Towards evaluating the conditional probability of waterborne microbial risks associated with critical rainfall events following land application of animal waste — A focus on Irish pastures

ABSTRACT

Modelling surface runoff and infiltration in an agricultural watershed is essential for understanding the nutrient cycle and water quality management. This research evaluates the critical rainfall events causing maximum surface runoff and infiltration. Empirical models such as Soil Conservation Service (SCS) curve number and Explicit Green-Ampt (EGA) were analysed for different soil hydraulic conditions and storm events with specific return periods. The present study forecasted the maximum daily rainfall and intensity as 113.6 mm and 19.9 cm h^–1, respectively, considering a 100-year return period storm. The deterministic part of the model calculates the daily maximum surface runoff as 5.51 cm (from the SCS model). The EGA model revealed that the rainfall intensity of 0.143, 0.163, 0.175, 0.179, 0.181, 0.182, and 0.182 cm h⁻¹ (duration of 24 h) was found critical for 1, 2, 5, 10, 25, 50, 100 year return period of the storm, respectively in different soil texture classes (sand, loamy sand, sandy loam, loam, silt loam, sandy clay loam, clay loam, silty clay soils). Exceptions imply for three occasions where the intensity of 0.407 cm h⁻¹ and duration of 18 h produced maximum infiltration for silty clay loam, and intensity of 0.352 and 0.354 cm h⁻¹ with 9 h rainfall (each) produced maximum infiltration for clay. The probabilistic model revealed that a daily storm event probability of 2.74 × 10^–5 is associated with a simulated mean runoff depth of 0.69 cm and infiltration of 20.7 cm. Critical rainfall probabilities calculated in this study can be multiplied with the overall microbial/pollutant human health risk assessment framework to calculate conditional probability and better estimate microbial risk through the drinking water pathway. This study is very relevant for the wet climatic condition of Ireland, where most land use is pastures.

KEYWORDS:

• Precipitation characteristics
• infiltration
• surface runoff
• empirical model
• conditional probability
• risk assessment

1. Introduction

Good surface or groundwater quality is essential for sustainable economic development and biodiversity. However, anthropogenic activities, including the use of agricultural fertilisers, antibiotics, resistive genes, pesticides, septic leakage, livestock excreta and climate change can change river systems, leading to degradation of water quality, aquatic habitat and loss of biodiversity (The European Union 2019, EPA 2020, Meshesha et al. 2020a, 2020b). Therefore, sustainable management of river systems requires a fundamental understanding of anthropogenic drivers, hydrological processes and ecological response. Drinking water directive (98/83/EC) (The European Commission 1998) sets indicator parameters such as specific metal/ metallic ion, halogen concentration, microbial count (total coliform, E. coli, enterococci, spore-forming Clostridium perfringens), colour, odour, turbidity, total organic carbon, oxidisability, conductivity. These are significant markers in the aquatic species allocation and health and play a vital role in regulating water resources for human use and the aquatic habitat's health (Meshesha et al. 2020b).

A pollutant may be transported through either advection or dispersion processes in the environment (Kirchner et al. 2001). Advection is a transportation process by fluid flow, i.e. vertical flow by infiltration (preferential flow) and horizontal flow by groundwater flow. In contrast, dispersion is a mixing process due to the random stochastic motion of solute molecules in the water entrapped in the soil's capillary pores, called fingered flow (Darnault et al. 2004). Groundwater can be contaminated by seepage and percolation of contaminated water from the vadose zone (Darnault et al. (2004), cited in Pandey et al. (2014)). A significant connection was found between rainfall events and global waterborne disease outbreaks (Efstratiou et al. 2017), where precipitation may advance the saturated wetting front depth towards the groundwater table, potentially containing FYM&S-associated pathogens. According to the European Commission (EC 2015), reactive transport and/or diffusion might significantly impact the amount and concentration of pollutants in groundwater. Advection is a faster process compared to dispersion. Therefore, the typical movement of pollutants can be faster through surface runoff compared to infiltration towards the groundwater table.

Infiltration is controlled by the rate and duration of precipitation, soil physical properties, slope, vegetation, surface roughness (US EPA 1998), depth of ponding, and suction head (Ali et al. 2013). The critical parameters that dictate the runoff and infiltration process are soil porosity, soil saturation, moisture content before rainfall events, hydraulic gradient, saturated hydraulic conductivity, unsaturated hydraulic conductivity, and capillary pressure (Zhang et al. 2019). Maximum infiltration is associated with a longer rainfall duration, whereas maximum surface runoff is related to a higher intensity of rainfall (Teng et al. 2012). From a microbial pollution management point of view, uncontrollable parameters are weather, soil temperature (for molecular diffusion), geology, topography, soil type, and distance to water, whereas a partially controllable parameter is soil physical status. The controllable parameters are soil chemistry, pollutant characteristics, the timing of land application, initial concentration of pathogen in FYM&S, vegetation type, and perimeter controls such as treatment and riparian buffer zones (Polyakov et al. 2005).

The water balance equation governs the hydrological cycle by describing water flow into and out of a system for a specific period, shown in Equation (1) where P is precipitation, Q_s is a surface runoff, ET is evapotranspiration, ΔSM is the change in soil moisture, and ΔGW is the change in groundwater storage. In a simplified way, precipitation can be primarily expressed as a summation of surface runoff and infiltration, two principal components (Williams et al. 1998). However, the relationship between precipitation and surface runoff, precipitation and infiltration is not linear (Teng et al. 2012). Maximum infiltration and runoff depend on the Depth-Duration-Frequency (DDF) precipitation (Leahy and Kiely 2011). Therefore, the same rainfall incident would probably not be responsible for yielding both the maximum infiltration and surface runoff for a specific return period (Teng et al. 2012). Hence, it is vital to establish a conditional probability estimate of the maximum infiltration amount and surface runoff for Ireland's critical rainfall conditions. (1) $P=Q_s+\mathrm{ET}+\mathrm{\Delta SM}+\mathrm{\Delta GW}$(1) Waterborne infectious diseases such as diarrhoea and gastrointestinal infection remain significant global morbidity and mortality, causing > 2.2 million deaths annually and far more illness cases daily (Efstratiou et al. 2017). Land spreading of farmyard manure and slurry is an important measure to minimise waste disposal, and it provides key nutrients to the soil, which are essential for plant growth (Nag et al. 2019). However, this animal waste contains significant pathogens (Nag et al. 2021a), contaminating surface water and groundwater (Pandey et al. 2016). Also, precipitation may produce contaminated runoff from agricultural fields that can enter drinking water resources, increasing the microbial burden at the drinking water treatment plants’ abstraction points. In addition, Identifying pollution sources in water systems, particularly in pressurised distribution networks and sewers, is crucial for public health. Wastewater quality affects system operation and can lead to contamination events. Establishing a chemical monitoring network is essential for timely detection and containment of pollutants, safeguarding water quality (Mariacrocetta et al. 2022). Furthermore, contaminated surface water may pollute recreational water bodies, too (Teng et al. 2012). Cryptosporidiosis is one example of such waterborne disease associated with rainfall events (Zintl et al. 2006a, 2006b, Haas et al. 2014). The Health Protection Surveillance Centre (HSE 2019) suggests that Clostridium spp., Cryptosporidium spp., pathogenic E. coli, and Salmonella spp. are the primary pathogens of human health concern in Ireland through drinking water pathway (Nag et al. 2020). This evidence suggests the need for modelling the hydrological and soil parameters to assess the critical rainfall events responsible for maximum infiltration and runoff, which can be helpful for future calculation of microbial burden in surface runoff and groundwater.

Modelling surface runoff and infiltration in the agricultural watershed is notable for understanding the nutrient cycle and water quality management. The main approaches to surface runoff and infiltration modelling are process-based and empirical modelling (Adams et al. 2013, Melaku et al. 2020). The process-based method simulates detailed physical or biological processes that explicitly describe system behaviour. In contrast, the empirical approach relies on correlative relationships in line with mechanistic understanding but without fully describing system behaviours and interactions (Adams et al. 2013). Many studies (Shrestha and Wang 2018, 2020, Melaku et al. 2020, Tu et al. 2020) have modelled surface runoff and infiltration with the SWAT tool, a process-based model (Shrestha and Wang 2020). The Soil & Water Assessment Tool (SWAT) is a small watershed-to-river basin-scale model used to simulate the quality and quantity of surface and groundwater and predict the environmental impact of land use, land management practices, and climate change. SWAT is widely used in assessing soil erosion prevention and control, nonpoint source pollution control and regional management in watersheds (United States Department of Agriculture (USDA) 2020). In Ireland, Coffey et al. (2010); Tang et al. (2011) also used SWAT for the pathogen transport model in small ungauged agricultural catchments. This study aimed to have a bird's-eye view on quantifying maximum runoff and infiltration for different soil texture classes concerning Irish climatic conditions (rainfall) nationally; the SWAT model could not be used. Instead, a probabilistic model has been developed to capture the variability of input parameters using US EPA empirical models.

Irish national water framework directive (EPA 2005) classified groundwater, rivers and lakes as ‘at risk’ at the rate of 5%, 29%, and 18%, respectively, out of which diffuse source of pollution was identified for rivers and lakes as 13% and 1%, respectively. However, EPA reserved a classification as ‘probably at risk’ for groundwater, rivers, and lakes at the rate of 56%, 35%, and 20%, respectively, out of which 37%, 32%, and 18% are the diffuse source of pollution, which is very high. Similarly, polluted surface runoff is a leading cause of damage to nearly 40% of the US water bodies failing water quality standards (Arnone and Walling 2007). Ireland reports the highest human incidence of verotoxigenic E. coli (VTEC) infection in Europe (Óhaiseadha et al. 2017), and VTEC infection in the Republic of Ireland is mainly associated with rural areas due to the high risk of exposure related to contact with cattle and unregulated groundwater supplies. Hence, there is a need to estimate risks individually for different site conditions. The probability calculated in this study corresponding to the critical rainfall can be implemented in the overall risk assessment framework (Zhang et al. 2009). The generalised precipitation-frequency maps the Met Éireann (2020) provide return periods for rainfall intensities associated with different durations. However, other runoffs and infiltration probabilities are not directly available, as these probabilities depend on the soil and field characteristics. In this study, these probabilities are derived by identifying the maximum runoff and the maximum infiltration associated with any duration of storm events for a given return period. To date, there is no such study for Ireland (as per the author's knowledge) and this research can be very useful for predicting critical rainfall events for Ireland for maximum infiltration and the surface runoff which can further be used for input parameters for future quantitative microbial risk assessment models with a focus on water pathway. The overall aim of this study was (i) to forecast rainfall intensity for a 100 year return period (ii) to determine the critical rainfall events generating the maximum runoff and infiltration depth examining the effects of soil textures and precipitation characteristics and (iii) to estimate the probability of maximum infiltration and runoff to the first-order streams.

