Effects of hysteresis, rainfall dynamics, and temporal resolution of rainfall input data in solute transport modelling in uncropped soil

ABSTRACT

Numerical simulations were carried out using the HYDRUS 1D model for three different types of uncropped soils. Input data were observed of rainfall during a 15-year period at three sites in Sweden. Simulations were run with and without consideration of hysteresis. Three different rainfall input time steps were used: 0.5, 4, and 24 h. Solute transport was evaluated using the centre of mass (z_COM) of breakthrough curves (BTCs) and largest depth where a pre-defined limit concentration was exceeded (z_LC). Results showed that hysteretic flow was slower as compared to the non-hysteretic case. Results also showed that z_COM generally had a positive correlation with the number of high-intensity rainfalls and that the correlations were higher for the non-hysteretic case. The results show that it is important to use a sufficiently short rainfall input time step and an accurate description of the soil hysteresis when assessing the effects of a future higher-intensive rainfall climate with longer dry periods.

Editor D. Koutsoyiannis; Associate editor D. Yang

KEYWORDS:

• unsaturated zone
• solute transport
• HYDRUS
• hysteresis
• rainfall dynamics
• climate change

1 Introduction

Accurate prediction of solute concentration profiles and maximum solute transport depths are key parameters in protecting groundwater resources. Detailed numerical simulation models are the most important tools in this context. Usually, these models are based on the Richards equation describing water flow and the convection dispersion equation describing solute transport. Soil heterogeneity, hysteresis and macropore flow are important factors affecting field-scale flow of conservative solutes. Natural heterogeneity of soil properties, e.g. porosity and soil hydraulic characteristics, have been shown to lead to slower transport rates as compared to homogeneous soil (Russo et al. 1989). Inclusion of soil water hysteresis also leads to a slower water and solute transport (Russo et al. 1989, Elmaloglou and Diamantopoulos 2008). Occurrence of active macropores, such as cracks, root channels, and worm holes, on the other hand, leads to deep and fast water and solute transport (Beven and Germann 1982, 2013). Solute transport in macropores is normally triggered by high water content (Roth et al. 1991, Pot et al. 2005). A number of studies have shown that short-term high-intensity rainfall events have a significant impact on macropore transport (e.g. Bicki and Guo 1991, Jarvis 2007, McGrath et al. 2007, Lewan et al. 2009, Mohammadi and Vanclooster 2011; McGrath et al. 2010b).

The infiltration from rainfall drives the displacement of solutes in the unsaturated zone. Until recently, there have been remarkably few studies on the effect of rainfall dynamics on solute transport. Some studies have compared solute transport fluxes for steady-state and transient irrigation regimes with the same time-averaged flux. Sharma and Taniguchi (1991) conducted a series of steady-state and transient solute transport experiments in small disturbed soil columns. They showed that the concentration peak moved faster when water application was steady-state rather than transient. They concluded that the effect was due to soil water hysteresis. Jones and Watson (1987) came to the same conclusion after comparing numerical simulations of solute transport including and excluding the effects of hysteresis. Russo et al. (1989) performed several numerical simulations of transient solute transport and compared the results with a steady-state model. They included the effects of heterogeneity, hysteresis and immobile water in their model simulations. These three phenomena, in combination with transient flow, resulted in a retardation of the modelled solute transport velocity as compared to the homogeneous and non-hysteretic steady-state model.

Persson and Berndtsson (1999) conducted a series of column experiments with transient flows of different irrigation frequencies but with the same time-averaged flux. They concluded that a more even temporal distribution of the infiltration leads to faster solute flow displaying lower dispersion. In column experiments using two different soil types with both steady-state and transient irrigation, Vanderborght et al. (2000) showed that solute transport was faster and displayed lower apparent dispersion for the steady-state irrigation. The differences between the two irrigation regimes were larger in more fine-textured soil containing macropores. Malone et al. (2004) studied herbicide leaching under two types of rainfall forcing: constant and variable intensity, with the same total rainfall depth. They found that the variable intensity rainfall lead to an increased leaching which they explained by increased macropore flow. McGrath et al. (2010b) studied bromide and herbicide leaching in unvegetated soil columns under forcing of natural rainfall. They found that water and bromide transport was better explained by a fortnightly or monthly water balance, whereas herbicide leaching was better predicted by considering single storm events with a total volume of 19 mm or more. McGrath et al. (2010a) came to a similar conclusion: heavy rainfall controls adsorbing chemical transport but non-adsorbing chemicals are mainly transported using matrix flow. Graham and Lin (2011) studied preferential water flow in a hill slope during 175 individual rainfall events. They concluded that events that caused widespread preferential flow in general had a long duration, high intensity and a large total volume.

