Comparing Transient and Steady-State Analysis of Single-Ring Infiltrometer Data for an Abandoned Field Affected by Fire in Eastern Spain

This study aimed at determining the field-saturated soil hydraulic conductivity, Kfs, of an unmanaged field affected by fire by means of single-ring infiltrometer runs and the use of transient and steady-state data analysis procedures. Sampling and measurements were carried out in 2012 and 2017 in a fire-affected field (burnt site) and in a neighboring non-affected site (control site). The predictive potential of different data analysis procedures (i.e., transient and steady-state) to yield proper Kfs estimates was investigated. In particular, the transient WU1 method and the BB, WU2 and OPD methods were compared. The cumulative linearization (CL) method was used to apply the WU1 method. Values of Kfs ranging from 0.87 to 4.21 mm·h−1 were obtained, depending on the considered data analysis method. The WU1 method did not yield significantly different Kfs estimates between the sampled sites throughout the five-year period, due to the generally poor performance of the CL method, which spoiled the soil hydraulic characterization. In particular, good fits were only obtained in 23% of the cases. The BB, WU2 and the OPD methods, with a characterization based exclusively on a stabilized infiltration process, yielded an appreciably lower variability of the Kfs data as compared with the WU1 method. It was concluded that steady-state methods were more appropriate for detecting slight changes of Kfs in post-fire soil hydraulic characterizations. Our results showed a certain degree of soil degradation at the burnt site with an immediate reduction of the soil organic matter and a progressive increase of the soil bulk density during the five years following the fire. This general impoverishment resulted in a slight but significant decrease in the field-saturated soil hydraulic conductivity. Water 2018, 10, 514; doi:10.3390/w10040514 www.mdpi.com/journal/water Water 2018, 10, 514 2 of 17


Introduction
Assessing the effects of fire on soil hydraulic properties in the Mediterranean area is crucial to evaluate the role of fire in land degradation and erosion processes.Among the soil hydraulic properties, field-saturated hydraulic conductivity, K fs , exerts a key role in the partitioning of rainfall into runoff and infiltration [1].Therefore, estimates of K fs are essential for evaluating the hydrological response of fire-affected soils [2].Soil properties are highly affected by fires due to the removal of the aboveground vegetation, the heat impact on the soil, the removal of the organic matter, the ash cover and the changes induced by rainfall on the soil surface [3][4][5].Most of the research carried out on fire-affected land has paid attention to the "window of disturbance", which is the period during which the soil losses are higher than before the fire and which lasts for a few years [6][7][8].In order to understand the evolution of soil erosion after forest fires it is necessary to monitor fire-affected sites over a long period of time, in order to enable the assessment of the period affected by the window of disturbance [9].Moreover, it is also possible to carry out measurements and experiments in areas with a different fire history.This gives information about the temporal changes in soil erosion after fire.
For this purpose, speed and ease of field procedures for soil hydraulic characterization are essential [10,11].The single-ring infiltrometer technique [12,13] is a routinely used method for measuring K fs in the field (e.g., [14][15][16][17]).With a single-ring infiltrometer, a constant or falling-head infiltration process has to be established.In the field, a constant-head single-ring infiltrometer often needs level-control setups or expensive devices with monitoring equipment containing proprietary technology with prohibitive costs [18][19][20].Therefore, a falling-head experiment is preferable since it minimizes the complexity of implementation, characterizing an area of interest with minimal experimental efforts [11,21].Recently, Nimmo et al. [11] developed the so-called bottomless bucket, named BB method hereafter, which uses a portable, falling-head, small-diameter single-ring infiltrometer.These authors adapted the Reynolds and Elrick (1990) formula to be applied instantaneously during a falling-head test.However, only few comparisons of BB estimates with other procedures can be found in the literature (e.g., [2,22]), notwithstanding that this method of soil hydraulic characterization is of noticeable practical interest.In general, establishing the reliability of new methods is not a simple task, also due to the high K fs variability both in space and time [23,24].Moreover, many other sources of variability may also arise when comparing different field measurement techniques, such as sample size [25], ring diameter [26], source shape [27] and field sampling procedure [28,29].One could expect that considering laboratory measurements as targeted values would help to check the reliability of field data.However, this approach may be questioned due to the difficulty of representing the soil heterogeneity encountered in the field in small-scale laboratory samples (e.g., [24,[30][31][32][33]).An alternative approach, considering different calculation techniques applied to the same dataset, is expected to facilitate the interpretation rising from the comparison [24].Different methods of calculating K fs from single-ring data were developed over time (e.g., [10][11][12]21,[34][35][36][37]).Among them, the one ponding depth (OPD) calculation approach of Reynolds and Elrick [12] and Method 2 by Wu et al. [38] (WU2) have in common with the BB method that all these approaches analyze steady-state single-ring infiltrometer data, thus considering the same part of the infiltration process [24].Moreover, they all require an estimate of the sorptive number (or macroscopic capillary length parameter), α* (L −1 ), expressing the relative importance of gravity and capillary forces during a ponding infiltration process [1].
The general objective of this work was to determine the K fs of an abandoned unmanaged field affected by fire by means of single-ring infiltrometer runs and the use of transient and steady-state data analysis procedures.Sampling and measurements were carried out in 2012 and 2017 in a fire-affected (on 15 July) field (burnt site) and in a neighboring non-affected site (control site).The focus was put on the predictive potential of different data analysis procedures (i.e., transient and steady-state) to yield proper K fs estimates and to detect the effect of fire on saturated hydraulic conductivity.More specifically, we chose to test the bottomless bucket method by comparing the field-saturated soil hydraulic conductivity estimates with those obtained by other well-tested methods.

