The study area was located at the dryland floodplains under wild life and aquafer water management of the Anglo American Kolomela Iron Ore mine, situated 30 km south of the Postmasburg town, Northern Cape Province of South Africa (Figure 1(a)). The area had a common slope of 1% with three dominant soil types (Figure 1(b)). These included the Addo, Augrabies and Brandvlei soil forms [18] , which also referred respectively as Greysols, Ferralsols and Cambisols by the International Union of Soil Science (IUSS) Working Group World Resource Base (WRB) [19] . The Food Agriculture Organisation (FAO)WRB, [20] for soil resources generally referred to these floodplain soils types as fluvisols. A summary of soils physical and chemical properties is shown in Table 1. The Addo and Brandvlei soil forms found at altitude of 1252 m while the Augrabies at altitude of 2060 m.

A long-term rainfall data constituting monthly minimum, maximum and averages over a 98- year period of the Postmasburg area was summarised in Table 2. The wettest months are January to March and the driest months are June to August. Rainfalls with amounts of 130 mm and 104.5 mm were the highest recorded rainstorms and occurred in the months of February and January, respectively. Needle like vegetation and sedges were common in the Addo while clusters of tussock grasses and bushy plants were observed in the Brandvlei and Augrabies soil forms. Vegetation was withered and dormant with the ground virtually bare.

The HYDRUS-1D model have an inverse modelling capability and was required to optimise unknown parameters for van Genuchten [6] model characterising rainstorm infiltration in the water flow equation (Equation (1)). The objective function constituted residuals between observed and predicted soil water contents at different depths and times and was minimised using the Levenberg-Marquardt nonlinear minimization method ( [23] [24] ). Mathematically, the objective function may be defined as

( β , θ ) = ∑ i = 1 N W i [ θ i * ( z , t i ) − θ i ( z , t i ) , β ] 2 (4)

where ɸ(β) is the objective function of the parameter vector, β; θ_i* and θ_i are measured and predicted soil water contents, respectively; z is the depth; t is the time and N is the number of observations available; W is the weight of specific measurement by standard deviation.

The surface horizon constituted the flow domain discretised into upper (0 - 50) and lower (50 - 250 mm) layers with observation points at 30 mm and 230 mm depths, respectively. HYDRUS-1D model predicts well infiltration properties near the surface but because of neglecting the effect of entrapped air on water infiltration, it often underestimates the infiltration depth [25] . The two-layered horizon was discretised into 101 nodes with specified nodal density of 0.01 and 1 for the upper and lower layers. The high density of the near surface superficial layer was aimed to capture rapid changes in water contents by the advancing wetting front. Infiltration was initiated by atmospheric boundary condition with surface runoff and was maintained for period of the simulated rainstorm. Rainstorms intensity and zero values of evapotranspiration were specified. Free drainage was prescribed for the lower boundary condition and initial conditions given in terms of water contents measurements. Time discretization was in minutes with 20 maximum number of iterations and initial time step of 0.01.

To improve parameter identification and uniqueness for upper and lower layers the surface horizon, a two-step inverse parameter optimisation [17] was conducted. The first step estimated soil hydraulic optimal parameter values of the upper and lower surface horizon layers as separate independent layers. The second step estimated hydraulic parameters of a two-layered surface horizon simultaneously with optimal values from the first step as initial estimates. The Rosetta pedotransfer program contained in HYDRUS-1D estimated initial parameter values using soil type sand, silt and clay fractions and bulk density (Table 1). Time dependent soil-water contents measurements at 30 mm and 230 mm were used in the objective function for the first and second step inversion. HYDRUS calculates infiltration-excess runoff in the absence of ponding by the system-independent atmospheric boundary conditions. The surface water-infiltration flux was limited by the following two conditions [26] :

| K ( h ) ( ∂ h ∂ z + 1 ) | ≤ q , (5)

h A ≤ h ≤ h S , (6)

where, q maximum potential infiltration flux under the current atmospheric conditions, h is the matric suction potential at soil surface, z is depth, K(h) is unsaturated hydraulic conductivity, and h_A and h_S are, respectively, minimum and maximum matric suction potential allowed under the prevailing soil conditions.