Transient irrigation used in many of the above-mentioned studies is typically regular and periodic. Natural rainfall, however, displays a high degree of variability and it is not clear whether results from irrigation experiments can be used in rainfall infiltration studies. During recent years this research area has gained much interest. Global circulation models predict a future change in the rainfall dynamics for many regions of the world with resulting higher maximum rainfall intensities, longer drought periods between rainfall events, and a higher annual rainfall amount (IPCC 2007, Olsson and Foster 2013). There are only a few published studies that have tried to evaluate the change in solute transport or soil moisture distribution for future rainfall climates (Arheimer et al. 2005, Gu and Riley 2010, Stuart et al. 2011, Thomey et al. 2011). Based on both numerical and experimental results, Knapp et al. (2008) concluded that future higher-intensity rainfalls separated with longer dry periods would lead to a higher temporal variability of soil moisture in the topsoil. Beier et al. (2012) pointed out the lack of understanding of how ecosystems would respond to a future changed rainfall climate and suggested recommendations for precipitation manipulation experiments. Since terrestrial ecosystems are largely based on the interaction between water, soil and plant roots, the understanding of how water transport and distribution depends on the rainfall variability must be the first step of such an analysis. The difference between the rainfall climates of today and future scenarios, however, is still small compared to the inter-annual variability of today’s rainfall climate. Therefore, it is reasonable to first resolve the linkage between solute transport and rainfall variability of today before assessing the future scenarios. The positive correlation between high-intensity rainfall and macropore flow is fairly clear; however, there is limited knowledge of how a changing rainfall climate affects matrix flow. Undoubtedly, the preferential flow is important, especially for deep and fast solute transport in close connection to heavy rainfall in many soils. Among others, Jarvis et al. (2012) and Koestel and Jorda (2014) tried to find different factors controlling the susceptibility of preferential flow. They found that many soils exhibit preferential flow, but in some soils, especially those with a low clay content, the main part of the solute transport is still taking place within the soil matrix.

In view of the above, the objectives of the present study were to investigate the effects of hysteresis, rainfall dynamics, and temporal resolution of rainfall input data on transport of non-adsorbing solutes in uncropped soil. Both rainfall dynamics and the input time step are closely related to each other and we believe that both must be studied simultaneously to achieve useful results. Previous studies on relationships between rainfall and solute transport have mainly focused on macropore flow. In this study we instead focused on matrix flow. Numerical simulations were made using the one-dimensional (1D), deterministic HYDRUS model with observed high-resolution rainfall from three locations in Sweden as input. A correlation analysis between solute transport properties and rainfall dynamics was made to find the most important variability parameters driving rainfall on unsaturated solute transport.

2 Materials and methods

2.1 Rainfall and evapotranspiration data

Rainfall data observed for a period of 15 years, 1996–2010, at three different locations in Sweden, namely, Malmö, Norrköping and Petisträsk, were used in the simulations. The locations of the rainfall observation sites are shown in Fig. 1. The rainfall data were collected by the Swedish Meteorological and Hydrological Institute (SMHI) using gauges of weighing type (GEONOR A/S, Oslo, Norway) with a 0.1-mm volume resolution. The original time resolution was 15 min but in this study 30-min accumulations were used as a shortest input time step. The sites were selected as they represent climatic conditions for farmlands in southern, middle, and northern Sweden, respectively.

Figure 1. Location of the three rainfall observation sites in Sweden: (A) Malmö, (B) Norrköping, and (C) Petisträsk.

Evapotranspiration data with high temporal resolution were not available for the period 1996–2010, instead we used 30-year (1961–1990) averaged monthly values of potential evapotranspiration provided by SMHI for three meteorological stations close to the three sites. The monthly evapotranspiration data were evenly distributed over each month with a sinusoidal variation over each day, reaching the maximum value at noon. Between 18:00 and 06:00 h, the evapotranspiration was set to 0.

2.2 Soil properties

At all three sites, simulation of solute transport was carried out for three different soil types with different textures referred to as soils 1, 2 and 3, respectively. The three soil types represent three actual soil profiles found in Sweden and they can be assumed to be representative of typical agricultural soils. The soil properties of the three soils are listed in Table 1.

Table 1. Soil properties, soil texture according to FAO (2006).

