Comparison of infiltration model performance based on basic infiltration rate for small watersheds in Papua region, Indonesia

Research on soil water infiltration in equatorial climates like Indonesia is limited. Despite Papua accounting for 29% of Indonesia’s surface water, there’s a shortage of hydrological data. This study aimed to identify the best infiltration model tailored to the characteristics of basic infiltration rates in Papua’s small watersheds. Observations were made at 95 points across 11 small watersheds in Papua. Based on equatorial basic infiltration rate theories, analysis classified infiltration values against observation time. The performance of four infiltration models — Horton, Philip, Kostiakov, and Green Ampt — were compared. The results indicated the Philip model as superior, with average scores of 0.901 (R), 0.814 (NSE), and 0.424 (RSR), followed by the Horton and Green Ampt models. These three models showed excellent performance. However, the Kostiakov model was found lacking and needs modification. Further research on rapid and very rapid classifications is vital for enhancing infiltration rate predictions in small equatorial watersheds.


Introduction
Based on Triatmodjo, infiltration is a hydrological process through which water enters the soil surface [1].We can find information about the infiltration rate through field research or literature studies from reputable scientific publications.Research results on infiltration from equatorial climates, such as Indonesia, have constituted only 7.7% of publications, and globally, they are limited compared to those from warm temperate climate regions [2].Papua possesses 2,214 watersheds, with the majority being small [3].It is one of Indonesia's equatorial climate regions, holding 29% of the surface water.Nonetheless, scant hydrological data describe the river's characteristics, including the research results on infiltration rates [4].Runoff emerging on the surface when rainfall surpasses the infiltration rate is a watershed's response to rain events.Consequently, infiltration rate data in a watershed will be pivotal for planning activities in the water resources sector.Existing infiltration models necessitate scientific evaluation to determine their alignment with the infiltration rate characteristics of specific areas.Field infiltration rate data is also crucial for validating or refining a model's suitability to represent the studied region better.

Infiltration rate and classification based on basic infiltration rate
When the soil is dry, water infiltrates the soil surface due to the influence of gravity and capillary forces acting across the entire surface.As the soil becomes wet, capillary action decreases because of reduced capillary forces, leading to a decrease in the infiltration rate.While capillary flow in the surface layer decreases, the flow fills the soil pores under the influence of gravity.As the soil pores become saturated with water, the infiltration rate gradually decreases until it reaches a constant condition.In this condition, the infiltration rate equals the percolation rate through the soil [1].This constant infiltration rate is called the basic infiltration rate (Figure 2).

Figure 2. Basic infiltration rate
Infiltration rates varied widely in space and time, making it necessary to ensure that a series of measurements represented the area under study.In practice, the infiltration rate could be well determined using an infiltrometer.An infiltrometer is an instrument designed to measure the water absorption rate by a soil surface covered in a small defined area.There are two types of infiltrometers: flooding and sprinkler [18].This study observed field infiltration rates using a double-ring infiltrometer, while a double-ring infiltrometer referred to SNI 7752: 2012 [19].In practice, field infiltration testing must be strictly adhered to in that the test should not be carried out during a rain event, and for rainfall that exceeds 12.7 mm/day, the test should be carried out at least 48 hours after the rain event [20].Observation time had the highest effect on cumulative infiltration, followed by % silt, % clay, % sand, water content, soil density, and infiltration rate [21].Table 1 describes the classification of infiltration rates in the tropics and subtropics based on the interval of the basic infiltration rate [14].

Data analysis A. Statistical analysis
The statistical tool for analyzing the research data was the IBM SPSS ver. 25 statistical program packages.The analysis proceeded through the following stages: (a) testing data normality using the Shapiro-Wilk test [22]; (b) testing the feasibility of a regression model by examining the significance value of the ANOVA [23]; (c) given that the theoretical graph (Figure 2) represents a nonlinear regression model, a nonlinear regression model analysis was used [23]; and (d) employing a curve estimation tool to select nonlinear regression model equations that aligned with the theoretical graphs.