The objective function minimised in inverse parameter optimisation should provide sufficient information about the unknown parameters to be identified [24] . This is only possible if the objective function is sensitive enough to track changes in the unknown parameters. The ability of the objective function to capture these variations presumably within the vicinity of true parameter values can be evaluated using sensitivity analysis. Various methods exist including the coefficient method or finite difference, a sensitivity equation method and a variation method [27] . Sensitivities between different parameters for selected model outputs was compared using the unit less coefficient method as normalised by Simunek and van Genucthten [28] with 1% change effected on parameters written as:

e i j = 100 β | ∂ a i ∂ β j | = 100 β j | a i ( β + Δ β e j ) − a i ( β ) | 1.01 β j − β j = | a i ( β + B e j ) − a i ( β ) | (7)

where e_ij, is the change in the auxiliary variable a_i corresponding to 1% change in parameter β_j. Thereby β is the parameter vector, while e_j is the j^th unit vector. The parameter vector included the optimised θr, θs, α, n and Ks van Genuchten-Mualem parameters. Sensitivities conducted involved soil water content, infiltration rates, accumulative infiltration, runoff rate and accumulative runoff. A high sensitivity suggested a well-defined minimum and the parameter can be optimised with greater certainty once the global minimum is verified.

The HYDRUS-1D model performance assessed with the Nash-Sutcliffe model efficiency coefficient (NSE) [29] and root mean square error (RMSE). The NSEwas calculated by the expression:

N S E = 1 − ∑ i = 1 N ( θ i − θ i * ) 2 ∑ i = 1 N ( θ i * − θ a v e ) 2 (8)

where θ₁ is the predicted soil water content; θ*₁ is the observed soil water content; θ_ave is the average soil water content of all the observed events, and N is the number of observations i.e., the number of measured events.

The RMSE is widely used to measure agreement between the observed data and model prediction and represented by the expression:

R M S E = ∑ I = 1 N ( θ i * − θ i ) 2 N (9)

The Duncan’s multiple range test (DMRT) was used to compare infiltration rates and accumulation infiltration of the three soil types and simulated rainstorms. The means were ranked from the highest to lowest values and ranks were compared to shortest significant ranges (R_p). The R_p was computed as follows:

R p = ( r p ) ( s d − ) 2 (10)

s d − = 2 s 2 r (11)

where rp, tabular values of the significant studentized ranges at 0.05, s d − standard error of the mean difference and s is the variance [30] .

Time dependent soil water contents at 30 mm and 230 mm depth measured from simulated (high, medium and low) rainstorms were minimised in the objective function and results for the model fit at 30 mm depth were presented in Figure 3. The model was able to reproduce the water contents for the three soil types very well with NSE not falling below 0.99. The lower layer had constant water content values suggesting the infiltration-wetting front was not detected or unable to reach this depth (results not shown). In all soil types, soil water content decreased with rainstorm size with the Addo and Brandvlei having earliest and latest response times regardless of rainstorm size. The good fit by the HYDRUS-1D code was not surprising because the model’s ability to reproduce measured infiltration data either on bare or vegetated surfaces is well documented ( [25] [31] [32] [33] ). Although a good fit is desirable for the minimization process, it is not sufficient for parameter identification because data used in the objective function directly or indirectly should relate to the unknown parameters ( [24] [28] ). Soil water content, pressure head and infiltration rate as well as accumulative infiltration data are acceptable for inverse parameter estimation ( [28] [34] ).

Figure 4 and Figure 5 showed respective water infiltration rates and accumulative infiltration of studied soils and rainstorms estimated by HYDRUS-1D inverse parameter optimisation procedure. Final infiltration rates and total infiltration rates were summarised alongside runoff parameters in Table 5. Final infiltration rates and accumulative infiltration decreased with rainstorm intensity and size in all soil types. This finding was consistent with the observation that higher rainstorm amounts and intensity resulted to higher final infiltration rate ( [35] [36] [37] ).