Depth (cm)	Sand (%)	Silt (%)	Clay (%)	Bulk density (g cm^-^3)
Soil 1
0–20	80	16.5	3.5	1.53
20–45	78.8	18.3	2.9	1.55
45–70	84.3	11.8	3.9	1.55
>70	93.4	4.8	1.8	1.56
Soil 2
0–20	68.0	27.2	4.8	1.48
20–150	58.2	33.0	8.9	1.48
>150	40.5	44.6	14.9	1.65
Soil 3
0–120	59.0	25.6	15.4	1.45
120–150	36.9	32.8	30.3	1.50
>150	35.3	36.5	28.2	1.60

2.3 Numerical simulations

The purpose of the numerical simulations presented in this paper is not to describe the solute transport processes at a few specified sites. Instead, the purpose is to evaluate the effects of the temporal distribution of rainfall input on solute transport in a general sense. Even if the results do not exactly predict what will happen to a specific site, the general patterns described by the outcome of the simulations inform how different soils behave across different climates.

The HYDRUS-1D numerical model was used to simulate solute transport in the unsaturated zone. The HYDRUS-1D model is a finite-element numerical model simulating water flow, solute transport and heat transport in variably saturated porous media under a wide range of boundary conditions. Assuming a homogeneous and isotropic soil within each layer, the model uses the Galerkin finite-element method to numerically solve Richards’ equation for saturated and unsaturated water flow and Fickian-based advection–dispersion equations for solute and heat transport. For more details about HYDRUS code and its applications, see Radcliffe and Šimůnek (2010). The period 1 March to 25 September (5000 h) was used in the simulations for each of the 15 years. This period was selected since it approximately represents the growing season. In addition, problems associated with soil freezing could be neglected. Root water uptake was not considered in the model.

For modelling purposes, the van Genuchten-Mualem single porosity model was used. The parameters needed for this model are residual and saturated water contents, saturated hydraulic conductivity, pore connectivity parameter, and the empirical coefficients α and n. To predict the values of these parameters, HYDRUS-1D uses the Rosetta model (Schaap et al. 2001) with soil texture and bulk density as input parameters. For the hysteretic case, hysteresis was considered in both the water retention and hydraulic conductivity relationships. Hysteresis was simulated by setting the α-value for the wetting curve at twice the value for the drying curve (e.g. Kool and Parker 1987). The dispersivity was set to 1/10 of the modelling domain, i.e. 0.25 m.

The total depth of each soil profile was 2.5 m, a typical depth of the unsaturated zone in Sweden. The model domain was divided into 100 elements. Initial soil water pressure head was set to vary linearly between 0 at 2.5 m depth and –2.5 m at the soil surface. This is probably representative of the typical condition in Sweden after snowmelt at the end of the winter when the soil profile has received plenty of water, but before the onset of the higher evaporation rates during summer. During the first day of every year of the simulation period, 100 g of an inert solute was spread evenly at the top 0.05 m of the soil profile. The boundary conditions for the bottom of the profile was constant pressure head (=0). Atmospheric boundary condition with surface layer was used for the upper boundary. Surface runoff was not considered; excess water during high-intensity rainfall was allowed to pond on the surface. The upper- and lower-boundary conditions for solute transport were concentration flux BC and zero concentration gradient, respectively.

2.4 Effects of hysteresis and rainfall input time step

Modelling with HYDRUS-1D was performed with and without hysteresis for all three sites and three soil types with different temporal variability of rainfall and evapotranspiration input data. The input time steps used were 0.5, 4 and 24 h. At the end of each simulation period the profiles of water content and solute concentration were saved. Two parameters were calculated for each simulation; the depth of the centre of mass of solutes, z_COM (the solute masses above and below this depth are equal), and the largest depth for which the concentration exceeded a limit concentration, z_LC (in our case arbitrarily set to 0.2 g L^-1). These parameters were selected since they represent average and deep solute transport, respectively.

2.5 Effect of rainfall dynamics

To investigate how the rainfall characteristics influence the solute transport, especially z_COM and z_LC, several rainfall dynamic parameters were determined, as seen from Table 2. The parameters are: total rainfall during the 5000-h period (P_tot), standard deviation of the rainfall time series (SD), wet fraction (number of 30-min periods with rainfall divided by total number of 30-min periods), mid day (the day where the accumulated precipitation exceeds half the total precipitation), number of 30-min periods with precipitation higher than 3 mm, number of 30-min periods with precipitation higher than 5 mm, number of all rainfall events with total precipitation larger than 0.5 mm (a rainfall event was defined as a continuous period when the rainfall was at least 0.1 mm/30 min), number of heavy rain events with total precipitation larger than 10 mm, total volume for all events larger than 0.5 mm, total volume for all events larger than 10 mm. These parameters were chosen more or less arbitrarily, but they are believed to give a good representation of rainfall variability and number of low-, medium- and high-intensity rainfall events.