Steady-State Analysis of Single-Ring Infiltrometer Data
The bottomless bucket method of Nimmo et al. [11] considers the analysis developed by Reynolds and Elrick [12] of three-dimensional (3D), steady, ponded infiltration below a finite insertion depth, accounting for the hydrostatic pressure of the ponded water, gravity and capillarity of the unsaturated soil [1].These authors adapted Reynolds and Elrick's (1990) formula to be applied instantaneously during a falling-head test.With this method, K fs (L•T −1 ) is calculated by the following equation: where H 0 (L) is the initially established ponded depth of water, H(t) (L) is the ponded depth of water at time t, λ c (L) is the macroscopic capillary length of the soil [39], and the so-called ring installation scaling length, L G (L), is calculated as follow: where r (L) is the radius of the disk source and d (L) is the ring insertion depth in the soil.The one ponding depth calculation approach by Reynolds and Elrick [12] makes use of the steady infiltrating flux, Q s (L 3 •T −1 ), which is estimated from the flow rate versus time plot.The following relationship is used to obtain K fs : where γ G is a shape factor that can be estimated as follows: Method 2 by Wu et al. [38] assumes steady-state infiltration.With this method, K fs is calculated by the following equation: where i s (L•T −1 ) is the slope of the straight line fitted to the data describing steady-state conditions on the cumulative infiltration, I (L), versus time, t (T), relation, a is a dimensionless constant equal to 0.9084 [36], and f is a correction factor that depends on soil initial and boundary conditions and ring geometry: where the G* (L) term is equal to:

Transient Analysis of Single-Ring Infiltrometer Data
For comparative purposes, Method 1 by Wu et al. [38] (WU1) was also applied to estimate K fs .In addition, this method offered the possibility to check the assumed α* value by directly estimating this parameter from a single-ring test and a measurement of the soil water content.This method is based on the assumption that the cumulative infiltration can be described by a relation formally identical to the two-term infiltration model by Philip [40]: where C 1 (L•T −0.5 ) and C 2 (L•T −1 ) are infiltration coefficients.With method 1, K fs is calculated by the following equation: where ∆θ (L 3 •L −3 ) is the difference between the saturated volumetric soil water content, θ s (L 3 •L −3 ), and the initial one, θ i (L 3 •L −3 ).The λ c (L) and T c (T) terms have the following expressions: where H (L) is the established ponding depth of water, G* (L) is defined by Equation ( 7), a and b are dimensionless constants respectively equal to 0.9084 and 0.1682 [36], and the C (L) term is equal to: An estimate of the sorptive number, α* (L −1 ), may also be obtained taking into account that: For a given infiltration run we determined the C 1 and C 2 coefficients according to the fitting method referred to as cumulative linearization (CL, [41]).With the CL method, Equation ( 8) is linearized by dividing both sides by √ t , giving: Then, the C 1 and C 2 coefficients are determined respectively as the intercept and the slope of the I/ √ t vs. √ t plot.