Initial infiltration rates declined sharply under the high rainstorm suggesting that the 1.62 mm・min⁻¹ intensity was higher than soils infiltration capacity. The Addo and Augrabies approached steady infiltration rates after 20 minutes recording final infiltration rates and total infiltration of 0.71 mm・min⁻¹ and 34.8 mm, and 0.91, mm・min⁻¹ and 36.5 mm respectively. The lower infiltration values of the Addo was explained by the total fine silt plus clay content of 47.7% of the surface horizon compared to the 20.6% from the Augrabies. The Brandvlei had a constant initial infiltration rate for the first 5 min before declining to a final infiltration rate of 1.14 mm・min⁻¹ and total infiltration of 50.51 mm. The Brandvlei higher infiltration capacity was consistent to the lower total fine silt plus clay content of 17.7%. Silt plus clay fraction were easily mobilised by high-energy raindrops into formation of surface crusts and seals that can reduce infiltration capacity by several orders of magnitudes ( [38] [39] [40] ). Although the high rainstorm had significantly (P < 0.05) higher final infiltration rates, these values were lower when compared to Ks from double ring infiltrometers (Table 4). Despite double rings overestimations, the lower than expected steady infiltration rates confirmed that rainfall amount and intensity influenced steady state infiltrability especially when intensity excess steady infiltration rate [41] .

The medium rainstorm had constant initial infiltration rates in the first 10 min from the Addo and Augrabies, and 15 min from the Brandvlei, before declining to significantly similar (P < 0.05) final infiltration rates of 0.38, 0.14 and 0.38 mm・min⁻¹, respectively. Corresponding accumulative infiltration were 22, 15.2 and 22.5 mm, respectively. The Augrabies produced lower infiltration rates under the medium rainstorm, which were also indifferent when compared to the low rainstorm. This result was attributed to the higher surface bulk density (1.71 g・cm⁻³) that supported low porosity and permeability. Compacted or crusted surfaces of 0.1 mm thick were observed to reduce final infiltration rates by more than 10 times [8] . Soils with surface crust of 1 mm thickness had final infiltration rate of 0.34 mm・mm⁻¹ and crust thicker than 2 mm did not exceed 0.16 mm・min⁻¹ [42] .

Note: superscript letters, statistical different means depicted by different letters based on least significant Difference (LSD) mean separation test P ≤ 0.05; SD, standard deviation; CV coefficient of variation.

Note: superscript letters, statistical different means depicted by different letters based on the Duncan Multiple Range Test (DMRT) mean separation test at 95% confident intervals (P < 0.05). Superscripts letters also applicable for accumulative runoff (not shown).

Under the low rainstorm, initial infiltration rates were constant in the first 20, 25 and 35 min from the Addo, Augrabies and Brandvlei, respectively. Correspondingly, final or steady infiltration rates and total infiltration were 0.21, 0.15 and 0.18 mm・min⁻¹ and 13.4, 12.7 and 14 mm, respectively. The longer constant initial infiltration rates showed that the low rainstorm intensity of 0.27 mm・min⁻¹ was close to soil-types infiltration capacity, hence steady infiltration rates were significantly similar (P < 0.05). However, this result was not surprising because as rainstorm decreases the wetting rate and infiltration curve decreases slowly resulting to lower final infiltration rates ( [37] [43] ). Interestingly, the Addo despite a finer texture had a higher final infiltration rate: a phenomenon that can be attributed to mineralogy and distribution of exchangeable cations. The surface horizon had exchangeable cations of calcium (7650 mg・kg⁻¹) and magnesium (1340 mg・kg⁻¹) recognised as good flocculators versus exchangeable sodium (60 mg・kg⁻¹) with high dispersivity. Such a distribution favoured a stable than dispersive surface aggregates, which supported infiltration especially under less disruptive rainstorm intensity. Stern et al. [44] observed that final infiltration rates greater than 0.13 mm・min⁻¹ were associated with stable aggregates while less than 0.08 mm・min⁻¹ characterised dispersive soils. In this study, final infiltration rate was greater than 0.13 mm・min⁻¹ from all soil types suggesting that distribution of exchangeable cation did not favour dispersive infiltration reduction. However, in less dispersive soils, surface crusting and rainfall characteristics controlled final infiltration rates [39] . Prevalence of finer aeolian sand fractions under arid drylands climates favoured surface crust formations in South Africa soils ( [45] [46] ).