Table 2. Parameters describing the rainfall properties.

Parameter	Unit	Malmö			Norrköping			Petisträsk
		Min	Max	Mean	Min	Max	Mean	Min	Max	Mean
Ptot	mm	248	574	362	288	409	343	250	500	370
SD		0.199	0.371	0.272	0.184	0.349	0.265	0.165	0.410	0.265
Max P/30 min	mm	6.2	18.9	11.7	4.7	18	10.1	5.8	28.8	13.2
Mid day	d	94	161	121	103	152	126	96	150	132
Wet fraction	%	4.6	7.9	5.9	4.54	7.8	6.0	5.7	10.4	7.8
No. of 30-min periods with P > 3 mm		6	34	13.5	5	23	14.1	1	21	10.9
No. of 30-min periods with P > 5 mm		2	10	5	0	12	4.8	1	10	3.9
No. of rain events (>0.5 mm)		73	131	96.5	72	115	96.3	84	143	104.1
No. of large rain events (>10 mm)		0	14	7.8	2	12	7.4	2	12	7.1
P/event (>0.5 mm)	mm	2.6	4.6	3.5	2.3	3.7	3.0	2.2	4.2	3.1
P/large event (>10 mm)	mm	0	26.2	16.3	12.32	19.4	15.8	13.4	24.9	16.6
Volume of rain for rain events >10 mm	mm	0	262.2	134.9	27.1	192.2	118.3	34	251.9	120.9

In general many of the above parameters are highly correlated to P_tot; also the z_LC and especially z_COM are related to P_tot. In order to investigate the effects of rainfall dynamics only, the yearly z_LC and z_COM was divided by P_tot of that year to compensate for the differences in P_tot between the years. A correlation analysis was performed and the correlation coefficients between the rainfall dynamic parameters and the z_COM/P_tot and z_LC/P_tot were calculated.

3 Results and discussion

During the 5000-h simulation periods in the period 1996–2010, the precipitation varied from 248 to 574 mm in Malmö, 288 to 409 mm in Norrköping, and 250 to 500 mm in Petisträsk. The total potential evapotranspiration over the simulation period was 610, 577 and 433 mm for Malmö, Norrköping and Petisträsk, respectively. The z_COM for the different simulations was in the range of 0.2–0.9 m depending on soil type and location. The z_LC was in the range of 0.6–1.9 m. As an example of the variability in precipitation and z_COM, data from Malmö and Soil 1 are presented in Fig. 2. The average z_COM and z_LC for the 15-year period in each site, soil type and input time step are presented in Tables 3 and 4. For the simulations the accumulated mass of applied solute transported out through the lower boundary of the modelling domain to the groundwater was negligible (at most a few mg). Mass balance errors of water and solutes were small. In general the deepest transport depths were found in Soil 1 followed by Soil 2, as expected considering the differences in soil texture. The transport depths are related to the effective precipitation with a deeper transport in the northernmost site (Petisträsk). The lowest transport depths were found in Norrköping where the effective rainfall was slightly higher compared to Malmö. The reason for this can be found in differences in the rainfall dynamics for the two sites, with a higher variability in Malmö with more extreme events (for further details, see Section 3.3.

Figure 2. Data from Malmö, Soil 1. Top pane precipitation, middle z_com considering hysteresis, and bottom z_com without considering hysteresis with a 0.5-h input time step.

Table 3. Mean z_COM (m) for the simulation period at all sites and soil types.

Input time step (h)	Soil 1		Soil 2		Soil 3
	Hysteresis	No hysteresis	Hysteresis	No hysteresis	Hysteresis	No hysteresis
Malmö
0.5	0.623	0.733	0.311	0.387	0.282	0.302
4	0.656	0.761	0.335	0.383	0.287	0.301
24	0.728	0.673	0.364	0.369	0.303	0.295
Norrköping
0.5	0.466	0.627	0.258	0.307	0.212	0.240
4	0.536	0.611	0.276	0.302	0.238	0.239
24	0.523	0.530	0.273	0.284	0.232	0.229
Petisträsk
0.5	0.851	0.988	0.465	0.522	0.393	0.414
4	0.893	0.975	0.473	0.518	0.395	0.410
24	0.938	0.933	0.506	0.503	0.404	0.404