Soil Sampling
We selected two study sites on abandoned fields within the "Serra de Mariola Natural Park" in Alcoi, Eastern Spain.The coordinates of the study area are 38 • 43 32.15"N, 0 • 28 54.70" W. Sampling and measurements were carried out in November 2012 and five years later, in November 2017, in a fire-affected (on 15 July) field (burnt site) and in a neighboring non-affected site (control site).The study area is characterised by typical Mediterranean climatic condition with drought from June till September, with high temperatures (25 • C in average), and mild spring, autumn and winter seasons.The mean annual rainfall at the nearby Cocentaina meteorological station is 480 mm, and during the study period the mean annual rainfall was 418 mm.The wettest year was 2012 with 576 mm and the driest 2014 with 209 mm.October used to be the month with the largest rainfall amount, although during the study period the wettest month was December 2015 with 295 mm, and the driest months were May 2017 and July 2014 with 0 mm of rainfall.Mean monthly rainfall data are reported in Figure 1.The mean monthly temperature was 16.5 • C, with values in July of 28.3 • C and January with 7.0 • C. The vegetation cover was dominated by a scrubland developed after the abandonment that took place in 1950s.The main plant species were Rosmarinus officinalis, Thymus vulgaris, and Ulex parviflorus, and five years after the fire the vegetation was dominated by Cistus albidus, although Rosmarinus officinalis and Ulex parviflorus were also present.The parent material is marls and the soils developed on this south-facing slope are very breakable.The soil is classified as a Typic Xerorthent [42].According to the USDA standards, the three fractions, i.e., clay (0-2 µm), silt (2-50 µm) and sand (50-2000 µm), averaged for the two sites were 14.5%, 57.5% and 29.1%, respectively (corresponding standard deviations = 6.6, 4.3 and 5.0, respectively), and the soil of the studied area was classified as silt loam.

Single-Ring Infiltrometer
A total of forty infiltration runs (10 runs × 2 plots × 2 sampling campaigns) of the bottomless bucket type were carried out [11].A 100-mm inner diameter ring was inserted into the soil to a depth of d = 50 mm.At the start of the experiments, water was poured into the ring to establish an initial ponding depth H 0 = 50 mm.In this investigation, the possible occurrence of soil water repellency was not considered, given that this phenomenon is uncommon for scrub terrain on calcareous soils in the region, even after fire [50,51].Therefore, the use of ponding experiments, which are known to overwhelm positive soil-water-entry values induced by water repellency (e.g., [2,[52][53][54]), was not expected to induce bias.The rate of drop of the water level was monitored by measuring the ponding depth at prescribed time intervals, H(t).After each measurement, another volume of water was poured immediately into the ring to re-establish a ponded depth of water of 50 mm.During the first minutes, small time intervals were used.The time interval was increased up to 5 min in the late phase of the experiment.Steady-state conditions were attained within 60 min of all experiments.This procedure differs from the one proposed by Nimmo et al. [11], since these authors logged the time needed for the water to reach a minimum fixed H(t) value, thus pouring in known water volumes to re-establish the initial ponding depth.The obvious advantage to consider prescribed time intervals instead of a preselected water amount, is that monitoring time is significantly easier than monitoring water levels.Moreover, in their investigation Nimmo et al. [11] stated that the "modification of these procedures is likely to be necessary for different soils and conditions".In our case, the sampled soils were characterized by low permeability.In such conditions, logging the time needed for the water to reach a minimum fixed H(t) value, such as the Nimmo's procedure, would imply obtaining less data points for the same duration of the experiment, or alternatively it would imply considerably extending the experiment duration to have a similar number of data points and, thus, to properly evaluate the steady-state phase of the infiltration process.Therefore, the applied criterion also allowed us to increase our confidence in the sampled data.A total of forty experimental cumulative infiltrations versus time were then deduced.Cumulative infiltration data were firstly analyzed according to the criterion suggested by Bagarello et al. [55].Specifically, apparent steady-state infiltration rates were estimated by linear regression analysis of the last three (I, t) data points.Then, the equilibration time, t s (min), namely the duration of the transient phase of the infiltration process, was determined as the first value for which: where I reg is estimated from the regression analysis of the I versus t plot, and E is a criterion to check linearity.Equation ( 15) is applied from the start of the experiment and progressively excludes the first data points until E ≤ 2 [1,24].An illustrative example of the t s estimation is reported in Figure 2.