2. Materials and methods

The principal methodology behind this research is based on three significant aspects: (i) rainfall data analysis, (ii) calculation of runoff and infiltration with empirical models, and (iii) identifying the critical rainfall responsible for producing maximum runoff and infiltration. A schematic diagram of the methodology, in brief, is presented in Figure 1. Firstly, the proposed approach predicts rainfall intensity based on collected historical data from 25 meteorological stations (return period 30 years) in Ireland. Next, the top 20 storm events were ranked to produce DDF in log–log scale or depth vs quantile plot for all 25 stations. This step was followed by forecasting rainfall intensity for 0.083, 0.167, 0.25, 0.5, 1, 2, 3, 6, 9, 12, 18, and 24 h storm durations from DDF curves for return periods of 1, 2, 5, 10, 25, 50, 100 years. Extrapolation was done for a duration of < 1 h and a return period of > 30 years. Next, appropriate empirical US EPA models were selected for runoff and infiltration predictions. Several scenarios were conducted for different possible soil and drainage conditions in ‘pastures’ land use. Finally, runoff and infiltration predictions were conducted for a specific return period. Critical rainfall (a combination of intensity and duration) responsible for maximum runoff and maximum infiltration was determined to compare different scenarios.

Figure 1. Schematic of the steps taken to achieve the objectives showing the steps and data inputs.

2.1. Study area

According to the CORINE land use map of Ireland (EPA 2012), there are 34 categories of land use (total 7,110,695 ha) excluding sea and ocean area (4,054,027 ha) (Figure 2a). Pastures, land principally occupied by agriculture, with significant areas of natural vegetation, non-irrigated arable land, complex cultivation patterns, and natural grasslands are 5 land use classes closely related to agricultural production, including animal grazing having a total area of 4,837,337 ha (Figure 2b). Overall, pastures hold 55.1% of Ireland's comprehensive land use (inland area) and 81.0% of the agricultural area.

Figure 2. CORINE (EPA 2012) land use map of Ireland showing pastures, holding the leading share of land use (81% of the total agricultural land) and the potential areas of biosolids application.

2.2. Meteorological data

The spatial distribution of annual average rainfall (30-year observation: 1981 to 2010 (Met Éireann 2020)) is presented in Figure 3. It shows that the West coast of Ireland experiences significantly higher annual average rainfall than the eastern coast. The World Meteorological Organization (WMO) recommends that climate averages be computed over 30 years of consecutive records, as 30 years is considered long enough to smooth out variabilities (Met Éireann 2020). A complete dataset for 30 years (1990–2020) was available for Shannon Airport, Dublin Airport, Mullingar, Roches Point, Malin Head, Claremorris, Valentia Observatory, Belmullet, Casement, and Cork Airport (Table 1). Data was downloaded from Met Éireann (2020) for 25 meteorological weather stations (Figure 4). A typical summary of the top 20 rainfall events was ranked by magnitude for each meteorological weather station (Table 2 for Valentia Observatory, typical). Rainfall totals were calculated over 1, 2, 3, 6, 9, 12, 18 and 24 h aggregation levels. These levels were chosen to cover a range of rain events from brief, convective storms of 1 h duration to moving frontal depressions delivering rainfall from several hours up to a day (Leahy and Kiely 2011). Independent (completely non-overlapping) and overlapping events were considered for each duration.

Figure 3. Spatial distribution of annual average rainfall observed between 1981 and 2010, 30-year average; interpolation was performed on 84291 data pints by Inverse Distance Weighting (IDW) method; data source (Met Éireann 2020).

Figure 4. Available data for 25 meteorological weather stations; coordinate system: the Irish national grid, data source Met Éireann (2020a).

Table 1. Meteorological stations, altitude, locations, and observation period for rainfall data.

Serial number	Station name	Altitude (m)	Coordinates		Year of observation		Observation period (years)
			Latitude (° N)	Longitude (° E)	From	To
1	Phoenix Park	48	53.364	−6.35	01.05.2005	01.06.2020	15
2	Mace Head	21	53.326	−9.901	01.08.2004	01.06.2020	16
3	Oak Park	62	52.861	−6.915	01.08.2003	01.06.2020	17
4	Shannon Airport	15	52.69	−8.918	01.01.1990	01.06.2020	30
5	Dublin Airport	71	53.428	−6.241	01.01.1990	01.06.2020	30
6	Moore Park	46	52.164	−8.264	01.08.2003	01.06.2020	17
7	Ballyhaise	78	54.051	−7.31	01.01.2004	01.06.2020	16
8	Sherkin Island	21	51.476	−9.428	30.04.2004	01.06.2020	16
9	Mullingar	101	53.537	−7.362	01.01.1990	01.06.2020	30
10	Roches Point	40	51.793	−8.244	01.01.1990	01.06.2020	30
11	Newport	22	53.922	−9.572	31.12.2004	01.06.2020	16
12	Markree	34	54.175	−8.456	19.08.2007	01.06.2020	13
13	Dunsany	83	53.516	−6.66	31.12.2006	01.06.2020	14
14	Gurteen	75	53.053	−8.009	31.12.2007	01.06.2020	13
15	Malin Head	20	55.372	−7.339	01.01.1990	01.06.2020	30
16	Johnstown II	62	52.298	−6.497	01.01.2004	01.06.2020	16
17	Athenry	40	53.289	−8.786	26.06.2011	01.06.2020	9
18	Mountdillon	39	53.727	−7.981	08.12.2006	01.06.2020	14
19	Finner	33	54.494	−8.243	29.05.1997	01.06.2020	23
20	Claremorris	68	53.711	−8.993	01.01.1990	01.06.2020	30
21	Valentia Observatory	24	51.938	−10.241	01.01.1990	01.06.2020	30
22	Belmullet	9	54.228	−10.007	01.01.1990	01.06.2020	30
23	Casement	91	53.306	−6.439	01.01.1990	01.06.2020	30
24	Cork Airport	155	51.847	−8.486	01.01.1990	01.06.2020	30
25	Knock Airport	201	53.906	−8.817	10.04.1996	01.06.2020	24

Table 2. Top 20 rainfall events for durations 1, 2, 3, 6, 9, 12, 18, 24 h; data shown for Valentia Observatory (typical).

Rank	Estimated quantile Q	Q*100 (%)	1 h	2 h	3 h	6 h	9 h	12 h	18 h	24 h
1	0.05	4.76	21.1	23.8	28.3	47.9	66.5	79	94.1	95.8
2	0.10	9.52	17.2	22.7	28	46.6	65.9	77.6	93.6	95.5
3	0.14	14.29	16.4	21.2	27.2	46	62.5	76.7	93.5	94.7
4	0.19	19.05	15.3	21.1	24.9	43.7	59.6	75	92.7	94.3
5	0.24	23.81	14.3	20.9	24.5	43.7	59.6	73.3	89.2	94.3
6	0.29	28.57	13	20.7	24.4	43.5	56.8	71.9	88.2	94.3
7	0.33	33.33	12.8	19.9	24.2	43.1	55.1	68.3	81.8	94.1
8	0.38	38.10	12.5	19.6	24.1	40.9	54.6	63.9	81.1	93.6
9	0.43	42.86	12.1	19.2	23.8	38.7	50.2	61.9	80.6	93.5
10	0.48	47.62	12	18.9	23.5	38.1	49.9	60.4	78.8	92.7
11	0.52	52.38	11.3	18.5	23.3	37.2	49.1	54.6	73.8	90.7
12	0.57	57.14	11.3	18.4	23	36.3	48.1	53.7	73.3	88.2
13	0.62	61.90	11.3	18	22.8	35.3	46.3	52.9	69.8	82.6
14	0.67	66.67	11.2	17.8	22.8	32.8	45.8	52.4	69	82.1
15	0.71	71.43	10.8	17.8	22.8	32.8	44.5	52.3	68.5	81.8
16	0.76	76.19	10.8	17.5	22.7	32.2	44.2	50.9	68.3	79.9
17	0.81	80.95	10.6	17.4	22	32	43.9	50.7	65.6	74.1
18	0.86	85.71	10.6	17.2	22	32	42.3	50.7	65.6	73.3
19	0.90	90.48	10.5	17.1	21.8	31.8	42.2	50.5	64.7	71.4
20	0.95	95.24	10.3	17	21.5	31.8	42.1	50.4	61.9	71.4

2.3. Depth-Duration-Frequency (DDF) analysis and forecasting intensity of rainfall

A DDF model was developed to estimate point rainfall frequencies for various durations (1, 2, 3, 6, 9, 12, 18, 24 h). A typical DDF (in log–log scale) or depth vs quantile plot for Valentia Observatory is presented in Figure 5. Next; the fitted equations were used to forecast shorter duration-rainfall events with a duration of 5 min or 0.083 h, 10 min or 0.167, 0.25, and 0.5 h for each weather station. As 30 year-data (where possible) was used (Table 1) for building this model, the same forecast model was also used to predict the intensity of rainfalls corresponding to 50 and 100 years (> 30 years) of the return period (Table 3).

Figure 5. Depth-Duration-Frequency DDF (log-log scale) or depth vs quantile plot (typical).

Table 3. Forecasted intensity (mm h⁻¹) of rainfall events for durations: 5 min or 0.083 h, 10 min or 0.167, 0.25, 0.5, 1, 2, 3, 6, 9, 12, 18, 24 h.

Return period (years)	Daily probability (%)		Exceedance probability (%)	0.083 h	0.167 h	0.25 h	0.5 h	1 h	2 h	3 h	6 h	9 h	12 h	18 h	24 h
1	0.274		100	101.5	50.8	33.8	16.9	8.5	8.0	6.9	4.7	4.2	3.6	3.2	3.0
2	0.137		50	153.2	76.6	51.1	25.5	12.8	9.6	8.0	6.4	5.7	5.1	4.3	3.6
5	0.055		20	184.3	92.1	61.4	30.7	15.4	10.6	8.7	7.4	6.6	6.0	5.0	4.0
10	0.027		10	194.6	97.3	64.9	32.4	16.2	10.9	8.8	7.7	7.0	6.3	5.2	4.1
25	0.011		4	200.8	100.4	66.9	33.5	16.7	11.1	8.9	7.9	7.1	6.5	5.3	4.2
50 *	0.005		2	202.9	101.4	67.6	33.8	16.9	11.2	9.0	8.0	7.2	6.6	5.4	4.2
100 *	0.003		1	203.9	102.0	68.0	34.0	17.0	11.2	9.0	8.0	7.2	6.6	5.4	4.2

Note:

Extrapolated values are highlighted for duration < 1 h.