3.1 Effects of hysteresis

In general the solute transport is retarded when hysteresis is considered in the model. This is clearly reflected in both z_COM and z_LC. Several previous studies have also shown that hysteretic flow impedes water flow and solute transport relative to non-hysteretic conditions (Jones and Watson 1987, Russo et al. 1989, Elmaloglou and Diamantopoulos 2008). The magnitude of the retardation is related to the variability in water contents, many wetting–drying cycles will lead to a higher retardation for hysteretic flow. This was also shown in our study where the differences between hysteretic and non-hysteretic flow was lowest in Petisträsk, the site with the lowest potential evaporation and, thus, the lowest temporal variability in soil moisture in the topsoil. The difference between hysteretic and non-hysteretic flow was also highest in the coarse Soil 1 and lowest in the fine-textured Soil 3 (see Tables 3 and 4). One explanation of this is that in a fine-textured soil the temporal variability of soil moisture is lower due to the lower hydraulic conductivity and, thus, slower water movement.

Table 4. Mean z_LC (m) for the simulation period at all sites and soil types.

Input time step (h)	Soil 1		Soil 2		Soil 3
	Hysteresis	No hysteresis	Hysteresis	No hysteresis	Hysteresis	No hysteresis
Malmö
0.5	1.480	1.612	0.795	0.833	0.696	0.704
4	1.508	1.599	0.809	0.828	0.701	0.702
24	1.548	1.536	0.820	0.816	0.713	0.699
Norrköping
0.5	1.341	1.558	0.756	0.807	0.653	0.675
4	1.400	1.522	0.775	0.796	0.671	0.669
24	1.422	1.397	0.771	0.791	0.665	0.670
Petisträsk
0.5	1.766	1.917	0.937	0.981	0.796	0.809
4	1.819	1.899	0.950	0.982	0.801	0.810
24	1.864	1.852	0.975	0.970	0.808	0.805

It is also apparent from Fig. 2 that, on the seasonal scale, hysteresis reduces the low Z_COM more than the high Z_COM and thus increases inter-annual variability in transport depths. This was highly pronounced for all sites in Soil 1 and, to a lesser degree, in Soil 2. In the fine-textured Soil 3, however, the reduction in Z_COM considering hysteresis was more or less uncorrelated to the total precipitation.

The differences decreased with an increasing time step, which is also related to the fact that when the precipitation time step is longer, the precipitation is more evenly distributed over time leading to a lower temporal variability of the soil moisture. It is interesting to note that, for the 24-h input time step, the z_COM was slightly deeper (but not significant at the p = 0.1 level) for hysteretic flow compared to the non-hysteretic flow in some cases. This could be explained by the fact that the temporal variability in soil moisture is reduced and that the soil is close to the wetting part of the hysteretic curve. Since the hydraulic conductivity of the wetting part of the hysteresis curve is larger as compared to the drying part, this leads to a faster solute transport

The effect of hysteresis on z_LC was less prominent as compared to z_COM, but the overall pattern was the same. Again the z_LC was larger for non-hysteretic flow using a 0.5-h time step, but the differences became smaller as the time step increased. With the 24-h input time step the z_LC was often larger for the hysteretic case as compared to the non-hysteretic case (in seven cases out of nine). The difference was, however, not statistically significant at the p = 0.1 level.

3.2 Effects of rainfall input time step

For hysteretic flow, z_COM and z_LC increased with an increasing input time step, whereas the opposite trend was observed for non-hysteretic flow (Tables 3 and 4). Gu and Riley (2010) similarly found that solute transport was faster for the non-hysteretic case when the rainfall input was more evenly distributed over time. Wang et al. (2009) showed that solutes were transported deeper when a daily input time step was used instead of monthly or yearly time steps. Lewan et al. (2009) found a deeper solute transport when using a 1-h input time step as compared to a 24-h time step. In their study, hysteresis was not considered, however, their model included macropore flow. In contrast, McGrath (2010b) found that a fortnightly or monthly water balance was sufficient to calculate bromide transport.

The increase of z_COM and z_LC for hysteretic flow is explained by a lower temporal variability of the water content at longer input time steps. The decrease in z_COM and z_LC for the non-hysteretic case is more difficult to explain. Probably the highest rainfall intensities occurring when using a small input time step are important for the solute transport. When using the 24-h time step the difference between hysteretic and non-hysteretic flow was small. The basic trend was the same both for z_COM and z_LC; however, the difference for z_LC was smaller.