Data Analysis and Calculations
The BB procedure was applied to determine K fs (K fs-BB ) by Equation (1), assuming λ c = 1/α* = 0.25 m.A value of α* = 4 m −1 for unstructured fine-textured soils (strong soil capillarity category) was selected from the soil texture-structure categories defined by Elrick and Reynolds [56].
The last determinations of K fs-BB , representative of steady-state conditions, were averaged to obtain an estimate of K fs-BB for a given test, as suggested by Angulo-Jaramillo et al. [1].Equations ( 3) and ( 5) were applied to estimate K fs data, which were denoted with the symbols K fs-WU2 and K fs-OPD , for WU2 and OPD, respectively.It has to be noted that these latter methods are theoretically usable for a constant ponded depth of water on the infiltration surface.
However, in our case, the variation of the water level during the late-phase of the infiltration process never exceeded 1-2 mm.Therefore, the ponded depth at the late-phase of the run was assumed to be practically constant.
For comparative purposes, the transient WU1 method was also applied to estimate K fs and α* by Equations ( 9) and ( 13), respectively.These estimates were denoted with the symbols K fs-WU1-CL and α* CL .We first obtained the C 1 and C 2 values with the CL method by fitting Equation (14).The adequacy of the fitting procedure was evaluated by checking both the linearity of the data and the relative error defined as: where are the experimental data and x i are the corresponding values deduced by fitting the functional relationship.According to the criterion proposed by Lassabatere et al. [10], values of Er < 5% were assumed to be indicative of a satisfactory fitting ability.
The statistical frequency distributions of the K fs and α* data were assumed to be lognormal, as is common for these variables (e.g., [57,58]).Therefore, geometric means and associated coefficients of variation, CV, were calculated using the appropriate "log-normal equations" [59].The other variables considered in this investigation were summarized by calculating the arithmetic mean and the associated CV, since the characterization of an area of interest is generally based on arithmetic averages of individual determinations [60].To compare mean values, untransformed and natural log-transformed data were used for the normal and the natural log-normal distributed variables, respectively.Different K fs datasets were also compared in terms of factors of difference (FoD), calculated as the ratio between the maximum and minimum of two K fs values estimated by different calculation techniques from a run [24].Following Elrick and Reynolds [56], FoD values not exceeding a factor of two or three were considered indicative of similar estimates.

Physical Properties
The results of the physical analysis were represented using box plot graphics (Figure 3).A major effect of fire was a consistent reduction of soil organic matter in the burnt site.SOM was measured to decrease by 22% four months after the fire, and 30% after five years.This reduction was in line with previous investigations (e.g., [3,[61][62][63]).As a consequence, dryer conditions persisted in the burnt site, due to the known effect of a reduction of soil organic matter on soil water retention [64].Specifically, the initial soil water content differed appreciably among the control and burnt sites, with average θ i values equal to 0.141 and 0.137 m 3 •m −3 at the control site and 0.096 and 0.087 m 3 •m -3 at the burnt site, for the 2012 and 2017 sampling campaigns, respectively.No significant differences in terms of soil dry bulk density were detected between the control and burnt sites four months after the fire.On the contrary, our results showed a significant increase of the bulk density five years after the fire, due probably to a progressive collapse of aggregates [9], highlighting a certain degree of soil degradation at the burnt site.

