water models. Recom-

mendations should be given for rainfall–runoff simulations

in ungauged areas in terms of in which cases the tabulated

values of which source are suitable to estimate infiltration or

giving tendencies how to adapt them. After describing the

applied methods, the characteristics and setups of different

test cases with measured data are represented. For one test

case, a sensitivity analysis is carried out to study the effects

of different parameters on infiltration. Afterwards, the results

of several simulations with different parameter sets are pre-

sented for each test case to evaluate the performance of the

model when taking into account the average parameter val-

ues compared to the calibrated ones. Three of the test cases

are laboratory experiments and one is a field experiment

on a small plot in the Thiès catchment in Senegal, where

also the extension for crusted soils is exemplarily taken into

account to evaluate its effect. Finally, a case study on flash

floods in an ungauged desert region in Egypt is shown and

the plausibility of the results based on the average values

for the Green–Ampt parameters and the impact of a surface

crust and friction on infiltration is analyzed.

2 Material andMethods

2.1 2D Shallow Water Model forOverland Flow

The Hydroinformatics Modelling Sytem (hms) is used to

simulate the flow field in terms of flow velocities and water

depths. It is a Java-based flexible and extendable modeling

framework, which has been developed at the Chair of Water

Resources Management and Modeling of Hydrosystems of

the Technische Universität Berlin, Germany. Previous stud-

ies using hms have been carried out, for example, by Hassan

etal. [57], Özgen etal. [58], Simons [59], and Tügel etal.

[11]. In hms, the depth-averaged 2D shallow water equa-

tions are solved with an explicit cell-centered finite volume

207

F.Tügel et al.

1 3

method, and incorporates robust numerical methods such as

the HLLC Riemann solver and a sophisticated total variation

diminishing method (TVD) to deal with the numerical chal-

lenges, which are associated, for example, with the simula-

tion of very small water depths over complex topography or

propagating wet-dry fronts [6]. The general form of the 2D

conversation law can be expressed as follows:

where q is the vector of conserved state variables, t is the

time, f and g denote the vectors of advective and diffusive

fluxes in x- and y-direction, respectively, and the vector s

represents the source terms. This equation describes math-

ematically, that a temporal change of the conserved variables

in the control volume can only be caused by a net flux over

the surface of the control volume and/or by sinks/sources

within the control volume. Inserting the following vectors

in the general conservation law (Eq.1) yields in the shallow

water equations (Eq.2):

Here, the first row of each vector contains the mass balance

equation and the second and third rows represent the

momentum balance equations in x- and y-direction, respec-

tively. h is the water depth, u and v are the velocity vector

components in x- and y-direction, respectively, and

is the

bottom elevation above datum. uh and vh represent the spe-

cific discharge in x- and y-direction, respectively. r is a mass

source/sink term accounting for precipitation, infiltration or

injection/abstraction of water, and g denotes the gravita-

tional acceleration. The bottom slope terms are

−

𝜕z

𝜕x

and

−

𝜕z

𝜕

and the momentum sinks due to bottom friction are

denoted with

sf,x

and

sf,y

in x- and y-direction, respectively.

The well-known friction law after Manning was used for test

cases 2 and 3 as well as for the case study about flash floods

in El Gouna:

where n denotes the Manning roughness coefficient. In the

test case 4, the depth-dependent Manning‘s coefficient after

Jain etal. [60] was used, as Mügler etal. [5] showed that the

application results in the best representation of the velocity

field for the considered area:

(1)

𝜕𝐪

𝜕t

𝜕

𝐟

𝜕x

𝜕𝐠

𝜕y

=𝐬

(2)

𝐪=

⎡

⎢

⎣

⎤

⎥

⎦

,𝐟=

⎡

⎢

⎣

uuh +gh2∕2

uvh

⎤

⎥

⎦

𝐠

⎡

⎢

⎣

vuh

vvh +gh2∕2

⎤

⎥

⎦

𝐬=

⎡

⎢

⎣

−gh𝜕zB

𝜕x−sf,x

−gh𝜕zB

𝜕y−sf,y

⎤

⎥

⎦

(3)

f,x =g⋅n

√

u2+v2,sf,y =g⋅n

√

u2+v2

where n(h) denotes the depth-dependent Manning‘s friction

coefficient,

the minimum land surface-dependent Man-

ning‘s friction coefficient corresponding to flow depth

beyond which n is assumed to be constant, and

𝜀

is a param-

eter accounting for drag due to vegetation.

As laminar flow conditions were proven in the laboratory

experiment after Smith and Woolhiser [61], the laminar fric-

tion law as described in Smith and Woohlhiser (1971) and

Delfs etal. [62], was used in the first test case:

where

Clam

denotes the laminar friction coefficient. The

general form of the balance equation is discretized with a

cell-centered finite volume method in space and the forward

Euler method in time to calculate the conserved variables at

the next time step qn+1 as follows:

where n + 1 and n denote the new and the old time level,

respectively,

t is the time step and A the area of the con-

sidered cell. F denotes the vector of advective and diffusive

fluxes over the edge k of the considered cell,

is the num-

ber of cell edges, n is the normal vector pointing outward

of a face, and l is the length of a face. s denotes the source

vector at time level n, while for the friction source term the

splitting point-implicit method is used to avoid numerical

instabilities. A more detailed description can be found in

[59].