*Extrapolated return periods (> 30 years) are in italics.

2.4. Selection of models

There are 6 major infiltration models (US EPA 1998). The uniqueness of the semi-empirical infiltration ‘Soil Conservation Service’ (SCS) model is the only model used to simulate surface runoff conditions (Table 4). Similarly, layered Green-Ampt is used for multiple layers, and the infiltration/ exfiltration model is the only model capable of simulating wetting, evaporation, and vegetation cover. Philip 2-Term method can be applied to initial infiltration stages when infiltration is very short, and the approach is not valid for longer times (US EPA 1998). A layered Green-Ampt model requires soil property data for each layer. The explicit Green-Ampt (EGA) model facilitates a straightforward and accurate infiltration estimation for any given time. This model yields < 2% error when compared to the exact values from the implicit Green-Ampt model (US EPA 1998). The constant flux Green-Ampt model can estimate infiltration until the soil gets saturated (Teng et al. 2012). The effect of infiltration can be maximised when evaporation and transpiration (vegetation cover) are considered a minimum, and surface runoff is generated by a combination of two mechanisms, saturation excess and infiltration excess (US EPA 2017). Therefore, infiltration allows SCS and EGA to estimate the maximum surface runoff and wetting front depth. The EGA model is appropriate for a homogeneous soil profile and a constant surface ponding depth; however, the EGA model used in this study is suitable for no surface ponding conditions (model limitation).

Table 4. Capabilities of the models to simulate site conditions. ‘Y’ indicates suitability, and ‘N’ indicates incompatibility—source (US EPA 1998).

Site conditions	Model name
	SCS	Philip 2-Term	Layered Green-Ampt*	Explicit Green-Ampt	Constant Flux Green-Ampt	Infiltration/ Exfiltration
Surface ponding	N	N	Y	Y	N	N
Surface runoff	Y	N	N	N	N	N
Rainfall and irrigation	Y	N	N	N	Y	Y
Multiple layers	N	N	Y	N	N	N
Wetting and evaporation	N	N	N	N	N	Y
Homogeneous soil profile	Y	Y	Y	Y	Y	Y
Vegetation cover	N	N	N	N	N	Y

Note: * requires information for multiple layers; the uniqueness of the models is highlighted.

2.5. Soil Conservation Service (SCS) model

The SCS Weighted Curve Number method was developed by the United States Department of Agriculture (US EPA 2017). The SCS Weighted Curve Number is an empirical calculation method for surface runoff. The purpose of the curve number is to describe average conditions for design purposes. The curve number was initially developed for agricultural watersheds with a land slope of 5% and an initial abstraction of 20% due to infiltration. The initial abstractions include interception loss, surface storage, and infiltration before the runoff. The curve number is determined by the hydrologic soil group inputs, land cover type, and hydrologic condition (Table 5). According to the infiltration rates, four soil groups are defined as A, B, C, and D. Cover types are determined by photographs and land use maps, ranging from developed surfaces to agricultural and forest areas. The table above exemplifies the curve numbers associated with a few land cover types. The amount of rainfall translated into surface runoff. The curve number method assumes that the ratio of actual runoff to potential runoff equals the accurate to possible retention ratio, a purely empirical process for determining runoff. The curve number calculation has no temporal resolution to consider rainfall duration and intensity. SCS model is also used in ungauged areas within other models such as the Soil and Water Assessment Tool (SWAT) (US EPA 2017). The USDA developed an equation Equation (2) in 1957 for a rainfall-runoff relationship based on daily rainfall data as input, given P > 0.2 F_w and R equals 0 Equation (3) when P ≤ 0.2 F_w (Williams et al. 1998): (2) $R={\displaystyle \frac{{(P-0.2\times F_w)}^2}{P+0.8\times F_w},\mathrm{if}P>0.2F_w}$(2) (3) $R=0,\mathrm{if}P\le 0.2F_w$(3) where R is the amount of runoff (inches), P is the daily rainfall amount (inches) and can be derived from Table 3 (24 h forecasted values), F_w is a statistically derived parameter (also called the retention parameter) with the units of inches (Williams et al. 1998). A principal limitation of applying the SCS model is that the coefficients in Equation (4) must be evaluated with field data for each specific site. Since the model is not derived from fundamental physical principles, it can only be used as a screening tool for initial approximations. The following section discusses the methodology behind the estimation of F_w.

Table 5. Curve numbers CN_II for hydrologic soil-cover complex for the antecedent moisture condition II and initial water abstraction (I_a) = 0.2 F_w (USDA-SCS 1972).

Land use or crop	Treatment or agricultural practice	Hydrologic Condition	Hydrologic Soil Group based on soil texture class
			A^a	B^b	C^c	D^d
Fallow	Straight Row	–	77	86	91	94
Row Crops	Straight Row	Poor	72	81	88	91
	Straight Row	Good	67	78	85	89
	Contoured	Poor	70	79	84	88
	Contoured	Good	65	75	82	86
	Terraced	Poor	66	74	80	82
	Terraced	Good	62	71	78	81
Small Grain	Straight Row	Poor	65	76	84	88
	Straight Row	Good	63	75	83	87
	Contoured	Poor	63	74	82	85
	Contoured	Good	61	73	81	84
	Terraced	Poor	61	72	79	82
	Terraced	Good	59	70	78	81
Close-seeded	Straight Row	Poor	66	77	85	89
Legumes or Rotation	Straight Row	Good	58	72	81	85
Meadow	Contoured	Poor	64	75	83	85
	Contoured	Good	55	69	78	83
	Terraced	Poor	63	73	80	83
	Terraced	Good	51	67	76	80
Pasture or Range		Poor	68	79	86	89
		Fair	49	69	79	84
		Good	39	61	74	80
	Contoured^e	Poor	47	67	81	88
	Contoured^e	Fair	25	59	75	83
	Contoured^e	Good	6	35	70	79
Meadow		Good	30	58	71	78
Woods		Poor	45	66	77	83
		Fair	36	60	73	79
		Good	25	55	70	77
Farmsteads		–	59	74	82	86
Roads and Right of Way (ROW): hard surfaces		–	74	84	90	92

Note: Predominating land use of Ireland – highlighted, most applicable curve numbers CN_II is marked as bold.

^a ‘A’ means the lowest runoff potential. Includes deep sands with very little silt and clay, also deep, rapidly permeable loess.

^b ‘B’ stands for moderately low runoff potential. Mostly sandy soils are less deep than Group A and loess less deep or less aggregated than group A, but the group has above-average infiltration after thorough wetting.

^c ‘C’ denotes moderately high runoff potential. It comprises shallow soils and soils containing considerable clay and colloids, though less than group D's. The group has below-average infiltration after pre-saturation.

^d ‘D’ represents the highest runoff potential. Includes mostly clays of increased swelling per cent, but the group also consists of some shallow soils with nearly impermeable sub-horizons near the surface.

^e Not so common in Ireland.

2.5.1. The statistically derived parameter with some resemblance to the initial water content (Fw)

The statistically derived parameter F_w utilised in the SCS model can be estimated based on the Equation (4) (Williams et al. 1998): (4) $F_w={\displaystyle \frac{1000}{C{N}_I}-10}$(4)

CN_I is the ‘soil moisture condition curve number’ or hydrologic soil-cover complex number. CN_I is related to the soil moisture condition II curve number, CN_II, with the polynomial: (5) $C{N}_I=-16.91+1.348\times C{N}_{\mathrm{II}}-0.01379\times (C{N}_{\mathrm{II}}{)}^2+0.0001177\times (C{N}_{\mathrm{II}}{)}^3$(5) F_w can be considered an estimate of the maximum potential difference between rainfall and runoff (Schwab 1981). The CN_II is based on an antecedent moisture condition (AMC) II determined by the total rainfall in the 5 days preceding a storm (USDA-SCS 1972). Three levels of AMC are used: (1) lower limit of moisture content, (2) average moisture content, and (3) upper limit of moisture content. Table 5 lists values for CN_II at the average AMC. As pasture land use covers 81% of the agricultural land in Ireland (Figure 2), this study only focusses on pastures (highlighted in Table 5). Contour farming is not common in Ireland; according to the LUCAS survey in 2012, the presence of stone walls and grass margins in Ireland was observed in 13.9% (346 observations) and 16.8% (419 observations) cases, respectively (Panagos et al. 2015). Therefore, the critical curve numbers in the Irish context would be 39, 49, 61, 68, 69, 74, 79, 80, 84, 86, and 89, combining variabilities of influencing parameters of surface runoff such as hydrologic condition and soil texture class (highlighted in Table 5).

2.6. Explicit Green-Ampt (EGA) infiltration model

The EGA model has the following form Equations (6) to (16). When no measurement is available, θ_r, the residential volumetric water constant, can be used in place of θ₀ (Williams et al. 1998)., Different soil hydraulic property parameters (K_s, θ_s, θ_r, h_b, and λ) were selected to model infiltration and runoff. In this paper, soil properties from (Brakensiek et al. 1981, Pajian 1987, Carsel and Parrish 1988), cited in Williams et al. (1998), were chosen accordingly (Table 6). A simulated mean value of θ_s, θ_r, h_b, and λ experimental parameters (Table 6) was used for scenario analysis, whereas the uniform distributions (Table 6) were used for Monte Carlo simulation.

• when r < K_s, and when both r > K_s and t < t₀ (named as Case 1 for future reference) (6) $q=r$(6) (7) $I=r\times t$(7)

• When r > K_s and t > t₀ (named as Case 2 for future reference) (8) $q=K_s\times \left({\displaystyle \frac{\sqrt{2}}{2}\times {\tau }^{-{\displaystyle \frac{1}{2}}}+{\displaystyle \frac{2}{3}-{\displaystyle \frac{\sqrt{2}}{6}\times {\tau }^{{\displaystyle \frac{1}{2}}}+{\displaystyle \frac{1-\surd 2}{3}\times \tau }}}}\right)$(8)

  (9) $I=K_s\times \left\{\begin{array}{c}\left(1-{\displaystyle \frac{\sqrt{2}}{3}}\right)\times t+{\displaystyle \frac{\sqrt{2}}{3}\times \sqrt{\chi \times t+t^2}}\\ +\left({\displaystyle \frac{\sqrt{2}-1}{3}}\right)\times \chi \times [\ln (t+\chi )-\mathrm{ln\chi }]+{\displaystyle \frac{\sqrt{2}}{3}\times \chi }\\ \times \left[\ln \left(t+{\displaystyle \frac{\chi }{2}+\sqrt{\chi \times t+t^2}}\right)-\ln \left({\displaystyle \frac{\chi }{2}}\right)\right]\end{array}\right\}$(9) (10) $Z={\displaystyle \frac{I}{{\theta }_s-{\theta }_0}}$(10) (11) $\chi ={\displaystyle \frac{(h_s-h_f)\times ({\theta }_s-{\theta }_0)}{K_s}}$(11) (12) $\tau ={\displaystyle \frac{t}{t+\chi }}$(12) (13) $t_0={\displaystyle \frac{-K_s\times h_f\times ({\theta }_s-{\theta }_0)}{r\times (r-K_s)}}$(13) (14) $h_f={\displaystyle \frac{\eta }{\eta -1}\times h_e}$(14) (15) $\eta =2+3\lambda$(15) (16) $h_e={\displaystyle \frac{1}{2}\times h_b}$(16)

where,

q = surface infiltration rate (cm h⁻¹), I = cumulative infiltration (cm), Z = wetting front depth (cm), r = constant water application rate at the surface (cm h⁻¹), t = Time (h), K_s = saturated hydraulic conductivity (cm h⁻¹), θ_s = saturated volumetric water content (cm ³ cm⁻³), θ₀ = initial volumetric water content (cm ³ cm⁻³), h_f = capillary pressure head (< 0) at the wetting front (cm), h_s = ponding depth or capillary pressure head at the surface (cm), t₀ = the time when surface saturation occurs (h), h_e = air exit head (cm), h_b = air entry head (cm), λ = Brooks-Corey water retention constant (unitless), η = Brooks-Corey conductivity constant (unitless).