Performance of the Cumulative Linearization (CL) Method
The application of the transient WU1 method to determine K fs and α* required the estimation of the C 1 and C 2 coefficients.We obtained the C 1 and C 2 values with the CL fitting method.This method showed general poor performance both in terms of the linearity of the data and the relative error.The ∆I/∆ √ t vs. √ t plots did not show the expected linear relationship between the considered variables for the entire infiltration run.Therefore, we progressively excluded the first data points selecting the C 1 and C 2 values when the following criteria were fulfilled: (i) positive values of the C 2 parameter (yielding physically plausible K fs estimates i.e., K fs > 0); and (ii) a linear relationship between the considered variables.An example of the applied selection procedure for the infiltration coefficients is depicted in Figure 4.The example refers to the case of an infiltration run carried out at the burnt site in 2017.The exclusion of no or one data point yielded negative C 2 values (Figure 4a,b).The exclusion of two data points yielded a positive C 2 value, but a value of Er = 6.6% was obtained due to the departure of the first point from the general linear behaviour (Figure 4c).In this case, the C 2 coefficient should make it possible to obtain an apparently physically plausible K fs estimate, i.e., K fs > 0. However, given that the dataset was not linear, Equation ( 8) was considered inappropriate and hence the fitted parameters were considered as meaningless from a physical point of view [65].
Finally, the C 1 and C 2 coefficients could be properly estimated by excluding the first three data points (Figure 4d).Other investigations also suggested removing the fitting procedures the early stage of the infiltration process when a perturbation occurs (e.g., [21,38,46,66]).In contrast, the last points may be removed since the CL method mostly applies to the transient state [65,67].Only one test never yielded positive C 2 values whatever the number of data points excluded.Good fits, i.e., fitting yielding Er values lower than 5% [10], were only obtained in 23% of the cases (Figure 5).

Estimation of K fs Data with the WU1 Method
Table 1 summarizes the field-saturated soil hydraulic conductivity obtained with the WU1 method.The average K fs-WU1-CL values ranged from 0.87 to 1.50 mm•h −1 .All average K fs values were lower than the expected saturated conductivity on the basis of the soil textural characteristics alone, e.g., K s = 4.5 mm•h −1 for a silt loam soil according to Carsel and Parrish [68].This suggested that soil macroporosity in the control and burnt site did not influence the results [28].All differences between the average K fs values of different sites and sampling campaigns were not statistically significant according to the Tukey honestly significant difference test (p < 0.05).A high variability of K fs was detected in most cases, with coefficient of variations (CVs) ranging from 100.7% to 373.1% (Table 1).
The average α* values ranged from 2.42 to 6.45 m −1 (Table 2).We never detected extremely unreliable α* values, i.e., lower than 0.1 m −1 and higher than 1000 m −1 [56,69].All differences between the average α* CL values of different sites and sampling campaigns were not statistically significant according to the Tukey honestly significant difference test (p < 0.05).Considering all the infiltration measurements, the average α* CL value was equal to 3.89 m -1 .This value was in line with the one suggested by Elrick and Reynolds [56] for strong capillarity soils (α* = 4 m −1 ) in their soil texture-structure categories.All differences between two mean values were not statistically significant according to the Tukey honestly significant difference test (p < 0.05).