3.3 Effects of rainfall properties

The minimum, maximum, and mean of rainfall parameters at the three different sites are presented in Table 2. From a general perspective, the difference between the sites is small. The measured rainfall in Malmö displayed a higher variability, indicated by having the highest SD, lowest wet fraction, highest number of 30-min periods with P > 5 mm, highest number of large events, and greatest total volume of large events. In addition, Malmö had the highest evapotranspiration, probably leading to a larger temporal variability of surface soil moisture as compared to the other sites.

In Tables 5–8 results of the correlation analysis are presented for both hysteretic and non-hysteretic flow. In the tables correlation coefficients significant at the P = 0.05 level are marked in italics and coefficients significant at the P = 0.01 level are marked in bold.

Table 5. Correlation coefficients between rainfall dynamic parameters and z_COM/P_tot for hysteretic flow. Values in italics are significant at the p = 0.05 level, values in bold are significant at the p = 0.01 level.

	Malmö			Norrköping			Petisträsk
Parameter	Soil 1	Soil 2	Soil 3	Soil 1	Soil 2	Soil 3	Soil 1	Soil 2	Soil 3
Ptot	0.629	0.701	0.605	0.355	0.251	−0.001	0.434	0.539	0.413
SD	0.534	0.746	0.699	0.592	0.191	−0.080	0.613	0.694	0.629
Max P/30 min	0.100	0.218	0.129	0.330	−0.033	−0.208	0.463	0.560	0.514
Mid day	0.332	0.691	0.765	0.268	0.378	0.320	0.073	0.358	0.348
Wet fraction	0.422	0.413	0.326	−0.159	0.241	0.288	0.220	0.244	0.130
No. of 30-min periods with P > 3 mm	0.331	0.510	0.466	0.490	0.354	0.110	0.591	0.711	0.619
No. of 30-min periods with P > 5 mm	0.361	0.686	0.717	0.733	0.404	0.175	0.597	0.634	0.549
No. of rain events (>0.5 mm)	0.322	0.528	0.441	−0.029	0.250	0.209	0.220	0.234	0.126
No. of large rain events (>10 mm)	0.511	0.331	0.279	0.074	−0.424	−0.623	0.444	0.521	0.409
P/event (>0.5 mm)	0.709	0.576	0.513	−0.275	0.108	0.248	−0.403	−0.517	−0.428
P/large event (>10 mm)	0.543	0.490	0.451	0.250	0.146	−0.089	0.541	0.700	0.724
Volume of rain for rain events >10 mm	0.687	0.570	0.495	0.208	−0.251	−0.521	0.544	0.679	0.594

Table 6. Correlation coefficients between rainfall dynamic parameters and z_COM/P_tot for non-hysteretic flow. Values in italics are significant at the p = 0.05 level, values in bold are significant at the p = 0.01 level.

	Malmö			Norrköping			Petisträsk
Parameter	Soil 1	Soil 2	Soil 3	Soil 1	Soil 2	Soil 3	Soil 1	Soil 2	Soil 3
Ptot	0.768	0.820	0.720	0.779	0.366	0.128	0.464	0.559	0.469
SD	0.662	0.758	0.747	0.799	0.464	0.090	0.575	0.641	0.591
Max P/30 min	0.280	0.125	0.129	0.429	0.219	−0.002	0.385	0.455	0.475
Mid day	0.416	0.565	0.688	0.299	0.516	0.518	−0.016	0.240	0.307
Wet fraction	0.618	0.500	0.393	−0.182	0.011	0.288	0.252	0.311	0.228
No. of 30-min periods with P > 3 mm	0.373	0.577	0.527	0.851	0.555	0.210	0.568	0.653	0.588
No. of 30-min periods with P > 5 mm	0.397	0.623	0.694	0.789	0.576	0.245	0.567	0.601	0.520
No. of rain events (>0.5 mm)	0.535	0.557	0.489	0.072	0.114	0.258	0.225	0.309	0.190
No. of large rain events (>10 mm)	0.716	0.556	0.420	0.287	−0.260	−0.593	0.523	0.561	0.443
P/event (>0.5 mm)	0.726	0.744	0.655	−0.511	−0.145	0.196	−0.440	−0.493	−0.436
P/large event (>10 mm)	0.492	0.549	0.505	0.450	0.324	0.119	0.551	0.633	0.695
Volume of rain for rain events >10 mm	0.791	0.779	0.649	0.483	−0.034	−0.408	0.607	0.672	0.610

Table 7. Correlation coefficients between rainfall dynamic parameters and z_LC/P_tot for hysteretic flow. Values in italics are significant at the p = 0.05 level, values in bold are significant at the p = 0.01 level.