2.2 Green–Ampt Model forInfiltration

To calculate the mass sink due to infiltration, the Green–Ampt

model is used, in which the cumulative infiltration and the

infiltration rate are calculated with the following equations:

where F(t) denotes the cumulative depth of infiltration, f(t)

the infiltration rate, K the hydraulic conductivity at residual

air saturation; according to Whisler and Bouwer [63], K is

assumed to be 50 % of the saturated hydraulic conductivity

(4)

(h)=

{

−𝜀

for h<h0

n0for h≥h0

(5)

f,x =

Clam

2h3𝜕zB

𝜕x

√

u2+v2,sf,y=

Clam

2h3𝜕zB

𝜕y

√

u2+v2

(6)

𝐪

n+1 =𝐪n−Δt

∑

k=1

𝐅n

k𝐧klk+Δt𝐬n

(7)

(t)=Kt +(h0−hf)Δ𝜃ln

(

1+F(t)

(h0−hf)Δ

𝜃

(8)

f(t)=K

(

−

)Δ

𝜃

F(t)

)

=dF

208

Applicability ofLiterature Values forGreen–Ampt Parameters toAccount forInfiltration in…

1 3

is the wetted front capillary suction head, and

is the

ponding water depth, which is provided by the surface run-

off calculation.

Δ𝜃

denotes the soil moisture deficit, which

is the difference between the saturated soil water content

𝜃s

, usually considered with the effective porosity

neff

, and

the initial moisture content

𝜃i

. The wetted front capillary

suction head, effective porosity, and hydraulic conductivity

are called Green–Ampt parameters. The infiltration rate is

calculated for each cell and time step depending on the water

depth and water saturation of the soil of the previous time

step in the considered cell. The calculated infiltration rates

for all cells are then taken into account as mass sinks in the

mass balance equation (see r in Eq.2, vector s, first row),

while rainfall is represented by a mass source.

When the considered soil tends to generate a surface crust

of lower hydraulic conductivity, Brakensiek and Rawls [55]

proposed to calculate the effective hydraulic conductivity of a

two-layer soil—crust and subcrust—by a harmonic mean [56]:

where

is the effective hydraulic conductivity,

is the

hydraulic conductivity of the crust, K is the hydraulic con-

ductivity of the subcrust soil as used in Eqs.7 and 8.

the crust thickness, and

denotes the wetted depth which

is calculated by the cumulative infiltration depth from the

previous time step divided by the soil moisture deficit. Fur-

thermore, they proposed an equation for the prediction of the

steady-state crust conductivity depending on tabled values

for a reduction factor for the subcrust conductivity, and the

steady state matric potential drop at the crust/subcrust inter-

face (Eq.10). For more details on this approach, the reader

is referred to Rawls etal. [56].

(9)

{

Kefor Zf≤Zc

Zf−Zc

+Zc

for Zf>Zc

(10)

1+Ψ

i∕

⋅Ks

where SC denotes the reduction factor for subcrust conduc-

tivity,

Ψi

stands for the steady state capillary potential drop at

the crust/subcrust interface, and

is the saturated subcrust

conductivity, which was set in this study to the same values

as the hydraulic conductivity of the subcrust soil as given

in the literature values for Green–Ampt parameter K. The

approach of calculating the effective conductivity in unsatu-

rated layered soils with a thickness-weighted harmonic aver-

age has been considered as suitable approach in several stud-

ies [31, 64, 65]. But in formations with fine soil over coarse

layers, non-piston flow might be dominating, which is not

included in the simplifications of the Green–Ampt model.

Zhu and Warrick [65] observed that the harmonic average

tends to overestimate infiltration in these cases. Neverthe-

less, we applied this simplified approach given in Eqs.9 and

10, to evaluate its performance in our cases.

2.3 Literature Values ofGreen–Ampt andCrust

Parameters

Rawls etal. [1] analyzed different soils and determined aver-

age Green–Ampt parameters based on soil texture classes,

where seven of them are shown in Table1.

Other values are, for example, given in the help documen-

tation of the hydraulic and hydrologic modeling software

XPStorm and XPSWMM of the Innovyze company [2]. The

values for seven different soil texture classes are given in

Table2.

They refer to typical values for the minimum (asymp-

totic) infiltration rate corresponding to the saturated

hydraulic conductivity for different soil texture classes

after Akan [67], which were determined from measured

rainfall, runoff and infiltrometer data [68, 69], typical

values for the average capillary suction head from several

published values, as well as typical values for the initial

soil moisture deficit at wilting point [66]. The authors

state that these values for the initial soil moisture deficit

would apply for very dry conditions, and lower values

Table 1 Average values and

ranges of the Green–Ampt

parameters after Rawls etal. [1]

* Numbers in parentheses: one standard deviation around the average

** Antilog of the log mean and standard deviation

Texture class Effective porosity

neff

(-) Capillary suction at wetted

front

(cm)

Hydraulic

conductivity K

(cm/h)

Sand 0.417 (0.354–0.480)*4.95 (0.97–25.36)** 11.78

Loamy sand 0.401 (0.329–0.473) 6.13 (1.35–27.94) 2.99

Sandy loam 0.412 (0.283–0.541) 11.01 (2.67–45.47) 1.09

Loam 0.434 (0.334–0.534) 8.89 (1.33–59.38) 0.34

Sandy clay loam 0.330 (0.235–0.425) 21.85 (4.42–108.0) 0.15

Clay loam 0.309 (0.279–0.501) 20.88 (4.79–91.10) 0.10

Clay 0.385 (0.269–0.501) 31.63 (6.39–156.5) 0.03

209

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