Table 6. Saturated hydraulic conductivity (Ks), fitted distributions and average values of saturated volumetric water content (θs), residual volumetric water content (θr), air-entry head (h_b), pore size index (λ) derived from Brakensiek et al. (1981); Pajian (1987); Carsel and Parrish (1988) cited in Williams et al. (1998).

Soil Texture Class	A typical value for Saturated Hydraulic Conductivity Ks(cm hr^−1)	Saturated volumetric water content (θs)					Residual volumetric water content (θr)					Air-entry head (hb)(cm)					Pore size index (λ)
		Brakensiek et al. (1981)	Pajian (1987)	Carsel and Parrish (1988)	Fitted distribution	Average	Brakensiek et al. (1981)	Pajian (1987)	Carsel and Parrish (1988)	Fitted distribution	Average	Brakensiek et al. (1981)	Pajian (1987)	Carsel and Parrish (1988)	Fitted distribution	Average	Brakensiek et al. (1981)	Pajian (1987)	Carsel and Parrish (1988)	Fitted distribution	Average
Sand	21	0.35	0.38	0.43	Uniform(0.35,0.43)	0.390	0.054	0.02	0.045	Uniform(0.02,0.54) *	0.037	35.3	3.58	6.9	Uniform(3.58,35.3) *	19.440	0.57	0.4	1.68	Uniform(0.4,1.68)	1.040
Loamy Sand	6.11	0.41	0.43	0.41	Uniform(0.41,0.43)	0.420	0.060	0.032	0.057	Uniform(0.032,0.060)	0.046	15.85	1.32	8.06	Uniform(1.32,15.85) *	8.585	0.46	0.47	1.28	Uniform(0.46,1.28)	0.870
Sandy Loam	2.59	0.42	0.44	0.41	Uniform(0.41,0.44)	0.425	0.118	0.045	0.065	Uniform(0.045,0.118)	0.081	29.21	9.01	13.33	Uniform(9.01,29.21)	19.110	0.4	0.52	0.89	Uniform(0.4,0.89)	0.645
Loam	1.32	0.45	0.44	0.43	Uniform(0.43,0.45)	0.440	0.078	0.057	0.078	Uniform(0.057,0.078)	0.067	50.94	19.61	27.78	Uniform(19.61,50.94)	35.275	0.26	0.4	0.56	Uniform(0.26,0.56)	0.410
Silt Loam	0.68	0.48	0.49	0.45	Uniform(0.45,0.49)	0.470	0.038	0.026	0.067	Uniform(0.026,0.067)	0.047	69.55	31.25	50	Uniform(31.25,69.55)	50.400	0.22	0.42	0.41	Uniform(0.22,0.42)	0.320
Sandy Clay Loam	4.3	0.41	0.48	0.39	Uniform(0.39,0.48)	0.435	0.188	0.093	0.1	Uniform(0.093,0.188)	0.141	46.28	7.81	16.95	Uniform(7.81,46.28)	27.045	0.37	0.44	0.48	Uniform(0.37,0.48)	0.425
Clay Loam	0.23	0.48	0.47	0.41	Uniform(0.41,0.48)	0.445	0.185	0.107	0.095	Uniform(0.095,0.185)	0.140	42.28	31.25	52.63	Uniform(31.25,52.63)	41.940	0.28	0.4	0.31	Uniform(0.28,0.4)	0.340
Silty Clay Loam	0.15	0.47	0.48	0.43	Uniform(0.43,0.48)	0.455	0.155	0.089	0.089	Uniform(0.089,0.155)	0.122	57.78	30.3	100	Uniform(30.3,100)	65.150	0.18	0.36	0.23	Uniform(0.18,0.36)	0.270
Silty Clay	0.09	0.48	0.49	0.36	Uniform(0.36,0.49)	0.425	0.182	0.102	0.07	Uniform(0.07,0.182)	0.126	41.72	15.87	200	Uniform(15.87, 200) *	107.935	0.21	0.38	0.09	Uniform(0.09,0.38)	0.235
Clay	0.06	0.48	0.49	0.38	Uniform(0.38,0.49)	0.435	0.226	0.178	0.068	Uniform(0.068,0.226)	0.147	63.96	10	125	Uniform(10,125) *	67.500	0.21	0.41	0.09	Uniform(0.09,0.41)	0.250

Note: * Major variability observed in the input, i.e. maximum limit is approximately > 10 times the minimum limit.

2.7. Monte Carlo simulation and scenario analysis

A Monte Carlo simulation method was followed (100,000 iterations) using @RISK 7.5 software (PALISADE Cooperation) which is an add-in to Microsoft Excel to capture the variabilities of SCS and EGA model input parameters such as rainfall intensity, curve numbers CN_II, soil parameters (K_s, θ_s, θ_r, h_b, and λ) and to get the final uncertainty distribution for runoff and infiltration. An IntUniform function was used to randomise the soil texture class parameter (10 possible cases as per Table 6) with equal probability. Minimum, average, and maximum rainfall intensities were analysed for both the SCS EGA model, and an additional hypothetical scenario was performed for the EGA model where the rainfall intensity (r_hyp) was considered as 10 times the average rainfall intensity (r_avg) to examine the effect of higher rainfall intensity on infiltration in different soil texture class.

3. Results

The forecast of constant precipitation rate r (mm h⁻¹) for 25 meteorological stations in Ireland corresponding to various durations of rainfall (5 min or 0.083 h, 10 min or 0.167, 0.25, 0.5, 1, 2, 3, 6, 9, 12, 18, 24 h) and return period (1, 2, 5, 10, 25, 50, 100 years) is shown in Table 7. Newport, Phoenix Park, Ballyhaise, Roches Point, Dunsany, and Moore Park show a higher constant precipitation rate at a shorter rainfall duration. In contrast, Casement, Valentia Observatory, Dublin Airport, Cork Airport, and Phoenix Park displayed higher constant precipitation rates at longer (24 h) rainfall events. The variability of 25 weather stations is presented in Figure 6, where more significant variability or error can be observed towards a longer duration (24 h) of rainfall. In comparison with a similar study by Leahy and Kiely (2011) (maximum daily rainfall 117.6 mm for Valentia), this study found the maximum daily rainfall for Valentia island was 101.5 mm, and in the mainland, maximum daily rainfall was estimated for Casement station as 113.6 mm for a 24 h storm.

Figure 6. Constant rainfall rate variability (simulated mean and errors represent 5th and 95th percentile) based on observed rainfall data in 25 meteorological stations in Ireland (legend represents durations of rainfall as 5 min or 0.083 h, 10 min or 0.167, 0.25, 0.5, 1, 2, 3, 6, 9, 12, 18, 24 h).

Table 7. Forecast of constant precipitation rate r (mm h⁻¹) for 25 meteorological stations in Ireland corresponding to various durations of rainfall (5 min or 0.083 h, 10 min or 0.167, 0.25, 0.5, 1, 2, 3, 6, 9, 12, 18, 24 h) and return period (1, 2, 5, 10, 25, 50, 100 years).