Estimation of K fs Data with Steady-State Methods
We discriminated the transient and steady-state phase of the infiltration process according to the criterion suggested by Bagarello et al. [55] (Figure 2).This procedure allowed us to consider, for a given run, exactly the same final part of the curve for all the three applied methods.After a duration of 60 min, the total infiltrated depth was, on average, 64 mm.The equilibration time, t s (min), namely the duration of the transient phase of the infiltration process, was reached, on average, after 33 min, with a mean volume of infiltrated water I(t s ) = 56 mm.All the experiments exhibited a sufficiently long steady-state phase ranging from 10 to 45 min (Table 3).Table 4 summarizes the field-saturated soil hydraulic conductivity, K fs , obtained with the BB, OPD and WU2 methods.The average K fs-BB , K fs-OPD and K fs-WU2 values ranged from 2.0 to 3.96, from 2.03 to 4.21 and from 1.92 to 3.91 mm•h −1 , respectively.The applied methods yielded similar information, i.e., the differences between average K fs values of the control site were never statistically significant at p < 0.05.On the contrary, for the burnt site, the field campaign carried out in 2017 yielded, in all cases, two times lower K fs values than the previous campaign, and the differences between sampling campaigns were always statistically significant at p < 0.05 (Table 4).Figure 6 depicts the box plots of the factor of difference values, i.e., a "point-by-point" comparison between all K fs datasets.FoD values never exceeded 1.3 between steady-state methods.Therefore, the three steady-state methods considered in this investigation yielded similar results, supporting the soundness of the BB analysis procedure.On the contrary, appreciably higher FoD values were obtained with the WU1 method (Figure 6).In this case, the high variability of the data affected K fs comparisons between sites and sampling campaigns (Table 1).For a given method (BB, WU2 and OPD), means that do not share a letter are significantly different according to the Tukey honestly significant difference test (p < 0.05).
Figure Box plots of the factor of difference, FoD, between the field-saturated hydraulic conductivity, K fs (mm•h −1 ), data sets obtained by the BB, WU2, and OPD methods and the WU1 method with the cumulative linearization (CL) fitting method.The median values are also reported.

Discussion
Under the specific conditions encountered in this investigation, the transient analysis of single-ring data revealed that alternative procedures should be applied to properly the analyze infiltration data, in order to avoid a misestimation of the soil hydraulic properties [66].Specifically, the main reason for choosing other approaches was that invalid early data were detected in most cases with the CL method, and hence they were excluded from the analysis.The need to exclude the first data points when fitting the data was likely due to the highly sorptive nature of the sampled soils.Specifically, the porous media exhibited relatively low hydraulic conductivity compared to their sorptive capacity [37].Indeed, cumulative infiltrations exhibited a marked concave part corresponding to the transient state and a linear part at the end of the curves related to the steady state [70].This condition also made it difficult to estimate C 1 values due to the importance of the lateral capillary flow [65].As a result, a reliable estimation of K fs was unlikely.In other words, the generally poor performance of the fitting method spoiled the soil hydraulic characterization, affecting the general quality of the K fs estimates and, thus, the comparison between the sampled sites and field campaigns.Indeed, this method relies on an infiltration model, i.e., Equation (8), that does not account for such a time evolution of soil properties between the early-and late-time infiltration stages responsible for the observed strong concavity of cumulative curves [71].Moreover, it has to be remarked that the transient portion of the infiltration curves is frequently not usable to estimate steady-state infiltration rates, since it could be affected by several factors, including soil permeability, antecedent soil water content, ring radius and insertion depth (e.g., [1,13,21]).Although the poor performance of the CL method likely affected the reliability of the WU1 estimates, by increasing parameter variability, it has to be noted that the WU1 method allowed at least a check of the α* value, which was selected a priori from the soil texture-structure categories to apply steady-state methods.
All steady-state methods revealed a slight but statistically significant K fs decrease five years after the fire.These methods, with a characterization based exclusively on a stabilized infiltration process, yielded an appreciably lower variability of K fs data compared to the WU1 method (Table 1).Steady-state methods were expected to give less variable K fs estimates when compared to WU1, also as a consequence of the use of a fixed α* value for the whole field, whereas variations of this parameter exist in the field depending on the texture and structure [1].On the other hand, this assumption substantially facilitated the hydraulic characterization, yielding at the same time a sufficient level of accuracy for determining K fs (e.g., [11,15,38]).
The considered soil properties unanimously highlighted the deterioration of the soil's physical quality after the fire.The results of this study suggested that the soil was not completely recovered five years after fire, and the negative effects resulting from the vegetation burning and soil organic matter removal have not yet been mitigated.One would expect that the degraded soil, i.e., with lower organic matter and higher bulk density, could be prone to runoff and erosion processes than the unburned soil [72].However, despite common perceptions, Mediterranean vegetation adapts to fire and plant recolonization in burnt areas relatively quickly (e.g., [3,73,74]).According to many authors, vegetation recovering promptly reduces post-fire runoff and soil erosion rates (e.g., [75,76]).For instance, Cerdà and Doerr [9] observed, under Mediterranean environmental conditions, a fast recovery (2-4 years) of the terrain to pre-fire erosion rates.In our investigation, vegetation recovery, reaching 70% in 2017, could have had an effective role in preventing soil erosion.In other words, the prompt recovery of the vegetation cover may have mitigated the impacts of the worsening soil quality on erosion rates.In the future, erosion-focused studies may support the above hypothesis, increasing our understanding of the effects of soil impoverishment on erosion processes at the burnt sites.