Figure 6 shows predicted van Genuchten-Mualem model K(θ) of the Addo, Augrabies and Brandvlei upper surface horizons. Corresponding Ks values determined with double ring infiltrometersis presented in Table 4. Saturated hydraulic conductivity between soil types were significantly different with the least (0.05 mm・min⁻¹) and highest (2.02 mm・min⁻¹) from the Addo and Brandvlei, respectively. Unsaturated hydraulic conductivity of soil types showed greater variation among rainstorms at near saturation. Corresponding K(θ) values at near saturation of the Addo, Augrabies and Brandvleifor high, medium and low rainstorms are 0.66, 0.23 and 0.11 mm・min⁻¹, 0.09, 0.03 and 0.02 mm・min⁻¹, and 0.53, 0.16 and 0.07 mm・min⁻¹, respectively. The result showed that K(θ) function at near saturation increased with rainstorm amount and intensity suggesting volume of hydraulic active pores increases with rainstorm size until rainstorm intensity excess steady infiltration rate ( [35] [37] [43] ). The K(θ) values at near saturation of the Augrabies and Brandvlei under high rainstorm were respective lower by 1.41 and 1.49 mm・min⁻¹ when compared to corresponding Ks values. Such a reduction in near saturation conductivity is explained by the breaking down and slaking of soil surface aggregates by raindrop energy impact, which can reduce Ks exponentially [47] . Nciizah and Wakindiki [47] and Fohree, et al. [48] also observed that physical properties of surface crusts affecting K(θ) during and between rainstorms were always changing. This phenomenon explained the inter-changes of K(θ) functions between high and medium rainstorms from the Addoand, between medium and low rainstorms from the Augrabies and Brandvlei soil forms. Apart from these interchanges, K(θ) under all rainstorms merged at lower water contents suggesting rainstorms affected soil infiltration properties at near saturation water contents.

In addition to soil-types infiltration, Table 5 presented observed and predicted time to runoff, final runoff rate and accumulative runoff. Even though runoff data was not part of the objective function, HYDRUS-1D model generated infiltration-excess runoff using Neumans type system-dependent conditions (Equations (5) and (6)). Figures 7-9 presented a 1:1 line comparing observed and predicted runoff rates and accumulative runoff for the Addo, Augrabies and Brandvlei, respectively. The model predicted poorly (NSE ≤ 0.27) rainstorm runoff rates for all soil types. However, prediction of accumulative runoff was satisfactory with NSE ranging from 0.53 to 0.98. Model prediction was highest and lowest for medium and lower rainstorms, respectively. In all cases, the model overestimated runoff rates and total runoff production, a phenomenon attributed to the exclusion of ponding conditions.

Due to shorter simulation periods (≤56 min), ponding was assumed to be negligible at small plots scale. Presence of dry and dormant vegetation on plots that can influence surface water storage and delay time to runoff [49] were not specified as part of the upper boundary conditions, hence the model runoff overestimation. Nevertheless, spatiality of vegetal cover and surface roughness in-situ can make ponding parameter(s) difficult to determine [21] . Agreement between observed and predicted accumulative runoff was sufficient though to describe soil-type surface runoff properties using optimised parameters. However, this should be done with caution only applicable for the prevailing soil surface condition.

The Brandvlei had longest time to runoff (4.3 to 38 min) for all rainstorms while the Addo and Augrabies had shortest times for the high and lower rainstorms, respectively. Total runoff increased with opportunity time making the Addo and Augrabies to have highest runoff for the respective high (27.5 mm) and lower (2.41 mm) rainstorms. This result collaborated with the higher total fine silt plus clay (47.7%) fraction of the Addo and bulk density (1.76 g・cm⁻³) of the Augrabies; observed earlier in this study as factors that reduced infiltration. Soils with high quartz fraction like in the Augrabies have poor bonding properties to protect aggregates against raindrop impact and hence, are highly dispersive and susceptible to surface crusting [42] . Total clay plus fine silt was lowest (17.7%) from the Brandvlei suggesting clogging of hydraulic pores by fine sediments was too low to affect infiltration a sentiment that was shared by Lado et al. [50] . In addition, excluding course and medium fractions, the Brandvlei had total sand fraction of 76% suggesting it had more uniform particle size distribution a property that discouraged translocation of dispersed fine articles and deposition into voids. Such a property is common among the wind-blown sands of arid and semi-arid regions of South Africa and in the absence of impervious underlying horizon, these soils supported deep infiltration and drainage ( [50] [51] ).