Duration of infiltration t (h)	Return period (year)	Daily probability (%)	Constant precipitation rate r (mm h^−1) for 25 meteorological stations in Ireland
			Phoenix Park	Mace Head	Oak Park	Shannon Airport	Dublin Airport	Moore Park	Ballyhaise	Sherkin Island	Mullingar	Roches Point	Newport	Markree	Dunsany
0.083	1	0.274	70.9	92.3	86.5	84.4	76.9	93.8	48.0	98.2	74.2	64.5	60.6	88.4	65.4
0.083	2	0.137	151.7	123.8	135.2	127.3	127.1	151.3	140.3	131.7	122.8	146.0	150.7	116.4	143.9
0.083	5	0.055	200.1	142.8	164.4	153.1	157.2	185.8	195.7	151.8	152.0	194.9	204.8	133.2	191.0
0.083	10	0.027	216.3	149.1	174.2	161.7	167.3	197.3	214.2	158.5	161.8	211.2	222.8	138.8	206.6
0.083	25	0.011	226.0	152.9	180.0	166.8	173.3	204.2	225.3	162.5	167.6	220.9	233.6	142.2	216.1
0.083	50	0.005	229.2	154.1	182.0	168.6	175.3	206.5	229.0	163.9	169.5	224.2	237.2	143.3	219.2
0.083	100	0.003	230.8	154.8	182.9	169.4	176.3	207.7	230.8	164.5	170.5	225.8	239.0	143.9	220.8
0.167	1	0.274	35.5	46.1	43.2	42.2	38.4	46.9	24.0	49.1	37.1	32.3	30.3	44.2	32.7
0.167	2	0.137	75.8	61.9	67.6	63.7	63.5	75.7	70.2	65.9	61.4	73.0	75.4	58.2	71.9
0.167	5	0.055	100.1	71.4	82.2	76.5	78.6	92.9	97.9	75.9	76.0	97.4	102.4	66.6	95.5
0.167	10	0.027	108.1	74.5	87.1	80.8	83.6	98.7	107.1	79.3	80.9	105.6	111.4	69.4	103.3
0.167	25	0.011	113.0	76.4	90.0	83.4	86.6	102.1	112.6	81.3	83.8	110.5	116.8	71.1	108.0
0.167	50	0.005	114.6	77.1	91.0	84.3	87.7	103.3	114.5	81.9	84.8	112.1	118.6	71.7	109.6
0.167	100	0.003	115.4	77.4	91.5	84.7	88.2	103.8	115.4	82.3	85.3	112.9	119.5	71.9	110.4
0.25	1	0.274	23.6	30.8	28.8	28.1	25.6	31.3	16.0	32.7	24.7	21.5	20.2	29.5	21.8
0.25	2	0.137	50.6	41.3	45.1	42.4	42.4	50.4	46.8	43.9	40.9	48.7	50.2	38.8	48.0
0.25	5	0.055	66.7	47.6	54.8	51.0	52.4	61.9	65.2	50.6	50.7	65.0	68.3	44.4	63.7
0.25	10	0.027	72.1	49.7	58.1	53.9	55.8	65.8	71.4	52.8	53.9	70.4	74.3	46.3	68.9
0.25	25	0.011	75.3	51.0	60.0	55.6	57.8	68.1	75.1	54.2	55.9	73.6	77.9	47.4	72.0
0.25	50	0.005	76.4	51.4	60.7	56.2	58.4	68.8	76.3	54.6	56.5	74.7	79.1	47.8	73.1
0.25	100	0.003	76.9	51.6	61.0	56.5	58.8	69.2	76.9	54.8	56.8	75.3	79.7	48.0	73.6
0.5	1	0.274	11.8	15.4	14.4	14.1	12.8	15.6	8.0	16.4	12.4	10.8	10.1	14.7	10.9
0.5	2	0.137	25.3	20.6	22.5	21.2	21.2	25.2	23.4	22.0	20.5	24.3	25.1	19.4	24.0
0.5	5	0.055	33.4	23.8	27.4	25.5	26.2	31.0	32.6	25.3	25.3	32.5	34.1	22.2	31.8
0.5	10	0.027	36.0	24.8	29.0	26.9	27.9	32.9	35.7	26.4	27.0	35.2	37.1	23.1	34.4
0.5	25	0.011	37.7	25.5	30.0	27.8	28.9	34.0	37.5	27.1	27.9	36.8	38.9	23.7	36.0
0.5	50	0.005	38.2	25.7	30.3	28.1	29.2	34.4	38.2	27.3	28.3	37.4	39.5	23.9	36.5
0.5	100	0.003	38.5	25.8	30.5	28.2	29.4	34.6	38.5	27.4	28.4	37.6	39.8	24.0	36.8
1	1	0.274	5.9	7.7	7.2	7.0	6.4	7.8	4.0	8.2	6.2	5.4	5.1	7.4	5.5
1	2	0.137	12.6	10.3	11.3	10.6	10.6	12.6	11.7	11.0	10.2	12.2	12.6	9.7	12.0
1	5	0.055	16.7	11.9	13.7	12.8	13.1	15.5	16.3	12.7	12.7	16.2	17.1	11.1	15.9
1	10	0.027	18.0	12.4	14.5	13.5	13.9	16.4	17.8	13.2	13.5	17.6	18.6	11.6	17.2
1	25	0.011	18.8	12.7	15.0	13.9	14.4	17.0	18.8	13.5	14.0	18.4	19.5	11.8	18.0
1	50	0.005	19.1	12.8	15.2	14.0	14.6	17.2	19.1	13.7	14.1	18.7	19.8	11.9	18.3
1	100	0.003	19.2	12.9	15.2	14.1	14.7	17.3	19.2	13.7	14.2	18.8	19.9	12.0	18.4
2	1	0.274	0.0	5.6	6.3	4.9	6.5	5.3	3.0	7.4	5.3	5.8	4.4	6.0	5.0
2	2	0.137	10.3	7.5	8.6	7.9	8.2	9.6	8.7	8.6	7.5	8.8	9.8	7.2	9.7
2	5	0.055	12.8	8.7	9.9	9.7	9.3	12.2	12.2	9.3	8.9	10.5	13.0	7.9	12.5
2	10	0.027	13.6	9.1	10.4	10.3	9.7	13.0	13.3	9.5	9.3	11.1	14.1	8.2	13.5
2	25	0.011	14.2	9.3	10.6	10.7	9.9	13.5	14.0	9.7	9.6	11.5	14.7	8.3	14.0
2	50	0.005	14.3	9.4	10.7	10.8	9.9	13.7	14.2	9.7	9.7	11.6	15.0	8.3	14.2
2	100	0.003	14.4	9.4	10.8	10.9	10.0	13.8	14.3	9.7	9.7	11.7	15.1	8.4	14.3
3	1	0.274	5.3	4.7	5.1	4.6	5.7	4.5	3.0	6.3	4.9	5.0	3.8	4.5	4.7
3	2	0.137	9.0	6.4	7.2	6.7	7.0	8.1	7.3	7.2	6.3	7.0	8.3	6.0	8.5
3	5	0.055	11.5	7.6	8.7	8.3	8.0	10.5	10.1	8.0	7.3	8.3	11.2	7.2	11.1
3	10	0.027	12.0	7.7	8.8	8.4	8.0	10.9	10.7	8.0	7.4	8.5	11.8	7.2	11.6
3	25	0.011	12.4	7.9	9.1	8.7	8.2	11.3	11.2	8.1	7.6	8.7	12.4	7.4	12.0
3	50	0.005	12.6	7.9	9.1	8.7	8.3	11.5	11.3	8.2	7.6	8.8	12.5	7.5	12.2
3	100	0.003	12.6	8.0	9.2	8.8	8.3	11.5	11.4	8.2	7.7	8.9	12.6	7.5	12.3
6	1	0.274	4.6	4.0	4.0	4.0	4.0	3.3	2.8	4.4	4.0	3.9	4.4	3.6	4.4
6	2	0.137	7.2	4.6	5.0	4.7	5.7	5.7	5.1	5.1	4.6	4.8	6.7	4.6	6.0
6	5	0.055	8.7	4.9	5.6	5.2	6.7	7.2	6.6	5.5	4.9	5.3	8.0	5.2	7.0
6	10	0.027	9.3	5.1	5.8	5.3	7.0	7.6	7.0	5.7	5.0	5.5	8.4	5.4	7.4
6	25	0.011	9.6	5.1	5.9	5.4	7.2	7.9	7.3	5.8	5.1	5.6	8.7	5.5	7.6
6	50	0.005	9.7	5.2	6.0	5.4	7.3	8.0	7.4	5.8	5.1	5.6	8.8	5.5	7.6
6	100	0.003	9.7	5.2	6.0	5.5	7.3	8.1	7.5	5.8	5.1	5.7	8.8	5.5	7.7
9	1	0.274	4.4	3.3	3.1	2.9	3.5	2.9	2.9	3.7	3.3	3.6	4.4	3.1	3.9
9	2	0.137	5.9	3.9	4.0	3.7	5.2	4.5	4.1	4.1	4.0	4.0	5.4	3.7	4.7
9	5	0.055	6.9	4.2	4.5	4.2	6.2	5.5	4.9	4.4	4.5	4.3	6.1	4.1	5.1
9	10	0.027	7.2	4.3	4.7	4.3	6.5	5.8	5.1	4.5	4.7	4.4	6.3	4.2	5.2
9	25	0.011	7.4	4.3	4.8	4.4	6.7	6.0	5.3	4.6	4.7	4.5	6.4	4.3	5.3
9	50	0.005	7.4	4.3	4.8	4.5	6.8	6.0	5.3	4.6	4.8	4.5	6.5	4.3	5.4
9	100	0.003	7.4	4.3	4.9	4.5	6.8	6.1	5.3	4.6	4.8	4.5	6.5	4.3	5.4
12	1	0.274	3.8	3.0	2.8	2.9	3.0	2.8	2.7	3.3	3.1	3.2	4.1	3.0	3.4
12	2	0.137	4.9	3.4	3.4	3.2	4.7	3.8	3.4	3.7	3.7	3.7	4.6	3.2	3.9
12	5	0.055	5.5	3.6	3.7	3.3	5.7	4.4	3.8	3.9	4.1	4.0	4.9	3.3	4.2
12	10	0.027	5.7	3.7	3.8	3.3	6.0	4.6	3.9	4.0	4.2	4.1	5.0	3.3	4.3
12	25	0.011	5.9	3.8	3.9	3.4	6.2	4.8	4.0	4.1	4.3	4.2	5.0	3.4	4.3
12	50	0.005	5.9	3.8	3.9	3.4	6.3	4.8	4.0	4.1	4.3	4.2	5.1	3.4	4.3
12	100	0.003	5.9	3.8	3.9	3.4	6.3	4.8	4.0	4.1	4.3	4.2	5.1	3.4	4.4
18	1	0.274	3.1	2.5	2.5	2.2	2.8	2.6	2.4	2.5	2.8	2.7	3.3	2.4	2.4
18	2	0.137	3.6	2.8	2.6	2.2	4.0	2.9	2.6	3.1	3.0	3.3	3.6	2.8	3.0
18	5	0.055	4.0	3.0	2.6	2.3	4.7	3.1	2.7	3.5	3.2	3.6	3.7	3.1	3.4
18	10	0.027	4.1	3.1	2.6	2.3	5.0	3.1	2.7	3.6	3.2	3.7	3.8	3.1	3.5
18	25	0.011	4.2	3.1	2.7	2.3	5.1	3.2	2.8	3.7	3.3	3.7	3.8	3.2	3.6
18	50	0.005	4.2	3.1	2.7	2.3	5.2	3.2	2.8	3.7	3.3	3.7	3.8	3.2	3.6
18	100	0.003	4.2	3.1	2.7	2.3	5.2	3.2	2.8	3.7	3.3	3.7	3.9	3.2	3.6
24	1	0.274	2.9	2.3	1.9	1.8	3.0	2.2	1.7	2.2	2.4	2.7	2.9	2.4	2.3
24	2	0.137	3.0	2.4	2.1	1.9	3.5	2.3	2.2	2.7	2.5	2.9	3.2	2.7	2.5
24	5	0.055	3.1	2.5	2.2	1.9	3.8	2.3	2.5	3.0	2.6	2.9	3.3	2.9	2.7
24	10	0.027	3.1	2.5	2.2	2.0	3.9	2.3	2.6	3.0	2.6	3.0	3.3	2.9	2.8
24	25	0.011	3.2	2.5	2.2	2.0	4.0	2.3	2.7	3.1	2.7	3.0	3.4	3.0	2.8
24	50	0.005	3.2	2.5	2.2	2.0	4.0	2.3	2.7	3.1	2.7	3.0	3.4	3.0	2.8
24	100	0.003	3.2	2.5	2.2	2.0	4.0	2.3	2.7	3.1	2.7	3.0	3.4	3.0	2.8