	Malmö			Norrköping			Petisträsk
Parameter	Soil 1	Soil 2	Soil 3	Soil 1	Soil 2	Soil 3	Soil 1	Soil 2	Soil 3
Ptot	0.197	–0.700	–0.859	0.073	–0.426	–0.565	–0.486	–0.633	–0.840
SD	0.099	–0.590	–0.687	0.625	0.215	0.023	–0.068	–0.119	–0.366
Max P/30 min	–0.057	–0.397	–0.435	0.487	0.224	0.057	0.068	0.142	–0.119
Mid day	0.081	–0.079	–0.091	0.272	0.446	0.410	–0.623	–0.593	–0.578
Wet fraction	0.157	–0.576	–0.722	–0.475	–0.435	–0.351	–0.452	–0.648	–0.763
No. of 30-min periods with P > 3 mm	–0.121	–0.666	–0.717	0.396	0.015	–0.109	–0.162	–0.204	–0.445
No. of 30-min periods with P > 5 mm	–0.022	–0.390	–0.405	0.692	0.229	0.149	–0.004	0.007	–0.297
No. of rain events (>0.5 mm)	–0.009	–0.604	–0.733	–0.422	–0.591	–0.471	–0.480	–0.714	–0.777
No. of large rain events (>10 mm)	0.314	–0.345	–0.534	0.310	–0.057	–0.277	–0.376	–0.497	–0.706
P/event (>0.5 mm)	0.380	–0.454	–0.596	–0.500	–0.290	–0.068	0.382	0.482	0.681
P/large event (>10 mm)	0.231	–0.574	–0.623	0.137	0.161	–0.013	0.100	0.173	0.011
Volume of rain for rain events >10 mm	0.353	–0.540	–0.722	0.349	0.011	–0.248	–0.264	–0.296	–0.547

Table 8. Correlation coefficients between rainfall dynamic parameters and z_LC/P_tot for non-hysteretic flow. Values in italics are significant at the p = 0.05 level, values in bold are significant at the p = 0.01 level.

	Malmö			Norrköping			Petisträsk
Parameter	Soil 1	Soil 2	Soil 3	Soil 1	Soil 2	Soil 3	Soil 1	Soil 2	Soil 3
Ptot	0.250	–0.632	–0.785	0.131	–0.312	0.589	–0.722	–0.690	–0.835
SD	0.238	–0.573	–0.641	0.732	0.408	0.645	–0.309	–0.217	–0.404
Max P/30 min	0.098	–0.394	–0.425	0.429	0.367	0.430	–0.161	0.007	–0.190
Mid day	0.233	–0.100	–0.090	0.275	0.410	0.646	–0.722	–0.666	–0.587
Wet fraction	0.224	–0.475	–0.630	–0.755	–0.637	–0.094	–0.641	–0.677	–0.721
No. of 30-min periods with P > 3 mm	–0.048	–0.668	–0.695	0.641	0.168	0.632	–0.371	–0.272	–0.463
No. of 30-min periods with P > 5 mm	0.083	–0.403	–0.363	0.751	0.338	0.632	–0.201	–0.068	–0.294
No. of rain events (>0.5 mm)	0.103	–0.551	–0.643	–0.594	–0.661	0.038	–0.635	–0.723	–0.728
No. of large rain events (>10 mm)	0.502	–0.326	–0.513	0.458	0.093	0.054	–0.573	–0.529	–0.716
P/event (>0.5 mm)	0.366	–0.396	–0.566	–0.748	–0.464	–0.407	0.592	0.539	0.717
P/large event (>10 mm)	0.116	–0.488	–0.545	0.336	0.302	0.360	–0.064	0.061	–0.059
Volume of rain for rain events >10 mm	0.409	–0.480	–0.676	0.542	0.195	0.246	–0.480	–0.368	–0.587

In Table 5 it is seen that z_COM/P_tot has the highest correlation to the number of 30-min periods with P >5 mm and lowest correlation to the number of rainfall events with P > 0.5 mm. The differences between sites and soil types are large, however, some interesting observations can be made. The highest correlation coefficients were typically found at Malmö (the site with the highest temporal variability in rainfall data). Here, the difference between soil types was most pronounced, in many cases the correlation coefficient was decreasing or increasing when going from the coarsest (Soil 1) to the finest (Soil 3) soil texture. All parameters related to large (P > 10 mm) rainfall events have progressively higher correlation coefficients as the soil becomes more coarse textured. There are two conflicting hypotheses regarding how the rainfall properties affect the solute transport. A more evenly distributed rainfall over time leads to a lower temporal variability of soil moisture and, thus, a higher solute flow, especially for the hysteretic case. This was clearly shown in the previous section (and in Table 3). On the other hand, during a heavy rainstorm the water content can temporarily increase leading to increased hydraulic conductivity and thus faster solute flow. Due to the faster response time of coarse-textured soils, both these hypotheses are likely to be true. Apparently, the latter of the above hypotheses is more important in Malmö; with an increased occurrence and accumulated volume of heavy rainfall events that show a deeper transport. The effect is more pronounced for the coarse-textured soils. The pattern is not so clear at the other sites, however. Norrköping displays the smallest correlation and also the most negative correlation coefficients.