Summary and Conclusions
In this study we analyzed changes in physical and hydrological soil properties few months and five years after a fire in a semi-arid environment in Eastern Spain.With this aim, we sampled both a burned and an unburned site and compared transient and steady-state analysis of single-ring infiltrometer data.The bottomless bucket method of Nimmo et al. [11] was selected in conjunction with other well-tested methods to estimate the field-saturated soil hydraulic conductivity.Any of the tested infiltration techniques appeared usable to obtain the order of magnitude of K fs at the field sites.However, with the WU1 method, the variability in K fs made it difficult to draw conclusions regarding the changes in the fire-affected soil.The choice of the method of soil hydraulic characterization led to contrasting conclusions, thus highlighting the need to choose the appropriate techniques.All the applied steady-state methods appeared more appropriate to detect and quantify slight changes in K fs , whereas WU1 allowed at least a check of the selected α* value.Our results showed a certain degree of soil degradation at the burnt site with an immediate reduction of the soil organic matter and a progressive increase of the soil bulk density during the five years following the fire.This general impoverishment resulted in a slight but significant decrease of the field-saturated soil hydraulic conductivity.A main implication of these results is the importance of long-term investigations of fire effects, since shorter-term studies may not always be sufficient for detecting and characterizing changes to the hydrological processes caused by a fire.This investigation also yielded encouraging signs on the applicability of the bottomless bucket method for a plausible estimation of K fs .The comparison with other steady-state methods and the similarity of the results support this assessment.

Figure 1 .
Figure 1.Mean monthly rainfall data recorded at the Cocentaina meteorological station during the study period (2012-2017).

Figure 2 .
Figure 2. Procedure for estimating equilibration time, t s (min), and infiltrated depth at the equilibration time, I(t s ) (mm), from cumulative infiltrations.Case of an infiltration run carried out at the burnt site in 2012.

Figure 4 .
Figure 4. Examples of the estimation of the C 1 (mm•h −0.5 ) and C 2 (mm•h −1 ) parameters by the cumulative linearization (CL) approach excluding a different number of data points of an infiltration run carried out at the burnt site in 2017.The values of the ratio between the cumulative infiltration, I (mm), and the square root of time, t (h), are plotted against the square root of t.(a) Exclusion of zero data points: C 2 < 0. (b) Exclusion of one data point: Lower Er value (3.0%) but C 2 < 0. (c) Exclusion of two data points: C 2 > 0 but Er = 6.6%.(d) Exclusion of three data points: C 2 > 0 and lowest Er value (1.8%; selected case).

Figure 5 .
Figure 5. Cumulative frequency distribution of the relative errors, Er (%), of the fitting of the functional relationship (i.e., Equation (14)) for the CL method to the experimental data.Er values not exceeding 5% denote a satisfactory fitting ability of the infiltration model to the data[10].

Table 1 .
Summary of the field-saturated hydraulic conductivity, K fs (mm•h −1 ), values obtained by the WU1 method for each sampling campaign and site.All differences between two mean values were not statistically significant according to the Tukey honestly significant difference test (p < 0.05).

Table 2 .
Summary of the α* CL (m −1 ) values obtained by the WU1 method for each sampling campaign and site.

Table 3 .
Summary of the time, t s (min), and infiltrated depth at the equilibration time, I(t s ) (mm).Sample size, N = 10 for each site and sampling campaign.

Table 4 .
Summary of the field-saturated hydraulic conductivity, K fs (mm•h −1 ), data sets obtained by the BB, WU2, and OPD methods.Sample size, N = 10 for each site and sampling campaign.