Duration of infiltration t (h)	Return period (year)	Daily probability (%)	Constant precipitation rate r (mm h^−1) for 25 meteorological stations in Ireland
			Gurteen	Malin Head	Johnstown II	Athenry	Mount Dillon	Finner	Claremorris	Valentia Observatory	Belmullet	Casement	Cork Airport	Knock Airport
0.083	1	0.274	75.5	86.9	109.8	77.2	73.2	40.2	74.2	101.5	82.3	81.2	108.9	91.8
0.083	2	0.137	120.0	113.1	148.4	136.0	140.5	83.6	135.4	153.2	127.0	127.4	159.8	146.6
0.083	5	0.055	146.7	128.8	171.6	171.2	180.9	109.7	172.1	184.3	153.7	155.2	190.3	179.4
0.083	10	0.027	155.6	134.1	179.3	183.0	194.3	118.4	184.4	194.6	162.7	164.4	200.5	190.4
0.083	25	0.011	160.9	137.2	184.0	190.1	202.4	123.6	191.7	200.8	168.0	170.0	206.6	196.9
0.083	50	0.005	162.7	138.3	185.5	192.4	205.1	125.3	194.2	202.9	169.8	171.8	208.6	199.1
0.083	100	0.003	163.6	138.8	186.3	193.6	206.5	126.2	195.4	203.9	170.7	172.7	209.6	200.2
0.167	1	0.274	37.8	43.4	54.9	38.6	36.6	20.1	37.1	50.8	41.2	40.6	54.4	45.9
0.167	2	0.137	60.0	56.6	74.2	68.0	70.3	41.8	67.7	76.6	63.5	63.7	79.9	73.3
0.167	5	0.055	73.3	64.4	85.8	85.6	90.4	54.9	86.1	92.1	76.9	77.6	95.2	89.7
0.167	10	0.027	77.8	67.0	89.7	91.5	97.2	59.2	92.2	97.3	81.3	82.2	100.2	95.2
0.167	25	0.011	80.4	68.6	92.0	95.0	101.2	61.8	95.9	100.4	84.0	85.0	103.3	98.5
0.167	50	0.005	81.3	69.1	92.8	96.2	102.6	62.7	97.1	101.4	84.9	85.9	104.3	99.6
0.167	100	0.003	81.8	69.4	93.1	96.8	103.2	63.1	97.7	102.0	85.4	86.4	104.8	100.1
0.25	1	0.274	25.2	29.0	36.6	25.7	24.4	13.4	24.7	33.8	27.4	27.1	36.3	30.6
0.25	2	0.137	40.0	37.7	49.5	45.3	46.8	27.9	45.1	51.1	42.3	42.5	53.3	48.9
0.25	5	0.055	48.9	42.9	57.2	57.1	60.3	36.6	57.4	61.4	51.2	51.7	63.4	59.8
0.25	10	0.027	51.9	44.7	59.8	61.0	64.8	39.5	61.5	64.9	54.2	54.8	66.8	63.5
0.25	25	0.011	53.6	45.7	61.3	63.4	67.5	41.2	63.9	66.9	56.0	56.7	68.9	65.6
0.25	50	0.005	54.2	46.1	61.8	64.1	68.4	41.8	64.7	67.6	56.6	57.3	69.5	66.4
0.25	100	0.003	54.5	46.3	62.1	64.5	68.8	42.1	65.1	68.0	56.9	57.6	69.9	66.7
0.5	1	0.274	12.6	14.5	18.3	12.9	12.2	6.7	12.4	16.9	13.7	13.5	18.1	15.3
0.5	2	0.137	20.0	18.9	24.7	22.7	23.4	13.9	22.6	25.5	21.2	21.2	26.6	24.4
0.5	5	0.055	24.4	21.5	28.6	28.5	30.1	18.3	28.7	30.7	25.6	25.9	31.7	29.9
0.5	10	0.027	25.9	22.3	29.9	30.5	32.4	19.7	30.7	32.4	27.1	27.4	33.4	31.7
0.5	25	0.011	26.8	22.9	30.7	31.7	33.7	20.6	32.0	33.5	28.0	28.3	34.4	32.8
0.5	50	0.005	27.1	23.0	30.9	32.1	34.2	20.9	32.4	33.8	28.3	28.6	34.8	33.2
0.5	100	0.003	27.3	23.1	31.0	32.3	34.4	21.0	32.6	34.0	28.5	28.8	34.9	33.4
1	1	0.274	6.3	7.2	9.2	6.4	6.1	3.3	6.2	8.5	6.9	6.8	9.1	7.7
1	2	0.137	10.0	9.4	12.4	11.3	11.7	7.0	11.3	12.8	10.6	10.6	13.3	12.2
1	5	0.055	12.2	10.7	14.3	14.3	15.1	9.1	14.3	15.4	12.8	12.9	15.9	15.0
1	10	0.027	13.0	11.2	14.9	15.2	16.2	9.9	15.4	16.2	13.6	13.7	16.7	15.9
1	25	0.011	13.4	11.4	15.3	15.8	16.9	10.3	16.0	16.7	14.0	14.2	17.2	16.4
1	50	0.005	13.6	11.5	15.5	16.0	17.1	10.4	16.2	16.9	14.2	14.3	17.4	16.6
1	100	0.003	13.6	11.6	15.5	16.1	17.2	10.5	16.3	17.0	14.2	14.4	17.5	16.7
2	1	0.274	6.0	5.5	7.0	4.9	5.2	3.2	5.6	8.0	5.5	6.6	7.2	6.7
2	2	0.137	7.5	7.2	9.6	8.4	8.6	5.7	9.0	9.6	8.4	7.9	10.6	8.5
2	5	0.055	8.4	8.2	11.2	10.5	10.6	7.3	11.0	10.6	10.2	8.7	12.6	9.5
2	10	0.027	8.7	8.5	11.7	11.2	11.3	7.8	11.7	10.9	10.8	8.9	13.3	9.9
2	25	0.011	8.9	8.7	12.0	11.7	11.7	8.1	12.1	11.1	11.2	9.1	13.7	10.1
2	50	0.005	8.9	8.8	12.1	11.8	11.8	8.2	12.2	11.2	11.3	9.1	13.8	10.2
2	100	0.003	9.0	8.8	12.2	11.9	11.9	8.2	12.3	11.2	11.3	9.2	13.9	10.2
3	1	0.274	5.3	5.1	5.7	4.3	4.3	2.9	5.2	6.9	5.1	5.5	5.8	5.7
3	2	0.137	6.1	6.0	8.1	6.9	7.0	5.0	7.5	8.0	7.2	7.0	8.9	6.8
3	5	0.055	6.7	6.7	9.8	8.7	8.8	6.6	9.2	8.7	8.7	8.1	11.0	7.5
3	10	0.027	6.8	6.7	10.0	9.0	9.1	6.6	9.4	8.8	8.9	8.2	11.4	7.6
3	25	0.011	6.9	6.8	10.3	9.3	9.4	6.8	9.7	8.9	9.1	8.3	11.8	7.7
3	50	0.005	6.9	6.9	10.4	9.4	9.5	6.9	9.7	9.0	9.2	8.4	11.9	7.8
3	100	0.003	6.9	6.9	10.5	9.4	9.6	6.9	9.8	9.0	9.2	8.4	11.9	7.8
6	1	0.274	4.0	3.9	4.5	3.8	3.8	2.9	4.6	4.7	4.0	4.5	5.4	4.1
6	2	0.137	4.6	4.3	6.0	4.7	4.8	3.8	5.3	6.4	4.9	6.2	6.6	4.6
6	5	0.055	4.9	4.5	6.9	5.2	5.4	4.3	5.8	7.4	5.4	7.2	7.3	4.9
6	10	0.027	5.0	4.6	7.2	5.4	5.7	4.5	6.0	7.7	5.5	7.5	7.6	5.0
6	25	0.011	5.1	4.7	7.4	5.5	5.8	4.6	6.1	7.9	5.6	7.7	7.7	5.1
6	50	0.005	5.1	4.7	7.5	5.5	5.8	4.6	6.1	8.0	5.7	7.8	7.7	5.1
6	100	0.003	5.1	4.7	7.5	5.5	5.8	4.6	6.1	8.0	5.7	7.8	7.8	5.1
9	1	0.274	3.1	3.0	4.1	3.1	3.1	2.4	3.8	4.2	3.4	4.0	5.0	3.3
9	2	0.137	3.6	3.3	4.9	3.6	3.5	3.0	4.0	5.7	3.7	5.7	5.7	3.6
9	5	0.055	4.0	3.6	5.3	3.8	3.8	3.3	4.1	6.6	3.9	6.8	6.1	3.8
9	10	0.027	4.1	3.6	5.5	3.9	3.9	3.4	4.1	7.0	3.9	7.2	6.2	3.9
9	25	0.011	4.1	3.7	5.6	4.0	4.0	3.5	4.2	7.1	4.0	7.4	6.3	3.9
9	50	0.005	4.2	3.7	5.6	4.0	4.0	3.5	4.2	7.2	4.0	7.4	6.4	3.9
9	100	0.003	4.2	3.7	5.6	4.0	4.0	3.5	4.2	7.2	4.0	7.5	6.4	3.9
12	1	0.274	2.6	2.7	3.4	2.6	2.4	2.2	3.0	3.6	2.6	3.7	4.2	2.7
12	2	0.137	3.0	2.9	4.1	3.0	2.8	2.5	3.3	5.1	3.0	5.3	5.1	3.0
12	5	0.055	3.3	3.0	4.5	3.2	3.0	2.6	3.4	6.0	3.2	6.3	5.7	3.1
12	10	0.027	3.4	3.0	4.6	3.2	3.0	2.7	3.4	6.3	3.3	6.7	5.9	3.2
12	25	0.011	3.5	3.0	4.7	3.3	3.1	2.7	3.5	6.5	3.3	6.8	6.0	3.2
12	50	0.005	3.5	3.0	4.7	3.3	3.1	2.7	3.5	6.6	3.4	6.9	6.0	3.2
12	100	0.003	3.5	3.0	4.7	3.3	3.1	2.7	3.5	6.6	3.4	6.9	6.1	3.2
18	1	0.274	2.0	2.0	2.6	2.0	2.2	1.7	2.2	3.2	2.0	3.6	3.8	2.2
18	2	0.137	2.3	2.4	3.2	2.5	2.3	1.8	2.7	4.3	2.6	4.7	4.2	2.5
18	5	0.055	2.5	2.6	3.5	2.8	2.3	1.9	2.9	5.0	2.9	5.4	4.4	2.7
18	10	0.027	2.6	2.7	3.6	2.9	2.3	2.0	3.0	5.2	3.0	5.6	4.5	2.8
18	25	0.011	2.6	2.7	3.7	3.0	2.3	2.0	3.1	5.3	3.1	5.7	4.5	2.8
18	50	0.005	2.6	2.7	3.7	3.0	2.3	2.0	3.1	5.4	3.1	5.8	4.6	2.8
18	100	0.003	2.6	2.7	3.7	3.0	2.3	2.0	3.1	5.4	3.1	5.8	4.6	2.8
24	1	0.274	1.7	1.9	2.2	1.9	2.0	1.4	1.9	3.0	1.8	3.4	3.0	1.9
24	2	0.137	2.0	2.0	2.6	2.2	2.1	1.6	2.3	3.6	2.3	4.1	3.4	2.2
24	5	0.055	2.1	2.0	2.9	2.4	2.2	1.7	2.5	4.0	2.6	4.5	3.6	2.3
24	10	0.027	2.2	2.1	3.0	2.5	2.2	1.8	2.6	4.1	2.7	4.6	3.6	2.4
24	25	0.011	2.2	2.1	3.0	2.5	2.2	1.8	2.6	4.2	2.7	4.7	3.7	2.4
24	50	0.005	2.2	2.1	3.0	2.5	2.2	1.8	2.6	4.2	2.7	4.7	3.7	2.4
24	100	0.003	2.2	2.1	3.0	2.5	2.2	1.8	2.6	4.2	2.7	4.7	3.7	2.4