Table 6 presented initial and optimised parameters of the Genucthen-Mualem model for the respective Addo, Augrabies and Brandvlei soil forms at 30 mm and 230mm depths. Inverse parameter optimisation was able to minimise objective function from the Addo, Augrabies and Brandvlei with RMSE not higher than 0.01. Initial and optimised parameters were considerable different among soil types and rainstorms with the exception of θr in the Addo and Brandvlei. The Addo and Bransdvlei were initially described as the least (Ks = 0.05 min⁻¹) and most (Ks = 0.23 mm・min⁻¹) permeable, respectively. However, optimised Ks values described the Addo as the most permeable (Ks; 0.11 to 0.78 mm・min⁻¹) and the Augrabies as least permeable (Ks; 0.2 to 0.52 mm・min⁻¹). This result showed that parameters derived from theoretical pedo-transfer functions were ill posed for describing soil-water dynamic processes in-situ. Soil heterogeneity and occurrence of superficial crusted surface layers and variability in atmospheric-surface boundary conditions are among the common reasons ( [52] [53] [54] ). Nevertheless, parameters estimated from laboratory soil-water retention curves and pedo-transfer functions provided reliable initial parameter estimates foroptimisation of unknown parameters ( [11] [55] ).

Optimised parameters varied considerably for upper and lower surface horizons. The Ks fitted for upper layer was always lower when compared to the lower surface horizon. This result showed that the soil surface was susceptible to compaction and raindrop impact especially under higher rainstorm intensities [33] . Lower Ks values of the upper surface horizon corresponded with lower θs for the Augrabies and Brandvlei soil forms under the high rainstorm in particular. Higher surface bulk density of not less than 1.67 g・cm⁻³ and disruptive power of high intensity raindrop were the reasons. Despite the initially higher α parameters, which represented the coarseness of the Augrabies (0.004) and Brandvlei (0.003), the optimised α values for the former was remarkably lower (0.002). The lowest α parameter depicted the Augrabies as a fine textured soil because of higher bulk density of 1.76 g・cm⁻³, which reduced permeability and porosity for the upper surface horizon in particular. Larger n parameter represented greater pore-size distribution uniformity. The Addo had lowest n parameter (1.674 to 1.890) and were always lower in the upper compared to lower surface horizon. This result corresponded to the lower bulk density (1.52 g・cm⁻³) and higher total fine silt and clay (47.7%). Bonding and cementing properties of clays improved aggregate stability and inter-aggregate porosity [56] ; a phenomenon that supported higher θs parameter for the Addo’s upper horizon especially under the higher intensity rainstorms. Aggregate stability against dispersion in the Addo was also supported by large exchangeable magnesium and calcium compared to exchangeable sodium [57] .

Larger n parameter (2.801 to 3.857) characterised the Brandvlei followed by the Augrabies (2.680 to 2.919). Greater uniformity depicted by larger n values for the Brandvlei collaborated with the 76% total sand fraction excluding course and medium sand fraction. In addition to larger n parameter, larger α parameter (0.007 to 0.14) described the Brandvlei surface horizon suggesting it was a uniformly course textured soil. This description supported the higher infiltration and lower runoff of the Brandvlei from all rainstorm treatment.