In Table 6 the z_COM/P_tot correlation for the non-hysteretic flow is presented. The general pattern is the same as for Table 5 but the values are slightly higher. An explanation for this is that a higher temporal variability in the rainfall retards solute transport when hysteresis is considered. For the non-hysteretic case, a high variability with a few high-intensity rainfalls means that the soil periodically becomes wetter with an increased hydraulic conductivity as a consequence.

In Table 7 the z_LC/P_tot correlations are presented. In contrast to Tables 5 and 6, most correlation coefficients are negative. Since many of the rainfall parameters are related to rainfall variability, this means that a high temporal variability of rainfall leads to a less deep solute transport. This result is in line with experimental findings of Persson and Berndtsson (1999), who showed that if the infiltration is evenly distributed over time a sharper breakthrough curve (BTC) develops, leading to a lower effective dispersion. This effect seems to be more important for fine textured soils. The results for the non-hysteretic case were essentially the same, albeit the correlation values were slightly smaller.

It should be noted here that the above results are valid only if the solute transport process can be accurately described by the convective-dispersive process with a constant dispersivity over depth and time. In some soils the solute transport process is instead better modelled using the stochastic-convective process, with a linearly increasing dispersivity with depth (Sposito et al. 1986, Jury and Roth 1990). In some soils the solute transport changes character as the flow rate changes: at low flow rates solutes are allowed to mix horizontally and at higher flow rates solutes tend to move in preferential pathways with a limited exchange between macro and micro porosity. This leads to a solute transport process that is better modelled using a convective-dispersive assumption at low flows and a stochastic-convective assumption at high flows (e.g. Kahn and Jury 1990, Mohammadi and Vanclooster 2011). To improve the description of the dependency of rainfall properties on solute transport in these soils new models are required.

4 Summary and conclusions

The results showed that both z_COM and z_LC were larger for the non-hysteretic case with the 0.5-h input time step. This is in agreement with results from earlier modelling studies (Jones and Watson 1987, Russo et al. 1989, Elmaloglou and Diamantopoulos 2008). A shorter input time step leads to a larger temporal variability of soil moisture leading to more wetting and drying cycles. As the input time step increases the difference between the hysteretic and non-hysteretic case decreases. For the 24-h input time step the solute transport is larger than for the non-hysteretic case at some locations and soil types. This is probably due to the fact that the temporal variability in soil moisture is reduced and that the soil is more often close to the wetting part of the hysteretic curve. Since the hydraulic conductivity of the wetting part of the hysteresis curve is larger as compared to the drying part, this leads to a faster solute transport. The results clearly show that using a rainfall input data series with too low a time resolution will lead to errors.

The correlation analysis between rainfall dynamics parameters and z_COM and z_LC provided interesting results. Several of the rainfall parameters were significantly correlated with z_COM/P_tot. The highest correlation coefficients were found for Malmö that had the largest temporal variability in rainfall together with the largest potential evapotranspiration. All parameters related to large (p > 10 mm) rainfall events had progressively higher correlation coefficients for increasingly coarse-textured soils.

In contrast to macropore flow, deep solute transport in matrix flow is negatively correlated with a rainfall with a high variability (as shown in Tables 7 and 8). This effect is more pronounced for fine-textured soils. A large temporal variability in soil moisture leads to a sharper solute front with a smaller difference between z_COM and z_LC. This effect is more pronounced for hysteretic flow.

Acknowledgements

Ruslana Gladnyeva is gratefully acknowledged for conducting some of the HYDRUS 1D simulations. The authors would also like to thank the Swedish Meteorological and Hydrological Institute for providing meteorological data.

Disclosure statement

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

Additional information

Funding

The study is a part of the Hydroimpacts 2.0 project, financed by The Swedish Research Council FORMAS. We also acknowledge funding from the MECW project through the Center for Middle Eastern Studies, Lund University, Sweden.