Estimated daily surface runoff (duration t = 24 h) with SCS method corresponding to various rainfall data (minimum, average, and maximum daily rainfall) for specific return periods (1, 2, 5, 10, 25, 50, 100 years) is displayed in Table 8. Daily maximum surface runoff was observed as 5.51 cm corresponding to curve number (CN_II) 89. Overall observation suggests that higher surface runoff is directly proportional to curve number and rainfall (longer return period). When r is < q, water infiltrates at the same rate as the rainfall intensity. Conversely, when r is > q, excess water becomes runoff once the soil is saturated. Lower CN_II represents a permeable layer and good drainage or hydraulic condition consisting of deep sands with very little silt and clay (Table 5). Higher CNII represents mostly clays with shallow soils with nearly impermeable soil sub-horizons near the surface resulting in poor drainage conditions. The first runoff value was observed for combinations of (i) minimum rainfall category and CN_II of 79, (ii) average rainfall category and CN_II of 68 and (iii) maximum rainfall category and CN_II of 61.

Table 8. Estimated daily surface runoff (duration t = 24 h) with SCS method corresponding to various rainfall intensity r (cm h⁻¹) calculated for specific return periods (1, 2, 5, 10, 25, 50, 100 years).

The simulated (100,000 iterations) daily surface runoff is presented in Table 9. The 5th percentile of the daily surface runoff shows no surface runoff was produced immediately after rainfall. The mean daily surface runoff from pastures land use is estimated as 0.36, 0.51, 0.62, 0.65, 0.68, 0.68, and 0.69 cm for 1, 2, 5, 10, 25, 50, 100 year return periods, respectively. The 95th percentile of daily surface runoff from pasture land use was 1.58, 2.05, 2.40, 2.51, 2.59, 2.59, and 2.62 cm for 1, 2, 5, 10, 25, 50, and 100-year return periods, respectively. Therefore, the daily probability of potentially contaminated mean runoff of depth 0.69 cm is estimated as 2.74 × 10^–5.

Table 9. Estimated surface runoff (cm) for 24 h duration of rainfall.

Return period	Daily probability	Estimated surface runoff
		5th percentile	Mean	95th percentile
(year)	(in 24 h)	(cm)	(cm)	(cm)
1	2.74 × 10^–3	0.0	0.36	1.58
2	1.37 × 10^–3	0.0	0.51	2.05
5	5.48 × 10^–4	0.0	0.62	2.40
10	2.74 × 10^–4	0.0	0.65	2.51
25	1.1 × 10^–4	0.0	0.68	2.59
50	5.48 × 10^–5	0.0	0.68	2.59
100	2.74 × 10^–5	0.0	0.69	2.62

Table 10 shows the wetting front depth produced by combining the different intensities of rainfall (classified as minimum, average, and maximum as per Figure 6) and soil texture classes under several return periods (1, 2, 5, 10, 25, 50, and 100 years). Maximum infiltration was observed for clay soil for the minimum and average rainfall intensity. As intensity increases (towards maximum), the maximum infiltration was observed in clay loam, silty clay loam, and silty clay. A detailed estimate of wetting front depth for minimum, average, and maximum rainfall intensity, along with a hypothetical scenario where intensity is assumed to be 10 times higher than the average intensity forecasted at weather stations, is provided in the supplementary tables ST1, ST2, ST3, and ST4, respectively. A combination of critical rainfall intensity and duration is presented in Table 11, responsible for producing maximum wetting front depth (Z) or infiltration. The intensity of 0.143, 0.163, 0.175, 0.179, 0.181, 0.182, and 0.182 cm h⁻¹ of the duration of 24 h was found the critical rainfall for 1, 2, 5, 10, 25, 50, 100 year return period respectively in the sand, loamy sand, sandy loam, loam, silt loam, sandy clay loam, clay loam, silty clay soils. Some exceptions were found for silty clay loam and clay. Overall the intensity and duration mentioned earlier produce maximum Z in silty clay loam and clay except for three occasions where the intensity of 0.407 cm h⁻¹ and duration of 18 h makes maximum Z for silty clay loam and intensity of 0.352 and 0.354 cm h⁻¹ with 9 h rainfall (each) produced maximum Z for clay (Table 11). A detailed result can be found in the supplementary material (Table ST5).

Table 10. Maximum wetting front depth (cm) representing the infiltration estimated for different soil texture classes.

Table 11. Determination of critical condition, intensity, and rainfall duration producing maximum wetting front depth (Z, in cm).

Rainfall intensity (scenarios)	Return period (year)	Probability of occurrence (in 24 h)	Intensity (cm h^−1)	Duration (h)	Sand	Loamy Sand	Sandy Loam	Loam	Silt Loam	Sandy Clay Loam	Clay Loam	Silty Clay	Intensity (cm h^−1)	Duration (h)	Silty Clay Loam	Intensity (cm h^−1)	Duration (h)	Clay
Minimum	1	2.74 × 10^–3	0.143	24	9.72	9.17	9.99	9.21	8.10	11.65	11.25	11.47	0.143	24	10.30	0.143	24	11.91^a
	2	1.37 × 10^–3	0.163	24	11.07	10.45	11.38	10.49	9.23	13.27	12.82	13.07	0.163	24	11.74	0.163	24	13.57^a
	5	5.48 × 10^–4	0.175	24	11.89	11.22	12.22	11.26	9.91	14.25	13.76	14.03	0.175	24	12.60	0.175	24	14.57^a
	10	2.74 × 10^–4	0.179	24	12.16	11.47	12.49	11.52	10.13	14.57	14.07	14.35	0.179	24	12.89	0.179	24	14.90^a
	25	1.1 × 10^–4	0.181	24	12.32	11.63	12.66	11.68	10.27	14.77	14.26	14.55	0.181	24	13.06	0.181	24	15.10^a
	50	5.48 × 10^–5	0.182	24	12.37	11.68	12.72	11.73	10.31	14.83	14.32	14.61	0.182	24	13.12	0.352^b	9^b	15.38^a
	100	2.74 × 10^–5	0.182	24	12.40	11.71	12.74	11.75	10.34	14.86	14.35	14.64	0.182	24	13.15	0.354^b	9^b	15.38^a
Average	1	2.74 × 10^–3	0.228	24	15.49	14.62	15.92	14.68	12.91	18.57	17.93	18.29	0.228	24	16.42	0.228	24	26.45^a
	2	1.37 × 10^–3	0.257	24	17.45	16.47	17.93	16.53	14.54	20.91	20.19	20.60	0.257	24	18.49	0.257	24	26.45^a
	5	5.48 × 10^–4	0.274	24	18.62	17.57	19.13	17.64	15.52	22.32	21.55	21.98	0.274	24	19.74	0.274	24	26.45^a
	10	2.74 × 10^–4	0.280	24	19.01	17.94	19.53	18.01	15.84	22.78	22.00	22.44	0.280	24	20.15	0.280	24	26.45^a
	25	1.1 × 10^–4	0.283	24	19.24	18.16	19.78	18.24	16.04	23.07	22.27	22.72	0.283	24	20.40	0.283	24	26.45^a
	50	5.48 × 10^–5	0.284	24	19.32	18.24	19.86	18.31	16.10	23.16	22.36	22.81	0.284	24	20.48	0.284	24	26.45^a
	100	2.74 × 10^–5	0.285	24	19.36	18.27	19.90	18.35	16.14	23.21	22.41	22.86	0.285	24	20.52	0.285	24	26.45^a
Maximum	1	2.74 × 10^–3	0.339	24	23.03	21.74	23.67	21.82	19.19	27.60^a	26.65	27.19	0.339	24	24.41	0.339	24	26.45
	2	1.37 × 10^–3	0.407	24	27.64	26.09	28.41	26.20	23.04	33.14	32.00	40.11^a	0.407	18^b	34.22	0.407	24	26.45
	5	5.48 × 10^–4	0.447	24	30.41	28.71	31.26	28.82	25.35	36.46	46.36^a	40.11	0.447	24	40.54	0.447	24	26.45
	10	2.74 × 10^–4	0.461	24	31.34	29.58	32.20	29.70	26.12	37.56	46.36^a	40.11	0.461	24	40.54	0.461	24	26.45
	25	1.1 × 10^–4	0.469	24	31.89	30.10	32.77	30.22	26.58	38.23	46.36^a	40.11	0.469	24	40.54	0.469	24	26.45
	50	5.48 × 10^–5	0.472	24	32.08	30.28	32.96	30.40	26.74	38.45	46.36^a	40.11	0.472	24	40.54	0.472	24	26.45
	100	2.74 × 10^–5	0.473	24	32.17	30.36	33.06	30.48	26.81	38.56	46.36^a	40.11	0.473	24	40.54	0.473	24	26.45

Note: Maximum wetting front depth (Z) in cm highlighted in bold, and italics values show the interrupted trend of intensity (row-wise) and duration (column-wise)

^a Maximum wetting front depth (Z)

^b The interrupted trend of intensity (row-wise) and duration (column-wise)

The infiltration rate, cumulative infiltration, and wetting front depth vs rainfall intensity plot is presented in Figure 7 for three classified rainfall intensities (minimum, average, and maximum as per Figure 6). The infiltration rate was proportional and positively correlated to rainfall intensity for coarse soil particles such as sand and loamy sand texture class. However, the infiltration rate of loamy sand achieves its highest value at 6 to 7 cm h⁻¹; towards the finer soil grain size, the infiltration rate peaks in shorter intensity than the coarser texture class. As rainfall intensifies, wetting front depth and infiltration drop with a steeper slope up to 1 to 2 cm h⁻¹ intensity and then follows a plateau. The infiltration rate, cumulative infiltration, and wetting front depth vs rainfall duration plot is presented in Figure 8 for three classified rainfall intensities (minimum, average, and maximum). For larger grain size soil particles (sand, loamy sand), a sharp decline of infiltration rate was observed for rainfall duration (up to 1 to 2 h duration); beyond that, no change of infiltration rate was observed. Even this variation at a shorter duration could not be observed for finer soil particles. The wetting front depth and cumulative infiltration were proportional and positively correlated with rainfall duration for all texture classes, which agrees with the interpretations derived from Table 11.