B. Performance-tested infiltration models
Based on the gap analysis process of previous studies, we examined the performance of 4 infiltration models: the Horton model, the Philip model, the Kostiakov model, and the Green Ampt model.The four infiltration models were the most appropriate to test the characteristics of the current research area, namely the watershed in equatorial climates.Tables 2 to 5 describe each model and its parameter estimation procedures.
Table 2. Description and procedure for estimating the parameters of the Horton model

Model Description
Parameter estimation procedure [16] Horton, in 1938, developed the infiltration equation [24]: () =  + ( −  ). .............. where fc is the steady state value of f, fo is the value of f at t=0, and k is the infiltration decay factor Plot ln(f-fc) on the y-axis and time (t) on the xaxis, and then we obtain the linear regression equation y=ax+b.From infiltration equation, we can determine the value of ln(f-fc) from (b) and k from the (a) value in the linear equation.where Y i obs is the ith observation for the evaluated constituent, Y i sim is the ith simulated value for the evaluated constituent, Y mean is the average of the observed data for the evaluated constituent, and n is the total number of observations.c.Index Errors: The RMSE-observations standard deviation ratio (RSR) can be calculated using the equation:

Research novelties
The novelty of this research was its attempt to describe the existing conditions that define the response of small watersheds to the infiltration process in the hydrological cycle.Specifically, the study (a) determined infiltration rate model equations based on their basic infiltration rate, and (b) provided conclusions from the performance tests of the Horton, Philip, Kostiakov, and Green Ampt models.

Data distribution
The constant infiltration rate is called the basic infiltration rate (Figure 2).The grouping of observational data based on the identification of the basic infiltration rate [14] was as follows: very slow (12 points), slow (17 points), moderately slow (25 points), moderate (23 points), moderately rapid (11 points), rapid (5 points) and very rapid (2 points).This grouping made the observation data more organized and more accessible to analyze.

Statistic test
At this stage, we carried out three statistical tests using the SPSS application to ensure normal data distribution (Shapiro-Wilk test), ensure variable X could explain variable Y at a 95% confidence level (ANOVA), and determine if variable X significantly affected Y (Coefficients Model).Table 7 describes a summary of the statistical test process.Table 7 shows that: 1.All groups of observation data have passed the statistical test, and the data is normally distributed (based on p-values from the Shapiro-Wilk test > 0.05).Previously, there was an elimination process for some extreme values in each data classification group.
2. The observation time variable can explain the infiltration rate at the 95% confidence level (based on the p-value from the ANOVA test < 0.05).3.Then, the observation time variable significantly affects the existing infiltration rate (based on the p-value from the coefficients model < 0.05).4. If a model evaluation result shows an NSE value above 0.75, the model has a very good performance rating [26].The existing models perform very well for all basic infiltration rate classifications in the 11 watersheds studied.

Results and discussion of performance evaluation of the infiltration model
The next stage, according to the purpose of this study, was to evaluate the performance of the Horton, Philip, Kostiakov, and Green Ampt infiltration model against the existing infiltration model using the procedures described in the previous section referring to the Engineering Hydrology book [16].The evaluation results were displayed and defined for each classification of the basic infiltration rate to clarify the hydrological characteristics of the watershed area under review.Figures 3 to 9 and Tables 8 show the results of statistical model evaluation using graphical, dimensionless, and index error methods.Furthermore, we analyzed the model parameters to obtain equations for each infiltration model tested (Table 8).

Figure 3 .
Figure 3.The results of evaluating the model's performance for the very slow classification.

Figure 4 .
Figure 4.The results of evaluating the model's performance for the slow classification.

Figure 5 .Figure 6 .
Figure 5.The results of evaluating the model's performance for moderately slow classification.

Figure 7 .
Figure 7.The results of evaluating the model's performance for moderately rapid classification.

Figure 8 .
Figure 8.The results of evaluating the model's performance for rapid classification.

Figure 9 .
Figure 9.The results of evaluating the model's performance for very rapid classification.

Table 1 .
Interval of basic infiltration rate

Table 6
summarises the decision-making techniques in the model evaluation techniques.

Table 6 .
[26]sion-making techniques of the performance rating for watershed model[26]The research began with field infiltration measurements using a double-ring infiltrometer.It produced observational data in 32-time SNI-determined formats and grouped infiltration rate data from 95 observation points according to their basic infiltration rate[14].Statistical analysis was then carried out, including the normality test, ANOVA test, analysis of nonlinear regression equation models, model coefficient tests, and selection of the nonlinear regression equation.Finally, the model's performance was tested graphically and statistically by comparing the existing infiltration models in each basic infiltration rate classification at the research watershed location against the Horton, Philip, Kostiakov, and Green Ampt model equations.

Table 7 .
Results of statistical analysis of the existing infiltration rate data group