Sensitivities of soil water content (θ), infiltration rate (I), accumulative infiltration (Z), runoff rate (Ro_r) and accumulative runoff (Acc. Ro) to 1% change in optimised parameters for the medium rainstorm were presented in Figures 10-12 for the Addo, Augrabies and Brandvlei soil forms, respectively. Similar results were observed under the high and low rainstorms (data not shown).Sensitivities of model output to 1% change in parameters were noticeable at two infiltration stages; firstly, passing of wetting front at 30 mm depth resulting to a sharp rise in θ and secondly, when θ approached near saturation values. Table 7 also showed model output sensitivity to 1% change in hydraulic parameters as inferred from the RMSE. Deviation of RMSE from the optimised value due to 1% change in parameters was limited to θs and Ks parameters had greater influence on model output. Considerable deviation was from the Addo and Brandvlei with the latter higher RMSE suggesting model output showed greater parameter sensitivity.

Sensitivities of soil water content to 1% change in parameters were highly variable among soil types. In the Addo, soil water content sensitivity to all parameters was limited to the first 15 minutes with well-defined peaks at 10 minutes of 0.02 and 0.01 for respective θr and θs after which became constant. Soil water content from the Augrabies showed greater sensitivity to θs and Ks after 10 minutes reaching respective peaks of 0.005 and 0.007 at 15 and 30 minutes, consecutively. Brandvlei soil water contents after 15 minutes showed sensitivity to all with the least being n parameter. Only θs had a well-defined peak at 18 min of 0.006 while α, θr and Ks parameters increased with time reaching respective peaks of 0.009, 0.008 and 0.007, before assuming nearly constant trends. Sensitivity of soil water content to Ks appeared to increase with infiltration time especially for the Augrabies and Brandvlei, soils forms, and both clay content of less than 20% in all their horizons.

Sensitivities of infiltration rates to 1% change of parameters was characterised by defined peaks after detection of the wetting front with some parameters increasing sensitivity with time. In the Addo, except n parameter, parameters had distinct peaks within 12 to 20 minutes after which all parameter sensitivity to infiltration rate were diffused to nearly constant rates of less than 0.004. Soil water content displayed a different parameter sensitivity for the Augrabies and Brandvlei. Infiltration rate showed greater sensitivity to θs and Ks that increased after the 25 min time mark to reach sensitivities of 0.18 and 0.23, respectively. From the Brandvlei, all parameters had definite peaks at 18 minutes with the α, θr and Ks assuming sensitivities that increased with time after the 20 min time mark suggesting that increasing infiltration time measurement would have improved these parameters information. However, research has showed that sensitivity of infiltration rate to hydraulic parameters was limited to the period when of detecting wetting front to the time when gravity began to influence infiltration [58] . This conditions appeared to apply in the Addo which was least affected by surface compaction and raindrop impact. However, in the Augrabies and Brandvlei sensitivity of infiltration rate to parameters extended over longer period especially for θs and Ks. Clogging of pores and densification due to raindrop impact on soils with higher (≥72%) sand fraction was the reason. Parameter sensitivity showed by runoff rates was similar to that of infiltration rates for the respective soil types. This observation suggested that estimated soil hydraulic parameters from prescribed near-surface time-variable soil-moisture and atmospheric boundary conditions with surface-runoff represented the partitioning of rainwater infiltration and runoff fluxes.

Sensitivities of accumulative infiltration from soil types increased with time following rapid increase in soil water content. For the Addo sensitivities increased after 12 min from all parameters reaching 0.189 for α parameter by the end of the infiltration. Despite Ks being the least sensitive from the Addo, it was the most sensitive along with θs in the Augrabies increasing after the 30 min time mark to reach 0.447 the highest realised from this study. This trend would have continued further with time suggesting that increasing duration of the infiltration experiment would have improved parameter identification especially θs and Ks parameters. Simunek and van Genuchten [28] shared the same sentiment and indicated that benefit of information gained by extending duration of the infiltration experiment was limited to the occurrence of steady state conditions. In the Brandvlei sensitivity of accumulative infiltration to θs and Ks had well-defined peaks of 0.26 at the 8 min time mark. However, after the 25 min mark sensitivity to α and θr parameters increased with time a phenomenon that collaborated with the notion that measurements taken further with time would improve information about unknown parameters [28] . Parameter sensitivities of accumulative runoff showed similar trends to that of accumulative infiltration. This was not surprising given soil hydraulic parameters that encouraged infiltration had opposite effect on runoff.