Figure 7. Infiltration rate, cumulative infiltration, wetting front depth vs rainfall intensity plot for different soil texture class; intensity (cm h⁻¹) on the x-axis.

Figure 8. Infiltration rate, cumulative infiltration, wetting front depth vs rainfall duration plot for different soil texture class, duration (h) on the x-axis.

In most cases, the maximum infiltration was observed at 24 h. However, a dissimilarity was observed for the clay texture class and minimum intensity of rainfall combination (Figure 8). Between 9 and 12 h, a declination of infiltration was observed against the duration increase. The hypothetical scenario (r_hyp = 10 × r_avg) also showed a similar pattern (SF1, supplementary material) that was obtained for the maximum rainfall intensity scenario in Figure 7 and Figure 8. A summary of maximum wetting front depths produced by r_avg and r_hyp is displayed in Figure 9a and Figure 9b, respectively. The maximum wetting front depth was observed for finer soil particles (clay), followed by sandy clay loam and silty clay at a lower storm intensity. Conversely, the maximum wetting front depth was observed for sandy clay loam, followed by sandy loam and sand at a higher intensity (Figure 9). The simulated (100,000 iterations) wetting front depths (5th percentile, mean, and 95th percentile) are presented in Table 12. The range of Z varies from 10.48 cm (5th percentile) with a daily probability of 2.74 × 10^–3 to 32.85 cm (95th percentile) with a daily probability of 2.74 × 10^–5). Therefore, there is a daily probability of 2.74 × 10^–5 for a 100-year return period storm, producing a mean infiltration of 20.7 cm into the ground and may cause potential groundwater contamination if a shallow groundwater table (depth < 20.7 cm) exists.

Figure 9. Wetting front depth Z (cm) corresponds to different soil texture classes and rainfall intensities.

Table 12. Estimated wetting front depth (cm) for 24 h duration of rainfall.

Return period	Daily probability	Estimated wetting front depth
		5th percentile	Mean	95th percentile
(year)	(in 24 h)	(cm)	(cm)	(cm)
1	2.74 × 10^–3	10.48	16.65	26.00
2	1.37 × 10^–3	11.75	18.73	29.44
5	5.48 × 10^–4	12.39	19.93	31.47
10	2.74 × 10^–4	12.58	20.34	32.16
25	1.1 × 10^–4	12.66	20.59	32.74
50	5.48 × 10^–5	12.72	20.67	32.84
100	2.74 × 10^–5	12.72	20.70	32.85

4. Discussion and significance

The findings of this study (Figures 7 and 8) are in line with the previously published study (Teng et al. 2012). The probability of infiltration and runoff can be calculated by inverting the critical rainfall event's return period. The risk of infection, such as infiltration to potable drinking water wells or runoff to surface water, is conditional on the infiltration and runoff characteristics. Given two events, A and B, the conditional probability of B given A is defined as the quotient of the probability of the union P(A ∩ B) of events A and B and the probability of A Equation (17) (Vose 2009). The union of two events is presented as the intersection (Figure 10). If A and B are replaced by rainfall and infection, respectively, the union of the two events is determined by Equation (18). (17) $P(B|A)={\displaystyle \frac{P(B\cap A)}{P(A)}}$(17) (18) $\mathrm{Risk}(\mathrm{infection}\cap \mathrm{rainfall})=\mathrm{Risk}(\mathrm{infection}|\mathrm{rainfall})\times P(\mathrm{rainfall})$(18) This research produces the maximum infiltration and runoff values under a known-frequency wet-weather event P(rainfall). The risk associated with a given rainfall return period would be the union of the risk associated with the maximum runoff and maximum infiltration. The determination of ‘Risk (infection | rainfall)’ requires an integrated fate, transport, human exposure, and risk model (Nag et al. 2019). Following the application of fertilisers, the pollutants diffuse into a larger volume of the soil and migrate from the solid phase to the aqueous phase with dilution, inactivation, adsorption, and sedimentation processes during their flow through the surface/ subsurface to a nearby drinking water intake point (Devane et al. 2018). In the past, studies similar to Cummins et al. (2010), Peyton et al. (2016), Clarke et al. (2017), and Nolan et al. (2020) evaluated the microbial exposure or risk linked with land spreading of biosolids to the Irish grasslands following rainfall events. As the calculated P(rainfall) is always < 1, the risk estimates in current studies are overestimated. Therefore, the influence of the probability of critical rainfall events calculated in this study could improve the confidence around the estimated risk.

Figure 10. Towards estimating the risk of microbial infection associated with wet-weather events using the union function of probabilities (intersection) of two events.

4.1. Limitations and future work

1. A simplified hydrological mass balance was considered: precipitation equals the summation of surface runoff outflow and evapotranspiration. At the same time, at most scales, ‘groundwater in’ is assumed to be equal to ‘groundwater out’; at the catchment scale, surface runoff inflow is zero.

2. A significant limitation of applying the SCS model is that the Equation (4) (SCS model) coefficients must be evaluated with field data for each site. Since the model is not derived from fundamental physical principles, it can only be used as a screening tool for initial approximations. However, the SCS model includes the influence of vegetation characteristics and slope of the field with the curve numbers (Table 5), and the impact of these parameters could not be included in the EGA model. Future work is proposed to improve this limitation in the model. Field experiments are therefore proposed for validation purposes.

3. No surface ponding was considered in the EGA model, and this model is applicable for vertical one-dimensional fluid flow and deep, homogenous soil columns. In the ponding scenario, the pressure head of surface ponding would increase the infiltration. The influence of macropores in the soil and preferential flow may result in higher infiltration and cannot be estimated by the EGA model (Darnault et al. 2004).

4. As a future work, a national scale groundwater table map is proposed, which can be further compared with the maximum wetting front depth calculated in this study and rainfall variations captured in weather stations (Figure 4), field drainage property, and soil texture class variation (EPA 2018).

5. The simulated surface runoff depths derived from the SCS model may also help develop predictive models of the short-term nutrient losses (Peyton et al. 2016) due to rainfall events following treated sludge and dairy cattle slurry application to Irish grassland soils.

6. The disease burden is closely linked to the impact (mortality in untreated patients) and probability (prevalence and concentration) of pathogens and their environmental fate, viz. growth, no-growth, survival rate, and environmental decay rate (Nag et al. 2020, 2019) and potential pathogenic attenuation process, which may occur along the transfer continuum in the field before reaching surface water (Nag et al. 2021b). As a part of future work, it will be worth exploring the frequency and level of pathogens (case-specific (Davies et al. 2005)) released during infiltration and runoff events, as rapid, intense events might pose less risk compared to prolonged, low-intensity events. For example, spore-forming bacteria’s vegetative cells may die soon, but spores can survive longer. The same applies to protozoan parasites, such as Cryptosporidium parvum: the oocyst may survive months/ years in the dark (Davies et al. 2005; Erickson and Ortega 2006).

5. Conclusions

Maximum 1 hourly rainfall intensity (19.9 cm h⁻¹) was observed on the West Coast (Newport). However, the maximum rainfall for the Casement station was forecasted as a 113.6 mm 100-year return period with an average intensity of 4.7 cm h⁻¹. SCS model disclosed that daily maximum surface runoff was observed as 5.51 cm corresponding to curve number (CN_II) 89. First surface runoff was produced by combinations of (i) 0.625 cm h⁻¹ and CN_II of 79, (ii) 0.925 cm h⁻¹ and CN_II of 68 and (iii) 0.554 cm h⁻¹ and CN_II of 61. The mean daily surface runoff from pastures land use is estimated as 0.36, 0.51, 0.62, 0.65, 0.68, 0.68, and 0.69 cm (95th percentile 1.58, 2.05, 2.40, 2.51, 2.59, 2.59, and 2.62 cm) for 1, 2, 5, 10, 25, 50, 100 year return period, respectively. The Explicit Green-Ampt model shows that the intensity of 0.143, 0.163, 0.175, 0.179, 0.181, 0.182, and 0.182 cm h⁻¹ of the duration of 24 h was found the critical rainfall for 1, 2, 5, 10, 25, 50, 100 year return period respectively in the sand, loamy sand, sandy loam, loam, silt loam, sandy clay loam, clay loam, silty clay soils. Some exceptions were found for silty clay loam and clay. Overall the intensity and duration mentioned earlier produced maximum Z in silty clay loam and clay except for three occasions where the intensity of 0.407 cm h⁻¹ and duration of 18 h produced maximum Z for silty clay loam and intensity of 0.352 and 0.354 cm h⁻¹ with 9 h rainfall (each) had maximum Z for clay. The infiltration rate was directly proportional to rainfall intensity for coarse soil particles such as sand and loamy sand texture class. However, the infiltration rate of loamy sand achieves its highest value at 6 to 7 cm h⁻¹; towards the finer soil grain size, the infiltration rate peaks in shorter intensity than the coarser texture class. As rainfall intensifies, wetting front depth and infiltration drop with a steeper slope up to 1 to 2 cm h⁻¹ intensity and then follows a plateau. For larger grain size soil particles (sand, loamy sand), a sharp decline of infiltration rate was observed for rainfall duration (up to 1 to 2 h duration). Beyond that, no change in infiltration rate was observed. Even this variation at a shorter duration could not be observed for finer soil particles. The maximum wetting front depth was observed for finer soil particles (clay), followed by sandy clay loam and silty clay at a lower storm intensity. Conversely, the maximum wetting front depth was observed for sandy clay loam, followed by sandy loam and sand at a higher intensity. The range of wetting front depth varies from 10.48 cm (5th percentile) with a daily probability of 2.74 × 10^–3 to 32.85 cm (95th percentile) with a daily probability of 2.74 × 10^–5). A daily probability of 2.74 × 10^–5 is associated with a mean runoff depth of 0.69 cm and infiltration of 20.7 cm and may cause potential surface water and groundwater contamination (shallow water table < 20.7 cm), respectively. The probabilities corresponding to critical rainfall events can be incorporated into the overall risk assessment framework to improve the conditional probability estimate using the multiplication rule.

CRediT authorship contribution statement

Rajat Nag: The solo author has prepared every aspect of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

All spreadsheets are available on the open repository.